THE ENCYCLOPEDIA BRITANNICA ELEVENTH EDITION FIRST edit! on, published n three volumes, 1768- -1771. SECOND » ,, ten >> 1777- -1784. THIRD > , eighteen » 1788- -1797. FOURTH > y twenty »> 1801- -1810. FIFTH > j twenty » 1815- -1817. SIXTH * , twenty »» 1823- -1824. SEVENTH » > twenty-one >» 1830- -1842. EIGHTH » » twenty-two >> 1853- -i860 NINTH > 7 twenty-five >j 1875- -1889. TENTH 9 ninth ed ition and eleven supplementary volumes, 1902- -1903. ELEVENTH > > pub] ished in twenty-nine volumes, 1910 — 1911, COPYRIGHT in all countries subscribing to the Bern Convention by THE CHANCELLOR, MASTERS AND SCHOLARS of the UNIVERSITY OF CAMBRIDGE All rights reserved THE ENCYCLOPEDIA BRITANNICA A DICTIONARY OF ARTS, SCIENCES, LITERATURE AND GENERAL INFORMATION ELEVENTH EDITION VOLUME XIV HUSBAND to ITALIC New York Encyclopaedia Britannica, Inc. 342 Madison Avenue Copyright, in the United States of America, 191 1, by The Encyclopaedia Britannica Company. INITIALS USED IN VOLUME XIV. TO IDENTIFY INDIVIDUAL CONTRIBUTORS, 1 WITH THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED. A* lift* A. Bo.* A. Cy. A. C. G Adolfo Bartoli (1833-1894). f Formerly Professor of Literature at the Istituto di studi superior! at Florence. "1 Italian Literature (in part). A. E. G.* A. E. H. L. A. F. C. A. G. A. Ge. A. Go.* A. G. G. A. H.-S. A. M. C. A. N. A. So. A S. Wo. A . W. H.* A . W. Po. Honorary Canon of Author of Sto in delta letter atura Italiana; &c. Augxiste Boudinhon, D.D., D.C.L. Professor of Canon Law at the Catholic University of Paris. Paris. Editor of the Canonists contemporain. Arthur Ernest Cowley, M.A., Litt.D. Sub-Librarian of the Bodleian Library, Oxford. Fellow of Magdalen College. Albert Charles Lewis Gotthilf Gunther, M.A., M.D., Ph.D., F.R.S. Keeper of Zoological Department, British Museum, 1875-1895. Cold Medallist, Royal Society, 1878. Author of Catalogues of Colubrine Snakes, Balrachia Salientia, - and Fishes in the British Museum ; Reptiles of British India ; Fishes of Zanzibar ; Reports on the " Challenger " Fishes; &c. Rev. Alfred Ernest Garvie, M.A., D.D. Principal of New College, Hampstead. Member of the Board of Theology and the . Board of Philosophy, London University. Author of Studies in the inner Life of Jesus ; &c. Augustus Edward Hough Love, M.A., D.Sc, F.R.S. Sedleian Professor of Natural Philosophy in the University of Oxford. Hon. _ Fellow of Queen's College, Oxford ; formerly Fellow of St John's College, Cambridge. Secretary to the London Mathematical Society. Alexander Francis Chamberlain, A.M., Ph.D. Assistant Professor of Anthropology, Clark University, Worcester, Massachusetts. . Member of American Antiquarian Society; Hon. Member of American Folk-lore Society. Author of The Child and Childhood in Folk Thought. Major Arthur George Frederick Griffiths (d. 1908). H.M. Inspector of Prisons, 1878-1896. Author of The Chronicles of Newgale; Secrets of the Prison House ; &c. Sir Archibald Geikie, LL.D. See the biographical article, Geikie, Sir A. Rev. Alexander Gordon, M.A. Lecturer on Church History in the University of Manchester. Sir Alfred George Greenhill, M.A., F.R.S. Formerly Professor of Mathematics in the Ordnance College, Woolwich. Author of Differential and Integral Calculus with Applications; Hydrostatics; Notes on Dynamics ; &c. Sir A. Houtum-Schindler, CLE. General in the Persian Army. Author of Eastern Persian Irak. Agnes Mary Clerke. See the biographical article, Clerke, A. M. Alfred Newton, F.R.S. See the biographical article, Newton, Alfred. Albrecht Socin, Ph.D. (184.4-1899). Formerly Professor of Semitic Philology in the Universities of Leipzig and Tubingen. Author of Arabische Grammatik; &c. Arthur Smith Woodward, LL.D., F.R.S. Keeper of Geology, Natural History Museum, South Kensington. Secretary of the Geological Society, London. Arthur -William Holland. Formerly Scholar of St John's College, Oxford. Bacon Scholar of Gray's Inn, 1900. Alfred William Pollard, M.A. Assistant Keeper of Printed Books, British Museum. Fellow of King's College, London. Hon. Secretary Bibliographical Society. Editor of Books about Books and Bibliographica. Joint-editor of The Library. Chief Editor of the " Globe " Chaucer. Index Librorum Prohl- bitorum; Infallibility. f Ibn Gabirol; \ Inscriptions: Semitic. Ichthyology (in part). Immortality; Inspiration. Infinitesimal Calculus. Indians, North American. -! Identification. \ Hutton, James. \ Illuminati. \ Hydromechanics. -j Isfahan (in part). -j Huygens, Christiaan. \ Ibis; Icterus. Irak-Arabi (in pari). ( Ichthyosaurus; 1 Iguanodon. Imperial Cities; Instrument of Government Incunabula. tk» W. K. Alexander Wood Renton, M.A., LL.B. J Inebriety, Law of; Puisne Judge of the Supreme Court of Ceylon. Editor of Encyclopaedia of the~] i ns anity: Law. Laws of England. *- 1 A complete list, showing all individual contributors, appears in the final volume. VI CP.A. ao. C. H. Ha. C. LI M. C. R. B. INITIALS AND HEADINGS OF ARTICLES c.s.* C. T.L. C. We. D. B. Ma. D. G. H. D. H. D. P. T. D. S. M. E. A. M. E.Br. E. Bra. E. C. B. E. C. Q. E. P.S. E. P. S.D E. G. E Htt. E H. B. E . H. M. E . H. P. Charles Francis Atkinson. J Infantry; Formerly Scholar of Queen's College, Oxford. Captain, 1st City of London (Royal | Julian Wars. Fusiliers). Author of The Wilderness and Cold Harbour. Colonel Charles Grant. Formerly Inspector of Military Education in India. Carlton Huntley Hayes, A.M., Ph.D. Assistant Professor of History at Columbia University, New York City, of the American Historical Association. { India: Costume. Member! Innocent V., VIII. J Instinct; Principal of University College, | Inte lligence in Animals, Ibn Batuta Iclrisi. part) ; | Italian Language {in pari). Insurance {in part). Barrister-at-Law, Inner Temple. Infant Schools. Author J Theory ; j Imam. Ionia {in Isauria. part); Author of Short History of Royal 1 Impressment, Instrumentation. Conway Lloyd Morgan, LL.D., F.R.S. Professor of Psychology at the University of Bristol. Bristol, 1887-1909. Author of Animal Life and Intelligence; Habit and Instinct. Charles Raymond Beazley, M.A., D.Litt., F.R.G.S., F.R.Hist.S. Professor of Modern History in the University of Birmingham. Formerly Fellow of Merton College, Oxford; and University Lecturer in the History of Geography. Lothian Prizeman, Oxford, 1889. Lowell ^ Lecturer, Boston, 1908. Author of Henry the Navigator; The Dawn of Modern Geography; &c. Carlo Sat.viont. Professor of Classical and Romance Languages, University of Milan. Charlton Thomas Lewis, Ph.D. (1834-1904}. Formerly Lecturer on Life Insurance, Harvard and Columbia Universities, and on. Principles of Insurance. Cornell University. Author of History of Germany; Essays; Addresses; &c. Cecil Weatherly. Formerly Scholar of Queen's College, Oxford. Duncan Black Macdonald, M.A., D.D. Professor of Semitic Languages, Hartford Theological Seminary, U.S.A. of Development of Muslim Theology, Jurisprudence and Constitutional Selection from Ibn Khaldum; Religious Attitude and Life in Islam; &c. Davtd George Hogarth, M.A. Keeper of the Ashmolean Museum, Oxford. Fellow of Magdalen College, Oxford. Fellow of the British Academy. Excavated at Paphos, 1888; Naucratis, 1 899 and - 1903; Ephesus, 1904-1905; Assiut, 1906-1907; Director, British School at Athens. 1897-1900; Director, Cretan Exploration Fund, 1899. David Hannay. Formerly British Vice-Consul at Barcelona. Navy, 1 217-1688; Life of Emilio Castelar; &c. Donald Francis Tovey. _ . Author of Essays in Musical Analysis; comprising The Classical Concerto, The Goldberg Variations, and analyses of many other classical works. Dugald Sutherland MacColl, M.A., LL.D. f Keeper of the National Gallery of British Art (Tate Gallery). Lecturer on the History J Impressionism. of Art, University College, London; Fellow of University College, London, j Author of Nineteenth Century Art; &c. L Edward Alfred Minchin, M.A., F.Z.S. f Professor of Protozoology in the University of London. Formerly Fellow of Merton J ny° r 0meausae; College, Oxford ; and Lecturer on Comparative Anatomy in the University of Oxford, j Hydrozoa. Author of " Sponges and Sporozoa " in Lankester's Treatise on Zoology; &c. *~ Erjtest Barker, M.A. f Fellow and Lecturer in Modern History, St John's College, Oxford. Formerly -\ Imperial Chamber. Fellow and Tutor of Merton College. Craven Scholar, 1895. . I Edwin Bramwell, M.B., F.R.C.P., F.R.S. (Edin.). f Assistant Physician, Royal Infirmary, Edinburgh. -^Hysteria {in part). Right Rev. Edward Cuthbert Butler, O.S.B., D.Litt. r AbDot of Downside Abbey, Bath. An+tiru- n( " The. I ^,1=1^ H,"ctr,^i, ,-,f Polios;, ,.= " J in Cambridge Texts and Studies. Edmund Crosby Quiggin, M.A. Fellow, Lecturer in Modern History, and Monro Lecturer in Celtic, Gonville and -i Ireland: Early History. Caius College, Cambridge. Edward Fairbrother Strange. Assistant Keeper, Victoria and Albert Museum, South Kensington. Council, Japan Society. Author of numerous works on art subjects, of Bell's " Cathedral " Series. Lady Dilke. See the biographical article: Dilke, Sir C. W., Bart. Edmund Gosse, LL.D. See the biographical article, Gosse, Edmund. EMIL HUBNER. See the biographical article, Hubner, Emil. Sir Edward Herbert Bunbury, Bart., M.A., F.R.G.S. (d. 1895). f M.P. for Bury St Edmunds, 1 847-1 852. Author of a History of Ancient Geography; \ Ionia {in part).- &c. L Author of " The Lausiac History of Palladius " i Imitation of Christ. Member of J Illustration: Technical Joint-editor | Developments. \ Ingres. f Huygen \ Ibsen; '. \ Inscriptions: Latin {in pari). ("Huygens, Sir Constantijn; 1 Ibsen; Idyl. Ellis Hovell Minns, M.A. Lecturer and Assistant Librarian, and formerly Fellow, Pembroke College, Cambridge University Lecturer in Palaeography. Edward Henry Palmer, M.A. See the biographical article, Palmer, E. H. Iazyges; Issedones. Ibn Khaldun [in part). INITIALS AND HEADINGS OF ARTICLES Vll E, K. E. L.H. Ed. M. E. M. T. E.O.* F. A. F. F. C. C. F. G. M. B. F. J. H. F. LI. G. F. P.* F. S.P. F. Wa. F. W. R.* F. Y. P. G A. B. G. A. Gr. G. A. J. C. G. B. G. F. H.* G. G. Co. 3. H. C. Edmund Knecht, Ph.D., M.Sc.TECH.(Manchester), F.I.C. Professor of Technological Chemistry, Manchester University. Head of Chemical Department, Municipal School of Technology, Manchester. Examiner in Dyeing, " City and Guilds of London Institute. Author of A Manual of Dyeing; &c. Editor of Journal of the Society of Dyers and Colourisls. The Right Rev. the Bishop of Lincoln (Edward Lee Hicks). Honorary Fellow of Corpus Christi College, Oxford. Formerly Canon Residentiary, of Manchester. Fellow and Tutor of Corpus Christi College. Author of Manual of Greek Historical Inscriptions ; &c. Eduard Meyer, Ph.D., D.Lrrr.(Oxon.), LL.D. * Professor of Ancient History in the University of Berlin. Author of Geschichte des ~ Alterthums ; Geschichte des alien Aegyptens; Die Israelilen und ihre Nachbarsldmme. Sir Edward Maunde Thompson, G.C.B., I.S.O., D.C.L., Litt.D., LL.D. Director and Principal Librarian, British Museum, 1 898-1 909. Sandars Reader in Bibliography, Cambridge, 1895-1896. Hon. Fellow of University College, Oxford. Correspondent of the Institute of France and of the Royal Prussian . Academy of Sciences. Author of Handbook of Greek and Latin Palaeography. Editor of Chronicon Angliae. Joint-editor of publications of the Palaeographical Society, the New Palaeographical Society, and of the Facsimile of the Laurentian Sophocles. Edmund Owen, M.B., F.R.C.S., LL.D., D.Sc. Consulting Surgeon to St Mary's Hospital, London, and to the Children's Hospital, . Great Ormond Street; late Examiner in Surgery at the Universities of Cambridge, Durham and London. Author of A Manual of Anatomy for Senior Students. Frank Albert Fetter, Ph.D. Professor of Political Economy and Finance, Cornell University. Member of the State Board of Charities. Author of The Principles of Economics; &c. Frederick C'ornwallis Conybeare, M.A., D.TH.(Giessen). Fellow of the British Academy. Formerly Fellow of University College, Oxford. Author of The Ancient Armenian Texts of Aristotle; Myth, Magic and Morals; &c. Frederick George Meeson Beck, M.A. Fellow and Lecturer in Classics, Clare College, Cambridge. Francis John Haverfield, M.A., LL.D., F.S.A. Camden Professor of Ancient History in the University of Oxford. Fellow of Brasenose College. Fellow of the British Academy. Formerly Censor, Student, - Tutor and Librarian of Christ Church, Oxford. Ford's Lecturer, 1906-1907. Author of Monographs on Roman History, especially Roman Britain; &c. Francis Llewellyn Griffith, M.A., Ph.D., F.S.A. Reader in Egyptology, Oxford University. Editor of the Archaeological Survey and Archaeological Reports of the Egypt Exploration Fund. Fellow of Imperial German Archaeological Institute. Frederick Peterson M.DPh.D j Insanity: Hospital Professor of Psychiatry, Columbia University. President of New York State ^ r Commission in Lunacy, 1902-1906. Author of Mental Diseases; &c. Francis Samuel Philbrick, A.M., Ph.D. Formerly Fellow of Nebraska State University, and Scholar and Resident Fellow of Harvard University. Member of American Historical Association. Indigo. Inscriptions: Greek {in pari). Hystaspes; Iran. Illuminated MSS. Hydrocephalus. Interstate Commerce. j Iconoclasts; [Image Worship. j Hwicce. Icknield Street. Hyksos; Isis. I Treatment. Independence, Declaration of. Francis Watt, M.A. Barrister-at-Law, Middle Temple. Author of Law's Lumber Room. Frederick William Rudler, I.S.O., F.G.S. Curator and Librarian of the Museum of Practical Geology, London, 1879-1902. President of the Geologists' Association, 1 887-1 889. Frederick York Powell, D.C.L., LL.D. See the biographical article, Powell, Frederick York. George A. Boulenger, F.R.S., D.Sc, Ph.D. In charge of the collections of Reptiles and Fishes, Department of Zoology, British Museum. Vice-President of the Zoological Society of London. George Abraham Grierson, CLE., Ph.D., D.Litt. (Dublin). Member of the Indian Civil Service, 1873-1903. In charge of Linguistic Survey of India, 1898-1902. Gold Medallist, Royal Asiatic Society, 1909. Vice-President of the Royal Asiatic Society. Formerly Fellow of Calcutta University. Author of The Languages of India ; &c. Grenville Arthur James Cole. r Director of the Geological Survey of Ireland. Professor of Geology, Royal College -j of Science for Ireland, Dublin. Author of Aids in Practical Geology; &c. I Sir George Christopher Molesworth Birdwood, K.C.I.E. f See the biographical article, Birdwood, Sir G. C. M. ^ George Francis Hill, M.A. Assistant in Department of Coins and Medals, British Museum. Author of Sources for Greek History 478-431 B.C.; Handbook of Greek and Roman Coins; &c. George Gordon Coulton, M.A. Birkbeck Lecturer in Ecclesiastical History, Trinity College, Cambridge, of Medieval Studies; Chaucer and his England; &c. Inn and Innkeeper. Hyacinth; Iolite. r i { f Iceland: History, and l Ancient Literature. Ichthyology {in part). Indo-Aryan Languages. Ireland: Geology. Incense. Inscriptions: Greek {in part). Author-! Indulgence. Gf.org;; Herbert Carpenter, B.Sc. (Lond.). Professor of Zoology in the Royal College of Science, Dublin. their Structure and Life. Author of Insects: Hymenoptes^g Ichneumon-Fly; Insect. Vlll INITIALS AND HEADINGS OF ARTICLES G. I. A. G.J. G. K. G. P. M. G. W. K. G. W. T. H. Ch. H. C. R. H. L. H. H. M. H. H. N. B. H 0. H. St. H. T. A. H y. I. A. J. A. P. J. Bs. J. B. T. GRA/ Senator L ot S th e L Kingdom of Italy. Professor of Comparative Grammar at the! Italian Language (in part). University of Milan. Author of Codice Islandese; &c. I George Jamieson, C.M.G., M.A. J Formerly Consul-General at Shanghai, and Consul and Judge of the Supreme Court, 1 Hwang HO. Shanghai. ^- Gustav Kruger, Ph.D. f Professor of Church History in the University of Giessen. Author of Das Papstthum ; i lrenaeus. &c. <- George Percival Mudge, A.R.C.S., F.Z.S. Lecturer on Biology, London Hospital Medical College, and London School of * Medicine for Women, University of London. Author of A Text Book of Zoology ; &c. Very Rev. George William Kitchin, M.A., D.D., F.S.A. Dean of Durham, and Warden of the University of Durham. Hon. Student of - x Christ Church, Oxford. Fellow of King's College, London. Dean of Winchester, 1883-1894. Author of A History of France; &c. Incubation and Incubators. Rev. Griffithes Wheeler Thatcher, M.A., B.D. Warden of Camden College, Sydney, N.S.W. Formerly Tutor in Hebrew and Old Testament History at Mansfield College, Oxford. Author of a Commentary on Judges; An Arabic Grammar; &c. Hutten, Ulrieh von. Ibn 'Abd Rabbihi; Ibn 'Arabi; Ibn Athlr; Ibn Duraid; Ibn Farad!; Ibn Farid; Ibn Hazm; Ibn Hisham; Ibn Ishaq; Ibn Jubair; Ibn Khaldun (in part); Ibn Khallikan; Ibn Qutaiba; Ibn Sa'd; Ibn fufail; Ibn Usaibi'a; Ibrahim Al-MausUT. Iron Mask; Ismail. 1 1 Isfahan: History. J Infancy; I Intestinal Obstruction. Iron and Steel. Hugh Chisholm, M.A. Formerly Scholar of Corpus Christi College, Oxford. Editor the 11th edition - of the Encyclopaedia Britannica; Co-editor of the 10th edition. Sir Henry Creswicke Rawlinson, Bart., K.C.B. See the biographical article, Rawlinson, Sir Henry Creswicke, Harriet L. Hennessv, M.D., (Brux.) L.R.C.P.I., L.R.C.S.I. Henry Marion Howe, A.M., LL.D. Professor of Metallurgy, Columbia University. Author of Metallurgy of Steel; &c. Henry Newton Dickson, M.A., D.Sc, F.R.G.S. J Professor of Geography, University College, Reading. Author of Elementary] Indian Ocean. Meteorology ; Papers on Oceanography; &c. *- Hermann Oelsner, M.A., Ph.D. f Taylorian Professor of the Romance Languages in University of Oxford. Member J xtalian Literature (in part). of Council of the Philological Soaety. Author of A History of Provencal Literature; &c. > Henry Sturt. M.A. \ induction. Author of Idola Thealri; The Idea of a Free Church; and Personal Idealism. I Rev. Herbert Thomas Andrews. f Professor of New Testament Exegesis, New College, London. Author of the J Ignatius. " Commentary on Acts " in the Westminster New Testament; Handbook on the ' Apocryphal Books in the " Century Bible." I Ibn Batuta (in part). %J. C. H. J. C. Van D. Sir Henry Yule, K.C.S.I., C.B. See the biographical article, Yule, Sir Henry. Israel Abrahams, M.A. Reader in Talmudic and Rabbinic Literature in the University of Cambridge. J Ibn Tlbbon; Formerly President, Jewish Historical Society in England. Author of A Short Immanuel Ben Solomon. History of Jewish Literature; Jewish Life in the Middle Ages; &c. *- John Ambrose Fleming, M.A., F.R.S., D.Sc. _ _ f Pender Professor of Electrical Engineering in the University of London. Fellow of University College, London. Formerly Fellow of St John's College, Cambridge, \ Induction Coil. and Lecturer on Applied Mechanics in the University. Author of Magnets and Electric Currents. \_ James Burgess, CLE., LL.D., F.R.S.(Edin-), F.R.G.S., Hon.A.R.I.B.A. r Formerly Director General of Archaeological Survey of India. Author of Archaeo- ! . M ArnhitontnrA logical Survey of Western India. Editor of Fergusson's History of Indian Archi-'\ MOJan Arcnueciure. lecture. I Sir Tohn Batty Tuke, Kt., M.D., F.R.S.(Edin.), D.Sc, LL.D. f „ .„.„ ,. . ,. President of the Neurological Society of the United Kingdom. Medical Director J HySiena \m part), of New Saughton Hall Asylum, Edinburgh. M.P. for the Universities of Edinburgh ] Insanity: Medical. and St Andrews, 1900-1910. *- Right Rev. John Cuthbert Hedley, O.S.B., D.D. J K.C. Bishop of Newport. Author of The Holy Eucharist; &c. 1 John Charles Van Dyke. I Professor of the History of Art, Rutgers College, New Brunswick, N.J. Formerly < Editor of The Studio and Art Review. Author of Art for Art's Sake; History of Painting; Old. English Masters; &c. Immaculate Conception. Inness, George. INITIALS AND HEADINGS OF ARTICLES IX J. c. w. J. D. B. J. P. P. J. F.-K. J. G. K. J. G. Sc. J. H. A. H. J. H. Mu. J. H. Be. J. H. van't H. J. L. M. J. Mn. J. M. A. de L. J. M. M. J. P. E. J. P. Pe. J. S. Bl. J. S. Co. J. S. F. J. T. Be. J. V.* Jno. W. { Inns of Court. James Claude Webster. Barrister-at-Law, Middle Temple. James David Bourchier, M.A., F.R.G.S. f King's College, Cambridge. Correspondent of The Times in South-Eastern Europe. J j on j an Islands. Commander of the Orders of Prince Danilo of Montenegro and of the Saviour of Greece, and Officer of the Order of St Alexander of Bulgaria. *- John Faithfull Fleet, CLE. Ph.D. Commissioner of Central and Southern Divisions of Bombay, 1891-1897. of Inscriptions of the Early Gupta Kings ; &c. Author j Inscriptions: Indian. Isla, J. F. de. James Fitzmaurice-Kelly, Litt.D., F.R.Hist.S. Gilmour Professor of Spanish Language and Literature, Liverpool University. Norman McColl Lecturer, Cambridge University. Fellow of the British Academy. ' Member of the Royal Spanish Academy. Knight Commander of the Order of Alphonso XII. Author of A History of Spanish Literature; &c. John Graham Kerr, M.A., F.R.S. f Regius Professor of Zoology in the University of Glasgow. Formerly Demonstrator J .. in Animal Morphology in the University of Cambridge. Fellow of Christ's College, 1 Ichthyology Km part). Cambridge, 1 898-1904. Walsingham Medallist, 1898. Neill Prizeman, Royal Society of Edinburgh, 1904. Sir James George Scott, K.C.I.E. j Superintendent and Political Officer, Southern Shan States. Author of Burma, 1 Irrawaddy. a Handbook ; The Upper Burma Gazetteer ; &c. <■ John Henry Arthur Hart, M.A. j Hyrcanus. Fellow, Theological Lecturer and Librarian, St John's College, Cambridge. I John Henry Muirhead, M.A., LL.D. f Professor of Philosophy in the University of Birmingham. Author of Elements^ Idealism. of Ethics ; Philosophy and Life ; &c. Editor of Library of Philosophy. I Very Rev. John Henry Bernard, M.A., D.D., D.C.L. f Dean of St Patrick's Cathedral, Dublin. Archbishop King's Professor of Divinity J , . , and formerly Fellow of Trinity College, Dublin. Joint-editor of the Irish Liber \ "eland, Lnurcn 01. Hymnorum ; &c. I Isomerism. Iberians; Ionians. Jacobus Henricus van't Hoff, LL.D., D.Sc, D.M. See the biographical article van't Hoff, Jacobus Henricus. John Lynton Myres, M.A., F.S.A., F.R.G.S. Wykeham Professor of Ancient History in the University of Oxford. Formerly . Gladstone Professor of Greek and Lecturer in Ancient Geography, University of Liverpool. Lecturer in Classical Archaeology in University of Oxford. John Macpherson, M.D. Formerly Inspector-General of Hospitals, Bengal. Jean Marie Antoine de Lanessan. See the biographical article, Lanessan, J. M. A. de. John Malcolm Mitchell. f Sometime Scholar of Queen's College, Oxford. Lecturer in Classics, East London dVldt, (3) an expression first proposed by L. M. H. Navier. The coefficient m is termed the coefficient of viscosity. According to J. Clerk Maxwell, the value of m for air at 0° Fahr. in pounds, when the velocities are expressed in feet per second, is ix = o-ooo 000 025 6(46i°-f-0); that is, the coefficient of viscosity is proportional to the absolute temperature and independent of the pressure. The value of « for water at 77° Fahr. is, according to H. von Helmholtz and G. Piotrowski, M = o-ooo 018 8, the units being the same as before. For water p decreases rapidly with increase of temperature. § 4. When a fluid flows in a very regular manner, as for instance when it flows in a capillary tube, the velocities vary gradually at any moment from one point of the fluid i, 2 V- - - ^ to a neighbouring „ r !_.' [TJZ'.'S-'SZZZZZZZZZZ point. The layer ad- jacent to the sides of the tube adheres to it and is at rest. The layers more interior than this slide on each other. But the resist- ance developed by these regular move- ments is very small. If in large pipes and open channels.there were a similar regularity of movement, the neighbouring filaments would acquire, especially near the sides, very great relative velocities. V. J. Boussinesq has shown that the central filament in a semicircular canal of 1 metre radius, and inclined at a slope of only o-oooi, would have a velocity of 187 metres per second, 2 the layer next the boundary remaining at rest. But before such a difference of velocity can arise, the motion of the fluid becomes much more complicated. Volumes of fluid are detached continually from the boundaries, and, revolving, form eddies traversing the fluid in all directions, and sliding with finite relative velocities against those surrounding them. These slidings develop resistances incomparably greater than the viscous resistance due to movements varying continuously from point to point. The movements which produce the phenomena commonly ascribed to fluid friction must be regarded as rapidly or even suddenly varying from one point to another. The internal resistances to the motion of the fluid do not depend merely on the general velocities of translation at different points of the fluid (or what Boussinesq terms the mean local velocities), but rather on the intensity at each point of the eddying agitation. The problems of hydraulics are therefore much more complicated than problems in which a regular motion of the fluid is assumed, hindered by the viscosity of the fluid. Relation of Pressure, Density, asd Temperature of Liquids § 5. Units of Volume. — In practical calculations the cubic foot and gallon are largely used, and in metric countries the litre and cubic metre ( = 1000 litres). The imperial gallon is now exclusively used in England, but the United States have retained the old English wine gallon. 2 Journal de M. Liouville, t. xiii. (1868); Memoires de I' Academic, des Sciences de I'Institut de France, t. xxiii., xxiv. (1877). 36 HYDRAULICS [KINEMATICS OF FLUIDS I cub. ft. = 6-236 imp. gallons 1 imp. gallon = 0-1605 cub. ft. 1 U.S. gallon = 0-1337 cub. ft. I litre = 0-2201 imp. gallon = 7-481 U.S. gallons. = 1 -200 U.S. gallons. = 0-8333 imp. gallon. = 0-2641 U.S. gallon. Density of Water. — Water at 53° F. and ordinary pressure contains 62-4 ft per cub. ft., or 10 lb per imperial gallon at 62° F. The litre contains one kilogram of water at 4 C. or 1000 kilograms per cubic metre. River and spring water is not sensibly denser than pure water. But average sea water weighs 64 lb per cub. ft. at 53° F. The weight of water per cubic unit will be denoted by G. Ice free from air weighs 57-28 ft per cub. ft. (Leduc). § 6. Compressibility of Liquids. — The most accurate experiments show that liquids are sensibly compressed by very great pressures, and that up to a pressure of 65 atmospheres, or about 1000 lb per sq. in., the compression is proportional to the pressure. The chief results of experiment are given in the following table. Let Vi be the volume of a liquid in cubic feet under a pressure pi lb per sq. ft., and V2 its volume under a pressure pi. Then the cubical compres- sion is (V2 — Vi)/Vi, and the ratio of the increase of pressure pi— pi to the cubical compression is sensibly constant. That is, k — (,p2~ pi)\'il(Vz — Vi) is constant. This constant is termed the elasticity of volume. With the notation of the differential calculus, '-»/(-$)-- -V dp dV Elasticity of Volume of Liquids. Canton. Oersted. Colladon and Sturm. Regnault. Water . . Sea water Mercury Oil . . . Alcohol 45,990,000 52,900,000 705,300,000 44,090,000 32,060,000 45,900,000 42,660,000 626,100,000 23,100,000 44,090,000 604,500,000 According to the experiments of Grassi, the compressibility of water diminishes as the temperature increases, while that of ether, alcohol and chloroform is increased. § 7. Change of Volume and Density of Water with Change of Tem- perature. — Although the change of volume of water with change of temperature is so small that it may generally be neglected in ordinary hydraulic calculations, yet it should be noted that there is a change of volume which should be allowed for in very exact calculations. The values of p in the following short table, which gives data enough for hydraulic purposes, are taken from Professor Everett's System of Units. Density of Water at Different Temperatures. Temperature. P G 1 Temperature. p G ensity of Water. Weight of Density of Water. Weight of Cent. Fahr. 1 cub. ft. in TK ' Cent. Fahr. 1 cub. ft. in It). 320 999884 62-417 20 68-o •998272 62316 I 33*8 999941 62-420 22 71-6 •997839 62-28Q 2 35-6 999982 62-423 24 75-2 •997380 62-26I 3 37-4 1 OOOO04 62-424 26 78-8 •996879 62229 4 39-2 1 OOOO13 62-425 28 82-4 •996344 62-196 5 41-0 1 OOOOO3 62-424 30 86 •995778 62-I6I 6 42-8 999983 62-423 35 95 •99469 62-093 7 44-6 999946 62-421 40 104 ■99236 61-947 8 46-4 999899 62-418 45 "3 •99038 61-823 9 48-2 999837 62-414 50 122 •9882I 61-688 10 50-0 999760 62-409 55 131 •98583 61-540 11 5i-8 999668 62-403 60 140 •98339 61-387 12 53-6 999562 62-397 65 149 •98075 61-222 '3 55-4 999443 62-389 70 158 •97795 61-048 14 57-2 999312 62-381 75 167 •97499 60-863 15 59-0 999173 62-373 80 176 •97195 60-674 16 6o-8 999015 62-363 85 185 •96880 60-477 17 62-6 998854 62-353 90 194 •96557 60-275 18 64-4 998667 62-341 100 212 •95866 59-844 19 66-2 •998473 62-329 The weight per cubic foot has been calculated from the values of p, on the assumption that 1 cub. ft. of water at 39-2° Fahr. is 62-425 ft. For ordinary calculations in hydraulics, the density of water (which will in future be designated by the symbol G) will be taken at 62-4 ft per cub. ft., which is its density at 53° Fahr. It may be noted also that ice at 32° Fahr. contains 57-3 ft per cub. ft. The values of p are the densities in grammes per cubic centimetre. § 8. Pressure Column. Free Surface Level. — Suppose a small vertical pipe introduced into a liquid at any point P (fig. 3). Then the liquid will rise in the pipe to a level 00, such that the pressure due to the column in the pipe exactly balances the pressure on its mouth. If the fluid is in motion the mouth of the pipe must be supposed accurately parallel to the direction of motion, or the impact of the liquid at the mouth of the pipe will have an influence on the height of the column. If this condition is complied with, the height h of the column is a measure of the pressure at the point P. Let o> be the area of section of the pipe, h the height of the pressure column, p the intensity of pressure at P; then pw=Ghoi%, p/G = h; that is, h is the height due to the pressure at p. The level 00 will be termed the free surface level corresponding to the pressure at P. Relation of Pressure, Temperature, and Density of Gases § 9. Relation of Pressure, Volume, Temperature and Density in Compressible Fluids. — Certain problems on the flow of air and steam are so similar to those relating to the flow of water that they are conveniently treated together. It is neces- sary, therefore, to state as briefly as possible the properties ol compres- sible fluids so far as know- ledge of them is requisite in the solution of these problems. Air may be taken as a type of these fluids, and the numerical data here given will relate to air. Relation of Pressure Fig. 3. and Volume at Constant Temperature. — At constant temperature the product of the pressure p and volume V of a given quantity of air is a constant (Boyle's law). Let po be mean atmospheric pressure (2116-8 ft per sq. ft.), Vo the volume of 1 ft of air at 32° Fahr. under the pressure po. Then poVo = 26214. (1) If Go is the weight per cubic foot of air in the same conditions, Go = i/Vo = 2ii6-8/262i4 = -o8o75. (2) For any other pressure p, at which the volume of 1 ft is V and the weight per cubic foot is G, the temperature being 32° Fahr., pV= p!G =26214; or G=£/262i4. (3) Change of Pressure or Volume by Change of Temperature. — Let pn, Vo, Go, as before be the pressure, the volume of a pound in cubic feet, and the weight of a cubic foot in pounds, at 32° Fahr. Let p, V, G be the same quantities at a temperature / (measured strictly by the air thermometer, the degrees of which differ a little from those of a mercurial thermometer). Then, by experiment, £V = £oVo(46o-6+/)/(46o-6+32) =A,V t/t , (4) where t, t are the temperatures / and 32° reckoned from the absolute zero, which is —460-6 Fahr. ; pjG = £ot/Got ; (4a) G=pT Go/poT. (5) If £0 = 2116-8, Go = -08075, to = 460-6+32 =492-6, then p/G = 53-27-. (5a) Or quite generally p/G = Rt for all gases, if R is a constant varying inversely as the density of the gas at 32° F. For steam R = 85-5- II. KINEMATICS OF FLUIDS § 10. Moving fluids as commonly observed are conveniently classified thus: (1) Streams are moving masses of indefinite length, completely or incompletely bounded laterally by solid boundaries. When the solid boundaries are complete, the flow is said to take place in a pipe. When the solid boundary is incomplete and leaves the upper surface of the fluid free, it is termed a stream bed or channel or canal. (2) A stream bounded laterally by differently moving fluid of the same kind is termed a current. (3) A jet is a stream bounded by fluid of a different kind. (4) An eddy, vortex or whirlpool is a mass of fluid the particles of which are moving circularly or spirally. (5) In a stream we may often regard the particles as flowing along definite paths in space. A chain of particles following each other along such a constant path may be termed a fluid filament or elementary stream. § 11. Steady and Unsteady, Uniform and Varying, Motion. — There are two quite distinct ways of treating hydrodynamical questions. We may either fix attention on a given mass of fluid and consider its changes of position and energy under the action of the stresses to which it is subjected, or we may have regard to a given fixed portion of space, and consider the volume and energy of the fluid entering and leaving that space. KINEMATICS OF FLUIDS] HYDRAULICS 37 If, in following a given path ab (fig. 4), a mass of water a has a constant velocity, the motion is said to be uniform. The kinetic energy of the mass a remains unchanged. If the velocity varies from point to point of the path, the motion is called varying motion. If at a given point a in space, the particles of water always arrive with the same velocity and in the same direction, during any given time, then the motion is termed steady motion. On the contrary, if at the point a the velocity or direction varies from moment to moment the motion is termed a. — a Fig. 4. unsteady. A river which ex- cavates its own bed is in unsteady motion so long as the slope and form of the bed is changing. It, however, tends always towards a condition in which the bed ceases to change, and it is then said to have reached a condition of permanent regime. No river probably is in absolutely permanent regime, except perhaps in rocky channels. In other cases the bed is scoured more or less during the rise of a flood, and silted again during the subsidence of the flood. But while many streams of a torrential character change the condition of their bed often and to a large extent, in others the changes are comparatively small and not easily observed. As a stream approaches a condition of steady motion, its regime becomes permanent. Hence steady motion and permanent regime are sometimes used as meaning the same thing. The one, however, is a definite term applicable to the motion of the water, the other a less definite term applicable in strictness only to the condition of the stream bed. § 12. Theoretical Notions on the Motion of Water. — The actual motion of the particles of water is in most cases very complex. To simplify hydrodynamic problems, simpler modes of motion are assumed, and the results of theory so obtained are compared ex- perimentally with the actual motions. Motion in Plane Layers. — The simplest kind of motion in a stream is one in which the particles initially situated in any plane cross section of the stream con- tinue to be found in plane cross sections during the subsequent motion. Thus, if the particles in a thin plane layer ab (fig. 5) are found again in a thin plane layer a'V after any interval of time, the motion is said to be motion in plane layers. In such motion the internal work in deforming the layer may usually be disregarded, and the resist- ance to the motion is confined to the circumference. . Laminar Motion. — In the case of streams having solid boundaries, it is observed that the central parts move faster than the lateral parts. To take account of these differences of velocity, the stream may be conceived to be divided into thin laminae, having cross sections somewhat similar to the solid boundary of the stream, and sliding on each other. The different laminae can then be treated as having differing velocities according to any law either observed or deduced from their mutual friction. A much closer approxima- tion to the real motion of ordinary streams is thus obtained. Stream Line Motion. — In the preceding hypothesis, all the particles in each lamina have the same velocity at any given cross section of the stream. If this assumption is abandoned, the cross section of the stream must be supposed divided into indefinitely small areas, each representing the section of a fluid filament. Then these fila- ments may have any law of variation of velocity assigned to them. If the motion is steady motion these fluid filaments (or as they are then termed stream lines) will have fixed positions in space. Periodic Unsteady Motion. — In ordinary streams with rough boundaries, it is observed that at any given point the velocity varies from moment to moment in magnitude and direction, but that the average velocity for a sensible period (say for 5 or 10 minutes) varies very little either in magnitude or velocity. It has hence Fig. 5. be the velocity of the fluid. Then the volume flowing through the surface A in unit time is Q=coV. _ (1) Thus, if the motion is rectilinear, all the particles at any instant in the surface A will be found after one second in a similar surface A', at a distance V, and as each particle is followed by a continuous thread of other particles, the volume of flow is the right prism AA' having a base w and length V. If the direction of motion makes an angle 8 with the normal to the surface, the volume of flow is represented by an oblique prism AA' (fig. 7), and in that case Q = wV cos 9. If the velocity varies at different points of the surface, let the sur- face be divided into very small portions, for each of which the W»- V Fig. 6. been conceived that the variations of direction and magnitude of the velocity are periodic, and that, if for each point of the stream the mean velocity and direction of motion were substituted for the actual more or less varying motions, the motion of the stream might be treated as steady stream line or steady laminar motion. § 13. Volume of Flow. — Let A (fig. 6) be any ideal plane surface, of area u>, in a stream, normal to the direction of motion, and let V W» Fig. 7. velocity may be regarded as constant. If da is the area and v, or v cos 0, the normal velocity for this element of the surface, the volume of flow is Q =fvdo>, or fv cos 9 da, as the case may be. § 14. Principle of Continuity. — If we consider any completely bounded fixed space in a moving liquid initially and finally filled continuously with liquid, the inflow must be equal to the outflow. Expressing the inflow with a positive and the outflow with a negative sign, and estimating the volume of flow Q for all the boundaries, S Q=.°- In general the space will remain filled with fluid if the pressure at every point remains positive. There will be a break of continuity, if at any point the pressure becomes negative, indicating that the stress at that point is tensile. In the case of ordinary water this statement requires modification. Water contains a variable amount of air in solution, often about one-twentieth of its volume. This air is disengaged and breaks the continuity of the liquid, if the pressure falls below a point corresponding to its tension. It is for this reason that pumps will not draw water to the full height due to atmospheric pressure. Application of the Principle of Continuity to the case of a Stream. — If Ai, A2 are the areas of two normal cross sections of a stream, and Vi, V 2 are the velocities of the stream at those sections, then from the principle of continuity, ViA^ViA; V 1 /V 2 =A 2 /A 1 (2) that is, the normal velocities are inversely as the areas of the cross sections. This is true of the mean velocities, if at each section the velocity of the stream varies. In a river of varying slope the velocity varies with the slope. It is easy therefore to see that in parts of large cross section the slope is smaller than in parts of small cross section. If we conceive a space in a liquid bounded by normal sections at Ai, A 2 and between Ai, A 2 by stream lines (fig. 8), then, as there is no flow across the stream lines, V 1 /V 2 = A 2 /A I , as in a stream with rigid boundaries. In the case of compressible fluids the variation of volume due to the difference of pressure at the two sections must be taken into Fig. 8. account. If the motion is steady the weight of fluid between two cross sections of a stream must remain constant. Hence the weight flowing in must be the same as the weight flowing out. Let pi, pz be the pressures, v x , v 2 the velocities, Gi, G 2 the weight per cubic foot of fluid, at cross sections of a stream of areas Ai, A 2 . The volumes of inflow and outflow are Ai»i and A 2 t> 2 , and, if the weights of these are the same, GiAi!>i = G 2 A 2 z> 2 ; and hence, from (50) § 9, if the temperature is constant, piAiVi=p 2 A 2 v 2 . (3) 38 HYDRAULICS [DISCHARGE OF LIQUIDS § IS. Stream Lines. — The characteristic of a perfect fluid, that is, a fluid free from viscosity, is that the pressure between any two parts ' into which it is divided by a plane must be normal to the plane. One consequence of this is that the particles can have no rotation impressed upon them, and the motion of such a fluid is irrotational. A stream line is the line, straight or curved, traced by a particle in a current of fluid in irrotational movement. In a steady current Fig. 9. each stream line preserves its figure and position unchanged, and marks the track of a stream of particles forming a fluid filament or elementary stream. A current in steady irrotational movement may be conceived to be divided by insensibly thin partitions follow- ing the course of the stream lines into a number of elementary streams. If the positions of these partitions are so adjusted that the volumes of flow in all the elementary streams are equal, they represent to the mind the velocity as well as the direction of motion of the particles in different parts of the current, for the velocities "r Fig. 11. Fig. 12. are inversely proportional to the cross sections of the elementary streams. No actual fluid is devoid of viscosity, and the effect of viscosity is to render the motion of a fluid sinuous, or rotational or eddying under most ordinary conditions. At very low velocities in a tube of moderate size the motion of water may be nearly pure stream line motion. But at some velocity, smaller as the diameter of the tube is greater, the motion suddenly becomes tumultuous. The laws of simple stream line motion have hitherto been investi- gated theoretically, and from mathematical difficulties have only been determined for certain simple cases. Professor H. S. Hele Shaw has found means of exhibiting stream line motion in a number of very interesting cases experimentally. Generally in these ex- periments a thin sheet of fluid is caused to flow between two parallel plates of glass. In the earlier experiments streams of very small air bubbles introduced into the water current rendered visible the motions of the water. By the use of a lantern the image of a portion of the current can be shown on a screen or photo- graphed. In later experiments streams of coloured liquid at regular distances were intro- duced into the sheet and these much more clearly marked out the forms of the stream lines. With a fluid sheet 0-02 in. thick, the stream lines were found to be stable at almost any required velocity. For certain simple cases Professor Hele Shaw has shown that the experimental stream lines of a viscous fluid are so far as can be measured identical with the calculated stream lines of a perfect fluid. Sir G. G. Stokes pointed out that in this case, either from the thinness of the stream between its glass walls, or the slowness of the motion, or the high viscosity of the liquid, or from a combination of all these, the flow is regular, and the effects of inertia disappear, the viscosity dominating everything. Glycerine gives the stream lines very satisfactorily. Fig. 9 shows the stream lines of a sheet of fluid passing a fairly Fig. 13. shipshape body such as a screwshaft strut. The arrow shows the direction of motion of the fluid. Fig. 10 shows the stream lines for a very thin glycerine sheet passing a non-shipshape body, the stream lines being practically perfect. Fig. II shows one of the earlier air-bubble experiments with a thicker sheet of water. In this case the stream lines break up behind the obstruction, forming an eddying wake. Fig. 12 shows the stream lines of a fluid passing a sudden contraction or sudden enlargement of a pipe. Lastly, fig. 13 shows the stream lines of a current passing an oblique plane. H. S. Hele Shaw, " Experiments on the Nature of the Surface Re- sistance in Pipes and on Ships," Trans. Inst. Naval Arch. (1897). " Investigation of Stream Line Motion under certain Experimental Conditions," Trans. Inst. Naval Arch. (1898) ; " Stream Line Motion of a Viscous Fluid," Report of British Association (1898). III. PHENOMENA OF THE DISCHARGE OF LIQUIDS FROM ORIFICES AS ASCERTAINABLE BY EXPERIMENTS § 16. When a liquid issues vertically from a small orifice, it forms a jet which rises nearly to the level of the free surface of the liquid in the vessel from which it flows. The difference of level h, (fig. 14) is so small that it may be at once suspected to be due either to air resistance on the surface of the jet or to the viscosity of the liquid or to friction against the sides of the orifice. Neglecting for the moment this small quantity, we may infer, from the eleva- tion of the jet, that each molecule on leaving the orifice possessed the velo- city required to lift it against gravity to the height h. From ordinary dynamics, the relation between the velocity and height of projection is given by the equ ation V = ij2gh._ (1) As this velocity is nearly reached in the flow from well-formed orifices, it is sometimes called the theoretical velocity of discharge. This relation was first obtained by Torricelli. If the orifice is of a suitable conoidal form, the water issues in filaments normal to the plane of the orifice. Let o> be the area of the orifice, then the discharge per second must be, from eq. (1), Q = av = w V 2gh nearly . (2 ) This is sometimes quite improperly called the theoretical dis- charge for any kind of orifice. Except for a well-formed conoidal orifice the result is not approximate even, so that if it is supposed to be based on a theory the theory is a false one. Use of the term Head in Hydraulics. — The term head is an old millwright's term, and meant primarily the height through which a mass of water descended in actuating a hydraulic machine. Since the water in fig. 14 descends through a height h to the orifice, we may say there are h ft. of head above the orifice. Still more generally any mass of liquid h ft. above a horizontal plane may be said to have h ft. of elevation head relatively to that datum plane. Further, since the pressure p at the orifice which produces outflow is connected with h by the relation p/G = h, the quantity p/G may be termed the pressure head at the orifice. Lastly, the velocity v is connected with h by the relation D 2 /2g = /s, so that v 2 /2g may be termed the head due to the velocity v. § 1 7. Coefficients of Veloc ity a nd Resistance. — As the actual velocity of discharge differs from V 2gh by a small quantity, let the actual velocity = V a =C v Tj2gh, (3) where c„ is a coefficient to be determined by experiment, called the coefficient of velocity. This coefficient is found to be tolerably con- stant for different heads with well-formed simple orifices, and it very often has the value 0-97. The difference between the velocity of discharge and the velocity due to the head may be reckoned in another way. The total height h causing outflow consists of two parts — one part h e expended effectively in producing the velocity of outflow, another hr in over- coming the resistances due to viscosity and friction. Let h r = C r ke, where c, is a coefficient determined by experiment, and called the coefficient of resistance of the orifice. It is tolerably constant for different heads with well-formed orifices. Then J>„ = V 2gh, = V \2gh!{\ +C r )}. (4) DISCHARGE OF LIQUIDS] HYDRAULICS 39 The relation between c» and c, for any orifice is easily found : — Va = C„V 2gA = V [2ghKl +C r )} e. = V|i/(i+*)}. (5) Cr=l/C„ 2 -I. (5fl) Thus if c, =0-97, then c r = o-o628. That is, for such an orifice about 6j % of the head is expended in overcoming frictional resistances to flow. Coefficient of Contraction — Sharp-edged Orifices in Plane Surfaces. — When a jet issues from an aperture in a vessel, it may either spring Fig. 15. clear from the inner edge of the orifice as at a or & (fig. 15), or it may adhere to the sides of the orifice as at c. The former condition will be found if the orifice is bevelled outwards as at a, so as to be sharp edged, and it will also occur generally for a prismatic aperture like b, provided the thickness of the plate in which the aperture is formed is less than the diameter of the jet. But if the thickness is greater the condition shown at c will occur. When the discharge occurs as at a or b, the filaments con- verging towards the orifice continue to converge beyond it, so that the section of the jet where the filaments have become parallel is smaller than the section of the orifice. The inertia of the filaments opposes sudden change of direction of motion at the edge of the orifice, and the convergence continues for a distance of about half the diameter of the orifice beyond it. Let u be the area of the orifice, and c c a> the area of the jet at the point where convergence ceases; then c c is a coefficient to be determined experi- mentally for each kind of orifice, called the coefficient of contraction. When the orifice is a sharp-edged orifice in a plane surface, the value of c e is on the average 0-64, or the section of the jet is very nearly five-eighths of the area of the orifice. Coefficient of Discharge. — In applying the general formula Q=ui> to a stream, it is assumed that the filaments have a common velocity v normal to the section u. But if the jet contracts, it is at the con- tracted section of the jet that the direction of motion is normal to a transverse section of the jet. Hence the actual discharge when contraction occurs is Qo = c„z)XCcw = CcCi,wV ( 2 gh), or simply, if c = cc c , Qa = ClW(2g/l),' where c is called the coefficient of discharge. Thus for a sharp- edged plane orifice c = o-gjX o-64 = o-62. § 18. Experimental Determina- tion of c„, c c , and c. — The co- efficient of contraction c c is directly determined by measur- ing the dimensions of the jet. the orifice, and t the time in which a particle moves from O to A, then x=v a l;y = \gP. Eliminating t, Va = <{gX i l2y). Then c v =VaH (2gh) = V (x*/4yh). In the case of large orifices such as weirs, the velocity can be directly determined by using a Pitot tube (§ 144). The coefficient of discharge, which for practical purposes is the most important of the three coefficients, is best determined by tank measurement of the flow from the given orifice in a suitable time. If Q is the discharge measured in the tank per second, then C=Q/„ is the velocity at into the waste channel. D is a stilling screen to prevent agitation of the surface at the measuring point, E, and F is a discharge valve for emptying the measuring tank. The rise of level in the tank, the time of the flow and the head over the orifice at that time must be exactly observed. For well made sharp-edged orifices, small relatively to the water surface in the supply reservoir, the coefficients under different conditions of head are pretty exactly known. Suppose the same quantity of water is made to flow in succession through such an orifice and through another orifice of which the coefficient is re- quired, and when the rate of flow is constant the heads over each orifice are noted. Let hi, fe be the heads, coi, coj the areas of the orifices, c\, Ci the coefficients. Then since the flow through each orifice is the same Q =CiwiV (2gfcl) =c 2 wjV (2gfe). c 2 = ci(wi/cu 2 ) V (hi/h). § 19. Coefficients for Bellmoulhs and Bellmouthed Orifices. — If an orifice is furnished with a mouthpiece exactly of the form of the -D'l-2Sd- tfS*«**"'j 0-3 D -OG2.5 d d-0-8D .— r Fig. 19. contracted vein, then the whole of the contraction occurs within the mouthpiece, and if the area of the orifice is measured at the smaller end, c„ must be put = i. It is often desirable to bellmouth the ends of pipes, to avoid the loss of head which occurs if this is 4° HYDRAULICS [DISCHARGE OF LIQUIDS not done; and such a bellmouth may also have the form of the con- tracted jet. Fig. 19 shows the proportions of such a bellmouth or bellmouthed orifice, which approximates to the form of the con- tracted jet sufficiently for any practical purpose. For such an orifice L. J. Weisbach found the following values of the coefficients with different heads. Head over orifice, in ft. = h •66 1-64 11-48 5577 337-93 Coefficient of velocity = c„ . Coefficient of resistance = c r •959 •087 •967 •069 •975 •052 •994 •012 •994 •012 As there is no contraction after the jet issues from the orifice, c c — I , c = c v ; and therefore Q =c„«V (2gh) =«V \2gh/(l +c r )}. § 20. Coefficients for Sharp-edged or virtually Sharp-edged Orifices. — There are a very large number of measurements of discharge from sharp-edged orifices under different conditions of head. An account of these and a very careful tabulation of the average values of the coefficients will be found in the Hydraulics of the late Hamilton Smith (Wiley & Sons, New York, 1886). The following short table abstracted from a larger one will give a fair notion of how the co- efficient varies according to the most trustworthy of the experiments. Coefficient of Discharge for Vertical Circular Orifices, Sharp-edged, with free Discharge into the Air. Q = c«V (2gh). Head measured to Centre of Orifice. °'3 0-4 o-6 0-8 i-o 2-0 4-0 8-o 20-O Diameters of Orifice. ■04 •40 ■60 Values of C. ■655 •648 •644 •632 •623 •614 •601 •637 •630 •626 •623 •614 •609 •605 •599 621 618 613 •601 •596 •588 610 •601 •597 •594 •58.3 608 •600 •598 •595 •59i 604 •599 •599 •597 •595 602 •599 •598 •597 •596 600 •598 •597 •596 •596 596 •596 •596 ■596 •594 At the same time it must be observed that differences of sharpness in the edge of the orifice and some other circumstances affect the results, so that the values found by different careful experimenters are not a little discrepant. When exact measurement of flow has to be made by a sharp-edged orifice it is desirable that the coefficient for the particular orifice should be directly determined. The following results were obtained by Dr H. T. Bovey in the laboratory of McGill University. Coefficient of Discharge for Sharp-edged Orifices. Head in ft. Form of Orifice. Cir- cular. Square. Rectangular Ratio of Sides 4:1. Rectangular Ratio of Sides 16:1. Tri- angular. Sides vertical. Dia- gonal vertical. Long Sides vertical. Long Sides hori- zontal. Long Sides vertical. Long Sides hori- zontal. I 2 4 6 8 10 12 14 16 18 20 •620 •613 •608 •607 ■606 ■605 •604 •604 •603 •603 •603 •627 •620 •616 •614 •613 •6l2 •6ll •6lO •6lO •6l0 •609 ■628 •628 •618 •616 •614 •613 •612 •6l2 •6ll •6ll •6ll •642 •634 •628 ■626 •623 ■622 •622 •621 •620 •620 •620 •643 •636 •629 •627 •625 •624 •623 •622 •622 •621 •621 •663 •650 ■64I •637 •634 •632 •63I ■630 •63O •630 ■629 •664 •6 5 I •642 •637 ■635 •633 ■631 •630 ■630 •629 ■628 •636 •628 •623 •620 •619 •618 •618 •618 •617 •616 ■616 The orifice was 0-196 sq. in. area and the reductions were made with g =32- 176 the value for Montreal. The value of the coefficient appears to increase as (perimeter) / (area) increases. It decreases as the head increases. It decreases a little as the size of the orifice is greater. Very careful experiments by J. G. Mair (Proc. Inst. Civ. Eng. lxxxiv.) on the discharge from circular orifices gave the results shown on top of next column. The edges of the orifices were got up with scrapers to a sharp square edge. The coefficients generally fall as the head increases and as the diameter increases. Professor W. C. Unwin found that the results agree with the formula c = 0-6075 +0-0098/V h- o-ootfd, where h is in feet and d in inches. Coefficients of Discharge from Circular Orifices Temperature 51° to 55°. 1 Head in Diameters of Orifices in Inches (d). feet h. 1 ii 1 1 1* 2 ai 2i 2i 3 •75 Coefficients (c). •616 •614 •616 •610 •616 •612 •607 •607 •609 I-O •613 •612 •612 •611 •612 •611 •604 •608 •609 1-25 ■613 •614 ■610 •608 •612 •608 •605 •60s ■606 I -50 •610 ■612 •611 •606 •610 •607 •603 •607 •605 i-75 •612 •611 •611 •605 •611 •605 •604 ■607 •605 2-00 •609 •613 •609 •606 ■609 ■606 •604 ■604 •605 The following table, compiled by J. T. Fanning (Treatise on Water Supply Engineering), gives values for rectangular orifices in ver- tical plane surfaces, the head being measured, not immediately over the orifice, where the surface is depressed, but to the still- water surface at some distance from the orifice. The values were obtained by graphic interpolation, all the most reliable ex- periments being plotted and curves drawn so as to average the discrepancies. Coefficients of Discharge for Rectangular Orifices, Sharp- in Vertical Plane Surfaces. Head to Centre of Orifice. Ratio of Height to Width. Feet. 0-2 •3 •4 •5 •6 •7 •8 •9 i-o 1-25 1-50 1-75 2 2-25 2-50 2-75 3 3-5 4 4-5 5 6 7 8 9 10 15 20 25 30 35 40 45 50 •6290 •6280 •6273 •6250 •6245 •6226 •6208 ■6158 •6124 •6090 •6060 ■6035 •6040 •6045 •6048 •6054 ■6060 •6066 •6054 •6086 •6188 •6187 •6186 •6183 ■6180 •6176 •6i73 •6170 •6160 ■6150 •6138 •6124 •6094 •6064 •6036 •6020 •6015 ■6018 ■6024 •6028 •6034 •6039 ■6045 •6052 •6060 •6130 •6134 •6i35 •6140 •6144 •6145 •6144 •6143 •6139 •6136 •6132 •6123 •6110 ■6100 •6088 •6063 •6038 •6022 •6014 •6010 ■6010 •6012 •6014 •6017 ■6021 ■6025 •6029 •6034 '.3 'is •5984 •5994 •6000 ■6006 •6010 •6018 •6026 •6033 •6036 ■6029 •6043 •6046 •6048 •6050 •6047 •6044 •6038 •6020 •601 1 •6010 •6010 •6010 •601 1 •6012 •6012 ■6013 •6014 •6015 •6016 •6018 i •6050 ■6063 •6074 •6082 •6086 •6090 ■6095 ■6100 •6103 •6104 •6103 •6102 •6101 ■6100 ■6094 •6085 •6074 •6063 •6044 •6032 •6022 •6015 ■6010 •6012 •6014 •6016 •6018 •6022 •6026 •6030 •6035 6140 6150 6156 6162 6165 6168 6172 6i73 6172 6168 6166 6163 6i57 6i55 6i53 6146 6136 6125 6114 6087 6058 6033 6020 6010 6013 6018 6022 6027 6032 6037 6043 6050 23 •6293 •6306 •6313 •6317 •6319 •6322 •6323 •6320 •6317 •6313 •6307 •6302 •6293 •6282 •6274 •6267 •6254 •6236 •6222 •6202 •6154 •6lIO •6073 •6045 •6O30 ■6033 •6036 •604O •6044 •6049 •6055 •6062 •6070 •6333 •6334 •6334 •6333 •6332 •6328 •6326 •6324 •6320 ■6312 •6303 •6296 ■6291 ■6286 •6278 •6273 •6267 •6254 •6236 •6222 •6202 •6154 •6II4 •6087 •6O70 •606O •6066 •6074 •6083 •6092 •6IO3 •6II4 •6125 •6I4O §21. Orifices with Edges of Sensible Thickness. — When the edges of the orifice are not bevelled outwards, but have a sensible thickness, the coefficient of discharge is somewhat altered. The following table gives values of the coefficient of discharge for the arrangerrieats of the orifice shown in vertical section at P, Q, R (fig. 20). The plan of all the orifices is shown at S. The planks forming the orifice and sluice were each 2 in. thick, and the orifices were all 24 in. wide. The heads were measured immediately over the orifice. In this case, Q=r&(H-ft)V{2g(H+ft)/2}. § 22. Partially Suppressed Contraction. — Since the contraction of the jet is due to the convergence towards the orifice of the issuing streams, it will be diminished if for any portion of the edge of the orifice the convergence is prevented. Thus, if an internal rim or border is applied to part of the edge of the orifice (fig. 21), the con- vergence for so much of the edge is suppressed. For such cases G. Bidone found the following empirical formulae applicable : — DISCHARGE OF LIQUIDS] HYDRAULICS 4i Table of Coefficients of Discharge for Rectangular Vertical Orifices in Fig . 20. Head h above upper edgj oi Height of Orifice, H - h, in feet. i-3i 0-66 0-16 O-IO Orifice in feet. P Q R P Q R P R p Q R 0-328 0-598 0-644 0-648 0-634 0-665 0-668 0-691 0-664 o-666 0-710 0-694 0-696 •656 0-609 0-653 0-657 0-640 0-672 0-675 0-685 0-687 0-688 0-696 0-704 0-706 •787 0-612 0-655 0-659 0-641 0-674 0-677 0-684 0-690 0-692 0-694 0-706 0-708 ■984 0-616 0-656 o-66o 0-641 0-675 0-678 0-683 0-693 0-695 0-692 0-709 0-711 1-968 0-618 0-649 0-653 0-640 0-676 0-679 0-678 0-695 0-697 o-688 0-710 0-712 3-28 0-608 0-632 0-634 0-638 0-674 0-676 0-673 0-694 0-695 0-680 0-704 0-705 4-27 0-602 0-624 0-626 0-637 0-673 0-675 0-672 0-693 0-694 0-678 0-701 0-702 4-92 0-598 0-620 0-622 0-637 0-673 0-674 0-672 0-692 0-693 0-676 0-699 0-699 5-58 0-596 0-618 0-620 0-637 0-672 0-673 0-672 0-692 0-693 0-676 0-698 0-698 6-56 0-595 0-615 0-617 0-636 0-671 0-672 0-671 0-691 0-692 0-675 0-696 0-696 9-84 0-592 o-6u 0-612 0-634 0-669 0-670 0-668 0-689 0-690 0-672 0-693 0-693 For rectangular orifices, c c =0-62(1 +o-l52«/£) ; and for circular orifices, c c = 0-62(1 -\~o-l28n/p) ; when n is the length of the edge of the orifice over which the border extends, and p is the whole length of edge or perimeter of the orifice. The following are the values of c c , when the border extends over i, J or j of the whole perimeter: — nip Cc Rectangular Orifices. Cc Circular Orifices. 0-25 0-50 o-75 0-643 0-667 0-691 •640 •660 •680 For larger values of nip the formulae are not applicable. C. R. Bornemann has shown, however, that these for- mulae for suppressed con- traction are not reliable. § 23. Imperfect Con- traction. — If the sides of the vessel approach near to the edge of the orifice, they interfere with the convergence of the streams ^ to which the contraction is due, and the contraction is then modified. It is generally stated that the influence of the sides begins to be felt if their distance from the edge of the orifice is less than 2-7 times the corresDonding § 24. Orifices Furnished with Channels of Discharge. — These ex- ternal borders to an orifice also modify the contraction. The following coefficients of discharge were obtained with open- ings 8 in. wide, and small in proportion to the channel of approach (fig. 22, A, B, C). ft-j— k\ in feet. h\ in feet. ■0656 'l64 •328 •656 1-640 3' 28 4-92 656 984 B \ 0-656 C) A ) B \ 0-164 c) •480 ■48O •527 •488 •487 •585 •5" •510 •553 •577 •57i •614 ■542 •538 •574 ■624 •606 ■633 •574 •506 •592 •631 •617 •645 •599 •592 •607 •625 •626 •652 •601 •600 •610 ■624 •628 ■651 •601 •602 •610 •619 •627 •650 •601 •602 •609 ■613 •623 •650 ■601 ■601 •608 ■606 •618 ■649 § 25. Inversion of the Jet. — When a jet issues from a horizontal orifice, or is of small size compared with the head, it presents no A Fig. 20. Fig. 21. Fig. 23. width of the orifice. The coefficients of contraction for this case | marked peculiarity of form. But if the orifice is in a vertical sur- are imperfectly known. | face, and if its dimensions are not small compared with the head, _l *l h 3 1 .-i- -\- 1 * Fig. 22. Slope 2 in 10 U- ■#- 4 42 HYDRAULICS [STEADY MOTION OF FLUIDS it undergoes a series of singular changes of form after leaving the orifice. These were first investigated by G. Bidone (1781-1839); subsequently H. G. Magnus (1802-1870) measured jets from different orifices; and later Lord Rayleigh {Proc. Roy. Soc. xxix. 71) in- vestigated them anew. Fig. 23 shows some forms, the upper figure giving the shape of the orifices, and the others sections of the jet. The jet first contracts as described above, in consequence of the convergence of the fluid streams within the vessel, retaining, however, a form similar to that of the orifice. Afterwards it expands into sheets in planes per- pendicular to the sides of the orifice. Thus the jet from a triangular orifice expands into three sheets, in planes bisecting at right angles the three sides of the triangle. Generally a jet from an orifice, in the form of a regular polygon of n sides, forms n sheets in planes perpendicular to the sides of the polygon. Bidone explains this by reference to the simpler case of meeting streams. If two equal streams having the same axis, but moving in opposite directions, meet, they spread out into a thin disk normal to the common axis of the streams. If the directions of two streams intersect obliquely they spread into a symmetrical sheet perpendicular to the plane of the streams. Let 01, a 2 (fig. 24) be two points in an orifice at depths hi, hi from the free surface. The filaments issuing at ai, 02 will have the different velocities V 2ghi and V 2ghi. Consequently they will tend to describe parabolic paths dicbi and ancbz of different horizontal range, and intersecting in the point c. But since two filaments cannot simul- taneously flow through the same point, they must exercise mutual pressure, and will be deflected out of the paths they tend to describe. It is this mutual pressure which causes the expansion of the jet into sheets. Lord Rayleigh pointed out that, when the orifices are small and the head is not great, the expansion of the sheets in directions per- pendicular to the direction of flow reaches a limit. Sections taken at greater distance from the orifice show a contraction of the sheets until a compact form is reached similar to that at the first contrac- tion. Beyond this point, if the jet retains its coherence, sheets are thrown out again, but in directions bisecting the angles between the previous sheets. Lord Rayleigh accepts an explanation of this con- traction first suggested by H. Buff (1805-1878), namely, that it is due to surface tension. § 26. Influence of Temperature on Discharge of Orifices. — Professor VV. C. Unwin found {Phil. Mag., October 1878, p. 281) that for sharp-edged orifices temperature has a very small influence on the discharge. For an orifice I cm. in diameter with heads of about I to 1 5 ft. the coefficients were: — Temperature F C. 2°5° • -594 62 -598 For a conoidal or bell-mouthed orifice I cm. diameter the effect of temperature was greater: — Temperature F C. 190 0-987 130° 0-974 60 . 0-942 an increase in velocity of discharge of 4% when the temperature increased 130 . J. G. Mair repeated these experiments on a much larger scale (Proc. Inst. Civ. Eng. lxxxiv.). For a sharp-edged orifice 2§ in. diameter, with a head of 1-75 ft., the coefficient was 0-604 at 57 and 0607 at 179 F., a very small difference. With a conoidal orifice the coefficient was 0-961 at 55 and 0-981 at 170 F. The corresponding coefficients of resistance are 0-0828 and 0-0391, showing that the resistance decreases to about half at the higher temperature. § 27. Fire Hose Nozzles. — Experiments have been made by J. R. Freeman on the coefficient of discharge from smooth cone nozzles used for fire purposes. The coefficient was found to be 0-983 for f-in Fig. 24. 82 for in. 0-972 for 1 in.; 0-976 for if in.; and open channel, for instance, when the effect of eddies produced by the roughness of the sides is neglected, the pressure at each point is simply the hydrostatic pressure due to the depth below the free surface. (6) If the velocity of the fluid is very small, the distribution of pressure is approximately the same as in a fluid at rest. (c) If the fluid molecules take precisely the accelerations which they would have if independent and submitted only to the external forces, the pressure is uniform. Thus in a jet falling freely in the air the pressure throughout any cross section is uniform and equal to the atmospheric pressure. (d) In any bounded plane section traversed normally by streams which are rectilinear for a certain distance on either side of the section, the distribution of pressure is the same as in a fluid at rest. Distribution of Energy in Incompressible Fluids. § 29. Application of the Principle of the Conservation of Energy to Cases of Stream Line Motion. — The external and internal work done on a mass is equal to the change of kinetic energy produced. In many hydraulic questions this principle is difficult to apply, be- cause from the complicated nature of the motion produced it is difficult to estimate the total kinetic energy generated, and because in some cases the internal work done in overcoming frictional or viscous resistances cannot be ascertained ; but in the case of stream line motion it furnishes a simple and important result known as Bernoulli's theorem. Let AB (fig. 25) be any one elementary stream, in a steadily moving fluid mass. Then, from the steadiness of the motion, AB is a fixed path in space through which a stream of fluid is constantly flowing. Let 00 be the free surface and XX any horizontal datum line. Let o o nozzle ; o 097 1 for 1} in. The nozzles were fixed on a taper play-pipe, and the coefficient includes the resistance of this pipe (Amer. Soc. Civ. Eng. xxi.. 1889). Other forms of nozzle were tried such as ring nozzles for which the coefficient was smaller. IV. THEORY OF THE STEADY MOTION OF FLUIDS. § 28. The general equation of the steady motion of a fluid given under Hydrodynamics furnishes immediately three results as to the distribution of pressure in a stream which may here be assumed. (a) If the motion is rectilinear and uniform, the variation of pressure is the same as in a fluid at rest. In a stream flowing in an Fig. 25. w be the area of a normal cross section, v the velocity, p the intensity of pressure, and 2 the elevation above XX, of the elementary stream AB at A, and o>i, pi, Vi, 21 the same quantities at B. Suppose that in a short time t the mass of fluid initially occupying AB comes to A'B'. Then AA', BB' are equal to vt, Vit, and the volumes of fluid AA', BB' are the equal inflow and outflow = Qt = uvt = uiVit, in the given time. If we suppose the filament AB surrounded by other filaments moving with not very different velocities, the frictional or viscous resistance on its surface will be small enough to be neglected, and if the fluid is incompressible no internal work is done in change of volume. Then the work done by external forces will be equal to the kinetic energy produced in the time considered. The normal pressures on the surface of the mass (excluding the ends A, B) are at each point normal to the direction of motion, and do no work. Hence the only external forces to be reckoned are gravity and the pressures on the ends of the stream. The work of gravity when AB falls to A'B' is the same as that of transferring AA' to BB'; that is, GQt (z—Zi). The work of the pressures on the ends, reckoning that at B negative, because it is opposite to the direction of motion, is (puiy.vt) — (piuiXvit) = Qt{p—pi). The change of kinetic energy in the time / is the differ- ence of the kinetic energy originally possessed by AA' and that finally acquired by BB', for in the intermediate part A'B there is no change of kinetic energy, in consequence of the steadiness of the motion. But the mass of AA' and BB' is GQt/g, and the change of kinetic energy is therefore (GQ//g) (z>i 2 /2 — 1> 2 /2). Equating this to the work done on the mass AB, GQt(z- Zl )+Qt(p-Pi) = (GQt/g)Wl2-vV2). Dividing by GQt and rearranging the terms, vV2g+plG+z=v 1 -/2g+p 1 IG+z 1 ; (1) or, as A and B are any two points, » 2 /2g+p/G-r-3=constant = H. _ (2) Now n 2 /2g is the head due to the velocity v, pjG is the head equivalent to the pressure, and 2 is the elevation above the datum (see § 16). Hence the terms on the left are the total head due to velocity, pressure, and elevation at a given cross section of the filament, 2 is easily seen to be the work in foot-pounds which would be done by I lb of fluid falling to the datum line, and similarly pjG and i> 2 /2g are the quantities of work which would be done by I lb of fluid due to the pressure p and velocity v. The expression on the left of the equation is, therefore, the total energy of the stream at the section considered, per lb of fluid, estimated with reference to the STEADY MOTION OF FLUIDS] datum line XX. Hence we see that in stream line motion, under the restrictions named above, the total energy per lb of fluid is uniformly distributed along the stream line. If the free surface of the fluid 00 is taken as the datum, and -h, -hi are the depths of A and a measured down from the free surface, the equation takes the form ^/2g+plG-h=v 1 */2g+p l /G-h l ; (,) or generally i' 2 /2£ +p/G — h = constant . ( 3 o) § 30. Second Form of the Theorem of Bernoulli.— Suppose at the two sections A, B (fig. 26) of an elementary stream small vertical pipes are introduced, which may be termed pressure columns HYDRAULICS 4-3 projected surface as HI, and the pressures parallel to the axis of the pipe, normal to these projected surfaces, balance each other Similarly the pressures on BC, CD balance those on GH, EG In the same way, in any combination of enlargements and contrac- tions, a balance of pressures, due to the flow of liquid parallel to the ^^^ ~-~-^Y ~ "~ a~ 1 — )• , 1 H 1 1 -vl '? Fig. 26. (I 8), having their lower ends accurately parallel to the direction of flew. In such tubes the water will rise to heights corresponding to the pressures at A and B. Hence b = p/G, and b'=p,/G. Conse- quently the tops of the pressure columns A' and B' will be at total heights b -\ c=p/G+z and b'+c' = p l /G+z 1 above the datum line XX. Ihe difference of level of the pressure column tops, or the fall of free surface level between A and B, is therefore . S = (i>-£i)/G + (z-z,); and this by equation (1), § 29 is (i^-i^g. That is, the fall of free surface level between two sections is equal to the difference of the heights due to the velocities at the sections. The line A'B' is sometimes called the line of hydraulic gradient, though this term is also used in cases where friction needs to be taken into account. It is the line the height of which above datum is the sum of the elevation and pressure head at that point, and it falls below a horizontal line A"B" drawn at H ft. above XX by the quantities a=t' 2 /2g and a' =vi 2 /2g, when friction is absent. § 31. Illustrations of the Theorem of Bernoulli. In a lecture to the mechanical section of the British Association in 1875, W. Fronde gave some experimental illustrations of the principle of Bernoulli. He remarked that it was a common but erroneous impression that a fluid exercises in a contracting pipe A (fig. 27) an excess of pressure against the entire converging surface which it meets, and that, conversely, as it enters an enlargement B, a relief of pressure is experienced by the entire diverging surface of the' pipe. Further it is commonly assumed that when passing through a contraction C, there is in the narrow neck an excess of pressure due to the squeezing together of the liquid at that point. These impressions are in no respect correct; the pressure is smaller as the section of the pipe is smaller and conversely. Fig. 28 shows a pipe so formed that a contraction is followed by an enlargement, and fig. 29 one in which an enlargement is followed by a contraction. The A B vertical pressure columns show the decrease of pressure at the contrac- tion and increase of pressure at the enlarge- ment. The line 06c in both figures shows the variation of free surface level, supposing the pipe frictionless. In actual pipes, however, work is expended in friction ..,,,,..., . , against the pipe; the total head diminishes in proceeding along the pipe, and the free surface level is a line such as ahc u falling below abc. Froude further pointed out that, if a pipe contracts and enlarges again to the same size, the resultant pressure on the converging part exactly balances the resultant pressure on the diverging part so that there is no tendency to move the pipe bodily when water flows through it. Thus the conical part AB (fig. 30) presents the same axis of the pipe, will be found, provided the sectional area and direction of the ends are the same. The following experiment is interesting. Two cisterns provided with converging pipes were placed so that the jet from one was ex- actly opposite the entrance to the other. The cisterns being filled -0- „ Fig. 29. very nearly to the same level, the jet from the left-hand cistern A entered the right-hand cistern B (fig. 31), shooting across the free space between them without any waste, except that due to indirect- ness of aim and want of exact correspondence in the form of the onhces. In the actual experiment there was 18 in. of head in the right and 2o| in. of head in the left-hand cistern, so that about Fig. 27. Fig. 30. 2| in. were wasted in friction. It will be seen that in the open space between the orifices there was no pressure, except the atmospheric pressure acting uniformly throughout the system. § 32- Ventur-- Meter.— An ingenious application of the variation oi pressure a-.d velocity in a converging and diverging pipe has been Fig. 31. made by Clemens Herschel in the construction of what he terms a Ventun Meter for measuring the flow in water mains. Suppose that, as in ng. 32, a contraction is made in a water main, the change of section being gradual to avoid the production of eddies. The ratio p 44 HYDRAULICS [STEADY MOTION OF FLUIDS of the cross sections at A and B, that is at inlet and throat, is in actual meters 5 to I to 20 to I , and is very carefully determined by the maker of the meter. Then, if v and u are the velocities at A and B, -u — pv. Let pressure pipes be introduced at A, B and C, 8 and let Hi, H, H2 be the pressure heads at those points. Since the velocity at B is greater than at A the pressure will be less. Neglect- ing friction Hi+P 2 /2g = H+K 2 /2g, Hi-H = (u^u-)l2g = *-l)v*/2g. Let h = Hi-H be termed the Venturi head, then M = V!p 2 .2g/*/(p--l)j, from which the velocity through the throat and the discharge of the main can be calculated if the areas at A and B are known and h observed. Thus if the diameters at A and B are 4 and 12 in., the areas are 12-57 an d 113-1 sq. in., and p = 9, m = V8i/8oV (2gft) = i-007V (2gh). If the observed Venturi head is 12 ft., m = 28 ft. per sec, and the discharge of the main is 28X12-57=351 cub. ft. per sec. Hence by a simple observation of pressure difference, the flow in the main -at any moment can be determined. Notice that the pressure height at C will be the same as at A except for a small loss hf due to friction and eddying between A and B. To get the pressure at the throat very exactly Herschel surrounds it by an annular passage communicating with the throat by several small holes, sometimes formed in vulcanite to prevent corrosion. Though con- structed to prevent eddying as much as possijle there is some eddy loss The main effect of this is to cause a loss of head between A and C which may vary from a fraction of a foot to perhaps 5 ft. at the highest velocities at which a meter can be used. The eddying also affects a little the Venturi head h. Consequently an experi- mental coefficient must be determined for each meter by tank measure- ment. The range of this coefficient is, however, surprisingly small. If to allow for friction, u = k\j |p 2 /(p 2 -i))v (2gh), then Herschel found values of k from 0-97 to i-o for throat velocities varying from 8 to 28 ft. per sec. The meter is extremely con- venient. At Staines reser- voirs there are two meters of this type on mains 94 in. in diameter. Herschel con- trived a recording arrange- ment which records the variation of flow from hour to hour and also the total flow in any g ; ven time. In Great Britain Jie meter is constructed by 3. Kent, who has made improvements in the recording arrange- ment. In the Deacon Waste Water Meter (fig. 33) a different principle is used. A disk D, partly counter- balanced by a weight, is suspended in the water flow- ing through the main in a conical chamber. The un- balanced weight of the disk is supported by the impact of the water. If the discharge of the main increases the disk rises, but as it rises its position in the chamber is such that in consequence of the larger area the velocity is less. It finds, therefore, a new position of equilibrium. A pencil P records on a drum moved by clockwork the position of the disk, and from this the variation of flow is in- ferred. § 33. Pressure, Velocity and Energy in Different Stream Lines.— The equation of Bernoulli gives the variation of pressure and velocity Outlet from point to point along a stream line, and shows that the total energy of the flow across any two sections is the same. Two other directions may be defined, one normal to the stream line and in the plane containing its radius of curvature at any point, the other normal to the stream line and the radius of curvature. For the problems most practically useful it will be sufficient to consider the stream lines as parallel to a vertical or horizontal plane. If the motion is in a vertical plane, the action of gravity must be taken into the reckoning ; if the motion is in a horizontal plane, the terms expressing variation of elevation of the filament will disappear. 1 Let AB, CD (fig. 34) be two consecutive stream lines, at present assumed to be in a vertical plane, and PQ a normal to these lines j»dp A - P: ■v*d\r But (1) Fig. 34. making an angle <#> with the vertical. Let P, Q be two particles moving along these lines at a distance PQ = ds, and let z be the height of Q above the horizontal plane with reference to which the energy is measured, v its velocity, and p its pressure. Then, if H is the total energy at Q per unit of weight of fluid, n=z+p/G+v 2 /2 S . Differentiating, we get dH=ds+dp/G+vdv/g, for the increment of energy between Q and P. dz — PQ cos = ds cos 4> \ .'.dH^dp/G+vdv/g+ds cos 0, (ia) where the last term disappears if the motion is in a horizontal plane. Now imagine a small cylinder of section w described round PQ as an axis. This will be in equilibrium under the action of its centrifugal force, its weight and the pressure on its ends. But its volume is cods and its weight Gads. Hence, taking the components of the forces parallel to PQ — o>dp = Gv 2 oids/gp-Gui cos i/G +Kr/2g = pzfG +v 2 2 /2g ; = ptlG+nWlrf2g; (&-£i)/G=i', 2 (i-n7>Y ! )/2g; (5) (6) Hence the pressure increases from the interior outwards, in a way indicated by the pressure columns in fig. 36, the curve through the free surfaces of the pressure columns being, in a radial section, the quasi-hyperbola of the form xy l = c z . This curve is asymptotic to a horizontal line, H ft. above the line from which the pressures are measured, and to the axis of the current. Free Circular Vortex. — A free circular vortex is a revolving mass ){ water, in which the stream lines are concentric circles, and in which Fig. 36. the total head for each stream line is the same. Hence, if by any slow radial motion portions of the water strayed from one stream line to another, they would take freely the velocities propei to their' new positions under the action of the existing fluid pressures only. For such a current, the motion being horizontal, we have for all the circular elementary streams ] H = p/G+v 2 /2g = constant; \dH = dp/G -\-vdvjg = o. (7) pressure increasing according to the law stated above, and the head along each spiral stream line is constant. § 35. Forced Vortex. — If the law of motion in a rotating current is different from that in a free vortex, some force must be applied to cause the variation of velocity. The simplest case is that of a rotating current in which all the particles have equal angular velocity, as for instance when they are driven round by radiating paddles revolving uniformly. Then in equation (2), § 33, considering two circular stream lines of radii r and r-\-dr (fig. 37), we have p = r, ds = dr. If the angular velocity is a, then v = ar and dv = adr. Hence dH — a. 2 rdrjg-{-a-rdrlg = 2tt.' 1 rdrlg. Comparing this with (1), § 33, and putting /2g = p i /G+v 1 '/2g. (1) 4 6 HYDRAULICS [DISCHARGE FROM ORIFICES Fig. 38. DUf But if work is expended in producing irregular eddying motion, the head at the section CD will be diminished. Suppose the mass ABCD comes in a short time t to A'B'C'D'. The resultant force parallel to the axis of the stream is pill +/>o(wi-w)— pltAl, where p is put for the unknown pressure on the annular space between AB and EF. The impulse of that force is \P"+Po("i-")-pi^\)t. I he horizontal change of momentum in the same time is the differ- _ _. ence of the momenta of - £ -^ pCDC'D' and ABA'B', . because the amount of momentum be- tween A'B' and CD remains unchanged if the motion is steady. The volume of ABA'B' or CDC'D', being the inflow and outflow in the time t, is Qt = owt = aiVit, and the momentum of these masses is (G/g)QvUnd(Glg)Qv 1 t. lhe change of mo- mentum is therefore (G/g)Qt(vi-v). Equating this to the impulse, {pu+M-*i-«>)-pi<'>i)t = (G/g)Q/(»i-»). Assume that po = p, the pressure at AB extending unchanged through the portions of fluid in contact with AE, BF which lie out of the path of the stream. Then (since Q=wifi) (£-£i) = (G/g)i>i(i'i-tO; P/G-p l /G=v l (vi-n)lg; (2) p/G+v i l2 S = p 1 IG+v 1 y2g+(v-v i yi2g. (3) This differs from the expression (1), § 29, obtained for cases where no sensible internal work is done, by the last term on the right. That is, (»-z>i) 2 /2g has to be added to the total head at CD, which is pi!'G+Vi*/2g, to make it equal to the total head at AB, or {v-^i) 2 /2g is the head lost in shock at the abrupt change of section. But r-i'i is the relative velocity of the two parts of the stream. Hence, when an abrupt change of section occurs, the head due to the relative velocity is lost in shock, or (i>-»i) 2 /2g foot-pounds of energy is wasted for each pound of fluid. Experiment verifies this result, so that the assumption that po = p appears to be admissible. If there is no shock, pilG=p/G + (v 2 ^)l3g. It there is shock, PiiG = £/G-t>i (»r-»)/g. Hence the pressure head at CD in the second case is less than in the former by the quantity (v-viffeg, or, putting o>iVi=uv, by the quantity (t' 2 /2g)(l-o>/ Ul ) 2 . (4) V. THEORY OF THE DISCHARGE FROM ORIFICES AND MOUTHPIECES § 37. Minimum Coefficient of Contraction. Re-entrant Mouth- piece of Borda. — In one special case the coefficient of contraction can be determined theoretically, and, as it is the case where the convergence of the streams approaching the orifice takes place through the greatest possible angle, the co- efficient thus deter- mined is the minimum coefficient. Let fig. 39 represent a vessel with vertical sides, 00 being the free water surface, at which the pressure is pa. Suppose the liquid issues by a horizontal mouthpiece, which is re-entrant and of the greatest length which permits the jet to spring clear from the inner end of the orifice, without adher- ing to its sides. With such an orifice the velocity near the points CD is negligible, and the pressure at those points may be taken equal to the hydro- static pressure due to the depth from the free surface. Let S2 be the area of the mouthpiece AB, w that of the contracted jet aa Fig. 39. Suppose that in a short time /, the mass OOaa comes to the position O'O' a'a'; the impulse of the horizontal external forces acting on the mass during that time is equal to the horizontal change of momentum. The pressure on the side OC of the mass will be balanced by the pressure on the opposite side OE, and so for all other portions of the vertical surfaces of the mass, excepting the portion EF opposite the mouthpiece and the surface AaoB of the jet. On EF the pressure is simply the hydrostatic pressure due to the depth, that is, (p a +Gh)Q. On the surface and section AaaB of the jet, the horizontal resultant of the pressure is equal to the atmospheric pressure pa acting on the vertical projection AB of the jet; that is, the resultant pressure is -paQ. Hence the resultant horizontal force for the whole mass OOaa is (p a +Gh)p-pail = Ghii. Its impulse in the time / is GhSl t. Since the motion is steady there is no change of momentum between O'O' and aa. The change of horizontal momentum is, therefore, the difference of the horizontal momentum lost in the space OOO'O' and gained in the space aaa'a'. In the former space there is no horizontal momentum. The volume of the space aaa'a' is uvt; the mass of liquid in that space is (Glg)arvt; its momentum is (G/g)«i/ 2 /. Equating impulse to momentum gained, Gto = (G/g)utft; .'. »/Q = gh/v 2 . But u 2 = 2gh, and a/Q = c c ; .'.a}/Q = i=c c ; a result confirmed by experiment with mouthpieces of this kind. A similar theoretical investigation is not possible for orifices in plane surfaces, because the velocity along the sides of the vessel in the neighbourhood of the orifice is not so small that it can be neglected. The resultant horizontal pressure is therefore greater than Ghil, and the contraction is less. The experimental values of the coefficient of discharge for a re-entrant mouthpiece are 0-5149 (Borda), 0-5547 (Bidone), 0-5324 (Weisbach), values which differ little from the theoretical value, 0-5, given above. § 38. Velocity of Filaments issuing in a Jet. — A jet is composed of fluid filaments or elementary streams, which start into motion at some point in the interior of the vessel from which the fluid is discharged, and gradually acquire the velocity of the jet. Let Mot, fig. 40 be such a fila- ment, the point M being taken where the velocity is in- sensibly small, and m at the most con- tracted section of the jet, where the filaments have be- come parallel and exercise uniform mutual pressure. Take the free surface AB for datum line, and let pi, i'i, hi, be the pressure, velocity and depth below datum at M; p, v, h, the corresponding quantities at m. Then § 29, eq. (3a), vJfrg+pilG-hi^ffeg+plG-h. (1) But at M, since the velocity is insensible, the pressure is the hydro- static pressure due to the depth'; that is, »i=o, pi=p a -\-Ghi. At m, p — pa, the atmospheric pressure round the jet. Hence, inserting these values, o+palG+hi-h=&l2g+palG-k ; vV2g = h; (2) or ti = V (2g/i)= 8-025 V A. (2a) That is, neglecting the viscosity of the fluid, the velocity of fila- ments at the contracted section of the jet is simply the velocity due to the difference of level of the free surface in the reservoir and the orifice. If the orifice is small in dimensions compared with h, the filaments will all have nearly the same vel- ocity, and if h is measured to the centre of the orifice, the equation above gives the mean velocity of the jet. Case of a Submerged Orifice. — Let the orifice discharge below the level of the tail water. Then Fig. 40. Fig. 4i- using the notation shown in fig. 41, we have at M, Vi = o,pi = Gh;+p. at m, p = Gh 3 +pa. Inserting these values in (3), § 29, o+hi+ptlG-h^ifi/ag+hx-hi+palG; v 2 /2g = h r h2 = k. (3) DISCHARGE FROM ORIFICES] HYDRAULICS 47 where h is the difference of level of the head and tail water, and may be termed the effective head producing flow. Case where the Pressures are different on the Free Surface and at the Orifice.— -Let the fluid flow from a vessel in which the pressure is pa into a vessel in which the pressure is p, fig. 42. The pres- sure po will produce the same effect as a layer of fluid of thickness po/G added to the head water; and the pres- sure p , will produce the same effect as a layer of thickness pjG added to the tail water. Hence the effective difference of level, or effective head producing flow, will be h = ho+p IG-p/G; and the velocity of discharge will be f = V[2g{fc>+0-£)/Gi]. (4) We may express this result by saying that differences of pressure at the free surface and at the orifice are to be reckoned as part of the effective head. Hence in all cases thus far treated the velocity of the jet is the velocity due to the effective head, and the discharge, allowing for contraction of the jet, is Q=OM=Cuyl(2gh), (5) where « is the area of the orifice, co> the area of the contracted section of the jet, and h the effective head measured to the centre of the orifice. If h and 01 are taken in feet, Q is in cubic feet per second. It is obvious, however, that this formula assumes that all the filaments have sensibly the same velocity. That will be true for horizontal orifices, and very approximately true in other cases, if the dimensions of the orifice are not large compared with the head h. In large orifices in say a vertical surface, the value of h is different for different filaments, and then the velocity of different filaments is not sensibly the same. Simple Orifices — Head Constant § 39. Large Rectangular Jets from Orifices in Vertical Plane Sur- faces. — Let an orifice in a vertical plane surface be so formed that it produces a jet having A B\ a rectangular con- tracted section with vertical and horizon- tal sides. Let b (fig. 43) be the breadth of the jet, hi and fe the depths below the free surface of its upper and lower surfaces. Consider a lamina of the jet between the depths h and h+dh. Its normal section is bdh, and the velocity of discharge -^2gh. The discharge pet Fig. 43. second in this lamina jet is therefore therefore b^2gh dh, and that of the whole Q=/£w(2«ft)) ; dy = \d sin d. Let e = d/(2ki+d), then Q = i. From eq. (5), putting co = «P/4, h = hi+dJ2, c = i when d is the diameter of the jet and not that of the orifice, Qi = i^y|2g(Ai+V {1— ecos 4>\d.' ■ -• imperfectly known. Fig. 50. § 47. Bazin's Researches on Weirs. — H. Bazin has executed a long series of researches on the flow over weirs, so systematic and complete that they almost supersede other observations. The account of them is contained in a series of papers in the Annates des Ponts et Chaussees (October 1888, January 1890, November 1891, February 1894, December 1896, 2nd trimestre 1898). Only a very abbreviated account can be given here. The general plan of the experiments was to establish first the coefficients of discharge for a standard weir without end contractions; next to establish weirs of other types in series with the standard weir on a channel with steady flow, to compare the observed heads on the different weirs and to determine their coefficients from the discharge computed at the standard weir. A channel was constructed parallel to the Canal de Bourgogne, taking water from it through three sluices 0-3X1-0 metres. The water enters a masonry chamber 15 metres long by 4 metres wide where it is stilled and passes into the canal at the end of which is the standard weir. The canal has a length of 15 metres, a width of 2 metres and a depth of 1-6 metres. From mmmmmmmmM. Fig. 51.1 this extends a channel 200 metres in length with a slope of 1 mm. per metre. The channel is 2 metres wide with vertical sides. The channels were constructed of concrete rendered with cement. The water levels were taken in chambers constructed near the canal, by floats actuating an index on a dial. Hook gauges were used in determining the heads on the weirs. Standard Weir. — The weir crest was 3-72 ft. above the bottom of the canal and formed by a plate i in. thick. It was sharp-edged with free overfall. It was as wide as the canal so that end con- tractions were suppressed, and enlargements were formed below the crest to admit air under the water sheet. The channel below the weir was used as a gauging tank. Gaugings were made with the weir 2 metres in length and afterwards with the weir reduced to 1 metre and 0-5 metre in length, the end contractions being sup- pressed in all cases. Assuming the general formula Q = mlH{2gh), (1) 5o Bazin arrives at the following values of m : — Coefficients of Discharge of Standard Weir. HYDRAULICS [DISCHARGE FROM ORIFICES Head h metres. Head h feet. m 0-05 •164 0-4485 I O-IO ■328 0-4336 ! 0-15 •492 0-4284 ! 0-20 •656 0-4262 0-25 •820 o-4259 1 0-30 •984 0-4266 j o-35 1-148 o-4275 j 0-40 1-312 0-4286 o-45 1-476 0-4299 0-50 1-640 o-43i3 o-55 1-804 0-4327 o-6o 1-968 0-4341 Bazin compares his results with those of Fteley and Stearns in 1877 and 1879, correcting for a different velocity of approach, and finds a close agreement. Influence of Velocity of Approach. — To take account of the velocity of approach u it is usual to replace h in the formula by h+ay?/2g where o is a coefficient not very well ascertained. Then Q = M /(fc+a«*/2g)V \2g{h + au'/2g)} =nlhT](2gh){i+aii i !2gh)i. (2) The original simple equation can be used if m = )i(l-\-au 2 l2gh)i or very approximately, since u?J2gh is small, m=n{i+Uu'l2gh). (3) Now if p is the height of the weir crest above the bottom of the canal (fig. 52), « = Q//(/>+ft). Replacing Q by its value in (1) = m?{h((,p+h)\\ (4) so that (3) may be written m=*[i+k{h[(p+h)n. (5) Gaugings were made with weirs of 0-75, 0-50, 0-35, and 0-24 metres height above the canal bottom and the results compared with those of the standard weir taken at the same time. The discussion of the results leads to the following values of m in the general equation (1) : — W=M(l+2-5M 2 /2gW =n[i+o-55\h/(.P+h)n. Values of m — w//////////////////////mc Fig. 52. Head h metres. Head h feet. 0-05 . •164 0-4481 O-IO •328 0-4322 0-20 ■656 p-4215 0-30 .984 0-4174 0-40 1-312 0-4144 0-50 1-640 0-4118 o-6o 1-968 0-4092 An approximate formula for y. is : M = 0-405 +0-003//! (h in metres) M = 0-405+0-01 (h (h in feet). Inclined Weirs.- — Experiments were made in which the plank weir was inclined up or down stream, the crest being sharp and the end contraction suppressed. The following are coefficients by which the discharge of a vertical weir should be multiplied to obtain the discharge of the inclined weir. Inclination up stream Vertical weir Inclination down stream 1 to 1 3 to 2 3 to 1 Coefficient. o-93 0-94 0-96 1 -oo 1-04 1-07 I-IO I-I2 1-09 from the weir, but encloses a volume of air which is at less than atmospheric pressure, and the tail water rises under the sheet. The discharge is a little greater than for free overfall. At greater head the air disappears from below the sheet and the sheet is said to be " drowned." The drowned sheet may be independent of the tail water level or influenced by it. In the former case the fall is followed by a rapid, terminating in a standing wave. In the latter case when the foot of the _ _ _ _ sheet is drowned the level - - - - - -T— ^o^^ of the tail water influences b Vc- the discharge even if it is below the weir crest. Weirs with Flat Crests.— The water sheet may spring clear from the upstream edge . or may adhere to the fa%V/jMW/////////////, m ■ 3 to I ,, „ 3 to 2 1 to 1 ,, I to 2 1 to 4 The coefficient varies appreciably, if h/p approaches unity, which case should be avoided. In all the preceding cases the sheet passing over the weir is de- tached completely from the weir and its under-surface is subject to atmospheric pressure. These conditions permit the most exact determination of the coefficient of discharge. If the sides of the canal below the weir are not so arranged as to permit the access of air under the sheet, the phenomena are more complicated. So long as the head does not exceed a certain limit the sheet is detached W////S////////J crest falling free beyond the downstream edge. In the former case the condition is that of a sharp-edged weir and it is realized when the head is at least double the width of crest. It may arise if the head is at least i^ the width of crest. Between these limits the condition of the sheet is unstable. When the sheet is adherent the coefficient m depends on the ratio of the head h to the width of crest c (fig. 53), and is given by the equation m = mi [0-70+0- i85h/c], where mi is the coefficient for a sharp- edged weir in similar con- ditions. Rounding the up- stream edge even to a small extent modifies the dis- charge. If R is the radius of the rounding the co- efficient m is increased in the ratio 1 to 1 +R/& nearly. The results are limited to R less than \ in. Drowned Weirs.— Let h ^^^p^^W5^?W^ (fig. 54) be the height of F head water and hi that of . . tail water above the weir crest. Then Bazin obtains as the approxi- mate formula for the coefficient of discharge m = 1 -05Wi[i +lhlp] $ { Qi - hi)lh), where as before mi is the coefficient for a sharp-edged weir in similar conditions, that is, when the sheet is free and the weir of the same height. § 48. Separating Weirs. — Many towns derive their water-supply from streams in high m o o rl a n d dis- tricts, in which the flow is extremely variable. The water is collected in large storage reservoirs, from which an uniform supply can be sent to the town. In Fig. 55. JPlarv of C&st Iran Key Fig. 56. such cases it is desirable to separate the coloured water which comes down the streams in high floods from the purer water of ordinary flow. The latter is sent into the reservoirs; the former is allowed DISCHARGE FROM ORIFICES] HYDRAULICS 5 1 to flow away down the original stream channel, or is stored in separate reservoirs and used as compensation water. To accomplish the separation of the flood and ordinary water, advantage is taken of the different horizontal range of the parabolic path of the water falling over a weir, as the depth on the weir and, consequently, the velocity change. Fig. 55 shows one of these separating weirs in the form in which they were first introduced on the Manchester Water- works; fig. 56 a more modern weir of the same kind designed by Sir A. Binnie for the Bradford Waterworks. When the quantity of water coming down the stream is not excessive, it drops over the weir into a transverse channel leading to the reservoirs. In flood, the water springs over the mouth of this channel and is led into a waste channel. ' It may be assumed, probably with accuracy enough for practical purposes, that the particles describe the parabolas due to the mean velocity of the water passing over the weir, that is, to a velocity §V(2gfc), where h is the head above the crest of the weir. Let cb = x be the width of the orifice and ac=y the difference of level of its edges (fig. 57). Then, if a particle passes from a to b in t seconds, y = \gf, * = f V(2gfc)<; ■ :y=&xi/h, which gives the width * for any given difference of level y and head h, which the jet will just pass over the orifice. Set off ad vertically 9 2 ^ \\\ :-■•'' ; \^\ W:\; ;- ■ \N\VJH i V\\\KI ■-•: \\\ :\: O 1 \ V, d A e -i-^h- Fig. 57. and equal to §g on any scale; af horizontally and equal to | V (g^)- Divide af, fe into an equal number of equal parts. Join a with the divisions on ef. The intersections of these lines with verticals from the divisions on af give the parabolic path of the jet. Mouthpieces — Head Constant § 49. Cylindrical Mouthpieces. — When water issues from, a short cylindrical pipe or mouthpiece of a length at least equal to I J times its smallest transverse dimension, the stream, after contraction within the mouthpiece, expands to fill it and issues full bore, or without contraction, at the point of discharge. The discharge is found to be about one-third greater than that from a simple orifice of the same size. On the other hand, the energy of the fluid per unit of weight is less than that of the stream from a simple orifice with the same head, because part of the energy is wasted in eddies produced at the point where the stream expands to fill the mouthpiece, the action being something like that which occurs at an abrupt change of section. Let fig. 58 represent a vessel discharging through a cylindrical mouthpiece at the depth h from the free surface, and let the axis of the jet XX be taken as the datum with reference to which the head is estimated. Let 12 be the area of the mouthpiece, o> the aiea of the stream at the contracted section EF. Let v, p be the velocity and pressure at EF, and vi, p\ the same quantities at GH. If the discharge is into the air, pi is equal to the atmospheric pressure p a . The total head of any filament which goes to form the jet, taken at a point where its velocity is sensibly zero, is h-\-p a jG; at EF the total head is v^feg+p/G; at GH it is vf^g+pi/G. Between EF and GH there is a loss of head due to abtupt change of velocity, which from eq. (3), § 36, may have the value (»-Z>l) 2 /2g. Adding this head lost to the head at GH, before equating it to the heads at EF and at the point where the filaments start into motion, — h+pa/G =vy 2 g+p/G = Vl *l2g+p i IG+{v-v l yi2g. But arj = Qvi, and w=c c ft, if c c is the coefficient of contraction within the mouthpiece. Hence » = fii'i/o^ri/c. Supposing the discharge into the air, so that pi=p«, h+p„IG=v^f 2 g+p a /G-\-(v l V2g) (l/c-i)*; (»i/?f) (i+(ifc-i) 2 j=A; ••■ vi= ,1 (2gh)H [i + U/cc-i)*); (1) where the coefficient on the right is evidently the coefficient of velocity for the cylindrical mouthpiece in terms of the coefficient of con- traction at EF. Let £0=0-64, the value for simple orifices, then the coefficient of velocity is c„ = i/V!i+(i/cc-i) ! ! =0-87 (2) The actual value of c v found by experiment is 0-82, which does not differ more from the theoretical value than might be expected if the friction of the mouthpiece is allowed for. GH, C„=0-82 Fig. 58. Hence, for mouthpieces of this kind, and for the section at c c = i-oo c = o-82, Q=0-82flV(2g/t). It is easy to see from the equations that the pressure p at EF is less than atmospheric pressure. Eliminating v u we get (pa~P)IG = ih nearly; (3) or P = P*~ iGhVo per sq. ft. If a pipe connected with a reservoir on a lower level is introduced into the mouthpiece at the part where the contraction is formed (fig- 59)i the water will rise in this pipe to a height KL = (/>„-£)/G = ffc nearly. If the distance X is less than this, the water from the lower reservoir will be forced continuously into the jet by the atmospheric pressure, and discharged with it. This is the crudest form of a kind of pump known as the jet pump. § 50. Convergent Mouthpieces. — With convergent mouthpieces there is a contraction within the mouthpiece causing a loss of head, and a diminution of the velocity of discharge, as with cylindrical mouthpieces. There is also a second contraction of the stream out- side the mouthpiece. Hence the discharge is given by an equation of the form Q=Cc c QV(2gft), _ (4) where fl is the area of the external end of the mouthpiece, and c c Sl the section of the contracted jet beyond the mouthpiece. Convergent Mouthpieces (Castel's Experiments). — Smallest diameter of orifice = 0-05085 //. Length of mouthpiece — 2-6 Diameters. Angle of Convergence. Coefficient of Coefficient of Coefficient of Contraction, Cc Velocity, Cv Discharge, c 0° 0' •999 •830 •829 i°3°' i- 000 ■866 866 3° 10' I-OOI •894 895 4° 10' 1-002 •910 912 K 26 ', I-004 ■920 924 7° 52' •998 •931 929 8° 58' •992 •942 934 10° 20' •987 •950 938 12° 4' •986 •955 942 , 13° 24' •983 •962 946 14 28 •979 •966 941 16° 36' .969 •971 938 19" 28' •953 •97° 924 21° O' •945 •971 918 23° 0' •937 •974 913 29° 58' •919 •975 896 40 20 •887 •980 869 4 8° 50' •861 ■984 •847 The maximum coefficient of discharge is that for a mouthpiece with a convergence of 13 24'. HYDRAULICS The values of c v and c c must here be determined by experiment. The above table gives values sufficient for practical purposes. Since the contraction beyond the mouthpiece increases with the convergence, or, what is the same thing, c c diminishes, and on the other hand the loss of energy diminishes, so that Cv increases with the convergence, there is an angle for which the product c c c v , and con- sequently the discharge, •is a maximum. § 51. Divergent Con- oidal Mouthpiece. — Sup- pose a mouthpiece so designed that there is no abrupt change in the section or velocity of the stream passing through it. It may have a form at the inner end approxi- mately the same as that of a simple contracted vein, and may then enlarge gradu- ally, as shown in fig. 60. Suppose that at EF it becomes cylindrical, so that the jet may be taken to be of the diameter EF. Let -v?)l2g. Let Uja=m. Then v — v\m ; £/G = />«/G-f, ! (»» 2 -i)/2g = Pa/G-(m 2 -i)h; whence we find that pjG will become zero or nega- tive if ahm^J\(h+pJG)lh\ -V!i+A./GA); or, putting £«/G = 34 ft., if In practice there will be an interruption of the full bore flow with a less ratio of Sljw, because of the disengagement of air from the water. But, supposing this does not occur, the maximum discharge of a mouthpiece of this kind is Q= w V{2g(A+*>./G)|; that is, the discharge is the same as for a well-bellmouthed mouth- piece of area a, and without the expanding part, discharging into a vacuum. § 32. Jet Pump. — A divergent mouthpiece may be arranged to act as a pump, as shown in fig. 62. The water which supplies the energy [DISCHARGE OF ORIFICES Fig. 60. required for pumping enters at A. The water to be pumped enters at B. The streams combine at DD where the velocity is greatest and the pressure least. Beyond DD the stream enlarges in section, Fig. 62. arid its pressure increases, till it is sufficient to balance the head due to the height of the lift, and the water flows away by the discharge pipe C. Fig. 63 shows the whole arrangement in a diagrammatic way. A is the reservoir which supplies the water that effects the pumping; Fig. 63. B is the reservoir of water to be pumped ; C is the reservoir into which the water is pumped. Discharge with Varying Head § 53. Flow from a Vessel when the Effective Head varies with the Time. — Various useful problems arise relating to the time of empty- ing and filling vessels, reservoirs, lock chambers, &c, where the flow is dependent on a head which increases or diminishes during the operation. The simplest of these problems is the case of filling or emptying a vessel of constant horizontal section. Time of Emptying or Filling a Vertical-sided Lock Chamber. — Suppose the lock chamber, which has a water surface of O square ft., is emptied through a sluice in the tail gates, of area w, placed below the tail-water level. Then the effective head producing flow through the sluice is the difference of level in the chamber and tail bay. Let H (fig. 64) be the initial difference of level, h the difference Head, water Uvr.l Fig. 64. of level after t seconds. Let — dh be the fall of level in the chamber during an interval dt. Then in the time dt the volume in the chamber is altered by the amount —Qdh, and the outflow from the sluice in the same time is cuV {2gh)dt. Hence the differential equation con- necting h and t is cwV (2gh)dt+Qh =0. DISCHARGE FROM ORIFICES] HYDRAULICS 53 For the time /, during which the initial head H diminishes to any other value h, -in/(l loge Vs/vi=piUi loge pi/pt. (i) Since the weight per cubic foot is the reciprocal of the volume per pound, this may be written (P1IG1) loge G1/G2. (10) Then the expansion curve ab is a common hyperbola. Case 2. — No heat is supplied to the air during expansion. Then the air loses an amount of heat equivalent to the external work done and the temperature falls. Adiabatic expansion. In this case it can be shown that pvy=piv{*, where 7 is the ratio of the specific heats of air at constant pressure and volume. Its value for air is 1-408, and for dry steam 1-135. Work done during expansion per pound of air. = flpdv = p l v l yfl°dvlvy = -{Ml?/(t-i)HiM?- 1 -iM v - 1 } = [?.w/(7-i)](iM y - 1 -iM'-'] = \PiV l /(y-i)}{i-(v 1 lvd y - 1 l (2) The value of piVi for any given temperature can be found from the data already given. As before, substituting the weights Gi, G 2 per cubic foot for the volumes per pound, we get for the work of expansion (i>./G,){i/(7-i)i fi-(G 2 /G 1 ) y - 1 !. (2a) =*Wi/(7-i)} [i-fa/pov-v/y]- (2b) § 62. Modification of the Theorem of Bernoulli for the Case of a Compressible Fluid. — In the application of the principle of work to a filament of compressible fluid, the internal work done by the ex- pansion of the fluid, or absorbed in its compression, must be taken into account. Suppose, as before, that AB (fig. 77) comes to A'B' in a short time t. Let pi, Mi, Vi, Gi be the pres- sure, sectional area of stream, velocity and weight of a cubic foot at A, and p 2 , « 2 , v*, G2 the same quantities at B. Then, from the steadiness of motion, the weight of fluid passing A in any given time must be equal to the weight passing fi : GiioiVit = GzoizVzt. Let Zi, z 2 be the heights of the sections A and B above any given datum. Then the work of gravity on the mass AB in t seconds is Gia>iz>i<(zi — z 2 ) = W(zi — zi)t, where W is the weight of gas passing A or B per second. As in the case of an incompressible fluid, the work of the pressures on the ends of the mass AB is plQJlVit — p^tfl-it, = (pilGi-p 2 /G i Wt. The work done by expansion of Wi lb of fluid between A and B is W« f^pdv. The change of kinetic energy as before is (W/2g) (u 2 2 — »i 2 )f. Hence, equating work to change of kinetic energy, W(z 1 -z 2 )Z+(^i/G 1 -^/G 2 )W/+W = (W/2g) W-vi*)t; .'. zi+Pi/Gi+vi' i J2g=z 2 +pVG 2 +v 2 y2g-p^pdv. (1) Now the work of expansion per pound of fluid has already been given. If the temperature is constant, we get (eq. ia, § 61) Zl+£l/Gl+»r72g=S2+£2/G 2 +Z> 2 72g-(£l/Gl) loge (G1/G2). But at constant temperature pi/Gi = £ 2 /G 2 ; /. Zi+»i 2 /2g = Z2-|-I>2 2 /2g-(£l/Gi) loge (pl/pz), or, neglecting the difference of level, (tf-l'l 2 )/2g = (^l/G 1 )loge (pi/pl). Similarly, if the expansion is adiabatic (eq. 2a, § 61), zi+pi/Gi -Hi 2 /2g = z 2 -r-fc/Gs +f2 2 /2g - (pi/Gi) 1 1 l(y - 1 ) j [i-(ptfpi)Wy\; or neglecting the difference of level W -tf )/2g = (A/G0[i +1/(7 - i){i - (frlpiW-viyft-ptlGi. It will be seen hereafter that there is a limit in the ratio pilpt beyond which these expressions cease to be true. § 63. Discharge of Air from an Orifice.— The form of the equation of work for a steady stream of compressible fluid is Zi+WGi+!>i 2 /2g = Z2+£2/G2+%V2g-(£i/Gi){i/(7-i)} , , s/V „, , (2) (2a) (3) (30) FRICTION OF LIQUIDS] HYDRAULICS 57 the expansion being adiabatic, because in the flow of the streams of air through an orifice no sensible amount of heat can be communi- cated from outside. Suppose the air flows from a vessel, where the pressure is pi and the velocity sensibly zero, through an orifice, into a space where the pressure is pi. Let vt be the velocity of the jet at a point where the convergence of the streams has ceased, so that the pressure in the jet is also p 2 . As air is light, the work of gravity will be small compared with that of the pressures and expansion, so that Ziz 2 may be neglected. Putting these values in the equation above — A/G 1 =/> 2 /G 2 +tf/2g-(A/G 1 )!i/(7-i)){i-(^2/A) (v - l)/Y ; ^/2g = WG 1 -^/G 2 + (A/G 1 )(i/(T-i)){i-to/pi) (v - l)/Y ) = (?i/G 1 )!t/(t-i)-(^/A) 7 - i/v /(t-i)}-^/G 2 . But NU y = £2/W .-. fc/G 2 = fi>i/Gi)(p 2 /pi) (l '- l)/1 ' »iV2« = (fr/G,){7/(Y-l)} \i-(p2/Pi) iy ~ l)/y h (0 or _ vi-/2g = [7/ (7 - 1) j j (pi/Gi) - (> 2 /G 2 )) ; an equation commonly ascribed to L. J. Weisbach (Civilingenieur, 1856), though it appears to have been given earlier by A. J. C. Barre de Saint Venant and L. Wantzel. It has already (§ 9, eq. 4a) been seen that ^/G I = (^„/Go)(7- 1 /r ) where for air £0 = 2116-8, Go = -o8o75 and 1-0 = 492-6. *<2 2 /2g = {/>oTi->7Goro(7-l)! \l-(p2/pi) (y - l)/y }; (2) or, inserting numerical values, »2 2 /2g = i83-6ti( i - (P2IP1) °- 29 | ; (20) which gives the velocity of discharge v 2 in terms of the pressure and absolute temperature, pi, n, in the vessel from which the air flows, and the pressure pi in the vessel into which it flows. Proceeding now as for liquids, and putting w for the area of the orifice and c for the coefficient of discharge, the volume of air dis- charged per second at the pressure pi and temperature t 2 is Q 2 = CM , 2 = c<0 V [(2g7M7- I)G,)(I - 0/fr) (y - l)/Y )] = loS-jco 1 ^[n\i-(p 2 lPir^)). (3) If the volume discharged is measured at the pressure pi and absolute temperature n in the vessel from which the air flows, let Qi be that volume ; then piQi y =p2QS; Qi = (ft/£i) l/Y Q2; Qi=cu V[{2g7M7-i)G 1 | \(p 1 /p0 2/y -(p2/Pi) iy+t)/y \]- Let (p2/pi) 2/y -(p-2lPi) {y - l)/y = (p2/piy n -(p2/Piy-'= + ; then Qi =coi V [2gypnpi{y — l)Gi] = lo8-7co>V(riiA). (4) The weight of air at pressure pi and temperature n is Gi =£1/53-2x1 lb per cubic foot. Hence the weight of air discharged is W = GiQi=cw V[2g7£iGi^/(7-i)] = 2-043c0'5t the formulae above were trustworthy, when pi was taken to be the general external pressure, but that, if pi/pii> 2 /2g, (2) where £ is, like /, nearly constant for a given surface, and is termed the coefficient of friction. The following are average values of the coefficient of friction for water, obtained from experiments on large plane surfaces, moved in an indefinitely large mass of water. 5» HYDRAULICS [FRICTIONlOF LIQUIDS Coefficient of Friction, I Frictional Resistance in lb per sq. ft. / New well-painted iron plate . Painted and planed plank (Beaufoy) Surface of iron ships (Rankine) . Varnished surface (Froude) . Fine sand surface ,, ... Coarser sand surface ,, . •00489 •00350 •00362 •00258 •00418 •00503 •00473 •00339 •00351 •00250 •00405 •00488 The distance through which the frictional resistance is overcome is r ft. per second. The work expended in fluid friction is therefore given by the equation — Work expended =/wi> 3 foot-pounds per second ( (3). = £Guv 3 /2g „ ,, ] The coefficient of friction and the friction per square foot of surface can be indirectly obtained from observations of the discharge of pipes and canals. In obtaining them, however, some assumptions as to the motion of the water must be made, and it will be better therefore to discuss these values in connexion with the cases to which they are related. Many attempts have been made to express the coefficient of friction in a form applicable to low as well as high velocities. The older hydraulic writers considered the resistance termed fluid friction to be made up of two parts, — a part due directly to the distortion of the mass of water and proportional to the velocity of the water relatively to the solid sur- face, and another part due to kinetic energy imparted to the water striking the roughnesses of the solid surface and proportional to the square of the velocity. Hence they proposed to take | = o+/3/o in which expression the second term is of greatest importance at very low == _____^_____ velocities, and of comparatively little k^JJ^jJ^^^s^g^-sMJ importance at velocities over about j ft. r— per second. Values of £ expressed in this ~_Z and similar forms will be given in con- ; i^S» A nexion with pipes and canals. ■ All these expressions must at present 1 - be regarded as merely empirical ex- ;_~ ' ~ pressions serving practical purposes. — — ■ — • — — — - The frictional resistance will be seen' to vary through wider limits than these expressions allow, and to depend on circumstances of which they do not take account. § 67. Coulomb's Experiments. —The first direct experiments on fluid friction were made by Coulomb, who employed a circular disk suspended by a thin brass wire and oscillated in its own plane. His experiments were chiefly made at very low velocities. When the disk is rotated to any given angle, it oscillates under the action of its inertia and the torsion of the wire. The oscillations diminish gradually in consequence of the work done in overcoming the friction of the disk. The diminution furnishes a means of determining the friction. Fig. 78 shows Coulomb's apparatus. LK supports the wire and disk; ag is the brass wire, the torsion of which causes the oscilla- tions ; DS is a graduated disk serving to measure the angles through which the apparatus oscillates. To this the friction disk is rigidly attached hang- ing in a vessel of water. The friction disks were from 4-7 to 7-7 in. dia- meter, and they gener- ally made one oscillation in from 20 to 30 seconds, through angles varying from 360° to 6°. When the velocity of the cir- cumference of the disk was less than 6 in. per second, the resistance was sensibly propor- tionalto the velocity. Beaufoy' s Experiments. — Towards the end of the 18th century Colonel Mark Beaufoy (1 764-1 827) made an immense mass of experiments on the resistance of bodies moved through water (Nautical and Hydraulic Experiments, London, 1834). Of these the only ones directly bearing on surface friction were some made in 1796 and 1798. Smooth painted planks were drawn through water and the resistance measured. For two planks differing in area by 46 sq. ft., at a velocity of 10 ft. per second, the difference of resistance, measured on the difference of area, was 0-339 lb per square foot. Also the resistance varied as the 1 -949th power of the velocity. § 68. Froude's Experiments. — The most important direct experi- ments on fluid friction at ordinary velocities are those made by William Froude (1810-1879) at Torquay. The method adopted in these experiments was to tow a board in a still water canal, the velocity and the resistance being registered by very ingenious re- cording arrangements. The general arrangement of the apparatus is shown in fig. 79. AA is the board the resistance of which is to be determined. B is a cut-water giving a fine entrance to the plane surfaces of the board. CC is a bar to which the board AA is attached, and which is suspended by a parallel motion from a carriage running on rails above the still water canal. G is a link by which the re- sistance of the board is transmitted to a spiral spring H. A bar I rigidly connects the other end of the spring to the carriage. The dotted lines K, L indicate the position of a couple of levers by which the extension of the spring is caused to move a pen M, which records the extension on a greatly increased scale, by a line drawn on the paper cylinder N. This cylinder revolves at a speed proportionate to that of the carriage, its motion being obtained from the axle of the carriage wheels. A second pen O, receiving jerks at every second and a quarter from a clock P, records time on the paper cylinder. The scale for the line of resistance is ascertained by stretching the spiral spring by known weights. The boards used for the experiment Fig. 78. Fig. 79. were ^ in. thick, 19 in. deep, and from I to 50 ft. in length, cutwater included. A lead keel counteracted the buoyancy of the board. The boards were covered with various substances, such as paint, varnish, Hay's composition, tinfoil, &c, so as to try the effect of different degrees of roughness of surface. The results obtained by Froude may be summarized as follows : — 1. The friction per square foot of surface varies very greatly for different surfaces, being generally greater as the sensible roughness of the surface is greater. Thus, when the surface of the board was covered as mentioned below, the resistance for boards 50 ft. long, at 10 ft. per second, was— Tinfoil or varnish 0-25 fb per sq. ft. Calico 0-47 ,, ,, Fine sand 0-405 ,, ,, Coarser sand 0-488 ,, ,, 2. The power of the velocity to which the friction is proportional varies for different surfaces. Thus, with short boards 2 ft. long, For tinfoil the resistance varied as v 2,16 . For other surfaces the resistance varied as v i,ta . With boards 50 ft. long, For varnish or tinfoil the resistance varied as t 4 " 83 . For sand the resistance varied as t> 2 ' ra . 3. The average resistance per square foot of surface was much greater for short than for long boards; or, what is the same thing; the resistance per square foot at the forward part of the board was greater than the friction per square foot of portions more sternward. Thus, Mean Resistance in lb per sq . ft. Varnished surface . . 2 ft. long 0-41 50 „ 0-25 Fine sand surface . . 2 ,, o-8l 50 ,, 0-405 This remarkable result is explained thus by Froude : " The portion of surface that goes first in the line of motion, in experiencing resistance from the water, must in turn communicate motion to the water, in the direction in which it is itself travelling. Consequently STEADY FLOW IN PIPES] HYDRAULICS 59 the portion of surface which succeeds the first will be rubbing, not against stationary water, but against water partially moving in its owrl direction, and cannot therefore experience so much resistance from it." § 69. The following table gives a general statement of Froude's results. In all the experiments in this table, the boards had a fine cutwater and a fine stern end or run, so that the resistance was entirely due to the surface. The table gives the resistances per square foot in pounds, at the standard speed of 600 feet per minute, and the power of the speed to which the friction is proportional, so that the resistance at other speeds is easily calculated. Length of Surface, or Distance from Cutwater, in feet. 2 ft. 8 ft. 20 ft. 50 ft. A B C A B C A B C A B C Varnish Paraffin 1 Tinfoil I Calico ! Fine sand Medium sand Coarse sand . 2-00 2-l6 i-93 2-O0 2-00 2-00 •41 •38 •30 •87 •81 •90 I-IO •390 •37° •295 725 •690 •730 •880 1-85 1-94 1-99 1-92 2-00 2-00 2-00 •325 •3H •278 ■626 •583 •625 ■714 •264 •260 •263 •504 ■450 •488 •520 1-85 1-93 1-90 1-89 2-00 2-00 2-00 •278 •271 •262 •S3i •480 •534 •588 •240 •237 •244 •447 •3"84 •465 •490 1-83 1 -83 1-87 2-06 2-00 •250 •246 •474 •405 •488 •226 •232 •423 •337 •456 Columns A give the power of the speed to which the resistance is approximately proportional. Columns B give the mean resistance per square foot of the whole surface of a board of the lengths stated in the table. Columns C give the resistance in pounds of a square foot of surface at the distance sternward from the cutwater stated in the heading. Although these experiments do not directly deal with surfaces of greater length than 50 ft., they indicate what would be the resistances of longer surfaces. For at 50 ft. the decrease of resistance for an increase of length is so small that it will make no very great difference in the estimate of the friction whether we suppose it to continue to diminish at the same rate or not to diminish at all. For a varnished surface the friction at 10 ft. per second diminishes from 0-41 to 0-32 ft per square foot when the length is increased from 2 to 8 ft., but it only diminishes from 0-278 to 0-250 lb per square foot for an increase from 20 ft. to 50 ft. If the decrease of friction sternwards is due to the generation of a current accompanying the moving plane, there is not at first sight any reason why the decrease should not be greater than that shown by the experiments. The current accompanying the board might be assumed to gain in volume and velocity sternwards, till the velocity was nearly the same as that of the moving plane and the friction per square foot nearly zero. That this does not happen appears to be due to the mixing up of the current with the still water surrounding it. Part of the water in contact with the board at any point, and receiv- ing energy of motion from it, passes afterwards to distant regions of still water, and portions of still water are fed in towards the board to take its place. In the forward part of the board more kinetic energy is given to the current than is diffused into surrounding space, and the current gains in velocity. At a greater distance back there is an approximate balance between the energy communicated to the water and that diffused. The velocity of the current accompanying the board becomes constant or nearly constant, and the friction per square foot is therefore nearly constant also. § 70. Friction of Rotating Disks. — A rotating disk is virtually a surface of unlimited extent and it is convenient for experiments on friction with different surfaces at different speeds. Experiments carried out by Professor W. C. LTnwin {Proc. Inst. Civ. Eng. lxxx.) are useful both as illustrating the laws of fluid friction and as giving data for calculating the resistance of the disks of turbines and centrifugal pumps. Disks of 10, 15 and 20 in. diameter fixed on a vertical shaft were rotated by a belt driven by an engine. They were enclosed in a cistern of water between parallel top and bottom fixed surfaces. The cistern was suspended by three fine wires. The friction of the disk is equal to the tendency of the cistern to rotate, and this was measured by balancing the cistern by a fine silk cord passing over a pulley and carrying a scale pan in which weights could be placed. If w is an element of area on the disk moving with the velocity v, the friction on this element is fun", where / and n arc constant for any given kind of surface. Let a be the angular velocity of rotation, K the radius of the disk. Consider a ring of the surface between rand r+dr. Its area is 2ivrdr, its velocity ar and the friction of this ring is f2irrdra"r n . The moment of the friction about the axis of rotation is 2ira"fr" + -dr, and the total moment of friction for the two sides of the disk is M = ^Ijfr^dr = |4*-a»/(» +3) !/R n+3 - If N is the number of revolutions per sec, M = 52"«7r»+ 1 N"/(n+3)!/R»« l and the work expended in rotating the disk is Ma = !2" +3 7r" +2 N" +1 /(«+3)!/R" +3 foot lb per sec. The experiments give directly the values of M for the disks corre- sponding to any speed N. From these the values of/ and n can be deduced, / being the friction per square foot at unit velocity. For comparison with Froude's results it is convenient to calculate the resistance at 10 ft. per second, which is F=/io". The disks were rotated in chambers 22 in. diameter and 3, 6 and 12 in. deep. In all cases the friction of the disks increased a little as the chamber was made larger. This is probably due to the stilling of the eddies against the surface of the chamber and the feeding back of the stilled water to the disk. Hence the friction depends not only on the surface of the disk but to some extent on the surface of the chamber in which it rotates. If the surface of the chamber is made rougher by covering with coarse sand there is also an increase of resistance. For the smoother surfaces the friction varied as the 1 -85th power of the velocity. For the rougher surfaces the power of the velocity to which the resistance was proportional varied from 1-9 to 2-1. This is in agreement with Froude's results. Experiments with a bright brass disk showed that the friction decreased with increase of temperature. The diminution between 41 and 130° F. amounted to 18%. In the general equation M =cN" for any given disk, Ct=o-i328(i — 0-002I(), where c t is the value of c for a bright brass disk 0-85 ft- i n diameter at a temperature t° F. The disks used were either polished or made rougher by varnish or by varnish and sand. The following table gives a comparison of the results obtained with the disks and Froude's results on planks 50 ft. long. The values given are the resistances per square foot at 10 ft. per sec. Froude's Experiments. Tinfoil surface . . 0-232 Varnish 0-226 Fine sand .... 0-337 Medium sand . . 0-456 Disk Experiments. Bright brass . 0-202 to 0-229 Varnish . . 0-220 to 0-233 Fine sand °'339 Very coarse sand 0-587 to 0-715 '-dl VIII. STEADY FLOW OF WATER IN PIPES OF UNIFORM SECTION. § 71. The ordinary theory of the flow of water in pipes, on which all practical formulae are based, assumes that the variation of velocity at different points of any cross section may be neglected. The water is considered as moving in plane layers, which are driven through the pipe against the frictional resistance, by the difference of pressure at or elevation of the ends of the pipe. If the motion is steady the velocity at each cross section remains the same from moment to moment, and if the cross sectional area is constant the velocity at all sections must be the same. Hence the motion is uniform. The most important resistance to the motion of the water is the surface friction of the pipe, and it is convenient to estimate this independently of some smaller resistances which will be ac- counted for presently. In any portion of a uniform pipe, excluding for the present the ends of the pipe, the water enters and leaves at the same velocity. For that portion there- fore the work of the external forces and of the surface friction must be equal. Let fig. 80 represent a very short portion of the pipe, of length dl, be- tween cross sections at 2 and z-\-dz ft. above any horizontal datum line xx, the pressures at the cross Sections being -~ A ^" V p and p+dp lb per ' square foot. Further, p g let Q be the volume of flow or discharge of the pipe per second, it the area of a norma! cross section, and x the perimeter of the pipe. The Q cubic feet, which flow through the space considered per second, weigh GQ lb, and fall through a height — dz ft. The work done by gravity is then -GQ!*__• - v**~'iy**' r>V s* ■ ~1 ^^'f^'^C^ 1 y^ xPs J? j - pr" J ' ^^ s\°> j X —L J^.—^^^k,^ — — ^' wOV \rf-T J 1 ^ ^' 4I$»L^l_ /" it ^^^Jgfe^^te'' ' " ^" ^^qj^: ^ ^Sfc d^< ^^%^^ iga? ^ _^<^L^ l •5 ft^" „-^^ -^ ,^? 6 >^{ V 8 j£< • . _ . _ _ : __ ■a. •*[ =V^o«l ... ..._.. ._ , — — -^^§\iv ■ •3 - -2 .1.1 , . _ _ 1 _J 29 io 1 -2 -3 4 -5 6 -7 -8 -9 00 .1 .2 -3 4 <5 -6 -7 -8 -9 Fig. 83. In 1886, Professor \V. C. Unwin plotted logarithmically all the most trustworthy experiments on flow in pipes then available. 1 Fig. 83 gives one such plotting. The results of measuring the slopes of the lines drawn through the plotted points are given in the table. It will be seen that the values of the index n range from 1-72 for the smoothest and cleanest surface, to 2-00 for the roughest. The numbers after the brackets are rounded off numbers. The value of n having been thus determined, values of mid" were next found and averaged for each pipe. These were again plotted logarithmically in order to find a value for x. The lines were not very regular, but in all cases the slope was greater than I to I, so that the value of x must be greater than unity. The following table gives the results and a comparison of the value of x and Reynolds's value 3-H. Kind of Pipe. n 3-» ■ X Tin plate .... 1-72 1-28 I-IOO Wrought iron (Smith). i-75 1-25 I-2I0 Asphalted pipes 1-85 115 1-127 i Wrought iron (Darcv) . 1 -87 i-i3 l-68o Riveted wrought iron . 1-87 I-I3 1-390 Xew cast iron . i-95 1-05 1-168 Cleaned cast iron 2-00 l-OO 1-168 ilncrusted cast iron 2-00 I'OO 1 160 Here, considering the great range of diameters and velocities in the experiments, the constancy of m is very satisfactorily close. The asphalted pipes give lather variable values. But, as some of these were new and some old, the variation is, perhaps, not surprising. The incrusted pipes give a value of m quite double that for new pipes but that is perfectly consistent with what is known of fluid friction in other cases. With the exception of the anomalous values for Darcy's wrought- iron pipes, there is no great discrepancy between the values of x and 3-ra, but there is no appearance of relation in the two quantities. For the present it appears preferable to assume that x is independent of n. It is now possible to obtain values of the third constant m, using the values found for n and x. The following table gives the results, the values of m being for metric measures. Kind of Pipe. 1 " Formulae for the Flow of Water in Pipes," Industries (Man- chester, 1886). Tin plate Wrought iron Asphalted pipes Riveted wrought iron New cast iron Cleaned cast iron Incrusted cast iron Diameter in Metres. Value of •01697"! •01676/ •01302 1 ■01319J •01749 •02058 •02107 •01650 •01317 •02107 •01370-1 •01440 •01390 y •01368 ■01 448 J •01725] •01427 1 •01734 •01745J ■01979 •02091 f- •01913J •03693 1 •03530 y •03706 j Mean Value of m. Authority. •01686 •01310 •01831 • •01403 •01658 ■01994 03643 Bossut Hamilton Smith Hamilton Smith W. W. Bonn W. W. Bonn Lampe Stearns Gale Hamilton Smith Darcy Darcy Darcy STEADY FLOW IN PIPES] HYDRAULICS 63 General Mean Values of Constants. The general formula (Hagen's) — hjl = mv n /d".2g — can therefore be taken to fit the results with convenient closeness, if the following mean values of the coefficients are taken, the unit being a metre : — Kind of Pipe. m X n Tin plate .... •0169 I-IO 1-72 Wrought iron •0131 I-2I i-75 Asphalted iron . •0183 I-I27 1-85 Riveted wrought iron . •0140 I -390 1-87 New cast iron •0166 I- 168 1-95 Cleaned cast iron •0199 1-168 2-0 Incrusted cast iron •0364 1-160 2-0 The variation of each of these coefficients is within a comparatively narrow range, and the selection of the proper coefficient for any given case presents no difficulty, if the character of the surface of the pipe is known. It only remains to give the values of these coefficients when the quantities are expressed in English feet. For English measures the following are the values of the coefficients : — Kind of Pipe. m X • ! Tin plate .... •0265 I-IO 1-72 Wrought iron •0226 I-2I i-75 Asphalted iron . •0254 1-127 1-85 Riveted wrought iron . ■0260 I -390 1-87 New cast iron . •0215 1-168 i-95 Cleaned cast iron •0243 I- 168 2-0 Incrusted cast iron •0440 i- 160 2-0 § 78. Distribution of Velocity in the Cross Section of a Pipe. — Darcy made experiments with a Pitot tube in 1850 on the velocity at different points in the cross section of a pipe. He deduced the relation V — » = ll'3(/3/R)V*\ where V is the velocity at the centre and v the velocity at radius r in a pipe of radius R with a hydraulic gradient i. Later Bazin repeated the experiments and extended them (Mem. de V Acadimie des Sciences, xxxii. No. 6). The most important result was the ratio of mean to central velocity. Let b = Ri/U 2 , where U is the mean velocity in the pipe; then V/U = 1 +9-03V6. A very useful result for practical purposes is that at 0-74 of the radius of the pipe the velocity is equal to the mean velocity. Fig. 84 gives the velocities at different radii as determined by Bazin. § 79. Influence of Temperature on the Flow through Pipes. — Very careful experiments on the flow through a pipe 0-1236 ft. in diameter This shows a marked decrease of resistance as the temperature rises. If Professor Osborne Reynolds's equation is assumed h — niLV n /d i ~", and n is taken 1-795, then values of m at each temperature are practically constant — Temp. F. m. Temp. F. m. 57 0-000276 100 0-000244 70 0-000263 no 0-000235 80 0-000257 120 0-000229 90 0-000250 130 0-000225 160 0-000206 where again a regular decrease of the coefficient occurs as the temperature rises. In experiments on the friction of disks at different temperatures Professor W. C. Unwin found th-at the re- sistance was proportional to constant X (i-o-oo2i<) and the values of m given above are expressed almost exactly by the relation m =0-00031 1 (1-0-00215 /). In tank experiments on ship models for small ordinary variations of temperature, it is usual to allow a decrease of 3 % of resistance for io° F. increase of temperature. § 80. Influence of Deposits in Pipes on the Discharge. Scraping Water Mains. — The influence of the condition of the surface of a pipe on the friction is shown by various facts known to the engineers of waterworks. Jn pipes which convey certain kinds of water, oxidation proceeds rapidly and the discharge is considerably diminished. A main laid at Torquay in 1858, 14 m. in length, consists of 10-in., 9-in. and 8-in. pipes. It was not protected from corrosion by any coating. But it was found to the surprise of the engineer that in eight years the discharge had diminished to 51 % of the original discharge. J. G. Appold suggested an apparatus for scraping the interior of the pipe, and this was constructed and used under the direction of William Froude (see " Incrustation of Iron Pipes," by W. Ingham, Proc. Inst. Mech. Eng., 1899). it was found that by scraping the interior of the pipe the discharge was increased 56%. The scraping requires to be repeated at intervals. After each scraping the dis- charge diminishes rather rapidly to 10% and afterwards more slowly, the diminution in a year being about 25 %. Fig. 85 shows a scraper for water mains, similar to Appold's but modified in details, as constructed by the Glenfield Company, at Kilmarnock. A is a longitudinal section of the pipe, showing the scraper in place; B is an end view of the plungers, and C, D sections of the boxes placed at intervals on the main for introducing or with- drawing the scraper. The apparatus consists of two plungers, packed with leather so as to fit the main pretty closely. On the spindle of these plungers are fixed eight steel scraping blades, with curved scraping edges fitting the surface of the main. The apparatus is placed in the main by removing the cover from one of the boxes shown at C, D. The cover is then replaced, water pressure is ad- mitted behind the plungers, and the apparatus driven through the Fig. 84. and 25 ft. long, with water at different temperatures, have been made by J. G. Mair (Proc. Inst. Civ. Eng. lxxxiv.). The loss of head was measured from a point 1 ft. from the inlet, so that the loss at entry was eliminated. The 15 in. pipe was made smooth inside and to gauge, by drawing a mandril through it. Plotting the results logarithmically, it was found that the resistance for all temperatures varied very exactly as » 1795 , the index being less than 2 as in other experiments with very smooth surfaces. Taking the ordinary equation of flow /j = f(4L/D)(» 2 /2g), then for heads varying from 1 ft. to nearly 4 ft., and velocities in the pipe varying from 4 ft. to 9 ft. per second, the values of f were as follows: — Temp. F. f Temp. F. f 57 •0044 to -0052 100 •0039 to -0042 70 •0042 to -0045 no •0037 to -0041 80 •0041 to -0045 120 ■0037 to -0041 90 •0040 to -0045 130 •0035 to -0039 160 •003-5 to -0038 Fig. 85. Scale ^ 5 . main. At Lancaster after twice scraping the discharge was increased 56!%, at Oswestry 545%. The increased discharge is due to the diminution of the friction of the pipe by removing the roughnesses due to oxidation. The scraper can be easily followed when the mains are about 3 ft. deep by the noise it makes. The average speed of the scraper at Torquay is 2\ rri. per hour. At Torquay 49 % of the deposit is iron rust, the rest being silica, lime and organic matter. In the opinion of some engineers it is inadvisable to use the scraper. The incrustation is only temporarily removed, and if the use of the scraper is continued the life of the pipe is reduced. The only treatment effective in preventing or retarding the incrustation due to corrosion is to coat the pipes when hot with a smooth and perfect layer of pitch. With certain waters such as those derived from the chalk the incrustation is of a different character, consisting of nearly pure calcium carbonate. A deposit of another character which has led to trouble in some mains is a black slime containing a good deal of iron not derived from the pipes. It appears to be an 6 4 HYDRAULICS [STEADY FLOW IN PIPES organic growth. Filtration of the water appears to prevent the growth of the slime, and its temporary removal may be effected by a kind of brush scraper devised by G. F. Deacon (see " Deposits in Pipes," by Professor J. C. Campbell Brown, Eroc. Inst. Civ. Eng., 1 903- 1 904). § 81. Flow of Water through Fire Hose. — The hose pipes used for fire purposes are of very varied character, and the roughness of the surface varies. Very careful experiments have been made by J. R. Freeman' (Am. Soc. Civ. Eng. xxi., 1889). It was noted that under pressure the diameter of the hose increased sufficiently to have a marked influence on the discharge. In reducing the results the true diameter has been taken. Let v = mean velocity in ft. per sec; r = hydraulic mean radius or one-fourth the diameter in feet; »' = hydraulic gradient. Then i> = »V (ri). Diameter Gallons (United Inches. States) per min. 1 V n Solid rubber \ 2-65 215 •1863 12-50 i23'3 hose ,, 344 ■4714 20-00 124-0 Woven cotton, \ 2-47 200 •2464 13-40 119-1 rubber lined ,, 299 •5269 2O-00 I2I-5 Woven cotton, { 2-49 200 •2427 13-20 117-7 rubber lined ,, 319 •5708 21 -OO 122- 1 Knit cotton, ( 2-68 132 •0809 7-50 III-6 rubber lined ( ,, 299 •3931 I7-00 II4-8 Knit cotton, ( 2-69 204 •2357 11-50 100- 1 ! rubber lined ( ,, 319 •5165 18-00 105-8 Woven cotton , t 2-12 154 •3448 1.4-00 "3-4 rubber lined ( 240 •7673 2I-8I n8-4 Woven cotton, \ 2-53 54-8 •0261 3-50 94-3 rubber lined 298 •8264 19-00 91-0 Unlined linen { 2-60 57-9 •0414 3-50 73-9 hose " 33i 1-1624 20-00 79-6 § 82. Reduction of a Long Pipe of Varying Diameter to an Equivalent Pipe of Uniform Diameter. Dupuit's Equation. — Water mains for the supply of towns often consist of a series of lengths, the diameter being the same for each length, but differing from length to length. In approximate calculations of the head lost in such mains, it is generally accurate enough to neglect the smaller losses of head and to have regard to the pipe friction only, and then the calcula- tions may be facilitated by reducing the main to a main of uniform diameter, in which there would be the same loss of head. Such a uniform main will be termed an equivalent main. — h- -U — 1$ - 1 "W B Fig. 86. § 83. Other Losses of Head in Pipes. — Most of the losses of head in pipes, other than that due to surface friction against the pipe, are due to abrupt changes in the velocity of the stream producing eddies. The kinetic energy of these is deducted from the general energy of translation, and practically wasted. Sudden Enlargement of Section. — Suppose a pipe enlarges in section from an area too to an area «i (fig. 87); then II fli/vo •= «o/ wi ; i^^HH^MaJI or, if the section is circular, »iM> = (do/'di) 2 . The head lost at the abrupt change of velocity has already been wm shown to be the head due to the relative velocity of the two parts of the stream. Hence head lost In fig. 86 let A be the main of variable diameter, and B the equiva- lent uniform main. In the given main of variable diameter A, let h, h... be the lengths, di, di... the diameters, »i, »2... the velocities, ii, ii... the slopes, for the successive portions, and let I, d, v and i be corresponding quantities for the equivalent uniform main B. The total loss of head in A due to friction is h = i 1 l 1 -\-i 2 l 2 -\- . . . = f W-4il2&di) + f W-<\kl2ga\) + ... and in the uniform main il = ?(fl 2 - 4l/2gd). If the mains are equivalent, as defined above, f(y-4//2g 2 = vtPjcL? . . . Also suppose that f may be treated as constant for all the pipes. Then lid = (rfVdi 4 ) (hid,) + (dW) (hid*) + ... l=(d°jd l >)h + (d i /d 2 °)h+... which gives the length of the equivalent uniform main which would have the same total loss of head for any given discharge. V. Fig. 87. h = (l'»-ViYl2g = (W"0 - I ) V/2g = { (djdtf- Or fi e = £eVl*/2g, if f,. is put for the expression in brackets. ■i}V/2g (1) ui/uo = 1.1 1.2 1-5 1-7 1.8 1-9 2.0 2-5 30 3-5 4-0 5-0 6.0 7.0 S.o di/do = 1.05 1. 10 1.22 1.30 1-34 1.38 1.41 1.58 1-73 1.87 2.00 2.24 2.45 2.65 2.83 f.= .01 .04 •25 •49 .64 .81 1. 00 2.25 4.00 6.2s 9.00 16.00 25-00 36.0 49-0 Abrupt Contraction of Section. — When water passes from a larger to a smaller section, as in figs. 88, 89, a contraction is formed, and the contracted stream abruptly expands to fill the section of the pipe. Fig. Fig. Let &> be the section and v the velocity of the stream at bb. At aa the section will be c c a, and the velocity (io/ccu)v = v/ci, where c c is the coefficient of contraction. Then the head lost is T)m = (vlc c -vy/2g=(i/c c -i)V/2g; and, if c c is taken 0-64, | m = o-3i6i- 2 /2g. (2) The value of the coefficient of contraction for this case is, however, not well ascertained, and the result is somewhat modified by friction. For water entering a cylindrical, not bell-mouthed, pipe from a reservoir of indefinitely large size, experiment gives §.. = 0-505 vy 2 g. (3) If there is a diaphragm at the mouth of the pipe as in fig. 89, let wi be the area of this orifice. Then the area of the contracted stream is c C ">i, and the head lost is h c = !(a)/CcWi)-llV/2g = f^/2g (4) if f, is put for { (w/c c o>i) — I ) 2 . Weisbach has found experimentally the following values of the coefficient, when the stream approaching the orifice was considerably larger than the orifice : — OJl/W = 0.1 0.2 0-3 0.4 0-5 0.6 0.7 0.8 0.9 1.0 C c = .616 .614 .612 .610 .617 .605 .603 .601 ■598 •596 f.= 231-7 5°-99 19.78 9.612 5-256 3-077 1.876 1 169 0-734 0.480 When a diaphragm was placed in a tube of uniform section (fig. 90) JL Fig. 90. the following values were obtained, ui being the area of the orifice and w that of the pipe: — t*)i/co = O.I 0.2 0.3 O.A OS 0.6 0.7 0.8 0.0 1.0 Ce = .624 .632 .643 •659 .68: .712 • 755 .813 .892 1 .00 *« = 225.9 47-77 30.83 7.801 1.753 1.796 • 797 .290 .060 .000 STEADY FLOW IN PIPES] HYDRAULICS 65 Elbows. — Weisbach considers the loss of head at elbows (fig.91) to be due to a contraction formed by the stream. From experiments with a pipe 1 { in. diameter, he found the loss of head fi« = f^/2g; (5) fe =0-9457 sin 2 j0+2-o47 sin 4 \$. = 20° O.O46 40° 0.130 60° 0.364 80° 0.740 90 O.984 I0O° 1.260 IIO° 1.556 120° 1. 861 I30° 2.IS8 I40 2.431 Hence at a right-angled elbow the whole head due to the velocity very nearly is lost. Bends. — Weisbach traces the loss of head at curved bends to a similar cause to that at elbows, but the coeffi- cients for bends are not very satisfactorily ascer- tained. Weisbach ob- tained for the loss of head at a bend in a pipe of circular section ^ = fi,f 2 /2g; (6) ft =0-131 +i-847(d/2p)S, where d is the diameter V of the pipe and p the Fig. 91. radius of curvature of the bend. The resistance at bends is small and at present very ill determined. Valves, Cocks and Sluices. — These produce a contraction of the water-stream, similar to that for an abrupt diminution of section already discussed. The loss of head may be taken as before to be $» = f,»72g; (7) where v is the velocity in the pipe beyond the valve and f„ a coefficient determined by experiment. The following are Weisbach's results. Sluice in Pipe of Rectangular Section (fig. 92). Section at sluice =wi in pipe=co. Fig. 92. 1 f - 1-0 0-00 0-9 •09 o-8 •39 0-7 •95 o-6 2-08 o-5 4-02 0-4 8-12 o-3 17-8 0-2 44-5 O-I 193 Sluice in Cylindrical Pipe (fig. 93). Ratio of height oft opening to diameter > 1.0 4 i * * if } i of pipe ] wi/co — 1. 00 0.948 .856 .740 .609 .466 ■315 • 159 f.= 0.00 0.07 0.26 0.81 2.06 552 17.0 07.8 Fig. 93. Fig. 94. Cock in a Cylindrical Pipe (fig. 94). Angle through which cock is turned =0. 8 = 5° 10° 15° 20° 25° 30° 35° Ratio of"j cross :- sections J •926 •850 •772 •692 ■613 •535 •458 f > = ■05 •29 •75 1-56 3-10 5-47 9-68 8 = Ratio of cross sections f- = 40" •385 17-3 45° •315 31-2 J 55 •250 526 •190 10G 60° •137 2"6 65° •091 486 82° o 00 Throttle Valve in a Cylindrical Pipe (fig. 95) " = _ 10° 15° 20° 25° 30* 35° 40° f» = •24 •52 •90 i-54 2-51 3-91 6-22 io-8 = r.= 45° i8- 7 5o° 32-6 55° 58-8 60 ° 118 65° 256 70° 751 90° 00 M\'fi'-l'«^ „i § 84. Practical Calculations on the Flow of Water in Pipes. — In the following explanations it will be assumed that the pipe is of so great a length that only the loss of head in friction against ..-'' the surface of the pipe needs to be considered. In general it is one of the four quantities d, i, v or Q which requires to be determined. For since the loss of head h is given by the relation h = il, this need not be separately considered. There are then three equa tions (see eq. 4, as arise : — f = o(i + i/i2d); where 0=0-005 for new and=o-oi for incrusted pipes. f» 2 /2g = \di. Q = l-xdh). w///,w/w/#. // Y'f/?0/////tf///ttS//{//////M} t Fig. 95. 72, and 9a, § 76) for the solution of such problems (1) (2) (3) Problem 1. Given the diameter of the pipe and its virtual slope, to find the discharge and velocity of flow. Here d and i are given, and Q and v are required. Find f from (1) ; then v from (2) ; lastly Q from (3). This case presents no difficulty. By combining equations (1) and (2), v is obtained directly: — !> = V(g = 55-3iV (di) for new pipes £ (4a) = 39-1 1 V (di) for incrusted pipes 5 ' Within the limits stated, these are accurate enough for practical purposes, especially as the precise value of the coefficient \ cannot be known for each special case. Problem 2. Given the diameter of a pipe and the velocity of flow, to find the virtual slope and discharge. The discharge is given by (3); the proper value of f by (1); and the virtual slope by (2). This also presents no special difficulty. Problem 3. Given the diameter of the pipe and the discharge, to find the virtual slope and velocity. Find v from (3); f from (1); lastly i from (2). If we combine (1) and (2) we get * = f(W2g) (4/d)=2a{i + i/i2dy/gd; (5) and, taking the mean values of f for pipes from 1 to 4 ft. diameter, given above, the approximate formulae are 1 = 0-0003268 v 2 /d for new pipes \ (5a) = 0-0006536 v*/d for incrusted pipes ) " Problem 4. Given the virtual slope and the velocity, to find the diameter of the pipe and the discharge. The diameter is obtained from equations (2) and (1), which give the quadratic expression d i — d(2av 2 jgi) — av 2 /6gi = o . .■.d = avygi+ij{( a v l 'lgi) (a.vVgi+l/6)}. (6). For practical purposes, the approximate equations d = 2av i lgi + ili2 (6a) = 0-00031 v 2 /i+-o83 for new pipes = 0-00062 ti 2 /i+-o83 for incrusted pipes are sufficiently accurate. Problem 5. Given the virtual slope and the discharge, to find the diameter of the pipe and velocity of flow. This case, which often occurs in designing, is the one which is least easy of direct solution. From equations (2) and (3) we get— <2 B = 32fQ7g*- 2 *'- (7) If now the value of f in (1) is introduced, the equation becomes very cumbrous. Various approximate methods of meeting the difficulty may be used. (a) Taking the mean values of f given above for pipes of 1 to 4 ft. diameter we get i 2 /2g) (^lifdi) = 32fQ' 2 />/g*- 2 d l 5 ; h'-h c = i{v^l2g){4zld,) =32fQ%fer 2 d3 5 ; where Q' is the common discharge of the two portions of the pipe. Hence (/i„-/0/(/i'-W=W3 5 /Wi 5 , from which h' is easily obtained. If then V is greater than hb. opening the sluice between X and B will allow flow towards B, and the case in hand is case I. If h' is less than h b , opening the sluice will allow flow from B, and the case is case III. If h' = h b , the case is case II., and is already completely solved. ar COMPRESSIBLE FLUIDS IN PIPES] HYDRAULICS 67 The true value of h must lie between V and lib- Choose a new value of h, and recalculate Qi, Q 2 , Q 3 . Then if Qi>Qi+Qs in case I., or 0i+Q2>Qa in case III., the value chosen for h is too small, and a new value must be chosen. If Qi; and for / = /, let H = Hi, and p — pi. log (Hi/Ho) + (gfiVWVr) (p? - pj) + Him = o. (5a) where pa is the greater pressure and pi the less, and the flow is from Ao towards Ai. By replacing W and H, log(pt>/p 1 ) + (gcTi'uti i p, u = u po!p; (12) which gives the velocity at any section in terms of the pressure, which has already been determined. Fig. 101 gives the velocity ,_^---Hr*55*^^^-£ Vo*" 1 "^— — - ■ Pr*asur* — . _- —yrvl ' — — — "jfe*"** — _ — -~Y2*- fl ?22' a 1 T»* 1 1 1 1 1 I 21I.i-.SH. +2 27 n. 634-oatt. 04-54 than to telegraph by electricity. The tubes are laid underground with easy curves; the messages are made into a roll and placed in a light felt carrier, the resistance of which in the tubes in Lor.don is only J oz. A current of air forced into the tube or drawn through it propels the carrier. In most systems the current of air is steady and continuous, and the carriers are introduced or removed without materially altering the flow of air. Time of Transit through the Tube. — Putting t for the time of transit from o to /, t= I dl/u, 1 From (40) neglecting rfH/H, and putting m=dja r% dl = gdSPpdpfciW'-cr. From (1) and (3) Fig. ioi. curves for the two experiments of Culley and Sabine, for which the pressure curves have already been drawn. It will be seen that the velocity increases considerably towards that end of the pipe where the pressure is least. § 93. 'Weight of Air Flowing per Second. — The weight of air dis- charged per second is (equation 30) — W = S2woft/ci-. From equation (76), for a pipe of circular section and diameter d, W = iH kdHpf-pVlrlcT), = -6nVi<2 5 (A> 2 -£iWr|. (13) Approximately W = (-6916ft- -4438ft) (d b l^r)i. (13a) § 94. A pplication to the Case cf Pneumatic Tubes for the Trans- mission of Messages. — In Paris, Berlin, London, and other towns, it has been found cheaper to transmit messages in pneumatic tubes w = Wc-r/ft2; dlju =gda 3 p-dp/2^WVT- ; / = ( ^gda 3 pHpl2tw s c 2 T\ = g rf O = -3 rt > ■sl'1 a a, > C O ■3 m ni S3 •S-o n 3 — 2 > $ a z l.S-3 Aug •25 125 95 57 26 i8-5 8-5 147 130 112 89 •5 135 no 72 36 25-6 9-0 147 130 112 90 7i •75 139 lib 81 42 30-8 9-5 147 130 112 90 1-0 141 119 87 48 34-9 100 147 130 112 91 72 i-5 143 122 94 56 41-2 11 147 130 113 92 2-0 144 124 98 62 46-0 12 147 130 113 93 74 2-5 145 126 101 67 13 147 130 "3 94 3-0 H5 126 104 70 53 H 147 130 113 95 3-5 146 127 105 73 15 147 130 114 96 77 4-0 146 128 106 76 58 16 147 130 II4 97 4-5 146 128 107 78 17 147 130 114 97 5-0 146 128 108 80 62 18 147 130 II4 98 ,V5 146 129 109 82 20 147 131 II4 98 80 6-0 147 129 no «4 65 25 I48 131 "5 100 6-5 H7 129 no «5 30 148 131 "5 102 8.3 7-0 147 129 no 8b 67 40 I48 I.3I 116 103 8.5 7-5 H7 129 in 87 5° I48 I.3I lib 104 86 8-0 147 130 in 88 69 00 I48 131 117 108 91 § 99. Ganguillet and Kutter's Modified Darcy Formula. — Starting from the general expression v = c^mi, Ganguillet and Kutter examined the variations of c for a wider variety of cases than those discussed by Darcy and Bazin. Darcy and Bazin's experiments were confined to channels of moderate section, and to a limited variation of slope. Ganguillet and Kutter brcugnt into the dis- cussion two very distinct and important additional series of results. The gaugings of the Mississippi by A. A. Humphreys and H. L. Abbot afford data of discharge for the case of a stream of exceotion- ally large section and or very low slope, on tne otner nana, their own measurements of the flow in the regulated channels of some 7° HYDRAULICS [FLOW IN RIVERS Swiss torrents gave data for cases in which the inclination and roughness of the channels were exceptionally great. Darcy and Bazin's experiments alone were conclusive as to the dependence of the coefficient c on the dimensions of the channel and on its rough- ness of surface. Plotting values of c for channels of different in- clination appeared to indicate that it also depended on the slope of the stream. Taking the Mississippi data only, they found £ = 256 for an inclination of 0-0034 per thousand, = 154 .. .. °-° 2 .... so that for very low inclinations no constant value of c independent of the slope would furnish good values of the discharge. In small rivers, on the other hand, the values of c vary little with the slope. As regards the influence of roughness of the sides of the channel a different law holds. For very small channels differences of rough- ness have a great influence on the discharge, but for very large channels different degrees of roughness have but little influence, and for indefinitely large channels the influence of different degrees of roughness must be assumed to vanish. The coefficients given by Darcy and Bazin are different for each of the classes of channels of different roughness, even when the dimensions of the channel are infinite. But, as it is much more'probable that the influence of the nature of the sides diminishes indefinitely as the channel is larger, this must be regarded as a defect in their formula. Comparing their own measurements in torrential streams in Switzerland with those of Darcy and Bazin, Ganguillet and Kutter found that the four classes of coefficients proposed by Darcy and Bazin were insufficient to cover all cases. Some of the Swiss streams gave results which showed that the roughness of the' bed was markedly greater than in any of the channels tried by the French engineers. It was necessary therefore in adopting the plan of arranging the different channels in classes of approximately similar roughness to increase the number of classes. Especially an additional class was required for channels obstructed by detritus. To obtain a new expression for the coefficient in the formula z> = V (2g/f)V {mi) =cV {mi), Ganguillet and Kutter proceeded in a purely empirical way. They found that an expression of the form c = o/(i+(S/V»0 could be made to fit the experiments somewhat better than Darcy's expression. Inverting this, we get l/c = l/a+/S/aV»», an equation to a straight line having i/Vwz for abscissa, i/c for ordinate, and inclined to the axis of abscissae at an angle the tangent of which is /3/o. Plotting the experimental values of l/c and i/V m, the points so found indicated a curved rather than a straight line, so that /3 must depend on o. After much comparison the following form was arrived at — c = (A+//»)/(i -f-A»/V m), where 11 is a coefficient depending only on the roughness o| the sides of the channel, and A and / are new coefficients, the value of which remains to be determined. From what has been already stated, the coefficient c depends on the inclination of the stream, decreasing as the slope i increases. Let A = a+p/i. Then c = (a+l/n+p/i)/li + {a-{-p/i)n/^m.}, the form of the expression for c ultimately adopted by Ganguillet and Kutter. For the constants a, /, p Ganguillet and Kutter obtain the values 23, 1 and 0-00155 for metrical measures, or 41-6, i-8n and 0-00281 for English feet. The coefficient of roughness n is found to vary from 0-008 to 0-050 for either metrical or English measures. The most practically useful values of the coefficient of roughness n are given in the following table : — Nature of Sides of Channel. Coefficient of Roughness ». Well-planed timber 0-009 Cement plaster o-oio Plaster of cement with one-third sand .... o-oi I Unplaned planks 0-012 Ashlar and brickwork 0-013 Canvas on frames 0-015 Rubble masonry 0-017 Canals in very firm gravel 0-020 Rivers and canals in perfect order, free from stones ) or weeds \ Rivers and canals in moderately good order, not / _ quite free from stones and weeds . . . . \ Rivers and canals in bad order, with weeds and , „ „ detritus _ \ °-°35 Torrential streams encumbered with detritus . . 0-050 Ganguillet and Kutter's formula is so cumbrous that it is difficult to use without the aid of tables. Lowis D'A. Jackson published complete and extensive tables for facilitating the use of the Ganguillet and Kutter formula {Canal and Culvert Tables, London, 1878). To lessen calculation he puts the formula in this form : — M =n(4.i-6-\-0-0028i (i) • z> = (Vm/»)l(M + i-8ii)/(M+Vm))V (»*')• The following table gives a selection of values of M, taken from Jackson's tables: — '•025 3-030 i — Values of M for n — O-OIO 0-012 0-015 0-017 0-020 0-025 OO3O •0000 1 3-2260 3-8712 4-8390 5-4842 6-4520 8-0650 9-6780 •00002 I-82IO 2-1852 2-73I5 3-0957 3-6420 4-5525 5-4630 •00004 1-1185 1-3422 1-6777 1-9014 2-2370 2-7962 3-3555 •00006 0-8843 1-0612 1-3264 1-5033 1-7686 2-2107 2-6529 •00008 0-7672 0-9206 1-1508 1-3042 1-5344 1-9180 2-3016 •OOOIO 0-6970 0-8364 1 -0455 1 • 1 849 1-3940 1-7425 2-0910 •00025 0-5284 0-6341 0-7926 0-8983 1-0568 1-3210 1-5852 •00050 0-4722 0-5666 0-7083 0-8027 0-9444 1-1805 1-4166 •00075 0-4535 0-5442 0-6802 0-7709 0-9070 I-I337 1-3605 •OOIOO 0-4441 0-5329 o-666i 0-7550 0-8882 I-II02 1-3323 •00200 0-4300 0-5160 0-6450 0-7310 o-86oo 1-0750 1-2900 •00300 0-4254 0-5105 0-6381 0-7232 0-8508 I-0635 1-2762 A difficulty in the use of this formula is the selection of the co- efficient of roughness. The difficulty is one which no theory will overcome, because no absolute measure of the roughness of stream beds is possible. For channels lined with timber or masonry the difficulty is not so great. The constants in that case are few and sufficiently defined. But in the case of ordinary canals and rivers the case is different, the coefficients having a much greater range. For artificial canals in rammed earth or gravel n varies from o 0163 to 0-0301. For natural channels or rivers » varies from 0-020 to 0-035. In Jackson's opinion even Kutter's numerous classes of channels seem inadequately graduated, and he proposes for artificial canals the following classification : — I. Canals in very firm gravel, in perfect order w = o-02 II. Canals in earth, above the average in order ^ = 0-0225 III. Canals in earth, in fair order .... n =0-025 ■ IV. Canals in earth, below the average in order n = 0-0275 V. Canalsin earth, inratherbad order, partially ) overgrown with weeds and obstructed by > n = 0-03 detritus . . ' Ganguillet and Kutter's formula has been considerably used partly from its adoption in calculating tables for irrigation work in India. But it is an empirical formula of an unsatisfactory form. Some engineers apparently have assumed that because it is com- plicated it must be more accurate than simpler formulae. Com- parison with the results of gaugings shows that this is not the case. The term involving the slope was introduced to secure agreement with some early experiments on the Mississippi, and there is strong reason for doubting the accuracy of these results. § 100. Bazin's New Formula. — Bazin subsequently re-examined all the trustworthy gaugings of flow in channels and proposed a modification of the original Darcy formula which appears to be more satisfactory than any hitherto suggested {iLtude d'une nouvelle formule, Paris, 1898). He points out that Darcy's original formula, which is of the form mi/v 2 = a-}-p/m, does not agree with experiments on channels as well as with experiments on pipes. It is an objection to it that if m increases indefinitely the limit towards which mi/v 2 tends is different for different values of the roughness. It would seem that if the dimensions of a canal are indefinitely increased the variation of resistance due to differing roughness should vanish. This objection is met if it is assumed that V {mijv 1 ) =a-f-/3/Vm, so that if a is a constant mi/v* tends to the limit a when m increases. A very careful discussion of the results of gaugings shows that they can be expressed more satisfactorily by this new formula than by Ganguillet and Kutter's. Putting the equation in the form $> l l2g = mi, f = 0-002594(1 +7/Vm), where y has the following values: — I. Very smooth sides, cement, planed plank, 7= 0-109 II. Smooth sides, planks, brickwork .... 0-290 III. Rubble masonry sides 0-833 IV. Sides of very smooth earth, or pitching . . 1-539 V. Canals in earth in ordinary condition . . . 2-353 VI. Canals in earth exceptionally rough . . . 3-168 § 101. The Vertical Velocity Curve. — If at each point along -a vertical representing the depth of a stream, the velocity at that point is plotted horizontally, the curve obtained is the vertical velocity curve and it has been shown by many observations that it approximates to a parabola with horizontal axis. The vertex of the parabola is at the level of the greatest velocity. Thus in fig. 104 OA is the vertical at which velocities are observed ; v is the sur- face; v z the maximum and Vd the bottom velocity. B C D is the vertical velocity curve which corresponds with a parabola having its vertex at C. The mean velocity at the vertical is Vm = \\2V z +V d -\- {dz/d) (»„ —Vd)]. The Horizontal Velocity Curve. — Similarly if at each point along a horizontal representing the width of the stream the velocities are AND CANALS] HYDRAULICS 7 plotted, a curve is obtained called the horizontal velocity curve. In streams of symmetrical section this is a curve symmetrical about the centre line of the stream. The velocity varies little near the centre of the stream, but very rapidly near the banks. In un- symmetrical sections the greatest velocity is at the point where the stream is deepest, and the general form of the horizontal velocity curve is roughly similar to the section of the stream. § 102. Curves or Contours of Equal Velocity. — If velocities are observed at a number of points at different widths and depths in a stream, it is possible to draw curves on the cross section through points at which the velocity is the same. These repre- sent contours of a solid, the volume of which is the discharge of the stream per second. Fig. 105 shows the vertical and horizontal velocity curves and the contours of equal velocity in a rectangular channel, from one of Bazin's gaugings. § 103. Experimental Observations on the Vertical Velocity Curve. — A preliminary difficulty arises in observing the velocity at a given point in a stream because the velocity rapidly varies, the motion not being strictly steady. If an average of several velocities at the same point is taken, or the average velocity for a sensible period of time, this average is found to be constant. It may be inferred that Fig. 104. .1 .-' ""1' Vertical Velocity [ Curves • i Horizontal Velocity Cuijves ; I * 1 < i i , 1 1 ' ►1 I Vertical Velocity I Curves e f g h i j k Contours of Ecjual Velocity Fig. 105. though the velocity at a point fluctuates about a mean value, the fluctuations being due to eddying motions superposed on the general motion of the stream, yet these fluctuations produce effects which disappear in the mean of a series of observations and, in calculating the volume of flow, may be disregarded. In the next place it is found that in most of the best observations on the velocity in streams, the greatest velocity at any vertical is found not at the surface but at some distance below it. In various river gaugings the depth d z at the centre of the stream has been found to vary from o to o-^d. § 104. Influence of tlie Wind. — In the experiments on the Missis- sippi the vertical velocity curve in calm weather was found to agree fairly with a parabola, the greatest velocity being at i^ths of the depth of the stream from the surface. With a wind blowing down stream the surface velocity is increased, and the axis of the parabola approaches the surface. On the contrary, with a wind blowing up stream the surface velocity is diminished, and the axis of the para- bola is lowered, sometimes to half the depth of the stream. The American observers drew from their observations the conclusion that there was an energetic retarding action at the surface of a stream like that due to the bottom and sides. If there were such a retarding action the position of the filament of maximum velocity below the surface would be explained. It is not difficult to understand that a wind acting on surface ripples or waves should accelerate or retard the surface motion of the stream, and the Mississippi results may be accepted so far as showing that the surface velocity of a stream is variable when the mean velocity of the stream is constant. Hence observations of surface velocity by floats or otherwise should only be made in very calm weather. But it is very difficult to suppose that, in still air, there is a resistance at the free surface of the stream at all analogous to that at the sides and bottom. Further, in very careful experi- ments, P. P. Boileau found the maximum velocity, though raised a little above its position for calm weather, still at a considerable distance below the surface, even when the wind was blowing down stream with a velocity greater than that of the stream, and when the action of the air must have been an accelerating and not a re- tarding action. A much more probable explanation of the diminution of the velocity at and near the free surface is that portions of water, with a diminished velocity from retardation by the sides or bottom, are thrown off in eddying masses and mingle with the rest of the stream. These eddying masses modify the velocity in all parts of the stream, but have their greatest influence at the free surface. Reaching the free surface they spread out and remain there, mingling with the water at that level and diminishing the velocity which would otherwise be found there. Influence of the Wind on the Depth at which the Maximum Velocity is found. — In the gaugings of the Mississippi the vertical velocity curve was found to agree well with a parabola having a horizontal axis at some distance below the water surface, the ordinate of the parabola at the axis being the maximum velocity of the section. During the gaugings the force of the wind was registered on a scale ranging from o for a calm to 10 for a hurricane. Arranging the velocity curves in three sets — (1) with the wind blowing up stream, (2) with the wind blowing down stream, (3) calm or wind blowing across stream — it was found that an up-stream wind lowered, and a down-stream wind raised, the axis of the parabolic velocity curve. In calm weather the axis was at j^ths of the total depth from the surface for all conditions of the stream. Let h' be the depth of the axis of the parabola, m the hydraulic mean depth, / the number expressing the force of the wind, which may range from + 10 to — 10, positive if the wind is up stream, negative if it is down stream. Then Humphreys and Abbot find their results agree with the expression h'/m = 0-3 1 7 ± 0-06/. Fig. 106 shows the parabolic velocity curves according to the American observers for calm weather, and for an up- or down-stream wind of a force represented by 4. Fig. 106. It is impossible at present to give a theoretical rule for the vertical velocity curve, but in very many gaugings it has been found that a parabola with horizontal axis fits the observed results fairly well. The mean velocity on any vertical in a stream varies from 0-85 to 0-0,2 of the surface velocity at that vertical, and on the average if v is the surface and Vm the mean velocity at a vertical v m = %v , a result useful in float gauging. On any vertical there is a point at which the velocity is equal to the mean velocity, and if this point were known it would be useful in gauging. Humphreys and Abbot in the Mississippi found the mean velocity at o-66 of the depth ; G. H. L. Hagen and H. Heinemann at 0-56 to 0-58 of the depth. The mean of observations by various observers gave the mean velocity at from 0-587 to 0-62 of the depth, the average of all being almost exactly 0-6 of the depth. The mid-depth velocity is therefore nearly equal to, but a little greater than, the mean velocity on a vertical. If Vmd is the mid-depth velocity, then on the average v m = o-g8v md . § 105. Mean Velocity on a Vertical from Two Velocity Observations. — A. J. C. Cunningham, in gaugings on the Ganges canal, found the following useful results. Let v be the surface, v m the mean, and v x d the velocity at the depth xd ; then am = iOo+3»2/3<;) = h(v.m d +v. 7 M d ). § 106. Ratio of Mean to Greatest Surface Velocity, for the whole Cross Section in Trapezoidal Channels. — It is often very important to be able to deduce the mean velocity, and thence the discharge, from observation of the greatest surface velocity. The simplest method of gauging small streams and channels is to observe the greatest surface velocity by floats, and thence to deduce the mean velocity. In general in streams of fairly regular section the mean velocity for the whole section varies from 0-7 'to 0-85 of the greatest surface velocity. For channels not widely differing from those experimented on by Bazin, the expression obtained by him for the ratio of surface to mean velocity may be relied on as at least a good approximation to the truth. Let v be the greatest surface velocity, v m the mean velocity of the stream. Then, according to Bazin, v m = v — 25-4 V {mi). But v m = c^J (mi), where c is a coefficient, the values of which have been already given in the table in § 98. Hence »m = tW(c+25-4). 72 HYDRAULICS [FLOW IN RIVERS Values of Coefficient cl{c-\-2§-$) in the Formula v m =cv /(c+2^-^) Hydraulic Mean Depth Very Smooth Rough Very Rough Channels Smooth Channels. Channels. Channels. encumbered Channels. Ashlar or Rubble Canals in with Cement. Brickwork. Masonry. Earth. Detritus. 0-25 •83 •79 •69 ■51 •42 o-5 •84 •81 •74 •58 •50 o-75 ■84 •82 •76 •63 •55 1-0 •85 •77 •65 ■58 2-0 •83 •79 •71 ■64 3-0 ■80 •73 •67 4-o •81 •75 •70 5-o •76 •71 6o •8 4 •77 •72 7-o •78 •73 8-o 9-o •82 •74 10-0 15-0 •79 •75 20-0 •80 •76 300 •82 •77 40-0 500 00 •79 general mass of water must flow outwards to take its place. Fig. 107 shows the directions of flow as observed in a small artificial stream, by means of light seeds and specks of aniline dye. The lines CC show the directions of flow immediately in contact with the sides and bottom. The dotted line AB shows the direction of motion of floating particles on the surface of the stream. § 108. Discharge of a River when flowing at different Depths. — When frequent observations must be made on the flow of a river or canal, the depth of which varies at different times, it is very convenient to have to observe the depth only. A formula can be established giving the flow in terms of the depth. Let Q be the discharge in cubic feet per second ; H the depth of the river in some straight and uniform part. Then Q = aH + &H 2 , where the constants a and b must be found by preliminary gaugings in different con- ditions of the river. M. C. Moquerey found for part of the upper Saone, Q = 64-71! +8-2H 2 in metric measures, or Q = 696H+26-8H 2 in English measures. § 109. Forms of Section of Channels. — The simplest form of section for channels is the semicircular or nearly semicircular channel (fig. log), a form now often adopted from the facility with which it can be § 107. River Bends. — In rivers flowing in alluvial plains, the wind- ings which already exist tend to increase in curvature by the scouring away of material from the outer bank and the deposition of detritus along the inner bank. The sinuosities sometimes increase till a loop is formed with only a narrow strip of land between the two encroaching branches of the river. Finally a " cut off " may occur, a waterway being opened through the strip of land and the loop left separated from the iCWMillim^^ stream, forming a horse- "-*-""""'"■ shoe shaped lagoon or marsh. Professor James Thomson pointed out (Proc. Roy. Soc, 1877, p. 356; Proc. Inst, of Mech. Eng., 1879, p. 456) that the usual supposi- tion is that the water jy tending to go forwards in a straight line rushes against the outer bank and scours it, at the same time creating de- posits at the inner bank. That view is very far from a complete account of the matter, and Pro- fessor Thomson gave a p much more ingenious ' ' account of the action at the bend, which he completely confirmed by experiment. When water moves round a circular curve under the action of gravity only, it takes a motion like that in a free vortex. Its velocity is greater parallel to the axis of the stream at the inner than at the outer side of the bend. Hence the scouring at the outer side and the deposit at the inner side of the bend are not due to mere difference of velocity of flow in the general direction of the stream; but, in virtue of the centrifugal force, the water passing round the bend presses outwards, and the free surface in a radial cross section has a slope from the inner side upwards to the outer side (fig. 108). For the greater part of the water flowing in curved paths, this difference of pressure produces no tendency to transverse motion. But the water im- Inner Bank Outer Bank mediately in contact with the rough bot- tom and sides of the channel is retarded, and its centrifugal force is insufficient to balance the pressure due to the greater depth at the outside of the bend. It there- fore flows inwards towards the inner side of the bend, carrying with it detritus which is deposited at the inner bank. Con- jointly with this flow inwards along the bottom and sides, the Section at M N. Fig. 108. Fig. 109. executed in concrete. It has the advantage that the rubbing surface is less in proportion to the area than in any other form. Wooden channels or flumes, of which there are examples on a large scale in America, are rectangular in section, and the same form is adopted for wrought and cast-iron aqueducts. Channels built with brickwork or masonry may be also rectangular, but they are often trapezoidal, and are always so if the sides are pitched with masonry laid dry. In a trapezoidal channel, let b (fig. no) l^. . % = 2£ vFwj-rzEr- "^ 1= : :3£E^f^y — J i ^■5^vjYjQS2 nanrrmfei YrTflPj:£-'pr~C Concrete Fig. no. be the bottom breadth, 6 the top breadth, d the depth, and let the slope of the sides be n horizontal to 1 vertical. Then the area of section is fl = {b+nd)d — (b — nd)d, and the wetted perimeter X = b+2d V(» ! + l). When a channel is simply excavated in earth it is always originally trapezoidal, though it becomes more or less rounded in course of time. The slope of the sides then depends on the stability of the earth, a slope of 2 to 1 being the one most commonly adopted. Figs, in, 112 show the form of canals excavated in earth, the former being the section of a navigation canal and the latter the section of an irrigation canal. §110. Channels of Circular Section. — The following short table facilitates calculations of the discharge with different depths of water in the channel. Let r be the radius of the channel section; then for a depth of water = «r, the hydraulic mean radius is /xr and the area of section of the waterway vr 2 , where k, m. and v have* the following values : — Depth of water in ) _ terms of radius . . ) ~ .01 •OS .10 ■IS .20 ■25 ■30 ■3S .40 •45 •SO •S5 .60 • 65 .70 •75 .80 •85 .90 ■95 1.0 Hydraulic mean depth ) _ in termsof radius . S .00668 .0321 ■0523 .0963 .1278 ■ 1574 ■ I8S2 .2142 .242 .269 ■ 293 .320 ■343 ■ 365 .387 .408 .429 ■ 449 .466 .484 ■ Soo Waterway in terms of ( v _ square of radius . . ) .00189 .0211 •0598 .1067 .i6si .228 .294 •370 ■450 ■S3 2 .614 .709 ■795 .885 ■979 I-C75 I-I75 1.276 I-37I 1.470 1. 571 AND CANALS] HYDRAULICS 73 § in. Egg-Shaped Channels or Sewers. — In sewers for discharging | could be found satisfying the foregoing conditions. To render storm water and house drainage the volume of flow is extremely variable ; and there is a great liability for deposits to be left when the flow is small, which are not removed during the short periods when the flow is large. The sewer in consequence becomes choked. a given discharge Oco y/ x, amount of excavation will the least wetted perimeter. In Bank In Cutti Fig. i ii. — Scale 20 ft. = 1 in. Fig. 112. — Scale 80 ft. = 1 in. To obtain uniform scouring action, the velocity of flow should be constant or nearly so ; a complete uniformity of velocity cannot be obtained with any form of section suitable for sewers, but an ap- proximation to uniform velocity {s obtained by making the sewers of oval section. Various forms of oval have been suggested, the simplest being one in which the radius of the crown is double the radius of the invert, and the greatest width is two- thirds the height. The section of such a sewer I is shown in fig. 113, the numbers marked on the figure being proportional numbers. § 112. Problems on Channels in which the Flow is Steady and at Uniform Velocity. — The general equations given in §§ 96, 98 are f = a(i+/S/m); (1) fi;2/2g =mi; (2) Fig- "3- Q = Qp. (3) Problem I. — Given the transverse section of stream and dis- charge, to find the slope. From the dimensions of the section find it and m; from (1) find f, from (3) find v, and lastly from (2) find i. Problem II. — Given the transverse section and slope, to find the discharge. Find v from (2), then Q from (3). Problem III. — Given the discharge and slope, and either the breadth, depth, or general form of the section of the channel, to determine its remaining dimensions. This must generally be solved by approximations. A breadth or depth or both are chosen, and the discharge calculated. If this is greater than the given discharge, the dimensions are reduced and the discharge recalculated. Since m lies generally between the limits m = d and m = \d, where j d is the depth of the stream, and since, moreover, the velocity varies as V (m) so that an error in the value of m leads only to a much less error in the value of the velocity calculated from it, we may proceed thus. Assume a value for m, and calculate v from it. Let i'i be this first approximation to v. Then Q/i'i is a first approxi- mation to SI, say fii. With this value of design the section of the channel ; calculate a second value for m ; calculate from it a second _^___ value of v, and from that a 7 i\ " ~ ' i 7 second value for Q. Repeat the process till the succes- sive values of m approxi- mately coincide. § 113. Problem IV. Most Economical Form of Channel p for given Side Slopes. — Sup- 4- pose the channel is to be trapezoidal in section (fig. 114), and that the sides are to have a given slope. Let the longitudinal slope of the stream be given, and also the mean velocity. An infinite number of channels the problem determinate, let it be remembered that, since for other things being the same, the be least for that channel which has Let d be the depth and b the bottom width of the channel, and let the sides slope n horizontal to I vertical (fig. 114), then tt = (b+nd)d; X-=i+2dV(re 2 + i). Both fi and x are to be minima. Differentiating, and equating to zero. (db/dd+n)d+b+nd = o, <26/; EF = EH=c; and EG=d. fi = area AEB+BEC+CED, = ac-\-\od. X = 2a+b. Putting these values in (1), ac-\-\bd={a J r\b)d; and hence c = d. E 7D IB. Fig. 115. That is, EF, EG, EH are all equal, hence a semicircle struck io the depth of the stream will pass a --&.... from E with radius equal through F and H and be tangential to the sides of the channel. To draw the channel, describe a semicircle on a' horizontal line with , radius = depth of channel. k- -b- The bottom will be a Fig. 116. horizontal tangent of that semicircle, and the sides slopes. The above result may be obtained thus (fig. 116) :- tangents drawn at the required side x — b-{-2djs\n p. U = d(b+d cot p); il/d = b+d cot P; i2ld? = b/d+cotp. From (1) and (2), X = fi/ = k 2 ds 1 =:kHdx'-+dy*) and dx = kdyH {f-h?). Integrating, x-k \oge\y-\- V(y" — fe 1 ))+constant ; and, since y = b, ! 2 when x = o, .r = felog,[iy+V(y a -fc 2 )}/U&+va = o. The mass of fluid passing through the element of section w, in 8 seconds, is (G/g)wv8, and its kinetic energy is (G/2g)uv 3 8. For the whole section, the kinetic energy of the mass A0B0C0D0 passing in 8 seconds is (G0/2g)2«f s - (Gt9/2g)2a)(«o 3 +3«o 2 Jf+3«oie' 2 +w 3 ), = (Gt9/2£){»o 3 fl+2aja> 2 (3« +Kj)}. The factor 3U0+W is equal to 2Uo+v, a quantity necessarily positive. Consequently 2*oi l3 > fioWo 3 , and consequently the kinetic energy of A0B0C0D0 is greater than (G0/2g)ftotto 3 or (G8/2g)Qu \ which would be its value if all the particles passing the section had the same velocity #0. Let the kinetic energy be taken at o( G8/2g) SW = a(G0/2g) Q«o 2 , where a is a corrective factor, the value of which was estimated by J. B. C. J. Belanger at l-i. 1 Its precise value is not of great im- portance. In a similar way we should obtain for the kinetic energy of A 1 BiCiDj the expression a(G0/2g)»Ki 3 = a(Gf?/2g)Q«i 2 , where ft, «i are the section and mean velocity at AiBj, and where a may be taken to have the same value as before without any im- portant error. Hence the change of kinetic energy in the whole mass A0B0A1B1 in 8 seconds is t(G6/2g)Q( Ml 2 -«o 2 ). (1) Motive Work of the Weight and Pressures. — Consider a small filament aodi which comes in 8 seconds to foci. The work done by gravity during that movement is the same as if the portion aoCo were carried to aiCi. Let dQ8 be the volume of aoco or a\c\, and yo, y\ the depths of do, l2g)\l\i-Wg)(xln).\ (4) Further Restriction to the Case of a Stream of Rectangular Section and of Indefinite Width. — The equation might be discussed in the form just given, but it becomes a little simpler if restricted in the way just stated. For, if the stream is rectangular, xh = Q, and if x is large compared with h, tt/x = xh/x = h nearly. Then equation (4) becomes dh/ds = ((i -r« 2 /2g*)/(i -u*/gh). (5) § 117. General Indications as to the Form of Water Surface fur- nished by Equation (5). — Let A0A1 (fig. 121) be the water surface, Fig. 121. if the stream is diminishing in depth from Bo towards Bi. If dh/ds = 0, the surface of the stream is parallel to the bed, as in cases of uniform motion. But from equation (4) dh/ds = o, if ;-(x/S2)f(w 2 /2g)=o; .". f(w 2 /2g) = (O/xH = mi, which is the well-known general equation for uniform motion, based on the same assumptions as the equation for varied steady motion now being considered. The case of uniform motion is therefore a limiting case between two different kinds of varied motion. Consider the possible changes of value of the fraction {l-W/2gih)l{l-li>lgh). As h tends towards the limit o, and consequently « is large, the numerator tends to the limit — 00. On the other hand if h = , in which case u is small, the numerator becomes equal to I. For a value H of h given by the equation l-f«72gi'H=o, H=f« 2 /2gi, we fall upon the case of uniform motion. The results just stated may be tabulated thus : — For h=o, H, >H, o, 1. Next consider the denominator, if h becomes very small, in which case u must be very large, the denominator tends to the limit — 00 . As h becomes very large and u consequently very small, the de- nominator tends to the limit 1. For h — u 2 /g, or « = V(g/»)> the denominator becomes zero. Hence, tabulating these results as before : — For h = 0, u 2 /g, > tt 2 /g, °° . the denominator becomes — 00, o, > o, 1. § 118. Case 1. — Suppose h>u?/g, and also h>H, or the depth greater than that corresponding to uniform motion. In this case dh/ds is positive, and the stream increases in depth in the direction of flow. In fig. 122 let B0B1 be the bed, CcCi a line parallel to the bed and at a height above it equal to H. By hypothesis, the surface Fig. 122. A0A1 of the stream is above C0C1, and it has just been shown that the depth of the stream increases from Bo towards Bi. But going up stream h approaches more and more nearly the value H, and there- fore dh/ds approaches the limit o, or the surface of the stream is asymptotic to C0C1. Going down stream h increases and u diminishes, thenumeratorand denominator of thefraction(i — fw 2 _/2gi/j)/(l — u'jgh) both tend towards the limit I, and dh/ds to the limit i. That is, the surface of the stream tends to become asymptotic to a horizontal line D0D1. The form of water surface here discussed is produced when the flow of a stream originally uniform is altered by the construction of a weir. The raising of the water surface above the level C0C1 is termed the backwater due to the weir. § 119. Case 2. — Suppose h>u l /g, and also hu 2 ,'g diminishes; the denominator of the frac- tion (i—t;u 2 i2gih)l{i-u'lgk-) tends to the limit zero, and con- sequently dhjds tends to co . That is, down stream A0A1 tends to a direction perpendicular to the bed. Before, however, this limit was reached the assumptions on which the general equation is based would cease to be even approximately true, and the equation would cease_ to be applicable. The filaments would have a relative motion, which would make the influence of internal friction in the fluid too important to be neglected. A stream surface of this form may be pro- duced if there is an abrupt fall in the bed of the stream (fig. 124). On the Ganges canal, as orig- inally con- structed, there were abrupt falls precisely of this kind, and it appears that the lowering of the water surface and increase of velocity which such falls occasion, for a distance of some miles up stream, was not foreseen. The result was that, the velocity above the falls being greater than was intended, the bed was scoured and considerable damage was done to the works. " When the canal was first opened the water was allowed to pass freely over the crests of the overfalls, which were laid on the level of the bed of the earthen channel; erosion of bed and sides for some miles up rapidly followed, and it soon became apparent that means must be adopted for raising the surface of the stream at those points (that is, the crests of the falls). Planks were accord- ingly fixed in the grooves above the bridge arches, or temporary weirs were formed over which the water was allowed to fall ; in some cases the surface of the water was thus raised above its normal height, causing a backwater in the channel above " (Crofton's Report on the Ganges Canal, p. 14). Fig. 125 represents in an ex- aggerated form what probably occurred, the diagram being intended Fig. 124. Fig. 125. to represent some miles' length of the canal bed above the fall. AA parallel to the cana! bed is the level corresponding to uniform motion with the intended velocity of the canal. In consequence of the presence of the ogee fall, however, the water surface would take some such form as BB, corresponding to Case 2 above, and the velocity would be greater than the intended velocity, nearly in the inverse ratio of the actual to the intended depth. By constructing a weir on the crest of the fall, as shown by dotted lines, a new water surface CC corresponding to Case 1 would be produced, and by suitably choosing the height of the weir this might be made to agree approximately with the intended level AA. § 120. Case 3. — Suppose a stream flowing uniformly with a depth hf/2. If such a stream is interfered with by the construction of a weir which raises its level, so that its depth at the weir becomes /fi>« 2 /g, then for a portion of the stream the depth h will satisfy the con- ditions hH, which are not the same as those assumed in the two previous cases. At some point of the stream above the weir the depth h becomes equal to u 2 /g, and at that point dh/ds becomes infinite, or the surface of the stream is normal to the bed. It is obvious that at that point the influence of internal friction will be too great to be neglected, and the general equation will cease to represent the true conditions of the motion of the water. It is known that, in cases such as this, there occurs an abrupt rise of the free surface of the stream, or a standing wave is formed, the conditions of motion in which will be examined presently. It appears that the condition necessary to give rise to a standing wave is that i>f/2. Now f depends for different channels on the roughness of the channel and its hydraulic mean depth. Bazin calculated the values of f for channels of different degrees of rough- ness and different depths given in the following table, and the corre- sponding minimum values of i for which the exceptional case of the production of a standing wave may occur. Slope below which a Stand- Standing Wave Formed. impossible in Slope in feet Least Depth feet per foot. per foot. in feet . ("0-002 0-262 Very smooth cemented surface 0-OOI47 < 0-003 •O98 1.0-004 •O65 ( O-O03 •394 Ashlar or brickwork . 0-OOI86 < 0-004 • 197 I 0-O06 •098 C 0-004 ■ 1-181 Rubble masonry .... 0-00235 < 0-006 •525 lo-oio •262 ro-oo6 3-478 Earth 0-00275 < 0-010 1-542 lo-OI5 •919 Standing Waves § 121. The formation of a standing wave was first observed by Bidone. Into a small rectangular masonry channel, having a slope of 0-023 ft- per foot, he admitted water till it flowed uniformly with a depth of 0-2 ft. He then placed a plank across the stream which raised the level just above the obstruction to 0-95 ft. He found that the stream above the obstruction was sensibly unaffected up to a point 15 ft. from it. At that point the depth suddenly increased from 0-2 ft. to 0-56 ft. The velocity of the stream in the part un- affected by the obstruction was 5-54 ft. per second. Above the point where the abrupt change of depth occurred w 2 = 5-54 2 = 30-7, and gh = 32-2X0-2 =6-44; hence « 2 was>g&. Just below the abrupt change of depth « = 5-54Xo-2/o-56 = i-97; « 2 = 3-88; and gh = 32-2X0-56 = 18-03; hence at this point u 2 — h$li) pounds, and the impulse in t seconds is G (/zofio — h\Q{) t second pounds. The horizontal change of momentum is the difference of the momenta of ede'd' and aba'V ; that is, (G/g)(n 1 « 1 2 -n « 2 )^ ON STREAMS AND RIVERS] HYDRAULICS 77 Hence, equating impulse and change of momentum, G(WJo-Ai«i)' = (G/g)(att! 2 -SW)<; .-. hno-h,i2i = (UiUi 2 -^ku 2 )/g. (i) For simplicity let the section be rectangular, of breadth B and depths Ho and Hi, at the two cross sections considered; then ho = jHo, and hi = jHi. Hence H„ 2 -Hi 2 = (2/g)(Hi«i 2 -Ho«o 2 ). But, since f2e«o = Bi«i, we have Wi a = «oW/Hi s , ■ H 2 -Hi 2 = (2M 2 /g)(H„ 2 /Hi-H„). (2) This equation is satisfied if H = Hi, which corresponds to the case of uniform motion. Dividing by Ho — Hi, the equation becomes (H I /H„)(H„+H,)=2«„ 2 /g; (3) .-. Hi = V(2«o 2 Ho/g+iI-Io 2 )-§Ho. (4) In Bidone's experiment 00 = 5-54, andH =o-2. Hence Hi=o-52, which agrees very well with the observed height. § 122. A standing wave is frequently produced at the foot of a weir. Thus in the ogee falls originally constructed on the Ganges canal a standing wave was observed as shown in fig. 127. The water falling over the weir crest A acquired a very high velocity on the Cultivated land and spring- ) forming declivities . . \ Wooded hilly slopes . Naked unfissured mountains Ratio of average Discharge to average Rainfall. •3 to -33 •35 to -45 ■55 to -6o Loss by Evaporation, &c, in percent of total Rainfall. 67 to 70 55 to 65 40 to 45 Fig. 127. steep slope AB, and the section of the stream at B became very small. It easily happened, therefore, that at B the depth h6, and from this the following values of the mean velocity are ob- tained : — Bottom Velocity Mean Velocity = V m . 1. Soft earth 2. Loam .... 3. Sand .... 4. Gravel 5. Pebbles 6. Broken stone, flint 7. Chalk, soft shale 8. Rock in beds . 9. Hard rock 0-25 0-50 I-OO 2-0O 3-40 4-00 5-00 6-oo 10-00 •33 •65 i-3° 2-62 4-46 5-25 656 7-87 13-12 The following table of velocities which should not be exceeded in channels is given in the Ingenieurs Taschenbuch of the Verein " Hiitte ": — Slimy earth or brown clay Clay Firm sand Pebbly bed Boulder bed . Conglomerate of slaty fragments Stratified rocks Hard rocks § 127. Regime of a River Channel. — A river channel is said to be in a state of regime, or stability, when it changes little in draught or form in a series of years. In some rivers the deepest part of the channel changes its position perpetually, and is seldom found in the same place in two successive years. The sinuousness of the river also changes by the erosion of the banks, so that in time the position of the river is completely altered. In other rivers the change from year to year is very small, but probably the regime is never perfectly stable except where the rivers flow over a rocky bed. If a river had a constant discharge it would gradually modify its bed till a permanent regime was established 9 3 it. Tijne 3-Sff: — - ym-.-- If* Fig. 131 discharged is constantly changing, and therefore the velocity, silt is deposited when the velocity decreases, and scour goes on when the velocity increases in the same place. When the scouring and silting are considerable, a perfect balance between the two is rarely established, and hence continual variations occur in the form of the river and the direction of its currents. In other cases, where the action is less violent , a tolerable balance may be established, and the deepening of the bed by scour at one time is compensated by the silting at another. In that case the general regime is permanent, though alteration is constantly going on. This is more likely to happen if by artificial means the erosion of the banks is prevented. If a river flows in soil incapable of resisting its tendency to scour it is necessarily sinuous (§ 107), for the slightest deflection of the current to either side begins an erosion which increases progres- sively till a considerable bend is formed. If such a river is straightened it becomes sinuous again unless its banks are pro- tected from scour. § 128. Longitudinal Section of River Bed. — The declivity of rivers decreases from source to mouth. In their higher parts rapid and torrential, flowing over beds of gravel or boulders, they enlarge in volume by receiving affluent streams, their slope diminishes, their bed consists of smaller materials, and finally they reach the sea. Fig. 131 shows the length in miles, and the surface fall in feet per mile, of the Tyne and its tributaries. The decrease of the slope is due to two causes. (1) The action of the transporting power of the water, carrying the smallest debris the greatest distance, causes the bed to be less stable near the mouth than in the higher parts of the river; and, as the river adjusts its slope to the stability of the bed by scouring or increasing its sinuous- ness when the slope is too great, and by silting or straightening its course if the slope is too small, the decreasing stability of the bed would coincide with a decreasing slope. (2) The increase of volume and section of the river leads to a decrease of slope; for the larger the section the less slope is necessary to ensure a given velocity. The following investigation, though it relates to a purely arbitrary case, is not without interest. Let it be assumed, to make the con- ditions definite — (1) that a river flows over a bed of uniform resist- ance to scour, and let it be further assumed that to maintain stability the velocity of the river in these circumstances is constant from source to mouth; (2) suppose the sections of the river at all points are similar, so that, b being the breadth of the river at any point, its hydraulic mean depth is ab and its section is cb"-, where a and c are constants applicable to all parts of the river; (3) let us further assume that the discharge increases uniformly in consequence of the supply from affluents, so that, if I is the length of the river from its source to any given point, the discharge there will be ^ jy % kl, where k is another — constant applicable to all points in the course of the river. Let AB (fig. 132) be the longitudinal section of the river, whose source is at A; and take A for the origin of vertical and horizontal coordinates. Let C be a point whose ordinates are x and y, and let the river at C have the breadth b, the slope i, and the velocity v. Since velocity X area of section = discharge, vcb 2 = kl, or i = V (kl/cv). Hydraulic mean depth — ab = a-4 (kl/cv). But, by the ordinary formula for the flow of rivers, mi — ty 1 ; :. i = tv 2 /m = (i'vVa)^ (c/kl). But i is the tangent of the angle which the curve at C makes with the axis of X, and is therefore = dy/dx. Also, as the slope is small, I = AC = AD =x nearly. .". dy/dx - (jti"/o) V (c/kx) ; and, remembering that v is constant, y = (2f»l/o)V(c*/*); or y 2 = constant X x ; so that the curve is a common parabola, of which the axis is hori- But as the volume zontal and the vertex at the source. This may be considered an ideal longitudinal section, to which actual rivers ap- proximate more or less, with exceptions due to the vary- ing hardness of their beds, and the irregular manner in which their volume increases. § 129. Surface Level of River. — The surface level of a river is a plane changing constantly in position from changes in the volume of water discharged, and more slowly from changes in the river bed, and the circum- stances affecting the drainage into the river. For the purposes 01 the engineer, it is important to determine (1) the extreme low water level, (2) the extreme high water or flood level, and (3) the highest navigable level. I. Low Water Level cannot be absolutely known, because a river reaches its lowest level only at rare inter- vals, and because alterations in the cultivation of the land, the drainage, tne removal of forests, the removal or erection of obstructions in the river bed, &c, gradu- ally alter the conditions of discharge. The lowest level of which records can be found is taken as the conven- tional or approximate low water level, and allowance is made for possible changes. 2. High Water or Flood Level. — The engineer assumes as the highest flood level the highest level of which records can be obtained. In forming a judgment of the data available, it must be remembered that the highest level at one point of a river is not always simultaneous Surface Mean Bottom Velocity. Velocity. Velocity. •49 •36 •26 •98 •75 •52 1-97 i-5i 1-02 4-00 3-15 2-30 5-00 4-o3 3-o8 7-28 6-io 4-90 8-oo 7-45 6-oo 14-00 12-15 10-36 AND RIVERS] HYDRAULICS 79 with the attainment of the highest level at other points., and that the rise of a river in flood is very different in different parts of its course. In temperate regions, the floods of rivers seldom rise more than 20 ft. above low-water level, but in the tropics the rise of floods is greater. 3. Highest Navigable Level. — When the river rises above a certain level, navigation becomes difficult from the increase of the velocity of the current, or from submersion of the tow paths, or from the head- way under bridges becoming insufficient. Ordinarily the highest navigable level may be taken to be that at which the river begins to overflow its banks. § 130. Relative Value of Different. Materials for Submerged Works. — That the power of water to remove and transport different materials depends on their density has an important bearing on the selection of materials for submerged works. In many cases, as in the aprons or floorings beneath bridges, or in front of locks or falls, and in the formation of training walls and breakwaters by pierres perdus, which have to resist a violent current, the materials of which the structures are composed should be of such a size and weight as to be able individually to resist the scouring action of the water. The heaviest materials will therefore be the best; and the different value of materials in this respect will appear much more striking, if it is remembered that all materials lose part of their weight in water. A block whose volume is V cubic feet, and whose density in air is w lb per cubic foot, weighs in air w\ lb, but in water only (w — 62-4.) V ft. Weight of a. Cub. Ft. in lb. In Air. In Water. Basalt Brick Brickwork .... Granite and limestone Sandstone Masonry .... 187-3 130-0 II2-0 I70-0 144-0 116-144 124-9 67-6 49-6 107-6 8i-6 53-6-81-6 river, and chained and levelled. The cross sections are referred to the line of stakes, both as to position and direction. The determina- tion of the surface slope is very difficult, partly from its extreme smallness, partly from oscillation of the water. Cunningham recom- mends that the slope be taken in a length of 2000 ft. by four simul- taneous observations, two on each side of the river. § 134. Cross Sections — A stake is planted flush with the water, and its level relatively to some point on the line of levels is determined. Then the depth of the water is determined at a series of points (if § 131. Inundation Deposits from a River. — When a river carrying silt periodically overflows its banks, it deposits silt over the area flooded, and gradually raises the surface of the country. The silt is deposited in greatest abundance where the water first leaves the river. It hence results that the section of the country assumes a peculiar form, the river flowing in a trough along the crest of a ridge, from which the land slopes downwards on both sides. The silt deposited from the water forms two wedges, having their thick ends towards the river (fig. 133). Fig. 133. This is strikingly the case with the Mississippi, and that river is now kept from flooding immense areas by artificial embankments or levees. In India, the term deltaic segment is sometimes applied to that portion of a river running through deposits formed by inunda- tion, and having this characteristic section. The irrigation of the country in this case is very easy; a comparatively slight raising of the river surface by a weir or annicut gives a command of level which permits the water to be conveyed to any part of the district. § 132. Deltas. — The name delta was originally given to the A- shaped portion of Lower Egypt, included between seven branches of the Nile. It is now given to the whole of the alluvial tracts round river mouths formed by deposition of sediment from the river, where its velocity is checked on its entrance to the sea. The characteristic feature of these alluvial deltas is that the river traverses them, not in a single channel, but in two or many bifurcating branches. Each branch has a tract of the delta under its influence, and gradually raises the surface of that tract, and extends it seaward. As the delta extends itself seaward, the conditions of discharge through the different branches change. The water. finds the passage through one of the branches less obstructed than through the others; the velocity and scouring action in that branch are increased ; in the others they diminish. The one channel gradually absorbs the whole of the water supply, while the other branches silt up. But as the mouth of the new main channel extends seaward the resistance in- creases both from the greater length of the channel and the formation of shoals at its mouth, and the river tends to form new bifurcations AC or AD (fig. 134), and one of these may in time become the main channel of the river. § 133. Field Operations preliminary to a Study of River Improve- ment. — There are required (1) a plan of the river, on which the positions of lines of levelling and cross sections are marked; (2) a longitudinal section and numerous cross sections of the river; (3) a series of gaugings of the discharge at different points and in different conditions of the river. Longitudinal Section. — This requires to be carried out with great accuracy. A line of stakes is planted, following the sinuosities of the Fig. 134. possible at uniform distances) in a line starting from the stake and perpendicular to the thread of the stream. To obtain these, a wire may be stretched across with equal distances marked on it by hang- ing tags. The depth at each of these tags may be obtained by a light wooden staff, with a disk-shaped shoe 4 to 6 in. in diameter. If the depth is great, soundings may be taken by a chain and weight. To ensure the wire being perpendicular to the thread of the stream, it is desirable to stretch two other wires similarly graduated, one above and the other below, at a distance of 20 to 40 yds. A number of floats being then thrown in, it is observed whether they pass the same graduation on each wire. For large and rapid rivers the cross section is obtained by sounding in the following way. Let AC (fig. 135) be the line on which sound- ings are required. A base line AB is measured out at right angles to AC, and ranging staves are set up at AB and at D in line with AC. A boat is allowed to drop down stream, and, at the moment it comes in line with AD, the lead is dropped, and an observer in the boat takes, with a box sextant, £ the angle AEB subtended by AB. The sounding line may have a weight of 14 lb of lead, and, if the boat drops down stream slowly, it may hang near the bottom, so that the observa- tion is made instantly. In ex- tensive surveys of the Missis- sippi observers with theodolites were stationed at A and B. The 1 I theodolite at A was directed towards C, that at B was kept on the boat. When the boat came on the line AC, the ob- server at A signalled, the sound- ing line was dropped, and the Fig. 135. observer at B read off the angle ABE. By repeating observations a number of soundings are ob- tained, which can be plotted in their proper position, and the form of the river bed drawn by connecting the extremities of the lines. From the section can be measured the sectional area of the stream SI and its wetted perimeter x; and from these the hydraulic mean depth m can be calculated. § 135. Measurement of the Discharge of Rivers. — The area of cross section multiplied by the mean velocity gives the discharge of the stream. The height of the river with reference to some fixed mark should be noted whenever the velocity is observed, as the velocity and area of cross section are different in differest states of the river. To determine the mean velocity various methods may be adopted; and, since no method is free from liability to error, either from the difficulty of the observations or from uncertainty as to the ratio of the mean velocity to the velocity observed, it is desirable that more than one method should be used. Instruments for Measuring the Velocity of Water § 136. Surface Floats are convenient for determining the surface velocities of a stream, though their use is difficult near the banks. The floats may be small balls of wood, of wax or of hollow metal, so loaded as to float nearly flush with the water surface. To render 6 B 8o HYDRAULICS [ON STREAMS A 9- B ii ll r !i il i / i i i * \v « I II ! X \ \ \ 1 ' ! \ ** 1:1 .4' them visible they may have a vertical painted stem. In experi- ments on the Seine, cork balls if in. diameter were used, loaded to float flush with the water, and provided with a stem. In A. J. C. Cunningham's observations at Roorkee, the floats were thin circular disks of English deal, 3 in. diameter and \ in. thick. For observa- tions near the banks, floats 1 in. diameter and \ in. thick were used. To render them visible a tuft of cotton wool was used loosely hxed in a hole at the centre. The velocity is obtained by allowing the float to be carried down, and noting the time of passage over a measured length of the stream. If 11 is the velocity of any float, I the time of passing over a length /, then v = l/t. To mark out distinctly the length of stream over which the floats pass, two ropes may be stretched across the stream at a distance apart, which varies usually from 50 to25oft., according to the size and rapidity of the river. In the Roorkee experiments a length of run of 50 ft. was found best for the central two- fifths of the width, and 25 ft. for the remainder, except very close to the banks, where the run was made 12J ft. only. The longer the run the less is the proportionate error of the time observations, but on the other hand the greater the deviation of the floats from a straight course parallel to the axis of the stream. To mark the precise position at which the floats cross the ropes, Cunningham used short white rope pendants, hanging so as nearly to touch the surface of the water. In this case the streams were 80 to 180 ft. in width. In wider streams the use of ropes to mark the length of run is impossible, and recourse must be had to box sextants or theodolites to mark the path of the floats. Let AB (fig. 136) be a measured base line strictly parallel to the thread of the stream, and AAi, BBi lines at right angles to AB marked out by ranging rods at Ai and Bi. Suppose observers stationed at A and B with sextants or theodolites, and let CD be the path of any float down stream. As the float approaches AAi, the observer at B keeps it on the cross wire of his instrument. The observer at A observes the instant of the float reaching the line AAi, and signals to B who then reads off the angle ABC. Similarly, as the float approaches BBi, the observer at A keeps it in sight, and when signalled to by B reads the angle BAD. The data so obtained are sufficient for plotting the path of the float and determining the distances AC, BD. The time taken by the float in passing over the measured distance may be ob- served by a chronograph, started as the float passes the upper rope or line, and stopped when it passes the lower. In Cunningham's observations two chrono- meters were sometimes used, the time of passing one end of the run being noted on one, and that of passing the other end of the run being noted on the other. The chronometers were compared immediately before the observations. In other cases a single chronometer was used placed midway of the run. The moment of the floats passing the ends of the run was signalled to a time- keeper at the chronometer by shouting. It was found quite pos- sible to count the chronometer beats to the nearest half second, and in some cases to the nearest quarter second. § 137. Sub-surface Floats. — The velocity at different depths below the surface of a stream may be obtained by sub-surface floats, used precisely in the same way as surface floats. The most usual arrange- ment is to have a large float, of slightly greater density than water, connected with a small and very light surface float. The motion of the combined arrangement is not sensibly different from that of the large float, and the small surface float enables an observer to note the path and velo- city of the sub-surface float. The in- strument is, however, not free from objection. If the large submerged float is made of very nearly the same density as water, then it is liable to be thrown upwards by very slight eddies in the water, and it does not maintain its position at the depth at which it is intended to float. On the other hand, if the large float is made sensibly heavier than water, the indicating or surface float must be made rather large, and then it to seme extent influences the motion of the submerged float. Fig. 137 shows one form of sub- surface float. It consists of a couple of tin plates bent at a right angle and soldered together at the angle. This is connected with a wooden ball at the surface by a very thin wire or cord. As the tin alone makes a heavy submerged float, it is better to attach to the tin float some pieces of wood to diminish its weight in water. Fig. 138 shows the form of submerged float used by Cunningham. It consists of a hollow metal ball connected to a slice of cork, which serves as the surface float. § 138. Twin Floats. — Suppose two equal and similar floats (fig. 139) connected by a wire. Let one float be a little lighter and the other a little heavier than water. Then the velocity of the combined Fig. 136. Fig. 138. Fig. 139. Fig. 137. floats will be the mean of the surface velocity and the velocity at the depth at which the heavier float swims, which is determined by the length of the connecting wire. Thus if v, is the surface velocity and v d the velocity at the depth to which the lower float is sunk, the velocity of the combined floats will be v = i(v s +v d ). Consequently, if v is observed, and v, determined by an experiment with a single float, Vd = 2V—V„ According to Cunningham, the twin float gives better results than the sub-surface float. § 139. Velocity Rods. — Another form of float is shown in fig. 140. This consists of a cylindrical rod loaded at the lower end so as to float nearly vertical in water. A wooden rod, with a metal cap at the bottom in which shot can be placed, answers better than anything else, and sometimes the wooden rod is made in lengths, which can be screwed together so as to suit streams of different depths. A tuft of cotton wool at the top serves to make the float more easily visible. Such a rod, so adjusted in length that it sinks nearly to the bed of the stream, gives directly the mean velocity of the whole vertical section in which it floats. § 140. Revy's Current Meter. — No in- strument has been so much used in directly determining the velocity of a stream at a given point as the screw current meter. Of this there are a dozen varieties at least. As an example of the instrument in its simplest form, Revy's meter may be selected. This is an ordinary screw meter of a larger size than usual, more carefully made, and with its I details carefully studied (figs. 141, 142). It was designed after experience in gaug- ing the great South American rivers. The screw, which is actuated by the water, is 6 in. in diameter, and is of the type of the Griffiths screw used in ships. The hollow spherical boss serves to make the weight of the screw sensibly equal to its displacement, so that friction is much reduced. On the axis aa of the screw is a worm which drives the counter. This consists of two worm wheels g and h fixed on a common axis. The worm wheels are carried on a frame attached to the pin I. By means of a string attached to / they can be pulled into gear with the worm, or dropped out of gear and stopped at any instant. A nut m can be screwed up, if necessary, to keep the counter per- manently in gear. The worm is two-threaded, and the worm wheel g has 200 teeth. Consequently it makes one rotation for 100 rota- tions of the screw, and the number of rotations up to 100 is marked by the passage of the graduations on its edge in front of a fixed index. The second worm wheel has 196 teeth, and its edge is divided into 49 divisions. Hence it falls behind the first wheel one division for a complete rotation of the latter. The number of hundreds of rota- tions of the screw are therefore shown by the number of divisions on h passed over by an index fixed to g. One difficulty in the use of the ordinary screw meter is that particles of grit, getting into the working parts, very sensibly alter the friction, and therefore the speed of the meter. Revy obviates this by enclosing the counter in a brass box with a glass face. This box is filled with pure water, which ensures a constant coefficient of friction for the rubbing parts, and prevents any mud or grit finding its way in. In order that the meter may place itself with the axis parallel to the current, it is pivoted on a vertical axis and directed by a large vane shown in fig. 142. To give the vane Fig. 140. AND RIVERS] HYDRAULICS 81 more directing power the vertical axis is nearer the screw than in ordinary meters, and the vane is larger. A second horizontal vane is attached by the screws x, x, the object of which is to allow the meter to rest on the ground without the motion of the screw being inter- fered with. The string or wire for starting and stopping the meter is counter has to be held in gear. For deep streams the meter A is suspended by a wire with a heavy lenticular weight below (fig. 144). The wire is payed out from a small winch D, with an index showing the depth of the meter, and passes over a pulley B. The meter is in gimbals and is directed by a conical rudder which keeps it facing the stream with its axis horizontal. There is an electric circuit from a battery C through the meter, and a contact is made closing the circuit every 100 revolutions. The moment the circuit closes a bell rings. By a subsidiary arrangement, when the foot of the instrument, 0-3 metres below the axis of the meter, touches the ground the circuit is also closed and the bell rings. It is easy to distinguish the continuous ring when the ground is reached from the short ring when the counter signals. A convenient winch for the wire is so graduated that if Fig. 141. carried through the centre of the vertical axis, so that the strain on it may not tend to pull the meter oblique to the current. The pitch of the screw is about 9 in. The screws at x serve for filling the meter with water. The whole apparatus is fixed to a rod (fig. 142), of a length proportionate to the depth, or for very great depths it is fixed to a weighted bar lowered by ropes, a plan invented by Revy. The instrument is generally used thus. The reading of the counter is noted, and it is put out of gear. The meter is then lowered into the water to the required position from a platform between two boats, or better from a temporary bridge. Then the counter is put into gear for one, two or five minutes. Lastly, the instrument is raised and the counter again read. The velocity is deduced from the number of rotations in unit time by the formulae given below. For surface velocities the counter may be kept permanently in gear, the screw being started and stopped by hand. § 141. The Harlacher Current Meter. — In this the ordinary counting apparatus is aban- doned. A worm drives a worm wheel, which makes an electrical contact once for each 100 rotations of the worm. This contact gives a signal above water. With this arrangement, a series of velocity observations can be made, without removing the instrument from the water, and a number of practical difficulties attending the accurate starting and stopping of the ordinary counter are entirely got rid of. Fig. 143 shows the meter. The worm wheel z makes one rotation for 100 of the screw. A pin moving the lever x makes the electrical contact. The wires b, c are led through a gas pipe B ; this also serves to adjust the meter to any required position on the wooden rod dd. The rudder or vane is shown at WH. The galvanic current acts on the electromagnet m, which is fixed in a small metal box containing also the battery. The magnet exposes and withdraws a coloured disk at an opening in the cover of the box. § 142. Amsler Laffon Current Meter. — A very convenient and accurate current meter is constructed by Amsler Laffon of Schaff- hausen. This can be used on a rod, and put into and out of gear by a ratchet. The peculiarity in this case is that there is a double ratchet, so that one pull on the string puts the counter into gear and a second puts it out of gear. The string may be slack during the action of the meter, and there is less uncertainty than when the Fig. 142. Fig. 143. set when the axis of the meter is at the water surface it indicates at any moment the depth of the meter below the surface. Fig. 144 shows the meter as used on a boat. It is a very convenient instru- ment for obtaining the velocity at different depths and can also be used as a sounding instrument. § 143. Determination of the Coefficients of the Current Meter. — Sup- pose a series of observations has been made by towing the meter in still water at different speeds, and that it is required to ascertain from these the constants of the meter. If v is the velocity of the water and n the observed number of rotations per second, let . v=a+0n (1) where a and /3 are constants. Now let the meter be towed over a measured distance L, and let N be the revolutions of the meter and t the time of transit. Then the speed of the meter relatively 10 the water is L/t = v feet per second, and the number of revolutions per second is N/t = n. Suppose m observations have been made in this way, furnishing corresponding values of v and ra, the speed in each trial being as uniform as possible, 2» = »l+«2+ . . . 2D=fl+t>2+ ■ ■ ■ 2nv = niVi+n 2 V2+ . . . 2« s = n;+«i+ . . . [2»] 2 = [»l+»2+ . . .f 82 HYDRAULICS [ON STREAMS Then for the determination of the constants a and /3 in (l), by the method of least squares — _2m 2 Sz> — S«Zra» a ~ mXn 2 -[Xnf ' m'Snv — TvTn P ~~ niZn* - [2w] 2 - In a few cases the constants for screw current meters have been determined by towing them in R. E. Froude's experimental tank in Fig. 144. which the resistance of ship models is ascertained. In that case the data are found with exceptional accuracy. § 144. Darcy Gauge or modified Pilot Tube. — A very old instru- ment for measuring velocities, invented by Henri Pitot in 1730 (Histoire de I'Acadcmie des Sciences, 1732, p. 376), consisted simply of a vertical glass tube with a right-angled bend, placed so that its mouth was normal to the direction of flow (fig. 145). The impact of the stream on the mouth of the tube balances a column in the tube, the height of which is approximately h = v 2 J2g, where v is the velocity |p] f-j ij — 11 at the depth x. Placed L '' ' with its mouth parallel to the stream the water inside the tube is nearly at the same level as the surface of the stream, and turned with the mouth down stream, the fluid sinks a depth /i'=» 2 /2g nearly, though the tube in that case interferes with the free flow of the liquid and somewhat modifies the result. Pitot expanded the mouth of the tube so as to form a funnel or bell mouth. In that case he found by experiment h = i-sv-/2g. But there is more disturbance of the stream. Darcy preferred to mak« the mouth of the tube very small to avoid interference with the stream and to check oscillations of the water column. Let the difference of level of a pair of tubes A and B (fig. 145) be taken to be h = kv 2 /2g, then k may be taken to be a corrective coefficient whose value in well-shaped instruments is very nearly unity. By placing his instrument in front of a boat towed through water Darcy found k = 1 -034 ; by placing the instrument in a stream the velocity of which had been ascertained by floats, he found k = 1 -006 ; by readings taken in different parts of the section of a canal in which a known volume of water was flowing, he found k =0-993. He believed the first value to be too high in con- sequence of the disturbance caused by the boat. The mean of the other two values is almost exactly unity {Recherches hydrauliques, Darcy and Bazin, 1865, p. 63). W. B. Gregory used somewhat differently formed Pitot tubes for which the k = 1 (Am. Soc. Mech. Eng., 1903, 25). T. E. Stanton used a Pitot tube in deter- mining the velocity of an air current, and for his instrument he found £ = 1-030 to £ = 1-032 (" On the Re- sistance of Plane Surfaces in a Current of Air," Proc. Inst. Civ. Eng., 1904, 156). One objection to the Pitot tube in its original form was the great difficulty and inconvenience of reading the height h in the imme- diate neighbourhood of the stream surface. This is obviated in the Darcy gauge, which can be removed from the stream to be read. Fig. 146 shows a Darcy gauge. It consists of two Pitot tubes having their mouths at right angles. In the instrument shown, the two tubes, formed of copper in the lower part, are united into one for strength, and the mouths of the tubes open vertically and horizon- tally. The upper part of the tubes is of glass, and they are provided with a brass scale and two verniers b, b. The whole instrument is sup- ported on a vertical rod or small pile AA, the fixing at B permitting the instrument to be adjusted to any height on the rod, and at the same time allowing free rotation, so that it can be held parallel to the current. At c is a two-way cock, which can be opened or closed by cords. If this is shut, the instrument can be lifted out of the stream for reading. The glass tubes are connected at top by a brass fixing, with a stop cock a, and a flexible tube and mouthpiece m. The use of this is as follows. If the velocity is re- quired at a point near the surface of the stream, one at least of the water columns would be below the level at which it could be read. It would be in the copper part of the instrument. Suppose then a little air is sucked out by the tube m, and the cock a closed, the two columns will be forced up an amount correspond- ing to the difference between atmospheric pressure and that in the tubes. But the difference of level will remain unaltered. When the velocities to be measured are not very small, this instru- ment is an admirable one. It requires observation only of a single linear quantity, and does not require any time observation. The law connecting the velocity and the observed height is a rational one, and it is not absolutely necessary to make any experiments on the coefficient of the instrument. If we take i> = £V(2gft), then it appears from Darcy's experiments that for a well-formed instrument k does not sensibly differ from unity. Jt gives the velocity at a definite point in the stream. The chief difficulty arises from the fact that at any given point in a stream the velocity is not absolutely constant, but varies a little from moment to moment. Darcy in some of his experiments took several readings, and deduced the velocity from the mean of the highest and lowest. § 145. Perrodil Hydrodynamometer. — This consists of a frame abed (fig. 147) placed vertically in the stream, and of a height not less than the stream's depth. The two vertical members of this frame are connected by cross bars, and united above water by a circular bar, situated in the vertical plane and carrying a horizontai 1 graduated circle ef. This whole system is movable round its axis, being suspended on a pivot at g connected with the fixed support mn. Other horizontal arms serve as guides. The central vertical rod gr forms a torsion rod, being fixed at r to the frame abed, and, passing freely upwards through the guides, it carries a horizontal AND RIVERS] HYDRAULICS »3 needle moving over the graduated circle ef. The support g, which carries the apparatus, also receives in a tubular guide the end of the torsion rod gr and a set screw for fixing the upper end of the torsion rod when necessary. The impulse of the stream of water is received on a circular disk *, in the plane of the torsion rod and the frame abed. To raise and lower the apparatus easily, it is not fixed directly to the rod mn, but to a tube kl sliding on mn. ■Suppose the apparatus arranged so that the disk x is at that level *he stream where the velocity is to be determined. The plane Fig. 146. abed is placed parallel to the direction of motion of the water. Then the disk * (acting as a rudder) will place itself parallel to the stream on the down stream side of the frame. The torsion rod will be un- strained, and the needle will be at zero on the graduated circle. If, then, the instrument is turned by pressing the needle, till the plane abed of the disk and the zero of the graduated circle is at right angles to the stream, the torsion rod will be twisted through an angle which measures the normal impulse of the stream on the disk x. That angle will be given by the distance of the needle from zero. Observation shows that the velocity of the water at a given point is not constant. It varies between limits more or less wide. When the apparatus is nearly in its right position, the set screw at g is made to clamp the torsion spring. Then the needle is fixed, and the apparatus carrying the graduated circle oscillates. It is not, then, difficult to note the mean angle marked by the needle. Let r be the radius of the torsion rod, / its length from the needle over ef to r, and a the observed torsion angle. Then the moment of the couple due to the molecular forces in the torsion rod is M=EJo/Z; where E ( is the modulus of elas- ticity for torsion, and I the polar moment of inertia of the section of the rod. If the rod is of circular section, I=Jirr 4 . Let R be the radius of the disk, and b its leverage, or the distance of its centre from the axis of the torsion rod. The moment of the pressure of the water on the disk is Fb = kb(Gl2g)vRV, where G is the heaviness of water and k an experimental coefficient. Then E ( Io// = *6(G/2g)irRV. For any given instrument, w = cV a, where c is a constant coefficient for the instrument. _ The instrument as constructed had three disks which could be used at will. Their radii and leverages were in feet Fig. 147. n\ R = 6 = 1st disk . . 0-052 0-16 2nd „ . . 0-105 0-32 3rd „ . 0-2IO o-66 For a thin circular plate, the coefficient k = i-i2. In the actual instrument the torsion rod was a brass wire 0-06 in. diameter and 6| ft. long. Supposing a measured in degrees, we get by calculation V = 0-335^Ja; 0-II5Va; 0-042V<*. Very careful experiments were made with the instrument. It was fixed to a wooden turning bridge, revolving over a circular channel of 2 ft. width, and about 76 ft 'circumferential length. An allowance was made for the slight current produced in the channel. These experiments gave for the coefficient c, in the f ormula v = cV a, 1st disk, c =0-3126 for velocities of 3 to 16 ft. 2nd ,, 0-1177 ., .. iito3} ,, 3rd „ 0-0349 .. » less than ij The instrument is preferable to the current meter in giving the velocity in terms of a single observed quantity, the angle of torsion, while the current meter involves the observation of two quantities, the number of rotations and the time. The current meter, except in some improved forms, must be withdrawn from the water to read the result of each experiment, and the law connecting the velocity and number of rotations of a current meter is less well-determined than that connecting the pressure on a disk and the torsion of the wire of a hydrodynamometer. _ The Pitot tube, like the hydrodynamometer, does not require a time observation. But, where the velocity is a varying one, and consequently the columns of water in the Pitot tube are oscillating, there is room for doubt as to whether, at any given moment of closing the cock, the difference of level exactly measures the impulse of the stream at the moment. The Pitot tube also fails to give measur- able indications of very low velocities. Processes for Gauging Streams § 146. Gauging by Observation of the Maximum. Surface Velocity. — The method of gauging which involves the least trouble is to deter- mine the surface velocity at the thread of the stream, and to deduce from it the mean velocity of the whole cross section. The maximum surface velocity may be determined by floats or by a current meter. Unfortunately the ratio of the maximum surface to the mean velo- city is extremely variable. Thus putting v„ for the surface velocity at the thread of the stream, and v m for the mean velocity of the whole cross section, v m /v has been found to have the following values: — V m /Vo De Prony, experiments on small wooden channels 0-8164 Experiments on the Seine 0-62 Destrem and De Prony, experiments on the Neva 0-78 Boileau, experiments on canals 0-82 Baumgartner, experiments on the Garonne . . o-8o Brunings (mean) 0-85 Cunningham, Solani aqueduct 0-823 8 4 HYDRAULICS [ON STREAMS AND RIVERS Various formulae, either empirical or based on some theory of the vertical and horizontal velocity curves, have been proposed for determining the ratio v m jv . Bazin found from his experiments the empirical expression "Om = Vo — 25 -4V {mi) ; where m is the hydraulic mean depth and i the slope of the stream. In the case of irrigation canals and rivers, it is often important to determine the discharge either daily or at other intervals of time, while the depth and consequently the mean velocity is varying. Cunningham {Roorkee Prof. Papers, iv. 47), has shown that, for a given part of such- a stream, where the bed is regular and of permanent section, a simple formula may be found for the variation of the central surface velocity with the depth. When once the constants of this formula have been determined by measuring the central surface velocity and depth, in different conditions of the stream, the surface velocity can be obtained by simply observing the depth of the stream, and from this the mean velocity and discharge can be calculated. Let z be the depth of the stream, and v a the surface velocity, both measured at the thread of the stream. Then v ft- n Fig. 148 divided into convenient compartments. The observations belonging to each compartment are then averaged, and the mean velocity and discharge calculated. It is obvious that, as the surface velocity is greatly altered by wind, experiments of this kind should be made in very calm weather. The ratio of the surface velocity to the mean velocity in the same vertical can be ascertained from the formulae for the vertical velocity curve already given (§ 101). Exner, in Erbkam's Zeitschrift for 1875, gave the following convenient formula. Let v be the mean and V the surface velocity in any given vertical longitudinal section, the depth of which is h v/V = (1 +0-I478V h)/{i +0-22I6V h). If vertical velocity rods are used instead of common floats, the mean velocity is directly determined for the vertical section in which the rod floats. No formula of reduction is then necessary. The observed velocity has simply to be multiplied by the area of the compartment to which it belongs. § 148. Mean Velocity of the Stream from a Series of Mid Depth Velocities. — In the gaugings of the Mississippi it was found that the mid depth velocity differed by only a very small quantity from the mean velocity in the vertical section, and it was uninfluenced by wind. If therefore a series of mid depth velocities are determined by double floats or by a current meter, they may be taken to be the mean velocities of the compartments in which they occur, and no formula of reduction is necessary. If floats are used, the method is precisely the same as that described in the last paragraph for sur- face floats. The paths of the double floats are observed and plotted, and the mean taken of those corresponding to each of the compart- ments into which the river is divided. The discharge is the sum of the products of the observed mean mid depth velocities and the areas of the compartments. § 149. P. P. Boileau's Process for Gauging Streams. — Let U be the mean velocity at a given section of a stream, V the maximum velocity, or that of the principal filament, which is generally a little below the surface, W and w the greatest and least velocities at the surface. The distance of the principal filament from the surface is generally less than one-fourth of the depth of the stream; W is a little less than V; and U lies between W and w. As the surface velocities change continuously from the centre towards the sides there are at the surface two filaments having a velocity equal to U. The deter- mination of the position of these filaments, which Boileau terms the gauging filaments, cannot be effected entirely by theory. But, for sections of a stream in which there are no abrupt changes of depth, their position can be very approximately assigned. Let A and / be the horizontal distances of the surface filament, having the velocity W, from the gauging filament, which has the velocity U, and from the bank on one side. Then A// = c 4 V{(W+2a;)/7(W T TO)!, c being a numerical constant. From gaugings by Humphreys and Abbot, Bazin and Baumgarten, the values c =0-919, 0-922 and 0-925 are obtained. Boileau adopts as a mean value 0-922. Hence, if W and w are determined by float gauging or otherwise, A can be found, and then a single velocity observation at A ft. from the filament of maximum velocity gives, without need of any reduction, the mean velocity of the stream. More conveniently W, w, and U can be measured from a horizontal surface velocity curve, obtained from a series of float observations. § 150. Direct Determination of the Mean Velocity by a Current Meter or Darcy Gauge. — The only method of determining the mean velocity at a cross section of a stream which involves no assumption of the ratio of the mean velocity to other quantities is this — a plank bridge is fixed across the stream near its surface. From this, velocities are observed at a sufficient number of points in the cross section of the stream, evenly distributed over its area. The mean of these is the true mean velocity of the stream. In Darcy and Bazin's ex- periments on small streams, the velocity was thus observed at 36 points in the cross section. When the stream is too large to fix a bridge across it, the observa- tions may be taken from a boat, or from a couple of boats with a gangway between them, anchored successively at a series of points across the width of the stream. The position of the boat for e=vm series of observations is fixed by angular observations to a base line on shore. § 151. A. R. Harlacher's Graphic Method of determining the Dis- charge jrom a Series of Current Meter Observations. — Let ABC (fig. 149) be the cross section of a river at which a complete series of *p5 Fig. 149. current meter observations have been taken. Let I., II., VI ... be the verticals at different points of which the velocities were men ^uted. HYDRAULIC MACHINES! HYDRAULICS »5 Suppose the depths at I., II., III., . . . (fig. 149), set off as vertical ordinates in fig. 150, and on these vertical ordinates suppose the velocities set off horizontally at their proper depths. Thus, if v is the measured velocity at the depth h from the surface in fig. 149, on vertical marked III., then at III. in fig. 150 take cd = h and ac=v. Then d is a point in the vertical velocity curve for the vertical III., and, all the velocities for that ordinate being similarly set off, the curve can be drawn. Suppose all the vertical velocity curves I. . . . V. (fig. 150), thus drawn. On each of these figures draw verticals corresponding to veloci- [ R m V 0> 1TMI 9 f ^ y //«• 1/ V which a Fig. 150.' ties of x, 2x, i,x . . . ft. second. Then for cd at III. (fig. the depth at which a velocity of 2x ft. per second existed on the vertical III. in fig. 149 and if cd is set off at III. in fig. 149 it gives a point in a curve passing through points of the section where the velocity was 2x ft. per second. Set off on each of the verticals in fig. 149 all the depths thus found in the corresponding diagram in fig. 150. Curves drawn through the corresponding points on the verticals are curves of equal velocity. The discharge of the stream per second may be regarded as a solid having the cross section of the river (fig. 149) as a base, and cross Left bank- out in this way. The upper figure shows the section of the river and the positions of the verticals at which the soundings and gaugings were taken. The lower gives the curves of equal velocity, worked out from the current meter observations, by the aid of vertical velocity curves. The vertical scale in this figure is ten times as great as in the other. The discharge calculated from the contour curves is 14-1087 cubic metres per second. In the lower figure some other interesting curves are drawn. Thus, the uppermost dotted curve is the curve through points at which the maximum velocity was found ; it shows that the maximum velocity was always a little below the surface, and at a greater depth at the centre than at the sides. The next curve shows the depth at which the mean velocity for each vertical was found. The next is the curve of equal velocity corre- sponding to the mean velocity of the stream; that is, it passes through points in the cross section where the velocity was identical with the mean velocity of the stream. Hydraulic Machines § 152. Hydraulic machines may be broadly divided into two classes: (1) Motors, in which water descending from a higher to a lower level, or from a higher to a lower pressure, gives up energy which is available for mechanical operations; (2) Pumps, in which the energy of a steam engine or other motor is expended in raising water from a lower to a higher level. A few machines such as the ram and jet pump combine the functions of motor Riqht bank . s S <» =• s S Sfc SS S5 ss ♦•08 4-80 6-66 7-30 9-2* 9-80 H-82 12-30 l*-fl 14-80 J6-92 17-30 SSI 19-80 22-15 22-30 24.-80 Discharge per Second = Q = 14-1087 cui> - m Curves of ean-aX velocity. 27-30 29-43 Fig. 151. sections normal to the plane of fig. 149 given by the diagrams in fig. 150. The curves of equal velocity may therefore be considered as contour lines of the solid whose volume is the discharge of the stream per second. Let ilo be the area of the cross section of the river, il u £1* ■ ■ • the areas contained by the successive curves of equal velocity, or, if these cut the surface of the stream, by the curves and that surface. Let x be the difference of velocity for which the successive curves are drawn, assumed above for simplicity at 1 ft. per second. Then the volume of the successive layers of the solid body whose volume represents the discharge, limited by successive planes passing through the contour curves, will be j*(!2o+$2i), ^(fii-Fty, and so on. Consequently the discharge is Q=*U(Qb+Q»)+Qi=0!+ -•- +Q»-i}. The areas I2o, Q t . . . are easily ascertained by means of the polar planimeter. A slight difficulty arises in the part of the solid lying above the last contour curve. This will have generally a height which is not exactly x, and a form more rounded than the other layers and less like a conical frustum. The volume of this may be estimated separately, and taken to be the area of its base (the area tt») multiplied by i to \ its height. Fig. 151 shows the results of one of Harlacher's gaugings worked' and pump. It may be noted that constructively pumps are essentially reversed motors. The reciprocating pump is a re- versed pressure engine, and the centrifugal pump a reversed turbine. Hydraulic machine tools are in principle motors com- bined with tools, and they now form an important special class. Water under pressure conveyed in pipes is a convenient and economical means of transmitting energy and distributing it to many scattered working points. Hence large and important hydraulic systems are adopted in which at a central station water is pumped at high pressure into distributing mains, which convey it to various points where it actuates hydraulic motors operating cranes, lifts, dock gates, and in some cases riveting and shearing machines. In this case the head driving the hydraulic machinery is artificially created, and it is the con- venience of distributing power in an easily applied form to distant points which makes the system advantageous. As there is some unavoidable loss in creating an artificial head this system is most suitable for driving machines which work intermittently 86 HYDRAULICS [IMPACT AND REACTION (see Power Transmission). The development of electrical methods of transmitting and distributing energy has led to the utilization of many natural waterfalls so situated as to be useless without such a means of transferring the power to points where it can be conveniently applied. In some cases, as at Niagara, the hydraulic power can only be economically developed in very large units, and it can be most conveniently subdivided and distributed by transformation into electrical energy. Partly from the development of new industries such as paper-making from wood pulp and electro-metallurgical processes, which require large amounts of cheap power, partly from the facility with which energy can now be transmitted to great distances electrically, there has been a great increase in the utilization of water-power in countries having natural waterfalls. According to the twelfth census of the United States the total amount of water-power reported as used in manufacturing establishments in that country was 1,130,431 h.p. in 1870; 1,263,343 h.p. in 1890; and 1,727,258 h.p. in 1900. The increase was 8-4% in the decade 1870-1880, 3-1% in 1880-1890, and no less than 36-7% in 1890-1900. The increase is the more striking because in this census the large amounts of hydraulic power which are transmitted electrically are not included. XII. IMPACT AND REACTION OF WATER § 153- When a stream of fluid in steady motion impinges on a solid surface, it presses on the surface with a force equal and opposite to that by which the velocity and direction of motion of the fluid are changed. Generally, in problems on the impact of fluids, it is necessary to neglect the effect of friction between the fluid and the surface on which it moves. During Impact the Velocity of the Fluid relatively to the Surface on ■which it impinges remains unchanged in Magnitude. — Consider a mass of fluid flowing in contact with a solid surface also in motion, the motion of both fluid and solid being estimated relatively to the earth. Then the motion of the fluid may be resolved into two parts, one a motion equal to that of the solid, and in the same direction, the other a motion relatively to the solid. The motion which the fluid has in common with the solid cannot at all be influenced by the con- tact. The relative component of the motion of the fluid can only be altered in direction, but not in magnitude. The fluid moving in contact with the surface can only have a relative motion parallel to the surface, while the pressure between the fluid and solid, if friction is neglected, is normal to the surface. The pressure therefore can only deviate the fluid, without altering the magnitude of the relative velocity. The unchanged common component and, combined with it, the deviated relative component give the resultant final velocity, which may differ greatly in magnitude and direction from the initial velocity. From the principle of momentum, the impulse of any mass of fluid reaching the surface in any given time is equal to the change of momentum estimated in the same direction. The pressure between the fluid and surface, in any direction, is equal to the change of momentum in that direction of so much fluid as reaches the surface in one second. If Pa is the pressure in any direction, m the mass of fluid impinging per second, v a the change of velocity in the direction of Pa due to impact, then Pa=mv a - If ;'i (fig. 152) is the velocity and direction of motion before impact, v* that after impact, then v is the total change of motion due to impact. The resultant pressure of the fluid on the surface is in the direction of », and is equal to v multiplied by the mass impinging per second. That is, putting ' P for the resultant pressure, P = mn. Let P be resolved into two components, N and T, normal and tangential to the direction of motion of the solid on which the fluid impinges. Then N is a lateral force producing a pressure on the supports of the solid, T is an effort which does work on the solid. If u is the velocity of the solid, Tm is the work done per second by the fluid in moving the solid surface. Let Q be the volume, and GQ the weight of the fluid impinging per second, and let Vi be the initial velocity of the fluid before striking the surface. Then GQ>i 2 /2g is the original kinetic energy of Q cub. ft. oi fluid, and the efficiency of the stream considered as an arrange- ment for moving the solid surface is i,=T«/(GQV/2g). § 154. Jet deviated entirely in one Direction. — Geometrical Solution (fig- J53)- — Suppose a jet of water impinges on a surface ac with a velocity ab, and let it be wholly deviated in planes parallel to the figure. Also let ae be the velocity and direction of motion of the surface. Join eb; then the water moves with respect to the surface in the direction and with the velocity eb. As this relative velocity is unaltered by contact with the surface, take cd = eb, tangent to the surface at c, then cd is the relative motion of the water with respect to the surface at c. Take df equal and parallel to ae. Then/c (obtained by compounding the relative motion of water to surface and common velocity of water and surface) is the absolute velocity and direction Fig. 152. Fig. 153. of the water leaving the surface. Take ag equal and parallel to fc. Then, since ab is the initial and ag the final velocity and direction of motion, gb is the total change of motion of the water. The resultant pressure on the plane is in the direction gb. Join eg. In the triangle gae, ae is equal and parallel to df, and ag to fc. Hence eg is equal and parallel to cd. But cd = eb = relative motion of water and surface. Hence the change of motion of the water is represented in magnitude and direction by the third side of an isosceles triangle, of which the other sides are equal to the relative velocity of the water and surface, and parallel to the initial and final directions of relative motion. Special Cases § 155- (1) -4 Jet impinges on a plane surface at rest, in a direction normal to the plane (fig. 154). — Let a jet whose section is w impinge with a velocity v on a plane surface at rest, in a direction normal to the plane. The particles approach the plane, are gradually- deviated, and finally flow away parallel to the plane, having then no velocity in the original direction of the jet. The quantity of water impinging per second is uiv. The pressure on the plane, which is equal to the change of momentum per second, is P = (G/g)o»». (2) If the plane is moving in the direction of the jet with the velocity =<=w, the quantity impinging per second is w(i> =*=«). The momentum of this quantity before impact is (G/g)u(u=t=w)ii. After impact, the water still possesses the velocity =*=u in the direction of the jet; and the momentum, in that direction, of so much water as impinges in one second, after impact, is =fc(G/g)w(»=Ftt)tt. The pressure on the plane, which is the change of momentum per second, is the difference of these quantities or P = (G/g)w(t)=F«) 2 . This differs from the expression obtained in the previous case, in that the relative velocity of the water and plane v=fu is sub- stituted iorv. Theexpression maybe written P = 2XGXw(d=f u) 2 l2g, where the last two terms are the volume of a prism of water whose section is the area of the jet and whose length is the head due to the relative velocity. The pressure on the plane is twice the weight of that prism of water. The work done when the plane =i— J Fig. 154. OF WATER HYDRAULICS is moving in the same direction as the jet is Pu = {G/g)u{v-ufu foot-pounds per second. There issue from the jet w cub. ft. per second, and the energy of this quantity before impact is (G/2g)wz> 3 . The efficiency of the jet is therefore 17 = 2 (v — u^n/v 3 . The value of u which makesthisa maximum isfound by differentiating and equating the differential coefficient to zero : — d-qjclu = 2 (v 2 - \vu +3» 2 )/i' 3 = o ; .'. u =v or jf. The former gives a minimum, the latter a maximum efficiency. Putting w = \v in the expression above, t) max. = s 3 7 . (3) If, instead of one plane moving before the jet, a series of planes are introduced at short intervals at the same point, the quantity of water impinging on the series will be wv instead of a(v-u), and the whole pressure = (G/g)wti(o-tt)- The work done is (G/g)avu (v-u). The efficiency 7;=-- (G!g)o>vu(v-u)-i-(Gl2g)uv* = 2u(v-u)/v 2 . This be- comes a maximum for d-qjdu = 2{v-2u)=o, or M = J», and the ?) = §. This result is often used as an approximate expression for the velocity of greatest efficiency when a jet of water strikes the floats of a water wheel. The work wasted in this case is half the whole energy of the jet when the floats run at the best speed. § T 56- (4) Case of a Jet impinging on a Concave Cup Vane, velocity of water », velocity of vane in the same direction u (fig. 155), weight impinging per second = Gw(v - u). If the cup is hemispherical, the water leaves the cup in a direction parallel to the jet. Its relative velocity is v-u when ap- proaching the cup, and -(»-«) when leaving it. Hence its absolute velocity when leaving the cup is u - (v - u) = 2u-v. The change of momentum per second = (G/g)w(i>-tt) \v- (2U-V)\ = 2(G/g)w(fl-K) 2 . Comparing this with case 2, it is seen that the pressure on a hemispherical cup is double that on a flat plane. p IG jcc The work done on the cup = 2(G/g)u (v-u) 2 u foot- pounds per second. The efficiency of the jet is greatest when z> = 3«; in that case the efficiency = \§. If a series of cup vanes are introduced in front of the jet, so that the quantity of water acted upon is us instead of u>(v-u), then the whole pressure on the chain of cups is (G/g)wi>Si>-(2tt-2))| = 2(G/g)uv(v-u). In this case the efficiency is greatest when t> = 2«, and the maximum efficiency is unity, or all the energy of the water is expended on the cups. §157- (5) Caseof a FlatVane oblique to the Jet (fig.156). — Thiscase presents some difficulty. The water spreading on the plane in all 87 2u Fig. 156. directions from the point of impact, different particles leave the plane with different absolute velocities. Let AB = v = velocity of water, AC = m = velocity of plane. Then, completing the parallelogram, AD represents in magnitude and direction the relative velocity of water and plane. Draw AE normal to the plane and DE parallel to the plane. Then the relative velocity AD may be regarded as con- sisting of two components, one AE normal, the other DE parallel to the plane. On the assumption that friction is insensible, DE is unaffected by impact, but AE is destroyed. Hence AE represents the entire change of velocity due to impact and the direction of that change. The pressure on the plane is in the direction AE, and its amount is = mass of water impinging per second X AE. Let DAE=0, and let AD=i>. Then AE=i>, cos0; DE=u, sin 9. If Q is the volume of water impinging on the plane per second, the change of momentum is (G/g)Qiv cos 0. Let AC = w = velocity of the plane, and let AC make the angle CAE = 8 with the normal to the plane. The velocity of the plane in the direction AE = u cos 8. The work of the jet on the plane = (G/g)G> r cos 6 u cos 8. The same problem may be thus treated algebraically (fig. 157). Let BAF =a, and CAF =5. The velocity v of the water may be de- composed into AF=i> cos a normal to the plane, and FB=i> sin a parallel to the plane. Similarly the velocity of the plane =w = AC = BD can be decomposed into BG = FE = u cos 5 normal to the plane, and DG -u sin 8 parallel to the plane. As friction is neglected, the velocity of the water parallel to the plane is unaffected by the im- pact, but its component v cos o normal to the plane becomes after impact the same as that of the plane, that is, u cos 8. Hence the change of velocity during impact =AE=t> cos a-u cos 8. The change of momentum per second, and consequently the normal i Fig. 157. pressure on the plane is N = (G/g) Q (» cos a-«cos 8). The pressure in the direction in which the plane is moving is P = N cos 8 = (GMQ &7T0? - " COS S) C0S S ' and the work done on the P lane is P« = (G/g)0> cos a- M cos 8) u cos 8, which is the same expression as before, since AE =v r cos =» cos a-u cos 8. In one second the plane moves so that the point A (fig. 1-58) comes to C, or from the position shown in full lines to the position shown in dotted lines. If the plane remained stationary, a length AB=j; of the jet would impinge on the plane, but, since the plane moves in the same direction as the jet, only the length HB=AB-AH impinges on the plane. But AH = AC cos 8/ cos o = « cos 8/ cos a, and therefore HB=s-m cos 8/ cos a. Let w = sectional area of jet; ''[■•'' volume impinging on plane P per second = Q = w(v-u cos IG- I 5°- 8/cos a) =«(«; cos a-u cos 8)/ cos a. Inserting this in the formulae above, we get N = (v cos a-u cos 8) 2 ; (1) g cos a ' ' v ' xi cos 8/ ... (v cos a-u cos 8) 2 ; cos a ' ' cos 8/ p_G 1 g G Pm w u ^"° " (v cos a-u cos 8) J . cos a ' (2) (3) Three cases may be distinguished : — (a) The plane is at rest. Then u =0, N = (G/g)wi; 2 cos o ; and the work done on the plane and the efficiency of the jet are zero. (b) The plane moves parallel to the jet. Then 8 = 0, and P« = (G/g) au cos 2 a(v — uY, which is a maximum when u = iv. When m = |zj then Pu max. = s % (Glg)uv 3 cos 2 a, and the efficiency = ij = J cos 2 a. (c) The plane moves perpendicularly to the jet. Then S = c.o°-a; cosS=sin a; and P M =^ u «2i n _?( t , cos a -Msina) 2 . This is a maxi- mum when u = \v cos a. When u = \v cos a, the maximum work and the efficiency are the same as in the last case. § 158. Best Form of Vane to receive Water. — When water impinges normally or obliquely on a plane, it is scattered in all directions a | ter impact, and the work carried away by the water is then gener- ally lost, from the impossibility of dealing afterwards with streams of water deviated in so many directions. By suitably forming the vane, Fig. 159. however, the water may be entirely deviated in one direction, anfc the loss of energy from agitation of the water is entirely avoided. Let AB (fig. 159) be a vane, on which a jet of water impinges at the point A and in the direction AC. Take AC =n = velocity of 88 HYDRAULICS [IMPACT AND REACTION water, and let AD represent in magnitude and direction the velocity of the vane. Completing the parallelogram, DC or AE represents the direction in which the water is moving relatively to the vane. If the lip of the vane at A is tangential to AE, the water will not have its direction suddenly changed when it impinges on the vane, and will therefore have no tendency to spread laterally. On the contrary it will be so gradually deviated that it will glide up the vane in the direction AB. This is sometimes expressed by saying that the vane receives the water without shock. § 159. Floats of Poncelet Water Wheels. — Let AC (fig. 160) repre- sent the direction of a thin horizontal stream of water having the cityu. — The relative velocity = v—u. The final velocity BF (fig. 162} is found by combining the relative velocity BD=i> — u tangential to the surface with the velocity BE = u of the surface. The intensity of normal pressure, as in the last case, is (G/g)t(v — u) 2 /r. The resultant velocity v. Let AB be a curved float moving horizontally with velocity u. The relative motion of water and float is then initially horizontal, and equal to v — u. In order that the float may receive the water without shock, it is necessary and sufficient that the lip of the float at A should be tangential to the direction AC of relative motion. At the end of (v — u)/g seconds the float moving with the velocity u comes to the position A1B1, and during this time a particle of water received at A and gliding up the float with the relative velocity v — u, attains a height DE = (zj — u)-J2g. At E the water comes to relative rest. It then descends along the float, and when after 2(y—u)/g seconds the float has come to A 2 B 2 the water will again have reached the lip at Ao and will quit it tangentially, that is, in the direction CA 2 , with a relative velocity — (v — u) = — V (2gDE) acquired under the influ- ence of gravity. The absolute velocity of the water leaving the float is therefore u— (v — u) =211 — v. If u = \ v, the water will drop off the bucket deprived of all energy of motion. The whole of the work of the jet must therefore have been expended in driving the float. The water will have been received without shock and discharged without velocity. This is the principle of the Poncelet wheel, but in that case the floats move over an arc of a large circle ; the stream of water has considerable thickness (about 8 in.); in order to get the water into and out of the wheel, it is then necessary that the lip of the float should make a small angle (about 15 ) with the direction of its motion. The water quits the wheel with a little of its energy of motion remaining. § 160. Pressure on a Curved Surface when the Water is deviated wholly in one Direction. — When a jet of water impinges on a curved surface in such a direction that it is received without shock, the pressure on the surface is due to its gradual deviation from its first direction. On any portion of the area the pressure is equal and opposite to the force required to cause the deviation of so much water as rests on that surface. In common language, it is equal to the centrifugal force of that quantity of water. Case I. Surface Cylindrical and Stationary. — Let AB (fig. 161) be the surface, having its axis at O and its radius ~r. Let the water impinge at A tangentially, and quit the surface tangentially at B. Since the surface is at rest, v is both the absolute velocity of the water and the velocity relatively to the surface, and this remains un- changed during contact with the surface, because the deviating force is at each point perpendicular to the direction of motion. The water is deviated through an angle BCD=AOB=<£. Each particle of water of weight p exerts radially a centrifugal force pv-/rg. Let the thickness of the stream = t ft. Then the weight of water resting on unit of surface = Gt lb ; and the normal pressure per unit of surface = n = Gtv-/gr. The resultant of the radial pressures uni- formly distiibuted from A to B will be a force acting in the direction OC bisecting AOB, and its magnitude will equal that of a force of intensity = n, acting on the projection of AB on a plane perpendicular to the direction OC. The length of the chord AB = 2r sin \if>\ let b = breadth of the surface perpendicular to the plane of the figure. The resultant pressure on surface = R , . 4, _ Gt v 2 = 2rt> sin — X = ■2 — to 2 sin — 1 g 2 2 g r which is independent of the radius of curvature. It may be inferred that the resultant pressure is the same for any curved surface of the same projected area, which deviates the water through the same angle. Case 2. Cylindrical Surface moving in the Direction AC with Velo- Tig. 162. normalpressureR = 2(G/g)6<(f— «) 2 sin j <#>. This resultant pressure may be resolved into two components P and L, one parallel and tne other perpendicular to the direction of the vane's motion. The former is an effort doing work on the vane. The latter is a lateral force which does no work. P = R sin l = (G/g)bt(v-uy{i -cos <#>) ; L = R cos i = (G/g)bt(v — u) 2 sin. The work done by the jet on the vane is Pu = (G/g)btu(v — tt) 2 (l- cos (j>), which is a maximum when m = Jz>. This result can also be obtained by considering that the work done on the plane must be equal to the energy lost by the water, when friction is neglected. If <£ = i8o°, cos <£= — 1, 1 -cos = 2; then P = 2{G/g)bt(v-u)\ the same result as for a concave cup. § 161. Position which a Movable Plane takes in Flowing Water. — ■ When a rectangular plane, movable about an axis parallel to one of its sides, is placed in an in- definite current of fluid, it takes a position such that the resultant of the normal pres- sures on the two sides of the axis passes through the axis. If, therefore, planes pivoted so that the ratio a/b (fig. 163) is varied are placed in water, and the angle they make with the direction of the stream is observed, the position of the resultar.t of the pressures on Fig. 163. the plane is determined for different angular positions. Experiments of this kind have been made by Hagen. Some of his results are given in the following table : — 1 Larger plane. Smaller Plane. a/b = 1 -o = .-.. 4> = 9o° 0-9 7 K 72i° o-8 6o° 57° 0-7 *K 43° o-6 25° 29° o-5 13 13° 0-4 8° 6i° o-3 6i° 0-2 4° § 162. Direct Action distinguished from Reaction (Rankine, Steam Engine, § 147). The pressure which a jet exerts on a vane can be distinguished into two parts, viz. : — (1) The pressure arising from changing the direct component of the velocity of the water into the velocity of the vane. In fig. J 53. § : 54i a° cos bae is the direct component of the water's velocity, or component in the direction of motion of vane. This is changed into the velocity ae of the vane. The pressure due to direct impulse is then Pi=GQ(ab cos bae — ae)/g. ' • For a flat vane moving normally, this direct action is the only action producing pressure on the vane. (2) The term reaction is applied to the additional action due to the direction and velocity with which the water glances off the vane. It is this which is diminished by the friction between the water and the vane. In Case 2, § 160, the direct pressure is Pi = G&*(»-w)7g- That due to reaction is P 2 = - Gbt{v - m) 2 cos lg. If <£<90°, the direct component of the water's motion is not wholly converted into the velocity of the vane, and the whoU OF WATER] HYDRAULICS 8 9 Fig. 164. pressure due to direct impulse is not obtained. If <£>ao°, cos 1^ is negative and an additional pressure due to reaction is obtained § 163. Jet Propeller. — In the case of vessels propelled by a jet of water (fig. 164), driven stern wards from orifices at the side of the vessel, the water, originally at rest out- side the vessel, is drawn into the ship and caused to move with the forward velocity V of the ship. Afterwards it is projected sternwards from the jets with a velocity v relatively to the ship, or v— V relatively to the earth. If Q is the total sectional area of the jets, Shv is the quantity of water discharged per second. The momentum generated per second in a sternward direction is (G/g)Sto(t>— V), and this is equal to the forward acting reaction P which propels the ship. The energy carried away by the water = i(Gk)Q-j(v-V)\ The useful work done on the ship PV = (C/g)Sto(»-V)V. (2) Adding (1) and (2), we get the whole work expended on the water, neglecting friction: — W = i(G/g)Sto(» 2 -V 2 ). Hence the efficiency of the jet propeller is PVAV = 2V/(»+V). (3) This increases towards unity as v approaches V. In other words, the less the velocity of the jets exceeds that of the ship, and there- fore the greater the area of the orifice of discharge, the greater is the efficiency of the propeller. In the " Waterwitch " v was about twice V. Hence in this case the theoretical efficiency of the propeller, friction neglected, was about f. § 164. Pressure of a Steady Stream in a Uniform Pipe on a Plane normal to the Direction of Motion. — Let CD (fig. 165) be a plane (1) \A \Aj \ A a 1 i i^^f^S^^; '■■ — ""nl i ^/r'C' ""- x -"" — '■ I . : :_ :^IUS5= "^-=1 _i ~~^>>X'<^^ ; ■ - 1 i I i ■ \A I A! \A B 1 an expression like that for the pressure of an isolated jet on an indefinitely extended plane, with the addition of the term in brackets, which depends only on the areas of the stream and the plane. For a given plane_ the expression in brackets diminishes as fi increases. If il/oi = p, the equation (4) becomes R = Go>— ! 2g I ■)"!■ (40) _ . Cc(p-l) which is of the form R = Gco(i» 2 /2g)K, where K depends only on the ratio of the sections of the stream and plane. For example, let c=o-85, a value which is probable, if we allow that the sides of the pipe act as internal borders to an orifice. Then p Fig. 165. placed normally to the stream which, for simplicity, may be sup- posed to flow horizontally. The fluid filaments are deviated in front of the plane, form a contraction at AiAt, and converge again, leaving a mass of eddying water behind the plane. Suppose the section A0A0 taken at a point where the parallel motion has not begun to be disturbed, and A2A2 where the parallel motion is re- established. Then since the same quantity of water with the same velocity passes A0A0, A2A2 in any given time, the external forces produce no change of momentum on the mass A0A0A2A2, and must therefore be in equilibrium. If U is the section of the stream at AoAo or AjAj, and u the area of the plate CD, the area of the con- tracted section of the stream at A1A1 will be c c (il— w), where c c is the coefficient of contraction. Hence, if v is the velocity at AoAo or A2A2, and "i>i the velocity at A1A1, vU— c c v (CI — «); .". fi = vQ/c c (Q — w). ( I ) Let pa, pi, p 2 be the pressures at the three sections. Applying Bernoulli's theorem to the sections AoAo and A1A1, G + 2g G^zg' Also, for the sections A1A1 and A 2 A 2 , allowing that the head due to the relative velocity Vi—v is lost in shock: — P\ . gl 2 _^2 , b 8 , (vi-v) 2 . G + 2g G _l "2g" 1 " 2g ' (2) ■ '■po-p2 = G(v 1 -v) 2 /2g; or, introducing the value in (1), Po -p 2 = ( i( _° -,y»» (3) 2g\c c (tt-u) ) _ w Now the external forces in the direction of motion acting on the mass A0A0A2A2 are the pressures pA —pitl at the ends, and the reaction — R of the plane on the water, which is equal and opposite to the pressure of the water on the plane. As these are in equilibrium, (i>o-£ 2 )n-R=0; .•■R=G0( ° , -.)¥; ( 4 ) K- 1-176- p = 1 2 3 4 5 10 50 100 K = CO 3-66 1-75 1-29 I-IO •94 2-00 3-50 The assumption that the coefficient of contraction c c is constant for different values of p is probably only true when p is not very large. Further, the increase of K for large values of p is contrary to experience, and hence it may be inferred that the assumption that ' all the filaments have a common velocity Vi at the section A1A1 and a common velocity v at the section A2A2 is not true when the stream is very much larger than the plane. Hence, in the expression R = KGcoz/ 2 /2g, K must be determined by experiment in each special case. For a cylindrical body putting o> for the section, c c for the coefficient of contraction, c c (Q— w) for the area of the stream at A1A1, vi=vil/c c (Q— w); D2=!>n/(fi — u) ; or, putting p = il/w, Vi=vplc c (p — i), v 2 = vpl(p~i). R = KiG«D 2 /2g, K H(^ra-)H-v-n- Then where Taking c c = o-85 and p=4, Ki =0-467, a value less than before. Hence there is less pressure on the cylinder than on the thin plane. § 165. Distribution of Pressure on a Surface on which a Jet impinges normally. — The principle of momentum gives readily enough the total or resultant pressure of a jet impinging on a plane surface, but in some cases it is useful to know the distribution of the pressure. The problem in the case in which the plane is struck normally, and the jet spreads in all directions, is one of great complexity, but even in that case the maximum intensity of the pressure is easily assigned. Each layer of water flowing from an orifice is gradually deviated (fig. 166) by contact with the sur- face, and during deviation exercises a centrifugal pressure towards the axis of the jet. The force exerted by each small mass of water is normal to its path and inversely as the radius of curvature of the path. Hence the greatest pressure on the plane must be at the axis of the jet, and the pressure must decrease from the axis outwards, in some such way as is shown by the curve of pressure in fig. 167, the branches of the curve being probably asymptotic to the plane. For simplicity suppose the jet is a vertical one. Let hi (fig. 167) be the depth of the orifice from the free surface, and Vi the velocity of discharge. Then, if a; is the area of the orifice, the quantity of water impinging on the plane is obviously Q = w»i=wV(2gW; that is, supposing the orifice rounded, and neglecting the coefficient of discharge. The velocity with which the fluid reaches the plane is, however, greater than this, and may reach the value v = V (2gh) ; where h is the depth of the plane below the free surface. The external layers of fluid subjected throughout, after leaving the orifice, to the atmospheric pressure will attain the velocity v, and will flow away with this velocity unchanged except by friction. The layers towards the interior of the jet, being subjected to a pressure greater than atmospheric pressure, will attain a less velocity, and so much less as they are nearer the centre of the jet. But the pressure Fig. 166. 9° HYDRAULICS [IMPACT AND REACTION can in no case exceed the pressure i> 5 /2g or h measured in feet of water, or the direction of motion of the water would be reversed, and there would be reflux. Hence the maximum intensity of the pressure Fig. 1 68 shows the pressure curves obtained in three experiments with three jets of the sizes shown, and with the free surface level in the reservoir at the heights marked. Fig. 167. of the jet on the plane is h ft. of water. If the pressure curve is drawn with pressures represented by feet of water, it will touch the free water surface at the centre of the jet. Suppose the pressure curve rotated so as to form a solid of revolu- tion. The weight of water contained in that solid is the total pressure of the jet on the surface, which has already been deter- mined. Let V = volume of this solid, then GV is its weight in pounds. Consequently GV = (G/g)«B l »; V = 2«V(«!l)- We have already, therefore, two conditions to be satisfied by the pressure curve. Some very interesting experiments on the distribution of pressure on a surface struck by a jet have been made by J. S. Beresford (Prof. Papers on Indian Engineering, No. cccxxii.), with a view to afford information as to the forces acting on the aprons of weirs. Cylindrical jets § in. to 2 in. diameter, issuing from a vessel in which the water level was constant, were allowed to fall vertically on a brass plate 9 in. in diameter. A small hole in the brass plate communicated by a flexible tube with a vertical pressure column. Arrangements were made by which this aperture could be moved jV in. at a time across the area struck by the jet. The height of the pressure column, for each position of the aperture, gave the pressure at that point of the area struck by the jet. When the aperture was I T , I I *---t-Diaii.-99--\ »-p Distance from axis of jet in inches. Fig. 168. — Curves of Pressure of Jets impinging normally on a Plane. exactly in the axis of the jet, the pressure column was very nearly level with the free surface in the reservoir supplying the jet; that is, the pressure was very nearly v*l2g. As the aperture moved away from the axis of the jet, the pressure diminished, and it became insensibly small at a distance from the axis of the jet about equal to the dia- meter of the jet. Hence, roughly, the pressure due to the jet extends over an area about four times the area of section of the jet. Experiment i. Experiment 2. Experiment 3. Jet "475 in. diameter. Jet '988 in. diameter. Jet 19' 5 in. diameter. 8 <* • £JJ JSVS Bus™ < <3 11 •;.s P S A u 1° Hi §0.2 w (1 ' £ =S ■a !-s ^ a c « rt"— » P 53 .at» A, »- S3 "5 io.s Id 8-9 U *j C •05 41-9 ,, •08 26-9 , •1 37-5-39-5 ,, •1 41-5-41-8 ,, •13 26-8 , ■15 35 ,, •15 4i ,, • 18 26-5-26-6 , •2 33-5-37 ,, •2 40-3 ,, •23 26-4-26-5 , •25 3i ,, ■25 39-2 ,, •28 26-3-26-6 t ■3 21-27 ,, •3 37-5 27 •33 26-2 , •35 21 ,, •35 34-8 ,, •38 25-9 , •4 14 ,, •45 27 j» •43 25-5 , •45 8 42-25 •5 23 ,, •48 25 , •5 3-5 ,, •55 i8-5 ,, •53 24-5 , •55 1 ,, •6 13 ,, •58 24 •b o-5 ,, •05 8-3 ,, •63 23-3 n •t>5 ,, •7 5 ,, •68 22-5 »» •75 3 ,, •73 21-8 ,, •8 2-2 M •78 21 42-15 •«5 •95 1-6 1 26-5 J) »» H >J •«3 •88 •93 •98 1-13 1-18 1-23 1-28 i-33 1-38 1-43 1-48 i-53 1-58 1-9 20-3 19-3 18 17 13-5 12-5 io-8 9-5 8 7 6-3 5 4-3 3-5 2 As the general form of the pressure curve has been already indi- cated, it may be assumed that its equation is of the form y = ab-' 2 - (1) But it has already been shown that for jc = o, y = ft, hence a = h. To determine the remaining constant, the other condition may be used, that the solid formed by rotating the pressure curve represents the total pressure on the plane The volume of the solid is V = I 2irxydx = 2irh I „ J = (7rA/log 6 6)[-6- l2 ]J = Trh/\og e b. Using the condition already stated, 2wV (hhi) =wh/\og e b, log e b = (7r/2w) V {hjhi). Putting the value of b in (2) in eq. (1), and also r for the radius of the jet at the orifice, so that with the plane. The resultant pressure between the fluid and the plane will be a normal pressure N. The component R of this normal pressure is the resistance to the motion of the plane and the other component L is a lateral force resisted by the guides which support the plane. Obviously R = N sin ; L = N cos 0. In the case of wind pressure on a sloping roof surface, R is the horizontal and L the vertical component of the normal pres- sure. In experiments with the whirling machine it is the resistance to motion, R, which is directly measured. Let P be the pressure on a plane moved normally through a fluid. Then, for the same plane inclined at an angle tj> to its direction of motion, the resistance was found by Hutton to be R = P(sin 0)1-842 cos*. A simpler and more convenient expression given by Colonel Duchemin is R = 2P sin 2 0/(i +sin 2 <*>). Consequently, the total pressure between the fluid and plane is N=2P sin /(l+sin z ), and the lateral force is L =2P sin /(i +sin 2 Z>(D<2-d 2 )/D = v b d nearly, 6 being the breadth of the wheel between the shrouds. If, however, this quantity of water were allowed to pass on to the wheel the buckets would begin to spill their contents almost at the top of the fall. To diminish the loss from spilling, it is not only necessary to give the buckets a suitable form, but to restrict the water supply to one-fourth or one-third of the gross bucket capacity. Let m be the value of this ratio; then, Q being the supply of water per second, Q = OT Qi = ntbdv. This gives the breadth of the wheel if the water supply is known. The form of the buckets should be determined thus. The outer element of the bucket should be in the direction of motion of the water entering relatively to the wheel, so that the water may enter without splashing or shock. The buckets should retain the water as long as possible, and the width of opening of the buckets should be 2 or 3 in. greater than the thickness of the sheet of water entering. For a wooden bucket (fig. 180, A), take ab = distance between two buckets on periphery of wheel. Make ed = \ eb. and bc = % to \ ab. Join cd. For an iron bucket (fig. 180, B), take ed = \ eb; bc= lab. Draw cO making an . „ angle of lo° to 15° with — -"* -" the radius at c. On Oc take a centre giving a circular arc passing near d, and round the curve into the radial part of the bucket de. There are two ways in which the power of a water wheel is given off to the machinery driven. In wooden wheels and wheels with rigid arms, a spur or bevil wheel keyed on the axle of the turbine will transmit FlG - l8 °' the power to the shafting. It is obvious that the whole turning moment due to the weight of the water is then trans- mitted through the arms and axle of the water wheel. When the water wheel is an iron one, it usually has light iron suspension arms incapable of resisting the bending action due to the transmission of the turning effort tc the axle. In that case spur segments are bolted to one of the shrouds, and the pinion to which the power is transmitted is placed so that the teeth in gear are, as nearly as may be, on the line of action of the resultant of the weight of the water in the loaded arc of the wheel. The largest high breast wheels ever constructed were probably the four wheels, each 50 ft. in diameter, and of 125 h.p., erected by Sir W. Fairbairn in 1825 at Catrine in Ayrshire. These wheels are still working. § 181. Poncelet Water Wheel. — When the fall does not exceed 6 ft., the best water motor to adopt in many cases is the Poncelet undershot water wheel. In this the water acts very nearly in the same way as in a turbine, and the Poncelet wheel, although slightly less efficient than the best turbines, in normal conditions of working, is superior to most of them when working with a reduced supply of water. A general notion of the action of the water on a Poncelet wheel has already been given in § 159. Fig. 181 shows its construction. The water penned back between the side walls of the wheel pit is allowed to flow to the Fig. 181. wheel under a movable sluice, at a velocity nearly equal to the velocity due to the whole fall. The water is guided down a slope of 1 in 10, or a curved race, and enters the wheel without shock. Gliding up the curved floats it comes to rest, falls back, ami acquires at the point of discharge a backward velocity relative to the wheel nearly equal to the forward velocity of the wheel. Consequently it leaves the wheel deprived of nearly the whole of its original kinetic energy. Taking the efficiency at o-6o, and putting H for the available fall, h.p. for the horse-power, and Q for the water supply per second, h.p. = 0-068 QH. The diameter D of the wheel may be taken arbitrarily. It should not be less than twice the fall and is more often four times the fall. For ordinary cases the smallest convenient diameter is 14 ft. with_ a straight, or 10 ft. with a curved, approach channel. The radial TURBINES] HYDRAULICS 97 depth of buckei should be at least half the fall, and radius of curvature of buckets about half the radius of the wheel. The shrouds are usually of cast iron with flanges to receive the buckets. The buckets may be of iron | in thick bolted to the flanges with f 6 in. bolts. Let H' be the fall measured from the free surface of the head- water to the point F where the mean layer enters the wheel ; then the velocity at which the water enters is t/ = V (2gH'), and the best circumferential velocity of the wheel is V = 0-551) to o-6». The number of rotations of the wheel per second is N = V/VD. The thickness of the sheet of water entering the wheel is very im- portant. The best thickness according to experiment is 8 to 10 in. The maximum thickness should not exceed 12 to 15 in., when there is a surplus water supply. Let e be the thickness of the sheet of water entering the wheel, and b its width ; then bev = Q ; or b — Q/ev. Grashof takes e = £H, and then i=6Q/HV(2 g H). Allowing for the contraction of the stream, the area of opening through the sluice may be 1-25 be to 1-3 be. The inside width of the wheel is made about 4 in. greater than b. Several constructions have been given for the floats of Poncelet wheels. One of the simplest is that shown in figs. 181, 182 Let OA (fig. 181) be the vertical radius of the wheel. Set off OB, OD making angles of 15 with OA. Then BD may be the length of WPMBMMPMiZmd^WU/M* Fig. 182. the close breasting fitted to the wheel. Draw the bottom of the head race BC at a slope of 1 in 10. Parallel to this, at distances \e and e, draw EF and GH. Then EF is the mean layer and GH the surface layer entering the wheel. Join OF, and make OFK = 23°. Take FK = o-5 to 0-7 H. Then K is the centre from which the bucket curve is struck and KF is the radius. The depth of the shrouds must be sufficient to prevent the water from rising over the top of the float. It is JH to §H. The number of buckets is not very important. They are usually I ft. apart on the circumference of the wheel. The efficiency of a Poncelet wheel has been found in experiments to reach 0-68. It is better to take it at o-6 in estimating the power of the wheel, so as to allow some margin. In fig. 182 s; is the initial and v the final velocity of the water, IV parallel to the vane the relative velocity of the water and wheel, and V the velocity of the wheel. Turbines. § 182. The name turbine was originally given in France to any water motor which revolved in a horizontal plane, the axis being vertical. The rapid development of this class of motors dates from 1827, when a prize was offered by the Societe d'Encouragement for a motor of this kind, which should be an improvement on certain wheels then in use. The prize was ultimately awarded to Benoit Fourneyron (1802-1867), whose turbine, but little modified, is still constructed. Classification of Turbines. — In some turbines the whole available energy of the water is converted into kinetic energy before the water acts on the moving part of the turbine. Such turbines are termed Impulse or Action Turbines, and they are distinguished by this that the wheel passages are never entirely filled by the water. To ensure this condition they must be placed a little above the tail water and discharge into free air. Turbines in which part only of die available energy is converted into kinetic energy before the water enters the wheel are termed Pressure or Reaction Turbines. In these there is a pressure which in some cases amounts to half the head in the clearance space between the guide vanes and wheel vanes. The velocity with which the water enters the wheel is due to the difference between the pressure due to the head and the pressure in the clearance space. In pressure turbines the wheel passages must be continuously filled with water for good efficiency, and the wheel may be and generally is placed below the tail water level. Some turbines are designed to act normally as impulse turbines discharging above the tail water level. But the passages are so designed that they are just filled by the water. If the tail water rises and drowns the turbine they become pressure turbines with a small clearance pressure, but the efficiency is not much affected. Such turbines are termed Limit turbines. Next there is a difference of constructive arrangement of turbines, which does not very essentially alter the mode of action of the water. In axial flow or so-called parallel flow turbines, the water enters and leaves the turbine in a direction parallel to the axis of rotation, and the paths of the molecules lie on cylindrical surfaces concentric with that axis. In radial outward and inward flow turbines, the water enters and leaves the turbine in directions normal to the axis of rotation, and the paths of the molecules lie exactly or nearly in planes normal to the axis of rotation. In outward flow turbines the general direction of flow is away from the axis, and in inward flow turbines towards the axis. There are also mixed flow turbines in which the water enters normally and is discharged parallel to the axis of rotation. Another difference of construction is this, that the water may be admitted equally to every part of the circumference of the turbine wheel or to a portion of the circumference only. In the former case, the condition of the wheel passages is always the same; they receive water equally in all positions during rotation. In the latter case, they receive water during a part of the rotation only. The former may be termed turbines with complete admission, the latter turbines with partial admission. A reaction turbine should always have complete admission. An impulse turbine may have complete or partial admission. When two turbine wheels similarly constructed are placed on the same axis, in order to balance the pressures and diminish journal friction, the arrangement may be termed a twin turbine. If the water, having acted on one turbine wheel, is then passed through a second on the same axis, the arrangement may be termed a compound turbine. The object of such an arrangement would be to diminish the speed of rotation. Many forms of reaction turbine may be placed at any height not exceeding 30 ft. above the tail water. They then discharge into an air-tight suction pipe. The weight of the column of water in this pipe balances part of the atmospheric pressure, and the difference of pressure, producing the flow through the turbine, is the same as if the turbine were placed at the bottom of the fall. I. Impulse Turbines. (Wheel passages not filled, and discharging above the tail water.) (a) Complete admission. (Rare.) (b) Partial admission. (Usual.) II. Reaction Turbines. (Wheel passages filled, discharg- ing above or below the tail water or into a suction-pipe.) Always with complete admis- sion. Axial flow, outward flow, inward flow, or mixed flow. Simple turbines ; twin turbines ; compound turbines. § 183. The Simple Reaction Wheel. — It has been shown, in § 162, that, when water issues from a vessel, there is a reaction on the vessel tending to cause motion in a direction opposite to that of the jet. This principle was applied in a rotating water motor at a very early period, and the Scotch turbine, at one time much used, differs in no essential respect from the older form of reaction wheel. The old reaction wheel consisted of a vertical pipe balanced on a vertical axis, and supplied with water (fig. 183). From the bottom of the vertical pipe two or more hollow horizontal arms extended, at the ends of which were orifices from which the water was dis- charged. The reaction of the jets caused the rotation of the machine. Let H be the available fall measured from the level of the water in the ver- tical pipe to the centres e f the orifices, r the radius from the axis of rotation to the centres of the orifices, v the velocity of discharge through the jets, a the angular velocity of Fig. 183. 9 8 HYDRAULICS [TURBINES the machine. When the machine is at rest the water issues from the orifices with the velocity V (2gH) (friction being neglected). But when the machine rotates the water in the arms rotates also, and is in the condition of a forced vortex, all the particles having the same angular velocity. Consequently the pressure in the arms at the orifices is H-)-aV 2 /2g ft. of water, and the velocity of discharge through the orifices is v = tl (2gH + a 2 r 2 ). If the total area of the orifices is «, the quantity discharged from the wheel per second is Q=wD=wV(2gH+aV). While the water passes through the orifices with the velocity v, the orifices are moving in the opposite direction with the velocity ar. The absolute velocity of the water is therefore v- ar = sl (2gH+aV 2 )-ar. The momentum generated per second is (GQ/g)(i>-ar), which is numerically equal to the force driving the motor at the radius r. The work done by the water in rotating the wheel is therefore (GQ/ g)(v-ar)ar foot-pounds per sec. The work expended by the water fall is GQH foot-pounds per second. Consequently the efficiency of the motor is _ (v-ar) ar _ }V2gH+aV 2 -ar)ar V ~~ gH ~~ gH . ,|H_g 2 H 2 V2gH-faV 2 Let then T) = i-gR! 2ar+ ... which increases towards the limit I as ar increases towards infinity. Neglecting friction, therefore, the maximum efficiency is reached when the wheel has an infinitely great velocity of rotation. But this condition is impracticable to realize, and even, at practicable but high velocities of rotation, the friction would considerably reduce the efficiency. Experiment seems to show that the best efficiency is reached when w = V (2gH). Then the efficiency apart from friction is i7 = {V(2o 2 »- 2 )-ar!ar/gH =0-4i4aV 2 /gH =0-828, about 1 7 % of the energy of the fall being carried away by the water discharged. The actual efficiency realized appears to be about 60 %, so that about 21 % of the energy of the fall is lost in friction, in addition to the energy carried away by the water. § 184. General Statement of Hydrodynamical Principles necessary for the Theory of Turbines. (a) When water flows through any pipe-shaped passage, such as the passage between the vanes of a turbine wheel, the relation be- tween the changes of pressure and velocity is given by Bernoulli's theorem (§ 29). Suppose that, at a section A of such a passage, hi is the pressure measured in feet of water, Vi the velocity, and Z\ the elevation above any horizontal datum plane, and that at a section B the same quantities are denoted by h%, i> 2 , Zi. Then h-hi = (% 2 -fi 2 )/2g +Z2-Z1. (1 ) If the flow is horizontal, z 2 =Zi; and h-ht - (» 2 2 -V)/2g. (la) (b) When there is an abrupt change of section of the passage, or an abrupt change of section of the stream due to a contraction, then, in applying Bernoulli's equation allowance must be made for the loss of head in shock (§ 36). Let »i, Vt be the velocities before and after the abrupt change, then a stream of velocity i\ impinges on a stream at a velocity v 2 , and the relative velocity is vi-v^. The head lost is (t>i-t> 2 ) 2 /2g- Then equation (la) becomes hi-h = (i , i 2 -T2 5 )/2g-(i'i-f2) 2 /2g =i> 2 (j>i-%)/g. (2) To diminish as much as possible the loss of energy from irregular eddying motions, the change of section in the turbine passages must be very gradual, and the curva- ture without discontinuity. (c) Equality of A ngular Impulse and Change of Angular Momen- tum. — Suppose that a couple, the moment of which is M, acts on a body of weight W for / seconds, during which it moves from Ai to A 2 (fig. 184). Let vi be the velocity of the body at Ai, ^2 its velocity at A 2 , and let p it pi be the perpendiculars from C on Vi and Vt. Then Mt is termed the angular impulse of the couple, and the quantity is the change of angular momen- p g turn relatively to C. Then, from "*' the equality of angular impulse and change of angular momentum m = QNIg)(viprDipi), or, if the change of momentum is estimated for one second, M=(W/g)(u 2 />2-!>lpl). Let n, n be the radii drawn from C to Ai, A 2 , and let w u Wi be the components of vi, i> 2 , perpendicular to these radii, making angles (3 and a with vi, v%. Then Vi = Wi sec ft ; vi = a> 2 sec a ; pi = ri cos /3 ; p 2 = r 2 cos a. .-. M = (W/g) (u^s-wi) , (3) where the moment of the couple is expressed in terms of the radii drawn to the positions of the body at the beginning and end of a second, and the tangential components of its velocity at those points. Now the water flowing through a turbine enters at the admission surface and leaves at the discharge surface of the wheel, with its angular momentum relatively to the axis of the wheel changed. It therefore exerts a couple — M tending to rotate the wheel, equal and opposite to the couple M which the wheel exerts on the water. Let Q cub. ft. enter and leave the wheel per second, and let v>\, Vh be the tangential components of the velocity of the water at the receiv- ing and discharging surfaces of the wheel, r it r% the radii of those surfaces By the principle above, - M = (GQ/g) (wr-Wi) . (4) If a is the angular velocity of the wheel, the work done by the water on the wheel is T = Mo= (GQ/g) (it'iri-tt> 2 r 2 ) a foot-pounds per second. (5) § 185. Total and Available Fall. — Let H, be the total difference of level from the head-water to the tail-water surface. Of this total head a portion is expended in overcoming the resistances of the head race, tail race, supply pipe, or other channel conveying the water. Let i) p be that loss of head, which varies with the local conditions in which the turbine is placed. Then H=HH> P is the available head for working the turbine, and on this the calcu- lations for the turbine should be based. In some cases it is necessary to place the turbine above the tail-water level, and there is then a fall h from the centre of the outlet surface of the turbine to the tail- water level which is wasted, but which is properly one of the losses belonging to the turbine itself. In that case the velocities of the water in the turbine should be calculated for a head H-b, but the efficiency of the turbine for the head H. § 186. Gross Efficiency and Hydraulic Efficiency of a Turbine. — Let Td be the useful work done by the turbine, in foot-pounds per second, T< the work expended in friction of the turbine shaft, gearing, &c, a quantity which varies with the local, conditions in which the turbine is placed. Then the effective work done by the water in the turbine is T = T,+T ( . The gross efficiency of the whole arrangement of turbine, races, and transmissive machinery is 7,«=T d /GQH,. (6) And the hydraulic efficiency of the turbine alone is ,=T/GQH. (7) It is this last efficiency only with which the theory of turbines is concerned. From equations (5) and (7) we get r/GQH = (GQ/g) (ovi-ws)"! ; i) = {wimiliTi) algii. (8) This is the fundamental equation in the theory of turbines. In general, 1 Wi and w-i, the tangential components of the water's motion on entering and leaving the wheel, are completely inde- pendent. That the efficiency may be as great as possible, it is obviously necessary that kj 2 = o. In that case ij = ttVia/gH. (9) ari is the circumferential velocity of the wheel at the inlet surface. Calling this Vi, the equation becomes ij=WiVi/gH. (90) This remarkably simple equation is the fundamental equation in the theory of turbines. It was first given by Reiche (Turbinen- baues, 1877). § 187. General Description of a Reaction Turbine. — Professor James Thomson's inward flow or vortex turbine has been selected as the type of reaction turbines. It is one of the best in normal conditions of working, and the mode of regulation introduced is decidedly superior to that in most reaction turbines. Figs. 185 and 186 are external views of the turbine case; figs. 187 and 188 are the corresponding sections; fig. 189 is the turbine wheel. The example chosen for illustration has suction pipes, which permit the turbine to be placed above the tail- water level. The water enters the turbine by cast-iron supply pipes at A, and is discharged through two suction pipes S, S. The water 1 In general, because when the water leaves the turbine wheel it ceases to act on the machine. If deflecting vanes or a whirlpool are added to a turbine at the discharging side, then Vi may in part depend on » 2 , and the statement above is no longer true. TURBINES] HYDRAULICS 99 on entering the case distributes itself through a rectangular supply chamber SC, from which it finds its way equally to the four guide-blade passages G, G, G, G. In these passages it in equal proportions from each guide-blade passage. It consists of a centre plate p (fig. 189) keyed on the shaft aa, which passes through stuffing boxes on the suction pipes. On each side of Fig. 185. Fig. 186. Fig. 187 Fig. 18 acquires a. velocity about equal to tnat due to half the fall, and is l the centre plate are the curved wheel vanes, on which the pressure directed into the wheel at an angle of about io° or 12 with the of the water acts, and the vanes are bounded on each side by tangent to its circumference. The wheel W receives the water I dished or conical cover plates c, c. Joint-rings j, j on the cover IOO HYDRAULICS [TURBINES plates make a sufficiently water-tight joint with the casing, to prevent leakage from the guide-blade chamber into the suction pipes. The pressure near the joint rings is not very great, probably not one-fourth the total head. The wheel vanes receive the water without shock, and deliver it into central spaces, from which it flows on either side to the suction pipes. The mode of regu- lating the power of the turbine is very simple. The guide- blades are pivoted to the case at their inner ends, and they are connected by a link- work, so that they all open and close simul- taneously and equally. In this way the area of opening through the guide- blades is altered with- out materially alter- ing the angle or the other conditions of the delivery into the wheel. The guide- blade gear may be variously arranged. In this example four spindles, passing through the case, are linked to the guide- blades inside the case, and connected together by the links Fig. i Fig. 190. I, I, I on the outside of the case. A worm wheel on one of the spindles is rotated by a worm d, the motion being thus slow enough to adjust the guide-blades very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal Fig. 190 shows another arrangement of a similar turbine, with some adjuncts not shown in the other drawings. In this case the turbine rotates horizontally, and the turbine case is placed entirely below the tail water. The water is supplied to the turbine by a vertical pipe, over which is a wooden pentrough, containing a strainer, which prevents sticks and other solid bodies getting into tH turbine. The turbine rests on three foundation stones, and, the pivot for the vertical shaft being under water, there is a screw and lever ar-ange- ment for adjusting it as it wears. The vertical shaft gives motion to the machinery driven by a pair of bevel wheels. On the rigb^ are the worm and wheel for working the guide-blade gear. § 188. Hydraulic Power at Niagara. — The largest development of hydraulic power is that at Niagara. The Niagara Falls Power Company have constructed two power houses on the United States side, the first with 10 turbines of 5000 h.p. each, and the second with 10 turbines of 5500 h.p. The effective fall is 136 to 140 ft. In the first power house the turbines are twin outward flow reaction turbines with vertical shafts running at 250 revs, per minute and driving the dynamos direct. In the second power house the turbines Fig. 191. are inward flow turbines with draft tubes or suction pipes. Fig. 191 shows a section of one of these turbines. There is a balancing piston keyed on the shaft, to the under side of which the pressure due to the fall is admitted, so that the weight of turbine, vertical shaft and part of the dynamo is water borne. About 70,000 h.p. is daily distributed electrically from these two power houses. The Canadian Niagara Power Company are erecting a power house to contain -eleven units of 10,250 h.p. each, the turbines being twin inward flow reaction turbines. The Electrical Development Com- pany of Ontario are erecting a power house to contain 1 1 units of 12,500 h.p. each. The Ontario Power Company are carrying out another scheme for developing 200,000 h.p. by twin inward flow turbines of 12,000 h.p. each. Lastly the Niagara Falls Power and Manufacturing Company on the United States side have a station giving 35,000 h.p. and are constructing another to furnish 100,000 h.p. The mean flow of the Niagara river is about 222,000 cub. ft. per second with a fall of 160 ft. The works in progress if completed will utilize 650,000 h.p. and require 48,000 cub. ft. per second or 2iJ % of the mean flow of the river (Unwin, " The Niagara Falls Power Stations," Proc. Inst. Mech. Eng., 1906). § 189. Different Forms of Turbine Wheel. — The wheel of a turbine or part of the machine on which the water acts is an annular space, furnished with curved vanes dividing it into passages exactly or roughly rectangular in cross section. For radial flow turbines the wheel may have the form A or B, fig. 192, A being most usual with «■ To Fig. 192. TURBINES] HYDRAULICS 101 inward, and B with outward flow turbines. In A the wheel vanes are fixed on each side of a centre plate keyed on the turbine shaft. The vanes are limited by slightly-coned annular cover plates. In B the vanes are fixed on one side of a disk, keyed on the shaft, and limited by a cover plate parallel to the disk. Parallel flow or axial flow turbines have the wheel as in C. The vanes are limited by two concentric cylinders. Theory of Reaction Turbines. § 190. Velocity of Whirl and Velocity of Flow. — Let acb (fig. 193) be the path of the particles of water in a turbine wheel. That path will be in a plane normal to the axis of rotation in radial flow turbines, and on a cylindrical surface in axial flow turbines. At any point c of the path the water will have some velocity v, in the direction of a tangent to the path. That velocity may be resolved into two components, a whirl- FlG. I<«. ' n .£ velocity w in the direction of the wheel's rotation at the point c, and a component u at right angles to this, radial in radial flow, and parallel to the axis in axial flow turbines. This second component is termed the velocity of flow. Let t» ? , Wo, Uo be the velocity of the water, the whirling velocity and velocity of flow at the outlet surface of the wheel, and Vi, Wi, Vi the same quantities at the inlet surface of the wheel. Let a and j8 be the angles which the water's direction of motion makes with the direction of motion of the wheel at those surfaces. Then Wo = o cos£; u =v An ) / IQ \ Wi~ViCosa: tii=v; sin ay The velocities of flow are easily ascertained independently from the dimensions of the wheel. The velocities of flow at the inlet and outlet surfaces of the wheel are normal to those surfaces. Let S2„, V.i be the areas of the outlet and inlet surfaces of the wheel, and Q the volume of water passing through the wheel per second; then Using the notation in fig. 191, we have, for an inward flow turbine (neglecting the space occupied by the vanes), n =2irr<,(J ; 0,=2irriii. (12a) Similarly, for an outward flow turbine, i2 = 27rr<,d; Qi=2irnd; (126) and, for an axial flow turbine, fio=Qi = x(r 2 --ri 2 ). (12c) Relative and Common Velocity of the Water and Wheel. — There is another way of resolving the velocity of the water. Let V be the velocity of the wheel at the point c, fig. 194. Then the velocity of the water mayj^e resolved into a component V, which the water has in common with the wheel, and a component v r , which is the velocity of the water relatively to the wheel. Velocity of Flow. — It is obvious that the frictional losses of head in the wheel passages will increase as the velocity of flow is greater, that is, the smaller the wheel is made. But if the wheel works under water, the skin friction of the wheel cover increases as the diameter of the wheel is made greater, and in any case the weight of the wheel and consequently the journal friction increase as the wheel is made larger. It is therefore desirable to choose, for the velocity of flow, as large a value as is consistent with the condition that the frictional losses in the wheel passages are a small fraction of the total head. The values most commonly assumed in practice are these : — In axial flow turbines, «„ = «<= Q- I5 to0 " 2 V ( 2 be the angles the wheel vanes make with the inlet and outlet surfaces; then !>„ 2 = V (v„, ! +V„ s -2V„lVo cos 4>) I , s v> =V>ri 2 +Vi 2 -2Vi% cos 61) y ( 3) equations which may be used to determine <£ and 8. § 192. Condition determining the Angle of the Vanes at the Outlet Surface of the Wheel. — It has been shown that, when the water leaves the wheel, it should have no tangential velocity, if the effici- ency is to be as great as possible ; that is, w<, = 0. Hence, from (10), cos /3 = o, = 90°, «o = »o, and the direction of the water's motion is normal to the outlet surface of the wheel, radial in radial flow, and axial in axial flow turbines. Drawing v or u„ radial or axial as the case may be, and V,, tangential to the direction of motion, v r , parallelogram of velocities. From fig. 195, tan=v fVo = u t ,[V„; (14) but is the angle which the wheel vane makes with the outlet surface of the wheel, which is thus determined when the velocity of flow « and velocity of the wheel V„ are known. When is thus determined, ti r< , = M<,cosec <#>=V<,V(i+w,,YVo 2 )- (14a) Correction of the Angle to allow for Thickness of Vanes. — In determining , it is most convenient to calculate its value approxi- mately at first, from a value of u obtained by neglecting the thick- ness of the vanes. As, however, this angle is the most important angle in the turbine, the value should be afterwards corrected to allow for the vane thickness. Let ' = tan-Kwo/V,) = tan->(Q/Q„V,) be the first or approximate value of <£, and let t be the thickness, and n the number of wheel vanes which reach the outlet surface of the wheel. As the vanes cut the outlet surface approximately at the angle ', their width measured on that surface is t cosec $'. Hence the space occupied by the vanes on the outlet surface is For A, fig. 192, ntd„ cosec 4> 1 B, fig. 192, ntd cosec >■ (15) C, fig. 192, ntir^-n) cosec ] Call this area occupied by the vanes a. Then the true value of the clear discharging outlet of the wheel is U - w, and the true value of ito is Qliito - w) . The, corrected value of the angle of the vanes will be <2> = tan[Q/V<,(n,,-co)]. (16) § 193. Head producing Velocity with which the Water enters the Wheel. — Consider the variation of pressure in a wheel passage, which satisfies the condition that the sections change so gradually that there is no loss of head in shock. When the flow is in a hori- zontal plane, there is no work done by gravity on the water passing through the wheel. In the case of an axial flow turbine, in which the flow is vertical, the fall d between the inlet and outlet surfaces should be taken into account. Fig. 195. can be found by the 102 HYDRAULICS [TURBINES Let Vi, V„ be the velocities of the wheel at the inlet and | outlet surfaces, I V(, v the velocities of the water, m, u„ the velocities of flow, Vri,v r „ the relative velocities, hi, ho the pressures, measured in feet of water, re, r c the radii of the wheel, o the angular velocity of the wheel. At any point in the path of a portion of water, at radius r, the velocity v of the water may be resolved into a component V = ar equal to the velocity at that point of the whee', and a relative com- ponent v r - Hence the motion of the water may be considered to consist of two parts: — (a) a motion identical with that in a forced vortex of constant angular velocity a; (i) a flow along curves parallel to the wheel vane curves. Taking the latter first, fand using Bernoulli's theorem, the change of pressure due to flow through the wheel passages is given by the equation h'i+VriV^g^h'o+vJ^g; h'i —h'o = (iVo 2 — iw 2 )/2g. The variation of pressure due to rotation in a forced vortex is *"i-&"„ = (V,- s -V nearly. Inserting these values, and remembering that for an axial flow turbine V,- = V„, i) = 0, and the fall d in the wheel is to be added, For an outward flow turbine, ,-WW H ^-l(-+«)+S!]' For an inward flow turbine, § 194. Angle which the Guide-Blades make with the Circumference of the Wheel. — At the moment the water enters the wheel, the radial component of the velocity is ut, and the velocity is Vi. Hence, if 7 is the angle between the guide-blades and a tangent to the wheel y=sin~ , (ui/vi). This angle can, if necessary, be corrected to allow for the thickness of the guide-blades. § 195. Condition determining the Angle of the Vanes at the Inlet Surface of the Wheel. — The single condition necessary to be satisfied at the inlet surface of the wheel is that the water should enter the wheel without shock. This condition is satis- fied if the direction of relative motion of the water and wheel is parallel to the first element of the wheel vanes. Let A (fig. 196) be a point on the inlet sur- face of the wheel, and let Vi represent in magnitude and direc- tion the velocity of the water entering the wheel, and V,- the velocity of the wheel. Completing the parallelogram, v r , is the direction of relative motion. Hence the angle between vh and Vi is the angle 9 which the vanes should make with the inlet surface of the wheel. § 196. Example of the Method of designing a Turbine. Professor James Thomson's Inward Flow Turbine. — Let H =the available fall after deducting loss of head in pipes and channels from the gross fall ; Q = the supply of water in cubic feet per second; and 7j =the efficiency of the turbine. The work done per second is ijGQH, and the horse-power of the turbine is h.p. =i;GQH/550. If t\ is taken at 0-75, an allowance will be made for the frictional losses in the turbine, the leakage and the friction of the turbine shaft. Then h.p. = o-o85QH. The velocity of flow through the turbine (uncorrected for the space occupied by the vanes and guide -blad es) may be taken Mi=«o=0-I25V2gH, in which case about ^th of the energy of the fall is carried away by the water discharged. The areas of the outlet and inlet surface of the wheel are then 2*rcdo = 2Widi = Q/o- 1 25V (2gH). If we take r„, so that the axial velocity of discharge from the central orifices of the wheel is equal to « , we get r„ = o-3984V(Q/VH), do = To- If, to obtain considerable steadying action of the centrifugal head, ri =2r , then di =\d . Speed of the Wheel. — Let Vi=o-66V2gH, or the speed due to half the fall nearly. Then the number of rotations of the turbine per second is N = V,/27rr ; = 1 -0579V (HV H/Q) ; also V„ = Vi>-„/n=o-33V2gH. Angle of Vanes with Outlet Surface. Tan0 = «„/V„=o-i25/o-33 = -3788; = 21° nearly. If this value is revised for the vane thickness it will ordinarily become about 25 . Velocity with which the Water enters the Wheel. — The head pro- ducing the velocity is H - (Vi 2 /2g) (I + M„ 2 /Vi 2 ) +«i 2 /2g = H{i --4356(1 +0-0358) -+-0156} = 0-564611. Then the velocity is Vi = -96V 2g(-5646H) =0-721 V2gH. Angle of Guide-Blades. Sin 7 = Mi M =0-125/0-721 =0-173; y — 10° nearly. Tangential Velocity of Water entering Wheel. Wi =ViCOS y =0-7101 V 2gH. Angle of Vanes at Inlet Surface. Cot e = (o»i-Vi)/«i = (-7ioi--66)/-i25 = -40o8; 9=68° nearly. Hydraulic Efficiency of Wheel. 7/=tt>iVi/gH = -7ioiX-66X2 = 0-9373- This, however, neglects the friction of wheel covers and leakage. The efficiency from experiment has been found to be 0-75 to o-8o. Impulse and Partial Admission Turbines. § 197. The principal defect of most turbines with complete admission is the imperfection of the arrangements for working with less than the normal supply. With many forms of reaction turbine the efficiency is considerably reduced when the regulating TURBINES] HYDRAULICS 103 sluices are partially closed, but it is exactly when the supply of water is deficient that it is most important to get out of it the greatest possible amount of work. The imperfection of the regulating arrangements is therefore, from the practical point of view, a serious defect. All turbine makers have sought by various methods to improve the regulating mechanism. B. Fourneyron, by dividing his wheel by horizontal diaphragms, virtually obtained three or more separate radial flow turbines, which could be successively set in action at their full power, but the arrangement is not altogether successful, because of the spreading of the water in the space between the wheel and guide-blades. Fontaine similarly employed two concentric axial flow turbines formed in the same casing. One was worked at full power, the other regulated. By this arrangement the loss of efficiency due to the action of the regulating sluice affected only half the water power. Many makers have adopted the expedient of erecting two or three separate turbines on the same waterfall. Then one or more could be put out of action and the others worked at full power. All these methods are rather palliatives than remedies. The movable guide-blades of Professor James Thomson meet the difficulty directly, but they are not applicable to every form of turbine. C. Callon, in 1840, patented an arrangement of sluices for axial or outward flow turbines, which were to be closed success- ively as the wat# supply diminished. By preference the sluices were closed by pairs, two diametrically opposite sluices forming a pair. The water was thus admitted to opposite but equal arcs of the wheel, and the forces driving the turbine were sym- metrically placed. As soon as this arrangement was adopted, Fig. 197. a modification of the mode of action of the water in the turbine became necessary. If the turbine wheel passages remain full of water during the whole rotation, the water contained in each passage must be put into motion each time it passes an open portion of the sluice, and stopped each time it passes a closed portion of the sluice. It is thus put into motion and stopped twice in each rotation. This gives rise to violent eddying motions and great loss of energy in shock. To prevent this, the turbine wheel with partial admission must be placed above the tail water, and the wheel passages be allowed to clear themselves of water, while passing from one open portion of the sluices to the next. But if the wheel passages are free of water when they arrive at the open guide passages, then there can be no pressure other than atmospheric pressure in the clearance space between guides and wheel. The water must issue from the sluices with the whole velocity due to the head; received on the curved vanes of the wheel, the jets must be gradually deviated and discharged with a small final velocity only, precisely in the same way as when a single jet strikes a curved vane in the free air. Turbines of this kind are therefore termed turbines of free deviation. There is no variation of pressure in the jet during the Whole time of its action on the wheel, and the whole energy of the jet is im- parted to the wheel, simply by the impulse due to its gradual change of momentum. It is clear that the water may be admitted in exactly the same way to any fraction of the circumference at pleasure, without altering the efficiency of the wheel. The diameter of the wheel may be made as large as convenient, and the water admitted to a small fraction of the circumference only. Then the number of revolutions is independent of the water velocity, and may be kept down to a manageable value. § 198. General Description of an Impulse Turbine or Turbine with Free Deviation. — Fig. 197 shows a general sectional elevation of a Girard turbine, in which the flow is axial. The water, . admitted above a horizontal floor, passes down through the annular wheel containing the guide- blades G, G, and thence into the re- volving wheel WW. The revolving wheel is fixed to a hollow shaft suspended from the pivot p. The solid internal shaft ss is merely a fixed column supporting the pivot. The advantage of this _ is that the pivot is tIG - *9 8 - accessible for lubrication and adjustment. B is the mortise bevel wheel by which the power of the turbine is given off. The sluices are worked by the hand wheel h, which raises them successively, in a way to be described presently, d, d are the sluice rods. Figs. iq8, 199 show the sectional form of the guide-blade chamber and wheel and the curves of the wheel vanes and guide-blades, when drawn on a plane de- velopment of the cylin- ' drical section of the wheel; a, a, a are the sluices for cutting off the water; b, b, b are apertures by which the entrance or exit of air is facilitated as the buckets empty and fill. Figs. 200, 201 show the guide-blade gear, a, a, a are the sluice rods as before. At the top of each sluice rod is a small block c, having a projecting tongue, which slides in the groove of the circular cam plate d, d. This circular plate is sup- ported on the frame e, and revolves on it by means of the flanged rollers/. Inside, at the top, the cam plate is toothed, and gears into a spur pinion connected with the hand wheel h. At gg is an inclined groove Or shunt. When the tongues of the blocks c, c arrive at g, they slide up to a second groove, or the reverse, according as the cam plate is revolved in one direction or in the other. As this operation takes place with each Fig. 199. 104 HYDRAULICS [TURBINES sluice successively, any number of sluices can be opened or closed as desired. The turbine is of 48 horse power on 5' 12 ft. fall, and the supply of water varies from 35 to 112 cub. ft. per second. The a a a Fig. 200. efficiency in normal working is given as 73 %. The mean diameter of the wheel is 6 ft., and the speed 27-4 revolutions per minute. As an example of a partial admission radial flow impulse turbine, a 100 h.p. turbine at Immenstadt may be taken. The fall varies from 538 to 570 ft. The external diameter of the wheel is 4i ft., and *fcA QF Q = Q=gD^ gm a 11 Fig. 201. its internal diameter 3 ft. 10 in. Normal speed 400 revs, per minute. Water is discharged into the wheel by a single nozzle, shown in fig. 202 with its regulating apparatus and some of the vanes. The water enters the wheel at an angle of 22° with the direc- tion of motion, and the final angle of the wheel vanes is 20 . The efficiency on trial was from 75 to 78%. § 199. Theory of the Impulse Turbine. — The theory of the im- pulse turbine does not essen- tially differ from that of the re- action turbine, except that there is no pressure in the wheel oppos- ing the discharge from the guide-blades. Hence the velocity with which the water enters the wheel is simply i\=o-96V2g(H-h), where h is the height of the top of the wheel above the tail water. If the hydropneumatic system is used, then 6=0. Let Q m be the maximum supply of water, n, r 2 the internal and external radii of the wheel at the inlet surface; then tti=Qm/ta-W -ri*)l. The value of m may be about o-45V2g(H-h), whence n, h can be determined. The guide-blade angle is then given by the equation , sin y = M; Ivi =0-45/0-94 = -48; 7 = 29°. The value of «; should, however, be corrected for the space occupied by the guide-blades. The tangential velocity of the enter ing water is # Wi=Vi COS7'=0-82V2g(H-t)). The circumferential velocity of t he wheel m ay be (at mean radius) V< =o-5V2g(H-h). Fig. 202. Hence the vane angle at inlet surface is given by the equation cote = (a)i-Vi)/«i = (o-82-o-5)/o-45 = -7i; = 55°- t The relative velocity of the water striking the vane at the inlet edge is v,i=m cosec0 = l-22«j. This relative velocity remains unchanged during the passage of the water over the vane; conse- quently the relative velocity at the point of discharge is v T0 = 1 -222*1. Also in an axial flow turbine V = V«. If the final velocity of the water is axial, then cos = V,,/f r( , = Vi/p,i =0-5/(1 -22 Xo-45)=cos24° 23'. This should be corrected for the vane thickness. Neglecting this, Wo=iVosin<£=tVisin <£ = «.- cosec sin = o-5«,-. The discharging area of the wheel must therefore be greater than the inlet area in the ratio of at least 2 to 1. In some actual turbines the ratio is 7 to 3. This greater outlet area is obtained by splaying the wheel, as shown in the section (fig. 199). § 200. Pelton Wheel. — In the mining district of California about i860 simple impulse wheels were used, termed hurdy-gurdy wheels. The wheels rotated in a vertical plane, being supported on a hori- zontal axis. Round the circumference were fixed flat vanes which were struck normally by a jet from a nozzle of size varying with the head and quantity of water. Such wheels have in fact long been used. They are not efficient, but they are very simply constructed. Then attempts were made to improve the efficiency, first by using hemispherical cup vanes, and then by using a double cup vane with a central dividing ridge, an arrangement invented by Pelton. In this last form the water from the nozzle passes half to each side of the wheel, just escaping clear of the backs of the advancing buckets. Fig. 203 shows a Pelton vane. Some small modifications have been made by other makers, but they are not of any great importance. Fig. 204 shows a complete Pelton wheel with frame and casing, supply pipe and nozzle. Pelton wheels have been very largely used in America and to some extent in Europe. They are extremely simple and easy to construct or repair and on falls of 100 ft. or more are very efficient. The jet strikes tangentially to the mean radius of the buckets, and the face of the buckets is not quite radial but at right angles to the direction of the jet at the point of first impact. For greatest efficiency the peripheral velocity of the wheel at the mean radius of the buckets should be a little less than half the velocity of the jet. As the radius of the wheel can be taken arbitrarily, the number of revolutions per minute can be accommodated to that of the machinery to be driven. Pelton wheels have been made as small Fig. 203. I MIL.'l , JJp Ifk \ 1 JJI ■ FlG.204. as 4 in. diameter, for driving sewing machines, and as large as 24 ft. The efficiency on high falls is about 80 %. - When large power is required two or three nozzles are used delivering on one wheel. The width of the buckets should be not less than seven times the diameter of the jet. At the Comstock mines, Nevada, there is a 36-in. Pelton wheel made of a solid steel disk with phosphor bronze buckets riveted to the rim. The head is 2100 ft. and the wheel makes 1 150 revolutions per minute, the peripheral velocity being 180 ft. per sec. With a J-in. nozzle the wheel uses 32 cub. ft. of water per minute and develops 100 h.p. At the Chollarshaft, Nevada, there are six Pelton wheels on a fall of 1680 ft. driving electrical generators. With f-in. nozzles each develops 125 h.p. § 201. Theory of the Pelton Wheel. — Suppose a jet with a velocity v strikes tangentially a curved vane AB (fig. 205) moving in the same direction with the velocity u. The water will flow over the vane with the relative velocity v — u and at B will have the tangential TURBINES] HYDRAULICS 105 Fig. 205. relative velocity v — u making .an angle o with the direction of the vane's motion. Combining this with the velocity w of the vane, the absolute velocity of the water leaving the vane will bew = Be. The com- ponent of w in the direction of motion of the vane is Bo = BJ— ab = « — (»—«) cos a. Hence if Q is the quantity of water reaching the vane per second the change of momentum per second in the direction of the vane's motion is (GQ/g) [» — {« — (v-u)cos o,[] = (GQ/g)(p-«) (I + cos a). If a = 0°, cos = 1, and the change of momentum per second, which is equal to the effort driving the vane, is P =2 (GQ/g) (»-«)! The work done on the vane is Pu = 2(GQ!g)(v-u)u. If a series of vanes are inter- posed in succession, the quantity of water imping- ing on the vanes per second is the total discharge of the nozzle, and the energy expended at the nozzle is GQtf 2 /2g. Hence the efficiency of the arrangement is, when a = o°, neglecting friction, t)=2Pk/GQ!/ 2 =4(ii-w)m/ii 2 , which is a maximum and equal to unity if « = §». In that case the whole energy of the jet is usefully expended in driving the series of vanes. In practice o cannot be quite zero or the water leaving one vane would strike the back of the next advancing vane. Fig. 203 shows a Pelton vane. The water divides each way, and leaves the vane on each side in a direction nearly parallel to the direction of motion of the vane. The best velocity of the vane is very approxi- mately half the velocity of the jet. § 202. Regulation of the Pelton Wheel. — At first Pelton wheels were adjusted to varying loads merely by throttling the supply. This method involves a total loss of part of the head at the sluice or throttle valve. In addition as the working head is reduced, the relation between wheel velocity and jet velocity is no longer that of greatest efficiency. Next a plan was adopted of deflecting the jet so that only part of the water reached the wheel when the load was reduced, the rest going to waste. This involved the use of an equal quantity of water for large and small loads, but it had, what in some cases is an advantage, the effect of preventing any water hammer in the supply pipe due to the action of the regulator. In most cases now regulation is effected by varying the section of the jet. A conical needle in the nozzle can be advanced or withdrawn so as to occupy more or less of the aperture of the nozzle. Such a needle can be controlled by an ordinary governor. § 203. General Considerations on the Choice of a Type of Turbine. — The circumferential speed of any turbine is necessarily a fraction of the initial velocity of the water, and therefore M greater as the head is greater. In reaction turbines with com- plete admission the number of revolutions per minute becomes inconveniently great, for the diameter cannot be increased beyond certain limits without greatly reducing the efficiency. In impulse turbines with partial admission the diameter can be chosen arbitrarily and the number of revolutions kept down on high falls to any desired amount. Hence broadly reaction turbines are better and less costly on low falls, and impulse turbines on high falls. For variable water flow impulse turbines have some advantage, being more efficiently regulated. On the other hand, impulse turbines lose efficiency seriously if their speed varies from the normal speed due to the head. If the head is very variable, as it often is on low falls, and the turbine must run at the same speed whatever the head, the impulse turbine is not suitable. Reaction turbines can be constructed so as to overcome this difficulty to a great extent. Axial flow turbines with vertical shafts have the disadvantage that in addition to the weight of the turbine there is an unbalanced water pressure to be carried by the footstep or collar bearing. In radial flow turbines the hydraulic pressures are balanced. The application of turbines to drive dynamos directly has involved some new con- ditions. The electrical engineer generally desires a high speed of rotation, and a very constant speed at all times. The reaction turbine is generally more suitable than the impulse turbine. As the diameter of the turbine depends on the quantity of water and cannot be much varied without great inefficiency, a difficulty arises on low falls. This has been met by constructing four independent reaction turbines on the same shaft, each having of course the diameter suitable for one-quarter of the whole dis- charge, and having a higher speed of rotation than a larger turbine. The turbines at Rheinfelden and Chevres are so con- structed. To ensure constant speed of rotation when the head varies considerably without serious inefficiency, an axial flow turbine is generally used. It is constructed of three or four concentric rings of vanes, with independent regulating sluices, forming practically independent turbines of different radii. Any one of these or any combination can be used according to the state of the water. With a high fall the turbine of largest radius only is used, and the speed of rotation is less than with a turbine of smaller radius. On the other hand, as the fall decreases the inner turbines are used either singly or together, according to the power required. At the Zurich waterworks there are turbines of 90 h.p. on a fall varying from 10^ ft. to 4$ ft. The power and speed are kept constant. Each turbine has three concentric rings. The outermost ring gives 90 h.p. with 105 cub. ft. per second and the maximum fall. The outer and middle compartments give the same power with 140 cub. ft. per second and a fall of 7 ft. 10 in. All three compartments working together develop the power with about 250 cub. ft. per second. In some tests the efficiency was 74% with the outer ring working alone, 75.4% with the outer and middle ring working and a fall of 7 ft., and 80-7 % with all the rings working. § 204. Speed Governing.^-'Wheii turbines are used to drive dynamos direct, the question of speed regulation is of great im- portance. Steam engines using a light elastic fluid can be easily regulated by governors acting on throttle or expansion valves. It is different, with water turbines using a fluid of great inertia. Hand Regulator Fig. 206. In one of the Niagara penstocks there are 400 tons of water flowing at 10 ft. per second, opposing enormous resistance to rapid change of speed of flow. The sluices of water turbines also are necessarily large and heavy. Hence relay governors must be IOt) HYDRAUlilCS [PUMPS used, and the tendency of relay governors to hunt must be overcome. In the Niagara Falls Power House No. i, each tur- bine has a very sensitive centrifugal governor acting on a ratchet relay. The governor puts into gear one or other of two ratchets driven by the turbine itself. According as one or the other ratchet is in gear the sluices are raised or lowered. By a sub- sidiary arrangement the ratchets are gradually put out of gear unless the governor puts them in gear again, and this prevents the over correction of the speed from the lag in the action of the governor. In the Niagara Power House No. 2, the relay is an hydraulic relay similar in principle, but rather more complicated in arrangement, to that shown in figi 206, which is a governor used for the 1250 h.p. turbines at Lyons. The sensitive governor G opens a valve and puts into action a plunger driven by oil pressure from an oil reservoir. As the plunger moves forward it gradually closes the oil admission valve by lowering the fulcrum end/ of the valve lever which rests on a wedge k> attached to the plunger. If the speed is still too high, the governor re- opens the valve. In the case of the Niagara turbines the oil pressure is 1200 lb per sq. in. One , millimetre of movement of the governor sleeve completely opens the relay valve, and the relay plunger exerts a force of 50 tons. The sluices can be completely opened or shut in twelve seconds. The ordinary variation of speed of the turbine with varying load does not exceed 1%. If all the load is thrown off, the momentary variation of speed is not more than 5 %. To prevent hydraulic shock in the supply pipes, a relief valve is provided which opens if the pressure is in excess of that due to the head. § 205. The Hydraulic Ram. — The hydraulic ram is an arrange- ment by which a quantity of water falling a distance h forces a portion of the water to rise to a height k\, greater than h. It consists of a supply reservoir (A, fig. 207), into which the water enters from some natural stream. A pipe j of considerable length conducts the water to a lower level, where it is discharged intermittently through a self-acting pulsating valve, at d. The supply pipe J may be fitted with a flap valve for stopping the ram, and this is attached in some cases to a float, so tlwtt the ram starts and stops itself automatically,; according as the supply cistern fills or empties. The lower float is just sumcienfc'to keep open the flap after it has been raised by the action of the upper float. The length of chain is adjusted so that the upper float opens the flap when the level in the cistern is at the desired height. If the water-level falls below the lower float the flap closes. The pipe s should be as long and as straight as possible, and as it is subjected to considerable pressure from the sudden arrest of the motion of the water, it must be strong and strongly Fig. 208. Fig. 207. jointed, a is an air vessel, and e the delivery pipe leading to the reservoir at a higher level than A, into which water is to be pumped. Fig. 208 shows in section the construction of the ram itself, d is the pulsating discharge valve already mentioned, which opens inwards and downwards. The stroke Of the valve is regulated by the cotter through the spindle, under which are washers by which the amount of fall can be regulated. At is a delivery valve, opening outwards, which is often a ball- valve but sometimes a flap-valve. The water which is pumped passes through this valve into the air vessel a, from which it flows by the delivery pipe in a regular stream into the cistern to which the water is to be raised. In the vertical chamber behind the outer valve a small air vessel is formed, and into this opens an aperture -J in. in'diameter, made in a brass screw plug b. The hole is reduced ■ to' iV in. in diameter at the outer end of the plug and is closed by a small valve opening inwards. Through this, during the rebound after each stroke of the ram, a small quantity of air is sucked in which keeps the air vessel supplied with its elastic cushion of air. During the recoil after a sudden closing of the valve d, the pressure below it is diminished and the valve opens, permitting outflow. In consequence of the flow through this valve, the Water in the supply pipe acquires a gradually increasing velocity. The upward flow of , the water, towards the valve d, increases the pressure tending to lift the valve, and at last, if the valve is not too heavy, lifts and closes it. The forward mo- mentum of thecolumn in the supply pipe being destroyed by the stoppage of the flow, the water exerts a pressure at the end of the pipe sufficient to open the delivery valve o, and to cause a portion of the water to flow into the air vessel. As the water in the supply pipe comes to rest and recoils, the valve d opens again and the operation is repeated. Part of the energy of the descending column is employed in compressing the air at the end of the supply pipe arid expanding the pipe itself. This causes a recoil of the water which momentarily diminishes the pressure in the pipe below the pressure due to the statical head. This assists in opening the valve d. The recoil of the water is sufficiently great to enable a pump to be attached to the ram body instead of the direct rising pipe. With this arrangement a ram working with muddy water may be employed to raise clear spring water. Instead of lifting the delivery valve as in the ordinary ram, the momentum of the column drives a sliding or elastic piston, and the recoil brings it back. This piston lifts and forces alternately the clear water through ordinary pump valves. Pumps § 206. The different classes of pumps corre- spond almost exactly to the different classes of water motors, although the mechanical details of the construction are somewhat different. They are properly reversed water motors. Ordinary reciprocating pumps corre- spond to water-pressure engines. Chain and bucket pumps are in principle similar to water wheels in which the water acts by weight. Scoop wheels are similar to undershot water wheels, and centrifugal pumps to turbines. Reciprocating Pumps are single or double acting, and differ from water-pressure engines in that the valves are moved by the water instead of by automatic machinery. They may be classed thus:-— 1. Lift Pumps. -—The water drawn through a foot valve on the ascent of the pump bucket is forced through the bucket valve when it descends, and lifted by the bucket when it reascends. Such pumps give an intermittent discharge. 2. Plunger or Force Pumps, in which the water drawn through the foot valve is displaced by the descent of a solid plunger, and forced through a delivery valve. They have the advantage that ilt ^ini, PUMPS] HYDRAULICS 107 the friction is less than that of lift pumps, and the packing round the plunger is easily accessible, whilst that round a lift pump bucket is not. The flow is intermittent. 3. The Double-acting Force Pump is in principle a double plunger pump. The discharge fluctuates from zero to a maximum and back to zero each stroke, but is not arrested for any appreciable time. 4. Bucket and Plunger Pumps consist of a lift pump bucket combined with a plunger of half its area. The flow varies as in a double-acting pump. 5. Diaphragm Pumps have been used, in which the solid plunger is replaced by an elastic diaphragm, alternately depressed into and raised out of a cylinder. As single-acting pumps give an intermittent discharge three are generally used on cranks at 120 . But with all pumps the variation of velocity of discharge would cause great waste of work in the delivery pipes when they are long, and even danger from the hydraulic ramming action of the long column of water. An air vessel is interposed between the pump and the delivery pipes, of a volume from 5 to 100 times the space described by the plunger per stroke. The air in this must be replenished from time to time, or continuously, by a special air-pump. At low speeds not exceeding 30 ft. per minute the delivery of a pump is about 90 to 05% of the volume described by the plunger or bucket, from 5 to 10% of the discharge being lost by leakage. At high speeds the quantity pumped. occasionally exceeds the volume described by the plunger, the momentum of the water keeping the valves open after the turn of the stroke. The velocity of large mining pumps is about 140 ft. per minute, the indoor or suction stroke being sometimes made at 250 ft. per minute. Rotative pumping engines of large size have a plunger speed of 90 ft. per minute. Small rotative pumps are run faster, but at some loss of efficiency. Fire-engine pumps have a speed of 180 to 220 ft. per minute. The efficiency of reciprocating pumps varies very greatly. Small reciprocating pumps, with metal valves on lifts of 15 ft., were found by Morin to have an efficiency of 16 to 40%, or on the average 25%. When used to pump water at considerable pressure, through hose pipes, the efficiency rose to from 28 to 57%, or on the average, with 50 to 100 ft. of lift, about 50%. A large pump with barrels 18 in. diameter, at speeds under 60 ft. per minute, gave the following results: — Lift in feet 141 34 47 Efficiency .... -46 -66 -70 The very large steam-pumps employed for waterworks, with 150 ft. or more of lift, appear to reach an efficiency of 90%, not including the friction of the discharge pipes. Reckoned on the indicated work of the steam-engine the efficiency may be 80%. Many small pumps are now driven electrically and are usually three-throw single-acting pumps driven from the electric motor by gearing. It is not convenient to vary the speed of the motor to accommodate it to the varying rate of pumping usually required. Messrs Hayward Tyler have introduced a mechanism for varying the stroke of the pumps (Sinclair's patent) from full stroke to nil, without stopping the pumps. § 207. Centrifugal Pump. — For large volumes of water on lifts not exceeding about 60 ft. the most convenient pump is the centrifugal pump. Recent improvements have made it available also for very high lifts. It consists of a wheel or fan with curved vanes enclosed in an annular chamber. Water flows in at the centre and is discharged at the periphery. The fan may rotate in a vertical or horizontal plane and the water may enter on one or both sides of the fan. In the latter case there is no axial unbalanced pressure. The fan and its casing must be filled with water before it can start, so that if not drowned there must be a foot valve on the suction pipe. When no special attention needs to be paid to efficiency the water may have a velocity of 6 to 7 ft. in the suction and delivery pipes. The fan often has 6 to 12 vanes. For a double-inlet fan of diameter D, the diameter of the inlets is D/2. If Q \i the discharge in cub. ft. per second D = about o-6 VQ in average cases. The peripheral speed is a little greater than the velocity due to the lift. Ordinary centrifugal pumps will have an efficiency of 40 to 60%. The first pump of this kind which attracted notice was one exhibited by J. G. Appold in 1851, and the special features of his pump have been retained in the best pumps since constructed. Appold's pump raised continuously a volume of water equal to 1400 times its own capacity per minute. It had no valves, and it permitted the passage of solid bodies, such as walnuts and oranges, without obstruction to its working. Its efficiency was also found to be good. Fig. 209 shows the ordinary form of a centrifugal pump. The pump disk and vanes B are cast in one, usually of bronze, and the disk is keyed on the driving shaft C. The casing A has a spirally enlarging discharge passage into the discharge pipe K. A cover L gives access to the pump. S is the suction pipe which opens into the pump disk on both sides at D. Fig. 210 shows a centrifugal pump differing from ordinary centrifugal pumps in one feature only. The water rises through a suction pipe S, which divides so as to enter the pump wheel W at the centre on each side. The pump disk or wheel is very similar to a turbine wheel. It is keyed on a shaft driven by a belt on a fast and loose pulley arrangement at P. The water rotating in the pump disk presses outwards, and if the speed is sufficient a continuous flow is maintained through the pump and into the discharge pipe D. The special feature in this pump is that the water, discharged by the pump disk with a whirling yelocity of not inconsiderable magnitude, is allowed to continue rotation in a chamber somewhat larger than the pump. The use of this whirlpool chamber was first suggested by Professor James Thomson. It utilizes the energy due to the whirling velocity of the water which in most pumps is wasted in eddies in the discharge pipe. In the pump shown guide-blades are also added which have the direction of the stream lines in a free vortex. They do not therefore interfere with the action of th"e. water when pumping the normal quantity, but only prevent irregular motion. At A is a plug by which the pump case is filled before starting. If the pump is above the water to be pumped, a foot valve is required to permit the pump to be filled. Sometimes instead of the foot valve a delivery valve is used, an air-pump or steam jet pump being employed to exhaust the air from the pump case. § 208. Design and Proportions 0} a Centrifugal Pump.— The design of the pump disk is very simple. Let r { , n be the radii of the inlet and outlet surfaces of the pump disk, &i, d the clear axial width at those radii. The velocity of flow through the pump may be taken io8 HYDRAULICS [PUMPS Fig. 2io. the same as for a turbine. If Q is the quantity pumped, and H the lift, Mi=0-25V2fiH. (i) 2-irndi =Q/m>. Also in practice di-V2Ti .... I Hence, f (2) r< = -257W(Q/VH).J Usually r = 2r>, and d =di or jd,- according as the disk is parallel-sided or coned. The water enters the wheel radially with the velocity «.-, and u =Ql2irr„d„. (3) Fig. 211 shows the notation adopted for the velocities. Suppose the water enters the wheel with the velocity Vi, while the velocity of the "• » ? wheel is V.-. Com- pleting the parallelo- gram, vh is the rela- tive velocity of the water and wheel, and is the proper direction of the wheel vanes. Also, by resolving, tu and Wi are the com- ponent velocities of flow and velocities of whir of the velocity k &f the water. At the outlet surface, v is the Fig. 211. finaV velocity of dis- charge, and the rest of the notation is similar to that for the inlet surface. _ Usually the water flows equally in all directions in the eye of the wheel, in that case d< is radial. Then, in normal conditions of work- ing, at the inlet surface, Vi = M; "| Wi=0 I /.s tane=UilWi J w v,i = Ui cosec = V(tti 2 +Vv 2 J u If the pump is raising less or more than its proper quantity, fl will not satisfy the last condition, and there is then some loss of head in shock. At the outer circumference of the wheel or outlet surface, »ro =«• cosec T W —Vo — Mo COt '{■ (5) »o = VK 2 + (V,,-M COt<*.) 2 !j Variation of Pressure in the Pump I>«fe.— Precisely as in the case of turbines, it can be shown that the variation of pressure between the inlet and outlet surfaces of the pump is h -hi = (Vo 2 -Vi 2 )/2g- (tv<, 2 -iVi 2 )/2«. Inserting the values of v r „ iw in (4) and (5), we get for normal conditions of working ho-h = (V„ ! -Vv 2 )/2g-«„ 2 COseC 2 4./2g + (Mi 2 +Vi 2 )/2g = V„ 2 /2g-M 2 cosec 2 0/2g + Z(i 2 /2g. (6) Hydraulic Efficiency of the Pump. — Neglecting disk friction, journal friction, and leakage, the efficiency of the pump can be found in the same way as that of- turbines (§ 186). Let M be the moment of the couple rotating the pump, and a its angular velocity; i»„ r„ the tangential velocity of the water and radius at the outlet surface; iw, n the same quantities at the inlet surface. Q being the discharge per second, the change of angular momentum per second is (GQ/g)(w.r„-«iiri). Hence M = (GQ/g) (tp„r„ — Win). In normal working, «i» = o. Also, multiplying by the angular velocity, the work done per second is Ma = {GQIg)w a r a. But the useful work done in pumping is GQH. Therefore the efficiency is ,, =GQH/Ma =gH/Kv„a =gH/wM . (7) § 209. Case 1. Centrifugal Pump with no Whirlpool Chamber. — When no special provision is made to utilize the energy of motion of the water leaving the wheel, and the pump discharges directly into a chamber in which the water is flowing to the discharge pipe, nearly the whole of the energy of the water leaving the disk is wasted. The water leaves the disk with the more or less considerable velocity v , and impinges on a mass flowing to the discharge pipe at the much slower velocity v,. The radial component of v is almost necessarily wasted. From the tangential component there is a gain of pressure («>„ 2 — l> s 2 )/2g— (w„ — fl s ) 2 /2g = V,(W — V.)[g, which will be small, if v, is small compared with iv . Its greatest value, if v, =!jWo, is \wJ-\2g, which will always be a small part of the whole head. Suppose this neglected. The whole variation of pressure in the pump disk then balances the lift and the head tti 2 /2g necessary to give the initial velocity of flow in the eye of the wheel. K.-^g+H =V„ 2 /2g-M„ 2 COSeC 2 /2g} r (8) or V„ = V (2gH -\-Uo- cosec 2 $ . ) and the efficiency of the pump is, from (7), ,=gH/V.w„=gH/{V(V„-»„cot0)), = (V«, 2 -«„ 2 cosec 2 \, (9) For<*>=90°, 77=(V„ 2 -m„ 2 )/2YV, which is necessarily less than J. That is, half the work expended in driving the pump is wasted. By recurving the vanes, a plan intro- duced by Appold, the efficiency is increased, because the velocity v, of discharge from the pump is diminished. If <#> is very small, cosec = cot ; and then ij = (V„+w„ cosec *)/2V„, which may approach the value I, as tends towards o. Equation (8) shows that u„ cosec 4> cannot be greater than V». Putting w„ =o - 25V (2gH) we S^t the following numerical values of the efficiency and the circumferential velocity of the pump:— PUMPS] HYDRAULICS 109 *o V 9°! 0-47 45: 0-56 3°: 0-65 20° o-73 IO° 0-84 v„ i-03V2gH 1-06 „ I-I2 „ 1-24 -, i-75 .. cannot practically be made less than 20°; and, allowing for the frictional losses neglected, the efficiency of a pump in which <£ = 20° is found to be about -6o. § 210. Case 2. Pump with a Whirlpool Chamber, as in fig. 210. — Professor James Thomson first suggested that the energy of the water after leaving the pump disk might be utilized, if a space were left in which a free vortex could be formed. In such a free vortex the velocity varies inversely as the radius. The gain of pressure in the vortex chamber is, putting r„, r„ for the radii to the outlet surface of wheel and to outside of free vortex, M-Sv-')- if k = rjr w . The lift is then, adding this to the lift in the last case, H = jV^-Mo 2 cosec 2 0+». s (i -* 2 )!/2£. But t , „ 2 =V 1 , 2 -2'V M o cot ip+Uo 1 cosec 2 -|>; .-.H = ((2 ~k r )V|/2g. (10) Putting this in the expression for the efficiency, we find a con- siderable increase of efficiency. Thus with = 90° and k = i, v\ nearly, ij> a small angle and k — \, ij = I nearly. With this arrangement of pump, therefore, the angle at the outer ends of the vanes is of comparatively little importance. A moderate angle of 30 or 40 may very well be adopted. The following numerical values of the velocity of the circumference of the pump = 0-25V(2gH). have been obtained by taking k - = J, and «„ = ()• V. 90 ■762 V 2gH < •842 „ 30 •911 .. 20° 1-023 „ The quantity of water to be pumped by a centrifugal pump neces- sarily varies, and an adjustment for different quantities of water can- not easily be introduced. Hence it is that the average efficiency of pumps of this kind is in practice less than the efficiencies given above. The advantage of a vortex chamber is also generally neglected. The velocity in the supply and discharge pipes is also often made greater than is consistent with a high degree of efficiency. Velocities of 6 or 7 ft. per second in the discharge and suction pipes, when the lift is small, cause a very sensible waste of energy; 3 to 6 ft. would be much better. Centrifugal pumps of very large size have been constructed. Easton and Anderson made pumps for the North Sea canal in Holland to deliver each 670 tons of water per minute on a lift of 5 ft. The pump disks are 8 ft. diameter. J. and H. Gwynne constructed some pumps for draining the Ferrarese Marshes, which together deliver 2000 tons per minute. A pump made under Pro- fessor J. Thomson's direction for drainage works in Barbados had a pump disk 16 ft. in diameter and a whirlpool chamber 32 ft. in diameter. The efficiency of centrifugal pumps. when delivering less or more than the normal quantity of water is discussed in a paper in the Proc. Inst. Civ. Eng. vol. 53. § 211. High Lift Centrifugal Pumps. — It has long been known that centrifugal pumps could be worked in series, each pump overcoming a part of the lift. This method has been perfected, and centrifugal pumps for very high lifts with great efficiency have been used by Sulzer and others. C. W. Darley (Proc. Inst. Civ. Eng., supplement to vol. 154, p. 156) has described some pumps of this new type driven by Parsons steam turbines for the water supply of Sydney, N.S.W. Each pump was designed to deliver 1 5 million gallons per twenty-four hours against a head of 240 ft. at 3300 revs, per minute. Three pumps in series give therefore a lift of 720 ft. The pump consists of a central double- sided impeller 12 in. diameter. The water entering at the bottom divides and enters the runner at each side through a bell-mouthed passage. The shaft is provided with ring and groove glands which on the suction side keep the air out and on the pressure side prevent leakage. Some water from the pressure side leaks through the glands, but beyond the first grooves it passes into a pocket and is returned to the suction side of the pump. For the glands on the suction side water is supplied from a low- pressure service. No packing is used in the glands. During the trials no water was seen at the gk>nds. The following are the results of tests made at Newcastle:- - Duration of test . hours Steam pressure lb per sq. in. Weight of steam per water h.p. hour ft Speed in revs, per min. Height of suction . . .ft. Total lift ft. Million galls, per day pumped — By Ventun meter By orifice ..... Water h.p. ....... 2 57 27-93 3300 11 762 1-573 1-623 252 II. 1-54 57 30-67 3330 11 744 1-499 1-513 235 III. 1-2 84 28-83 3710 II 917 1-689 1-723 326 IV. 1-55 55 27-89 3340 11 756 I-503 1-555 239 Stand Pipe In trial IV. the steam was superheated 95° F. From other trials under the same conditions as trial I. the Parsons turbine uses 15-6 lb of steam per brake h.p. hour, so that the combined efficiency of turbine and pumps is about 56%, a remarkably good result. § 212. Air-Lift Pumps.— -An interesting and simple method of pumping by compressed air, invented by Dr J. Pohle of Arizona, is likely to be Very useful in certain cases. Suppose a rising main placed in a deep bote hole in which there is a considerable depth of water. Air compressed to a sufficient pressure is con- veyed by an air pipe and introduced at the lower end of the rising main. The air rising in the main diminishes the average density of the contents of the main, and their aggregate weight no longer balances the pres- sure at the lower end of the main due to its sub- mersion. An up- ward flow is set up, and if the air supply is suffi- cient the water in the rising main is lifted to any Wg$0&g&$Pj required height. The higher the lift above the level in the bore hole the deeper must be the point at which air is injected. Fig. 212 shows an air- lift pump con- structed for W. H. Maxwell at the Tunbridge Wells water- works. There is a two-stage steam air compressor, compressing air to from 90 to 100 lb per sq. in. The bore hole is 3 50 ft. deep, lined with steel pipes 1 5 in^" diameter for 200 ft. and with perforated pipes i3j.in. diameter for the lower 150 ft. The rest level of the water is 96 ft. from the ground-level, and the level when pumping 32,000 gallons per hour is 1 20 ft. from the ground-level. The rising main is 7 in. diameter, and is carried nearly to the bottom of the bore hole and to 20 ft. above the ground-level. The air pipe is 25 in. diameter, In a trial run 31,402 gallons per hour were raised 133 ft. above the level in the well. Trials of the efficiency of the system made at San Francisco with varying conditions will be found in a paper by E. A. Rix (Journ. Amer. Assoc. Eng. Soc. vol. 25, I iffttSi U-Steel Tubes IS'piam. Main 7Diam. rfrrfi jilj Rising Air Pip* 2i' Dlam Fig. 212. no HYDRAZINE; 1 900) . Maxwell found the best results when the ratio of immersion to lift was 3 to i at the start and 2-2 to 1 at the end of the trial. In these conditions the efficiency was 37% calculated Ori the indicated h.p. of the steam-engine, and 46% calculated on the indicated work of the compressor. 2-7 volumes of free air were used to 1 of water lifted. The system is suitable for temporary purposes, especially as the quantity of water raised is much greater than could be pumped by any other system in a bore hole of a given size. It is useful for clearing a boring of sand and may be advantageously used permanently when a boring is in sand or gravel which cannot be kept out of the bore hole. The initial cost is small. § 213. Centrifugal Fans. — Centrifugal fans are constructed similarly ta centrifugal pumps, and are used for compressing air to pressures not exceeding 10 to 15 in. of water-column. With this small variation of pressure the variation of volume and density of the air may be neglected without sensible error. The conditions of pressure and discharge for fans are gener- ally less accurately known than in the case of pumps, and the design of fans is generally somewhat crude. They seldom have whirlpool chambers, though a large expanding outlet is pro- vided in the case of the important Guibal fans used in mine ventilation. It is usual to reckon the difference of pressure at the inlet and outlet of a fan in inches of water-column. One inch of water- column =64-4 ft. of air at average atmospheric pressure = 5-2lb per sq. ft. Roughly the pressure-head produced in a fan without means of utilizing the kinetic energy of discharge would be i s /2g ft. of air, or 0-00024 u ! in. of water, where v is the velocity of the tips of thefan blades in feet per second. If d is the diameter of the fan and t the width at the external circumference, then ndt is the discharge area of the fan disk. If Q is the discharge in cub. ft. per sec, u =Q/xdi is the radial velocity of discharge which is numerically equal to the discharge per square foot of outlet in cubic feet per second. As both the losses in the fan and the work done are roughly proportional to m 2 in fans of the same type, and are also proportional to the gauge pressure p, then if the losses are to be a constant percentage of the work done u may be taken proportional to V P- In ordinary cases « = about 22V p. The width t of the fan is generally from 0-35 to o-45<2. Hence if Q is given, the diameter of the fan should be: — For/=o-35d, d=o-2oV(Q/V/>) For<=o-45/<2 <•■ revs, per n>in. As the pressure difference is small, the work done in compressing the air is almost exactly $-2pQ foot-pounds per second. Usually, however, the kinetic energy of the air in the discharge pipe is not inconsiderable compared with the work done in compression. If w is the velocity of the air where the discharge pressure is measured, the air carries away w t /2g foot-pounds per lb of air as kinetic energy. In Q cubic feet or o-o8o7QIb the kinetic energy is 0-00125 Qw 2 foot-pounds per second. The efficiency of fans is reckoned in two ways. If B.H.P, is the effective horse-power applied at the fan shaft, then the efficiency reckoned on the work of compression is >> = 5-2pQ/55oB.H.P. On the other hand, if the kinetic energy in the delivery pipe is taken as part of the useful work the efficiency is ^ = (5-2£Q+a-ooi25Qa> 2 )/55oB.H.P. Although the theory above is a rough one it agrees sufficiently with experiment, with some merely numerical modifications. An extremely interesting experimental investigation of the action of centrifugal fans has been made by H. Heenan and W. Gilbert (Proc. Inst. Civ. Eng. vol. 123, p. 272). The fans delivered through an air trunk in which different resistances could be obtained by intro- ducing diaphragms with circular apertures of different sizes. Suppose a fan run at constant speed with different resistances and the com- pression pressure, discharge and brake horse-power measured. The results plot in such a diagram as is shown in fig. 213. The less the resistance to discharge, that is the larger the opening in the air trunk, the greater the quantity of air discharged at the given speed of the fan. On the other hand the compression pressure diminishes. The c*rve marked total gauge is the compression' pressure -(-the velocity head in the discharge pipe, both in inches of water,. This curve falls, but not nearly so much as the compression curve, when the resist- ance 13 the air trunk is diminished. The brake horse-power increases as tne resistance is diminished because the volume of discharge in- crease* very much. The curve marked efficiency is tile efficiency calculated on the work of compression only. It is zero for no dis- charge, and zero also when there is no resistance and all the energy given to the air is carried away as kinetic energy. There is a dis- charge for which this efficiency is a maximum ; it is about half the discharge which there is when there is no resistance and the delivery pipe is full open. The conditions of speed and discharge correspond- ing to the greatest efficiency of compression are those ordinarily taken as the best normal conditions of working. The curve marked «o *• ta- to e il- J i c * £ * 1 1 V J; .6 1 «5» y* l- 1 «• J . 0! 3P00 Discharge - C '.ft per min. Tip Speed * 100 ft. per sec. Fig. 213. • total efficiency gives the efficiency calculated on the work of com- pression and kinetic energy of discharge. Messrs Gilbert and Heenan found the efficiencies of ordinary fans calculated on the compression to be 40 to 60% when working at about normal conditions. Taking some, of Messrs Heenan and Gilbert's results for ordinary fans in normal conditions, they have been found to agree fairly with the following approximate rules. Let p c be the compression pressure and 5 the volume discharged per second per square foot of outlet area .of fan. . Then the total gauge pressure due to pressure of compression and velocity of discharge is approximately: p=p e +o-ooo±q 2 in. of water, so that if p c is given, p can be found approximately. The pressure p depends on the circumferential speed * of the fan disk — /► = 0-0O025f 2 in. oi water v = 63V P ft. per sec. The discharge per square foot of outlet of fan is — 2 = 15 to i8Vp cub. ft. per sec. The total discharge is Q—Tdtq = 47 to 56 dHp For • ' = -35^. d = o-22 to o-25V(Q/V£) ft. / = -45N-NO^^yf>N-NH 2 ^K 2 SO<+N,H 4 . HYDRAZONE^HYERQOBPHALUS in P. J. Schestakov (/. Smss. Phys. Chem. Sec.; 190$, 37, p. 1) obtained hydrazine by oxidizing urea with sodium hypochlorite in the presence of benzaldehyde, which, by combining with the hydrazine, protected it from oxidation. F. Raschig (German Patent 198307, 1908) obtained good yields by oxidizing ammonia with sodium hypochlorite in solutions made viscous with glue. Free hydrazine is a colourless liquid which boils at 113-5° C, and solidifies about o° C. to colourless crystals; it is heavier than water, in which it dissolves with' rise of temperature. It is rapidly oxidized on exposure, is a strong reducing agent, and reacts vigorously with the halogens. Under certain conditions it may be oxidized to azoimide (A. W, Browne and F. F. Shetterly, /. Amer. C.S., 1908, p. c^f By fractional distilla- tion of its aqueous solution hydrazine hydrate N2HVH2O (or perhaps H 2 N-NH»OH), a 'strong base, is obtained, which precipitates the metals from solutions of copper and silver salts at ordinary temperatures. It dissociates completely in a vacuum at 143°, and when heated under atmospheric pressure to 183 it decomposes into ammonia and nitrogen (A. Scott, /. Chem. Soc, 1904, 85, p. 913). The sulphate N2H<-H 2 S04, crystallizes in tables which are slightly soluble in cold water and readily soluble in hot water; it is decomposed by heating above 250 C. with explosive evolution of gas and liberation of sulphur. By the addition of barium chloride to the sulphate, a solution of the hydrochloride is obtained, from which the crystallized salt may be obtained on evaporation. Many organic derivatives of "hydrazine are known, the most important being phenylhydrazine^ which was discovered by Emil Fischer in 1877. It can be best prepared by V. Meyer and Lecco's method (Ber., 1883, 16, p. 2976), which consists in reducing phenyl- diazonium chloride in concentrated.hydrochloric acid, solution With stannous chloride also dissolved in, concentrated hydrochloric acid. Phenylhydrazine is liberated from the hydrochloride so obtained by adding sodium hydroxide, the solution being then extracted With ether, the ether distilled off, and the residual oil purified by distilla- tion under reduced pressure. Another method is, due to 13, Bam- berger. The diazonium chloride, by the addition of an alkaline sulphite, is converted into a diazosulphonate, which is then reduced by zinc dust and acetic acid to phenylhydrazine potassium sulphite. This salt is then hydrolysed by heating it with hydrochloric acid — C 6 H 5 XjCl + K 2 SO s = KC1 + C 6 H 6 NrSO s K, C 6 H 5 N,-S0 3 K + 2H = C 6 H 5 -NH-NH-S0 3 K, • C,H S NH-NHS0 3 K+HC1+ H20 = C,,H s -NHNH^Ha-f KHSO^. Phenylhydrazine is a colourless oily liquid which turns brown On exposure. It boils at 241 ° C, and melts at I7-5" G. It is slightly soluble in water, and is strongly basic, forming well-defined salts with acids. For the detection of substances containing- the carbonyl group (such for example as aldehydes and ketones) phenylhydrazine is a very important reagent, since it combines with them with elimination of water and the formation of well-defined hydrazines (see Aldehydes, Ketones and Sugars). It is a strong reducing agent; it precipitates cuprous oxide when heated , with FefUing's solution, nitrogen and benzene beiiig formed at the same time — C 6 H,NH-NH 2 + 2CuO ^CujO+Nj+riiO+CsIV By energetic re- duction of phenylhydrazine {e.g. by use of zisc dust ahd hydrochloric acid), ammonia and aniline are produced— C 6 H5NH-MHi + 2H * CjHjNHj + NH». It is also a most Important synthetic reagent, 1 1 combines with aceto-acetic ester to form phfenylrnethyilpyrazolone' from which antipyrine {q.v.) may be obtained. Indoles (q.v.) are formed by heating certain hydrazones with anhydrous zinc chloride; while semicarbazides, pyrrols (q.v.) and many other types of organic compounds may be synthesized by the use of suitable phenylhydrazine derivatives. HYDRAZONE, in chemistry, a compound formed by the con- densation of a hydrazine with a cafbonyl group (see Alde- hydes ; Ketones). HYDROCARBON, in chemistry, a compound of carbon and hydrogen. Many occur in nature in the free state: for example, natural gas, petroleum and paraffin are entirely composed of such bodies; other natural sources are india-rubber, turpentine and certain essential oils. They are also revealed by the spectro- scope in stars, comets and the sun. Of artificial productions the most fruitful and important is prpvided by the destructive or dry distillation of many organic substances; familiar examples are the distillation of coal, which yields ordinary lighting gas, composed of gaseous hydrocarbofis, ' and also coal tar, which; on subsequent fractional distillations, yields many liquid and solid hydrocarbons, all of high industrial value. For details reference should be made to the articles wherein the above subjects- are treated. From the chemical point of view the hydrocarbons are of fundamental importance, and, on account of their great number, and still greater number of derivatives, they are studied as a separate branch of the science, namely, organic chemistry. See Chemistry for an account of their classification, &c. HYDROCELE (Gr. i&sop, water, and k^Xjj, tumour), the medical term for arty collection of fluid other than pus or blood in the neighbourhood of the testis or cord. The fluid is usually serous. " Hydrocele may be congenital or arise in the middle-aged withdut apparent cause, but it is usually associated with chronic orchitis or with tertiary syphilitic enlargements. The hydrocele appears as a. rbunded, fluctuating translucent swelling in the scrotum, and wheri greatly distended causes a dragging pain; Palliative treatment consists in tapping aseptically and remov- ing the ' fluid, the patient afterwards wearing a suspenderi The condition frequently recurs and necessitates radical treatment. Various substances may be injected; or the hydrocele is incised,' the tunica partly removed and the cavity drained. '■ HYDROCEPHALUS (Gr. iiBwp, water, and KG/poKr/, head), a term applied to disease of the brain which is attended with excessive effusion of fluid into its cavities. It exists in two forms— acute and chronic hydrocephalus. Acute hydro- cephalus is another- name for tuberculous meningitis (see Meningitis). Chronic hydrocephalus, or "water on the brain," consists in an effusion of fluid into the lateral ventricles of the brain. It is not preceded by tuberculous deposit or acute inflammation, but depends upon congenital malformation or upon chronic inflammatory changes affecting the membranes. When the disease is congenital, its presence in the foetus isapt to be a source of difficulty ' in parturition. It is however more commonly developed in" the first six months of life; but it occaskmally arises in older children, or even in adults. The chief symptom is the gradual increase in size of the upper part of the head out of all proportion to the face or the rest of the body. Occurring at an age when as yet the txjnes of the skull have not; become welded together, the enla*gement may go on to an enormous extent, the Spaces betweek -the bones becoming more and more expanded.' In a well-marked' case the deformity is very striking; the tippet part of the forehead projects abnormally, and the orbital plates of the frontal bone being inclined forwards give a dd torn ward- tilt to the eyes, which have also peculiar rolling movements. The face is small, and this, with the enlarged head, gives' a- remarkable aged expression to the child. The body is illinoufisried; the bones are thin, the hair is scanty and fine and the teeth 'carious or absent. . ; The average circumference of* the adult head' is 22 in v - and in the normal child it is of course much less. In chronic hydro- cephalus the'head of an infant three months old has measured 29 in.; and in the* case of the man Cardinal, who died in Guy's Hospital'/the head measured 33 in. In such cases the head cannot be supported by the neck, and the patient has to keep mostly in the recumbent posture. The expansibility of the skull prevents destructive pressure on the brain, yet this organ is materially affected by the presence of the fluid. The cerebral ventricles are distended, and the convolutions are flattened, OCcasidnally the fluid escapes into the cavity of the cranium, which it fills, pressing down the brain to the base of the skull. ~ As a consequence, the functions of the brain are interfered with, and the 1 inefital condition is impaired. The child is dull, listless arid irritable, and sometimes imbecile. The special senses bfecbme affected as the disease advances; sight is often lost, as is also hearing. Hydrocephalic children generally sink in a few years;' nevertheless there have been instances of persons with this disease living to old age. There are, of course, grades of the affection; and children may present many of the symptoms of it in a slight degree, and yet recover, the head ceasing to expand, and becoming in due course" firmly ossified. 112 HYDR0CHARI0EAE Various methods of treatment have been employed, but the results are unsatisfactory. Compression of the head by bandages, and the administration of mercury with the view of promoting absorption of the fluid, are now little resorted to. Tapping the fluid from time to time through one of the spaces between the bones, drawing off a little, and thereafter employing gentle pressure, has been tried, but rarely with benefit. Attempts have also been made to establish a permanent drainage between the interior of the lateral ventricle and the sub-dura! space, tod between the lumbar region of the spine and the abdomen, but without satisfactory results. On the whole, the plan Of treatment which aims at maintaining the patient's nutrition by appropriate food and tonics is the most rational and successful. (E. O.*) HYDROCHARIDEAE, in botany, a natural order of Mono- cotyledons, belonging to the series Helobieae. They are water- plants, represented in Britain by frog-bit {Hydrocharis Morsus- ranae) and water-soldier (Stratiotes alotdes). The order contains about fifty species in fifteen genera, twelve of which occur in fresh water while three are marine: and includes both floating and submerged forms. Hydrocharis floats on the surface of still water, andh*s rosettes of kidney-shaped leaves, from among which spring the flower-stalks; stolons bearing new leaf- rosettes are sent out on all sides, the plant thus propagating itself in the same way as the strawberry. Stratiotes alotdes has a rosette of stiff sword- like leaves, which when the plant is in flower project above the surface; it is also stoloniferous, the young rosettes sinking to the bottom at the beginning of winter and rising again to the surface in the spring. Vallisneria (eel-grass) contains two species, one native of tropical Asia, the other, in- habiting the wanner parts of both hemi- spheres and reaching as far north as south Europe. It grows in the mud at the bottom of fresh water, and the short stem bears a cluster of long, narrow grass-like leaves; new plants are formed at Morsus-ranae — Fig. i. — Hydrocharis Frog-bit — male plant. 1, Female flower. 2, Stamens, enlarged. 3, Barren pistil of male flower, enlarged. 4, Pistil of female flower. 5, Fruit. 6, Fruit cut transversely. I) 9. Floral diagrams of male and female * he end f Iwfkontai flowers respectively. runners. Another type s, Rudimentary stamens. is represented by Elodea canadensis or water-thyme, which has been introduced into the British Isles from North America. It is a small, submerged plant with long, slender branching stems bearing whorls of narrow toothed leaves; the flowers appear at the surface when mature. Halophila, Enhalus and Thalassia are submerged maritime plants found on trppical coasts, mainly in the Indian and Pacific oceans; Halophila has an elongated stem rooting at the nodes; Enhalus a short, thick rhizome, clothed with black threads resembling horse-hair, the persistent hard-bast strands of the leaves; Thalassia has a creeping rooting stem with upright branches bearing crowded strap-shaped leaves in two rows. The flowers spring from, or are enclosed in, a spathe, and are unisexual and regular, with generally a calyx and corolla, each of three members; the stamens are in whorls of three, the inner whorls are often barren; the two to fifteen carpels form an inferior ovary containing generally numerous ovules on often large, produced, parietal placentas. The fruit is leathery or fleshy, opening irregularly. The seeds contain a large embryo and no endosperm. In Hydrocharis (fig. i), which is dioe- cious, the flowers are borne above the surface of the water, have con- spicuous white petals, contain honey and are pollinated by in- sects. Stratiotes has similar flowers which come above | the surface only for pollination, becoming sub- merged again during ripening of the fruit. In Val- lisneria (fig. 2), which is also dioe- cious, the small male flowers are borne in large numbers in short- stalked spathes; the petals are minute and scale- like, and only two of the three stamens are fer- Fig. spiralis — Eel grass — A, Female plant; B, _ _ 2. — Vallisneria tile; the flowers ^ bo . ut \ natural size - , ' , . , , Male plant, become detached r before opening and rise to the surface, where the sepals expand and form a float bearing the two projecting semi-erect stamens. The female flowers are solitary and are raised to the surface on a long, spiral stall:; the ovary bears three broad styles, on* which some of the large, sticky pollen-grains from the floating male flowers get de- posited (fig. 3). After pollination the female flower becomes drawn below the surface by the spiral con- traction of the long stalk, and the fruit ripens near the bottom. Elodea has poly- gamous flowers Fig. 3. (that is, male, female and hermaphrodite), solitary, in slender, tubular spathes; the male flowers become detached and rise to the surface; the females are raised to the surface when mature, and receive the floating pollen from the male. The flowers of Halophila are submerged and apetalous. The order is a widely distributed one; the marine forms are tropical or subtropical, but the fresh- water genera occur also in the temperate zones. HYDROCHLORIC ACID— HYDROGEN 113 HYDROCHLORIC ACID, also known in commerce as " spirits of salts " and " muriatic acid," a compound of hydrogen and chlorine. Its chemistry is discussed under Chlorine, and its manufacture under Alkali Manufacture. HYDRODYNAMICS (Gr. vScop, water, dvuatus, strength), the branch of hydromechanics which discusses the motion of fluids (see Hydromechanics). HYDROGEN [symbol H, atomic weight 1-008 (0=16)], one of the chemical elements. Its name is derived from Gr. vdup, water, and yevvauv, to produce, in allusion to the fact that water is produced when the gas burns in air. Hydrogen appears to have been recognized by Paracelsus in the 16th century; the combustibility of the gas was noticed by Turquet de Mayenne in the 17th century, whilst in 1700 N. Lemery showed that a mixture of hydrogen and air detonated on the application of a light. The first definite experiments concerning the nature of hydrogen were made in 1766 by H. Cavendish, who showed that it was formed when various metals were acted upon by dilute sulphuric or hydrochloric acids. Cavendish called it " in- flammable air," and for some time it was confused with other inflammable gases, all of which were supposed to contain the same inflammable principle, " phlogiston," in combination with varying amounts of other substances. In 1781 Cavendish showed that water was the only substance produced when hydrogen was burned in air or oxygen, it having been thought previously to this date that other substances were formed during the reaction, A. L. Lavoisier making many experiments with the object of finding an acid among the products of combustion. Hydrogen is found in the free state in some volcanic gases, in fumaroles, in the carnallite of the Stassfurt potash mines (H. Precht, Ber., 1886, 19, p. 2326), in some meteorites, in certain stars and nebulae, and also in the envelopes of the sun. In combination it is found as a constituent of water, of the gases from certain mineral springs, in many minerals, and in most animal and vegetable tissues. It may be prepared by the electro- lysis of acidulated water, by the decomposition of water by various metals or metallic hydrides, and by the action of many metals on acids or on bases. The alkali metals and alkaline earth metals decompose water at ordinary temperatures; magnesium begins to react above 70° C, and zinc at a dull red heat. The decomposition of steam by red hot iron has been studied by H. Sainte-Claire Deville (Comptes renins, 1870, 70, p. 1105) and by H. Debray (ibid., 1879, 88, p. 1341), who found that at about 1500 C. a condition of equilibrium is reached. H. Moissan (Bull. soc. chim., 1902, 27, p. 1 141) has shown that potassium hydride decomposes cold water, with evolution of hydrogen, KH + H 2 = KOH + H 2 . Calcium hydride or by drolite, prepared by passing hydrogen over heated calcium, decomposes water similarly, 1 gram giving 1 litre of gas; it has been proposed as a commercial source (Prats Aymerich, Abst. J.C.S., 1907, ii. p. 543), as has also aluminium turnings moistened with potassium cyanide and mercuric chloride, which decomposes water regularly at 70 , 1 gram giving 1-3 litres of gas (Mauricheau-Beaupre, Comptes rendus, 1908, 147, p. 310). Strontium hydride behaves similarly. In preparing the gas by the action of metals on acids, dilute sulphuric or hydrochloric acid is taken, and the metals commonly used are zinc or iron. So obtained, it contains many impurities, such as carbon dioxide, nitrogen, oxides of nitrogen, phosphoretted hydrogen, arseniuretted hydrogen, &c, the removal of which is a matter of great difficulty (see E. W. Morley, Amcr. Chem. Journ., 1890, 12,'p. 460). When prepared by the action of metals on bases, zinc or aluminium and caustic soda or caustic potash are used. Hydrogen may also be obtained by the action of zinc on ammonium salts (the nitrate excepted) (Lorin, Comptes rendus, 1865, 60, p. 745) and by heating the alkali formates or oxalates with caustic potash or soda, Na J C 2 0-4-r-2NaOH = H 2 +2Na 2 C0 3 . Technically it is prepared by the action of superheated steam on incandescent coke (see F. Hembert and Henry, Comptes rendus, 1885, 101, p. 797; A. Naumann and C. Pistor, Ber., 1885, 18, p. 1647), or by the electrolysis of a dilute solution of caustic soda (C. Winssinger, Chem. Zeit., 1898, 22, p. 609; " Die Elektrizitats-Aktiengesell- schaft," Zeit. f. Elektrochem., 1901, 7, p. 857). In the latter method a 15 % solution of caustic soda is used, and the electrodes are made of iron; the cell is packed in a wooden box , surrounded with sand, so that the temperature is kept at about 70 C; the solution is replenished, when necessary, with distilled water. The purity of the gas obtained is about 97 % Pure hydrogen is a tasteless, colourless and odourless gas of specific gravity 0-06947 (air= 1) (Lord Rayleigh, Proc. Roy. Soc., 1893, p. 319). It may be liquefied, the liquid boiling at -252-68° C. to -252-84°C, and it has also been solidified, the solid melting at -264° C. (J. Dewar, Comptes rendus, 1899, 129, p. 451; Chem. News, 1901, 84, p. 49; see also Liquid Gases). The specific heat of gaseous hydrogen (at constant pressure) is 3.4041 (water=i), and the ratio of the specific heat at constant pressure to the specific heat at constant volume is 1-3852 (W. C. Rontgen, Pogg. Ann., 1873, 148, p. 580). On the spectrum see Spectroscopy. Hydrogen is only very slightly soluble in water. It diffuses very rapidly through a porous membrane, and through some metals at a red heat (T. Graham, Proc. Roy. Soc, 1867, 15, p. 223; H. Sainte-Claire Deville and L. Troost, Comptes rendus, 1863, 56, p. 977). Palladium and some other metals are capable of absorbing large volumes of hydrogen (especially when the metal is used as a cathode in a water electrolysis apparatus). L. Troost and P. Hautefeuille (Ann. chim. phys., 1874, (5) 2, p. 279) considered that a palladium hydride of composition Pd 2 H was formed, but the investigations of C. Hoitsema (Zeit. phys. Chem., 1895, 17, p. 1), from the standpoint of the phase rule, do not favour this view, Hoitsema being of the opinion that the occlusion of hydrogen by palladium is a process of continuous absorption. Hydrogen burns with a pale blue non-luminous flame, but will not support the combustion of ordinary combustibles. It forms a highly explosive mixture with air or oxygen, especially when in the proportion of two volumes of hydrogen to one volume of oxygen. H. B. Baker (Proc. Chem. Soc, 1902, 18, p. 40) has shown that perfectly dry hydrogen will not unite with perfectly dry oxygen. Hydrogen combines with fluorine, even at very low temperatures, with great violence; it also combines with carbon, at the temperature of the electric arc. The alkali metals when warmed in a current of hydrogen, at about 360° C, form hydrides of composition RH(R = Na, K, Rb, Cs), (H. Moissan, Bull. soc. chim., 1902, 27, p. 1 141); calcium and strontium similarly form hydrides CaH 2 , SrH 2 at a dull red heat (A. Guntz, Comptes rendus, 1901, 133, p. 1209). Hydrogen is a very powerful re- ducing agent; the gas occluded by palladium being very active in this respect, readily reducing ferric salts to ferrous salts, nitrates to nitrites and ammonia, chlorates to chlorides, &c. For determinations of the volume ratio with which hydrogen and oxygen combine, see J. B. Dumas, Ann. chim. phys., 1843 (3), 8, p. 189; O. Erdmann [and R. F. Marchand, ibid. p. 212; E. H. Keiser, Ber., 1887, 20, p. 2323; J. P. Cooke and T. W. Richards, Amer. Chem. Journ., 1888, 10, p. 191; Lord Rayleigh, Chem. News, 1889, 59, p. 147; E. W. Morley, Zeit. phys. Chem., 1890, 20, p. 417; and S. A. Leduc, Comptes rendus, 1899, 128, p. 1158. Hydrogen combines with oxygen to form two definite com- pounds, namely, water (q.v.), H 2 0, and hydrogen peroxide, H 2 2 , whilst the existence of a third oxide, ozonic acid, has been indicated. Hydrogen peroxide, H2O2, was discovered by L. J. Thenard in 187.8 (Ann. chim. phys., 8, p. 306). It occurs in small quantities in the atmosphere. It may be prepared by passing a currentof carbon dioxide through ice-cold water, to which small quantities of barium peroxide are added from time to time (F. Duprey, Comptes rendus, 1862, 55, p. 736; A. J. Balard, ibid., p. 758), Ba0 2 -fC0 2 +H 2 = H 2 2 +BaC0 3 . E. Merck (Abst. J.C.S., 1907, ii., p. 859) showed that barium percarbonate, BaC0 4 , is formed when the gas is in excess; this substance readily yields the peroxide with an acid. Or barium peroxide may be decom- posed by hydrochloric, hydrofluoric, sulphuric or silicofluoric acids (L. Crismer, Bull. soc. chim., 1891 (3), 6, p. 24; Hanriot, Comptes rendus, 1885, 100, pp. 56, 172), the peroxide being added ii4 HYDROGRAPHY— HYDROLYSIS in small quantities to a cold dilute solution of the acid. It is necessary that it should be as pure as possible since the commercial product usually contains traces of ferric, manganic and aluminium oxides, together tvith some silica. To purify the oxide, it is dissolved in dilute hydrochloric acid until the acid is neatly neutralized, the solution is cooled, filtered, and baryta water is added until a faint permanent white precipitate of hydrated barium peroxide appears; the solution is now filtered, and a concentrated solution of baryta water is added to the filtrate, when a crystalline precipitate of hydrated barium peroxide, Ba0 2 8-H 2 0, is thrown down. This is filtered off and well washed with water. The above methods give a dilute aqueous solution of hydrogen peroxide, which may be concentrated somewhat by evaporation over sulphuric acid in vacuo. H. P. Talbot and H. R. Moody (Jour. Anal. Chem., 1892, 6, p. 650) prepared a more concentrated solution from the commercial product, by the addition of a 10% solution of alcohol and baryta water. The solution is filtered, and the barium precipitated by sulphuric acid. The alcohol is removed by distillation in vacuo, and by further concentration in vacuo a solution may be obtained which evolves 580 volumes of oxygen. R. Wolffenstein (Ber., 1804, 27, p. 2307) prepared practically anhydrous hydrogen peroxide (containing 99-x% H 2 2 ) by first removing all traces of dust, heavy metals and alkali from the commercial 3 % solution. The solution is then concentrated in an open basis on the water- bath until it contains 48% H2O2. The liquid so obtained is extracted with ether and the ethereal solution distilled under diminished pressure, and finally purified by repeated distillations. W. Staedel (Zeit. f. angew* Chem., 1902, 15, p. 642) has described solid hydrogen peroxide, obtained by freezing concentrated solutions. Hydrogen peroxide is also found as a product in many chemical actions, being formed when carbon monoxide and cyanogen burn in air (H. B. Dixon); by passing air through solutions of strong bases in the presence of such metals as do not react with the bases to liberate hydrogen; by shaking zinc amalgam with alcoholic sulphuric acid and air (M. Traube, Ber., ' t$82, 15, p. 659); in the oxidation of zinc, lead and copper 5 in presence of water, and in the electrolysis of sulphuric acid of such strength that it contains two molecules of water to one molecule of sulphuric acid (M. Berthelot, Comptcs rendus, 1878s 86, p. 71). ■ ■ ■ The anhydrous hydrogen peroxide obtained by Wolffenstein boils at 84-8 5°C. (68 mm.); its specific gravity is 1-4996 (1-5° C). It is very explosive (W. Spring, Zeit. anmg. Chem.j 1895, 8, p. 424). The explosion risk seems to be most marked in the preparations which have been extracted with ether previous to distillation, and J. W. Bruhl (Ber., 1895, 28, p. 2847) is of opinion that a very unstable, more highly oxidized product is produced in small quantity in the process. The solid variety prepared by Staedel forms colourless, prismatic crystals which melt at -2° C; it is decomposed with explosive violence by platinum sponge, and traces of manganese dioxide. , The dilute aqueous solution is very unstable, giving up oxygen readily, and decomposing with explosive violence at 100° C. An aqueous solution containing more than 1-5% hydrogen peroxide reacts slightly acid. To- wards lupetidin [aa' dimethyl piperidine, C 5 H 9 N(CHa)2l hydrogen peroxide acts as a dibasic acid (A. Marcuse and R. Wolffenstein, Ber., 1901, 34, p. 2430; see also G. Bredig, Zeit. Electrochem., 1 901, 7, p. 622). Cryoscopic determinations of its molecular weight show that it is H2O2. [G. Carrara, Rend, delta Accad. dei Lincei, 1892 (5), 1, ii. p; 19; W. R. Orndorff and J. White, Amer. Chem. Journ., 1893, 15, p. 347.] Hydrogen peroxide behaves very frequently as a powerful oxidizing agent; thus lead sulphide is converted into lead sulphate in presence of a dilute aqueous solution of the peroxide, the hydroxides of the alkaline earth metals are converted into peroxides of the type MCV8H2O, titanium, dioxide is converted into the trioxide, iodiae is liberated from potassium iodide, and nitrites (in alkaline solution) are converted into acid-amides (B. Radziszewski,Ber., 1884, .iii, p: 355). In many cases it is found that hydrogen peroxide will 'only act as an oxidant when in the presence of a catalyst; for example, formic, glygollic, lactic, tartaric, malic, benzoic and other organic acids are readily oxidized in the presence of ferrous sulphate (H. J. H. Fenton, Jour. Chem. Soc, 1900, 77, p. 69), and sugars are readily oxidized in the presence of ferric chloride (O. Fischer and M. Busch, Ber., 1891, 24, p. 187 1). It is sought to explain these oxidation processes by assuming that the hydrogen peroxide unites with the compound undergoing oxidation to form an addition compound, which subsequently decomposes (J. H. Kastle and A. S. Loevenhart, Amer. Chem. Journ., 1903, 29, pp. 397, 517). Hydrogen peroxide can also react as a reducing agent, thus silver oxide is reduced with a rapid evolution of oxygen. The course of this reaction can scarcely be considered as definitely settled; M. Berthelot considers that a higher oxide of silver is formed, whilst A. Baeyer and V. Villiger are of opinion that reduced silver is obtained [see Comptes rendus, 1001, 133, p. 555; Ann. Chim. Phys., 1897 (7), 11, p. 217, and Ber., 1901, 34, p. 2769]. Potassium- permanganate, in the presence of dilute sulphuric acid, is rapidly reduced by hydrogen peroxide, oxygen being given off, 2KM„0 4 + 3H 2 S04+5Hj>0 2 = KoS04-f-2MhS04+8H 2 0+502. Lead peroxide is reduced to the monoxide. Hypochlorous acid and its salts, together with the corresponding bromine and iodine compounds, liberate oxygen violently from hydrogen peroxide, giving hydro- chloric, hydrobromic and hydriodic acids (S. Tanatar, Ber., 1899, 32, p. 1013). On the constitution of hydrogen peroxide see C. F. Schonbein, Jour, pritk. Chem., 1858-1868; M. Traube, Ber., 1882-1889; J. W. Bruhl, Ber<; 1895, 28, p. 2847; 1900, 33, p. 1709; S. Tanatar, Ber., 1903, 36. P- I893-. . . . Hydrogen peroxide finds application as a bleaching agent, as an antiseptic, for the removal of tne last traces of chlorine and sulphur dioxide employed in bleaching, and for various quantitative separa- tions in analytical chemistry. (P. Jannasch, Ber., 1893, 26, p. 2908). It may be estimated. by titration with potassium permanganate in acid solution; wjth potassium ferricyanide. in alkaline solution, 2K 3 Fe(CN) 6 -|-2KOH-l-H 2 02=2K4Fe(CN)6-(-2H20+0 2 ;or by oxidiz- ing arsenious acid in alkaline solution with the peroxide and back- titration of the excess of arsenious acid with standard iodine (B. Grutzner, Arch, der Pharm., 1899, 237, p^ 705). It may be recognized by the violet coloration it gives when added to a very dilute solution of potassium bichromate in the presence of hydro- chloric acid; by the orange-red colour it gives with a solution of titanium dioxide in concentrated sulphuric acid ; and by the pre- cipitate of Prussian blue formed when it is added to a solution containing ferric chloride and potassium ferricyanide. Ozonic Acid, H2O4. By the action of ozone on a 40% solution of potassium hydroxide, placed in a freezing mixture, an orange- brown substance is obtained, probably K2O4, which A. Baeyer and V. Villiger [Ber., 1902, 35, p. 3038) think is derived from ozonic acid, produced according to the reaction O3 + H2O = H 2 4 . HYDROGRAPHY (Gr. vSup, water, and -ypd^eip, to write), the science dealing with all the waters of the earth's surface, including the description of their physical features and con- ditions; the preparation of charts andmaps showing the position of lakes, rivers, seas and oceans, the contour of the sea-bottom, the position of shallows, deeps, reefs and the direction and volume of currents; a scientific description of the position, volume, configuration, motion and condition of all the waters of the earth. See also Surveying (Nautical) and Ocean and Oceanography. The Hydrographic Department of the British Admiralty, established in 1795, undertakes the making of charts for the admiralty, and is under the charge of the hydrographer to the admiralty (see Chart). HYDROLYSIS (Gr. tiBoip, water, \vei.v, to loosen), in chemistry, a decomposition brought about by water after the manner shown in the equation R-X+H'OH = R-H+X-OH. Modern research has proved that such reactions are not occasioned by water acting as H 2 0, but really by its ions (hydrions and hydroxidions), for the velocity is proportional (in accordance with the law of chemical mass action) to the concentration of these ions. This fact explains the so-called " catalytic " action of acids and bases in decomposing such compounds as the esters. The term " saponification " (Lat. sapo, soap) has the same meaning, but it is more properly restricted to the hydrolysis of the fats, i.e. glyceryl esters of organic acids, into glycerin and a soap (see Chemical Action). HYDROMECHANICS 1 5 HYDROMECHANICS (Gr. v5poy.rixa.VLKa.), the science of the mechanics of water and fluids in general, including hydrostatics or the mathematical theory of fluids in equilibrium, and hydro- mechanics, the theory of fluids in motion. The practical applica- tion of hydromechanics forms the province of hydraulics (q.v.). Historical. — The fundamental principles of hydrostatics were first given by Archimedes in his work Ilepi w oxovixivuv, or De iis quae vehuntur in humido, about 250 B.C., and were afterwards applied to experiments by Marino Ghetaldi (1566-1627) in his Promotus Archimedes (1603). Archimedes maintained that each particle of a fluid mass, when in equilibrium, is equally pressed in every direc- tion ; and he inquired into the conditions according to which a solid body floating in a fluid should assume and preserve a position of equilibrium. In the Greek school at Alexandria, which flourished under the auspices of the Ptolemies, the first attempts were made at the construction of hydraulic machinery, and about 120 B.C. the fountain of compression, the siphon, and the forcing-pump were invented by Ctesibius and Hero. The siphon is a simple instrument; but the forcing-pump is a complicated invention, which could scarcely have been expected in the infancy of hydraulics. It was probably suggested to Ctesibius by the Egyptian Wheel or Noria, which was common at that time, and which was a kind of chain pump, con- sisting of a number of earthen pots carried' round by a wheel. In some of these machines the pots have a valve in the bottom which enables them to descend without much resistance, and diminishes greatly the load upon the wheel ; and, if we suppose that this valve was introduced so early as the time of Ctesibius, it is not difficult to perceive how such a machine might have led to the invention of the forcing-pump. Notwithstanding these inventions of the Alexandrian school, its attention does not seem to have been directed to the motion of fluids; and the first attempt to investigate this subject was made by Sextus Julius Frontinus, inspector of the public fountains at Rome in the reigns of Nerva and Trajan. In his work De aquae- ductibus urbis Romae commentarius , he considers the methods which were at that time employed for ascertaining the quantity of water discharged from ajutages, and the mode of distributing the waters of an aqueduct or a fountain. He remarked that the flow of water from an orifice depends not only on the magnitude of the orifice itself, but also on the height of the water in the reservoir; and that a pipe employed to carry off a portion of water from an aqueduct should, as circumstances required, have a position more or less inclined to the original direction of the current. But as he was unacquainted with the law of the velocities of running water as depending upon the depth of the orifice, the want of precision which appears in his results is not surprising. Benedetto Castelli (1577-1644), and Evangelista Torricelli (1608- 1647), two of the disciples of Galileo, applied the discoveries of their master to the science of hydrodynamics. In 1628 Castelli published a small work, Delia misura dell' acque correnti, in which he satis- factorily explained several phenomena in the motion of fluids in rivers and canals; but he committed a great paralogism in sup- posing the velocity of the water proportional to the depth of the orifice below the surface of the vessel. Torricelli, observing that in a jet where the water rushed through a small ajutage it rose to nearly the same height with the reservoir from which it was supplied, imagined that it ought to move with the same velocity as if it had fallen through that height by the force of gravity, and hence he deduced the proposition that the velocities of liquids are as the square root of the head, apart from the resistance of the air and the friction of the orifice. This theorem was published in 1643, at the end of his treatise De motu gravium projectorum, and it was con- firmed by the experiments of Raffaello Magiotti on the quantities of water discharged from different ajutages under different pressures (1648). In the hands of Blaise Pascal (1623-1662) hydrostatics assumed the dignity of a science, and in a treatise on the equilibrium of liquids (Sur t'equilibre des liqueurs), found among his manuscripts after his death and published in 1663, the laws of the equilibrium of liquids were demonstrated in the most simple manner, and amply confirmed by experiments. The theorem of Torricelli was employed by many succeeding writers, but particularly by Edme Mariotte (1620-1684), whose Traiti du mouvement des eaux, published after his death in the year 1686, is founded on a great variety of well-conducted experiments on the motion of fluids, performed at Versailles and Chantilly. In the discussion of some points he committed considerable mistakes. Others he treated very superficially, and in none of his experiments apparently did he attend to the diminution of efflux arising from the contraction of the liquid vein, when the orifice is merely a perforation in a thin plate ; but he appears to have been the first who attempted to ascribe the discrepancy between theory and experiment to the retardation of the water's velocity through friction. His contem- porary Domenico Guglielmini (1655-1710), who was inspector of the rivers and canals at Bologna, had ascribed this diminution of velocity in rivers to transverse motions arising from inequalities in their bottom. But as Mariotte observed similar obstructions even in glass pi[)es where no transverse currents could exist, the cause assigned by Guglielmini seemed destitute of foundation. The French philosopher, therefore, regarded these obstructions as the effects of friction. He supposed that the filaments of water which graze along the sides of the pipe lose a portion of their velocity; that the contiguous filaments, having on this account a greater velocity, rub upon the former, and suffer a diminution of their celerity; and that the other filaments are affected with similar retardations proportional to their distance from the axis of the pipe. In this way the medium velocity of the current may be diminished, and consequently the quantity of water discharged in a given time must, from the effects of friction, be considerably less than that which is computed from theory. The effects of friction and viscosity in diminishing the velocity of running water were noticed in the Principia of Sir Isaac Newton, who threw much light upon several branches of hydromechanics. At a time when the Cartesian system of vortices universally pre- vailed, he found it necessary to investigate that hypothesis, and in the course of his investigations he showed that the velocity of any stratum of the vortex is an arithmetical mean between the velocities of the strata which enclose it; and from this it evidently follows that the velocity of a filament of water moving in a pipe is an arith- metical mean between the velocities of the filaments which surround it. Taking advantage of these results, Henri Pitot (1695-1771) afterwards showed that the retardations arising from friction are inversely as the diameters of the pipes in which the fluid moves. The attention of Newton was also directed to the discharge of water from orifices in the bottom of vessels. He supposed a cylindrical vessel full of water to be perforated in its bottom with a small hole by which the water escaped, and the vessel to be supplied with water in such a manner that it always remained full at the same height. He then supposed this cylindrical column of water to be divided into two parts,— the first, which he called the " cataract," being an hyperboloid generated by the revolution of an hyperbola of the fifth degree around the axis of the cylinder which should pass through the orifice, and the second the remainder of the water in the cylindrical vessel. He considered the horizontal strata of this hyperboloid as always in motion, while the remainder of the water was in a state of rest, and imagined that there was a kind of cataract in the middle of the fluid. When the results of this theory were compared with the quantity of water actually discharged, Newton concluded that the velocity with which the water issued from the orifice was equal to that which a falling body would receive by descending through half the height of water in the reservoir. This conclusion, however, is absolutely irreconcilable with the known fact that jets of water rise nearly to the same height as their reservoirs, and Newton seems to have been aware of this objection. Accord- ingly, in the second edition of his Principia, which appeared in 1713, he reconsidered his theory. He had discovered a contraction in the vein of fluid {vena contractu) which issued from the orifice, and found that, at the distance of about a diameter of the aperture, the section of the vein was contracted in the subduplicate ratio of two to one. He regarded, therefore, the section of the contracted vein as the true orifice from which the discharge of water ought to be deduced, and the velocity of the effluent water as due to the whole height of water in the reservoir; and by this means his theory became more conformable to the results of experience, though still open to serious objections. Newton was also the first to investigate the difficult subject of the motion of waves (q.v.). In 1738 Daniel Bernoulli (1700-1782) published his Hydrodynamica seu de viribus et motibus fluidorum commentarii. His theory of the motion of fluids, the germ of which was first published in his memoir entitled Theoria nova de motu aquarum per canales quocun- que fluentes, communicated to the Academy of St Petersburg as early as 1726, was founded on two suppositions, which appeared to him conformable to experience. He supposed that the surface of the fluid, contained in a vessel which is emptying itself by an orifice, remains always horizontal; and, if the fluid mass is conceived to be divided into an infinite number of horizontal strata of the same bulk, that these strata remain contiguous to each other, and that all their points descend vertically, with velocities inversely pro- portional to their breadth, or to the horizontal sections of the reservoir. In order to determine the motion of each stratum, he employed the principle of the conservatio virium vivarum, and obtained very elegant solutions. But in the absence of a general demonstration of that principle, his results did not command the • confidence which they would otherwise have deserved, and it became desirable to have a theory more certain, and depending solely on the fundamental laws of mechanics. Colin Maclaurin (1698- 1746) and John Bernoulli (1667-1748), who were of this opinion^ resolved the problem by more direct methods, the one in his Fluxions, published in 1 742, and the other in his Hydraulica nunc primum detecta, et demonstrata direcle ex fundamentis pure mechanicis, which forms the fourth volume of his works. The method employed by Maclaurin has been thought not sufficiently rigorous; and that of John Bernoulli is, in the opinion of Lagrange, defective in clearness and precision. The theory of Daniel Bernoulli was opposed also by Jean le Rond d'Alembert. When generalizing the theory of pendu- lums of Jacob Bernoulli (1654-1705) he discovered a principle of dynamics so simple and general that it reduced the laws of the motions of bodies to that of their equilibrium. He applied this n6 HYDROMECHANICS [HYDROSTATICS principle to the motion of fluids, and gave a specimen of its applica- tion at the end of his Dynamics in 1743. It was more fully developed in his Traite des fluides, published in 1744, in which he gave simple and elegant solutions of problems relating to the equilibrium and motion of fluids. He made use of the same suppositions as Daniel Bernoulli, though his calculus was established in a very different manner. He considered, at every instant, the actual motion of a stratum as composed of a motion which it had in the preceding instant and of a motion which it had lost; and the laws of equili- brium between the motions lost furnished him with equations re- presenting the motion of the fluid. It remained a desideratum to express by equations the motion of a particle of the fluid in any assigned direction. These equations were found by d'Alembert from two principles — that a rectangular canal, taken in a mass of fluid in equilibrium, is itself in equilibrium, and that a portion of the fluid, in passing from one place to another, preserves the same volume when the fluid is incompressible, or dilates itself according to a given law when the fluid is elastic. His ingenious method, published in 1752, in his Essai sur la resistance des fluides, was brought to per- fection in his Opuscules mathematiques , and was adopted by Leonhard Euler. The resolution of the questions concerning the motion of fluids was effected by means of Euler's partial differential coefficients. This calculus was first applied to the motion of water by d'Alembert, md enabled both him and Euler to represent the theory of fluids in formulae restricted by no particular hypothesis. One of the most successful labourers in the science of hydro- dynamics at this period was Pierre Louis Georges Dubuat (1734- 1809). Following in the steps of the Abb6 Charles Bossut (Nouvelles Experiences sur la resistance des fluides, 1777), he published, in 1786, a revised edition of his Principes d'hydraulique, which contains a satisfactory theory of the motion of fluids, founded solely upon experiments. Dubuat considered that if water were a perfect fluid, and the channels in which it flowed infinitely smooth, its motion would be continually accelerated, like that of bodies descend- ing in an inclined plane. But as the motion of rivers is not continually accelerated, and soon arrives at a state of uniformity, it is evident that the viscosity of the water, and the friction of the channel in which it descends, must equal the accelerating force. Dubuat, therefore, assumed it as a proposition of fundamental importance that, when water flows in any channel or bed, the accelerating force which obliges it to move is equal to the sum of all the resistances which it meets with, whether they arise from its own viscosity or from the friction of its bed. This principle was employed by him in the first edition of his work, which appeared in 1779. The theory contained in that edition was founded on the experiments of others, but he soon saw that a theory so new, and leading to results so different from the ordinary theory, should be founded on new experiments more direct than the former, and he was employed in the performance of these from 1780 to 1783. The experiments of Bossut were made only on pipes of a moderate declivity, but Dubuat used declivities of every kind, and made his experiments upon channels of various sizes. The theory of running water was greatly advanced by the re- searches of Gaspard Riche de Prony (t 755-1839). From a collection of the best experiments by previous workers he selected eighty-two (fifty-one on the velocity of water in conduit pipes, and thirty-one on its velocity in open canals) ; and, discussing these on physical and mechanical principles, he succeeded in drawing up general formulae, which afforded a simple expression for the velocity of running water. J. A. Eytelwein (1764-1848) of Berlin, who published in 1801 a valuable compendium of hydraulics entitled Handbuch der Mechanik und der Hydraulik, investigated the subject of the discharge of water by compound pipes, the motions of jets and their impulses against plane and oblique surfaces; and he showed theoretically that a water- wheel will have its maximum effect when its circumference moves with half the velocity of the stream. J. N. P. Hachette (1769-1834) in 1816-1817 published memoirs containing the results of experiments on the spouting of fluids and the discharge of vessels. His object was to measure the contracted part of a fluid vein, to examine the phenomena attendant on additional tubes, and to investigate the form of the fluid vein and the results obtained when different forms of orifices are employed. Extensive experiments on the discharge of water from orifices (Experiences hydrauliques, Paris, 1832) were conducted under the direction of the French government by J. V. Poncelet (1788-1867) and J. A. Lesbros (1790-1860). P. P. Boileau (1811-1891) discussed their results and added experiments of his own [Traite de la tnesure des eaux courantes, Paris, 1854). K. R. Bornemann re-examined all these results with great care, and gave formulae expressing the variation of the co- efficients of discharge in different conditions (Civil lngtnieur, 1880). Julius Weisbach (1806-1 871) also made many experimental in- vestigations on the discharge of fluids. The experiments of J. B. Francis (Lowell Hydraulic Experiments, Boston, Mass., 1855) led him to propose variations in the accepted formulae for the discharge over weirs, and a generation later a very complete investigation of this subject was carried out by H. Bazin. An elaborate inquiry on the flow of water in pipes and channels was conducted by H. G. P. Darcy (1803-1858) and continued by H. Bazin, at the expense of the French government (Recherches hydrauliques, Paris, 1866). German engineers have also devoted special attention to the measurement of the flow in rivers; the Beitrdge zur Hydrographie des Konig- reiches Bbhmen (Prague, 1872-1875) of A. R. Harlacher (1842-1890) contained valuable measurements of this kind, together with a com- parison of the experimental results with the formulae of flow that had been proposed up to the date of its publication, and important data were yielded by the gaugings of the Mississippi made for the United States government by A. A. Humphreys and H. L. Abbot, by Robert Gordon's gaugings of the Irrawaddy, and by Allen J. C. Cunningham's experiments on the Ganges canal. The friction of water, investigated for slow speeds by Coulomb, was measured for higher speeds by William Froude (1810-1879), whose work is of great value in the theory of ship resistance (Brit. Assoc. Report., 1869), and stream line motion was studied by Professor Osborne Reynolds and by Professor H. S. Hele Shaw. (X.) Hydrostatics Hydrostatics is a science which grew originally out of a number of isolated practical problems; but it satisfies the requirement of perfect accuracy in its application to phenomena, the largest and smallest, of the behaviour of a fluid. At the same time, it delights the pure theorist by the simplicity of the logic with which the fundamental theorems may be established, and by the elegance of its mathematical operations, insomuch that hydro- statics may be considered as the Euclidean pure geometry of mechanical science. 1 . The Different Slates of a Substance or Matter. — All substance in nature falls into one of the two classes, solid and fluid; a solid substance, the land, for instance, as contrasted with a fluid, like water, being a substance which does not flow of itself. A fluid, as the name implies, is a substance which flows, or is capable of flowing; water and air are the two fluids distributed most universally over the surface of the earth. Fluids again are divided into two classes, termed a liquid and a gas, of which water and air are the chief examples. A liquid is a fluid which is incompressible or practically so, i.e. it does not change in volume sensibly with change of pressure. A gas is a compressible fluid, and the change in volume is considerable with moderate variation of pressure. Liquids, again, can be poured from one open vessel into another, and can be kept in an uncovered vessel, but a gas tends to diffuse itself indefinitely and must be preserved in a closed reservoir. The distinguishing characteristics of the three kinds of sub- stance or states of matter, the solid, liquid and gas, are summarized thus in 0. Lodge's Mechanics: — A solid has both size and shape. A liquid has size but not shape. A 1 gas has neither size nor shape. 2. The Change of State of Matter. — By a change of temperature and pressure combined, a substance can in general be made to pass from one state into another; thus by gradually increasing the temperature a solid piece of ice can be melted into the liquid state of water, and the water again can be boiled off into the gaseous state as steam. Again, by raising the temperature, a metal in the solid state can be melted and liquefied, and poured into a mould to assume any form desired, which is retained when the metal cools and solidifies again; the gaseous state of a metal is revealed by the spectroscope. Conversely, a combination of increased pressure and lowering of temperature will, if carried far enough, reduce a gas to a liquid, and afterwards to the solid state; and nearly every gaseous substance has now undergone this operation. A certain critical temperature is observed in a gas, above which the liquefaction is impossible; so that the gaseous state has two subdivisions into (i.)a true gas, which cannot be liquefied, because its temperature is above the critical temperature, (ii.) a vapour, where the temperature is below the critical, and which can ultimately be liquefied by further lowering of temperature or increase of pressure. 3. Plasticity and Viscosity. — Every solid substance is found to be plastic more or less, as exemplified by punching, shearing and cutting; but the plastic solid is distinguished from the viscous fluid in that a plastic solid requires a certain magnitude of stress to be exceeded to make it flow, whereas the viscous liquid will yield to the slightest stress, but requires a certain length of time for the effect to be appreciable. HYDROSTATICS] HYDROMECHANICS 117 According to Maxwell (Theory of Heat) " When a continuous alteration of form is produced only by a stress exceeding a certain value, the substance is called a solid, however soft and plastic it may be. But when the smallest stress, if only continued long enough, will cause a perceptible and increasing change of form, the substance must be regarded as a viscous fluid, however hard it may be." Maxwell illustrates the difference between a soft solid and a hard liquid by a jelly and a block of pitch; also by the experiment of supporting a candle and a stick of sealing- wax; after a considerable time the sealing-wax will be found bent and so is a fluid, but the candle remains straight as a solid. 4. Definition of a Fluid. — A fluid is a substance which yields continually to the slightest tangential stress in its interior; that is, it can be divided very easily along any plane (given plenty of time if the fluid is viscous) . It follows that when the fluid has come to rest, the tangential stress in any plane in its interior must vanish, and the stress must be entirely normal to the plane. This mechanical axiom of the normality oj fluid pressure is the foundation of the mathematical theory of hydrostatics. The theorems of hydrostatics are thus true for all stationary fluids, however, viscous they may be; it is only when we come to hydrodynamics, the science of the motion of a fluid, that viscosity will make itself felt and modify the theory; unless we begin by postulating the perfect fluid, devoid of viscosity, so that the principle of the normality of fluid pressure is taken to hold when the fluid is in movement. 5. The Measurement of Fluid Pressure. — The pressure at any point of a plane in the interior of a fluid is the intensity of the normal thrust estimated per unit area of the plane. Thus, if a thrust of P lb is distributed uniformly over a plane area of A sq. ft., as on the horizontal bottom of the sea or any reservoir, the pressure at any point of the plane is P/A lb per sq. ft., or P/144A lb per sq. in. (lb/ft. 2 and lb/in. 2 , in the Hospitalier notation, to be employed in the sequel). If the distribution of the thrust is not uniform, as, for instance, on a vertical or inclined face or wall of a reservoir, then P/A represents the average pressure over the area ; and the actual pressure at any point is the average pressure over a small area enclosing the point. Thus, if a thrust AP lb acts on a small plane area AA ft. 2 enclosing a point B, the pressure p at B is the limit of AP/AA ; and />=lt(AP/AA)= = P/A = W/B, (1) the pressure p of the liquid being supposed uniform; and, by making the ratio B/A sufficiently large, the mechanical advantage can be increased to any desired amount, and in the simplest manner possible, without the intervention of levers and machinery. Fig. lb shows also a modern form of the hydraulic press, applied to the operation of covering an electric'cable with a lead coating. 8. Theorem. — In a fluid at rest under gravity the pressure is the same at any two points in the same horizontal plane; in other words, a surface of equal pressure is a horizontal plane. This is proved by taking any two points A and B at the same pa— poa—wa. AB, p=a.kB+p . (I) (2) Thus in water, where w = 62-4lb/ft. s , the pressure increases 62-4 lb/ft. 1 , or 62-44- 144 =0-433 lb/in. 2 for every additional foot of depth. 10. Theorem. — If two liquids of different density are resting in vessels in communication, the height of the free surface of such liquid above the surface of separation is inversely as the density. For if the liquid of density a rises to the height h and of density p to the height fe^and po denotes the atmospheric pressure, the pressure in the liquid at the level of the surface of separation will be ah+pt and pk+po, and these being equal we have oh=pk. (1) The principle is illustrated in the article Barometer, where a column of mercury of density a and height h, rising in the tube to the Torricellian vacuum, is balanced by a column of air of density p, which may be supposed to rise as a homogeneous fluid to a height k, called the height of the homogeneous atmosphere. Thus water Deing about 800 times denser than air and mercury 13-6 times denser than water, £/fc = (r/p = 8ooXi3-6 = io,88o; (2) and with an average barometer height of 30 in. this makes k 27,200 ft., about 8300 metres. 1 1 . The Head of Water or a Liquid. — The pressure ah at a depth h ft. in liquid of density a is called the pressure due to a head of h ft. of the liquid. The atmospheric pressure is thus due to an average head of 30 in. of mercury, or 30X13-6-7-12 =34 ft. of water, or 27,200 ft. of air. The pressure of the air is a convenient unit to employ in practical work, where it is called an " atmosphere "; it is made the equivalent of a pressure of one kg/cm 2 ; and one ton/inch 2 , employed as the unit with high pressure as in artillery, may be taken as 150 atmospheres. 12. Theorem. — A body immersed in a fluid is buoyed up by a force equal to the weight of the liquid displaced, acting vertically upward through the centre of gravity of the displaced liquid. For if the body is removed, and replaced by the fluid as at first, this fluid is in equilibrium under its own weight and the thrust of the surrounding fluid, which must be equal and opposite, and the sur- rounding fluid acts in the same manner when the body replaces the displaced fluid again; so that the resultant thrust of the fluid a"cts vertically upward through the centre of gravity of the fluid displaced,- and is equal to the weight. When the body is floating freely like a ship, the equilibrium of this liquid thrust with the weight of the ship requires that the weight of water displaced is equal to the weight of the ship and the two centres of gravity are in the same vertical line. So also a balloon begins to rise when the weight of air displaced is greater than the weight of the balloon, and it is in equilibrium when the weights are equal. This theorem is called generally the principle of Archimedes. It is used to determine the density of a body experimentally; for if W is the weight of a body weighed in a balance in air (strictly in vacuo), and if W' is the weight required to balance when the body is suspended in water, then the upward thrust of the liquid U8 HTOROMEGHANICS [HYE>R6STATICS or weight of liquid displaced is W-W, so that the specific gravity (S.G.) r i defined 1 as the ratio of the weight of a body to the weight of an equal volume of water 1 , is W/(W-W). As stated first by Archimedes, the principle asserts the obvious fact that a body displaces its own vorume of water; and he utilized it in the problem of the determination of the adulteration of the crown of Hiero. He weighed out a lump of gold and of silver of the same weight *s the clown; and, immersing the three in succession in water, he found they spilt over measures of water in the ratio t 1 ? -A;i& or 33: 24: 44; thence it follows that the gold : silver alloy of tfiefiorown was as 1 1 : 9 by weight. 13. Theorem. — The resultant vertical thrust on any portion of a curyed suffice exposed to the pressure of a fluid at rest under gravity is the weifrht of fluid cut out by vertical lines drawn round the .boundary of the curved surface. TTieorent.—^-The resultant horizontal thrust in any direction is obtilned by\ dr$t\fShg parallel horizontal lines round the boundary, and- intejfsecting i plane perpendicular to their direction in a plane curve; and then investigating the thrust on this plane area, which will, be tfce same as on the curved surface. The iSe&of of these theorems proceeds as before, employing the normality principle; they are required, for instance, in the deter- minatidn of the liquid thrust on any portion of the bottom of a ship. In casting a thin hollow object like a bell, it will be seen that the resultant upward thrust on the mould may be many times greater than the weight of metal; many a curious' experiment has been devised to illustrate this property and classed 3s a hydrostatic paradox (Boyle,' Hydrostatical Paradoxes, 1666). Consider,, for instance, the operation of casting a hemispherical bell, in fig. 2. As the molten metal is run in, the upward thrust on- the outside mould, when K' *i •" - - ■ K j the level has Teached PP', is the weight of metal in the volume gen- erated by the revolution of APQ; and this, by a theorem of, Archimedes, has the same volume as the cone ORR', or iir^*, where y is the depth of metal, the horizontal sections being equal so long as y is less than the radius of the outside hemisphere. Af terwai 'd s » , when the metal has risen above B, to the level KK', the additional thrust is the weight of the cylinder of diameter KK' and height BH. The upward thrust is the same, however thin the metal may be in the interspace between the outer mould and the core inside; and this was formerly considered paradoxical. A nalytical Equations of Equilibrium of a Fluid at rest under any System of Force. ■..'.', 14. Referred to three fixed coordinate axes, a fluid, in which the pressure is p, the density p, and X, Y, Z the components of impressed force per unit mass, requires for the equilibrium of the part filling a fixed surface S, on resolving parallel to Ox, JJlpdS =jjfp^dxdydz, where I, m, n denote the direction cosines of the normal outward of the surface Si • But by Green's transformation fJlpdS=Jff d £dxdydz, thus leading to the differential relation at every point The three equations of equilibrium obtained by taking moments round the axes are then found to be satisfied identically. Hence the space variation of the pressure in any direction, or the pressure-gradient, is the resolved force per unit volume in that direction. : The resultant force is therefore in the direction of the steepest pressure-gradient, and this is normal to the surface of equal pressure; for equilibrium to exist in a fluid the lines of force must therefore be capable of being cut orthogonally by a system of surfaces, which will be surfaces of equal pressure. Ignoring temperature effect, and taking the density as a function of the pressure, surfaces of equal pressure are also of equal density, and the fluid is stratified by surfaces orthogonal to the lines of force; \%-\%'\%^>l "■■;. (4) are the partial differential coefficients of some function ¥,=*fdplp, of *, y, z; so that X, Y, Z must be the partial differential coefficients of * potential -V, such that the force in any direction is the down- ward gradient of V ; and then ./ i . ZF+ar*" ' orP,+V=»constant, (S) Fig. 2. = pZ. (1) drawn (2) (3) in which P may be 'called the hydrostatic head and V the head of potential. • With variation of temperature, the surfaces of equal pressure and density need not coincide; but, taking the pressure, density and temperature as connected by some relation^ such as the gas-equation, the surfaces of equal density and temperature must intersect in lines lying on a surface of equal pressure. 15. As an. .example, of the general equations, take the simplest case of a uniform field of gravity, with Oz directed vertically down- ward ; employing the gravitation unit of force, I dp_ 1 dp _ 1 dp pdx~°' P~d~y" > ~J*~ 1 ' (1) P ay • p dz P=J = p£ = Rp0, (6) where denotes the absolute temperature ; and then r,d»_d (p\ i_ 2/£i). (10) In the convective equilibrium of the atmosphere, the air is sup- posed to change in density and pressure without exchange of heat by conduction ; and then p/po = (9/eo) n , ^o = (9/9o)» +1 , (II) dz \ dp . ,. .* , . ._ ,1 d8 = p-m = ( n+I) pi=( n + I)R ' 7=I +»- where y is the ratio of the specific heat at constant pressure and constant volume. In the mqre gerteral case of the convective equilibrium of a spherical atmosphere surrounding the earth, of radius a, P, ■(•■+»>S5— r**' (12) gravity varying inversely as the square of the distance r from the centre; so that, A=*po/.pa, denoting the height of the homogeneous atmosphere at the surface,:^ is given by («+i>ft(i-tf/9o)=o(i-o/r), (13). or if c denotes the distance where 9 = o, (14); 0o~r ' c — a' When the compressibility of water is taken into account in: a deep ocean, an experimental law must be employed, such as ! • p— p„ = k(j>— po), or pfp -i + (p— po)!K X = *po, .(15) so that X is the pressure due to a head k of the liquid' at density po under atmospheric pressure po\ and it is the gauge pressure required on this law to double the density. Then dp/dz = kdpldz** P , p = poe*'*, p-po = kpt,(.e'"'-i); (16) and if the liquid Was incompressible, the depth at pressure p would be (p—po)/po, so that the lowering of the surface due tocompressionTs ke'l k — k—z = %z?lk, when k is large. (17) For sea water, X is about 25,000 atmospheres, and k is then 25,000 times the height of the water barometer, about 250,000 metres, so that in an ocean 10 kilometres deep the level is lowered about 200 metres by the compressibility of the water; and the density at the bottom is increased 4 %. On another physical assumption of constant cubical elasticity A. &p*>\dplp, (/>'~fc»)/X=log(p/po), (18) z3 "/t ai = * p ' \pt pi ' p k' \**kpt, (19) HYPfcOSXATie?} r. HlCDRQAifEGHftNIGS ■J 19 and the lowering of the surface is ^~2 = Alog^-z«-Mog(i-!) r-.zft;^ (20) (3) (4) (5) : (6) (7) (8) (9) : Po °ft " ""°\" ft/ '"""'*B as before in 17). 16. Centre of Pressure. — A plane area exposed to fluid pressure on one side experiences a, single resultant thrust, the integrated pressure over the area, acting through a definite point called the centre of pressure (C.P.) of the area. Thus if the plane is normal to Ox, the resultant.thrust R^jfpdxdy, . .. , ' (1). and the co-ordinates x, y of the C.P. are given by xR=ffxpdXdy, yR= ffypdxdy. - (2) The C.P. is thus the C.G. of a plane lamina bounded by the area, in which the surface density is p. If p is uniform, the C.P. and C.G. of the area coincide. For a homogeneous liquid at rest under gravity, p is proportional . to the depth below the surface, i.e. to the perpendicular distance from the line of intersection of the plane of the area with the free surface of the liquid. If the equation of this line, referred to new coordinate axes in the plane area, is written x cos a -+• y sin a — h — O, R = ffp(h—xcos a— y sin a)dxdy, iR= fjpx(h-+x cos o— ysin w)dxdy, yR=fjpy(h — xcosa — y sin a)dxdy. Placing the new origin at the C.G. of the area A, ffxdxdy=o, fjydxdy^o, R = P«A,; xhA = —cos affx 2 dA— sin affxydA, yh A = — cos affxydA — sin a ffy*dA . Turning the axes to make them coincide with the pr'yiqipal axes of the area A, thus making JfxydA = o, \ xh= — a'coso, yft = — ft'sinoi (to) where f(x*dA^Aa*. //y'dA=A6', . (n) a and b denoting the semi-axes of the momental ellipse of the area. This shows that the C.P. is the antipole ofthejineof intersection of its plane with the free surface with respect to the momehtal ellipse at the C.G. of the area. Thus the C.P. of a rectangle or parallelogram with a side in the surface is at § of the depth of the tower side; of a triangle with a vertex in the surface and base horizontal is J of the depth of the base ; but if the base is in the surface, the C.P. is at half the depth of the vertex; as on the faces of a tetrahedron', with one edge in the surface. The core of an area is the name giver) tp the limited area round its C.G. within which the C.P. must He when the area is immersed completely; the boundary of the core is therefore the locus of the antipodes with respect to the momental ellipse of water lines which touch the boundary of_ the area. Thus the core of a circle or an ellipse is a concentric circle or ellipse of one quarter the size ; The C.P. of water lines passing through a fixed point lies ona straight line, the antipolar of the point; and thus the core of a tri- angle is a similar triangle of one quarter the size, and the core of a parallelogram is another parallelogram, the diagonals of which are the middle third of the median lines. In the design of a structure such as a tall reservoir dam it is important that the line of thrUst in the material should pass inside the core of a section, so that' the material should not be in a state of tension anywhere and so liable to open and admit the water. 17. Equilibrium and Stability of a Ship or Floating Body. The Metacenlre.—-The principle of Archimedes, in § 12 leads immediately . to the conditions of equili- brium of a body sup- ported freely in fluid, like a fish in water or a balloon in the air, or like a ship (fig, 3) floating partly im- mersed in water and the rest in air. The body is in equili- brium under two forces: — (i.) its weight W acting vertically . downward through G, the C.G. of the body, and (ii.) the buoyancy of the fluid, equal to the weight of the displaced fluid, and acting vertically upward through B, the C.G. of the displaced fluid; I""' r* M L G F iGt 2* V B, J s±~r for equilibriufii these two forces must be equal and opposite in the same line. The conditions of equilibrium of a body, floating like a ship on the surface of a liquid, are therefore: — (i.) the weight of the body must be less than the weight of the total volume of liquid it can displace; or else the body will sink to the bottom of the liquid; the difference of the weights is called the "reserve of buoyancy." (ii.) the weight of liquid which the body displaces in the position of equilibrium is equal to. the weight W of the body; and (iii.) the C.G.j B, of the liquid displaced and G of the body, must lie in the same vertical line GB. 18. In addition to . satisfying these conditions of equilibrium, a ship must fulfil the further condition of stability, so as to keep upright; if displaced slightly from this position, the forces called into play must be such as to restore the ship to the upright again. The stability of a ship, is investigated practically by inclining it; a weight is moved across the deck and the angle is observed of the heel produced. Suppose P tons is moved c ft. across the deck of a ship of W tons displacement! the C.G. Will move from G to Gi the reduced distance GiCa = c (P/W); and if B, called the centre of buoyancy, moves to Bi, along the curye of buoyancy BBi, the normal of this curve at Bi will be the new vertical B.1G1, meeting the old vertical in a point Kl, the centre of curvature of BBi, called the metacentre. • If the ' ship heels J through an angle or a slope of r in m, GM = GGic6t9=mc(P/W), (1) and GM is called the metacentric height; and the ship must be Joallasted, so that G lies below M. If G was above M, the tangent drawn from G to the evolute of B, and normal to the curve of buoyancy, would: give the vertical, in a new position of equilibrium. Thus in H.M.S. "Achilles" of. 9000 tons displacement it was found that moving 20 tons' across the deck, a distance of 42 ft., caused the bob of a pendulum 20! ft. long to move through ro in., so that ' K Fig. 3. GM, 24°\>.„\. 20 r = -iF* 42X 9 -5oo^ 2 ' 2 4 f t.;. ..(*> also potfl-24, 0=2° 24'. (3),. In.a diagram it is_CQnducive.to clearness to draw the ship in on* position, and to incline the water-line; and the p^ge can be turned if it is desired to bring the new water-line horizontal. Suppose the ship turns about an axis through F in the water-line area, perpendicular to the plane of the paper; denoting by y the distance of an element dA if the water-line area from the axis of rotation; the change of displacement is XydA tan 0, so that there is ho change of displacement if 2ydA=o, that is, if the qxi^ passes through the C.G. of the water-line area, which we denote by F and call the centre of flotation. The righting couple of the wedges of immersion and emersion will be XwydA tiin&.y = w tan 6ifdA = w tan 0.A& 2 ft. tons, (4) ■w denoting the density of water in tons/ft. 3 , and W=k»V, for a displacement of V ft. 3 This couple, combined with the original buoyancy W through B, is equivalent to the new buoyancy through B, so that W.BBj^wA^tanfl, (5) • BM=BB 1 cot0 = A^/V, (6) giving the radius of curvature BM of the curve of buoyancy B, in terms of the displacement V, and Ak 2 the moment of inertia of the water-line area about /an axis through F, perpendicular to the- plane of displacement, , . An inclining couple due to moving a weight about in a ship will heel the, ship about an axis perpendicular to the plane of the couple* only when this axis is a principal axis at F of the momental ellipse of the water-line area A. For if the ship turns through a small angle; about the line FF.', then bi, 62, the C.G. qf the wedge of imwerslion and emersion, w)ll be the C.P. with respect to FF' of the two parts of the water-line area, so that JA will be conjugate to FF' with respect to the momental ellipse at F. . ' * ; The naval architect distinguishes between the stability of, form, represented by the righting couple W.BM, and the stability ' oj ' baUast- ing, represented by W.BG. Ballasted with G at B, the righting couple when the ship is heeled through 0is given by W.BM. tan0; but if weights inside the ship are raised to bring G above B, the righting couple is diminished. b_y, W.BG. tan 0, so that the resultant righting couple is W,GM/ tan '0. Provided the ship is designed to 'float upright at the smallest draft with no load on board, the stability at any other draft of water can be arranged by the stowage of the weight, high or low. 19. Proceeding as in § 16 for the determination of the C.P. of an area, the same argument will show that an inclining couple due to 120 HYDROMECHANICS (HYDRODYNAMICS the movement of a weight P through a distance c will cause the ship to heel through an angle about an axis FF' through F, which is conjugate to the direction of the movement of P with respect to an ellipse, not the mdmental ellipse of the water-line area A, but a confocal to it, of squared semi-axes a J -W/A, P-AV/A, (i) h denoting the vertical height BG between C.G. and centre of buoyancy. The varying direction of the inclining couple Pc may be realized by swinging the weight P from a crane on the ship, in a circle of radius c. But if the weight P was lowered on the ship from a crane on shore, the vessel would sink bodily a distance P/wA if P was deposited over F; but deposited anywhere else, say over Q on the water-line area, the ship would turn about a line the antipolar of Q with respect to the confocal ellipse, parallel to FF', at a distance FK from F FK = (#-W/A)/FQsinQFF' (2) through an angle $ or a slope of one in m, given by sin9= ^=i?A^ = W-ApIV F Q sin 2 FF '' ( 3> where k denotes the radius of gyration about FF' of the water-line area. Burning the coal on a voyage has the reverse effect on a steamer. Hydrodynamics 20. In considering the motion of a fluid we shall suppose it non-viscous, so that whatever the state of motion the stress across any section is normal, and the principle of the normality and thence of the equality of fluid pressure can be employed, as in hydrostatics. The practical problems of fluid motion, which are amenable to mathematical analysis when viscosity is taken into account, are excluded from treatment here, as constituting a separate branch called "hydraulics" (q.v.). Two methods are employed in hydrodynamics, called the Eulerian and Lagrangian, although both are due originally to Leonhard Euler. In the Eulerian method the attention is fixed on a particular point of space, and the change is observed there of pressure, density and velocity, which takes place during the motion; but in the Lagrangian method we follow up a particle of fluid and observe how it changes. The first may be called the statistical method; and the second the historical, according to J. C. Maxwell. The Lagrangian method being employed rarely, we shall confine ourselves to the Eulerian treatment. The Eulerian Form of the Equations of Motion. 21. The first equation to be established is the equation of continuity, which expresses the fact that the increase of matter within a fixed surface is due to the flow of fluid across the surface into its interior. In a straight uniform current of fluid of density p, flowing with velocity q, the flow in units of mass per second across a plane area A, placed in the current with the normal of the plane making an angle 8 with the velocity, is oAq cos 0, the product of the density p, the area A, and q cos the component velocity normal to the plane. Generally if S denotes any closed surface, fixed in the fluid, M the mass of the fluid inside it at any time t, and 9 the angle which the outward-drawn normal makes with the velocity q at that point, d"Stl/dt =rate of increase of fluid inside the surface, (1) = flux across the surface into the interior ■ = ~JJpq cos 0 ~Sy~ dpuw v dx' (5) (6) (7) with two similar equations. The absolute unit of force is employed here, and not the gravitation unit of hydrostatics; in a numerical application it is assumed that C.G.S. units are intended. These equations may be simplified slightly, using the equation of continuity (5) §21; for dpu It' dpu* , dpuv , dpuw r_ d7 + dy + dz (du . du . du . du\ = p Xdi+ u Tx +v dy- +w Tz) j... (dp .dpu dpv dpw\ +u \dt + -d-x-+-% + -dT)' (8) reducing to the first ljne, the second line vanishing in consequence of the equation of continuity; and so the equation of motion may be written in the more usual form du , du , du , du -v idp /„% 3r+«s+ B 3y +u, ar" x "7S' (9) with the two others dv +«; d7 T "3x dv , dv . dv v I dp dy dw dz dw (io) ffff/xdydz-ffWS (3) where the integrations extend throughout the volume and over the surface of a closed space S; I, m, n denoting the direction cosines of the outward-drawn normal at the surface element <2S, and £, ij, f any continuous functions of x, y, 2. The integral equation of continuity (1) may now be written ! z£dxdydz+ff(lpu+mpv+npw)dS=o, (4) fffi pdy' dw , dw , dw , dw 1 1 dp H+ u Tx +v dy-+ w dz- =Z -pTz- 23. As a rule these equations are established immediately by determining the component acceleration of the fluid particle which is passing through (x, y, z) at the instant t of tiwie con- sidered, and saying that the reversed acceleration or kinetic reaction, combined with the impressed force per unit of mass and pressure-gradient, will according to d'Alembert's principle form a system in equilibrium. To determine the_ component acceleration of a particle, suppose'E, to denote any function of x, y, z, t, and investigate the time rate of F for a moving particle ; denoting the change by DF /dt, DF = , F(x+uSl, y+vM, z+wSt, t+St)-¥(x, y, 2, t) IT it dF dF . dF . (I? ,-,.", dF, ~^i+ u dx- +v ly- +w dz-' and D/dt is called particle differentiation, because it follows the rate of change of a particle as it leaves the point x, y, 2; but dF/dt, dF/dx, dF/dy, dF/dz (2) represent the rate of change of F at the time t, at the point, *, y, z, fixed in space. HYDRODYNAMICS] HYDROMECHANICS 121 The components of acceleration of a particle of fluid are conse- quently Dm du . du . du . du dv (3) (4) (5) dt ~ dt ^"di^'dy Dr dv , dv , dv , -dT=Ji+ u dH +v d^+ w ^ Dw dw , dw , dw , dw -dT = W+ u -dH +v -dy +w Tz leading to the equations of motion above. If F (x, y, z, /) =o represents the equation of a surface containing always the same particles of fluid, DF dF , dF . dF . dF ,,, It = °' 0T dt +u di +v ly +W &~ < (6 > which is called the differential equation of the bounding surface. A bounding surface is such that there is no flow'of fluid across it, as expressed by equation (6). The surface always contains the same fluid inside it, and condition (6) is satisfied over the complete surface, as well as any part of it. But turbulence in the motion will vitiate the principle that a bounding surface will always consist of the same fluid particles, as we see on the surface of turbulent water. 24. To integrate the equations of motion, suppose the impressed force is due to a potential V, such that the force in any direction is the rate of diminution of V, or its downward gradient ; and then iVldz; (1) Putting x= = -dV/dx, Y = -dM/dy, Z and putting dw dy dv t -dz = 2 Z< du dz dw dx' = 2V, dv 2* if. dx , dv ,<*{-. r 2y + dz~ =0, dy 2f> the equations of motion may be written du _ , ,dH - Tt -2vi+2wn+-^=o, dv t , _+v 1 +w*, (2) (3) (4) (5) (6) (7) (8) JLu dv J.w . . /du . dv . dw\ . . ^dx'^dx'^dx+^dx+d^+Tz)" ' ®> (10) (U) (12) and the three terms in H may be called the pressure head, potential head, and head of velocity, when the gravitation unit is employed and \q % is replaced by hq'/g. Eliminating H between (5) and (6) 21 dt *dx ''dx "dx~ r ' i \dx~ r dy and combining this with the equation of continuity 1 Dp du . dv . dw p dt + dx + dy + dz~ ' we have g (?)- *^-2 * ?^ = 0> dt \p/ pdx pdx p dx ' with two similar equations. Putting a vortex line is defined to be such that the tangent is in the direction of u, the resultant of £, v, f, called the components of molecular rotation. A small sphere of the fluid, if frozen suddenly, would retain this angular velocity. If w vanishes throughout the fluid at any instant, equation (11) shows that it will always be zero, and the fluid motion is then called irrotalional; and a function exists, called the velocity function, such that udx-\-vdy+wdz = -d, (13) and then the velocity in any direction is the space-decrease or downward gradient of (j>. 25. But in the most general case it is possible to have three functions <£, \[<, m of x, y, 2, such that udx+vdy+wdz = -d4>-md\f', (1) as A. Clebsch has shown, from purely analytical considerations {Crelle, lvi.) ; and then and H- d$ m lt= K > (4) dK ■fa-2U$+2Wr,- ■ =0, . , rf(«A, m) 1 d(^,m) „ i d(f,m) ,, * _i (J(y, Z )' *~»d(*. *)' f- '+™ r >=-Ix-Tx< (7) and when q is stationary, the acceleration is normal to the surface H = constant, and the stream line is a geodesic. Calling the sum of the pressure and potential head the statical head, surfaces of constant statical and dynamical head intersect in lines on H, and the three surfaces touch where the velocity is stationary. Equation (3) is called Bernoulli's equation, and may be interpreted as the balance-sheet of the energy which enters and leaves a given tube of flow. If homogeneous liquid is drawn off from a vessel so large that the motion at the free surface at a distance may be neglected, then Bernoulli's equation may be written H=p!p+z+qV2g = Plp+h, (8) where P denotes the atmospheric pressure and h the height of the free surface, a fundamental equation in hydraulics; a return has been made here to the gravitation unit of hydrostatics, and Oz is taken vertically upward. In particular, for a jet issuing into the atmosphere, where /> = P, g 2 /2g=/i-z, (9) or the velocity of the jet is due to the head k—z of the still free surface above the orifice; this is Torricelli's theorem (1643), the foundation of the science of hydrodynamics. 27. Uniplanar Motion. — In the uniplanar motion of a homogeneous liquid the equation of continuity reduces to du , dv so that we can put dx+-dy-=°< u = — d^ldy , v = dt/dx, (1) (2) 122 HYDROMECHANICS [HYDRODYNAMICS where ^ is ? Junction of x, y, called the stream- or current-function ; interpreted physically, ^-^o. the difference of the value of ^ at a fixed point A and a variable point P is theflow, in ft. 3 / second, across any curved line AP from A to P, this being the same for all lines in accordance with the continuity. Thus if = vdx; and similarly di-=~udy with PP' parallel to Oy; and generally d^fds is the velocity across ds, in a direction turned through a right angle forward, against the clock. In the equations of uniplanar motion rf£_i« _ dty , dfy 2f dx dy ~ dx^dp -VV> suppose, so that in steady motion and vV must be a function of i£. If the motion is irrotational, d H , _, , dty 3? +vV = o, dx dy' d~y dx' (3) (4) (5) so that 4> and <£ are conjugate functions of * and, y, +*i=*f(x+yi), vV=o. v**=«o; (6) or putting +\j/i=w, x+yi-z, w=f{z). The curves = constant and 4> — constant form an orthogonal system; and the interchange of (j> and =mlogr, 4i=m$, ^-\-^i~m log re' 9 , vi—m log s. (7) Interchanging these values ^ = mlcgr, = m6, i=m log re* e (8) gives a state of vortex motion, circulating round Oz, called a straight or columnar vortex. A single vortex will remain at rest, and Cause a velocity at any point inversely as the distance from the axis and perpendicular to Its direc- tion i analogous to the magnetic field of a straight electric, curneat. If other vortices are present, any one may be supposed to move with the velocity due to the others, the resultant streaniifiHvction being i£=fc2»z log r=log Mm; (9) the path of a vortex is obtained by equating the value of $ at the vortex to a constant, omitting the rm of the vortex itself. When the liquid is bounded by a cylindrical surface, the motion of a vortex inside may be determined as due to a series of vortex- images, so arranged as to make the flow zero across the boundary. For a plane boundary the image is the optical reflection of the vortex. For example, a pair of equal opposite' vortices, moving on a line parallel to a plane boundary, will have a corresponding pair of images, forming a rectangle of vortices, and the path of a vortex will be the Cotes spiral r sin 20 = 2~Vx for the component velocity V along Oy; and generally <-/ = vfr+Uy-V* (4) is the relative stream-function, constant over a solid boundary moVing with components U and V of velocity. If the liquid is stirred up by the rotation R of a cylindrical body, d^tds <= normal velocity reversed = -Rx' dx ds *y% (5) •A-HR^-hy'W, (6) a constant over the boundary; and 4 1 ' is the current-function of the relative motion past the cylinder, but now W'+2R=o, (7) throughput thejliquid. Inside an equilateral triangle, for instance, of height h, +' = - 2Rapy!h, ' (8) where a, 0, y are the perpendiculars on the sides of the triangle. In the general ease ^'=^-f-Uy- Vjc+JROtf-f-y 2 ) is the relative stream function for velocity components, U, V, R. 39. Example 1. — Liquid motion past a circular cylinder. Consider the motion given by w=U(z+a«/z), (1) A single vortex in a circular cylinder of radius a at a distance c from the centre will move with the velocity due to an equal opposite image at a distance a 2 lc, and so describe a circle with velocity mcl(a*-r?)in the periodic time 2*(a*-c 2 )[m. (12) Conjugate functions can be employed also' for the motion of tiquicf in a thin sheet between two concentric spherical surfaces; the com- ponents of velocity along the meridian and parallel in colatitude 8 and longitude X can be written d4 = i_ d$ 1 djj> _ djj fiii de = sin 8 d\' sin d\ " d6' { 3; and then 4> + ^ i = F (tan \8. «*•') . (14) 28. Uniplanar Motion of a Liquid due to the Passage of a Cylinder through it. — A stream-function -constant, over any fixed boundary ; (2) d^/ds =• normal velocity reversed over a solid boundary, (3) so that, if the solid is moving with velocity U in the direction Ox, di>lds— — Vdy/ds, or ^+U> = constant over the moving cylinder; so that ^ = u(r+7)cos9=u(i+^)*, ^Tj(,-f)sin0 = u(i-g)y. (2) Then 4/ = over the cylinder r = a, which may be considered a fixed post; and a stream line past it along which ^ = Uc, a constant, is the curve ■ \ (3) a cubic curve (C3). Over a concentric cylinder, external or internal, of radius r = b, I r - —) sin 6 =>c, (* 5 +y 2 )(y-c) -o 2 y = o, .). ric cylinder, 1 *W+U,y-lu(i-g|)+Ui]y, (4) and $' is zero if Ui/U = (a 2 -frW; (5) so that the cylinder may swim for an instant in the liquid without distortion, with tb,is velocity Ui; and w in (1) will give the liquid motion in the, interspace between the fixed cylinder r = o and the concentric cylinder r = 6, moving with velocity Ui. When 6 = 0, Ui=oo; and when 6 = 00, Uj=>-U, so that at infinity the liquid is streaming in the direction *0 with velocity U. If the liquid is reduced to rest at infinity by the superposition of an opposite stream given by 10= — Uz, we are left with . «- = Ua 2 /z, (6) = U(a 2 /r) cos 8 = Ua'x/(x*+f), i*** -U(a 2 /r) sin = -Va'y/ix'+f), (7) (8) giving the motion due to the passage of the Cylinder r = a with velocity U through the origin O in the direction Ox. If the direction of motion makes an angle 8' with 0#, d(j> jd4> _2xy tan9 ' = Ty/^=^ f = tan 28, 8 = is', and the Velocity is Ua J /r 2 . . Along the path of a particle, defined by the C 3 of (3), _ y(y-c) x i + y i o 2 • sin 2 \8' = . . .,d0' iy -cdv (9) (JO) (») on the radius of curvature is Ja 2 /(y — %c), which shows that the curve is an Elastica or Lintearia. (J. C. Maxwell, Collected Works, ii. 208.) If cos 6. add = irpa 2 (u 55- and over r = 5 X, =ffxt>cosB.bdd = xpb 2 /u 5^ and the difference X-Xi is the component momentum of the liquid in the interspace ; with similar expressions for Y and Yi. Then, if the outside cylinder is free to move Y V, 2a 2 Y ,„V " 2 Ai=o, Tr = M_L.„2' -X. = 7rpa-U -a 2 )' (20) (21) U P-fa 2 ' "-""■-"&+&• But if the outside cylinder is moved with velocity Ui, inside cylinder is solid or filled with liquid of density a, 2pV> X = -TrirafV, -ft p(6 2 +a 2 )+o'(6 s -a s U-U. ._ (p-g)(y-a') Ui -p(V+a*)'+<,{&-a?)> (22) and the (23) to space filled with liquid, and at rest at infinity, the cylinder will experience components of force per unit length (i.) —2TpmV, 2irpwU, due to the vortex motion ; (ii.) — irpa 2 -T7-, —xpo?-37, due to the kinetic reaction of the liquid; (iii.) o, —r( or <<7. 30. The expression for w in (1) § 29 may be increased by the addition of the term i'm log z=~mB -f im log r, (1) representing vortex motion circulating round the annulus of liquid. Considered by itself, with the cylinders held fixed, the vortex sets up a circumferential velocity m/r on a radius r, so that the angular momentum of a circular filament of annular cross section dA. is pmd.\, and of the whole vortex is pmr(b 2 — a?). Any circular filament can be started from rest by the application of a circumferential impulse rpmdr at each end of a diameter; so that a mechanism attached to the cylinders, which can set up a uniform distributed impulse irpm across the two parts of a diameter in the liquid, will generate the vortex motion, and react on the cylinder with an impulse couple— pmira 2 and pmjri 2 , having re- sultant pm7r(6 2 — a 2 ), and this couple is infinite when b = 00 , as the angular momentum of the vortex is infinite. Round the cylinder r =0 held fixed in the U current the liquid streams past with velocity }'=2U s'me+m/a; (2) and the loss of head due to this increase of velocity from U to q' is 1*~ U " _ < 2lJ sin e + m l a ) i - U 8 2g 2g so that cavitation will take place, unless the head at a great distance exceeds this loss. The resultant hydrostatic thrust across any diametral plane of the cylinder will be modified, but the only term in the loss of head which exerts a resultant thrust on the whole cylinder,, is 2mU sin 6/ga, and its thrust is 2xpmU absolute units in the direction Cy, to be counteracted by a support at, the centre C; the liquid is streaming past r = a with velocity U reversed, and the cylinder is surrounded by a vortex. Similarly, the streaming velocity V reversed will give rise to a thrust 2xp»»V in the direction xC. Now if the cylinder is released, and the components U and V are reversed so as to become the velocity of the cylinder with respect (3) jrfU 1 dt = - irpa' „dV_ dt 2-rpmV, JV 2 iV . .. . ■ . , (4) (5) or, putting jm = ; in this way the velocity may be calculated of the propagation of ripples and waves on the surface of a vertical whirlpool in a sink. Restoring a will make the path of the cylinder a trochoid; and so the swerve can be explained of the ball in tennis, cricket, base- ball, or golf. Another explanation may be given of the sidelong force, arising from the velocity of liquid past a cylinder, which is encircled by a vortex. Taking two planes x — =*= b, and considering the increase of momentum in the liquid between' them, due to the entry and exit of liquid momentum, the increase across dy in the direction Oy, due to elements at P and P' at opposite ends of the diameter PP', is pdy (U ■ — UaV -2 cos 2 0+mr _1 sin ^(UoV -2 sin 2 e+mr~ l cosfl) -f pdy ( — U+UaV -2 cos2 0+«r~ 1 sin0)(UaV~ 2 sin20 — mr~ l cosS) =2pdymtJr- l (.cos6— a, 2 r^ cos 30), '(&)'' and with y = b tan 6, r = b sec 9, this is 2pmVd$(i— a'b-^coB 36 cos 6), (9) and integrating between the limits 6= ± 5T, the resultant, as before, is Ijrpmtj. 31. Example 2. — Confocal Elliptic Cylinders. — Employ the elliptic coordinates n, |, and f = i;+|t, such that 2=cchf, x = ccht) cos f, y — cshti sin£; (1) then the curves for which i\ and { are constant are confocal ellipses and hyperbolas, and = §c 2 (ch2i) — cos2£)=rir 2 = OD 2 , (2) if OD is the semi-diameter conjugate to OP, and n, r% the focal distances, n,r 2 = c(ch)j±cos£); (3) r* = x 2 +y- = c 1 (ch ! 7j - sin 2 ?) (4) = sC ! (ch2»;+cbS2j). Consider the streaming motion given by w = mch(f—y), 7 = a+/3i, (jj)

with the hyperbola /3; and with this velocity the ellipse ij can be swimming in the liquid, without distortion for an instant. At infinity Tj = --e "cos /S = -^TTjCOS /3, V = e _<, sin /3 = ■ a + b sin (S, (9) a and 6 denoting the semi-axes of the ellipse o; so that the liquid is streaming at infinity with velocity Q=m/(a+b) in the direction of the asymptote of the hyperbola /3. Art ellipse interior to r/ = a will move in a direction opposite to the exterior current ; and when 17 = o, U = 00 , but V = (m/c) 1 sh a sin 0. Negative values of ri must be interpreted by a streaming motion on a parallel plane at a level slightly different, as oil a double Riemann sheet, the 'Stream passing from 6ne: sheet to the other across a cut SS' joining the foci S, S'. A diagram has been drawn by Col. P.. L. Hippisley. 124 HYDROMECHANICS [HYDRODYNAMICS The components of the liquid velocity q, in the direction of the normal of the ellipse ij and hyperbola £ , are -wJ- 1 sh(^o)cos(t-(S),wJ-»ch(^-o)sin(^). do) The velocity q is zero in a corner where the hyperbola /S cuts the ellipse a; and round the ellipse a the velocity g reaches a maximum when the tangent has turned through a right angle, and then „ V (ch 2a-cos 20) s = Q ea sFi^ — • (II) and the condition can be inferred when cavitation begins. With = o, the stream is parallel to *o, and <£ = »»cb(T*a)cos£ = - Uc ch (ij-a) sh ij cos £/sh (17-0) (12) over the cylinder ij, and as in (12) § 29, /th(t)«a), reducing when = 00 to M' thij = M'(fr/o). Similarly, parallel to Oy, the increase of effective inertia is M'/th 17 th(i7-o), reducing to M'/th ij = M'(a/&), when = 00 , and the liquid extends to infinity. 32. Next consider the motion given by = wch 2(j)-a)sin2{, ^ = -w sh 2(i»-a)cos 2£; (1) in which ^=0 over the ellipse a, and fa=++hR(x 2 +?) = [-j»sh2(ij-a)+JRc 2 ]cos2{+|Rc ! ch2rj, (2) which is constant over the ellipse tj if iRc 2 = msh 2(1,-0); (3) so that this ellipse can be rotating with this angular velocity R for an instant without distortion, the ellipse o being fixed. For the liquid filling the interior of a rotating elliptic cylinder of cross section x* la* +?l& = i, (4) fa'=miWa*+y*/b') (5) with vVi'=-2R=-2Wi(i/o 2 +i/& 2 ;, *i =m(x'/a*+y'lb*) - iR(x 2 +f) ^~iR(x 2 -y 2 )(a 2 -b 2 )/(a 2 +b 2 ), (6) fa = Rxy(a 2 -o 2 )l(a 2 +b 2 ), Wi=fa+fai = - hiR(x+yi)*(a 2 -P)/(a 1 +b i ). The velocity of a liquid particle is thus (a 2 — £> 2 )/(a 2 +6 2 ) of what it would be if the liquid was frozen and rotating bodily with the ellipse; and so the effective angular inertia of the liquid is (a 2 — fc 2 ) 2 /(a 2 +6 2 )' of the solid; and the effective radius of gyration, solid and liquid, is given by * 2 = i(a 2 +& 2 ),andK<* 2 -& J )7(a 2 +* 2 ). (7) For the liquid in the interspace between o and tj, _ m ch 2fa-a) sin 2f fa ~ JRc 2 sh 2r, sin 2^(0? - b 2 )!(a 2 +b 2 ) = i/th2(jra)th2i;; (8) and the effective k 2 of the liquid is reduced to !c 2 /th2(>j-a)sh2i|, (9) which becomes }c 2 /sh 2ij = J(o*-6*)/a6, when = 00, and the liquid surrounds the ellipse ij to infinity. An angular velocity R, which gives components — Ry, Rx of velocity to a body, can be resolved into two shearing velocities, — R parallel to Ox, and R parallel to 0> ; and then \p > s resolved into ^1+^2, such that ^-1 + jRc 2 and fa+^Ry 2 is constant over the boundary. Inside a cylinder fa+fai = - JiR(*+yi) 2 . Similarly, with the function X+yi=H[sin(£+mi)] (17) *=QcshlO,-a)sini(£-<8) (18) will give motion streaming past the fixed cylinder ij = a, and dividing along 4 = /S; and then x 2 — y 2 =c t sinjchij, 2ry = e 2 cos£ shij. (19) In particular, with sh o = I , the cross-section of 7; = o is x*+6x 2 y i +y*=2c i , or x i +y 4 =c* (20) when the axes are turned through 45°. 33. Example 3. — Analysing in this way the rotation of a rectangle filled with liquid into the two components of shear, the stream function fa is to be made to satisfy the conditions (i.)vVi=o, (ii.) fa-\-$Rx 2 = iRa 2 , or f =owhenj= =*=a, (iii.) fa + iRx 2 = hRa 2 , ^ 1 = |R(a 2 -x 2 ), when y= ±6 Expanded in a Fourier series, a , . 32 ,-Sp cos(2n+i)Wa , . ° * 7T 3 ° Z~i (2M + I) 3 ' u > so that . _ p l6 ,X~* C0 s(2«+l)^7rx/q . ch(2»+i)|iry/a *' 1-K 7r 3a 2*~ (2n+i) 3 .ch(2n+i)^7rfe/a ' x , , . .,,16 ,^T^ . cos(2n+i)j7rz/a_ w^fa+fa—iR^a 2^(2»+i) 3 ch(2» + l)ix6/a' (2) an elliptic-function Fourier series; with a similar expression for ^2 with x and y, a and 6 interchanged; and thence

= 2qt, H-/(^)= constant, throughout the liquid. When the motion is irrotational, dQ^ldj, dy y dx' d 1 &p f =0 - u= -Tx = —yTy "=- V**« dV , d 2 ^ 1 df °' or oV+3? y dy' (2) (3)- (4) (5) (6) (7) HYDRODYNAMICS] HYDROMECHANICS Changing to polar coordinates, * = r cos 6, y = r sin ft, the equation (2) becomes, with cos ft=/i, !25 '■fgH-cl-rtg-'i**' (8) of which a solution, when f = 0, is *- (*"*+5) d-^-(A^+^) /£, (9) <^ = [(n + i)Ar»-nBr-»- 1 lP n , (10) where P„ denotes the zonal harmonic of the nth order; also, in the exceptional case of ^ = A cos ft, = A /r; t = B r, = - B log tan %0 = -JB sh- 1 x/y. (11) Thus cos 8 is the Stokes' function of a point source at O, and PA- PB of a line source AB. The stream function tp of the liquid motion set up by the passage of a solid of revolution, moving with axial velocity U, is such that yTs = -V% * + * U ?' constant, (12) over the surface of the solid ; and ^ must be replaced by^-' = 2 in the general equations of steady motion above to obtain the steady relative motion of the liquid past the solid. For instance, with n = i in equation (9), the relative stream function is obtained for a sphere of radius a, by making it ^'=^ + iUy = |U(r 2 -o 3 /r)sin 2 e, + = -iUa> sin 2 ft/r; (13) and then 0' = U*(i+§a 3 /r 2 ), <*> = JUa 3 cosft/r 2 , (14) d IT* 1 * a dd> nid 1 . „ (15) so that, if the direction of motion makes an angle ^ with O*, tan W--£)=Jtanfl, tan ^ = 3 tan ft/(2 -tan 2 ft). (16) Along the path of a liquid particle , (19) which leads to no simple relation. The velocity past the surface of the sphere is 1 <¥' itt/', ,a 3 \sin 2 ft , TT . „ . , . so that the loss of head is (J sin 2 ft — i)U 2 /2g, having a maximum |U 2 /2g, (21) which must be less than the head at infinite distance to avoid cavitation at the surface of the sphere. With n — 2, a state of motion is given by ^-JU/aV/r 4 , ^' = |Uy 2 (i-aV 4 ), (22) ' = Ux+, <*>=-£U(aV 3 )P2, P. = fAi'-i, (23) representing a stream past the surface r* = a*p. 35. A circular vortex, such as a smoke ring, will set up motion symmetrical about an axis, and provide an illustration; a half vortex ring can be generated in water by drawing a semicircular blade a short distance forward, the tip of a spoon for instance. The vortex advances with a certain velocity; and if an equal circular vortex is generated coaxially with the first, the mutual influence can be observed. The first vortex dilates and moves slower, while the second contracts and shoots through the first; after which the motion is reversed periodically, as if in a game of leap-frog. Projected perpendicularly against a plane boundary, the motion is determined by an equal opposite vortex ring, the optical image; the vortex ring spreads out and moves more slowly as it approaches the wall; at the same time the molecular rotation, inversely as the cross-section of the vortex, is seen to increase. The analytical treatment of such vortex rings is the same as for the electro-magnetic effect of a current circulating in each ring. 36. Irrotational Motion in General. — Liquid originally at rest in a singly-connected space cannot be set in motion by a field of force due to a single- valued potential function; any motion set up in the liquid must be due to a movement of the boundary, and the motion will be irrotational ; for any small spherical element of the liquid may be considered a smooth solid sphere for a moment, and the normal pressure of the surrounding liquid cannot impart to it anv rotation. The kinetic energy of the liquid inside a surface S due to the velocity function is given by (1) by Green's transformation, dv denoting an elementary step along the normal to the exterior of the surface ; so that d$jdv = o over the surface makes T = o, and then [Tx) + W +U> °' Tx =0 ' Ty=°' Tz =0 - V If the actual motion at any instant is supposed to be generated instantaneously from rest by the application of pressure impulse over the surface, or suddenly reduced to rest again, then, since no natural forces can act impulsively throughout the liquid, the pressure impulse a satisfies the equations 1 da pdx = -u, -os, (3) 1 da_ _ 1 da P dy ' ~ p ~dz' c = p^>+a constant, (4) and the constant may be ignored; and Green's transformation of the energy T amounts to the theorem that the work done by an impulse is the product of the impulse and average velocity, or half the velocity from rest. In a multiply connected space, like a ring, with a multiply valued velocity function = m6 = m ta.n~ l y/x (5) will give motion to the liquid, circulating in any ring-shaped figure of revolution round Oz. To find the kinetic energy of such motion in a multiply connected space, the channels must be supposed barred, and the space made acyclic by; a membrane, moving with the velocity of the liquid; and then if k denotes the cyclic constant of in any circuit, or the value by which has increased in completing the circuit, the values of on the two sides of the membrane are taken as differing by k, so that the integral over the membrane ff&->ff&>- (6) and this term is to be added to the terms in (1) to obtain the ad- ditional part in the kinetic energy; the continuity shows that the integral is independent of the shape of the barrier membrane, and its position. Thus, in (5), the cyclic constant k = 2Trm. In plane motion the kinetic energy per unit length parallel to Oz -Itfifc-bftgi,. ( 7 ) For example, in the equilateral triangle of (8) § 28, referred to co- ordinate axes made by the base and height, r = -2RaPy/h = - iRyl(h-y)*-3x*]lh (8) ^-mW + iWy+h^-y^-yc'y+yyh (9) and over the base y = o, dx\dv = -dx/dy = +iR(ih?-3x*)/h,+ = - \R(\W-\-x*). (10) Integrating over the base, to obtain one-third of the kinetic energy T, = P IW/i35V3 (11) so that the effective k? of the liquid filling the triangle is given bv * 2 =T/J P R 2 A = 2^/45 * b s X = | (radius of the inscribed circle) 2 , (12) or two-fifths of the A 2 for the solid triangle. Again, since d4ldv = d^jis, djds= -d, (13) T = Ipftdf = - \ptyd4. (14) With the Stokes' function ^ for motion symmetrical about an axis. T = ipj4> -^firyds = rpffrlf. \i 5 ) 37. Flow, Circulation, and VorUx Motion.— -The line integral of the tangential velocity along a curve from one point to another, defined by i ( u Ts+ v 27+ w dl) ds-fiudx+vdy+zdz), (1) is called the " flux " along the curve from the first to the second point ; and if the curve closes in on itself the line integral round the curve is called the " circulation " in the curve. With a velocity function , the flow -fd4>= l -4, 2 , ( 2 ) 126 HYDROMECHANICS [HYDRODYNAMICS U) so that the flow is independent of the curve for all curves mutually reconcilable ; and the circulation round a closed curve is zero, if the curve can be reduced to a point without leaving a region for which is single valued. If through every point of a small closed curve the vortex lines are drawn, a tube is obtained, and the fluid contained is called a vortex filament. By analogy with the spin of a rigid body, the component spin of the fluid in any plane at a point is defined as the circulation round a small area in the plane enclosing the point, divided by twice the area. For in a rigid body, rotating about Oz with angular velocity j", the circulation round a curve in the plane xy is f f ( x P -3-^) ds = J times twice the In a fluid, the circulation round an elementary area dxdy is equal to " dx + ( v +a% dx ) dy ~ { u+ % dy ) dx ~ vd y- (f x -%) dx ^ fc> ' so that the component spin is _*(£-g)-r. <»> in the previous notation of § 24; so also for the other two com- ponents £ and i;. Since the circulation round any triangular area of given aspect is the sum of the circulation round the projections of the area on the coordinate planes, the composition of the components of spin, £, 7;. f, is according to the vector law. Hence in any infinitesimal part of the fluid the circulation is zero round every small plane curve passing through the vortex line; and consequently the cir- culation round any curve drawn on the surface of a vortex filament is zero. If at any two points of a vortex line the cross-section ABC, A'B'C is drawn of the vortex filament, joined by the vortex line AA', then, since the flow in AA' is taken in opposite directions in the complete circuit ABC AA'B'C A'A, the resultant flow in AA' cancels, and the circulation in ABC, A'B'C is the same; this is expressed by saying that at all points of a vortex filament «o is constant where a is the cross-section of the filament and w the resultant spin (W. K. Clifford, Kinematic, book iii.). So far these theorems on vortex motion are kinematical ; but introducing the equations of motion of § 22, D? + ^S =0 5?! + « = o ^+<*2 = o (6) dt^dx °' dt^dy °' dt^dz °' K) Q=fdph+V, (7) and taking dx, dy, dz in the direction of u, v, w, and dx: dy: dz — u: v: w. ^(udx + vdy + wdz'j ^dx+u- s f + dt (8) (9) origin are denoted by U, V, W, and the components of angular velocity of the frame of reference by P, Q, R; and then if «, v, w denote the components of fluid velocity in space, and u', v', w' the components relative to the axes at a point (x, y, 2) fixed to the frame of reference, we have « = U +u'-yK +zQ, (1) » = V +v' -sP +xK, w = W +iv'— xQ +yP. Now if k denotes the component of absolute velocity in a direction fixed in space whose direction cosines are /, m, n, k — lu-\-mv-\-nw; (2) and in the infinitesimal element of time dt, the coordinates of the fluid particle at (*, y, 2) will have changed by («', v', w')dt; so that Dk dl , dm , dn W~dt u+ lt v +Ji w = -dQ + W. and integrating round a closed curve -r I (udx+vdy+wdz) =0, and the circulation in any circuit composed of the same fluid particles is constant; and if the motion is differential irrotational and due to a velocity function, the circulation is zero round all reconcilable paths. Interpreted dynamically the normal pressure of the' sur- rounding fluid on a tube cannot create any circulation in the tube. The circulation being always zero round a small plane curve passing through the axis of spin in vortical motion, it follows con- versely that a vortex filament is composed always of the same fluid particles; and since the circulation round a cross-section of a vortex filament is constant, not changing with the time, it follows from the previous kinematical theorem that aw is constant for all time, and the same for every cross-section of the vortex filament. A vortex filament must close on itself, or end on a bounding surface, as seen when the tip of a spoon is drawn through the surface of water. Denoting the cross-section a of a filament by dS and its mass by dm, the quantity udS/dm is called the vorticity; this is the same at all points of a filament, and it does not change during the motion; and the vorticity is given by u cos edS/dm, if dS is the oblique section of which the normal makes an angle e with the filament, while the aggregate vorticity of a mass M inside a surface S is M~ l fo> cos edS. Employing the equation of continuity when the liquid is homo- geneous, 2 \dy ~dz) V " V dx- df di" K '> which is expressed by ' V«(tt,ti,w)-2 curl (£, n, D, (e.iJ. ?)=• J c« rI («.'»■ w). (11) 38. Moving Axes in Hydrodynamics. — In many problems, such as the motion of a solid in liquid, it is convenient to take ceordinate axes fixed to the solid and moving with it as the movable! trihedron frame of reference. The components of velocity of the moving , , Idu , ,du , ,du , ,du\ +/ {Tt+ U dx- +V r y +W dz-) , , /dv . ,dv , ,dv , dv \ + tK {di +u Tx +v dy+ w dz) . (dv> . ,dw . ,dw . ,dw\ +n Kdi +u dx +v Ty +w lz-)- (3) But as/, m, n are the direction cosines of a line fixed in space, * = «R-«Q,f5-»P-/R*f-JQ-«P; (4) so that -K x -?2) + "( Y -ig) + »( z -^' (5) . for all values of /, m, n, leading to the equations of motion with lotion is such that dA dip dl> dS d)b ~—m-f-. = — -. — «jt— . w = — ^—m-f-. moving axes. When the motion is such that u =-dx- m dx' v = -dT m dy' w '- dz "'dz' (6) as in § 25 (1), a first integral of the equations in (5) may be written + C-O@+-^)+(«-0(S+^)-F«. (7) in which 64. dt 3-(.-«'>g-<-»'>g-<.--'>2 dd dy =^~(U-yR+ 2 Q)g~(V-2P+*R)g-(W-*Q+?P)g (8) is the time-rate of change of at a point fixed in space, which is left behind with velocity components u — u', v—v', w—w'. In the case of a steady motion of homogeneous liquid symmetrical about Ox, where O is advancing with velocity U, the equation (5) of § 34 £/p+V-H'), r 2 vv=-/'(^+iu^). (12) Thus, for example, with +' = lU?(r*=*•- z£+*f. rope »«,+y|. ( 2 ) Now suppose the liquid to be melted, and additional component* of angular' velocity fit, O2, £2j communicated to the ellipsoidal case; the additional velocity communicated to the liquid, will be due to a velocity-function ' V-c* „e 2 -a 2 „a 2 -& J , x as may be verified by considering one term at a time. If «', v', w' denote the components of the velocity of the liquid relative to the axes, (4) (5) 2a- ■HP Thus 26 s 26* v' =v+zP - xR =^rp^«i«-^f^ n »*' w'=ui+A^-3'P=^^a2*-p^a 1 y 1 (6) P=a+f,Q=fis+i7, R=n»+r. (7) "'|+4 2 +"F,= ' {8) and then so that a liquid particle remains always on a similar ellipsoid. The hydrodynamkal equations with moving axes, taking into account the mutual gravitation of the liquid, become lg + 4xpAx + g-,R + .Q + u^| +W ^=o,..,..,(o) where . n r _ f» abcdk A ' H,C ' _ Jo (a>+X,6 2 +\,c 2 +).)P (jo) (12) (13) P 2 = 4 (a 2 -|-X)(J 2 +X)(c 2 +X). With the values above of u, v, w, «', »', w', the equations become of the form ^ d £.+4irpAx + a.x+hy+gz = o, (11) and integrating ^-» + 2rp(A* s + B/ + Gg 2 ) +J(, as follows also by algebraical reduction; and 4c 2 (<: 2 -a 2 ) „, ( c'--a\ V 4 6*(a'-& 8 ) r /a J -6*. :«» -'): (15) 4£i ^^p[(?+V) (0! +0S) - <«tt+i*i}«J '7 ^[^-N^fJ^-Ml-N^}, _^+^H9^-£) 1 i6c*(a 2 -e*) * J (23) where Z is a quadratic in f 4 , so that f is an elliptic function of./, except when e = a, or 3a. Put Oi = il cos 4>, Ch= —Q sin *,' , (a 2 +6 2 ) 2 "' n » U'+fi 2 ' with similar equations for /3 and y. If we can make (4T P A+a)* J = ( 4l rpB+/3)6 2 = ( 4 7rpC+7)c 3 , (16) the surfaces of equal pressure are similar to the external case, which can then be removed Without' affecting the motion, provided a, 0, 7 remain constant. This is so when the axis of revolution is a principal axis, say Dz; when S2i = o, 122 = 0, { = 0, ij = o. (17) If ftj = o or 03 = f in addition, we obtain the solution of Jacobi's ellipsoid of liquid of three unequal axes, rotating bodily about the least axis; and putting -a = 6, Maclaurin's solution is obtained of the rotating spheroid. In the general motion again of the liquid filling a case, when a = b, Qt may be replaced by zero, and the equations, hydrodynamical and dynamical, reduce to dj 2C dC W+c* dn, d v _ dr & fi 3r = £«+? Qi f''s a?+c' iQ&'-Oiiv) (18) a*+c dOt -jr=^s+^—^i^ ir= -«>f dt 3/ which three integrals are „1 _ ,-2?S . (19) (20) (21) (22) d_dQi n n dik_ a '+ c V nir i_n %> d*_ a'—c a'-fe 2 . N+ 4c 1 M+ 2c 2 (a 2 -e 2 ) r ' (24) (45) a 2 +c 2 N+^-F .#f. M+ 2C 2 (0 2 -C i ) f (26) which, as Z is a quadratic function of f 2 . ar e non-elliptic integrals; sff also for ^, where I = w cos i?-, 1; =— u sin ^; In a state of steady motion #. fli Q2 , "2i 'J r q c >a. (27) (28) :(29) (30) (31) (32) (33) An experiment was davised by Lprd Kelvin for demonstrating this, in which the difference of steadiness was shown of a copper shell filled with liquid and spun gyroscopically, according as the shell was slightly oblate or prolate. According to the theory above the stability is regained when the length is more than three diameters, so that a modern projectile with a cavity more than three diameters long should fly steadily when filled with water; While the' old-fashioned type, not so elongated, would he highly unsteady; and for the same reason the gas bags of a dirigible balloon should be over rather than under three diameters long. 40. A Liquid Jet.— By the use of the complex variable and its conjugate functions, an, attempt can be made to give a mathe- matical interpretation of problems such as the efflux of water in a jet or of smoke from a chimney, the discharge through a weir, the flow of water through the piers of a bridge, or past the side of a ship, the wind blowing on a sail or aeroplane, or against a wall, or impinging jets of gas or water; cases where a surface of discontinuity is observable, more or less distinct, which separates the running stream from the dead water or air. Uniplanar motion alone is so far amenable to analysis; the velocity function and stream function $ are given as conjugate functions of the coordinates x, yby iv =/(2)i where 2 = x +yi, w = + ^i, (1 ) and then Tz = dH +t dH = - u + n ' W so that, with « = 3 cos 6,v = q sin 9, the function f=-Qs=5As=|("+^"f( cos e+isiao), (3) gives f as a vector representing the reciprocal of the velocity 2 m direction and magnitude, in terms of some standard velocity Q. To determine the motion of a jet which issues from a vessel with plane walls, the vector f must be Constructed so as to have a constant 128 HYDROMECHANICS [HYDRODYNAMICS direction 8 along a plane boundary, and to give a constant skin velocity over the surface of a jet, where the pressure is constant. It is convenient to introduce the function Q = logf = log(Q/g)+« (4) so that the polygon representing £2 conformally has a boundary given by straight lines parallel to the coordinate axes; a.id then to determine £2 and w as functions of a variable u (not to be confused . with the velocity component of c), 'J . such that in the conformal repre- "' sentation the boundary of the and w polygon is made to coincide with the real axis of «. It will be sufficient to give a few illustrations. Consider the motion where the liquid is coming from an infinite distance between two parallel walls at a distance xx' (fig. 4), and issues in a jet between two edges A and A' ; the wall xA being bent at a corner B, with the external angle $ — \vln. The theory of conformal representation shows that the motion is given by where « = a, a' at the edge A, A 1 ; u = b at a corner B; w = o across **' where 4> = oo;and tt = oo, = oo across the end J J' of the jet, bounded by the curved lines APJ, A'P'J', over which the skin velocity is Q. The stream lines *BAJ, xA J' are given by ^=0, m; so that if c denotes the ultimate breadth J J' of the jet, where the velocity may be supposed uniform and equal to the skin velocity Q, m = Qc, c — m[Q. If there are more B corners than one, either on *A or x'A', the expression for f is the product of corresponding factors, such as in (5). Restricting the attention to a single corner B, . /Q\ \ „ ! • • m V (&-a'.«-a)+V (b-o.u-a') cos nd+i sh log \*j-j If 9 = across the end JJ' of the jet, where « = 00 , q = Q, chnG=cos»a = \/— -7, sh nQ — i sin na.=i\-r — -,, (19) a — b.b—a' , . „ a— a' Then cos 2rt«— cos 2118=2 -7— 1 — 2 =>»"" ■""* 1 a—a.u — o ' u — b = 3 sin 2 2tia- V (a — 6.6— a')V (u—a.u — b') , . sm2»9 = 2-i „'»,:_ h l (20) =sin 2«o a—a'.u — b V(«—a.«— a') u-b '• 2rt e ( b y(a-b.b-a') chn« = H» j (cos n8+i sin nff) = : ! = chlog(2)' =«r + r»)=V^\fe» 1 !°g (g) cos n8+i ch log {*) _ q— a'+(o+a') cos 2Wa — [a-rV-Ha — a') cos 2na]cos 2nd (0—0') sin 2 2na cos 2no — cos 2nd Along the wall AB, cos »0=o, sin 116 = 1, a>u>b, sin 2nd (6) sin «0 sh n£2 = sh 1 sin tiB and then oo>a>b>o>a'> -co ; (7) (8) (9) (10) 12 polygon has a right angle at u = a, a', and a zero angle at •re 9 changes from o to jx/w and 12 increases by \iirfn; so dU 1 V (b—a.b—a') dw _m du ~ 2it(u — 6)V (u—a.u—a'y du ~ ru' the formulas by which the conformal representation is obtained. For the u = b, where that da A , . j(b-a.b-o') Tu = (u-b)j(u-a.u-a>y Where A = 5S And the w polygon has a zero angle at « = o, 06, where ^ changes from otom and back again, so that w changes by im, and dw d~u Along the stream line *BAPJ, ^ = 0, u=atr*$l"", and over the jet surface J PA, where the skin velocity is Q, 3F--2--Q. denoting the arc AP by 5, starting at u = a; -6)V(w-a , ) + V(6-s')V(a-«) ] ' '"du u • •]" (22) (23) (24) (25) (26) (27) (28) (29) (30) -—, where B = . U V ±ae" s Q.l m =ae m t c , '-. (n) (12) (13) (14) ch„ n =cos«*=V;r^'\fe. . .. la — b . u—a' infl=, \a^a 7 \^F' sh »£2=t sin 1 (15) (16) (17) >u = ae w,, '>a, and this gives the intrinsic equation of the jet, and then the radius of curvature ds _idj>_idw_idw JdQ p ~ dd~Qde~Qla~Q~duld~u _c u — b V(m— a.u — a') ~x- 2B u V(o-6.ft-o')' not requiring the integration of (11) and (12) .(18) ch^shlog^^VS sh„a = ,-chlo g (2)"^V^^' d±_d±d$_ ™ c Q du" ' d dt ~ %qu ~~w qu AB_ f'Qdu * c 'J „q u _f[±l2 . ~J l~~ V(a-o')V(«-6') Along the wall Bx, cos n$ = 1 , sin nS = o, 6>«>o chn« = chlo g (2)" = Va^VS sh„^shlo g (2)" = ^VS' At x where 4> = 00 , u =0, and q =qo. In crossing to the line of flow x' A'P'J', \f/ changes from o to m, so that with g = Q across JJ', while across **' the velocity is go, so that m=qo.xx' = Q.jy (31) giving the contraction of the jet compared with the initial breadth of the stream. Along the line of flow *'A'P'J', f = m, u = a' 'e-*4> I" , and from x' to A', cos M0 = i, sin n&=o, ch„«=chlog(2)*=V^'VS 03) sh^shloglf)"^^^' (34) o>u>a'. (35) Along the jet surface A'J', q = Q, . ch " n = cosne = \a^ 7 \S (3°) shnQ=isinne=»- N /^i S /|£^, (37) a' >u = a'e" '">-», (38) giving the intrinsic equation. 41. The first problem of this kind, worked out by H. v. Helnr- holtz, of the efflux of a jet between two edges A and Ai in an infinite wall, is obtained by the symmetrical duplication of the above, with » = I, 6=^0, a' = — 00, as in fig. 5, chn= \ ! ir' shn= \ir : and along the jet APJ, >u=ae"' ,: >a, sh 0=t sin B=i^ = ie-^'"', I PM=I sin$ds=Je ^"'C" = 7— sin 8, (0 (2) (3) HYDRODYNAMICS] HYDROMECHANICS so that PT = c/fr, and the curve AP is the tractrix; and the co- efficient of contraction, or breadth of the jet it breadth of the orifice ~r+2' (4) A change of fi and into »fi an d „g w ;fl g-, ve t jj e solution for two walls converging symmetrically to the orifice AAi at an angle »•/«. With * = i, the re-entrant walls are given of Borda's mouthpiece, and the coefficient of contraction becomes J. Generally, by making a'=—°o, the line x'A' may be taken as a straight stream line of infinite length, forming an axis of symmetry; and then by duplica- tion the result can be ob- 5 -j. tained, with assigned n, a, A and b, of the efflux from a symmetrical converging f, Fig. 5. Fig. 6. mouthpiece, or of the flow of_ water through the arches of a bridge, with wedge-shaped piers to divide the stream. 42 Other arrangements of the constants n, a, b, a' will give the results of special problems considered by J. M. Michell, Phil. Trans. 1890. Thus with a'=o, a stream is split symmetrically by a wedge of angle x/n as in Bobyleff's problem; and, by making a = », the wedge extends to infinity ; then chnQ= Vft^ ,shnn= V^hi- a) Over the jet surface ^ = m, g = Q, u = -r»tf" = ~be"'l* t ch n = cos ne = yjp^+i* sh ° = * sin " =«' ^/jST^? ( 2 ) eW=tan«0,^r- / c =eJ»*/«4- e J>rW«4- I . (5) With n = i, the jet is reversed in direction, and the profile is the catenary of equal strength. In Bobyleff's problem of the wedge of finite breadth, ^-sW^.**-^^' (6) cos na = yj-, sin na = yj^—, (7) and along the free surface APJ, g = Q, ^ = 0, u = e-*$l m z=ag*'l e , cos n0=cos nai £1" /c = 1 \eir'/ e — cos'no' cos*mo sin*n0 = sin"n0-siri»»a' ^ the intrinsic equation, the other free surface A'P'J' being given by cos'tta sin*M0 «T« I' = sin'no — sin 2 nfl' (9) Putting n = 1 gives the case of a stream of finite breadth disturbed by a transverse plane, a particular case of Fig. 7. When a = h, a=o, and the stream is very broad compared with the wedge or lamina; so, putting w = w' (a — b)/a in the penultimate case, and M = oe~"^ia — (a— b)w', .. /5l±i •w' ch na = V^ 1 sh *" = V v^" (10) • («) in which we. may write ai'=tf>-hW. (12) Along the stream line xABPJ, ^=0; and along the jet surface APJ, — 1>4>>— °o; and putting $= —rs/c — 1, the intrinsic equation is ts/c =cot 2 «0, (13) which for n = I is' the evolute of a catenary, xrv. s 129 43. When the barrier AA' is held oblique to the current, the stream line xE is curved to the branch point B on AA' (fig. 7), and so must be excluded from the boundary of u; the conformal re- presentation is made now with dil V(6- ■a.b-a') du («-6)V u—a.u — a') dw '_ m 1 ~ x u—j m' 1 Xtt-j' m+m' u-b x u -j-u-j' 6 = mj'+m'j m-tm' ' taking « = co at the source where Fig. 7. <*> = ao , u = 6 at the branch point B, u=j, j' at the end of the two diverging streams where tf>=— 00; while ^=0 along the stream hne which divides at B and passes through A, A'; and \fr = j», -m' stream. Then along the outside boundaries, so that m/Q, m'/Q is the final breadth of the jets,and (m+m')/Q is the initial breadth, c, of the impinging Then * *" V^\fe- ** *«- \fe> V==& (3) chn = 2b— a— a' N "u-b' Aa-VN V(u "',''- , ' ) , u—b ' N=2 : a—b.b—a' a-a> • Along a jet surface, a = Q, and cha = cos0=cosa — |sin*a((f— o')/(«— b), (5) if = a at the source x of the jet *B, where « = «> ; and supposing =0, P' at the end of the streams where u =j,f, i — 1 „:„ s cos 9— cos u-b a— a' u-f sin 1 " cos a -cos 8' a-a! ' sin a (cos a-cosfl) (cos a -cos 0)' (6) j cos 0— COS 0' (cos a— cos 0') (coso— COS0)' and ^ being constant along a stream line dcj>_dw rAl_d4; _dw du du~ du'^d6~d8 ~ du d»' tQ ds ^vds _ (cos a— cos /3) (cos a— cos/S') sin 6 m+m' de c dH (cos o -cos 8) (cos -cos /S) (cos -cos 4^' sin cos a— cos 0"""cos (3- cos a— cos /S cos a— cos p' sin -cos /3''cos 0— cos /S sin cos/S— cos |3' cos 0— cos p" (7) giving the intrinsic, equation of the surface of a jet, with proper attention to the sign. From A to B, a>u>b, 0=o, chQ = chlog^*=cos a — \ sin 2 a" a a a^F shlog Q = l(£ .... shn Q_ (m— 6) cos a u.u — a') -\{a—a') sin^a+V (a— u.u— a')sin a (8) fidj__ftds d$__ _Qdtp ^du ^d du~ q du m-t-m' (« — 6)cosa — |(q— qQsin'a-fy (a — w.u — aQsina x j — u.u—j' (9) AB / a (2!>-a-a')(u-!>)-2(a-6)(i)-a')4-2V(a-6.5-a'.a-M.«-a') j 1[ . . a—a'.j—u .u—j f ' \ 10 / with a similar expression for BA'. The motion of a jet impinging on an infinite barrier is obtained by putting j = a, j' = a'\ duplicated on the other side of the barrier, the motion reversed will represent the direct collision of two jets of unequal breadth and equal velocity. When the barrier is small compared with the jet, a=/9=/3', and G. Kirchhoff's solution is obtained of a barrier placed obliquely in an infinite stream. Two corners Bi a«d Bj in the wall xA, with a' = — « , and n — \, will give the solution, by duplication, of a jet issuing by a reentrant mouthpiece placed symmetrically in the end wall of the channel ; or else of the channel blocked partially by a diaphragm across the middle, with edges turned back symmetrically, problems discussed by J. H. Michell, A. E. H. Love and M. Rethy. 11 i30 HYDROMECHANICS [HYDRODYNAMICS When the polygon is closed by the walls joining, instead of reach- ing back to infinity at **', the liquid motion must be' due |tO a source, and this modification has beeriworked out by B, Hepkiftson in the Proc. Lond. Math. Soc, 1898.' Mkhell has discussed also the hollow vortex Stationary iflside a polygon (Phil. Trans., 1890); the solution is given by '■■' chnQ-sniv,shnQ=icnm (11) so that, round trfe' boundary of the polygpn, ,^ = K', sin «9=-o; and on the surface of the vortex ^ = 0, 2 = Q, and cos«0 = sn#, «0 = |ir — atn.sjc, (12) the intrinsic equation of the curve. This is a closed Sumner line for n — l, when the boundary consists of two parallel walls; and n = J gives an Elastica. 44. The Motion of a Solid through a Liquid.— An important problem in the motion of a liquid is the determination of the state of velocity set up by the passage of a solid through it; and thence of the pressure and reaction of the liquid on' trie surface of the solid) by which its motion is influenced when it is free. ' Beginning with a single body in liquid extending to infinity-;' and denoting 'by U, V, W, P, Q, ft the components of linear and angular wtocity with respect to axes fixed in the body, the velocity function takes the form -^Ufc+V-fc+W^+Pxi+QjO+Rxs, (1) where the 0's ajid x's are functions oi/x, y, z/depending on the shape of the body; interpreted dynamically, C— p represents the impulsive pressure required to stop the motion, or C+p to start it again from rest. The terms of 4> may be determined one at a time, and this problem is purely kinematicat; thus to determine u the component U alone is taken to exist, and then /, m, n, denoting the direction cosines of the normal of the surface drawn into the exterior liquid, the function £1 must be determined to satisfy the conditions (i.) V s «fo=o, throughout the liquid; ellipsoid; and the liquid flows over an ellipsoid along a line of slope with respect to O*, treated as the vertical. Along the normal itself g-j*+i(rf+X#jl. (10) so that over the surface of an ellipsoid where X : and . are constant, the normal velocity.is the same as that of the ellipsoid itself, moving as a solid with velocity parallel to Ox ' U=.-^-2(o 2 +X)^, vu). ; and so the boundary condition is satisfied; moreover, any ellipsoidal surface X may be supposed moving as if rigid with the velocity in (1 1), without disturbing the liquid motion for the moment. 'The continuity is secured if the liquid between two ellipsoids X and Xi,, moving with the velocity U and Ui of equation (11), is squeezed 'out or sucked in across the plane x = o at a rate equal to the integral 4°w of the velocity tp across the annular area 01 — o of the two ellipsoids, madeby x = o ; or if aU-^U^J^V^X, j (12) I a = W(& 2 + X.C 2 + X). (13) (ii.) d(j>i dv = — /, the gradient of 4> down the normaTat the surface of the moving solid ; (iii.) tp=o, over a fixed boundary, or at infinity; similarly for ife and <£ s . To determine xi the angular velocity P alone is introduced, and the conditions to be satisfied are (i.) V s Xi = o, throughout the liquid; (ij.) <*£! = mz-ny, at the surface of, the moving body, but zero over av a fixed surface, and at Infinity ; the same for xs and xs- For a cavity filled with liquid in the interior of the body, since the liqukfinside moves bodily for a motion of translation only, -y, *»=-»;■ (2) but a rotation will stir up the liquid in the cavity, so that the x's depend on the shape of the surface. The ellipsoid was the shape first worked Out, by George Green, in his Research on the Vibration of a Pendulum in a Fluid Meaiutk (1833) ; the extension to any other surface will form an important strep in this subject. A system of confocal ellipsoids is taken X? , y , z* and a velocity function of the form * = **• . . (4) . where ^ is a function of Xohly,' so that 3T dx , . . ■j^+X; = g*+ 2 (a 2 +X)g (5) (6) (7) (8) (9) Expressed as a differential relation, with the value of .U from (11), 34+ 2 <°^Jx(4!H (14) (15) and integrating so that we may put (a'+xyvJ^^a constant, , f Md\ (16) (17) (18) P 2 =4ta 2 +X)(J 2 +X)(c»+X), where M denotes a constant ; so that ^ is an elliptic integral of the second kind. The quiescent ellipsoidal surface, over which the motion is entirely tangential,- is the one for which 2(« 2 +X)g+* = d, (19) and this is the infinite boundary ellipsoid if we make the upper limit Xi = » . The velocity of the ellipsoid defined by X = is then 11—*$-,* M f° Md\ , abc, X (a 2 +x)P ..Ta&U-A.). (20) with the notation ? . af , ... r abc <*X AorA A Jk (a 2 +X)P , d r°d\ (21) so that in (4) M . U*A ' * a a * = S&* A = f^A? * l -T=T2 (22) in (1) for an ellipsoid. , The impulse required to set up the motion in liquid of density p is the resultant of an impulsive pressure p over the surface S of the ellipsoid, and is therefore ffpldS = p

fd\ along the notmar of the U T=AV in this way the air drag was calculated by Green for an ellipsoidal pendulum. Similarly, the inertia parallel to Oy and Oz is B A" G X' and W, yW = iT(P i-G abcd\ W, For a sphere of the liquid in the interspace as the ellipsoid X=o is passing with velocity ; U through the confocal position; mu6t now take the form*(^+N) and will satisfy the conditions in the shape abc . f ai abcd\ 4 = Ux-A+lh+C^ = U.t aiblCl J *(<*' + MP K Bo+Co-B,-Ci" _ abc aibiCi / X] abed X (1) „ (a 2 + X)P and any confocal ellipsoid defined by \ internal or external to X = X,, may be supposed to swim with the liquid for an instant, without distortion or rotation, with velocity along 0* tt Ba+Ca-Bi-Ci Bb + Co-Bi-C/ Since - U* is the velocity function for the liquid W' filling the ellipsoid X=o, and moving bodily with it, the effective inertia of the ■ liquid in the interspace is Ao+B.-fC is it cos PS*, and of the source H and line sink OH is tt(ajf). cos PH* and - ( M /o)(PO-PH); so that . / nc , " du PO-PH\ . . ^ = m (cosPSx+ jcosPHa:-'-— — 1, (4) and if— ~M> a constant, over the surface of the sphere, so that there is no flow across. When the source S is inside the sphere and H outside, the line sink must extend from H to infinity in the image system ; to realize physically the condition of zero flow across the sphere, an equal sink must be introduced at some other internal point S'. When S and S' lie pn the same radius, taken along O*, the Stokes' function can be written down ; and when S and S' coalesce a doublet is produced, with a doublet image at H. ' For a doublet at S, of moment m, the Stokes' function is m dj cos PS* = r ■.*PSj; and for its image at H the Stokes' function is jC0sPH*=m a' y* / 3 PH 3 (5) (6) 'Vppip-ps 5 ) ~ m f (w«*ff)' (7) Bo-hOi — Bi — Ci If the ellipsoid is of revolution, with 6* . i TT A + 2B, * = iU5C B7^Bl' W'. --C (2) (3) (4) (5) and the Stokes' current function \f/ can be written down reducing, when the liquid extends to infinity and Bi =0, to so that in the relative motion past the body, as when fixed in the current U parallel to xO, *'-iVx(i+£),+>-iV?(iS). (6) Changing the origin from the centre to the focus of a prolate spheroid, then putting V=pa, X=*X'a, and proceeding to the limit where a = 00 , we find for a paraboloid of revolution m 2J so that for the combination and this vanishes over- the surface of the sphere. There is ao Stokes' function when the axis of the doublet at S does not pass Jhrough O; the image system will consist of an inclined doublet at H, making an equal angle with OS as the doublet S, and of a parallel negative line doublet, extending from H to O, of moment varying as the distance from 0- A distribution of sources and doublets over a moving surface will enable an expression to be obtained for the velocity function of a body moving in the presence of a fixed sphere, or inside it. The method of electrical images will enable the stream function ^' to be inferred from a distribution of doublets, finite in number when the surface is composed of two spheres intersecting at an angle ir/m, where m is an integer (R. A. Herman, Quart. Jour, of Math. xxii.). Thus for m = 2, the spheres are orthogonal, and it can be verified that ■'•■'■ *>-&?{*-$-$+$). (8) B; b» -p+y *P+\" (7) (8) with X'=o over the surface of the paraboloid; and then *' = \V>\f-p V (^-f-y) +£*] ; *=-iUp[V(* 2 +;«-*]; ♦-- iu/> log w<«f*+y B )+*]< The relative path of a liquid particle is along a stream line $' = §Uc 2 , a constant, (12) 2K/-C 2 ) -w^y) my 1 -*) (9) do) do (13) where ai, . 1 46. Between two concentric spheres, with (14) (15) *■ a'+X = r 2 , rf 2 +Xi = a 1 s ; A = B=C=0 9 /3r', a 3 .■ a 3 i ! J~ 3+2 a? i-a'/ai* ■W+- £1 a, 3 i-cFJa?' and the effective inertia of the liquid in the interspace is Ao+aAi. .„„ _ 1 oi 3 _+2o 3 , 2A0 -2Al W ' = ^ rW. (1) (2) (3) When the spheres arenot concentric, ah expression for the effective inertia can be found by the method ©f images =xyx (1) for a rotation R about Oz; and a similar procedure shows, that an ellipsoidal surface X may be in rotation about Oz without disturbing the motion if dx R< / 1 1 \ 3-^ W+\+&+\) x+2 d\ iy(6»+X)-i/(a*+X) ' and that the continuity of the liquid is secured if (a 2 +X) 3 / 2 (& 2 +X) 3 / ! (c 2 +X)^=constant, _ f°° N) /(«» + &«) -(Bo -A,)' 132 HYDROMECHANICS [HYDRODYNAMICS The velocity function of the liquid inside the ellipsoid X=o due to the same angular velocity will be *i«R*)r(«*-a»)/(a>+i»), (7) and on the surface outside N Bq-Aq , q . so that the ratio of the exterior and interior value of 4> at the surface is ' = xy( x +M), _ (io) and the ratio of the effective angular inertia in (9) is changed to i-a k \ ra w . •Oi s -6i* abc Make c = 00 for confocal elliptic cylinders ; and then A x = /"°° ab ab ( L /b*+\ \ , J (o'+X)V ti.a*+\.b*+\) -tf^& V V?+X/ ,U2 > Ba= A(\/S+x- 1 )* Ca=o: and then as above in § 31, with a=cch o, 6«=csh a, 01 = V (o*+X) =cch 01, i^csh ai (13) the ratio in (11) agrees with § 31 (6). As before in § 31, the rotation may be resolved into a shear-pair, in planes perpendicular to O* and Oy. A torsion of the ellipsoidal surface will give rise to a velocity function of the form . 4> = xyzU, where SI can be expressed by the elliptic integrals A k , B K C K , in a similar manner, since Q dX/P 3 . 48. The determination of the 's and x's is a kinematical problem, solved as yet only for a few cases, such as those discussed above. But supposing them determined for the moti6n of a body through a liquid, the kinetic energy T of the system, liquid and body, is expressible as a quadratic function of the components U, V, W, P, Q, R. The partial differential coefficient of T with respect to a component of velocity, linear or angular, will be the component of momentum, linear or angular, which corresponds. Conversely, if the kinetic energy T is expressed as a quadratic function of *i, *j, x s , yi, yt, ya, the components of momentum, the partial differential coefficient with respect to a momentum com- ponent will give the component of velocity to correspond. > These theorems, which hold for the motion of a single rigid body, are true generally for a flexible system, such asPconsidered here for a liquid, with one or more rigid bodies swimming in it; and they ex- press the statement that the work done by an impulse is the product of the impulse and the arithmetic mean of the initial and final velocity; so that the kinetic energy is the work done by the impulse in starting the motion from rest. Thus if T is expressed as a quadratic function of U, V, W, P, Q, R) the components of momentum corresponding are dT it dT dT y.=jp y 2 =^ y*=M ; but when it is expressed. as a quadratic function of x u Xt, x 3 , y t yj. y>. dT] dT x *~dV' x '~dW (1) dxi dxi dT Q _dT *-£■ (2) d~y? ^~"dyj' d~y 3 ' R = dT The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; aid thence the dynamical equations follow „ dx\ dT . dT, v „ . . x= dr*w> +Xl W* '*-•••. z----. (3) , .-■ , dy, dT , dT dT , dT -, - T . , -' L= ~d7-yw> +y >d7r x *dT i +x '3z M= • • •• * - • • •• ( 4> where X, Y, Z, L, M, N denote components of external applied force on the body. = /Q-mP. These equations are proved by taking a line fixed in space, whose direction cosines are /, m, n, then j r mR~nQ, ^-»P-/R, |? = If P denotes the resultant linear impulse or momentum in this direction P = Ixi+mxi +nx s , dP _dl .dm ,dn 'dJ-de Cl+ <'dJ X2+ 'dl X3 (5) (6) +£ dxt . dxi +m- 3F +n dt for all values of I, m, n. Next, taking a fixed ='fd7-*' R+ *' Q ) +«(^-* 1 p+«r) =K+wY+nZ, (7) origin SI and axes parallel to Ox, by, Oz through O, and denoting by x, y, z the coordinates of O, and by G the component angular momentum about Si in the direction (/, /», n) G = l(yi-x,z+x 3 y) +m(y 2 -X)X+Xiz) +»(yr-*iy+*2*). (8) Differentiating with respect to t, and afterwards moving the fixed origin up to the moving origin O, so that *- y -.-o.b™t§-U.3-V.g-W. w= l {dT-y> R +y& -«w+*,v) +m (^-y,P+y,R-*,U+* 1 w) +« (^-yiQ+y a P-*iV+*ju) "IL+mM+nN, (9) for all values of /, m, n. When no external force acts, the case which we shall consider, there are three integrals of the equations of motion (i.) T= constant, (ii.) aci , +*j 2 +*j s =F 5 , a constant, (iii.) *iyi+*jyj-r-Xiyj = n = GF, a constant; and the dynamical equations in (3) express the fact that x x , &>, x 3 are the components of a constant vector having a fixed direction ; whije (4) shows that the vector resultant of y u y 2 , y 3 moves as if subject to a couple of components *iW-* 3 V, * 3 U-*iW, *iV-*,U, (10) and the resultant couple is therefore perpendicular to F, the re- sultant of *i, a*, x 3 , so that the component along OF is constant, as expressed by (iii). If a fourth integral is obtainable, the solution is reducible to a quadrature, but this is not possible except in a limited series of cases, investigated by H. Weber, F. Kotter, R. Liouville, Caspary, Jukovsky, Liapounoff, Kolosoff and others, chiefly Russian mathe- maticians; and the general solution requires the double-theta hyperelliptic function. 49, In the motion which can be solved by the elliptic function, the most general expression of the kinetic energy was shown by A. Clebsch to take the form T-fc>(*i J +*') +*/>'*,» +?(*iyi +xiyz) +q'x,y s +ir(yi*+y*)+ir'yf (1) so that a fourth integral is given by dy 3 /dt = o, yj = constant ; (2) •^=*i(2*s+rys)-*j(g*i+ryi) =K*iyj-xjyi)i (3) I (dx,\* r* Kdi) ' W+*2 2 )(yi 2 +y2 J ) - {xiyi+x^y in which so that = (*i«+^)(y.«+y4 l )-(FG-*,y,)» = W-i-x i >)(yi>+yt*+yi>-G*)-(GxrFy ll y, Xi'+x t i ~'F , -x, i , *iyi+*sy2=FG-* s y», r (yi J +yj J ) ~2T-p(xS+ xf)-p' Xs * -2q(.x 1 y l +x i y 1 )-2q'x 3 yr-r'ys* **fr-p')x>*->r2(.q-q.')xiyi+mu Wi «=2T-pF 1 -asFG-r,y 3 2 dx 3 \ i It) = X S (4) (5) (7) W where Xs is a quartic function of x 3 , and thus / is given by an elliptic HYDRODYNAMICS] HYDROMECHANICS 133 integral of the first kind ; and by inversion x 3 is in elliptic function of the time /. Now (xi—x 3 i)(y l +yti)=Xiyi+xty t +i(xiyt—x i yi) = FG-* 3 y3+iVXj, yi +y*i _ FG — y 3 y 3 +tV X 3 xi+Xii *i 2 +* 2 2 ' (9) (10) 2j(*i+*i») = -»[(s' -Q)xs+r'y 3 ]+irxa(yi+y2i), (11) & 1 / 1 -\ / 1 •, c 1 FG— x 3 y 3 +i'VX 3 . . 3jjlog(*i+w) = -(g'-2)* 3 -r'y 3 +rx 3 p±^2 . (12) d , / xi+xji , , . , , . _ Fy 3 — Gx 3 , requiring the elliptic integral of the third kind; thence the ex- pression of xi+x 2 i and yi+y 2 t. Introducing Euler's angles 8, , ^, Xi=F sin 8 sin , * 2 = F sin 8 cos , *i+* 2 i = JF sinfle - *', * 3 = Fcos9; sin 8jt = P sin <£+Q cos , „ . ,M dT , oT Fslaie di = dJ l Xi +dJ 1 x ' = (qxi+ryi)xi + (gxi+ry,)x t = c(xi 2 +x 2 2 ) +r(x l yi+x i y i ) = gF 2 sin a e+r(FG-* 3 y 3 ), 1 „t?/ fFG-^syj Frixs (14) (15) (16) (17) elliptic integrals of the third kind. Employing G. Kirchhoff's expressions for X, Y, Z, the coordinates of the centre of the body, FX =yi cos *Y+y 2 cos y¥+y 3 cos zY, (18) FY = - yi cos *X+y 2 cos yX+y 3 cos 2X, (19) G=y t cos *Z+y 2 cos yZ+y 3 cos zZ, (20) FHX'+Y^^+^+^-G 2 , (2I) F(X+Y«)- Fy 7gl+g X V i. (22) Suppose X3--F is a repeated factor of X 3 , then y 3 = G, and X 3 = (* 3 -F)'[^(*3+F)'+2^G(* 3 +F)-G 2 ], (23) and putting x 3 -F=y, (g)Wy 2 [ 4 ^F'+ 4 ^FG-G 2 +2(2^F+tpG)y+^f], (24) so that the stability of this axial movement is secured if A= 4 ^F'+ 4 2-^FG-G' (25) is negative, and then the axis makes rV ( — A)/ir nutations per second. Otherwise, if A is positive -/: dy yV(A + 2By+Cy 2 ) ^sh" 1 VAV(A + 2By+Cy 2 ) = VAch-» yV (B 2 ~AC) = _l_ch-> A + By = VAsh-'yV(B 2 ~AC)' (26) weight W, and under no force the C.G. proceeds in a straight line, and the axis of rotation through the C.G. preserves its original direction, if a principal axis of the body; otherwise the axis describes a cone, right circular if the body has uniaxial symmetry, and a Poinsot cone in the general case. But the presence of the medium makes the effective inertia depend on the direction of motion with respect to the external shape of the body, and on W the weight of fluid medium displaced. Consider, for example, a submarine boat under water; the inertia is different for axial and broadside motion, and may be represented Ci = W+W'a,<:,=W+W'& (1) where 0, j3 are numerical factors depending on the external shape ; and if the C.G is moving with velocity V at an angle with the axis, so that the axial and broadside component of velocity is « = V cos (j>, u = V sin , the total momentum F of the medium, represented by the vector OF at an angle 8 with the axis, will have components, expressed in sec. lb, Fcose = c 1 j = (W+W'o)^cos<^, Fsin9 = c 2 |=(W+W'/3)^sin^.. (2) Suppose the body is kept from turning as it advances; after t seconds the C.G. will have moved from O to O', where 00' = V/; and at O' the momentum is the same in magnitude as before, but its vector is displaced from OF to O'F'. For the body alone the resultant of the components of momentum V V V W— cos 4> andW— sin tj> is W— sec. lb, (3) acting along 00', and so is unaltered. But the change of the resultant momentum F of the medium as well as of the body from the vector OF to O'F' requires an impulse couple, tending to increase the angle FOO', of magnitude, in sec' foot-pounds F.OO'.sin FOO' = FV/ sin (0-), (4) equivalent to an incessant couple N=FVsin (B-) = (F sin 6 cos 0— F cos 8 sin )V = (C2— Ci)(V 2 /g) sin cos = W'03-aWg. (5) This N is the couple in foot-pounds changing the .momentum of the medium, the momentum of the body alone remaining the same; the medium reacts on the body with the same couple N in the opposite direction, tending when c 2 -ci is positive to set the body broadside to the advance. An oblate flattened body, like a disk or plate, has Cr-Ci negative, so that the medium steers the body axially ; this may be verified by a plate dropped in water, and a leaf or disk or rocket-stick or piece of paper falling in air. A card will show the influence of the couple N if projected with a spin in its plane, when it will be found to change its aspect in the air. An elongated body like a ship has Ci-ci positive, and the couple N tends to disturb the axial movement and makes it unstable, so that a steamer requires to be steered by constant attention at the helm. Consider a submarine boat or airship moving freely with the direction of the resultant momentum horizontal, and the axis at a slight inclination 8. With no reserve of buoyancy W = W, and the couple N, tending to increase 8, has the effect of diminishing the metacentric height by h ft. vertical, where and the axis falls away ultimately from its original direction. A number of cases are worked out in the American Journal of Mathematics (1907), in which the motion is made algebraical by the use of the pseudo-elliptic integral. To give a simple instance, changing to the stereographic projection by putting tan \8 = x, (Nw+0" 2 = (*+i)VX 1 +i(^-i)VX 2 , (27) x '= =fcOX«+203C 3 ±3(0 + 6)^+26* ±6, (28) N 3 =-8(a+6), (29) will give a possible state of motion of the axis of the body; and the motion of the centre may then be inferred from (22). 50. The theory preceding is of practical application in the investigation of the stability of the axial motion of a submarine boat, of the elongated gas bag of an airship, or of a spinning rifled projectile. In the steady motion under no force of such a body in a medium, the centre of gravity describes a helix, while the axis describes a cone round the direction of motion of the centre of gravity, and the couple causing precession is due to the dis- placement of the medium. In the absence of a medium the inertia of the body to trans- lation is the same in all directions, and is measured by the W&tan0 = N: -(c i —ci)——tan8, , c 2 — Cl C\ u' ,. .1+0 « 2 (6) (7) W (id ^ — J l+$ g- 51. An elongated shot is made to preserve its axial flight through the air by giving it the spin sufficient for stability, without which it would turn broadside to its advance; a top in the same way is made to stand upright on the point in the position of equilibrium, unstable statically but dynamically stable if the spin is sufficient; and the investigation proceeds in the same way for the two problems (see Gyroscope). The effective angular inertia of the body in the medium is now required ; denote it by Q about the axis of the figure, and by Q about a diameter of the mean section. A rotation about the axis of a figure of revolution does not set the medium in motion, so that Cj is the moment of inertia of the body about the axis, denoted by Wfcjf. But if W&! is the moment of inertia of the body about a mean diameter, and a the angular velocity about it generated by animpluse couple M,and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', "W*fo> = M-M', W'£' ! a. = M', (1) (WH+W'£' 2 )w = M, (2) C 2 i"W£§+W'£' 2 = (W+W' e )fci, - -(3) in which we have put k' 2 = ek 2 , where e is a numerical factor depend- ing on the shape. 134 HYDROMECHANICS ^HYDRODYNAMICS If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate m about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is Cxpn sin 8 - C 2J u 2 sin 8 cos 8 ; (4) and equating this to the impressed couple (multiplied by g), that is, to *N = (£,-£,)£«» tan 9, (5) Ci and dividing out sin 8, which equated to zero would imply perfect centring, we obtain C2M 2 cos0-CipM + {Ci-Cifj-u 1 sec 8 = 0. (6) Cz The least admissible value of p is that which makes the roots equal of this quadratic in p, and then u = \r*-p sec 6 V-2 (7) the roots would be imaginary for a value of p smaller than given by (8) * '*q- (9) If the shot is moving as if fired from a gun of calibre d inches, in which the rifling makes one turn in a pitch of n calibres or nd inches, so that the angle S of the rifling is given by tan 8 = itdjnd = $dp/u, (10) C*^> 2 -4(C2-Ci)- i C 2 M 2 = 0, 3-4W-Ci)-fr r If o& 2 dX - . Ao Jo (a 2 +X)Vt4(a 2 +X)'(S 2 +Xj 2 ]-J r ^^vu.f^ivl'J) 2 +X)Vt4(a 2 +X)(S 2 +Xj 2 ] _ Ac+2Bo = l, 2(a 2 + X) 3/2 (6 a +X)' 52. In the steady motion the centre of the shot describes a helix, with axial velocity «cos8+»sin8 — ( l H — 'tan 2 0j « cos SazusecS, and transverse velocity u sin 0-»cos8. = (1 -)u sin 8 As O3-a)wsin0; and the time of completing a turn of the spiral is 2t//j, When p. has the critical value in (7), (1) (2) 2tt Att V_ 2 n 2lT/ 9 1 \ , — = - r 7=-cos0 =— (x 2 -r-i)cos6 M p Li p (3) which makes the circumference of the cylinder on which the helix is "wrapped — (Msin0-DCOS0)=2l^(/3-a)(z 2 +l)sin 2 0cos0 = «d(/3-a)(x 2 + l) sin0ebs«, and the length of one turn of the helix — {ucos9-\-v sin0) = ■nd(,x* + i); (4) (5) a=^-V, = Bo I - Ao = l+Ao" (H) (15) 1-A0' ^ I -Bo I+Ao l+2a' The length of the shot being denoted by / and the calibre by d, and the length in calibres by x lJd-2aJ2b = x, (16) x . . . 1 Ao (* 2 -i) 3 / 2 r ,»ch->^-- (17) v( J_ l) log[a;+V( : c 2 -i)]. (19) thus for * = 3, the length is 10 times the pitch of the rifling. 53. The Motion of a Perforated Solid in Liquid. — In the preceding investigation, the liquid stops dead when the body is brought to rest ; and when the body is in motion the surrounding liquid moves in a uniform manner with respect to axes fixed in the body, and the force experienced by the body from the pressure of the liquid on its surface is the opposite of that required to change the motion of the liquid ; this has been expressed by the dynamical equations given ' above. But if the body is perforated, the liquid can circulate through a hole, in reentrant stream lines linked with the body, even while the body is at rest; and no reaction from the surface can influence this circulation, which may be supposed started in the ideal manner described in § 29, by the application of impulsive pressure across an ideal membrane closing the hole, by means of ideal mechanism connected with the body. The body is held fixed, and the reaction of the mechanism and the resultant of the impulsive pressure on the surface are a measure of the impulse, linear J, ij, f, and angular X, fi, v, required to start the circulation. HYDROMEDUSM i35 This impulse will remain of constant magnitude, and fixed relatively to the body, which thus experiences an additional reaction from the circulation which is the opposite of the force required to change the position in space of the circulation impulse; and these extra forces must be taken into account in the dynamical equations. An article may be consulted in the Phil. Mag., April 1893, by G. H. Bryan, in which the analytical equations of motion are deduced of a perforated solid in liquid, from considerations purely hydrodynamical. The effect of an external circulation of vortex motion on the motion of a cylinder has been investigated in § 29; a similar pro- cedure will show the influence of circulation through a hole in a solid, taking as the simplest illustration a ring-shaped figure, with uni- planar motion, and denoting by { the resultant axial linear momentum of the circulation. As the ring is moved from O to O' in time t, with velocity Q, and angular velocity R, the components of liquid momentum change from oM'U -H and /SM'V along Ox and Oy to aM'U'-K and /SM'V along OV and O'y', (1) the axis of the ring changing from Ox to OV; and U =Qcos0, V=fQsin0, U' = Q cos (6-Rl), V' = Q sin (0-Ri), (2) so that the increase of the components of momentum, Xi, Yi, and Ni, linear and angular, are X, = (aM'U'-R) cos Rt-aM'U-Z-pM'V sin Rt = (o-/8)M'Qsin (9-R/) sinR/-{verR< (3) Y, = (aM'U'-H) sin Rt+HMV cos R*-0M'V = (a-/S)M'Qcos(0-ROsinR/-KsinRT, (4) Ni = [-(eM'U'-K) sin (e-RO-HSM'V' cos (0-Rt)\OO' = [-(a-£)M'Qcos(0-Ri)sin(0-Ri)-{sin(0-Rt)]Q/. (5) The components of force, X, Y, and N, acting on the liquid at 0, and reacting on the body, are then X = lt. X,/<=-(a-j3)M'QRsine = (o-/3)M'VR, (6) Y = lt. Yi/( = (o-,8)M'QRcos9-|-{R = (a-^)M'UR+jR, (7) Z = lt. Zi/^-Ca-^M'O/sinflcose-fQsinfl = [-(a-/?)M'U-K]V. \8) Now suppose the cylinder is free ; the additional forces acting on the body are the components of kinetic reaction of the liquid -M'(f-VR),^M'(g + UR), - 6 C'f, ( 9 , so that its equations of motion are M (^r-VR) = -aM' (^-VR) -(a-^M'VR, (to) M(^+UR) ^-^M'^+Ur) -(a-/3)M'UR-{R,(ii) (12) „ighly differentiated group of animals, typically marine, and. 'found in all seas and in all zones of marine life. Fte|h-w^ter forms, however, are also known, very few as regards* specifs or genera, but often extremely abundant as individuals. ^ Iif- the British fresh-water fauna only two genera, Hydra a»4 Cordylophora, are found; in America occurs an additional getn|sy Microhydra. The paucity of fresh-water forms contrasts sharply; with the great abundance of marine genera common in all seafe- and on every shore. The species of Hydra, however, are extremely common and familiar inhabitants of ponds and ditches. \ : ~ In fresh- water Hydromedusae the life-cycle fejusually second- arily simplified, but in marine forms the lif&icycle may be extremely Complicated, and a given species ortfcn passes in the course of its history through widely different /orms. adapted, to different habitats and modes of life. Apart ffftm-Wmil or embryonic forms there are found typically two tyjws of person, as already stated, the polyp and the medusa, each of which may vary independently of the other, since their enviroii'meht and life-conditions are usually quite different. Hence both polyp, and medusa present characters for classification, and a given species, genus or other taxonomic category may be defined by polyp-characters or medusa-characters or by both combined. If our knowledge of the life-histories of these organisms were perfect, their polymorphism would present no difficulties to classification; but unfortunately this is far from being the case. In the majority of cases we do not know the polyp corresponding to a given medusa, or the medusa that arises from a given polyp. 1 Even when a medusa is seen to be budded from a polyp under observation in an aquarium, the difficulty is not always solved,; since the freshly-liberated, immature medusa may differ greatly from the full-grown, sexually-mature medusa after several months of life on the high seas (see figs. 11, B,C, and 59, a, b, c): To establish the exact relationship it is necessary not only to breed but to rear the medusa, whiph cannot always be done in 1 In some cases hydroids have been reared in aquaria from ova of medusae, but these hydroids have not yet been found in the sea (Browne [10 a]). 136 HYDROMEDUSAE [ORGANIZATION confinement. The alternative is to fish all stages of the medusa in its growth in the open sea, a slow and laborious method in which the chance of error is very great, unless the series of stages is very complete. At present, therefore, classifications of the Hydromedusae have a more or less tentative character, and are liable to revision with increased knowledge of the life-histories of these organisms. Many groups bear at present two names, the one representing the group as defined by polyp-characters, the other as defined by medusa-characters. It is not even possible in all cases to be certain that the polyp-group corresponds exactly to the medusa- group, especially in minor systematic categories, such as families. The following is the main outline of the classification that is Adopted in the present article. Groups founded on polyp- characters are printed in ordinary type, those founded on medusa- characters in italics. For definitions of the groups see below. Sub-class Hydromedusae (Hydrozoa Craspedota). Order I. Eleutheroblastea. ,, II. Hydroidea (Leptolinae) . Sub-order 1. Gymnoblastea (Anthomedusae). „ 2. Calyptoblastea (Leplomedusae). Order III. Hydrocorallinae. „ IV. Graptolitoidea. „ V. Trachylinae. Sub-order 1. Trachomedusae. ,, 2. Narcomedusae. Order VI. Siphonophora. Sub-order 1. Chondrophorida. „ 2. Calycophorida. „ 3. Physophorida. „ 4. Cystophorida. Organization and Morphology of the Hydromedusae. As already stated, there occur in the Hydromedusae two distinct types of person, the polyp and the medusa; and either of them is capable of non-sexual reproduction by budding, a process which may lead to the formation of colonies, composed ,_j of more or fewer individuals com- bined and connected together. The morphology of the group ,A.f thus falls naturally into four sections — (1) the hydropolyp, (2) the polyp-colony, (3) the hydro- medusa, (4) the medusa-colonies. Since, however, medusa-colonies occur only in one group, the Siph- onophora, and divergent- views are held with regard to the morphological interpretation of the members of a siphonophore, only the first three of the above sub-divisions of hydromedusa morphology will be dealt with here in a general way, and the morphology of the Siphonophora will be considered under the head- ing of the group itself. 1. The Hydropolyp (fig. 1)— The general characters of this organism a, b, c> t, ps Fig. 1. — Diagram of a typical Hydropolyp. Hydranth ; Hydrocaulus ; Hydrorhiza; Tentacle ; Perisarc, forming in the _ region of the hydranth ar e described above and in the acuporhydrotheca(A,<), snides Hydrozoa and Polyp. It — which, however.is only | s rarely free, but usually fixed and found in polyps of the incapable of locomotion. The foot order Calyptoblastea. by which it is attached often sends out root-like processes — the hydro- rkita (c). The column (b) is generally long, slender and stalk- like (hydrocaulus). Just below the crown of tentacles, however, the body widens out to form a " head," termed the hydranth (a), containing a stomach-like dilatation of the digestive cavity. On the upper face of the hydranth the crown of tentacles (/) surrounds the peristome, from which rises the conical hypostome, bearing the mouth at its extremity. The general ectoderm covering the surface of the body has entirely lost the cilia present in the earlier larval stages (plariula), and may be naked, or clothed in a cuticle or exo- skeleton, the perisarc (ps), which in its simplest condition is a chitinous membrane secreted by the ectoderm. The perisarc when present invests the hydrorhiza and hydrocaulus; it may stop short below the hydranth, or it may extend farther. In general there are two types of exoskeleton, characteristic of the two principal divisions of the Hydroidea. In the Gymnoblastea the perisarc either stops below the hydranth, or, if continued on to it, forms a closely-fitting investment extending as a thin cuticle as far as the bases of the tentacles (e.g. Bimeria, see G. J. Allman [i], 1 pi. xii. figs. 1 and 3). In the Calyptoblastea the pensarc is always continued above the From Allman's Gymnobleslic Bydroiis, by permission of the Council of the Ray Society. Fig. 2. — Stauridium productum, portion of the colony magnified; p, polyp ; rh, hydrorhiza. hydrocaulus, and forms a cup, the hydrangium or hydrotheca (h, t), standing off from the body, into which the hydranth can be retracted for shelter and protection. The architecture of the hydropolyp, simple though it be, furnishes a long series of variations affecting each part of the body. The greatest variation, however, is seen in the tentacles. As regards number, we find in the aberrant forms Protohydra and Microhydra tentacles entirely absent. In the curious hydroid Monobrachium a single tentacle is present, and the same is the case in Clathrozoon; in Amphibrachium and in Lar (fig. 11, A) the polyp bears two tentacles only. The reduction of the tentacles in all these forms may be correlated with their mode of life, and especially with living in a constant current of water, which brings food- particles always from one direction and renders a complete whorl or circle of tentacles unnecessary. Thus Microhydra lives amongst Bryozoa, and appears to utilize the currents produced by these animals. Protohydra occurs in oyster- banks and Monobrachium also grows on the shells of bivalves, and both these hydroids probably fish in the currents produced by the lamellibranchs. Am- phibrachium grows in the tissues of a sponge, Euplectella, and protrudes its hydranth into the canal-system of the sponge; and Lar grows on the tubes of the worm Sabella. With the exception of these forms, reduced for the most part in correlation with a semi-parasitic mode of life, the tentacles are usually numerous. It is rare to find in the polyp a regular, symmetrical disposition of the tentacles as in the medusa. The primitive number of four in a whorl is seen, however, in Stauridium (fig. 2^ and Cladonema (Allman [1], pi. xvii.), and in Clavatella each whorl consists regularly of eight (Allman, loc. cit. pi. xviii.). As a rule, however, the number in a whorl is irregular. The tentacles may form a single whorl, or more than one; thus in Corymorpha (fig. 3) and Tubularia (fig. 4) there are two circlets; in Staur- idium (fig. 2) several; in Coryne and Cordylophora the tentacles are scattered irregularly over the elongated hydranth. As regards form, the tentacles show a number of types, of which the most important are (1) filiform, i.e. cylindrical or tapering from 1 The numbers in square brackets [ ] refer to the bibliography at the end of this article; but when the number is preceded by the word Hydrozoa, it refers to the bibliography at the end of the article Hydrozoa. Fig. 3. — Diagram of Corymorpha. A, A hydri- form person giving rise to medusiform persons by budding from the margin of the disk; B, free swimming medusa (Steenstrupia of Forbes) detached from the same, with manubrial genitalia,. (Anthomedusae) and only one tentacle. (After All- man). AND MORPHOLOGY] HYDROMEDUSAE i37 base to extremity, as in Clava (fig. 5); (2) capitate, i.e. knobbed at the extremity, as in Coryne (see Allman, loc. cit. pi. iv.) ; (3) branched, a rare form in the polyp, but seen in Cladocoryne (see Allman, loc. cit. p. 380, fig. 82). Sometimes more than one type of form is found in the same polyp; in Pennaria and Stauridium (fig. 2) the upper whorls are capitate, the lower filiform. Finally, as regards structure, the tentacles may retain their primitive hollow nature, or become solid by obliteration of the axial cavity. The hypostome of the hydropolyp may be small, or, on the other hand, as in Eudendrium (Allman, loc. cit. pis. xiii., xiv.), large and trumpet- shaped. In the curious polyp Myriothela the body of the polyp is differ- 4. — Diagram of Tubularia entiated into nutritive and Fig. indivisa. A single hydriform person reproductive portions a bearing a stalk carrying numerous Histology. — The ectoderm degenerate medusiform persons or of the hydropolyp is chiefly sporosacs b. (After Allman.) sensory, contractile and pro- tective in function. It may also be glandular in places. It consists of two regions, an external epithelial layer, and a more internal sub-epithelial layer. The epithelial layer consists of (1) so-called " indifferent " cells secreting the perisarc or cuticle and modified to form glandular cells in places; for example, the adhesive cells in the foot. (2) Sensory cells, which may be fairly numerous in places, especially on the tentacles, but which occur always scattered and isolated, never aggregated to form sense-organs as in the medusa. (3) Contractile stitial cells, lodged between the narrowed basal portions of the epithelial cells. From them are developed two distinct types of histological elements ; the genital cells and the cnidoblasts or mother- cells of the nematocysts. The sub-epithelial layer thus primarily constituted may be recruited by immigration from without of other From Allman's CynmoUastic Hydroids, by permission of the Council of the Ray Society. Fig. 5. — Colonies of Clava. A, Clava squamata, magnified. B, C. multicornis, natural size; p, polyp; gon, gonophores; rh, hydrorhiza. or myo-epithelial cells, with the cell prolonged at the base into a contractile muscle-fibre (fig. 6, B). In the hydropolyp the ectodermal muscle-fibres are always directed longitudinally. Belonging primarily to the epithelial layer, the muscular cells may become secondarily sub-epithelial. The sub-epithelial layer consists primarily of the so-called inter- Fig. 6 A. — Portion of the body-wall of Hydra, showing ecto- derm cells above, separated by " structureless lamella " from three flagellate endoderm cells below. The latter are vacuolated, and contain each a nucleus and several dark granules. In the middle ectoderm cell are seen a nucle'us and three nematocysts^ with trigger hairs projecting beyond the cuticle. A large nematocyst, with everted thread, is seen in the right-hand ectodermal cell. (After F. E. Schulze.) elements, more especially by nervous (ganglion) cells and nitiscle- cells derived from the epithelial layer. In its fullest development, therefore, the sub-epithelial layer consists of four classes of cell- elements. The genital cells are simple wandering cells (archaeocytes), at first minute and without any specially distinctive features, until they begin to develop into germ-cells. According to Wulfert [60] the primitive germ-cells of Gonothyraea can be distinguished soon after the fixation of the planula, appearing amongst the interstitial cells of the ectoderm. The germ-cells are capable of extensive migrations, not only in the body of the same polyp, but also from parent to bud through many non-sexual generations of polyps in a colony (A. Weismann [58]). The cnidoblasts are the mother-cells of the nematocysts, each' cell producing one nematocyst in its interior. The complete nemato- cyst (fig. 7) is a spherical or oval capsule containing a hollow thread, usually barbed, coiled in its interior. The capsule has a double wall, an outer one (o.c), tough and rigid __ in nature, and an inner one (i.e.) " of more flexible consistence. The outer wall of the capsule is in- complete at one pole, leaving an aperture through which the thread is discharged. The inner mem- brane is continuous with the wall Fi G . 6 B.— Epidermo-muscular of the hollow thread at a spot im- cells of Hydra, m, muscular-fibre mediately belowtheaperturein the processes. (After Kleinenberg, outer wall, so that the thread itself from Gegenbaur.) (/) is simply a hollow prolongation of the wall of the inner capsule inverted and pushed into its cavity. The entire nematocyst is enclosed in the cnidoblast which fornjfed it. When the nematocyst is completely developed, the cnidobUjst passes outwards so as to occupy a superficial position in the ectodertn, and a delicate protoplasmic process of sensory nature, termed tjhe cnidocil (en) projects from the cnidoblast like a fine hair or ciliufrn. Many points in the development and mechanism of the nematocyst are disputed, but it is tolerably certain (1) that the cnidocil is of sensory nature, and that stimulation, by contact with prey or in other ways, causes a reflex discharge of the nematocyst ; (2) that the dis- charge is an explosive change whereby the in-turned thread is suddenly everted and turned inside out, being thus shot throughthe opening in the outer wall of the capsule, and forced violently into the tissues of the prey, or, it may be, of an enemy ; (3) that the thrdad inflicts not merely a mechanical wound, but instils an irritant poison, numbing and paralysing in its action. The points most in dispute are, first, how the explosive discharge is brought about, whether by pressure exerted external to the capsule (i.e. by contraction of the cnidoblast) or by internal pressure. N. Iwanzov [27] has brought forward strong grounds for the latter view, pointing out that the cnidoblast has no contractile mechanism and that measurements show discharged capsules to be on the average slightly larger than undischarged ones. He believes that the capsule contains a sub- stance which swells very rapidly when brought into contact with water, and that in the undischarged condition the capsule has its opening closed by a plug of protoplasm (x, fig. 7) which prevents »3« HYDROMEDUSAE ORGANIZATION access of water to the contents; when the cnidocil isistimulated it sets in action a mechanism or perhaps a series of chemical changes by which the plug is dissolved or removed; as a result water pene- trates into the capsule and causes its contents to swell, with the result that the thread is everted violently. A second point of dispute concerns the spot at which thepoison is lodged. Iwanzov believes it to be contained within the -thread itself before dis- charge, and to. be intro- duced into the tissues of the prey by' the eversion of the thread. A third point of dispute is whether the nematocysts are formed in situ, or whether the cnidoblastr migrate with them to the region where they' are most needed; the fact that in Hydra, for example, there are no interstitial cells in the tentacles, where nema- tocysts are very abundant, is certainly in favour of the view that the cnido- blasts migrate on to the tentacles from the body, and that like the genital cells the cnidoblasts are wandering cells. The muscular tissue consists primarily of pro- cesses from the bases of the epithelial cells, pro- cesses which are contrac- tile in nature and may be distinctly striated. A Fig. a b, c, en, N, o.c, x, i.c, 7.— Diagrams to show the struc- further stage in evolution ture of Nematocysts and their mode of is that the muscle-cells working. (After Iwanzov.) lose their connexion with Undischarged nematocyst. the epithelium and come Commencing discharge. to He entirely beneath it, Discharge complete. forming a Sub-epithelial Cnidocil. contractile layer, de- Nucleus of cnidoblast. veloped chiefly in the ten- Outer capsule. tacles of the' polyp. The Plug closing the opening of the evolution of the ganglion- outer capsule, cells, is probably similar; Inner capsule, continuous with the a n epithelial cell develops wall of the filament, /. processes of nervous nature b, Barbs. from the base, which come , ■ , . into connexion with the bases of the sensory cells, with the muscular cells, and with the similar processes of other nerve-cells ; next the nerve-cell loses its connexion with the outer epithelium and becomes a sub-epithelial ganglion-cell which is closely connected with the muscular layer, conveying stimuli from the sensory c£lls to the contractile elements. The ganglion-cells of Hydromedusae are generally very small. In the polyp the nervous tissue is always in the form ' of a scattered plexus, never con- centrated to form a : definite nervous system! as in the medusa. The endoderm of the polyp is typically a flagellated epithelium of large cells (fig. 6), from the bases of which arise contractile muscular processes lying in the plane of the transverse section of the body. In different parts of the coelen- teron the endoderm 1 may be of three principal tvpes — (1) digestive endoderm, "the primi- . ., ., , tive type, with cells of large size and considerably vacuolated, found in the hydranth; sorrte of these cells may become special glandular cells, without tlagella or contractile processes; (2) circulatory endoderm, without vacuoles and without basal contractile processes, found in the hydro- rhiza and hydrocaulus; (3) supporting endoderm (fig. 8), seen in solid tentacles as a row of cubical vacuolated cells, occupying the axis ot the tentacle, greatly resembling notochordal tissue, particularly that of Atnphtoxus at a certain, stage of development; as a fourth variety of endodermal cells excretory cells should perhaps be reckoned as seen to the pores in the foot of Hydra and elsewhere (cf. C Chun' H.YDROZfM It], pp. 314, 315). The mesogloea in the hydropolyp is a thin elastic layer, in which From Gegenbaur's Elements of Com- parative Anatomy. Fig. 8. — Vacuolated Endo- derm Cells of cartilaginous consistence from the axis of the tentacle of a Medusa (Cunina). may be lodged the muscular fibres and ganglion cells mentioned above* but which never contains any connective tissue or skeletogenous cells or any other kind of special mesogloeal corpuscles. ■2. The Polyp-colony. — All known hydropolyps possess the power of reproduction by budding, and the buds produced may become either polyps or medusae. The buds may all be- come detached after a time and give rise to separate and in- dependent indi- viduals, as in the common Hydra, in which only polyp-individuals are produced and sexual elements From Allman's Gymnoblaslic Bydroiis, by permission ot arede veloped the Council of the Ray Society. upon the polyps Fig. 9 — Colony of Hydractinia echinata grow- themselves; or, i ng - on the Shell of a Whelk. Natural size on the other hand, the polyp individuals produced by budding may remain permanently in connexion with the parent polyp, in which case sexual elements are never developed on polyp-individuals but only on medusa-individuals, and a true colony is formed. Thus the typical hydroid colony starts from a " founder polyp, which in the vast majority of cases is fixed, but which may be floating, as in Nemopsis, Pelagohydra, &c. The founder-polyp usually produces by budding polyp-individuals, and these in thj;ir turn produce other buds. The polyps are all non-sexual individuals whose function is purely nutritive. After a time the polyps, or certain of them, produce by budding medusa-individuals, which sooner or later develop sexual elements; in some cases, however, the found* r~ polyp remains solitary, that is ' to say, does not produce polyp- buds, but only medusa-buds, from the first (Corymorpha, fig. 3, Myriothela, &c). In primitive forms the medusa-individuals are set free before reaching sexual maturity'and do hot con- tribute anything to the colony. In other cases, however, the medusa-indiyiduals become sexual}y mature while still at- tached to the parent polyp, and are then not set free at all, but become appanages of the hydroid colony and undergo degenerative changes leading to reduction and even to complete obliteration of their original medusan structure. In this way the hydroid colony becomes composed of two por- tions of different function, the nutritive "trophosome," com- posed of non-sexual polyps, and the reproductive " gonosome," composed of sexual medusa- individuals, which never exercise a nutritive function while at- tached to the colony. As a general rule polyp-buds are pro- duced from the hydrorhiza and hydrocaulus, while medusa-buds are formed on the hydranth. In some cases, however, medusa- buds are formed on the hydro- rhiza, as in Hydrocorallines. In such a colony of connected individuals, the exact limits of the separate " persons " are not always clearly marked out. Hence it is necessary to distin- guish between .first , the " zooids 99*1 From Allman's Gymnoblastic by permission of the Council of Society. Bydroids, the Ray r ,. , Fig. 10. — Polyps from a Colony indicated in the case of the polyps of Hydractinia, magnified, dz, by the hydranths, each with dactylozoid; gz, gastrozoid; b, mouth and, tentacles; and, blastostyle; gon, gonophores; secondly, the "coenosarc," or rh, hydrorhiza. common flesh, which cannot be assigned more to one individual than another, but consists of a more or less complicated network of tubes, corresponding to the hydrocaulus and hydrorhiza of the primitive independent polyp- lndividual. The coenosarc constitutes a system by which the digestive Cavity of any one polyp is put into communication with that of any other individual either of the trophosome or gonosome. In this manner the food absorbed by one individual contributes to the welfare of the whole colony, and the coenosarc has the AND MORPHOLOGY] HYDROMEDOSAE *39 function of circulating and distributing nutriment through the colony. The hydroid colony shows many variations in form and architec- ture which depend simply upon differences in the methods in which polyps are budded. In the first place, buds may be produced only from the hydro- rhiza, which grows out and branches to form a basal stolon, typically net-like* spreading over the substratum to which the founder- polyp attached itself. From the stolon the daughter-polyps grow up vertically. The re- sult is a spreading or creeping colony, with the coenosarc in the form of a root-like horizontal network (fig. 5, B; ii, A). Such a colony may undergo two principal modifica- tions. The meshes of the basal network may become very small or virtually obliterated, so that the coenosarc be- comes a crust of tubes tendingtofusetogether, and covered over by a common perisarc. Encrusting colonies of this kind are seen in Clava squamata (fig. 5, A) and Hydractinia (figs. 9, io), the latter having the perisarc calcified. A further very important modifi- cation is seen when the tubes of the basal perisarc do not remain spread out in one plane, but grow in all planes forming a felt-work ; the result is a massive colony, such as is seen in the so-called Hydrocorallines (fig. 6o), where the interspaces between the coenosarcal tubes are filled Up with calcareous matter, or coenosteum, replacing; the chitinous perisarc. The result is a stony, solid mass, which contributes to the building up of coral reefs. In massive colonies of this kind no sharp distinction can be drawn between hydrorhiza and hydro- -,.caulus in the ooeaosarc; it "\ is practically all hydrorhiza. ' Massive colonies may assume various forms and are often branching or tree-like. A fur- ther peculiarity of this type of colony is that the entire coeno- sarcal complex is covered ex- ternally by a common layer of ectoderm; it is not clear how this covering layer is developed. In the second place, the buds may be produced from the hydrocaulus, growing out laterally from it; the result is an arborescent, tree-like colony (figs. 12, 13). Budding from the hydrocaulus may be combined with budding from the hydrorhiza, so that numer- ous branching colonies arise from a common basal stolon. In the formation of arbores- cent colonies, two sharply distinct types of budding are found, which are best de- scribed in botanical termino- logy as the monopodial or racemose, and the sympodial or cymose types respectively; each is characteristic of one of the two sub-orders of the Hydroidea, the Gymnoblastea and Calypto- blastea. ■ In the- monopodial medhod (figs.'j 12, 14) the founder-polyp is, After Hincks, Forbes, and Browne. A and B modified from Hincks; C modified from Forbes's Brit, Naked- eyed Medusae. Fig. 1 1 .—Lar sabellarum and two stages of its Medusa, Willia stellata. A, colony of Lar;B and C, young and adult medusae. theoretically, of unlimited growth in a vertical direction, and as it grows up it throws out buds right and left alternately, so that the first bud produced by it is the lowest down, 1 he second bud is above the first, the third above this again, and so on. Each bud produced Fig. 12. — Colony of Bougninvillea fruticosa, natural size, attached to the underside of a piece of floating tim- ber. (After Allman.) Fig. 13. — Portion of colony of Bougainvillea fruticosa (Antho- medusae-Gymnoblastea) more magnified. (From Lubbock, after Allman.) by the founder proceeds to grow and to bud in the same way as the founder did, producing a side branch of the main stem. Hence, in a colony of gymnoblastic hydroids, the oldest polyp of each system, that is to say, of the main stem or of a branch, is the topmost polyp ; Fig. 14. — Diagrams of the monopodial method of budding, shown in five stages (1-5). F, the founder-polyp; 1, 2, 3, 4, the succession of polyps budded from the fou nder- polyp ; a', b , c' , the succession of polyps budded from t; a-, b-, polyps budded from 2; O'V polyp budded from 3. the youngest polyp of the system is the one nearest to the topmost polyp ; and the axis of the system is a true axis. In the sympodial method of budding, on the other hand, the founder-polyp is of limited growth, and forms a bud from its sidp , which is also of limited growth, and forms a bud in its turn, and so on (figs. 15, 16). Hence, in a colony of calyptoblastic hydroids, the oldest polyp of a system is the lowest ; the youngest polyp is the top- 140 HYDROMEDUSAE [ORGANIZATION 1 most one; and the axis of the system is a false axis composed of portions of each of the consecutive polyps. In this method of budding there are two types. In one, the biserial type (fig. 15), the polyps pro- duce buds right and left alter- nately, so that the hydranths are arranged in a zig- zag fashion, form- ing a " scorpioid cyme," as in Obelia and Sertularia. In the other, the uni- serial type (fig. 16), the b uds are formed always on •5 -L 5 the same side, * forming a " heii- Fig. 15. — Diagram of sympodial budding, coid cyme," as in biserial type, shown in five stages (1-5). F, Hydrallmania, founder-polyp; I, 2, 3, 4, 5, 6, succession of according to H. polyps budded from the founder; a, b, c, Driesch, in which, second series of polyps budded from the founder; however, the a', b 3 , series budded from 3. .primitively uni- serial arrange- ment becomes masked later by secondary torsions of the hydranths. In a colony formed by sympodial budding, a polyp always produces first a bud, which contributes to the system to which it belongs, i.e. continues the stem or branch of which its parent forms a part. The F polyp may then form a second 14 bud, which becomes the starting ^\ point of a new system, the 1 , \ beginning, that is, of a new *\ a ) branch; and even a third bud, starting yet another system, may be produced from the same polyp. Hence the colonies of Calyptoblastea may be com- plexly branched, and the bud- ding may be biserial through- out, uniserial ..throughout, or partly one, partly the other. _ Thus in Plumttlaridae (figs. 17, x- , t^. . T. , 18) there is formed a main stem Fig. 1 6.— Diagram of sympodial b y biserial budding; each polyp budding uniserial type shown £ the main st £ m forms a in four stages (1-4). F, founder- second bud, which usually P° l L P i. V 2 ' 3. succession of polyps forms a side branch or pi nnu i e budded from the founder. by uniserial budding. In this way are formed the familiar feathery colonies of Plumularia, in which the pinnules are all in one plane, while in the allied Anlen- nularia the pinnules are arranged in whorls round the main biserial stem. The pinnules never branch again, since in the uniserial mode of budding a polyp never forms a second polyp-bud. On the other hand, a polyp on the main stem may form a second bud which, instead of form- ing a pinnule by uni- serial budding, pro- duces by biserial bud- ding a branch, from which pinnules arise as from the main stem (fig. 18—3, 6). Or a polyp on the main stem, after having budded a second time to form a pinnule, may give rise to a third bud, which starts a new biserial system, from which uniserial pinnules arise as from the main stem -type of Aglaoplienia (fig. 19). The laws of budding in hydroids have been worked out in an interesting manner by H. Driesch [13], to whose memoirs the reader must be referred for further details. Individualization of Polyp-Colonies. — As in other cases where animal colonies are formed by organic union of separate individuals, there is ever a tendency for the polyp-colony as a whole to act as a Fig. 17. — Diagram'of sympodial budding, simple unbranched Plumularia-type. F, founder; 1-8, main axis formed by biserial budding from founder; a-e, pinnule formed by uniserial budding from founder; a l -d l , branch formed by similar budding from 1 ; a'-

3 4 ; 6 1 -6 3 ), which give off uniserial movement. Another class, branches in their turn, the gastrozoids (gz), have the tentacles reduced or absent, but have the mouth and stomach enlarged. The dactylozoids capture food and pass it on to the gastrozoids, which swallow and digest it. Besides the three types of individual above mentioned, there are other appendages of hydroid colonies, of which the individuality is doubtful. Such are the " guard-polyps " (machopolyps) of Plumu- laridae, which are often regarded as individuals of the nature of dac- tylozoids, but from a study of the mode of budding in this hydroid family Driesch concluded that the guard-polyps were not true polyp-individuals, although each is enclosed in a small protecting cup of the perisarc, known as a nematophore. Again, the spines arising from the basal crust of Podocoryne have been interpreted by some authors as reduced polyps. 3. The Medusa. — In the Hydro- medusae the medusa-individual occurs, as already stated, in one of two conditions, either as an inde- pendent organism leading a true life in the open seas, or as a subordinate individuality in the hydroid colony, from which it is never set free ; it then becomes a mere reproductive appendage or gono- phore, losing sue Fig. 19. — Diagram showing method of branch- cessively its organs ing in the Aglaophenia-type. Polyp 7 has pro- of sense, loco- duced as its first bud, 8; as its second bud, a f , motion and nutri- which starts a uniserial pinnule ; and as a third tion, until its bud I 7 , which starts a biserial branch (IP-VI 7 ) medusoid nature that repeats the structure of the main stem and and organization gives off pinnules. The main stem is indicated become scarcely by , the new stem by . recognizable. Hence it is convenient to consider the morphology of the medusa from these two aspects. (a) The Medusa as an Independent Organism. — The general structure and characteristics of the medusa are described elsewhere (see articles Hydrozoa and Medusa), and it is only necessary here to deal with the peculiarities of the Hydromedusa. As regards habit of life the vast majority of Hydromedusae are AND MORPHOLOGY] HYDROMEDUSAE 141 pelagic organisms, floating on the surface of the open sea, propelling I themselves feebly by the pumping movements of the umbrella produced by contraction of the sub-umbral musculature, and capturing their prey with their tentacles. The genera Cladonema (fig. 20) and Clava- teila (fig. 21), how- ever.are ambulatory, creeping forms.living in rock-pools and walking, as it were, on the tips of the proximal branches of each of the tentacles, while the remaining branches serve for capture of food. Cladonema still has the typical medusan structure, and is able toswim about, but in Clavatella the um- brella is so much re- duced that swimming is no longer possible. The remarkable medusa Mnestra parasites is ecto-para- sitic throughout life From Allman's Gymnoblastk Bydroids, by permission of on the pelagic mollusc the Council of the Ray Society. Phyihrrhoe, attached Fig. 20. — Cladonema radiatum, the medusa to i* °y the sub- walking on the basal branches of its tentacles umbral surface, and (<). which are turned up over the body. lts tentacles have become rudimentary or absent. It is inter- esting to note that Mnestra has been shown by J. W. Fewkes [15] and R. T. Gunther [19] to belong to the same family (Cladone- midae) as Cladonema and Clavatella, and it is reasonable to suppose that the non-parasitic ancestor of Mnestra was, like the other two genera, an ambu- latory medusa which acquired louse-like habits. In some species of the genus Cunina (Narcomedu- sae) the youngest individuals (actinu- lae) are parasitic on other medusae (see below), but in later life the parasitic habit is abandoned. No other instances are known of sessile habit in Hydro- medusae. The external form of the Hydromedusae varies from that of a deep bell or thimble, characteristic of the Anthomedusae, to the shallow saucer-like form characteristic of the Leptomedusae. It is usual for the umbrella to have an even, circular, uninterrupted margin; but in the order Narcomedusae secondary down-growths between the tentacles produce a lobed, indented margin to the umbrella. The marginal tentacles are rarely absent in non-parasitic forms, and are typically four in number, cor- responding to the four perradii marked by the radial canals. Interradial ten- tacles may be also developed, so that the total number present may be in- creased to eight or to an indefinitely large number. In Willia, Geryonia, &c, however, the tentacles and radir.l canals are on the plan of six instead of four (figs. 11 and 26). On the other hand, in some cases the tentacles are less in number than the perradii; in Corymorpha (figs. 3 and 22) there is but a single tentacle, while two are found in Amphinema and Gemmaria (An- thomedusae), and in Solmundella bitentaculata (fig. 67) and Aeginopsis hensenii (fig. 23) (Narcomedusae). The tentacles also vary considerably in other ways than in number: first, in being usually simple, with a basal bulb, but in Cladonem- From Allman's Gymnotlastic Bydroids, by permission of the Council of the Ray Society. Fig. 21. — Clavatella prolifera, ambulatory medusa. /, tentacles; oc, ocelli. After E. T, Browne, from Proc. Zod. Soc. of London. Fig. 22. — Corymorpha nutans, adult female Medusa. Magnified 10 diameters. form, thirdly, in position and origin, being usually implanted on the extreme edge of the umbrella, but in Narcomedusae they become secondarily shifted and are given off high up on the ex-umbrella (figs. 23 and 25); and, fourthly, in structure, being hollow or solid, as in the polyp. In some medusae, for instance, the remarkable deep-sea family Pectyllidae, the tentacles may bear suckers, by which the animal may attach itself temporarily. It should be mentioned finally that the tentacles are very contractile and extensible, and may therefore present themselves, in one and the same individual, as long, drawn-out threads, or in the form of short corkscrew - like ringlets ; they may stream downwards from the sub-umbrella, or be held out horizontally, or be directed upwards over the ex-umbrella (fig. 23). Each species of After O, Maas, Die craspedoten Medusen der Plankton Expedition, by permission of Lipsius and Tischer. Fig. 23. — Aegin- opsis hensenii, slightly magnified, showing the manner in which the ten- tacles are carried in life. After O. Maas, Craspedoten Medusen der Siboga~ Expedition, by permission of E. S. Brill & Co. Fig. 24. — Rathkea octonemalis. idae they are branched, often in complicated fashion; secondly, in grouping, being usually given off singly, and at regular intervals from the margin of the umbrella, but in Margelidae and in some Trachomedusae {hey are given off in tufts or bunches (fig. 24) ; medusa usually has a characteristic method of carrying its tentacles. The sub-umbrella invariably shows a velum as an inwardly projecting ridge or rim at its margin, within the circle of tentacles; hence the medusae of this sub-class are termed craspedote. The manubrium is absent altogether in the fresh-water medusa Limno- cnida, in which the diameter of the mouth exceeds half that of the umbrella; on the other hand, the manubrium may attain a great length, owing to the centre of the sub-umbrella with the stomach being drawn into it, as it were, to form a long proboscis, as in Geryonia. The mouth may be a simple, circular pore at the extremity of the manubrium, or by folding of the edges it may become square or shaped like a Maltese cross, with four corners and four lips. The corners of the mouth may then be drawn out into lobes or lappets, which may have a branched or fringed outline (fig. 27), and in Margelidae the subdivisions of the fringe simulate tentacles (fig. 24). The internal anatomy of the Hydromedusae shows numer- ous variations. The stomach may be altogether lodged in the manubrium, from which the radial canals then take origin directly as in Geryonia (Trachomedusae) ; it may be with or without gastric pouches. The radial canals may be simple or branched, primarily four, rarely six in number. The ring-canal is drawn out in Narcomedusae into festoons corresponding with the lobes of the margin, and may be obliterated altogether (Solmaris) . I n this order the radial canals are represented only^ by wide gastric pouches, and in the family Solmaridae are suppressed altogether, so that the tentacles and the festoons of the ring-canal arise directly from the stomach. In Geryonia, centripetal canals, ending blindly, arise from the ring-canal and run in a radial direction towards the centre of the umbrella (fig. 26). Histology of the Hydromedusa. — The histology described above for the polyp may be taken as the primitive type, from which that After O. Maas, Medusae, in Prinloe of Monaco's series. Fig. 25. — Aeginura grimaldii. I + 2 HYDROMEDUSAE [ORGANIZATION of the medusa differs only in greater elaboration and differentiation of the cell-elements, which are also more concentrated to form distinct tissues. The ectoderm furnishes the general epithelial covering of the body, and the muscular tissue, nervous system and sense-organs. The Fig. 26. — Carmarina (Gervonia) (After Nerve ring. ', Radial nerve. Tentaculocyst. Circular canal. Radiating canal. ", Ovary. Peronia or cartilaginous pro- cess ascending from the cartilaginous margin of the disk centripetally in the outer surface of the jelly- like disk; six of these are perradial, six interradial, corresponding to the twelve hastata, one of the Trachomedusae. Haeckel.) solid larval tentacles, re- sembling those of Cunina. k, Dilatation (stomach) of the manubrium. I, Jelly of the disk. p, Manubrium. /, Tentacle (hollow and tertiary, i.e. preceded by six per- radial and six interradial solid larval tentacles). u, Cartilaginous margin of the disk covered by thread- cells. *, Velum. After 0. Maas in Rtsulls oj the " Alhalross " Expedition, Museum of Comparative £oobgy, Cambridge, Mass., U.S.A. Fig. 27. — Stomoloca divisa, one of the Tiaridae ( Anthomedusae) . external epithelium is flat on the ex-timbral surface, more columnar )n the sub-umbral surface, where it forms the muscular tissue of the sub-umbrella and the velum. The nematocysts of the ectoderm may be grouped to form batteries on the tentacles, umbrellar margin and oral lappets. In places the nematocysts may be crowded so thickly as to form a tough, supporting, " chondral " tissue, resembling cartilage, chiefly developed at the margin of the umbrella and forming streaks or bars supporting the tentacles (" Tentakelspangeri, ' peronia) or the ten- taculocysts ( Gehorspangen," otoporpae). The muscular tissue of the Hydro- medusae is entirely ectodermal. The muscle-fibres arise as processes from the bases of the epithelial cells; such cells may individually become sub-epithelial in position, as in the polyp; or, in places where muscular tissue is greatly de- veloped, as in the velum or sub-umbrella, the entire muscular epithelium may be thrown into folds in order to increase its surface, so that a deeper sub-epithelial muscular layer becomes separated com- pletely from a more superficial body- epithelium. In its arrangement the muscular tissue forms two systems: the one composed of striated fibres arranged circularly, that is to say, concentrically round the central axis of the umbrella; the other of non- striated fibres running longitudinally, that is to say, in a radial direction from, or (in the manubrium) parallel to, the same ideal axis. The circular system is developed continuously over the entire sub- umbral surf ace, and the velum represents a special local develop- ment of this system, at a region where it is able to act at the greatest mechanical advantage in producing the contractions of the umbrella by which the animal progresses. The longitudinal system is dis- continuous, and is subdivided into proximal, medial and distal portions. The proximal portion forms the retractor muscles of the manubrium, or proboscis, well developed, for example, in Geryonia. The medial portion forms radiating tracts of fibres, the so-called " bell-muscles " running underneath, and parallel to, the radial canals; when greatly developed, as in Tiaridae, they form ridges, so-called mesenteries, projecting into the sub-umbral cavity. The distal portions form the muscles of the tentacles. In con- trast with the polyp, the longitudinal muscle-system is entirely ectodermal, there being no endodermal muscles in '«aspedote medusae. The nervous system of the medusa consists of sub-epithelial ganglion-cells, which form, in the first place, a diffuse plexus of nervous tissue, as in the polyp, but developed chiefly on the sub- umbral surface; and which are concen- trated, in the second place, to form a definite central ner- vous system, never found in the polyp. In Hydromedusae the central nervous system forms two Fig. 28.— Muscular Cells of Medusae concentric nerve- (Lizzia). The uppermost is a purely muscular rings at the margin ce ii f rom tne sub-umbrella ; the two lower are of the umbrella, near epidermo-muscular cells from the base of a thebaseof the velum, tentacle; the upstanding nucleated portion One, the upper forms part of the epidermal mosaic on the or ex-umbral nerve- f ree surface of the body. (After Hertwig.) ring, is derived from the ectoderm on the ex-umbral side of the velum; it is the larger of the two rings, containing more numerous but smaller ganglion- cells, and innervates the tentacles. The other, the " lower ' or sub- umbral nerve-ring, is derived from the ectoderm on the sub-umbral side of the velum; it Contains fewer but larger ganglion-cells and innervates the muscles of the velum (see diagram in article Medusae). The two nerve-rings are connected by fibres passing from one to the other. The sensory cells are slender epithelial cells, often with a cilium or stiff protoplasmic process, and should perhaps be regarded as the only ectoderm-cells which retain the primitive ciliation of the larval ectoderm, otherwise lost in all Hydrozoa. The sense-cells form, in the first place, a diffuse system of scattered sensory cells, as in the polyp, developed chiefly on the manubrium, the tentacles and the margin of the umbrella, where they form a sensory ciliated epithelium covering the nerve-centres; in the second place, the sense-cells are concentrated to form definite sense-organs, situated always at the margin of the umbrella, hence often termed "marginal bodies." The posses- sion of definite sense- organs at once dis- tinguishes the medusa from the polyp, in which they are never found. The sense-organs of medusae are of two kinds — first, organs sensitive to light, usually termed ocelli (fig. 29) ; secondly, organs commonly termed otocysts, on account of their re- semblance to the audi- tory vesicles of higher Mt£T Q M Craspedoten Medusa dcr Siboga animals, but serving Expedition, by permission of E. S. Brill & Co. for the sense of Fig. 29— TVaropw rosea (Ag. and Mayer) balance and orienta- s h ow ; ng the eight adradial Statocysts, each ti.on, * nd therefore close t0 6 an Ocellus. Cf. fig. 30. given the special name of statocysts (fig. 30). The sense-organs may be tentaculocysts, i.e. modifications of a tentacle, as in Trachylinae, or developed from the margin of the umbrella, in no connexion with a tentacle (or, if so connected, not producing any modification in the tentacle), as in Leptolinae. In Hydromedusae the sense-organs are always exposed at the umbrellar margin (hence Gymnophthalmata), while in Scypho- medusae they are covered over by flaps of the umbrellar margin (hence Steganophthalmata). The statocysts present in general the structure of either a knob or a closed vesicle, composed of (1 ) indifferent supporting epithelium : (2) sensory, so-called auditory epithelium of slender cells, each AND MORPHOLOGY] H¥DR0METCJSA1 M-S ex' bearing at its free upper end a stiff bristle and running out at its base into a nerve-fibre; (3) concrement-cells, which produce intercellular cc concretion's, So-called oto- /' liths. By means of vibrations or shocks transmitted through the ?Sub water, or by displace- ments in the balance or position of the animal, the otoliths are caused to impinge against the bristles of the sensory cells, now on one side, now on the other, causing shocks or stimuli which are transmitted by the basal nerve-fibre to the central nervous system. Two stages in the de- velopment of the otocyst can be recognized, the first that of an open pit Pig. 30.— -Section of a Statocyst and on a freely - projecting Ocellus of Tiaropsis diademata ; cf. fig. 29. knob, in which the oto- Modified after Linko, Travaux Soc. Imp. Nat., St. Petersbourg, xsix. ex, Ex-umbral ectoderm. sub, Sub-umbral ectoderm. cc. Circular canal. !', Velum. st.c, Cavity of statocyst. con, Concrement-cell with otolith. Ikhs are exposed, the second that of a closed vesicle, in which the oto- liths are covered over. Further, two distinct types of otocyst can be recognized in the Hydro- which the entire organ is mtb" medusae; that of the Leptolinae _ __ o ectodermal, concrement-cells and all, and the organ is not a tenta culocyst; and that of the Trachylinae, in which the organ is a tentaculocyst, and the con- crement-cells are endodermal, derived from the endoderm of the modified tentacle, while the rest of the organ is ecto- dermal. In the Leptolinae the oto- cysts are seen in their first stage in Mitrocoma annae (fig. 31) and Tiaropsis (figs. 29, 30) as an open. pit at the base of the velum, on its sub- umbral side. The pit has its opening turned towards the sub-umbral cavity, while its base or fundus forms a bulge, more or less pronounced, on the ex-umbral side of the velum. At the fundus are placed the concrement-cells Modified after O. and R. Hertwig, Nerven- system a und Sinnesorgane der Medusen, permission of F. C. W. Xog-A. by sub, Fig. 31. — Section of a Statocyst of with their conspicuous oto- liths (con) and the inconspicu- ous auditory cells, which are connected with . the sub- umbral nerve- ring. From the open condition arises the closed condition very simply by closing up of the aperture of the pit. We then find the typical otocyst of the Leptomedusae, a vesicle bulging on the ex-umbral side of the velum (.figs. 32, 33). The otocysts are s placed on the outer wall of the Sub Mitrocoma annae Sub-umbral ectoderm cc, Circular canal. r. Velum. st.c. Cavity of statocyst. con, Concrement-cell with otolith . — ex. con Modified after 0. and R. Hertwig, Nerven- system und Sinnesorgane der Medusen, by permission of F. C. W. Vogel. Fig. 32. — Section of a Statocyst of Phialidium. ex, Ex-umbral ectoderm. sub, Sub-umbral ectoderm. v, Velum. st.c, Cavity of statocyst. con. Concrement-cell with otolith. con st.c Modified after 0. and R. Hertwig, Xervensystem -und Sinnesorgane der Medusen, by permission of F. C. W. Vogel. Fig. 33. — Optical Section of a Statocyst of Ociorchis. con, Concrement - cell with otolith. st.c, Cavity of statocyst. vesicle (the fundus of the original pit) or on its sides ; their arrange- ment and number vary greatly and furnish useful characters for distinguishing genera. The sense-cells are innervated, as before, from the sub-umbral nerve-ring. The inner wall of the vesicle con end. n.c. (region of closure) is frequently thickened to form a so-called " sense; cushion," apparently a ganglionic offshoot from the sub-umbral nerve -nng. In many Leptomedusae the oto- cysts are very small, in- conspicuous and em- bedded completely in the tissues; hence they may be easily overlooked in badly-preserved material, and perhaps are present in many cases where they have been said to have been wanting. In the Trachylinae the simplest condition of the otocyst is a freely pro- jecting club, a so-called statorhabd (figs. 34, 35), representing a tentacle greatly reduced in size, covered with sensory ectodermal epithelium (ect.), and containing an endodermal core (end.), which is at first continu- ous with the endoderm of the ring-canal, but later becomes separated from it. In the endoderm large concretions are formed (con.) After 0. and R. Hertwig, Nenensyslem und Sinnes- organe der Medusen, by permission of F. C. W. Vogel. Fig. 34. — Tentaculocyst (statorhabd) of Cunina solmaris. n.c, Nerve-cushion; end, endodermal concrement-cells; con, otolith. . Other sensory cells with long cilia cover a sort of cushion (n.c.) at the base of the club ; the club may be long and the cushion small, or the cushion large and the club small. The whole structure is innervated, like the tentacles, from the. ex-umbral nerve-ring. An advance towards the second stage is seen in such a form as Rhopalo- nema (fig. 36), where the ectoderm of' the cushion rises up in a double fold to enclose the club in a protective covering form- ing a cup or vesicle, at first open distally ; finally the opening closes and the closed vesicle may sink inwards and be found: far removed from After O. and R. Hertwig, Nervensystem und Sinnes- the surface, as in Geryonia °n:».i. H jL ev are endodermal, £. ^^^^B^ft^^^T' ~J$w3$ forming a cup _ of pigment in which the visual cones are embedded. A / / nr, After 0. and R. Hertwig, Nervensyslem und Sinnesorgane ier Aledusen, by permission of F. C. W. Vogel. Fig. 37. — Section of statocyst of (Carmarina hastata). Statocyst containing the minute tentaculo- cyst. Ex-umbral nerve-ring. Sub-umbral nerve-ring. Ex-umbral ectoderm. sub, Sub-umbral ectoderm. c.c, Circular canal. v, Velum. similar formed among the Scypho- • .v.). ocellus is in Aurelia st.c, ex. ,-t medusae (BYDR®MfiTER the plane of flotation, the stability of the instrument when floating will be diminished or destroyed. The various devices which have been adopted to overcome this difficulty will be described in the account given of the several hydrometers which have been hitherto generally employed. The plan commonly adopted to obviate the necessity of incon- veniently long stems is to construct a number of hydrometers as nearly alike as may be, but to load them differently, sd that the scale- divisions at the bottom of the stem of one hydrometer just overlap those at the top of the stem of the preceding. By this means a set of six hydrometers, each having a stem rather more than 5 in. long, will be equivalent to a single hydrometer with a stem of 30 in. But, instead of employing a number of instruments differing only in the weights with which they are loaded, we may employ the same instrument, and alter its weight either by adding mercury or shot to the interior (if it can be opened) or by attaching weights; to the ex- terior. These two operations are not quite equivalent, since a weight added to the interior does not affect the volume of liquid displaced when the instrument is immersed up to a given division of the scale, while the addition of -weights to the exterior increases the displace- ment. This difficulty may be met, as in Keene's hydrometer, by having all the weights of precisely the same volume but of different masses, and never using the instrument except with one of these weights attached. The first hydrometer intended for the determination of the densities of liquids, and furnished with a set of weights to.be attached when necessary, was that con- structed by Mr Clarke (instrument-maker) and described by J. T. Desaguliers in the Philosophical Transactions for March and April 1730, No. 413, p. 278. The following is Desaguliers's account of the instrument (fig. a):— " After having made several fruitless trials with ivory, because it imbibes spirituous liquors, and thereby alters its gravity, he (Mr Clarke) at last made a copper hydrometer, represented in fig. 2, having a brass wire of about 1 in. thick sfoing through, and soldered into the copper ball Bfc. The upper part of this wire is filed flat on one side, for the stem of the hydrometer, with a mark at m, to which it sinks exactly in proof spirits. There are two other marks, A and B, at top and bottom of the stem, to show whether the liquor be -^th above proof (as when it sinks to A), or ^th under proof (as when it emerges to B), when a brass weight such as C has been screwed on to the bottom at c. There are a great many such weights, of different sizes, and marked to be screwed on instead of C, for liquors that differ more than ^th from proof, so as to serve for the specific gravities in all such propor- tions as relate to the mixture of spirituous liquors, in all the variety made use of in trade. There are also other balls for showing the specific gravities quite to common water, which make the instrument perfect in its kind." Fig. 2. — Clarke's Hydrometer. Fig. 3. — Nichol- son's Hydrometer. Clarke's hydrometer, as afterwards constructed for the purposes of the excise, was provided with thirty-two weights to adapt it to spirits of different specific gravities, and eleven smaller weights, or " weather weights " as they were called, which were attached to the instrument in order to correct for variations of temperature. The weights were adjusted for successive intervals of 5° F., but for degrees intermediate between these no additional correction was applied. The correction for temperature thus afforded was not sufficiently accurate for excise purposes, and William Speer in his essay on the hydrometer (Tilloch's Phil. Mag., 1802, vol. xiv.) mentions cases in which this imperfect compensation led to the extra duty payable upon spirits which were more than 10% over proof being demanded on spirits which were purposely diluted to below 10% over proof in order to avoid the charge. Clarke's hydrometer, however, remained the standard instrument for excise purposes from 1787 until it was displaced by that of Sikes. Desaguliers himself constructed a hydrometer of the ordinary type for comparing the specific gravities of different kinds of water (Desaguliers's Experimental Philosophy, ii. 234). In order to give great sensibility to the instrument, the large glass ball was made nearly 3 in. in diameter, while the stem consisted of a wire 10 in. in length and only ^y in. in diameter. The instrument weighed 4000 grains, and the addition of a grain caused it to sink through itn inch. By altering the quantity of shot in the small balls the instrument could be adapted for liquids other than water. To an instrument constructed for the same purpose, but on a still larger scale than that of Desaguliers, A. Deparcieux added a small dish on the top of the stem for the reception of the weights necessary to sink the instrument to a convenient depth. The effect of weights placed in such a dish or pan is of course the same as if they were placed within the bulb of the instrument , since they do not alter the volume of that part which is immersed. The first important improvement in the hydrometer after its reinvention by Boyle w T as introduced by G. D. Fahrenheit, who adopted the second mode of construction above referred to, arranging his instrument so as always to displace the same volume of liquid, its weight being varied accordingly. Instead of a scale, only a single mark is placed upon the stem, which is very slender, and bears at the top a small scale pan into which weights are placed until the instrument sinks to the mark upon its stem. The volume of the displaced liquid being then always the same, its density will be proportional to the whole weight supported, that is, to the weight of the instrument together with the weights required to be placed in the scale pan. Nicholson's hydrometer (fig. 3) combines the characteristics of Fahrenheit's hydrometer and of Boyle's essay instrument. 1 The following is the description given of it by W. Nicholson in the Manchester Memoirs, ii. 374: — " AA represents a small scale. It may be taken off at D. Dia- meter 1 j in., weight 44 grains. " B a stem of hardened steel wire. Diameter ,Jo in. " E a hollow copper globe. Diameter 2f\> in. Weight with stem 369 grains. .,.:,.' ' FF' a stirrup of 'wire screwed to the globe at C. "G a small scale, serving likewise as a counterpoise. Diameter I J in. Weight with stirrup 1634 grains. " The other dimensions may be had from the drawing, which is one-sixth of the linear magnitude of the instrument itself. " In the construction it is assumed that the upper scale shall constantly carry 1000 grains when the lower scale is empty, and the instrument sunk in distilled water at the temperature of 60° Fafir. to the middleof the wire or stem. The length of the stem is arbitrary, as is likewise the distance of the lower scale from the surface of the globe. But, the length of the stem being settled, the lower scale may be made lighter, and, consequently, the globe less, the greater its distance is taken from the surface of the globe; and the contrary. In comparing the densities of different liquids, it is clear that this instrument is precisely equivalent to that of Fahrenheit, and must be employed in the same manner, weights being placed in the top scale only until the hydrometer sinks to the mark on the wire, when the specific gravity of the liquid will be proportional to the weight of the instrument together with the weights in the scale. In the subsequent portion of the paper above referred to, Nicholson explains how the instrument may be employed as a thermometer, since, fluids generally expanding more than the solids of which the instrument is constructed, the instrument will sink as the temperature rises. To determine the density of solids heavier than water with . this instrument, let the solid be placed in the upper scale pan, and let the weight now required to cau.se the instrument to sink in distilled water at standard temperature to the mark B be denoted by w, while W denotes the weight required when the solid is not present. Then W-w is the weight of the solid. Now let the solid be placed in the lower pan, care being taken that no bubbles of air remain attached to it, and let Wi be the weight now required in the scale pan?" This weight will exceed w in consequence of the water displaced by the solid, and the weight of the water thus displaced will be Wi-w, which is therefore the weight of a volume of water equal to that of the solid. Hence, since the weight of the solid itself is W-ui, its density must be (W-tt>)/(iUi-i£»). The above example illustrates how Nicholson's or Fahrenheit's hydrometer may be employed as a weighing machine for small weights. In all hydrometers in which a part only of the instrument 1 Nicholson's Journal, vol. i. p. m, footnote. HYDROMETER is immersed, there is a liability to error in consequence of the surface tension, or capillary action, as it is frequently called, along the line of contact of the instrument and the surface of the liquid (see Capillary Action). This error diminishes as the diameter of the stem is reduced, but is sensible in the case of the thinnest stem which can be employed, and is the chief source of error in the employment of Nicholson's hydrometer, which otherwise would be an instrument of extreme delicacy and precision. The following is Nicholson's statement on this point: — " One of the greatest difficulties which attends hydrpstatical experiments arises from the attraction or repulsion that obtains at the surface of the water. After trying many experiments to obviate the irregularities arising from this cause, I find reason to prefer the simple one of carefully wiping the whole instrument, and especially the stem, with a clean cloth. The weights in the dish must not be esteemed accurate while there is either a cumulus or a cavity in the water round the stem." It is possible by applying a little oil to the upper part of the bulb of a common or of a Sikes's hydrometer, and carefully placing it in pure water, to cause it to float with the upper part of the bulb and the whole of the stem emerging as indicated in fig. 4, when it ought properly to sink almost to the top of the stem, the surface tension of the water around the circumference of the circle of contact, AA', providing the additional support required. The universal hydrometer of G. Atkins, described in the Phil. Mag. for 1808, xxxi. 25^, is merely Nicholson's hydro- meter with the screw at C projecting through the collar into which it is screwed, and terminating in a sharp point above the cup G. To this point soft bodies lighter than water (which would float if placed in the cup) could be attached, and thus com- pletely immersed. Atkins's instrument was constructed so as to weigh 700 grains, and when immersed to the mark on the stem in distilled water at 6o° F. it carried 300 grains in the upper dish. The hydrometer therefore displaced 1000 grains of distilled water at 6o c F.and hence the specific gravity of any other liquid was at once indicated by adding 700 to the number of grains in the pan required to make the instrument sink to the mark on the stem. The small divisions on the scale corresponded to differences of , l th of a grain in the weight of the instrument. The " Gravimeter," constructed by Citizen Guyton and described in Nicholson's Journal, 4to, i. no, differs from Nicholson's instru- ment in being constructed of glass, and having a cylindrical bulb about 21 centimetres in length and 22 millimetres in diameter. Its weight is so adjusted that an additional weight of 5 grammes must be placed in the upper pan to cause the instrument to sink to the mark on the stem in distilled water at the standard temperature. The instrument Is provided with an additional piece, or " plongeur," the weight of which exceeds 5 grammes by the weight of water which it displaces ; that is to say, it is so constructed as to weigh 5 grammes in water, and consists of a glass envelope filled with mercury. It is clear that the effect of this " plongeur," when placed in the lower pan, is exactly the same as that of the 5 gramme weight in the upper pan. Without the extra 5 grammes the instrument weighs about 20 grammes, and therefore floats in a liquid of specific gravity -8. Thus deprived of its additional weight it may be used for spirits. To use the instrument for liquids of much greater density than water additional weights must be placed in the upper pan, and the " plongeur " is then placed in the lower pan for the purpose of giving to the instrument the requisite stability. Charles's balance areometer is similar to Nicholson's hydrometer, except that the lower basin admits of inversion, thus enabling the instrument to be employed for solids lighter than water, the in- verted basin serving the same purpose as the pointed screw in Atkins's modification of the instrument. Adie's sliding hydrometer is of the ordinary form, but can be adjusted for liquids of widely differing specific gravities by drawing out a sliding tube, thus changing the volume of the hydrometer while its weight remains constant. The hydrometer of A. Baum6, which has been extensively used in France, consists of a common hydrometer graduated in the following manner. Certain fixed points were first detefmined upon the stem of the instrument. The first of these was found by immersing the hydrometer in pure water, and marking the stem at the level of the surface. This formed the zero of the scale. Fifteen standard solutions of pure common salt in water were then prepared, contain- 163 ing respectively 1, 2, 3, ... 15% (by weight) of dry salt. The hydrometer was plunged in these solutions in order, and the stem having been marked at the several surfaces, the degrees so obtained were numbered 1,2,3, ■ • • 15- Thesedegrees were, when necessary, repeated along the stem by the employment of a pair of compasses till 80 degrees were marked off. The instrument thus adapted to the determination of densities exceeding that of water was called the hydrometer for salts. The hydrometer intended for densities less than that of water, or the hydrometer for spirits, is constructed on a similar principle. The instrument is so arranged that it floats in pure water with most of the stem above the surface. A solution containing 10% of pure salt is used to indicate the zero of the scale, and the point at which the instrument floats when immersed in distilled water at io° R. (54J F.) is numbered 10. Equal divisions are then marked off upwards along the stem as far as the 50th degree. The densities corresponding to the several degrees of Baum6's hydrometer are given by Nicholson (Journal of Philosophy, i. 89) as follows :— Baume's Hydrometer for Spirits. Temperature 10° R. Fig. 4. Degrees. Density. Degrees. Density. Degrees. Density. 10 I -000 21 •922 31 ■861 n •990 22 •915 32 •856 12 •985 23 ■909 33 •852 13 ■977 24 •903 34 •847 14 ■970 25 •897 35 •842 15 •963 26 ■892 36 •837 16 •955 27 •886 37 •832 . 17 ■949 28 •880 38 •827 18 •943 29 •874 39 •822 19 ■935 30 •867 40 •817 20 ■928 | Baume's Hydrometer for Salts. Degrees. Density. Degrees. Density. Degrees. Density. ' I-OOO 27 1-230 5i 1-547 3 i- 020 30 1-261 54 t-594 6 1-040 33 1-295 57 1-659 9 1-064 36 1-333 60 1 717 12 1-089 39 1-373 63 1-779 15 1-114 42 1-414 66 1-848 18 1-140 45 1-455 69 1-920 1 21 1-170 48 1-500 72 2-000 1 24 1-200 ] Cartier's hydrometer was very similar to that of Baum6, Cartier having been employed by the latter to construct his instruments for the French revenue. The point at which the instrument floated in distilled water was marked 10° by Cartier, and 30 on Cartier's scale corresponded to 32 on Baume's. Perhaps the main object for which hydrometers have been constructed is the determination of the value of spirituous liquors, chiefly for revenue purposes. To this end an immense variety of hydrometers have been devised, differing mainly in the character of their scales. In Speer's hydrometer the stem has the form of an octagonal prism, and upon each of the eight faces a scale is engraved, indicating the percentage strength of the spirit corresponding to the several divisions of the scale, the eight ■ scales being adapted respectively to the temperature 35 °, 40 , 45 , 50 , 55 , 60°, 65° and 70° F. Four small pins, which can be inserted into the counterpoise of the instrument, serve to adapt the instrument to the temperatures intermediate between those for which the scales are constructed. William Speer was supervisor and chief assayer of spirits in the port of Dublin. For a more complete account of this instrument see Tilloch's Phil. Mag., xiv. 151. The hydrometer constructed by Jones, of Hol- born, consists of a spheroidal bulb with a rec- tangular stem (fig. 5). Between the bulb and counterpoise is placed a thermometer, which serves to indicate the temperature of the liquid, and the instrument is provided with three weights which can be attached to the top of the stem. On the four sides of the stem AD are engraved four scales corresponding respectively to the unloaded Fig. 5. — Jones'; instrument, and to the instrument loaded with the Hydrometer, respective weights. The instrument when unloaded serves for the range from 74 to 47 over proof ; when loaded with tht first weight it indicates from 46 to 13 over proof, with the second weight from 13 over proof to 29 under proof, and with the third 164 HYDROMETER i i 1 i Fig. 6. from 29 under proof to pure water, the graduation corresponding to which is marked W at the bottom of the fourth scale. One side of the stem AD is shown in fig. 5, the other three in fig. 6. The thermo- meter is also provided with four scales corresponding to the scales above mentioned. Each scale has its zero in the middle correspond- ®^„^ ing to 6o c F. If the mercury in the thermo- ^q\ (o\ meter stand above this zero the spirit must V J KZJ De reckoned weaker than the hydrometer in- &■_ jbl dicates by the number on the thermometer I i scale level with the top of the mercury, while — Kl fcrtl ;f tne thermometer indicate a temperature lower than the zero of the scale (60° F.) the spirit must be reckoned stronger by the scale reading. At the side of each of the four scales on the stem of the hydrometer is en- graved a set of small numbers indicating the contraction in volume which would be experi- enced if the requisite amount of water (or spirit) were added to bring the sample tested to the proof strength. The hydrometer constructed by Dicas of Liverpool is provided with a sliding scale which can be adjusted for different temperatures, and . . , which also indicates the contraction in volume incident on bringing the spirit to proof strength. It is provided with thirty-six different weights which, with the ten divisions on the stem, form a scale from o to 370. The employment of so many weights renders the instrument ill-adapted for practical work where speed is an object. This instrument was adopted by the United States in 1790, but was subsequently discarded by the Internal Revenue Service for another type. In this latter form the observations have to be made at the standard temperature of 6o° F., at which the graduation 100 corresponds to proof spirit and 200 to absolute alcohol. The need of adjustable weights is avoided by employing a set of five instru- ments, graduated respectively o°-loo°, 80-120°, ioo°-i4o°, i30°-i7o°, l6o°-200°. The reading gives the volume of proof spirit equivalent to the volume of liquor; thus the readings 8o° and 120° mean that 100 volumes of the test liquors contain the same amount of absolute alcohol as 80 and 120 volumes of proof spirit respectively. Proof spirit is defined in the United States as a mixture of alcohol and water which contains equal volumes of alcohol and water at 6o° F., the alcohol having a specific gravity of 0-7939 at 60° as compared with water at its maximum density. The specific gravity of proof spirit is 0- 93353 at 6o°; and 100 volumes oi the mixture is made from 50 volumes of absolute alcohol and 53-71 volumes of water. Quin's universal hydrometer is described in the Transactions of the Society of Arts, viii. 98. It is provided with a sliding rule to adapt it to different temperatures, and has four scales, one of which is graduated for spirits and the other three serve to show the strengths of worts. The peculiarity of the instrument con- sists in the pyramidal form given to the stem, which renders the scale-divisions more nearly equal in length than they would be on a pris- matic stem. Atkins's hydrometer, as originally constructed, is described in Nicholson's Journal, 8vo, ii. 276. It is made of brass, and is provided with a spheroidal bulb the axis of which is 2 in. in length, the conjugate diameter being 1 § in. The whole length of the instrument is 8 in., the stem square of about j-in. side, and the weight about 400 grains. It is provided with four weights, marked 1, 2, 3, 4, and weighing respectively 20, 40, 61 and 84 grains, which can be attached to the shank of the instrument at C (fig. 7) and retained there by the fixed weight B. The scale engraved upon one face of the stem contains fifty-five divisions, the top and bottom being marked o or zero and the alter- nate intermediate divisions (of which there are ;wenty-six) being marked with the letters of the alphabet in order. The four weights are so adjusted that, if the instrument floats with the stem emerging as far as the lower division o with one of the weights attached, then replacing the weight by the next heavier causes the instrument to sink through the whole leneth of the scale to the upper division o, and the first weight produces the same effect when applied to the naked instrument. The stem is thus virtually extended to five times its length, and the number of divisions in- creased practically to 272. When no weight is attached the instru- ment indicates densities from -806 to -843; with No. 1 it registers from -843 to -S8o, with No. 2 from -88o to -918, with No. 3 from -918 to -958, and with No. 4 from -958 to i-ooo, the temperature being C Fig. 7. — Atkins's Hydrometer. 55° F. It will thus be seen that the whole length of the stem corre- sponds to a difference of density of about -04, and one division to about -00074, indicating a difference of little more than i % in the strength of any sample of spirits. The instrument is provided with a sliding rule, with scales corre- sponding to the several weights, which indicate the specific gravity corresponding to the, several divisions of the hydrometer scale com- pared with water at 55° F. The slider upon the rule serves to adjust the scale for different temperatures, and then indicates the strength of the spirit in percentages over or under proof. The slider is also provided with scales, marked respectively Dicas and Clarke, which serve to show the readings which would have been obtained had the instruments of those makers been employed. The line on the scale marked " concentration " indicates the diminution in volume consequent upon reducing the sample to proof strength (if it is over proof, O.P.) or upon reducing proof spirit to the strength of the sample (if it is under proof, U.P.). By applying the several weights in succession in addition to No. 4 the instrument can be employed for liquids heavier than water; and graduations on the other three sides of the stem, together with an additional slide rule, adapt the instru- ment for the determination of the strength of worts. Atkins subsequently modified the instrument {Nicholson's Journal, 8vo, iii. 50) by constructing the different weights of different shapes, viz. ciicular, square, triangular and pentagonal, instead of numbering them I, 2, 3 and 4 respectively, a figure of the weight being stamped on the sliding rule opposite to every letter in the series to which it belongs, thus diminishing the probability of mistakes. He also replaced the letters on the stem by the corre- sponding specific gravities referred to water as unity. Further information concerning these instruments and the state of hydro* metry in 1803 will be found in Atkins's pamphlet On the Relation between the Specific Gravities and the Strength of Spirituous Liquors (1803); or Phil. Mag. xvi. 26-33, 205-212, 305-312; xvii. 204-210 and 329-341. In Gay-Lussac's alcoholometer the scale is divided into 100 parts corresponding to the presence of I, 2, ... % by volume of alcohol at 15° C, the highest division of the scale corresponding to the purest alcohol he could obtain (density -7947) and the lowest division corresponding to pure water. A table provides the necessary corrections for other temperatures. Tralles's hydrometer differs from Gay-Lussac's only in being graduated at 4 C. instead of 15° C, and taking alcohol of density •7939 at 15-5° C. for pure alcohol instead of -7947 as taken by Gay Lussac (Keene's Handbook of Hydrometry). In Beck's hydrometer the zero of the scale corresponds to density i-ooo and the division 30 to density -850, and equal divisions oiv the scale are continued as far as is required in both directions. In the centesimal hydrometer of Francoeur the volume of the stem between successive divisions of the scale is always j} B th of the whole volume immersed when the instrument floats in water at 4 C. In order to graduate the stem the instrument is first weighed, then immersed in distilled water at 4 C, and the line of flotation marked zero. The first degree is then found by placing on the top of the stem a weight equal to fjj,th of the weight of the instrument, which in- creases the volume immersed by t J th of the original volume. The addition to the top of the stem of successive weights, each jJoth of the weight of the instrument itself, serves to determine the succes- sive degrees. The length of 100 divisions of the scale, or the length of the uniform stem the volume of which would be equal to that of the hydrometer up to the zero graduation, Francoeur called the "modulus " of the hydrometer. He constructed his instruments of glass, using different instruments for different portions of the scale (Francoeur, Traiti d'areometrie, Paris, 1842). Dr Bories of Montpellier constructed a hydro- meter which was based upon the results of his experiments on mixtures of alcohol and water. The interval between the points corresponding to pure alcohol and to pure water Bories divided into 100 equal parts, though the stem was pro- Fig. 8. — Sikes's longed so as to contain only 10 of these divisions, Hydrometer, the other 90 being provided for by the addition of 9 weights to the bottom of the instrument as in Clarke's hydrometer The instrument which has now been exclusively used for revenue purposes for nearly a century is that associated with the name of Bartholomew Sikes, who was correspondent to the Board of Excise from 1774 to 1783, and for some time collector of excise for Hertford- shire. Sikes's hydrometer, on account of its similarity to that of Bories, appears to have been borrowed from that instrument. It is made of gilded brass or silver, and consists of a spherical ball A (fig. 8), 1-5 in. in diameter, below which is a weight B connected with the ball by a short conical stem C. The stem D is rectangular in section and about 3! in. in length. This is divided into ten equal parts, each of which is subdivided into five. As in Bories's instrument, a series of 9 weights, each of the form shown at E, serves to extend the scale ft V Ht HYDROPATHY 165 to 100 principal divisions. In the centre of each weight is a holt- capable of admitting the lowest and thickest end of the conical stem C, and a slot is cut into it just wide enough to allow the upper part of the cone to pass. Each weight can thus be dropped on to the lower stem so as to rest on the counterpoise B. The weights are marked 10, 20, ... 90; and in using the instrument that weight must be selected which will allow it to float in the liquid with a portion only of the stem submerged. Then the reading of the scale at the line of flotation, added to the number on the weight, gives the reading required. A small supernumerary weight F is added, which can be placed upon the top of the stem. F is so adjusted that when the 60 weight is placed on the lower stem the instrument sinks to the same point in distilled water when F is attached as in proof spirit when F is removed. The best instruments are now constructed tor revenue purposes of silver, heavily gilded, because it was found that saccharic acid contained in some spirits attacked brass behind the gilding. The following table gives the specific gravities corresponding to the principal graduations on Sikes's hydrometer at 60° F. and 62° F., together with the corresponding strengths of spirits. The latter are based upon the tables of Charles Gilpin, clerk to the Royal Society, for which the reader is referred to the Phil. Trans, for 1794. Gilpin's work is a model for its accuracy and thoroughness of detail, and his results have scarcely been improved upon by more recent workers. The merit of Sikes's system lies not so much in the hydrometer as in the complete system of tables by which the readings of the instru- ment are at once converted into percentage of proof-spirit. Table showing the Densities corresponding to the Indications of Sikes's Hydrometer. ■A 00° F. 62° F. 60° F. 62° F. V- Proof Proof -"\2 Proof Proof J5 £ c Density. Spirit per cent. Density. Spirit per cent. c/3'-3 Density. Spirit per cent. Density. Spirit per cent. 815297 1670 ■815400 1665 51 •905024 111-4 •905138 110-7 1 ■810956 1661 ■817059 165-6 52 •906869 110-0 ■906983 109-3 2 ■818«21 165-3 ■818725 164-8 53 •908722 108-6 ■908837 107-9 3 ■820294 164-5 •820397 163-9 54 ■910582 107-1 •910097 106-5 4 •821973 163-6 •822077 163-1 55 ■912450 105-6 •912565 105-0 5 ■823659 102-7 ■823763 162-3 56 •914320 104-2 '914441 103-5 tj 825352 161-8 ■825457 161-4 57 •916209 102-7 •916323 1020 7 ■827052 160-9 ■827157 160-5 58 •918100 101-3 ■918216 100-5 s ■828759 1600 ■828864 159-0 59 ■919999 99-7 ■920115 98-9 9 ■830473 1591 ■830578 158-7 60 •921906 98-1 ■922022 97-4 10 ■832195 15S-2 832300 157-8 OOb '921884 98-1 ■922000 97-4 11 •S338SS 157-3 ■833993 156-S 61 •923760 96-6 ■923877 95-9 12 •835587 156-4 ■835692 155-9 62 ■925643 950 '925700 94-2 13 •837294 155-5 •837400 155-0 63 ■927534 933 •927652 92-0 14 •839008 154-6 •839114 154-0 64 ■929433 91-7 ■929550 90-9 15 •840729 153-7 •840835 153-1 65 •931339 90-0 ■931457 89-2 IB •842458 152-7 •842504 152-1 66 ■933254 88-3 ■933372 87-5 17 •844193 151-7 •844299 151-1 67 ■935176 86-5 ■935294 85-8 IS •845930 1.50-7 •846042 150-1 68 ■937107 847 ■937225 84-0 19 •847685 149-7 •847792 149-1 69 •939045 82-9 •939163 822 20 •849442 148-7 •849549 148-1 70 •940991 81-1 ■941110 80-3 20b •849393 148-7 •849500 148-1 70b ■940981 Sl'l ■941100 80-3 21 •851122 147-6 ■851229 147-1 71 •942897 792 ■943016 78-4 ■>2 •852S57 146-6 •852964 146-1 72 ■944819 77-3 ■944938 76-5 33 •854599 145-6 •854707 145-1 73 ■946749 75-3 ■946869 74-5 24 ■S5634S 144-6 •856456 1440 74 ■948087 733 •948807 72-5 25 ■858105 143-5 •858213 142-9 75 •950634 7P2 ■950753 70-4 2(i ■859869 142-4 •859978 141-8 76 ■952588 69-0 ■952708 68-2 OV ■801640 141-3 ■861749 140-8 77 ■954550 66-8 ■954670 66-0 2S •863419 140-2 ■S63528 139-7 78 -956520 644 ■956641 63-5 29 ■835204 1391 ■865313 138 5 79 ■958498 6P9 ■958619 61-1 30 ■860998 138-0 ■867107 137-4 SO •960485 59-4 ■960600 58-5 30b •866991 13S-0 •867100 137-4 80b -960479 59-4 ■960000 58-5 31 ■8118755 136-9 -868865 136-2 81 •962433 56-7 ■962555 55-8 32 ■870526 135-7 •870636 1351 82 ■964395 53-9 ■964517 53-0 33 •872305 134-5 S72415 133-9 S3 •966366 50-9 •966488 50-0 34 ■874090 133-4 •874200 132-8 84 ■968344 47-8 •968466 47-0 35 ■S75883 132-2 ■875994 131-6 85 ■970331 44-5 '970453 43-8 36 ■877681 1310 ■S77995 130-4 86 ■972325 4V0 '972448 40-4 37 ■879492 129-8 -879603 129-1 87 •974328 37-5 ■974451 36-9 38 831307 128-5 ■8S1419 127-9 88 •976340 34-0 ■976463 33-5 39 ■883129 127-3 ■8S3241 126-7 89 ■978359 30 •978482 30-1 40 '884900 126-0 •885072 125-4 90 ■980386 27-2 •980510 26-7 40b ■SS48S8 1260 ■885000 125-4 90b ■980376 27-2 '980500 20-7 41 ■S8S6S9 124-8 •88580 i 124-2 91 ■982371 23-9 '982496 23-6 42 ■8SS497 1235 •888609 122-9 92 •984374 20-8 '984498 20-5 1 43 -S90312 122-2 ■S90425 121-6 93 ■986385 17-7 '986510 17-4 : 44 ■892135 120-9 •892248 1203 94 ■988404 148 ■988529 14-5 , 45 ■893965 1196 •S94078 1190 95 •990431 12-0 ■990557 11-7 i 4li ■8.15803 118-3 •8^5916 117-6 96 •992468 93 •992593 90 47 ■897647 1169 ■897761 116-3 97 •994512 0-7 •994637 6-5 48 ■899500 115-6 ■899614 114-9 98 •996565 4-1 •996691 40 49 i -901360 114-2 ■901417 113-5 99 ■998626 1-8 •998752 1-6 50 ■903229 112-8 ■903343 1121 100 1 000691 00 1000822 00 50b •903186 1128 ■903300J112-1 In the above table for Sikes's hydrometer two densities are given corresponding to each of the degrees 20, 30, 40, 50, 60, 70, 80 and 00, Indicating that the successive weights belonging to the particular Instrument for which the table has been calculated do not quite agree. The discrepancy, however, does not produce any sensible error in the strength of the corresponding spirit. A table which indicates the weight per gallon of spirituous liquors for every degree of Sikes's hydrometer is printed in 23 and 24 Vict. c. 114, schedule B. This table differs slightly from that given above, which has been abridged from the table given in Keene's Handbook of Hydrometry, apparently on account of the equal divisions on Sikes's scale having been taken as corresponding to equal increments of density. Sikes's hydrometer was established for the purpose of collecting the revenue of the United Kingdom by Act of Parliament, 56 Geo. III. c. 140, by which it was enacted that " all spirits shall be deemed and taken to be of the degree of strength which the said hydrometers called Sikes's hydrometers shall, upon trial by any officer or officers of the customs or excise, denote such spirits to be." This act came into force on January 5, 1817, and was to have remained in force until August 1, 1818, but was repealed by 58 Geo. II I.e. 28, which established Sikes's hydrometer on a permanent footing. By 3 and 4 Will. IV. c. 52, § 123, it was further enacted that the same instruments and methods should be employed in determining the duty upon im- ported spirits as should in virtue of any Act of Parliament be em- ployed in the determination of the duty upon spirits distilled at home. It is the practice of the officers of the inland revenue to adjust Sikes's hydrometer at 62° F., that being the temperature at which the imperial gallon is defined as containing 10 lb avoirdupois of distilled water. The specific gravity of any sample of spirits thus determined, when multiplied by ten, gives the weight in pounds per imperial gallon, and the weight of any bulk of spirits divided by this number gives its volume at once in imperial gallons. Mr (afterwards Colonel) J. B. Keene, of the Hydrometer Office, London, has constructed an instrument after the model of Sikes's, but provided with twelve weights of different masses but equal volumes, and the instrument is never used without having one of these attached. When loaded with either of the lightest two weights the instrument is specifically lighter than Sikes's hydrometer when unloaded, and it may thus be used for specific gravities as low as that of absolute alcohol. The volume of each weight being the same, the whole volume immersed is always the same when it floats at the same mark whatever weight may be attached. Besides the above, many hydrometers have been employed for special purposes. Twaddell's hydrometer is adapted for densities greater than that of water. The scale is so arranged that the reading multiplied by 5 and added to 1000 gives the specific gravity with reference to water as 1000. To avoid an inconveniently long stem, different instruments are employed for different parts of the scale as mentioned above. The lactometer constructed by Dicas of Liverpool is adapted for the determination of the quality of milk. It resembles Sikes's hydrometer in other respects, but is provided with eight weights. It is also provided with a thermometer and slide rule, to reduce the readings to the standard temperature of 55 ° F. Any determination of density can be taken only as affording prima facie evidence of the quality of milk, as the removal of cream and the addition of water are operations which tend to compensate each other in their influence on the density of the liquid, so that the lactometer cannot be regarded as a reliable instrument. The marine hydrometers, as supplied by the British government to the royal navy and the merchant marine, are glass instruments with slender stems, and generally serve to indicate specific gravities from i-ooo to 1-040. Before being issued they are compared with a standard instrument, and their errors determined. They are employed for taking observations of the density of sea-water. The sahnometer is a hydrometer originally intended to indicate the strength of the brine in marine boilers in which sea-water is employed. Saunders's salinometer consists of a hydrometer which floats in a chamber through which the water from the boiler is allowed to flow in a gentle stream, at a temperature of 200° F. The peculiarity of the instrument consists in the stream of water, as it enters the hydrometer chamber, being made to impinge against a disk of metal, by which it is broken into drops, thus liberating the steam, which would otherwise disturb the instrument. The use of Sikes's hydrometer necessitates the employment of a considerable quantity of spirit. For the testing of spirits in bulk Jio more convenient instrument has been devised, but where very small quantities are available more suitable laboratory methods must be adopted. In England, the Finance Act 1907 (7 Ed. VII. c. 13), section 4, provides as follows: (1) The Commissioners of Customs and the Commissioners of Inland Revenue may jointly make regulations authorizing the use of any means described in the regulations for ascertaining for any purpose the strength or weight of spirits. (2) Where under any enactment Sykes's {sic) Hydrometer is directed to be used or may be used for the purpose of ascertaining the strength or weight of spirits, any means so authorized by regulations may be used instead of Sykes's, Hydrometer and reference's to Sykes's Hydro- meter in any enactment shall be construed accordingly. (3) Any regulations made under this section shall be published in the London, Edinburgh and Dublin Gazette, and shall take effect from the date of publication, or such later date as may be mentioned in the regulations for the purpose. (4) The expression " spirits " in this section has the same meaning as in the Spirits Act 1880. (W. G.) HYDROPATHY, the name given, from the Greek, to the " water-cure," or the treatment of disease by water, used outwardly and inwardly. Like many descriptive names, the word " hydropathy " is defective and even misleading, the active agents in the treatment being heat and cold, of which water i66 HYDROPATHY is little more than the vehicle, and not the only one. Thermo- therapeutics (or thermotherapy) is a term less open to objection. Hydropathy, as a formal system, dates from about 1829, when Vincenz Priessnitz (1801-1851), a farmer of Grafenberg in Silesia, Austria, began his public career in the paternal homestead, extended so as to accommodate the increasing numbers attracted by the fame of his cures. Two English works, however, on the medical uses of water had been translated into German in the century preceding the rise of the movement under Priessnitz. One of these was by Sir John Floyer (1649- 1734), a physician of Lichfield, who, struck by the remedial use of certain springs by the neighbouring peasantry, investigated the history of cold bathing, and published in 1702 his "tyvxpo- \ovcia, or the History of Cold Bathing, both Ancient and Modern." The book ran through six editions within a few years, and the translation was largely drawn upon by Dr J . S. Hahn of Silesia, in a work published in 1738, On the Healing Virtues of Cold Water, Inwardly and Outwardly applied, as proved by Experience. The other work was that of Dr James Currie (1756-1805) of Liverpool, entitled Medical Reports on the Effects of Water, Cold and Warm, as a remedy in Fevers and other Diseases, published in 1797, and soon after translated into German by Michaelis (1801) and Hegewisch (1807). It was highly popular, and first placed the subject on a scientific basis. Harm's writings had meanwhile created much enthusiasm among his countrymen, societies having been everywhere formed to promote the medicinal and dietetic use of water; and in 1804 Professor Ortel of Ansbach republished them and quickened the popular movement by unqualified commendation of water drinking as a remedy for all diseases. In him the rising Priessnitz found a zealous advocate, and doubtless an instructor also. At Grafenberg, to which the fame of Priessnitz drew people of every rank and many countries, medical men were conspicuous by their numbers, some being attracted by curiosity, others by the desire of knowledge, but the majority by the hope of cure for ailments which had as yet proved incurable. Many records of experiences at Grafenberg were published, all more or less favourable to the claims of Priessnitz, and some enthusiastic in their estimate of his genius and penetration; Captain Claridge introduced hydropathy into England in 1840, his writings and lectures, and later those of Sir W. Erasmus Wilson (1809-1884), James Manby Gully (1808-1883) and Edward Johnson, making numerous converts, and filling the establishments opened soon after at Malvern and elsewhere. In Germany, France and America hydropathic establishments multiplied with great rapidity. Antagonism ran high between the old practice and the new. Unsparing condemnation was heaped by each on the other; and a legal prosecution, leading to a royal commission of inquiry, served but to make Priessnitz and his system stand higher in public estimation. Increasing popularity diminished before long that timidity which had in great measure prevented trial of the new method from being made on the weaker and more serious class of cases, and had caused hydropathists to occupy themselves mainly with a sturdy order of chronic invalids well able to bear a rigorous regimen and the severities of unrestricted crisis. The need of a radical adaptation to the former class was first adequately recognized by John Smedley, a manufacturer of Derbyshire, who, impressed in his own person with the severities as well as the benefits of " the cold water cure," practised among his work- people a milder form of hydropathy, and began about 1852 a new era in its history, founding at Matlock a counterpart of the establishment at Grafenberg. Ernst Brand (1826-1897) of Berlin, Raljen and Theodor von Jiirgensen of Kiel, and Karl Liebermeister (1833-1901) of Basel, between i860 and 1870, employed the cooling bath in abdominal typhus with striking results, and led to its introduc- tion to England by Dr Wilson Fox. In the Franco-German war the cooling bath was largely employed, in conjunction frequently with quinine; and it now holds a recognized position in the treatment of hyperpyrexia. The wet sheet pack has become part of medical practice; the Turkish bath, introduced by David Urquhart (1805-1877) into England on his return from the East, and ardently adopted by Dr Richard Barter (1802- 1870) of Cork, has become a public institution, and, with the " morning tub " and the general practice of water drinking, is the most noteworthy of the many contributions by hydropathy to public health (see Baths, ad fin.). The appliances and arrangements by means of which heat and cold are brought to bear on the economy are — (a) Packings, hot and cold, general and local, sweating and cooling; (b) hot air and steam baths;' (e) general baths, of hot water and cold; (d) sitz, spina!, head and foot baths; (e) bandages (or compresses), wet and dry; also (/) fomentations and poultices, hot and cold, sinapisms, stupes, rubbings and water potations, hot and cold. (a) Packings. — The full pack consists of a wet sheet enveloping the body, with a number of dry blankets packed tightly over it, in- cluding a macintosh covering or not. In an hour or less these are removed and a general bath administered. The pack is a derivative, sedative, sudorific and stimulator of cutaneous excretion. There are numerous modifications of it, notably the cooling pack, where the wrappings are loose and scanty, permitting evaporation, and the application of indefinite duration, the sheet being rewetted as it dries; this is of great value in protracted febrile conditions. There are also local packs, to trunk, limbs or head separately, which are derivative, soothing or stimulating, according to circumstance and detail. (b) Hot air baths, the chief of which is the Turkish (properly, the Roman) bath, consisting of two or more chambers ranging in temperature from 120 to 212 or higher, but mainly used at 150 for curative purposes. Exposure is from twenty minutes up to two hours according to the effect sought, and is followed by a general bath, and occasionally by soaping and shampooing. It is stimulating, deriva- tive, depurative, sudorific and alterative, powerfully promoting tissue change by increase of the natural waste and repair. It determines the blood to the surface, reducing internal congestions, is a potent diaphoretic, and, through the extremes of heat and cold, is an effective nervous and vascular stimulant and tonic. Morbid growths and secretions, as also the uraemic, gouty and rheumatic diathesis, are beneficially influenced by it. The full pack and Turkish bath have between them usurped the place and bettered the function of the once familiar hot bath. The Russian or steam bath and the lamp bath are primitive and inferior varieties of the modern Turkish bath, the atmosphere of which cannot be too dry and pure. (c) General baths comprise the rain (or needle), spray (or rose), shower, shallow, plunge, douche, wave and common morning sponge baths, with the dripping sheet, and hot and cold spongings, and are combinations, as a rule, of hot and cold water. They are stimulating, tonic, derivative and detergent. (d) Local baths comprise the sitz (or sitting), douche (or spouting), spinal, foot and head baths, of hot or cold water, singly or in com- bination, successive or alternate. The sitz, head and foot baths are used " flowing " on occasion. The application of cold by " Leiter's tubes " is effective for reducing inflammation (e.g. in meningitis and in sunstroke); in these a network of metal or indiarubber tubing is fitted to the part affected, and cold water kept con- tinuously flowing through them. Rapid alternations of hot and cold water have a powerful effect in vascular stasis and lethargy of the nervous system and absorbents, yielding valuable results in local congestions and chronic inflammations. (e) Bandages (or compresses) are of two kinds, — cooling, of wet material left exposed for evaporation, used in local inflammations and fevers; and heating, of the same, covered with waterproof material, used in congestion, external or internal, for short or long periods. Poultices, warm, of bread, linseed, bran, &c., changed but twice in twenty-four hours, are identical in action with the heating bandage, and superior only in the greater warmth and consequent vital activity their closer application to the skin ensures. (f) Fomentations and poultices, hot or cold, sinapisms, stupes, rubefacients, irritants, frictions, kneadings, calisthenics, gymnastics, electricity, &c, are adjuncts largely employed. Bibliography. — Among the numerous earlier works on hydro- pathy, the following are worth mention: Balbirnie, Water Cure in Consumption (1847), Hydropathic Aphorisms (1856) and A Plea for the Turkish Bath (1862) ; Beni-Barde, Traite d' hydrotherapy (1874); Claridge, Cold Water Cure, or Hydropathy (1841), Facts and Evidence in Support of Hydropathy (1843) and Cold Water, Tepid Water and Friction Cure (1849); Dunlop, Philosophy of the Bath (1873); Floyer, Psychrolousia, or the History of Cold-Bathing, &c. (1702) ; J. S. Hahn (Schweidnitz), Observations on the Healing Virtues of Cold Water (1738); Hunter, Hydropathy for Home t/se .(1879); E. W. Lane, Hydropathy, or the Natural System of Medical Treatment (1857); R. J. Lane, Life at the Water Cure (1851) ; Shew, Hydropathic Family Physician (1857) ; Smedley, Practical Hydropathy (1879) ; Smethurst, Hydrotherapia, or the Water Cure (1843); Wainwright, Inquiry into the Nature and Use of Baths (1737); Weiss, Handbook of Hydro- pathy (1844); Wilson Principles and Practice of the Cold Water Cure (1854.) and The Water Cure (1859). A useful recent work dealing comprehensively with the subject is Richard Metcalfe's Rise and Progress of Hydropathy (1906). HYDROPHOBIA 167 HYDROPHOBIA (Gr. v8up, water, and 4>6f5os, fear; so called from the symptom of dread of water), or Rabies (Lat.for" mad- ness "), an acute disease, occurring chiefly in certain of the lower animals, particularly the canine species, and liable to be com- municated by them to other animals and to man. In Dogs, &"e. — The occurrence of rabies in the fox, wolf, hyaena, jackal, raccoon, badger and skunk has been asserted; but there is every probability that it is originally a disease of the dog. It is communicated by inoculation to nearly all, if not all, warm- blooded creatures. The transmission from one animal to another only certainly takes place through inoculation with viruliferous matters. The malady is generally characterized at a certain stage by an irrepressible desire in the animal to act offensively with its natural weapons — dogs and other carnivora attacking with their teeth, herbivora with their hoofs or horns, and birds with their beaks, when excited ever so slightly. In the absence of excitement the malady may run its course without any fit of fury or madness. Symptoms.— The disease has been divided into three stages or periods, and has also been described as appearing in at least two ,'orras, according to the peculiarities of the symptoms. But, as a rule, one period of the disease does not pass suddenly into another, the transition being almost imperceptible; and the forms do not differ essentially from each other, but appear merely to constitute varieties of the same disease, due to the natural disposition of the animal, or other modifying circumstances. These forms have been designated true or furious rabies (Ft. rage vrai; Ger. rasende Wuth) and dumb rabies (Fr. rage mue\ Ger. stille Wuth). The malady does not commence with fury and madness, but in a strange and anomalous change in the habits of the dog : it becomes dull, gloomy, and taciturn, and seeks to isolate itself in out-of-the-way places, retiring beneath chairs and to odd corners. But in its retire- ment it cannot rest: it is uneasy and fidgety, and no sooner has it lain down than suddenly it jumps up in an agitated manner, walks backwards and forwards several times, again lies down and assumes a sleeping attitude, but has only maintained it for a few minutes when it is once more moving about. Again it retires to its corner, to the farthest recess it can find, and huddles itself up into a heap, with its head concealed beneath its chest and fore-paws. This state of continual agitation and inquietude is in striking contrast with its ordinary habits, and should therefore receive attention. Not unfrequently there are a few moments when the creature appears more lively than usual, and displays an extraordinary amount of affection. Sometimes there is a disposition to gather up straw, thread, bits of wood, &c, which are industriously carried away; a tendeflcy to lick anything cold, as iron, stones, &c, is also observed in many instances; and there is also a desire evinced to lick other animals. Sexual excitement is also frequently an early symptom. At this period no disposition to bite is observed ; the animal is docile with its master and obeys his voice, though not so readily as before, nor with the same pleased countenance. There is something strange in the expression of its face, and the voice of its owner is scarcely able to make it change from a sudden gloominess to its usual animated aspect. These symptoms gradually become more marked; the restlessness and agitation increase. If on straw the dog scatters and pulls it about with its paws, and if in a room it scratches and tumbles the cushions or rugs on which it usually lies. It is incessantly on the move, rambling about, scratching the ground, sniffing in corners and at the doors, as if on the scent or seeking for something. It indulges in strange movements, as if affected by some mental in- fluences or a prey to hallucinations. When not excited by any external influence it will remain for a brief period perfectly still and attentive, as if watching something, or following the movements of some creature on the wall; then it will suddenly dart forward and snap at the vacant air, as if pursuing an annoying object, or en- deavouring to seize a fly. At another time it throws itself, yelling and furious, against the wall, as if it heard threatening voices on the other side, or was bent on attac'king an enemy. Nevertheless, the animal is still docile and submissive, for its master's voice will bring it out of its frenzy. But the saliva is already virulent, and the ex- cessive affection which it evinces at intervals, by licking the hands or face of those it loves, renders the danger very great should there be a wound or abrasion. Until a late period in the disease the master's voice has a powerful influence over the animal. When it has escaped from all control and wanders erratically abroad, ferocious and restless, and haunted by horrid phantoms, the familiar voice vet exerts its influence, and it is rare indeed that it attacks its master. There is no dread of water in the rabid dog; the animal is generally thirsty, and if water be offered will lap it with avidity, and swallow it at the commencement of the disease. And when, at a later period, the constriction about the throat — symptomatic of the disease — renders swallowing difficult, the dog will none the less endeavour to drink, and the lappings are as frequent and prolonged when deglu- tition becomes impossible. So little dread has the rabid dog of water that it will ford streams and swim rivers ; and when in the ferocious stage it will even do this in order to attack other creatures on the opposite side. At the commencement of the disease the dog does not usually refuse to eat, and some animals are voracious to an unusual degree. But in a short time it becomes fastidious, only eating what it usually has a special predilection for. Soon, however, this gives place to a most characteristic symptom — either the taste becomes extremely depraved or the dog has a fatal and imperious desire to bite and ingest everything. The litter of its kennel, wool from cushions, carpets, stockings, slippers, wood, grass, earth, stones, glass, horse- dung, even its own faeces and urine, or whatever else may come in its way, are devoured. On examination of the body of a dog which has died of rabies it is so common to find in the stomach a quantity of dissimilar and strange matters on which the teeth have been exercised that, if there was nothing known of the animal's history, there would be strong evidence. of its having been affected with the disease. When a dog, then, is observed to gnaw and eat suchlike matters, though it exhibits no tendency to bite, it should be suspected. The mad dog does not usually foam at the mouth to any great extent at first. The mucus of the mouth is not much increased in quantity, but it soon becomes thicker, viscid, and glutinous, and adheres to the angles of the mouth, fauces and teeth. It is at this period that the thirst is most ardent, and the dog sometimes furiously attempts to detach the saliva with its paws; and if after a while it loses its balance in these attempts and tumbles over, there can no longer be any doubt as to the nature of the malady. There is another symptom connected with the mouth in that form of the disease named " dumb madness " which has frequently proved deceptive. The lower jaw drops in consequence of paralysis of its muscles, and the mouth remains open. The interior is dry from the air passing continually over it, and assumes a deep red tint, somewhat masked by patches of dust or earth, which more especially adhere to the upper surface of the tongue and to the lips. The strange alteration produced in the dog's physiognomy by its constantly open mouth and the dark colour of the interior is rendered still more characteristic by the dull, sad, or dead expression of the animal's eyes. In this condition the creature is not very dangerous, because generally it could not bite if it tried — -indeed there does not appear to be much desire to bite in dumb madness; but the saliva is none the less virulent, and acci- dental inoculations with it, through imprudent handling, will prove as fatal as in the furious form. The mouth should not be touched, — numerous deaths having occurred through people thinking the dog had some foreign substance lodged in its throat, and thrusting their fingers down to remove it. The sensation of tightness which seems to exist at the throat causes the dog to act as if a bone were fixed between its teeth or towards the back of its mouth, and to employ its fore-paws as if to dislodge it. This is a very deceptive symptom, and may prove equally dangerous if caution be not ob- served. Vomiting of blood or a chocolate-coloured fluid is witnessed in some cases, and has been supposed to be due to the foreign sub- stances in the stomach, which abrade the lining membrane; this, however, is not correct, as it has been observed in man. The voice of the rabid dog is very peculiar, and so characteristic that to those acquainted with it nothing more is needed to prove the presence of the disease. Those who have heard it once or twice never forget its signification. Owing to the alterations taking place in the larynx the voice becomes hoarse, cracked and stridulous, like that of a child affected with croup — the " voixducoq," as the French ha e it. A preliminary bark is made in a somewhat elevated tone and with open mouth; this is immediately succeeded by five, six or eight decreasing howls, emitted when the animal is sitting or standing, and always with the nose elevated, which seem to come from the depths of the throat, the jaws not coming together and closing the mouth during such emission, as in the healthy bark. This alteration in the voice is frequently the first observable indica- tion of the malady, and should at once attract attention. In dumb madness the voice is frequently lost from the very commencement — hence the designation. The sensibility of the mad dog appears to be considerably diminished, and the animal appears to have lost the faculty of ex- pressing the sensations it experiences: it is mute under the infliction of pain, though there can be no doubt that it still has peripheral sensation to some extent. Burning, beating and wounding produce much less effect than in health, and the animal will even mutilate itself with its teeth. Suspicion, therefore, should always strongly attach to a dog which docs not manifest a certain susceptibility to painful impressions and receives punishment without any cry or complaint. There is also reason for apprehension when a dog bites itself persistently in any part of its body. A rabid dog is usually stirred to fury at the sight of one of its own species: this test has been resorted to by Henrie Marie Bouley (1814-1885) to dissipate doubts as to the existence of the disease when the diagnosis is other- wise uncertain. As soon as the suspected animal, if it is really rabid, finds itself in the presence of another of its species it at once assumes the aggressive, and, if allowed, will bite furiously. All rabid animals indeed become excited, exasperated, and furious at the sight of a dog, and attack it with their natural weapons, even the timid sheep when rabid butts furiously at the enemy before which in health it would have fled in terror. This inversion of sentiment is sometimes i68 HYDROPHOBIA valuable in diagnosing the malady; it is so common that it may be said to be present in every case of rabies. When, therefore, a dog, contrary to its habits and natural inclination, becomes suddenly aggressive to other dogs, it is time to take precautions. In the large majority of instances the dog is inoffensive in the early period of the disease to those to whom it is familiar. It then flies from its home and either dies, is killed as '' mad," or returns in a miserable plight, and in an advanced stage of the malady, when the desire to bite is irresistible. It is in the early stage that sequestra- tion and suppressive measures are most valuable. The dogs which propagate the disease are usually those that have escaped from their owners. After two or three days, frequently in about twelve hours, more serious and alarming symptoms appear, ferocious instincts are developed, and the desire to do injury is irrepressible. The animal has an indefinable expression of sombre melancholy and cruelty. The eyes have their pupils dilated, and emit flashes of light when they are not dull and heavy; they always appear so fierce as to produce terror in the beholder; they are red, and their sensibility to light is increased; and wrinkles, which sometimes appear on the forehead, add to the repulsive aspect of the animal. If caged it flies at the spectator, emitting its characteristic howl or bark, and seizing the iron bars with its teeth, and if a stick be thrust before it this is grasped and gnawed. This fury is soon succeeded by lassitude, when the animal remains insensible to every excitement. Then all at once it rouses up again, and another paroxysm of fury commences. The first paroxysm is usually the most intense, and the fits vary in duration from some hours to a day, and even longer; they are ordinarily briefer in trained and pet dogs than in those which are less domesticated, but in all the remission is so complete after the first paroxysm that the animals appear to be almost well, if not in perfect health. During the paroxysms respiration is hurried and laboured, but tranquil during the remissions. There is an increase of temperature, and the pulse is quick and hard. When the animal is kept in a dark place and not excited, the fits of fury are not observed. Sometimes it is agitated and restless in the manner already described. It never becomes really furious or aggressive unless excited by external objects — the most potent of these, as has been said, being another dog, which, however, if it be admitted to its cage, it may not at once attack. The attacked animal rarely retaliates, but usually responds to the bites by acute yells, which contrast strangely with the silent anger of the aggressor, and tries to hide its head with its paws or beneath the straw. These repeated paroxysms hurry the course of the disease. The secretion and flowing of a large quantity of saliva from the mouth are usually only witnessed in cases in which swallowing has become impossible, the mouth being generally dry. At times the tongue, nose and whole head appear swollen. Other dogs frequently shun one which is rabid, as if aware of their danger. The rabid dog, if lodged in a room or kept in a house, is continually endeavouring to escape ; and when it makes its escape it goes freely forward, as if impelled by some irresistible force. It travels con- siderable distances in a short time, perhaps attacking every living creature it meets — preferring dogs, however, to other animals, and these to mankind; cats, sheep, cattle and horses are particularly liable to be injured. It attacks in silence, and never utters a snarl or a cry of anger ; should it chance to be hurt in return it emits no cry or howl of pain. The degree of ferocity appears to be related to natural disposition and training. Some dogs, for instance, will only snap or give a slight bite in passing, while others will bite furiously, tearing the objects presented to them, or which they meet in their way, and sometimes with such violence as to injure their mouth and break their teeth, or even their jaws. If chained, they will in some cases gnaw the chain until their teeth are worn away and the bones laid bare. The rabid dog does not continue its progress very long. Exhausted by fatigue and the paroxysms of madness excited in it by the objects it meets, as well as by hunger, thirst, and also, no doubt, by the malady, its limbs soon become feeble; the rate of travelling is lessened and the walk is unsteady, while its drooping tail, head inclined towards the ground, open mouth, and protruded tongue (of a. leaden colour or covered with dust) give the distressed creature a very striking and characteristic physiognomy. In this condition, however, it is much less to be dreaded than in its early fits of fury, since it is no longer capable or desirous of altering its course or going out of its way to attack an animal or a man not immediately in the path. It is very probable that its fast-failing vision, deadened scent, and generally diminished perception prevent its being so readily impressed or excited by surrounding objects as it previously was. To each paroxysm, which is always of short duration, there succeeds a degree pf ex- haustion as great as^ the fits have been violent and oft repeated. This compels the animal to stop; then it shelters itself in obscure places — frequently in ditches by the roadside — and lies there in a somnolescent state for perhaps hours. There is great danger, never- theless, in disturbing the dog at this period ; for when roused from its torpor it has sometimes sufficient strength to inflict a bite. This period, which may be termed the second stage, is as variable in its duration as the first, but it rarely exceeds three or four days. The above-described phenomena gradually merge into those of the third or last period, when symptoms of paralysis appear, which arc speedily followed by death. During the remission in the paroxysms these paralytic symptoms are more particularly manifested in the hind limbs, which appear as if unable to support the animal's weight, and cause it to stagger about; or the lower jaw becomes more or less drooping, leaving the parched mouth partially open. Emaciation rapidly sets in, and the paroxysms diminish in intensity, while the remissions become less marked. The physiognomy assumes a still more sinister and repulsive aspect; the hair is dull and erect; the flanks are retracted; the eyes lose their lustre and are buried in the orbits, the pupil being dilated, and the cornea dull and semi- opaque; very often, even at an early period, the eyes squint, and this adds still more to the terrifying appearance of the poor dog. The voice, if at all heard, is husky, the breathing laborious, and the pulse hurried and irregular. Gradually the paralysis increases, and the posterior extremities are dragged as if the animal's back were broken, until at length it becomes general ; it is then the prelude to death. Or the dog remains lying in a state of stupor, and can only raise itself with difficulty on the fore-limbs when greatly excited. In this condition it may yet endeavour to bite at objects within its reach. At times convulsions of a tetanic character appear in certain muscles; at other times these are general. A comatose condition ensues, and the rabid dog, if permitted to die naturally, perishes, in the great majority of cases, from paralysis and asphyxia. In dumb madness there is paralysis of the lower jaw, which im- parts a curious and very characteristic physiognomy to the dog; the voice is also lost, and the animal can neither eat nor drink. In this condition the creature remains with its jaw pendent and the mouth consequently wide open, showing the flaccid or swollen tongue covered with brownish matter, and a stringy gelatinous- looking saliva lying between it and the lower lip and coating the fauces, which sometimes appear to be inflamed. Though the animal is unable to swallow fluids, the desire to drink is neverthe- less intense; for the creature will thrust its face into the vessel of water in futile attempts to obtain relief, even until the approach of death. Water may be'poured down its throat without inducing a paroxysm. The general physiognomy and demeanour of the poor creature inspire the beholder with pity rather than fear. The symptoms due to cerebral excitement are less marked than in the furious form of the disease; the agitation is not so considerable, and the restlessness, tendency to run away, and desire to bite are nearly absent; generally the animal is quite passive. Not unfre- quently one or both eyes squint, and it is only when very much excited that the dog may contrive to close its mouth. Sometimes there is swelling about the pharynx and the neck ; when the tongue shares in this complication it hangs out of the mouth. In certain cases there is a catarrhal condition of the membrane lining the nasal cavities, larynx, and bronchi; sometimes the animal testifies to the existence of abdominal pain, and the faeces are then soft or fluid. The other symptoms — such as the rapid exhaustion and emaciation, paralysis of the posterior limbs towards the termination of the disease, as well as the rapidity with which it runs its course — are the same as in the furious form. The simultaneous occurrence of furious and dumb madness has frequently been observed in packs of fox-hounds. Dumb madness differs, then, from the furious type in the paralysis of the lower jaw, which hinders the dog from biting, save in very exceptional circumstances; the ferocious instincts are also in abeyance; and there is no tendency to aggression. It has been calculated that from 15 to 20% of rabid dogs have this particular form of the disease. Puppies and young dogs chiefly have furious rabies. These are the symptoms of rabies in the dog; but it is not likely, nor is it necessary, that they will all be present in every case. In other species the symptoms differ more or less from those mani- fested by the dog, but they are generally marked by a change in the manner and habits of the creatures affected, with strong indica- tions of nervous disturbance, in the majority of species amounting to ferociousness and a desire to injure, timid creatures becoming bold and aggressive. In Human Beings. — The disease of hydrophobia has been known from early times, and is alluded to in the works of Aristotle, Xenophon, Plutarch, Virgil, Horace, Ovid and many others, as well as in those of the early writers on medicine. Celsus gives detailed instructions respecting the treatment of men who have been bitten by rabid dogs, and dwells on the dangers attending such wounds. After recommending suction of the bitten pur.t by means of a dry cupping glass, and thereafter the application of the actual cautery or pf strong caustics, and the employment of baths and various internal remedies, he says: " Idque cum ita per triduum factum est, tutus esse homo a periculo videtur. Solet autem ex eo vulnere, ubi parum occursum est, aquae timor nasci, {iS/xxpojSiav Graeci appellant. Miserrimum genus morbi; in quo simul aeger et siti et aquae metu cruciatur; quo oppressis in angusto spes est." Subsequently Galen de- scribed minutely the phenomena of hydrophobia, and recom- mended the excision of the wounded part as a protection against HYDROPHOBIA i6g the disease. Throughout many succeeding centuries little or nothing was added to the facts which the early physicians had made known upon the subject. The malady was regarded with universal horror and dread, and the unfortunate sufferers were generally abandoned by all around them and left to their terrible fate. In later times the investigations of Boerhaave, Gerard van Swieten (1700-1772), John Hunter, Francois Magendie (1783-1855), Gilbert Breschet (1784-1845), Virchow, Albert Reder, as also of William Youatt (1776-1847), George Fleming, Meynell, Karl Hertwig (1798-1881), and others, have fur- nished important information; but all these were put into the shade by the researches of Pasteur. The disease is communicated by the secretions of the mouth of the affected animal entering a wound or abrasion of the human skin or mucous membrane. In the great majority of cases (qo%) this is due to the bite of a rabid dog, but bites of rabid cats, wolves, foxes, jackals, &c. are occasionally the means of conveying the disease. Numerous popular fallacies still prevail on the subject of hydrophobia. Thus it is supposed that the bite of an angry dog may produce the disease, and all the more if the animal should subsequently develop symptoms of rabies. The ground for this erroneous notion is the fact, which is unquestion- able, that animals in whom rabies is in the stage of incubation, during which there are few if any symptoms, may by their bites convey the disease, though fortunately during this early stage they are little disposed to bite. The bite of a non-rabid animal, however enraged, cannot give rise to hydrophobia. The period of incubation of the disease, or that time which elapses between the introduction of the virus and the develop- ment of the symptoms, appears to vary in a remarkable degree, being in some cases as short as a fortnight, and in others as long as several months or even years. On an average it seems to be from about six weeks to three months, but it mainly depends on the part bitten; bites on the head are the most dangerous. The incubation period is also said to be shorter in children. The rare instances of the appearance of hydrophobia many years after the introduction of the poison are always more or less open to question as to subsequent inoculation. When the disease is about to declare itself it not unfrequently happens that the wound, which had quickly and entirely healed after the bite, begins to exhibit evidence of irritation or in- flammatory action, or at least to be the seat of morbid sensations such as numbness, tingling or itching. The symptoms character- izing the premonitory stage are great mental depression and disquietude, together with restlessness and a kind of indefinite fear. There is an unusual tendency to talk, and the articulation is abrupt and rapid. Although in some instances the patients will not acknowledge that they have been previously bitten, and deny it with great obstinacy, yet generally they are well aware of the nature of their malady, and speak despairingly of its consequences. There is in this early stage a certain amount of constitutional disturbance showing itself by feverishness, loss of appetite, sleeplessness, headache, great nervous excitability, respiration of a peculiar sighing or sobbing character, and even occasionally a noticeable aversion to liquids. These symptoms — constituting what is termed the melancholic stage — continue in general for one or two days, when they are succeeded by the stage of excitement in which all the characteristic phenomena of the malady are fully developed. Sometimes the disease first shows itself in this stage, without antecedent symptoms. The agitation of the sufferer now becomes greatly increased, and the countenance exhibits anxiety and terror. There is noticed a marked embarrassment of the breathing, but the most striking and terrible features of this stage are the effects pro- duced by attempts to swallow fluids. The patient suffers from thirst and desires eagerly to drink, but on making the effort is seized with a most violent suffocative paroxysm produced by spasm of the muscles of swallowing and breathing, which con- tinues for several seconds, and is succeeded by a feeling of intense alarm and distress. With great caution and determina- tion the attempt is renewed, but only to be followed with a repetition of the seizure, until the unhappy sufferer ceases from sheer dread to try to quench the thirst which torments him. Indeed the very thought of doing so suffices to bring on a choking paroxysm, as does also the sound of the running of water. The patient is extremely sensitive to any kind of external impression; a bright light, a loud noise, a breath of cool air, contact with any one, are all apt to bring on one of these seizures. But besides these suffocative attacks there also occur general con- vulsions affecting the whole muscular system of the body, and occasionally a condition of tetanic spasm. These various paroxysms increase in frequency and severity with the advance of the disease, but alternate with intervals of comparative quiet, in which, however, there is intense anxiety and more or less constant difficulty of breathing, accompanied with a peculiar sonorous expiration, which has suggested the notion that the patient barks like a dog. In many instances there is great mental disturbance, with fits of maniacal excitement, in which he strikes at every one about him, and accuses them of being the cause of his sufferings — these attacks being succeeded by calm intervals in which he expresses great regret for his violent behaviour. During all this stage of the disease the patient is tormented with a viscid secretion accumulating in his mouth, which from dread of swallowing he is constantly spitting about him. There may also be noticed snapping movements of the jaws as if he were attempting to bite, but these are in reality a manifestation of the spasmodic action which affects the muscles generally. There is no great amount of fever, but there is constipation, diminished flow of urine, and often sexual excitement. After two or three days of suffering of the most terrible description the patient succumbs, death taking place either in a paroxysm of choking, or on the other hand in a tranquil manner from exhaustion, all the symptoms having abated, and the power of swallowing returned before the end. The duration of the disease from the first declaration of the symptoms is generally from three to five days. Apart from the inoculation method (see below), the treatment of most avail is that which is directed towards preventing the absorption of the poison into the system. This may be accom- plished by excision of the part involved in the bite of the rabid animal, or, where this from its locality is impracticable, in the application to the wound of some chemical agent which will destroy the activity of the virus, such as potassa fusa, lunar caustic (nitrate of silver), or the actual cautery in the form of a red-hot wire. The part should be thoroughly acted on by these agents, no matter what amount of temporary suffering this may occasion. Such applications should be resorted to immediately after the bite has been inflicted, or as soon thereafter as possible. Further, even though many hours or days should elapse, these local remedies should still be applied ; for if, as appears probable, some at least of the virus remains for long at the injured part, the removal or effectual destruction of this may prevent the dread consequences of its absorption. Every effort should be made to tranquillize and reassure the patient. Two special points of interest have arisen in recent years in connexion with this disease. One is the Pasteur treatment by inoculation with rabic virus (see also Parasitic Diseases), and the other was the attempt of the government to exterminate rabies in the British Isles by muzzling dogs. The Pasteur treatment was first applied to human beings in 1885 after prolonged investigation and experimental trial on animals. It is based on the fact that a virus, capable of giving rabies by inoculation, can be extracted t rea t m eat. from the tissues of a rabid animal and then intensified or attenuated at pleasure. It appears that the strength of the rabic virus, as determined by inoculation, is constant in the same species of animal, but is modified by passing through another species. For instance, the natural virus of dogs is always of the same strength, but when inoculated into monkeys it becomes weakened, and the process of attenuation can be carried on by passing the virus through a succession of monkeys, until it loses the power of causing death. If this weakened virus is then passed back through guinea-pigs, dogs or rabbits, it regains 170 HYDROPHOBIA its former strength. Again, if it be passed through a succession of dogs it becomes intensified up to a maximum of strength which is called the virus fixe. Pasteur further discovered that the strength can be modified by temperature and by keeping the dried tissues of a rabid animal containing the virus. Thus, if the spinal cord of a rabid dog be preserved in a dry state, the virus loses strength day by day. The system of treatment consists in making an emulsion of the cord and graduating the strength of the dose by using a succession of cords, which have been kept for a progressively diminishing length of time. Those which have been kept for fourteen days are used as a starting- point, yielding virus of a minimum strength. They are followed by preparations of diminishing age and increasing strength, day by day, up to the maximum, which is three days old. These are successively injected into the circulatory system. The principle is the artificial acquisition by the patient of resistance to the rabic virus, which is presumed to be already in the system but has not yet become active, by accustoming him gradually to its toxic effect, beginning with a weak form and progressively increasing the dose. It is not exactly treatment of the disease, because it is useless or nearly so when the disease has commenced, nor is it exactly preventive, for the patient has already been bitten. It must be regarded as a kind of anticipatory cure. The cords are cut into sections and preserved dry in sterilized flasks plugged with cotton-wool. Another method of preparing the inoculatory virus, which has been devised by Guido Tizzoni and Eugenio Centanni, consists in subjecting the virus fixe to peptic digestion by diluted gastric juice for varying periods of time. The first patient was treated by Pasteur's system in July 1885. He was successively inoculated with emulsions made from cords that had been kept fourteen and ten days, then eleven and eight days, then eight, seven, six days, and so on. Two forms of treatment are now used — (1) the " simple," in which the course from weak to strong virus is extended over nine days; (2) the " intensive," in which the maximum is reached in seven days. The latter is used in cases of very bad bites and those of some standing, in which it is desirable to lose no time. Two days are compressed into one at the commencement by making injections morning and evening instead of once a day, so that the fifth-day cord is reached in four days instead of six, as in the " simple " treatment. When the maximum — the third-day cord — is reached the injections are continued with fifth-, fourth-, and third-day cords. The whole course is fifteen days in the simple treatment and twenty-one in the intensive. The doses injected range from 1 to 3 cubic centimetres. Injections are made alternately into the right and left flanks. The following table shows the number treated from 1886 to 1905, with the mortality. Year. Patients Treated. Deaths. Mortality per cent. 1886 2671 25 •94 1887 1770 H •79 1888 1622 9 •55 1889 1830 7 •38 1890 1540 5 •32 1891 1559 4 •25 1892 1790 4 •22 1893 1648 6 •36 1894 1387 7 •50 1895 1520 5 •33 1896 1308 4 •30 1897 1521 6 •39 1898 H65 3 •20 1899 1614 4 •25 1900 1419 10 •70 1901 1318 5 •37 1902 1 105 2 •18 1903 630 4 •65 1904 757 5 •66 1905 727 4 •54 These figures do not include cases which develop hydrophobia during treatment or within fifteen days after treatment is com- pleted, for it is held that persons who die within that period have their nervous centres invaded by virus before the cure has time to act. The true mortality should therefore be considerably higher. For instance, in 1898 three deaths came within this category, which just doubles the mortality; and in 1899 the additional deaths were six, bringing the mortality up to two-and- a-half times that indicated in the table. When, however, the additional deaths are included the results remain sufficiently striking, if two assumptions are granted — (1) that all the persons treated have been bitten by rabid animals; (2) that a large proportion of persons so bitten usually have hydrophobia. Unfortunately, both these assumptions lack proof, and therefore the evidence of the efficacy of the treatment cannot be said to satisfy a strictly scientific standard. With regard to the first point , the patients are divided into three categories— -(1) those bitten by an animal the rabidity of which is proved by the development of rabies in other animals bitten by it or inoculated from its spinal cord; (2) those bitten by an animal pronounced rabid on a veterinary examination; (3) those bitten by an animal suspected of being rabid . The number of patients in each category in 1898 was (1) 141, (2) 855, (3) 469; and in 1899 it was (1) 152, (2) 1099, (3) 363. As might be expected, the vast majority came under the second and third heads, in which the evidence of rabidity is doubtful or altogether lacking. With regard to the second point, the proportion of persons bitten by rabid animals who ordinarily develop hydrophobia has only been " estimated " from very inadequate data. Otto Bollinger from a series of collected statistics states that before the introduction of the Pasteur treatment, of patients bitten by dogs undoubtedly rabid 47% died, the rate being 33% in those whose wounds had been cauterized and 83% when there had been no local treatment. If the number of rabid dogs be compared with the deaths from hydrophobia in any year or series of years, it can hardly be very high. For instance, in 1895, 668 dogs, besides other animals, were killed and certified to be rabid in England, and the deaths from hydrophobia were twenty. Of course this proves nothing, as the number of persons bitten is not known, but the difference between the amount of rabies and of hydrophobia is suggestively great in view of the marked propensity of rabid dogs to bite, nor is it accounted for by the fact that some of the persons bitten were treated at the Institut Pasteur. A comparison of the annual mortality from hydrophobia in France before and after the intro- duction of the treatment would afford decisive evidence as to its efficacy; but unfortunately no such comparison can be made for lack of vital statistics in that country. The experience of the Paris hospitals, however, points to a decided diminution of mortality. On the whole it must be said, in the absence of further data, that the Pasteur treatment certainly diminishes the danger of hydrophobia from the bites of rabid animals. More recently treatment with an anti-rabic serum has been suggested (see Parasitic Diseases). Victor Babes and Lepp and later Guido Tizzoni and Eugenio Centanni have worked out a method of serum treatment curative and protective. In this method not the rabic poison itself, as in the Pasteur treatment, but the protective substance formed is injected into the tissues. The serum of a vaccinated animal is capable of neutralizing the power of the virus of rabies not only when mixed with the virus before injection but even when injected simultaneously or within twenty-four hours after the introduction of the virus. These authors showed that the serum of a rabbit protects a rabbit better than does the serum of a dog, and vice versa. At the end of twenty days' injections they found they could obtain such*a large quantity of anti-rabic substance in the serum of an animal, that even 1 part of serum to 25,000 of the body weight would protect an animal. This process differs from that of Pasteur in so far as that in place of promoting the formation of the antidote within the body of the patient, by a process of vaccina- tion with progressively stronger and stronger virus, this part of the process is carried on in an animal, Babes using the dog and Centanni the sheep, the blood serum of which is injected. This method of vaccination is useful as a protective to those in charge of kennels. HYDROSPHERE— HYDROZOA 171 The attempt to stamp out rabies in Great Britain was an experiment undertaken by the government in the public interest. The principal means adopted were the muzzling of Muzzling ^ g S j n i n f ec ted. areas, and prolonged quarantine for England, imported animals. The efficacy of dog-muzzling in checking the spread of rabies and diminishing its prevalence has been repeatedly proved in various countries. Liable as other animals may be to the disease, in England at least the dog is pre-eminently the vehicle of contagion and the great source of danger to human beings. There is a difference of opinion on the way in which muzzling acts, though there can be none as to the effect it produces in reducing rabies. Probably it acts rather by securing the destruction of ownerless and stray — which generally includes rabid — dogs than by preventing biting; for though it may prevent snapping, even the wire-cage muzzle does not prevent furious dogs from biting, and it is healthy, not rabid, dogs that wear the muzzle. It has therefore been suggested that a collar would have the same effect, if all collarless dogs were seized; but the evidence goes to show that it has not, perhaps because rabid dogs are more likely to stray from home with their collars, which are constantly worn, than with muzzles which are not, and so escape seizure. Moreover, it is much easier for the police to see whether a dog is wearing a muzzle or not than it is to make sure about the collar. However this may be, the muzzle has proved more efficacious, but it was not applied systematically in England until a late date. Sometimes the regulations were in the hands of the government, and sometimes they were left to local authorities; in either case they were allowed to lapse as soon as rabies had died down. In April 1897 the Board of Agriculture entered on a systematic attempt to exterminate rabies by the means indicated. The plan was to enforce muzzling over large areas in which the disease existed, and to maintain it for six months after the occurrence of the last case. In spite of much opposition and criticism, this was resolutely carried out under Mr Walter Long, the responsible minister, and met with great success. By the spring of 1899 — that is, in two years — the disease had disappeared in Great Britain, except for one area in Wales; and, with this exception, muzzling was everywhere relaxed in October 1899. It was taken off in Wales also in the following May, no case having occurred since November 1899. Rabies was then pronounced extinct. During the summer of 1900, however, it reappeared in Wales, and several counties were again placed under the order. The year 1901 was the third in succession in which no death from hydro- phobia was registered in the United Kingdom. In the ten years preceding 1899, 104 deaths were registered, the death-rate reaching 30 in 1889 and averaging 29 annually. In 1902 two deaths from hydrophobia were registered. From that date to June 1909 (the latest available for the purpose of this article) no death from hydrophobia was notified in the United Kingdom. See Annates de llnstitut Pasteur, from 1886; Journal of the Board of Agriculture, 1899; Makins, " Hydrophobia," in Treves's System of Surgery; Woodhead, " Rabies," in Allbutt's System of Medicine. HYDROSPHERE (Gr. v5cop, water, and acupa, sphere), in physical geography, a name given to the whole mass of the water of the oceans, which fills the depressions in the earth's crust, and covers nearly three-quarters of its surface. The name is used in distinction from the atmosphere, the earth's envelope of air, the lithosphere (Gr. \Wos, rock) or solid crust of the earth, and the centrosphere or interior mass within the crust. To these " spheres " some writers add, by figurative usage, the terms "biosphere,!' or life-sphere, to cover all living things, both animals and plants, and " psychosphere," or mind-sphere, covering all the products of human intelligence. HYDROSTATICS (Gr. vdup, water, and the root ora-, to cause to stand), the branch of hydromechanics which discusses the equilibrium of fluids (see Hydromechanics). HYDROXYLAMINE, NH 2 OH, or hydroxy-ammonia, a com- pound prepared in 1865 by W. C. Lossen by the reduction of ethyl nitrate with tin and hydrochloric acid. In 1870 E. Ludwig And T. H. Hein (Chem. Centralblatt, 1870, 1, p. 340) obtained it by passing nitric oxide through a series of bottles containing tin and hydrochloric acid, to which a small quantity of platinum tetrachloride has been added; the acid liquid is poured ofl when the operation is completed, and sulphuretted hydrogen is passed in; the tin sulphide is filtered off and the filtrate evapor- ated. The residue is extracted by absolute alcohol, which dis- solves the hydroxylamine hydrochloride and a little ammonium chloride; this last substance is removed as ammonium platino- chloride, and the residual hydroxylamine hydrochloride is recrystallized. E. Divers obtains it by mixing cold saturated solutions containing one molecular proportion of sodium nitrate, and two molecular proportions of acid sodium sulphite, and then adding a saturated solution of potassium chloride to the mixture. After standing for twenty-four hours, hydroxylamine potassium disulphonate crystallizes out. This is boiled for some hours with water and the solution cooled, when potassium sulphate separates first, and then hydroxylamine sulphate. E. Tafel (Zeit. anorg. Chem., 1902, 31, p. 289) patented an electro- lytic process, wherein 50% sulphuric acid is treated in a divided cell provided with a cathode of amalgamated lead, 50% nitric acid being gradually run into the cathode compartment. Pure anhydrous hydroxylamine has been obtained by C. A. Lobry de Bruyn from the hydrochloride, by dissolving it in absolute methyl alcohol and then adding sodium methylate. The pre- cipitated sodium chloride is filtered, and the solution of hydroxyl- amine distilled in order to remove methyl alcohol, and finally fractionated under reduced pressure. The free base is a colourless, odourless, crystalline solid, melting at about 30 C, and boiling at 58° C. (under a pressure of 22 mm.). It deliquesces and oxidizes on exposure, inflames in dry chlorine and is reduced to ammonia by zinc dust. Its aqueous solution is strongly alkaline, and with acids it forms well-defined stable salts. E. Ebler and E. Schott (/. pr. Chem., 1908, 78, p. 289) regard it as acting with the formula NH 2 'OH towards bases, and as NHs:0 towards acids, the salts in the latter case being of the oxonium type. It is a strong reducing agent, giving a precipitate of cuprous oxide from alkaline copper solutions at ordinary temperature, con- verting mercuric chloride to mercurous chloride, and pre- cipitating metallic silver from solutions of silver salts. With aldehydes and ketones it forms oximes (q.v.). W. R. Dunstan (Jour. Chem. Soc, 1899, 75, p. 792) found that the addition of methyl iodide to a methyl alcohol solution of hydroxylamine resulted in the formation of trimethyloxamine, N(CH 3 )30. Many substituted hydroxylamines are known, substitution taking P a place either in the o or /S position (NH2-OH). /3-phenylhydroxyl- amine, C«H 5 NH-OH-, is obtained in the reduction of nitrobenzene in neutral solution (e.g. by the action of the aluminium-mercury couple and water), but better, according to C. Goldschmidt (Ber., 1896, 29, p. 2307) by dissolving nitrobenzene in ten times its weight of ether containing a few cubic centimetres of water, and heating with excess of zinc dust and anhydrous calcium chloride for three hours on a water bath. It also appears as an intermediate product in the electrolytic reduction of nitrobenzene in sulphuric acid solution. By gentle oxidation it yields nitrosobenzene. Derivatives of the type RzN-OH result in the action of the Grignard reagent on amyl nitrite. Dihydroxy-ammonia or nitroxyl, NH(OHV a very unstable and highly reactive substance, has been especially studied by A. Angeli (see A. W. Stewart, Recent Advances in Physical and Inorganic Chemistry, 1909). HYDROZOA, one of the most widely spread and prolific groups of aquatic animals. They are for the most part marine in habitat, but a familiar fresh-water form is the common Hydra of ponds and ditches, which gives origin to the name of the class. The Hydrozoa comprise the hydroids, so abundant on all shores, most of which resemble vegetable organisms to the unassisted eye; the hydrocorallines, which, as their name implies, have a massive stony skeleton and resemble corals; the jelly-fishes so called; and the Siphonophora, of which the species best known by repute is the so-called " Portuguese man-of-war " (Physaiia), dreaded by sailors on account of its terrible stinging powers. In external form and appearance the Hydrozoa exhibit such striking differences that there would seem at first sight to be little in common between the more divergent members of the group. Nevertheless there is no other class in the animal king- dom with better marked characteristics, or with more uniform HYDROZOA 172 morphological peculiarities underlying the utmost diversity of superficial characters. All Hydrozoa, in the first place, exhibit the three structural features distinctive of the Coelentera (q.v.). (1) The body is built up of two layers only, an external protective and sensory layer, the ectoderm, and an internal digestive layer, the endoderm. (2) The body contains but a single internal cavity, the coelenteron or gastrovascular space, which may be greatly ramified, but is not shut off into cavities distinct from the central digestive space. (3) The generative cells are produced in either the ectoderm or endoderm, and not in a third layer arising in the embryo, distinct from the two primary layers; in other words, there is no mesoderm or coelom. To these three characters the Hydrozoa add a fourth which is distinctive of the subdivision of the Coelenterata termed the Cnidaria; that is to say, they always possess peculiar stinging organs known as nettle-cells, or nematocysts (Cnidae), each produced in a cell forming an integral part of the animal's tissues. The Hydrozoa are thus shown to belong to the group of Coelenterata Cnidaria, and it remains to consider more fully their distinctive features, and in particular those which mark them off from the other main division of the Cnidaria, the Anthozoa {q.v.), comprising the corals and sea-anemones. The great diversity, to which reference has already been made, in the form and structure of the Hydrozoa is due to two principal causes. In the first place, we find in this group two distinct types of person or individual, the polyp and the medusa (qq.v.), each capable of a wide range of variations; and when both polyp and medusa occur in the life-cycle of the same species, as is frequently the case, the result is an alternation of genera- tions of a type peculiarly characteristic of the class. In the second place, the power of non-sexual reproduction by budding is practically of universal occurrence among the Hydrozoa, and by the buds failing to separate from the parent stock, colonies are produced, more or less complicated in structure and often of great size. We find that polyps may either bud other polyps or may produce medusae, and that medusae may bud medusae, though never, apparently, polyps. Hence we have a primary subdivision of the colonies of Hydrozoa into those produced by budding of polyps and those produced by budding of medusae. The former may contain polyp-persons and medusa-persons, either one kind alone or both kinds combined; the latter will contain only medusa-persons variously modified. The morphology of the Hydrozoa reduces itself, therefore, to a consideration of the morphology of the polyp, of the medusa and of the colony. Putting aside the last-named, for a detailed account of which see Hydromedusae, we can best deal with the peculiarities of the polyp and medusa from a developmental point of view. In the development of the Hydrozoa, and indeed of the Cnidaria generally, the egg usually gives rise to an oval larva which swims about by means of a coating of cilia on the surface of the body. This very characteristic larva is termed a planula, but though very uniform externally, the planulae of different species, or of the same species at different periods, do not always represent the same stage of embryonic development internally. On examining more minutely the course of the development, it is found that the ovum goes through the usual process of cleavage, always total and regular in this group, and so gives rise to a hollow sphere or ovoid with the wall composed of a single layer of cells, and containing a spacious cavity, the blastocoele or segmentation-cavity. This is the blastula stage occurring universally in all Metazoa, probably representing an ancestral Protozoan colony in phylogeny. Next the blastula gives rise to an internal mass of cells (fig. I , hy) which come from the wall either by immigration (fig. I, A) or by splitting off (delamina- tion). The formation of an inner cell-mass converts the single- layered blastula (monoblastula) into a double-layered embryo (diblastula) which may be termed a parenchymula, since at first the inner cell-mass forms an irregular parenchyma which may entirely fill up and obliterate the segmentation cavity (fig. I, B). At a later stage, however, the cells of the inner mass arrange them- selves in a definite layer surrounding an internal cavity (fig. 1, C, al), which soon acquires an opening to the exterior at one pole, and so forms the characteristic embryonic stage of all Enterozoa known as the gastrula (fig. 2). In this stage the body is composed of two layers, ectoderm (d) externally, and endoderm (e) internally, sur- rounding a central cavity, the archenteron (b), which communicates with the exterior by a pore (a), the blastopore, Thus a planula larva may be a blastula, or but slightly advanced beyond this stage, or it may be (and most usually is) a parenchymula ; or in some cases (Scyphomedusae) it may be a gastrula. It should be added that the process of development, the gastrulation as it is termed, may be shortened by the immigration of cells taking place From Balfour, after Kowalewsky. Fig. I. — Formation of the Diblastula of Eucope (one of the Calyptoblastic Hydromedusae) by immigration. A, B, C, three suc- cessive stages, ep, Ectoderm ; hy, endoderm ; al, enteric cavity. at one pole only, and in a connected layer with orderly arrangement, so that the gastrula stage is reached at once from the blastula without any intervening parenchymula stage. This is a process of gastrula- tion by invagination which is found in all animals above the Coelen- terata, but which is very rare in the Cnidaria, and is known only in the Scyphomedusae amongst the Hydrozoa. After the gastrula stage, which is found as a developmental stage in all Enterozoa, the embryo of the Hydrozoa proceeds to develop characters which are peculiar to the Coelen- terata only. Round the blastopore hollow outgrowths, variable in number, arise by the evagination ot the entire body-wall, both • ectoderm and endoderm. Each outgrowth con- tains a prolongation of the archenteric cavity (compare figs. 2 and 3, A). In this way is formed a ring of tentacles, the most character- istic organs of the Cnidaria. They surround a region which is termed the peristome, and which contains in the centre the blastopore, which becomes the adult mouth. The arch- enteron becomes the gastrovascular system or coelenteron. Between the ectoderm and endoderm a gelatinous supporting layer, termed the mesogloea, makes its appearance. The gastrula has now become an actinula, which may be termed the distinctive larva of the Cnidaria, and doubtless represents in a transitory manner the common ancestor of the group. In no case known, however, does the actinula become the adult, sexually mature individual, but always undergoes further modifications, whereby it develops into either a polyp or a medusa. To become a polyp, the actinula (fig. 3, A) becomes attached to some firm object by the pole farthest from the mouth, and its growth preponderates in the direction of the principal axis, that is to say, the axis passing through the mouth (fig. 3, a-b). As a result the body becomes columnar in form (fig. 3, B), and without further change passes into the characteristic polyp-form (see Polyp). From Gegenbaur's Ele- ments of Comparative Anatomy. Fig. 2. — Diagram ot a Diblastula. a, Blastopore. b, Archenteric cavity. c, Endoderm. d, Ectoderm. Fig. 3. — Diagram showing the change of the Actinula (A) into a Polyp (B); a-b, principal (vertical) axis; c-d, horizontal axis. The endoderm is shaded, the ectoderm is left clear. It is convenient to distinguish two types of polyp by the names hydro polyp and anthopolyp, characteristic of the Hydrozoa and HYENA 73 Anthozoa respectively. In the hydropolyp the body is typically elongated, the height of the column being far greater than the diameter. The peristome is relatively small and the mouth is generally raised on a projecting spout or hypostome. The ectoderm loses entirely the ciliation which it had in the planula and actinula stages and com- monly secretes on its external surface a protective or supporting in- vestment, the perisarc. Contrasting with this, the anthopolyp is generally of squat form, the diameter often exceeding the height; the peristome is wide, a hypostome is lacking, and the ectoderm, or so much of it as is exposed, i.e. not covered by secretion of skeletal or other investment, retains its ciliation throughout life. The internal structural differences are even more characteristic. In the hydropolyp the blastopore of the embryo forms the adult mouth situated at the extremity of the hypostome, and the ectoderm and a. a. R R Fir.. 4. — Diagram showing the change of the Actinula into a Medusa. A, Vertical section of the actinula; a-b and c-d as in fig. 3, B, transitional stage, showing preponderating growth in the horizontal plane. (",C, D,D', two types of medusa organization; C and D are composite sections, showing a radius (R) on one side, an interradius (IR1 on the other; C and D' are plans; the mouth and manubrium are indicated at the centre, leading into the gastral cavity subdivided by the four areas of concrescence in each interradius (IR). t, tentacle; g.p, gastric pouch; r.c, radial canal not present in C and C; r.c, circular or ring-canal; e.l, endoderm-lamella formed bv concrescence. For a more detailed diagram of medusa-structure see article Medusa. endoderm meet at this point. In the anthopolyp the blastopore is carried inwards by an in-pushing of the body-wall of the region of the peristome, so that the adult mouth is an opening leading into a short ectodermal oesophagus or stomodaeum, at the bottom of which is the blastopore. Further, in the hydropolyp the digestive cavity either remains simple and undivided and circular in transverse section, or may show ridges projecting internally, which in this case are formed of endoderm alona, without any participation of the mesogloea. In the anthopolyp, on the other hand, the digestive cavity is always subdivided by so-called mesenteries, in-growths of the endoderm containing vertical lamellae of mesogloea (see Anthozoa). In short, the hydropolyp is characterized by a more simple type of organization than the anthopolyp, and is in most respects less modified from the actinula type of structure. Returning now to the actinula, this form may, as already stated, develop into a medusa, a type of individual found only in the Hydrozoa, as here understood. To become a medusa, the actinula grows scarcely at all in the direction of the principal axis, but greatly along a plane at right angles to it. Thus the body becomes umbrella- shaped, the concave side representing the peristome, and the convex side the column, of the polyp. Hence the tentacles are found at the edge of the umbrella, and the hypostome forms usually a projecting tube, with the mouth at the extremity, forming the manubrium or handle of the umbrella. The medusa has a pronounced radial sym- metry, and the positions of the primary tentacles, usually four in number, mark out the so-called radii, alternating with which are four interradii. The ectoderm retains its ciliation only in the sensory organs. The mesogloea becomes enormously increased in quantity (hence the popular name " jelly-fish "), and in correlation with this the endoderm-layer lining the coelenteron becomes pressed together in the intermedial areas and undergoes concrescence, forming a more or less complicated gastrovascular system (see Medusa). It is sufficient to state here that the medusa is usually a free-swimming animal, floating mouth downwards on the open seas, but in some cases it may be attached by its aboral pole, like a polyp, to some firm basis, either temporarily or permanently. Thus the development of the two types of individual seen in the Hydrozoa may be summarized as follows: — Egg Free Planula " Stage Blastula Parenchymula Gastrula Actinula Polyp Medusa This development, though probably representing the primitive sequence of events, is never actually found in its full extent, but is always abbreviated by omission or elimination of one or more of the stages. We have already seen that the parenchymula stage is passed over when the gastrulation is of the invaginate type. On the other hand, the parenchymula may develop directly into the actinula or even into the polyp, with suppression of the intervening steps. Great apparent differences may also be brought about by variations in the period at which the embryo is set free as a larva, and since two free-swimming stages, planula and actinula, are unnecessary, one or other of them is always suppressed. A good example of this is seen in two common genera of British hydroids, Cordylophora and Tabu- laria. In Cordylophora the embryo is set free at the parenchymula stage as a planula which fixes itself and develops into a polyp, both gastrula and actinula stages being suppressed. In Tubularia, on the other hand, the parenchymula develops into an actinula within the maternal tissues, and is then set free, creeps about for a time, and after fixing itself, changes into a polyp; hence in this case the planula-stage, as a free larva, is entirely suppressed. The Hydrozoa may be defined, therefore, as Cnidaria in which two types of individual, the polyp and the medusa, may be present, each type developed along divergent lines from the primitive actinula form. The polyp (hydropolyp) is of simple structure and never has an ectodernal oesophagus or mesenteries. 1 The general ectoderm loses its cilia, which persist only in the sensory cells, and it frequently secretes external protective or supporting structures. An internal mesogloeal skeleton is not found. The class is divisible into two main divisions or sub-classes, Hydro- medusae and Scyphomedusae, of which definitions and detailed systematic accounts will be found under these headings. General Works on Hydrozoa. — C. Chun, " Coelenterata (Hohlthiere)," Bronn's Klassen und Ordnungcn des Thier-Reichs ii. 2 (1889 et seq.); Y. Delage, and E. Herouard, Traite de zoologie concrete, ii. part 2, Les CoelentSres (1901); G. H. Fowler, "The Hydromedusae and Scyphomedusae " in E. R. Lankester's Treatise on Zoology, ii. chapters iv. and v. (1900) ; S. J. Hickson, " Coelen- terata and Ctenophora," Cambridge Natural History, i. chapters x.-xv. (1906). (E. A. M.) HYENA, a name applicable to all the representatives of the mammalian family Hyaenidae, a group of Camivora (q.v.) allied to the civets. From all other large Camivora except the African hunting-dog, hyenas are distinguished by having only four toes on each foot, and are further characterized by the length of the fore-legs as compared with the hind pair, the non-retractile claws, and the enormous strength of the jaws and teeth, which enables them to break the hardest bones and to retain what they have seized with unrelaxing grip. 1 See further under Scyphomedusae. 174 HYERES The striped hyena (Hyaena striata) is the most widely dis- tributed species, being found throughout India, Persia, Asia Minor, and North and East Africa, the East African form constituting a distinct,, race, H. striata schillingsi; while there are also several distinct Asiatic races. The species resembles a wolf in size, and is greyish-brown in colour, marked with indistinct longitudinal stripes of a darker hue, while the legs are transversely striped. The hairs on the body are long, especially on the ridge of the neck and back, where they form a distinct mane, which is continued along the tail. Nocturnal in habits, Fig. i. — The Striped Hyena {Hyaena striata). it prefers by day the gloom of caves and ruins, or of the burrows which it occasionally forms, and issues forth at sunset, when it commences its unearthly howling. When the animal is excited, the howl changes into what has been compared to demoniac laughter, whence the name of " laughing-hyena." These creatures feed chiefly on carrion, and thus perform useful service by devouring remains which might otherwise pollute the air. Even human dead are not safe from their attacks, their powerful claws enabling them to gain access to newly interred bodies in cemeteries. Occasionally (writes Dr W. T. Blanford) sheep or Fig. 2. — The Spotted Hyena (Hyaena crocuta). goats, and more often dogs, are carried off, and the latter, at all events, are often taken alive to the animal's den. This species appears to be solitary in habits, and it is rare to meet with more than two together. The cowardice of this hyena is proverbial; despite its powerful teeth, it rarely attempts to defend itself. A very different animal is the spotted hyena, Hyaena {Crocuta) crocuta, which has the sectorial teeth 'of a more cat-like type, and is marked by dark-brown spots on a yellowish ground, while the mane is much less distinct. At the Cape it was formerly common, and occasionally committed great havoc among the cattle, while it did not hesitate to enter the Kaffir dwellings at night and carry off children sleeping by their mothers. By persistent trapping and shooting, its numbers have now been considerably reduced, with the result, however, of making it exceedingly wary, so that it is not readily caught in any trap with which it has had an opportunity of becoming acquainted. Its range extends from Abyssinia to the Cape. The Abyssinian form has been regarded as a distinct species, under the name of H. liontiewi, but this, like various more southern forms, is but regarded as a local race. The brown hyena (Sf. brunnea) is South African, ranging to Angola on the west and Kilimanjaro on the east. In size it resembles the striped hyena, but differs in appearance, owing to the fringe of long hair covering the neck and fore part of the back. The general hue is ashy-brown, with the hair lighter on the neck (forming a collar), chest and belly; while the legs are banded with dark brown. This species is not often seen, as it remains concealed during the day. Those frequenting the coast feed on dead fish, crabs and an occasional stranded whale, though they are also a danger to the sheep and cattle kraal. Strand-wolf is the local name at the Cape. Although hyenas are now confined to the warmer regions of the Old World, fossil remains show that they had a more northerly range during Tertiary times; the European cave-hyena being a form of the spotted species, known as H. crocuta spelaea. Fossil hyenas occur in the Lower Pliocene of Greece, China, India, &c; while remains indistinguishable from those of the striped species have been found in the Upper Pliocene of England and Italy. HYERES, a town in the department of the Var in S.E. France, ii m. by rail E. of Toulon. In 1906 the population of the com- mune was 17,790, of the town 10,464; the population of the former was more than doubled in the last decade of the 19th century. Hyeres is celebrated (as is also its fashionable suburb, Costebelle, nearer the seashore) as a winter health resort. The town proper is situated about. 25 m. from the seashore, and on the south- western slope of a steep hill (669 ft., belonging to the Maurettes chain, 961 ft.), which is one of the westernmost spurs of the thickly wooded Montagnes des Maures. It is sheltered from the north-east and east winds, but is exposed to the cold north-west wind or mistral. Towards the south and south-east a fertile plain, once famous for its orange groves, but now mainly covered by vineyards and farms, stretches to the sea, while to the south- west, across a narrow valley, rises a cluster of low hills, on which is the suburb of Costebelle. The older portion of the town is still surrounded, on the north and east, by its ancient, though dilapidated medieval walls, and is a labyrinth of steep and dirty streets. The more modern quarter which has grown up at the southern foot of the hill has handsome broad boulevards and villas, many of them with beautiful gardens, filled with semi- tropical plants. Among the objects of interest in the old town are: the house (Rue Rabaton, 7) where J. B. Massillon (1663- 1742), the famous pulpit orator, was born; the parish church of St Louis, built originally in the 13th century by the Cordelier or Franciscan friars, but completely restored in the earlier part of the 19th century; and the site of the old chateau, on the summit of the hill, now occupied by a villa. The plain between the new town and the sea is occupied by large nurseries, an excellent jardin d'acclimatation, and many market gardens, which supply Paris and London with early fruits and vegetables, especially artichokes, as well as with roses in winter. There are extensive salt beds (salines) both on the peninsula of Giens, S. of the town, and also E. of the town. To the east of the Giens peninsula is the fine natural harbour of Hyeres, as well as" three thinly populated islands (the Stoechades of the ancients), Porquerolles, Port Cros and Le Levant, which are grouped together under the common name of lies d'Hyeres. The town of Hyeres seems to have been founded in the 10th century, as a place of defence against pirates, and takes its name from the aires (hierbo in the Provencal dialect), or threshing- floors for corn, which then occupied its site. It passed from the possession of the viscounts of Marseilles to Charles of Anjou, count of Provence, and brother of St Louis (the latter landed here in 1254, on his return from Egypt). The chateau was HYGIEIA— HYKSOS r 75 dismantled by Henri IV., but thanks to its walls, the town resisted in 1 707 an attack made by the duke of Savoy. See Ch. Lentheric, La Provence Maritime ancienne et moderne (chap. 5) (Paris, 1880). (W. A. B. C.) HYGIEIA, in Greek mythology, the goddess of health. It seems probable that she was originally an abstraction, subse- quently personified, rather than an independent divinity of very ancient date.. The question of the original home of her worship has been much discussed. The oldest traces of it, so far as is known at present, are to be found at Titane in the territory of Sicyon, where she was worshipped together with Asclepius, to whom she appears completely assimilated, not an independent personality. Her cult was not introduced at Epidaurus till a late date, and therefore, when in 420 B.C. the worship of Asclepius was introduced at Athens coupled with that of Hygieia, it is not to be inferred that she accompanied him from Epidaurus, or that she is a Peloponnesian importation at all. It is most probable that she was invented at the time of the introduction of Asclepius, after the sufferings caused by the plague had directed special attention to sanitary matters. The already existing worship of Athena Hygieia had nothing to do with Hygieia the goddess of health, but merely denoted the recognition of the power of healing as one of the attributes of Athena, which gradually became crystallized into a concrete personality. At first no special relationship existed between Asclepius and Hygieia, but gradually she came to be regarded as his daughter, the place of his wife being already secured by Epione. Later Orphic hymns, however, and Herodas iv. 1-9, make her the wife of Asclepius. The cult of Hygieia then spread concurrently with that of Asclepius, and was introduced at Rome from Epidaurus in 293, by which time she may have been admitted (which was not the case before) into the Epidaurian family of the god. Her proper name as a Romanized Greek importation was Valetudo, but she was gradually identified with Salus, an older genuine Italian divinity, to whom a temple had already been erected in 302. While in classical times Asclepius and Hygieia are simply the god and goddess of health, in the declining years of paganism they are protecting divinities generally, who preserve mankind not only from sickness but from all dangers on land and sea. In works of art Hygieia is represented, together with Asclepius, as a maiden of benevolent appearance, wearing the chiton and giving food or drink to a serpent out of a dish. See the article by H. Lechat in Daremberg and Saglio's Diction- naire des antiquitSs, with full references to authorities; and E. Thramer in Roscher's Lexikon der Mythologie, with a special section on the modern theories of Hygieia. HYGIENE (Fr. hygiene, from Gr. vyiaivet.v, to be healthy), the science of preserving health, its practical aim being to render " growth more perfect, decay less rapid, life more vigorous, death more remote." The subject is thus a very wide one, embracing all the agencies which affect the physical and mental well-being of man, and it requires acquaintance with such diverse sciences as physics, chemistry, geology, engineering, architecture, meteorology, epidemiology, bacteriology and statistics. On the personal or individual side it involves con- sideration of the character and quality of food and of water and other beverages; of clothing; of work, exercise and sleep; of personal cleanliness, of special habits, such as the use of tobacco, narcotics, &c; and of control of sexual and other passions. In its more general and public aspects it must take cognizance of meteorological conditions, roughly included under the term climate; of the site or soil on which dwellings are placed; of the character, materials and arrangement of dwellings, whether regarded individually or in relation to other houses among which they stand; of their heating and ventilation; of the removal of excreta and other effete matters; of medical knowledge relating to the incidence and prevention of disease; and of the disposal of the dead. These topics will be found treated in such articles as Dietetics, Food, Food-Preservation, Adulteration, Water, Heating, Ventilation, Sewerage, Bacteriology, Housing, Cremation, &c. For legal enactments which concern the sanitary well-being of the community, see Public Health. HYGINUS, eighth pope. It was during his pontificate (c. 137-140) that the gnostic heresies began to manifest themselves at Rome. HYGINUS (surnamed Gromaticus, from gruma, a surveyor's measuring-rod), Latin writer on land-surveying, flourished in the reign of Trajan (a.d. 98-117). Fragments of a work on legal boundaries attributed to him will be found in C. F. Lach- mann, Gromatici Veteres, i. (1848). A treatise on Castrametation (De Muniiiortibus Castrorum), also attributed to him, is probably of later date, about the 3rd century a.d. (ed. W. Gemoll, 1879; A. von Domaszewski, 1887). HYGINUS, GAIUS JULIUS, Latin author, a native of Spain (or Alexandria), was a pupil of the famous Cornelius Alexander Polyhistor and a freedman of Augustus, by whom he was made superintendent of the Palatine library (Suetonius, De Gramma- ticis, 20). He is said to have fallen into great poverty in his old age, and to have been supported by the historian Clodius Licinus. He was a voluminous author, and his works included topographical and biographical treatises, commentaries on Helvius Cinna and the poems of Virgil, and disquisitions on agriculture and bee-keeping. All these are lost. Under the name of Hyginus two school treatises on mythology are extant: (1) Fabularum Liber, some 300 mythological legends and celestial genealogies, valuable for the use made by the author of the works of Greek tragedians now lost; (2) De Astronomia, usually called Poetica Astronomica, containing an elementary treatise on astronomy and the myths connected with the stars, chiefly based on the KaTaorepiCTjuot of Eratosthenes. Both are abridgments and both are by the same hand ; but the style and Latinity and the elementary mistakes (especially in the rendering of the Greek originals) are held to prove that they cannot have been the work of so distinguished a scholar as C. Julius Hyginus. It is suggested that these treatises are an abridgment (made in the latter half of the 2nd century) of the Genealogiae of Hyginus by an unknown grammarian, who added a complete treatise on mythology. Editions. — Fabulae, by M. Schmidt (1872); De Astronomia, by B. Bunte (1875) ; see also Bunte, De C. Julii Hygini, Augusti Liberti, Vita et Scriptis (1846). HYGROMETER (Gr. vypds, moist, \ikrpov, a measure), an instrument for measuring the absolute or relative amount of moisture in the atmosphere; an instrument which only qualitatively determines changes in the humidity is termed a " hygroscope." The earlier instruments generally depended for their action on the contraction or extension of substances when exposed to varying degrees of moisture; catgut, hair, twisted cords and wooden laths, all of which contract with an increase in the humidity and vice versa, being the most favoured materials. The familiar " weather house " exemplifies this property. This toy consists of a house provided with two doors, through which either a man or woman appears according as the weather is about to be wet or fine. This action is effected by fixing a catgut thread to the base on which the figures are mounted, in such a manner that contraction of the thread rotates the figures so that the man appears and extension so that the woman appears. Many of the early forms are described in C. Hutton, Math, and Phil. Dictionary (1815). The modern instruments, which utilize other principles, are described in Meteorology: II. Methods and Apparatus. HYKSOS, or " Shepherd Kings," the name of the earliest invaders of Egypt of whom we have definite evidence in tradition. Josephus (c. Apion. i. 14), who identifies the Hyksos with the Israelites, preserves a passage from the second book of Manetho giving an account of them. (It may be that Josephus had it, not direct from Manetho's writings, but through the garbled version of some Alexandrine compiler.) In outline it is as follows. In the days of a king of Egypt named Timaeus the land was suddenly invaded from the east by men of ignoble race, who conquered it without a struggle, destroyed cities and temples, and slew or enslaved the inhabitants. At length they elected a king named Salatis, who, residing at Memphis, made all Egypt tributary, and established garrisons in different parts, especially eastwards, fearing the Assyrians. He built also a great fortress at Avaris, in the Sethroite nome, east of the Bubastite branch of the Nile. Salatis was followed in succession by Beon, Apachnas, Apophis, Jannas and Asses. These six kings reigned 198 years and 10 months, and all aimed at extirpating the Egyptians. Their whole race was named Hyksos, i.e. "shepherd kings," and 176 HYLAS— HYMEN some say they were Arabs (another explanation found by Josephus is " captive shepherds ")• When they and their successors had held Egypt for 511 years, the kings of the Thebais and other parts of Egypt rebelled, and a long and mighty war began. Misphragmuthosis worsted the " Shepherds " and shut them up in Avaris; and his son Thutmosis, failing to capture the stronghold, allowed them to depart; whereupon they went forth, 240,000 in number, established themselves in Judea and built Jerusalem. In Manetho's list of kings, the six above named (with many variations in detail) form the XVth dynasty, and are called " six foreign Phoenician kings." The XVIth dynasty is of thirty-two " Hellenic (sic?) shepherd kings," the seventeenth is of " shepherds and Theban kings " (reigning simultaneously). The lists vary greatly in different versions, but the above seems the most reasonable selection of readings to be made. For " Hellenic " see below. The supposed connexion with the Israelites has made the problem of the Hyksos attractive, but light is coming upon it very slowly. In 1847 E. de Rouge proved from a fragment of a story in the papyri of the British Museum, that Apopi was one of the latest of the Hyksos kings, corresponding to Aphobis; he was king of the " pest " and suppressed the worship of the Egyptian gods, and endeavoured to make the Egyptians worship his god Setekh or Seti; at the same time an Egyptian named Seqenenre reigned in Thebes, more or less subject to Aphobis. The city of Hawari (Avaris) was also mentioned in the fragment. In 1850 a record of the capture of this city from the Hyksos by Ahmosi, the founder of the eighteenth dynasty, was discovered by the same scholar. A large class of monuments was afterwards attributed to the Hyksos, probably in error. Some statues and sphinxes, found in 1861 by Mariette at Tanis (in the north- east of the Delta), which had been usurped by later kings, had peculiar " un-Egyptian " features. One of these bore the name of Apopi engraved lightly on the shoulder; this was evidently a usurper's mark, but from the whole circumstances it was concluded that these, and others of the same type of features found elsewhere, must have belonged to the Hyksos. This view held the field until 1893, when Golenischeff produced an inferior example bearing its original name, which showed that in this case it represented Amenemhe III. In consequence it is now generally believed that they all belong to the twelfth dynasty. Meanwhile a headless statue of a king named Khyan, found at Bubastis, was attributed on various grounds to the Hyksos, the soundest arguments being his foreign name and the boastful un-Egyptian epithet " beloved of his ka," where " beloved of Ptah " or some other god was to be expected. His name was immediately afterwards recognized on a lion found as far away from Egypt as Bagdad. Flinders Petrie then pointed out a group of kings named on scarabs of peculiar type, which, including Khyan, he attributed to the period between the Old Kingdom and the New, while others were in favour of assigning them all to the Hyksos, whose appellation seemed to be recognizable in the title Hek-khos, ' 'ruler of the barbarians, ' ' borne by Khyan. The extraordinary importance of Khyan was further shown by the discovery of his name on a jar-lid at Cnossus in Crete. Semitic features were pointed out in the supposed Hyksos names, and Petrie was convinced of their date by his excavations of 1 905-1 906 in the eastern Delta. Avaris is generally assigned to the region towards Pelusium on the strength of its being located in the Sethroite nome by Josephus, but Petrie thinks it was at Tell el-Yahudiyeh (Yehudia), where Hyksos scarabs are common. From the remains of fortifications there he argues that the Hyksos were uncivilized desert people, skilled in the use of the bow, and must thus have destroyed by their archery the Egyptian armies trained to fight hand-to- hand; further., that their hordes were centered in Syria, but were driven thence by a superior force in the East to take refuge in the islands and became a sea-power— whence the strange description " Hellenic " in Manetho, which most editors have corrected to &XX01, "others." Besides the statue of Khyan, blocks of granite with the name of Apopi have been found in Upper Egypt at Gebelen and in Lower Egypt at Bubastis. The celebrated Rhind mathematical papyrus was copied in the reign of an Apopi from an original of the time of Amenemhe III. Large numbers of Hyksos scarabs are found in Upper and Lower Egypt, and they are not unknown in Palestine. Khyan 's monuments, inconspicuous as they are, actually extend over a wider area — from Bagdad to Cnossus — than those of any other Egyptian king. It is certain that this mysterious people were Asiatic, for they are called so by the Egyptians. Though Seth was an Egyptian god, as god of the Hyksos he represents some Asiatic deity. The possibility of a connexion between the Hyksos and the Israelites is still admitted in some quarters. Hatred of these impious foreigners, of which there is some trace in more than one text, aroused amongst the Egyptians (as nothing ever did before or since) that martial spirit which carried the armies of Tethmosis to the Euphrates. Besides the histories of Egypt, see J. H. Breasted, Ancient Records of Egypt; Historical Documents ii. 4, 125; G. Maspero, Contes populaires, 3me ed. p. 236; W. M. F. Petrie, Hyksos and Israelite Cities, p. 67; Golenischeff in Rectteil de travaux,xv. p. 131. (F. Ll. G.) HYLAS, in Greek legend, son of Theiodamas, king of the Dryopians in Thessaly, the favourite of Heracles and his com- panion on the Argonautic expedition. Having gone ashore at Kios in Mysia to fetch water, he was carried off by the nymphs of the spring in which he dipped his pitcher. Heracles sought him in vain, and the answer of Hylas to his thrice-repeated cry was lost in the depths of the water. Ever afterwards, in memory of the threat of Heracles to ravage the land if Hylas were not found, the inhabitants of Kios every year on a stated day roamed the mountains, shouting aloud for Hylas (Apollonius Rhodius i. 1207; Theocritus xiii.; Strabo xii. 564; Propertius i. 20; Virgil, Eel. vi. 43). But, although the legend is first told in Alexandrian times, the " cry of Hylas " occurs long before as the " Mysian cry " in Aeschylus (Persae, 1054), and in Aristo- phanes {Plutus, 1 1 27) " to cry Hylas " is used proverbially of seeking something in vain. Hylas, like Adonis and Hyacinthus, represents the fresh vegetation of spring, or the water of a foun- tain, which dries up under the heat of summer. It is suggested that Hylas was a harvest deity and that the ceremony gone through by the Kians was a harvest festival, at which the figure of a boy was thrown into the water, signifying the dying vegeta- tion-spirit of the year. See G. Turk in Breslauer Philologische Abhandlungen, vii. (1895) ; W. Mannhardt, Mythologische Forschungen (1884). HYLOZOISM (Gr. vkq, matter, fw^, life), in philosophy, a term applied to any system which explains all life, whether physical or mental, as ultimately derived from matter (" cosmic matter," Weldstoff). Such a view of existence has been common throughout the history of thought, and especially among physical scientists. Thus the Ionian school of philosophy, which began with Thales, sought for the beginning of all things in various material substances, water, air, fire (see Ionian School). These substances were regarded as being in some sense alive, and taking some active part in the development of being. This primitive hylozoism reappeared in modified forms in medieval and Renaissance thought, and in modern times the doctrine of materialistic monism is its representative. Between modern materialism and hylozoism proper there is, however, the dis- tinction that the ancients, however vaguely, conceived the elemental matter as being in some sense animate if not actually conscious and conative. HYMEN, or Hymenaeus, originally the nam* of the song sung at marriages among the Greeks. As usual the name gradually produced the idea of an actual person whose adventures gave rise to the custom of this song. He occurs often in association with Linus and Ialemus, who represent similar personifications, and is generally called a son of Apollo and a Muse. As the son of Dionysus and Aphrodite, he was regarded as a god of fruitful- ness. In Attic legend he was a beautiful youth who, being in love with a girl, followed her in a procession to Eleusis disguised as a woman, and saved the whole band from pirates. As reward HYMENOPTERA 177 he obtained the girl in marriage, and his happy married life caused him ever afterwards to be invoked in marriage songs (Servius on Virgil, Aen. i. 651). According to another story, he was a youth who was killed by the fall of his house on his wedding day; hence he was invoked to propitiate him and avert a similar fate from others (Servius, he. cit.). He is represented in works of art as an effeminate-looking, winged youth, carrying a bridal torch and wearing a nuptial veil. The marriage song was sung, with musical accompaniment, during the procession of the bride from her parents' house to that of the bridegroom, Hymenaeus being invoked at the end of each portion. See R. Schmidt, De Hymenaeo el Talasio (1886), and J.A. Hildin Daremberg and Saglis's Dictionnaire des antiquites. HYMENOPTERA (Gr. vfi-qv, a membrane, and irrtpov, a wing), a term used in zoological classification for one of the most im- portant orders of the class Hexapoda (airs of thoracic legs, and from six to eight pairs of abdominal pro- egs, the latter not possessing the hooks found on the pro-legs of lepidopterous caterpillars. Most saw-fly larvae devour leaves, and the beautifully serrate processes of the ovipositor are well adapted for egg-laying in plant tissues. Some saw-fly larvae are protected by a slimy secretion (fig. 6, c) and a few live concealed in galls. In the form of the feelers, the wing-neuration and minor structural details there is much diversity among the saw-flies. They have boon usually regarded as a single family, but VV. II. Ashmcad has lately differentiated eleven families of them. Apocrita. This sub-order includes the vast majority of the Hymenoptera, characterized by the narrowly constricted waist in the adult and by the legless condition of the larva. The trochanter is simple in some genera and divided in others. With regard to the minor divisions of this group, great difference of opinion has prevailed among students. _ In his recent classification Ashmead (1901) recognizes seventy-nine families arranged under eight " super-families." The number of _ species included in this division is enormous, and the multiplication of families is, to some extent, a natural result of increasingly close study. But the distinctions between many of these rest on comparatively slight characters, and it is likely that TERtl.-. After Marlatt, Enl. Circ. 26, U.S. Dept. Agric. Fig. 6. — a, Pear Saw-fly {Eriocampoides limacina) ; b, larva with- out, and c, with its slimy protective coat ; e, cocoon ; /, larva before pupation; g, pupa, magnified; d, leaves with larvae. the future discovery of new genera may abolish many among such distinctions as may now be drawn. It seems advisable, therefore, in the present article to retain the wider conception of the family that has hitherto contented most writers on the Hymenoptera. Ashmead's " super-families " have, however, been adopted as — founded on definite structural characters — they probably indicate relationship more nearly than the older divisions founded mostly on habit. The Cynipoidea include the gall-flies and their parasitic relations. In the Chalcidoidea, Ichneumonoidea arid Proctotry- poidea will be found nearly all the " parasitic Hymenoptera " of older classifications. The Formicoidea are the ants. The group of Fossores, or " digging-wasps," is divided by Ashmead, one section forming the Sphecoidea, while the other, together with the Chrysidae TEDZI After Howard, Ent Tech. Bull, s U.S. Dept. Agric. Fig. 7. — Chalcid (Dibrachys boucheanus), a hyper-parasite, a, Larva. b, Female fly. d, Its head more highly magni- c, Pupa of male. fied. e, Feeler, and the true wasps, make up the Vespoidea. The Apoidea consists of the bees only. Cynipoidea. — In this division the ovipositor issues fuom the ventral surface of the abdomen ; the pronotum reaches back to the tegulae ; the trochanter has two segments; the fore- wing (fig. 4, 2) has no stigma, but one or two areolets. The feelers with twelve to fifteen segments are thread-like and straight. All the insects included in this group are small and form two families — the Cynipidae and the Figitidae. They are the " gall-flies," many of the species laying eggs in various plant-tissues where the presence of the larva causes the formation of a pathological growth or gall, always of a definite form and characteristic of the species; the "oak-apple" and the i8o HYMENOPTERA bedeguar of the rose are familiar examples. Other flies of this group have the inquiline habit, laying their eggs in the galls of other species, while others again pierce the cuticle of maggots or aphids, in whose bodies their larvae live as parasites. Chalcidoidea. — This division resembles the Cynipoidea in the position of the ovipositor, and in the two segmented trochanters. The fore-wing also has no stigma, and the whole wing is almost destitute of nervurcs and areolets, while the pronotum does not reach back to the tegulae, and the feelers are elbowed (fig. 7). The vast majority of this group, including nearly 5000 known species, are usually reckoned as a single family, the ClwJcididae, comprising small insects, often of bright metallic colours, whose larvae are parasitic in insects of various orders. The " fig-insects," whose presence in ripening figs is believed essential to the proper develop- ment of the fruit, belong to Blastophaga and other genera of this family. They are remarkable in having wingless males and winged females. The " polyembryonic " development of an Encyrtus, as studied by P. Marchal, is highly remarkable. The female lays her egg in the egg of a small ermine moth (Hyponomettta) and the egg gives rise not to a single embryo but to a hundred, which develop as the host-caterpillar develops, being found at a later stage within the latter enveloped in a flexible tube. The Mymaridae or " fairy-flies " are distinguished from the Chalcididae by their narrow fringed wings (figs. 4, 5) and by the situation of the ovipositor just in front of the tip of the abdomen. They arc among the most minute of all insects and their larvae are probably all parasitic in insects' eggs. Ichneumonoidea. — The ten thousand known species included in this group agree with the Cynipoidea and Chalcidoidea in the iwsition of the ovipositor and in the jointed trochanters, but are distinguished by the fore-wing possessing a distinct stigma and usually a typical series of nervures and areolets (figs. 4, 8). Many of the species are of fair size. They lay their eggs (fig. 8) in the bodies of insects and their larvae belonging to various orders. A few small families such as the Evaniidae and the Stephanidae are in- cluded here, but the vast majority of the group fall into two large families, the Ichneumoni- /^*\ _ _ dae and the Braconidae, the former distinguished by the presence of two median (or discoidal) cells in the fore- wing (figs. 4, 7), while the latter has only one (figs. 4, 6). Not a few of these insects, however, are entirely wingless. On account of their work in destroying plant-eating insects, the ichneumon- flies are of great economic importance. Proctotrypoidea. — This group may be distin- guished from the pre- ceding by the position of the ovipositor at the extreme apex of the abdomen, and from the groups that follow (with very few exceptions) by the jointed trochanters of the legs. The pronotum reaches back to the tegulae. The Pelecinidae — included here by Ash- mead — are large insects with remarkably elongate abdomens and undivided trochanters. AH the other members of the group may be regarded as forming a single family — the Proctotrypidae, including an immense number of small parasitic Hymenoptcra, not a few of which are wingless. Of special interest are the transforma- tions of Platygaster, belonging' to this family, discovered by jVI. Ganift, and familiarized to English readers through the writings of Sir J. Lubbock (Lord Avebury). The first larva is broad in front and tapers behind to a " tail " provided with two divergent pro- cesses, so that it resembles a small crustacean. It lives in the grub of a gall-midge and it ultimately becomes changed into the usual white and fleshy hymenoptcrous larva. The four succeeding sections, in which the ovipositor is modified into a sting (always exserted from the tip of the abdomen) and the trochanters are with few exceptions simple, form the Aculeata of Linnaeus. Formicoidea. — The ants which form this group are readily dis- tinguished by the differentiation of the females into winged " queens" and wingless " workers." The pronotum extends back to the wing- bases, and the " waist " is greatly constricted and marked by one or two " nodes." The differentiation of the females leads to a complex social life, the nesting habits of ants and the various industries that they pursue being of surpassing interest (see Ant). Vespoidea. — This section includes a number of families char- acterized by the backward extension of the prothorax to the tegulae and distinguished from the ants by the absence of " nodes " at the base of the abdomen. The true wasps have the fore-wings folded lengthwise when at rest and the fore-legs of normal build — not specialized for digging. The Vespidae or social wasps have " queens " and " workers " like the ants, but both these forms of female are winged: the claws on their fret are simple. In the. Eumcvidar or solitarv wasps the female sex is undifferentiated, and the foot claws After Riley and Howard, Insect Li/e,vol. i. Fig. 8. — Ichneumon Fly (Rhyssa per- suasaria) ovipositing. arc toothed. (For the habits of these insects see Wasp.) The Chrysididiie or ruby wasps are small insects with a very hard cuticle exhibiting brilliant metallic colours — blue, green and crimson. Only three or four abdominal segments are visible, the hinder seg- ments being slender and retracted to form a telescope-like tube in which the ovipositor lies. When the ovipositor is brought into use this tube is thrust out. The eggs are laid in the nests of various bees and wasps, the chrysid larva living as a " cuckoo " parasite. The Trigonalidae, a small family whose larvae are parasitic in wasps' nests, also probably belong here. The other families of the Vespoidea belong to the series of ' ' Fos- sores " or digging-wasps. In two of the families — the Mutillidae and Thynnidae — the females are wingless and the larvae live as parasites in the larvae of other insects; the female Mutilla enters humble-bees' nests and lays her eggs in the bee-grubs. In the other families both sexes arc winged, and the instinct and industry of the females are among the most wonderful in the Hymenoptcra. They make burrows wherein they place insects or spiders which they have caught and stung, laying their eggs beside the victim so that the young larvae find themselves in presence of an abundant and appropriate food-supply. Valuable observations on the habits of these insects are due to J. H. Fabre and G. W. and E. Peckham. The prey is sometimes stung in the neighbourhood of the nerve ganglia, so that it is paralysed but not killed, the grub of the fossorial wasp devouring its victim alive ; but this instinct varies in perfection, and in many cases the larva flourishes equally whether its prey be killed or not. The females have a wonderful power of finding their burrows on returning from their hunting expeditions. Among the Vespoid families of fossorial wasps, the Pompilidae are the most important. They are recognizable by their slender and elongate hind-legs; many of them provision their burrows with spiders. The Sapygidae are parasitic on bees, while the Scoliidae are large, robust and hairy insects, many of which prey upon the grubs of chafers. Sphecoidea. — In this division are included the rest of the " digging- wasps," distinguished from the Vespoidea by the short pronotum not reaching backward to the tegulae. They have usually been reckoned as forming a single, very large family — the Sphegidae — but ten or twelve subdivisions of the group are regarded as distinct families by Ashmead and others. Great diversity is shown in the details of structure, habits and nature of the prey. Species of Sphex, studied by Fabre, provisioned their brood-chambers with crickets. Pelopoeus hunts spiders, while Ammophila catches cater- pillars for the benefit of her young. Fabre states that the last- rtamed insect uses a stone for the temporary closing of her burrow, and the Peckhams have seen a female Ammophila take a stone between her mandibles and use it as a hammer for pounding down the earth over her finished nest. The habits of Bembex are of especial interest. The female, instead of provisioning her burrow with a supply of food that will suffice the larva for its whole life, brings fresh flies with which she regularly feeds her young. In this instinct we have a correspondence with the habits of social wasps and bees. Yet it may be thought that the usual instinct of the " digging- wasps " to capture and store up food in an underground burrow for the benefit of offspring which they will never see is even more sur- prising. The habit of some genera is to catch the prey before making their tunnel, but more frequently the insect digs her nest, and then hunts for prey to put into it. Apoidea. — The bees which make up this group agree with the Sphecoidea in the short pronotum, but may be distinguished from all other Hymenoptcra by the widened first tarsal segment and the plumose hairs on head and body. They are usually regarded as forming a single family — the Apidae — but there is very great diversity in structural details, and Ashmead divides them into fourteen families. The " tongue," for example, is short and obtuse or emarginate in Colletes and Prosopis, while in all other bees it is pointed at the tip. But in Andrena and its allies it is comparatively short, while in the higher genera, such as Apis and Bombus, it is elongate and flexible, forming a most elaborate and perfect organ for taking liquid food. Bees feed on honey and pollen. Most of the genera are " solitary " in habit, the female sex being undifferenti- ated; but among the humble-bees and hive-bees we find, as in social wasps and ants, the occurrence of workers, and the consequent elaboration of a wonderful insect-society. (See Bee.) Bibliography. — The literature of several special families of the Hymenoptcra will be found under the articles Ant, Bee, Ichneumon- Fly, Wasp, &c, referred to above. Among earlier students on. structure may be mentioned P. A. Latreille, Families naturelles du regne animal (Paris, 1825), who recognized the nature of the " median segment." C. Gerstaecker (Arclu f. Nalurg. xx., 1867) and F. Brauer (Sitzb. K. Altai. Wiss. Wim. lxxxv., 1883) should also be consultsid on this subject. Fcr internal anatomy, specially the digestive organs, see L. Dufour, MZm, savants Strangers, vii. (1841), and Ann. Sci. Nat. Zool. (4), i. 1854. For nervous system H. Viallanes, Ann. Sci. Nat. Zool. (7), ii. iv. 1886-1887, and F. C. Kenyon, Journ. Comp. Neurol, vi., 1896. For poison and other glands, see L. Bordas, Ann. Sci. Nat. Zool. (7) xix., 1 895. For the sting and ovipositor H. Dewitz, Zeits. vAss. Zool. xxv., 1874, xxviii., 1877, and K. Zander, ih. Ixvi., l8oq. For male gcnj|al armature S. A. Peytoureau, Morphologic de Tarmure gtnitale des HYMETTUS— HYMNS 181 insectes (Bordeaux, 1895), and E. Zander, Zeits. wiss. Zool. lxvii., 1900. The systematic student of Hymenoptera is greatly helped by C. G. de Dalla Torre's Catalogus Hymenopterorum (10 vols., Leipzig, 1893-1902). For general classifications see F. W. Konow, Entom. Nachtr. (1897), and W. H. Ashmead, Proc. U.S. Nat. Mus. xxiii., 1901 ; the latter paper deals also especially with the Ichneu- monoidea of the globe. For habits and life histories of Hymenoptera see J. Lubbock (Lord Avebury), Ants, Bees and Wasps (9th ed., London, 1889); C. Janet, £tudes sur les fourmis, les gu&pes et les abeilles (Paris, &c, 1893 an d onwards); and G. W. and E. G. Peckham, Instincts and Habits of Solitary Wasps (Madison, Wis. U.S.A., 1898). Monographs of most of the families of British Hymenoptera have now been published. For saw-flies and gall- flies, see P. Cameron's British Phytophagous Hymenoptera (4 vols., London, Ray Soc, 1882-1893). For fchneumonoidea, C. Morley's Ichneumons of Great Britain (Plymouth, 1903, &c), and T. A. Marshall's " British Braconidae," Trans. Entom. Soc, 1885-1899. The smaller parasitic Hymenoptera have been neglected in this country since A. H. Hahday's classical papers Entom. Mag. i.-v., 1833-1838) but Ashmead's " North American Proctotrypidae " (Bull. U.S. Nat. Mus. xlv., 1893) is valuable for the European student. For the Fossores, wasps, ants and bees see E. Saunders, Hymenoptera Aculeata of the British Islands (London, 1896). Exhaustive refer- ences to general systematic works will be found inde Dalla Torre's Catalogue mentioned above. Of special value to English students are C. T. Bingham's Fauna of British India, " Hymenoptera " (London, 1897 and onwards), and P. Cameron's volumes on Hymenoptera in the Biologia Centrali- Americana. F. Smith's Catalogues of Hy- menoptera in the British Museum (London, J 853-1 859) are well worthy of study. (G. H. C.) HYMETTUS (Ital. Monte Matto, hence the modern name Trello Vouni), a mountain in Attica, bounding the Athenian plain on the S.E. Height, 3370 ft. It was famous in ancient times for its bees, which gathered honey of peculiar flavour from its aromatic herbs; their fame still persists. The spring mentioned by Ovid (Ars Amat. iii. 687) is probably to be re- cognized near the monastery of Syriani or Kaesariani on the western slope. This may be identical with that known as TLvKkov Tlijpa, said to be a remedy for barrenness in women. The marble of Hymettus, which often has a bluish tinge, was used extensively for building in ancient Athens, and also, in early times, for sculpture; but the white marble of Pentelicus was preferred for both purposes. See E. Dodwell, Classical and Topographical Tour (1819), i. 483. HYMNS.— 1. Classical Hymnody.— The word " hymn " (vlu/os) was employed by the ancient Greeks 1 to signify a song or poem composed in honour of gods, heroes or famous men, or to be recited on some joyful, mournful or solemn occasion. Polymnia was the name of their lyric muse. Homer makes Alcinous entertain Odysseus with a " hymn " of the minstrel Demodocus, on the capture of Troy by the wooden horse. The Works and Days of Hesiod begins with an invocation to the Muses to address hymns to Zeus, and in his Theogonia he speaks of them as singing or inspiring " hymns " to all the divinities, and of the bard as " their servant, hymning the glories of men of old, and of the gods of Olympus." Pindar calls by this name odes, like his own, in praise of conquerors at the public games of Greece. The Athenian dramatists (Euripides most frequently) use the word and its cognate verbs in a similar manner; they also describe by them metrical oracles and apophthegms, martial, festal and hymeneal songs, dirges and lamentations or incanta- tions of woe. Hellenic hymns, according to this conception of them, have come down to us, some from a very early and others from a late period of Greek classical literature. Those which passed by the name of Homer 2 were already old in the time of Thucydides. They are mythological poems (several of them long), in hexa- meter verse — some very interesting. That to Apollo contains a traditionary history of the origin and progress of the Delphic worship; those on Hermes and on Dionysus are marked by much liveliness and poetical fancy. Hymns of a like general character, but of less interest (though these also embody some fine poetical traditions of the Greek mythology, such as the story 'The history of the " hymn " naturally begins with Greece, but it may be found in some form much earlier; Assyria and Egypt have left specimens, while India has the Vedic hymns, and Confucius collected " praise songs " in China. 2 See Greek Literature. of Teiresias, and that of the wanderings of Leto), were written in the 3rd century before Christ, by Callimachus of Cyrene. Cleanthes, the successor of Zeno, composed (also in hexameters) an " excellent and devout hymn " (as it is justly called by Cudworth, in his Intellectual System) to Zeus, which is preserved in the Eclogae of Stobaeus, and from which Aratus borrowed the words, " For we are also His offspring," quoted by St Paul at Athens. The so-called Orphic hymns, in hexameter verse, styled TtKeral, or hymns of initiation into the " mysteries " of the Hellenic religion, are productions of the Alexandrian school, — as to which learned men are not agreed whether they are earlier or later than the Christian era. The Romans did not adopt the word " hymn "; nor have we many Latin poems of the classical age to which it can properly be applied. There are, however, a few — such as the simple and graceful " Dianae sumus in fide " (" Dian's votaries are we ") of Catullus, and " Dianam tenerae dicite virgines " (" Sing to Dian, gentle maidens ") of Horace-r— which approach much more nearly than anything Hellenic to the form and character of modern hymnody. 2. Hebrew Hymnody. — For the origin and idea of Christian hymnody we must look, not to Gentile, but to Hebrew sources. St Augustine's definition of a hymn, generally accepted by Christian antiquity, may be summed up in the words, " praise to God with song " ("cum cantico"); Bede understood the " canticum " as properly requiring metre; though he thought that what in its original language was a true hymn might retain that character in an unmetrical translation. Modern use has enlarged the definition; Roman Catholic writers extend it to the praises of saints; and the word now comprehends rhythmical prose as well as verse, and prayer and spiritual meditation as well as praise. The modern distinction between psalms and hymns is arbitrary (see Psalms). The former word was used by the LXX. as a generic designation, probably because it implied an accompani- ment by the psaltery (said by Eusebius to have been of very ancient use in the East) or other instruments. The cognate verb " psallere " has been constantly applied to hymns, both in the Eastern and in the Western Church; and the same com- positions which they described generically as " psalms " were also called by the LXX. "odes" (i.e. songs) and "hymns." The latter word occurs, e.g. in Ps. Ixxii. 20 ("the hymns of David the son of Jesse "), in Ps. lxv. 1, and also in the Greek titles of the 6th, 54th, 55th, 67th and 76th (this numbering of the psalms being that of the English version, not of the LXX.). The 44th chapter of Ecclesiasticus, " Let us now praise famous men," &c, is entitled in the Greek irarkpuv vlivos, " The Fathers' Hymn." Bede speaks of the whole book of Psalms as called " liber hymnorum," by the universal consent of Hebrews, Greeks and Latins. In the New Testament we find our Lord and His apostles singing a hymn (vixviiaavTes e^ffKdov), after the institution of the Lord's Supper; St Paul and Silas doing the same {ynvovv rdv Otbv) in their prison at Philippi; St James recommending psalm-singing (^aXXeno), and St Paul " psalms and hymns and spiritual songs " (\pa\ixols /cat vfivois (cot (jiSatj irvevixa.TiKo.li) St Paul also, in the 14th chapter of the first epistle to the Corin^ thians, speaks of singing (ij/akui) and of every man's psalm (e/cacrros vy£iv \f/a\iibv m a context which plainly has refer- ence to the assemblies of the Corinthian Christians for common worship. All the words thus used were applied by the LXX. to the Davidical psalms; it is therefore possible that these only may be intended, in the different places to which we have referred. But there are in St Paul's epistles several passages (Eph. v. 14; 1 Tim. iii. 16; 1 Tim. vi. 15, 16; 2 Tim. ii. 11,12) which have so much of the form and character of later Oriental hymnody as to have been supposed by Michaelis and others to be extracts from original hymns of the Apostolic age. Two of them are apparently introduced as quotations, though not found elsewhere in the Scriptures. A third has not only rhythm, but rhyme. The thanksgiving prayer of the assembled disciples, recorded in Acts iv., is both in substance and in manner poetical; I»2 HYMNS Then- peutae phonal Hinging. and in the canticles, " Magnificat," "Benedictus,". &c, which manifestly followed the form and style of Hebrew poetry, hymns or songs, proper for liturgical use, have always been recognized by the church. 3. Eastern Church Hymnody. — The hymn of our Lord, the precepts of the apostles, the angelic song at the nativity, and " Benedicite omnia opera " are referred to in a curious metrical prologue to the hymnary of the Mozarabic Breviary as preced- ents for the practice of the Western Church. In this respect, however, the Western Church followed the Eastern, in which hymnody prevailed frem the earliest times. Philo describes the Theraputae (q.v.) of the neighbourhood of Alexandria as composers of original hymns, which (as well as old) were sung at their great religious festivals — the people listening in silence till they came to the closing strains, or refrains, at the end of a hymn or stanza (the " acroteleutia " and " ephymnia "), in which all, women as well as men, heartily joined. These songs, he says, were in various metres (for which he uses a number of technical terms) ; some were choral, some not; and they were divided into variously constructed strophes or stanzas. Eusebius, who thought that the Theraputae were communities of Christians, says that the Christian practice of his own day was in exact accordance with this description. The practice, not only of singing hymns, but of singing them antiphonally, appears, from the well-known letter of Pliny to Trajan, to have been established in the Bithynian Anti- churches at the beginning of the 2nd century. They were accustomed " stato die ante lucem convenire, carmenque Christo, quasi Deo, dicere secum invicem." This agrees well, in point of time, with the tradition recorded by the historian Socrates, that Ignatius (who suffered martyr- dom about a.d. 107) wast led by a vision or dream of angels singing hymns in that manner to the Holy Trinity to introduce antiphonal singing into the church of Antioch, from which it quickly spread to other churches. There seems to be an allusion to choral singing in the epistle of Ignatius himself to the Romans, where he exhorts them," xop^s7«>^M«*t " (" having formed them- selves into a choir "), to " sing praise to the Father in Christ Jesus." A statement of Theodoret has sometimes been supposed to refer the origin of antiphonal singing to a much later date; but this seems to relate only to the singing of Old Testament Psalms (rr\v AavtSmiiv nt\w IXapov ayias 56£tjs " — translated by Canon Bright " Light of Gladness, Beam Divine "), holds its place to this day in the services of the Greek rite. In the 3rd century Origen seems to have had in his mind the words of some other hymns or hymn of like character, when he says (in his treatise Against Celsus): "We glorify in hymns God and His only begotten Son; as do also the Sun, the Moon, the Stars and all the host of heaven. All these, in one Divine chorus, with the just among men, glorify in hymns God who is over all, and His only begotten Son." So highly were these compositions esteemed in the Syrian churches that the council which deposed Paul of Samosata from the see of Antioch in the time of Aurelian justified that act, in its synodical letter to the bishops of Rome and Alexandria, on this ground (among others) that he had prohibited the use of hymns of that kind, by uninspired writers, addressed to Christ. After the conversion of Constantine, the progress of hymnody became closely connected with church controversies. There had been in Edessa, at the end of the 2nd or early in the 3rd century, a Gnostic writer of conspicuous ability, named Barde- sanes, who was succeeded, as the head of his sect or school, by his son Harmonius. Both father and son wrote hymns, and set them to agreeable melodies, which acquired, and in the 4th century still retained, much local popularity. Ephraem Syrus, the first voluminous hymn-writer whose works remain to us, thinking that the same melodies might be made useful to the faith, if adapted to more orthodox words, composed to them a large number of hymns in the Syriac language, principally in tetrasyllabic, pentasyllabic and heptasyllabic metres, divided into strophes of from 4 to 12,16 and even 20 lines each. When a strophe contained five lines, the fifth was generally an " ephymnium," detached in sense, and consisting of a prayer, invocation, doxology or the like, to be sung antiphonally, either in full chorus or by a separate part of the choir. The Syriac Chrestomathy of August Hahn (Leipzig, 1825), and the third volume of H. A. Daniel's Thesaurus Hymnologicus (Leipzig, 1841-1856), contain specimens of these hymns. Some of them have been translated into (unmetrical) English by the Rev. Henry Burgess {Select Metrical Hymns of Ephrem Syrus, &c, 1853). A considerable number of those so translated are on subjects connected with death, resurrection, judgment, &c, and display not only Christian faith and hope, but much sim- plicity and tenderness of natural feeling. Theodoret speaks of the spiritual songs of Ephraem as very sweet and profitable, and as adding much, in his (Theodoret's) time, to the brightness of the commemorations of martyrs in the Syrian Church. The Greek hymnody contemporary with Ephraem followed, with some licence, classical models. One of its favourite metres was the Anacreontic; but it also made use of the short anapaestic, Ionic, iambic and other lyrical measures, as well as the hexameter and pentameter. Its principal authors were Methodius, bishop of Olympus, who died about a.d. 311, Synesius, who became bishop of Ptolemais in Cyrenaica in 410, and Gregory Nazianzen, for a short time (380-381) patriarch of Constantinople. The merits of these writers have been perhaps, too much depreciated by the admirers of the later Greek " Melodists." They have found an able English translator in the Rev. Allen Chatfield (Songs and Hymns of Earliest Greek Christian Poets, London, 1876). Among the most striking of their works are nv&eo Xpicrk ("Lord Jesus, think of me"), by Synesius; olrbv a.diTOv ixovapxyv (" Thou, the One Supreme") andrio-oi 0e\£« yev'todat. ("0 soul of mine, repining"), byGregory; also Avwdtv irapOkvoi (" The Bridegroom cometh "), by Methodius. There continued to be Greek metrical hymn- writers, in a similar style, till a much later date. Sophronius, patriarch of Jerusalem HYMNS 183 coatro' versy. in tbe 7th century, wrote seven Anacreontic hymns; and St John Damascene, one of the most copious of the second school of '' Melodists," was also the author of some long compositions in trimeter iambics. An important development of hymnody at Constantinople arose out of the Arian controversy. Early in the 4th century Period Athanasius had rebuked, not only the doctrine of Alius, at Arian but the light character of certain hymns by which he endeavoured to make that doctrine popular. When, towards the close of that century (398), St John Chrysostom was raised to the metropolitan see, the Arians, who were still numerous at Constantinople, had no places of worship within the walls; but they were in the habit of coming into the city at sunset on Saturdays, Sundays and the greater festivals, and congregating in the porticoes and other places of public resort, where they sung, all night through, antiphonal songs, with " acroteleutia " (closing strains, or refrains), ex- pressive of Arian doctrine, often accompanied by taunts and insults to the orthodox. Chrysostom was apprehensive that this music might draw some of the simpler church people to the Arian side; he therefore organized, in opposition to it, under the patronage and at the cost of Eudoxia, the empress of Arcadius (then his friend), a system of nightly processional hymn-singing, with silver crosses, wax-lights and other circumstances of ceremonial pomp. Riots followed, with bloodshed on both sides, and with some personal injury to the empress's chief eunuch, who seems to have officiated as conductor or director of the church musicians. This led to the suppression, by an imperial edict, of all public Arian singing; while in the church the practice of nocturnal hymn-singing on certain solemn occasions, thus first introduced, remained an established institution. It is not improbable that some rudiments of the peculiar system of hymnody which now prevails throughout the Greek communion, and whose affinities are rather to the 0nek Hebrew and Syriac than to the classical forms, may hymnody. have existed in the church of Constantinople, even at that time. Anatolius, patriarch of Constantinople in the middle of the 5th century, was the precursor of that system; but the reputation of being its proper founder belongs to Romanos, of whom little more is known than that he wrote hymns still extant, and lived towards the end of that century. The importance of that system in the services of the Greek church may be understood from the fact that Dr J. M. Neale computed four-fifths of the whole space (about 5000 pages) contained in the different service-books of that church to be occupied by hymnody, all in a language or dialect which has ceased to be anywhere spoken. The system has a peculiar technical terminology, in which the words " troparion," " ode," " canon " and " hirmus " («Ip/n,s) chiefly require explanation. The troparion is the unit of the system, being a strophe or stanza, seen, when analysed, to be divisible into verses or clauses, with regulated caesuras, but printed in the books as a single prose sentence, without marking any divisions. The following (turned into English, from a " canon ' by John Mauropus) may be taken as an example: " The never-sleeping Guardian, | the patron of my soul, | the guide of my life, | allotted me by God, | I hymn thee, Divine Angel | of Almighty God." Dr Neale and most other writers regard all these " troparia " as rhythmical or modulated prose. Cardinal J. B. Pitra, on the other hand, who in 1867 and 1876 published two learned works on this subject, maintains that they are really metrical, and governed by definite rules of prosody, of which he lays down sixteen. According to him, each " troparion " contains from three to thirty-three verses; each verse varies from two to thirteen syllables, often in a continuous series, uniform, alternate or recip- rocal, the metre being always syllabic, and depending, not on the quantity of vowels or the position of consonants, but on an harmonic series of accents. In various parts of the services solitary troparia are sung, under various names, " contacion," " oecos," " cathisma," &c, which mark distinctions either in their character or in their use. An ode is a song or hymn compounded of several similar "troparia," — usually three, four or five. To these is always prefixed a typical or standard " troparion," called the hirmus, by which the syllabic measure, the periodic series of accents, and in fact the whole structure and rhythm of the stanzas which follow it are regulated. Each succeeding " troparion " in the same " ode " contains the same number of verses, and of syllables in each verse, and similar accents on the same or equivalent syllables. The " hirmus " may either form the first stanza of the " ode " itself, or (as is more frequently the case) may be taken from some other piece; and, when so taken, it is often indicated by initial words only, without being printed at length. It is generally printed within commas, after the proper rubric of the " ode." A hymn in irregular " stichera " or stanzas, without a " hirmus," is called " idiomelon." A system of three or four odes is " triodion " or " tetraodion." A canon is a system of eight (theoretically nine) connected odes, the second being always suppressed. Various pauses, relieved by the interposition of other short chants or readings, occur during the singing of a whole "canon." The final "troparion" in each ode of the series is not unfrequently detached in sense (like the " ephymnia " of Ephraem Syrus), particularly when it is in the (very common) form of a " theotokion," or ascription of praise to the mother of our Lord, and when it is a recurring refrain or burden. There were two principal periods of Greek hymnography constructed on these principles— the first that of Romanos and his followers, extending over the 6th and 7th centuries, the second that of the schools which arose during the Iconoclastic controversy in the 8th century, and which continued for some centuries afterwards, until the art itself died out. The works of the writers of the former period were collected in Tropologia, or church hymn-books, which were held in high esteem till the 10th century, when they ceased to be regarded as church-books, and so fell into neglect. ij m aDOS , They are now preserved only in a very small number of manuscripts. From three of these, belonging to public libraries at Moscow, Turin and Rome, Cardinal Pitra has printed, in his Analecta, a number of interesting examples, the existence of which appears to have been unknown to Dr Neale, and which, in the cardinal's estimation, are in many respects superior to the " canons," &c, of the modern Greek service-books, from which all Neale's translations (except some from Anatolius) are taken. Cardinal Pitra's selections include twenty-nine works by Romanos, and some by Sergius, and nine other known, as well as some unknown, authors. He describes them as having generally a more dramatic character than the " melodies " of the later period, and a much more animated style; and he supposes that they may have been originally sung with dramatic accompaniments, by way of substitution for the theatrical performances of Pagan times. As an instance of their peculiar character, he mentions a Christmas or Epiphany hymn by Romanos, in twentyrfive long strophes, in which there is, first, an account of the Nativity and its accompanying wonders, and then a dialogue between the wise men, the Virgin mother and Joseph. The magi arrive, are admitted; describe the moral and religious condition of Persia and the East, and the cause and adventures of their journey, and then offer their gifts. The Virgin intercedes for them with her Son, instructs them in some parts of Jewish history, and ends with a prayer for the salvation of the world. The controversies and persecutions of the 8th and succeeding centuries turned the thoughts of the " melodists " of the great monasteries of the Studium at Constantinople and M . .. . St Saba in Palestine and their followers, and those of the adherents of the Greek rite in Sicily and South Italy (who suffered much from the Saracens and the Normans), into a less picturesque but more strictly theological course; and the influence of those controversies, in which the final success of the cause of " Icons " was largely due to the hymns, as well as to the courage and sufferings, of these confessors, was probably the cause of their supplanting, as they did, the works of the older school. Cardinal Pitra gives them the praise of having discovered a graver and more solemn style of chant, and of having 'done much to fix the dogmatic theology of their church upon its present lines of near approach to the Roman. Among the " melodists " of this latter Greek school there were many saints of the Greek church, several patriarchs and two emperors — Leo the Philosopher, and Constantine Porphyrogenitus, his son. Their greatest poets were Theodore and Joseph of the Studium, and Cosmas and John (called Damascene) of St Saba. Neale translated into English verse several selected portions, or centoes, from the works of these and others, together with four selections from earlier works bv 184 HYMNS Anatolius. Some of his translations — particularly " The day is past and over," from Anatolius, and " Christian, dost thou see them," from Andrew of Crete — have been adopted into hymn- books used in many English churches; and the hymn " Art thou weary," which is rather founded upon than translated from one by Stephen the Sabaite, has obtained still more general popularity. 4. Western Church Hymnody. — It was not till the 4th century that Greek hymnody was imitated in the West, where its intro- duction was due to two great lights of the Latin Church — St Hilary of Poitiers and St Ambrose of Milan. Hilary was banished from his see of Poitiers in 356, and was absent from it for about four years, which he spent in Asia Minor, taking part during that time in one of the councils of the Eastern Church. He thus had full opportunity of becoming acquainted with the Greek church music of that day; and he wrote (as St Jerome, who was thirty years old when Hilary died, and who was well acquainted with his acts and writings, and spent some time in or near his diocese, informs us) a " book of hymns," to one of which Jerome particularly refers, in the preface to the second book of his own commentary on the epistle to the Galatians. Isidore, archbishop of Seville, who presided over the fourth council of Toledo, in his book on the offices of the church, speaks of Hilary as the first Latin hymn- writer; that council itself, in its 13th canon, and the prologue to the Mozarabic hymnary (which is little more than a versification of the canon), associate his name, in this respect, with that of Ambrose. A tradition, ancient and widely spread, ascribed to him the authorship of the remarkable " Hymnum dicat turba fratrum, hymnum cantus personet " (" Band of brethren, raise the hymn, let your song the hymn resound "), which is a succinct narrative, in hymnal form, of the whole gospel history; and is perhaps the earliest example of a strictly didactic hymn. Both Bede and Hincmar much admired this composition, though the former does not mention, in connexion with it, the name of Hilary. The private use of hymns of such a character by Christians in the West may probably have preceded their ecclesiastical use; for Jerome says that in his day those who went into the fields might hear " the ploughman at his hallelujahs, the mower at his hymns, and the vine-dresser singing David's psakns." Besides this, seven shorter metrical hymns attributed to Hilary are still extant. Of the part taken by Ambrose, not long after Hilary's death, in bringing the use of hymns into the church of Milan, we have a contemporary account from his convert, St Augustine. Justina, mother of the emperor Valentinian, favoured the Arians, and desired to remove Ambrose from his see. The " devout people," of whom Augustine's mother, Monica, was one, combined to protect him, and kept guard in the church. " Then," says Augustine, " it was first appointed that, after the manner of the Eastern churches, hymns and psalms should be sung, lest the people should grow weary and faint through sorrow; which custom has ever since been retained, and has been followed by almost all congregations in other parts of the world." He describes himself as moved to tears by the sweetness of these "hymns and canticles": — "The voices flowed into my ears; the truth distilled into my heart; I overflowed with devout affections, and was happy." To this time, according to an uncertain but not improbable tradition which ascribed the composition of the " Te Deum " to Ambrose, and connected it with the conversion of Augustine, is to be referred the com- mencement of the use in the church of that sublime" unmetrical hymn. It is not, however, to be assumed that the hymnody "thus introduced by Ambrose was from the first used according to the precise order and method of the later Western ritual. To bring it into (substantially) that order and method appears to have been the work of St Benedict. Walafrid Strabo, the earliest ecclesi- astical writer on this subject (who lived at the beginning of the 9th century), says that Benedict, on the constitution of the religious order known by his name (about 530), appointed the Ambrosian hymns to be regularly sung in his offices for the canonical hours. Hence probably originated the practice of the Italian churches, and of others which followed their example, to sing certain hymns (Ambrosian, or by the early successors of the Ambrosian school) daily throughout the week, at " Vespers," " Lauds " and " Nocturns," and on some days at " Compline " also — varying them with the different ecclesiastical seasons and festivals, commemorations of saints and martyrs and other special offices. Different dioceses and religious houses had their own peculiarities of ritual, including such hymns as were approved by their several bishops or ecclesiastical superiors, varying in detail, but all following the same general method. The national rituals, which were first reduced into a form substantially like that which has since prevailed, were probably those of Lom- bardy and of Spain, now known as the " Ambrosian " and the "Mozarabic." The age and origin of the Spanish ritual are uncertain, but it is mentioned in the 7th century by Isidore, bishop of Seville. It contained a copious hymnary, the original form of which may be regarded as canonically approved by the fourth council of Toledo (633). By the 13th canon of that council, an opinion (which even then found advocates) against the use in churches of any hymns not taken from the Scriptures — apparently the same opinion which had been held by Paul of Samosata — was censured; and it was ordered that such hymns should be used in the Spanish as well as in the Gallican churches, the penalty of excommunication being denounced against all who might presume to reject them. The hymns of which the use was thus established and authorized were those which entered into the daily and other offices of the church, afterwards collected in the " Breviaries "; in which the hymns " proper " for " the week," and for "the season," continued for many centuries, with very few exceptions, to be derived from the earliest epoch of Latin Church poetry — reckoning that epoch as extending from Hilary and Ambrose to the end of the pontificate of Gregory the Great. The " Ambrosian " music, to which those hymns were generally sung down to the time of Gregory, was more popular and con- gregational than the " Gregorian," which then came into use, and afterwards prevailed. In the service of the mass it was not the general practice, before the invention of sequences in the 9th century, to sing any hymns, except some from the Scriptures esteemed canonical, such as the " Song of the Three Children " (" Benedicite omnia opera "). But to this rule there were, according to Walafrid Strabo, some occasional exceptions; particularly in the case of Paulinus, patriarch of Aquileia under Charlemagne, himself a hymn-writer, who frequently used hymns, composed by himself or others, in the eucharistic office, especially in private masses. Some of the hymns called " Ambrosian " (nearly 100 in number) are beyond all question by Ambrose himself, and the rest probably belong to his time or to the following century. Four, those beginning " Aeterne rerum conditor " (" Dread Framer of the earth and sky "), " Deus Creator omnium " (" Maker of all things, glorious God "), " Veni Re'demptor Gentium " (" Redeemer of the nations, come ") and " Jam surgit hora tertia " (" Christ at this hour was crucified "), are quoted as works of Ambrose by Augustine. These, and others by the hand of the same master, have the qualities most valuable in hymns intended for congregational use. They are short and complete in themselves; easy, and at the same time elevated in their expression and rhythm; terse and masculine in thought and language; and (though sometimes criticized as deficient in theological precision) simple, pure and not technical in their, rendering of the great facts and doctrines of Christianity, which they present in an objective and not a subjective manner. They have exercised a powerful influence, direct or indirect, upon many of the best works of the same kind in all succeeding generations. With the Ambrosian hymns are properly classed those of Hilary, and the contemporary works of Pope Damasus I. (who wrote two hymns in commemoration of saints), and of Prudentius, from whose Caihc-merina (" Daily Devotions ") and Peristephana (" Crown-songs for Martyrs "), all poems of considerable, some of great length — about twenty-eight hymns. HYMNS 185 found in various Breviaries, were derived. Prudentius was a layman, a native of Saragossa, and it was in the Spanish ritual that his hymns were most largely used. In the Mozarabic Breviary almost the whole of one of his finest poems (from which most churches took one part only, beginning " Corde natus ex parentis ") was appointed to be sung between Easter and Ascension-Day, being divided into eight or nine hymns; and on some of the commemorations of Spanish saints long poems from his Peristephana were recited or sung at large. He is entitled *o a high rank among Christian poets, many of the hymns taken from his works being full of fervour and sweetness, and by no means deficient in dignity or strength. These writers were followed in the 5th and early in the 6th century by the priest Sedulius, whose reputation perhaps exceeded his merit; Elpis, a noble Roman lady 5 Differ- entials. 7. In the" process of § 4 the increment Ay is not in general equal to the product of the increment Ax and the derived function /'(x). In general we can write down an equation of the form Ay=/'(x)Ax+R, in which R is different from zero when Ax is different and then we have not only from lim. but also ,R=o, R lim -A*,o^ = °- We may separate Ay into two parts: the part fix) Ax and the part R. The part/'(x) Ax alone is useful for forming the differential coefficient, and it is convenient to give it a name. It is calledthe differential of f(x), and is written df(x), or dy when y is written for /(x). When this notation is adopted dx is written instead of Ax, and is called the " differential of x," so that we have df(x)=f'(x)dx. Thus the differential of an independent variable such as x is a finite difference; in other words it is any number we please. The differ- ential of a dependent variable such as y, or of a function of the independent variable x, is the product of the differential of x and the differential coefficient or derived function. It is important to observe that the differential coefficient is not to be defined as the ratio of differentials, but the ratio of differentials is to be defined as the previously introduced differential coefficient. The differentials NATURE] INFINITESIMAL CALCULUS 537 are either finite differences, or are so much of certain finite differences as are useful for forming differential coefficients. Again let F(x) be the indefinite integral of a continuous function /(.v), so that we have ^T = /(*), JV*)d* = F(»-F(o). When the points M of the process explained in § 5 are inserted be- tween the points whose abscissae are a and b, we may take them to be w — I in number, so that the segment AB is divided into n seg- ments. Let Xi, X2, . . . x n -i be the abscissae of the points in order. The integral is the limit of the sum f(a) {x l -a)+f(x t ) {xn-Xi)+. . .+f(x r ) (x r+ i-x r ) + . . . +/(£„_i)(6-x„_i), every term of which is a differential of the form f(x)dx. Further the integral is equal to the sum of differences jF(.v,)-F(o)!+jF(x !i )-F(* 1 ))+ ... +{F(* r+1 )-F(* r )j + ... +|F(i)-F(* ltJ )|, for this sum is F(6)— F(o). Now the difference FOxv+i) — F(* r ) is not equal to the differential i{x r ) (x T+ i— x r ), but the sum of the differences is equal to the limit of the sum of these differentials. The differential may be regarded as so much of the difference as is required to form the integral. From this point of view a differential is called a differential element of an integral, and the integral is the limit of the sum of differential elements. In like manner the differ- ential element ydx of the area of a curve (§ 5) is not the area of the portion contained between two ordinates, however near together, but is so much of this area as need be retained for the purpose of finding the area of the curve by the limiting process described. 8. The notation of the infinitesimal calculus is intimately bound up with the notions of differentials and sums of elements. The letter N tail n " d " ' s the initial letter of the word differentia (difference) and the symbol "/ " is a conventionally written " S," the initial letter of the word summa (sum or whole). The notation was introduced by Leibnitz (see §§ 25-27, below). 9. The fundamental artifice of the calculus is the artifice of forming differentials without first forming differential coefficients. From an F ada- equation containing x and y we can deduce a new equation, mental containing also Ax and Ay, by substituting x+Ax for x Artifice an ^ y^r^y Ior V- I £ there is a differential coefficient of y with respect to x, then Ay can be expressed in the form ^.Ax+R, where lim. A;l . = o(R/Ax)=o, as in § 7 above. The artifice consists in rejecting ab initio all terms of the equation which belong to R. We do not form R at all, but only 0.Ax, or <£. dx, which is the differential dy. In the same way, in all applications of the integral calculus to geometry or mechanics we form the element of an integral in the same way as the element of area y. dx is formed. In fig. 3 of § 5 the element of area y. dx is the area of the rectangle RM. The actual area of the curvilinear figure PQNM is greater than the area of this rectangle by the area of the curvilinear figure PQR ; but the excess is less than the area of the rectangle PRQS, which is measured by the product of the numerical measures of MN and QR, and we have MN.QR -0 lim. MN-0 MN Thus the artifice by which differential elements of integrals are formed is in principle the same as that by which differentials are formed without first forming differential coefficients. 10. This principle is usually expressed by introducing the notion of orders of small quantities. If x, y are two variable numbers which are Onfers of connected together by any relation, and if when x tends to small zero y a ' s0 tends to zero, the fraction y/x may tend to a finite limit. In this case x and y are said to be " of the same order." When this is not the case we may have quantities, either Vim -x=0y =O < lim. x=0 - = o. (iii.) For a product uv d{uv) dx du dx +v Tx I du dv\ I , = \ v dx~ u r x ) r- (iv.) For a quotient ujv djulv) dx (v.) For a function of a function, that is to say, for a function y expressed in terms of a variable 2, which is itself expressed as a function of x, dy_dy dz_ dx~ dz' dx' In addition to these formal rules we have particular results as to the differentiation of simple functions. The most important results are written down in the following table: — In the former case y is said to be " of a lower order " than x; in the latter case y is said to be " of a higher order " than x. In accordance with this notion we may say that the fundamental artifice of the infinitesimal calculus consists in the rejection of small quantities of an unnecessarily high order. This artifice is now merely an incident in the conduct of a limiting process, but in the 17th century, when limiting processes other than the Greek methods for quadratures were new, the introduction of the artifice was a great advance. 11. By the aid of this artifice, or directly by carrying out Kales of the appropriate limiting processes, we may obtain the Dltteren- rules by which differential coefficients are formed. These tlatlon. rules may Declassified as " formal rules " and " particular results." The formal rules may be stated as follows: — (i.) The differential coefficient of a constant is zero. (ii.) For a sum u-\-v+ . . . +2, where u, v, . . .are functions of x, d(u-\-v-\- . . . +z) du dv dz —+■■■ +2? y dy dx x n nx"' 1 for all values of n \og a X x~ l log a e a x a" log«a sin x cos X cos X — sin x sin~ x £ (1 -*»)-! tan" 4 * (1+* 2 )- 1 Each of the formal rules, and each of the particular results in the table, is a theorem of the differential calculus. All functions (or rather expressions) which can be made up from those in the table by a finite number of operations of addition, subtraction, multiplication or division can be differentiated by the formal rules. All such func- tions are called explicit functions. In addition to these we have implicit functions, or such as are determined by an equation contain- ing two variables when the equation cannot be solved so as to exhibit the one variable expressed in terms of the other. We have also functions of several variables. Further, since the derived function of a given function is itself a function, we may seek to differentiate it, and thus there arise the second and higher differential coefficients. We postpone for the present the problems of differential calculus which arise from these considerations. Again, we may have explicit functions which are expressed as the results of limiting operations, or by the limits of the results obtained by performing an infinite number of algebraic operations upon the simple functions. For the problem of differentiating such functions reference may be made to Function. The processes of the integral calculus consist largely in trans- formations of the functions to be integrated into such forms that they can be recognized as differential co- efficients of functions which have previously been differ- entiated. Corresponding to the results in the table of have those in the following table : — Indefinite Integrals. I 11 we /(*) ff{x)dx x n x n+1 n-\- 1 for all values of n except — 1 I X log e x e" x a -l e ax cos x sin x sin x —cos X (cfi-x*)- 1 * • -1* sin '-- a 1 1 i 1 x - tan ' - a a , where a is the radius of the auxiliary circle, and is the angle ACp, that is the eccentric angle of P on the ellipse. The area ASP bears to the area ASp the ratio of the minor to the major axis, a result known to Archimedes. Thus Kepler's radii are spaced according to the rule that the eccentric angles of their ends are equidifferent, and his " sum of radii " is proportional to the expression which we should now write ) ffa+ae cos 4>)d, where e is the eccentricity. Kepler evaluated the sum as proportional to -\-e sin . Kepler soon afterwards occupied himself with the volumes of solids. The vintage of the year 1612 was extraordinarily abundant, and the question of the cubic content of wine casks was brought under his notice. This fact accounts for the title of his work, Nova stereometria doliorum; accessit stereometriae Archimedeae supplementum (1615). In this treatise he regarded solid bodies as being made up, as it were {veluti), of " infinitely " many " infinitely " small cones or " infinitely " thin disks, and he used the notion of summing the areas of the disks in the way he had previously used the notion of summing the focal radii of an ellipse. 14. In connexion with the early history of the calculus it must not be forgotten that the method by which logarithms were invented (1614) was effectively a method of infinitesimals. Natural logarithms were not invented as the indices of a certain base, and the notation e for the base was first introduced by Euler more than a century after the invention. Logarithms were introduced as numbers which increase in arithmetic progression when other related numbers increase in geometric progression. The two sets of numbers were supposed to increase together, one at a uniform rate, the other at a variable rate, and the increments were regarded for purposes of calculation as very small and as accruing discontinuously. 15. Kepler's methods of integration, for such they must be called, were the origin of Bonaventura Cavalieri's theory of Cava- the summation of indivisibles. The notion of a lierPs continuum, such as the area within a closed curve, '"*" as being made up of indivisible parts, " atoms " of area, if the expression may be allowed, is traceable to the speculations of early Greek philosophers; and although the nature of continuity was better understood by Aristotle and many other ancient writers yet the unsound atomic concep- tion was revived in the 13th century and has not yet been finally uprooted. It is possible to contend that Cavalieri did not himself hold the unsound doctrine, but his writing on this point is rather obscure. In his treatise Geometria indivisibilibus continuorutn nova quadam ratione promota (1635) he regarded Logar- ithms. J: a plane figure as generated by a line moving so as to be always parallel to a fixed line, and a solid figure as generated by a plane moving so as to be always parallel to a fixed plane; and he compared the areas of two plane figures, or the volumes of two solids, by determining the ratios of the sums of all the indivisibles of which they are supposed to be made up, these indivisibles being segments of parallel lines equally spaced in the case of plane figures, and areas marked out upon parallel planes equally spaced in the case of solids. By this method Cavalieri was able to effect numerous integrations relating to the areas of portions of conic sections and the volumes generated by the revolution of these portions about various axes. At a later date, and partly in answer to an attack made upon him by Paul Guldin, Cavalieri published a treatise entitled Exercitationes geometricae sex (1647), in which he adapted his method to the determination of centres of gravity, in particular for solids of variable density. Among the results which he obtained is that which we should now write ! X m+l x m dx - — q— 1 {m integral) . He regarded the problem thus solved as that of determining the sum of the flrth powers of all the lines drawn across a parallelogram parallel to one of its sides. At this period scientific investigators communicated their results to one another through one or more intermediate persons. Such intermediaries were Pierre de Carcavy and Pater Marin Mersenne; and among the writers thus so *^of in communication were Bonaventura Cavalieri, Cavalieri. Christiaan Huygens, Galileo Galilei, Giles Personnier de Roberval, Pierre de Fermat, Evangelista Torricelli, and a little later Blaise Pascal; but the letters of Carcavy or Mersenne would probably come into the hands of any man who was likely to be interested in the matters discussed. It often happened; that, when some new method was invented, or some new result obtained, the method or result was quickly known to a wide circle, although it might not be printed until after the lapse of a long time. When Cavalieri was printing his two treatises there was much discussion of the problem of quadratures. Roberval (1634) regarded an area as made up of " infinitely " many " infinitely " narrow strips, each of which may be con- sidered to be a rectangle, and he had similar ideas in regard to lengths and volumes. He knew how to approximate to the quantity which we express by J x m dx by the process of forming the sum m + l m +2 m + ... (w-l) m n m+1 ' and he claimed tobe able to prove that this sum tends to x/(m-\-i), as n increases for all positive integral values of m. The method of integrating x m by forming this sum was found also p e rmat's by Fermat (1636), who stated expressly that he method of arrived at it by generalizing a method employed by , 'j te x r * m Archimedes (for the cases m = 1 and m = 2) in his books on Conoids and Spheroids and on Spirals (see T. L. Heath, The Works of Archimedes, Cambridge, 1897). Fermat extended the result to the case where m is fractional (1644), and to the case where m is negative. This latte r extension and the proofs were given in his memoir, Proportionis geometricae in quadrandis parabolis et hyperbolis usus, which appears to have received a final form before 1659, although not published until 1679. Fermat did not use fractional or negative indices, but he regarded his problems as the quadratures of parabolas and hyperbolas of various orders. His method was to divide the interval of integration into parts by means of intermediate points the ab- scissae of which are in geometric progression. . In the process of § s above, the points M must be chosen according to this rule. This restrictive condition being understood, we may say that Fermat's formulation of the problem of quadratures is the same as our definition of a definite integral. The result that the problem of quadratures could be solved for any curve whose equation could be expressed in the form y — x m (m=E — i), or in the form y = aiX m i+aix m 2-\- ... +a„x m », HISTORY] INFINITESIMAL CALCULUS 539 where none of the indices is equal to — i , was used by John Wallis in his Arithmetica inftnitorum (1655) as well as by Fermat (1659). The case in which m= — 1 was that of the Various ordinary rectangular hyperbola; and Gregory of tions. St Vincent in his Opus geometricum quadraturae circuit et sectionum coni (1647) had proved by the method of exhaustions that the area contained between the curve, one asymptote, and two ordinates parallel to the other asymptote, increases in arithmetic progression as the distance between the ordinates (the one nearer to the centre being kept fixed) increases in geometric progression. Fermat described his method of integration as a logarithmic method, and thus it is clear that the relation between the quadrature of the hyperbola and logarithms was understood although it was not expressed analytically. It was not very long before the relation was used for the calculation of logarithms by Nicolaus Mercator in his Logarithmotechnia (1668). He began by writing the equation of the curve in the form y=i/(i+x), expanded this expression in powers of x by the method of division, and in- tegrated it term by term in accordance with the well-understood rule for finding the quadrature of a curve given by such an equation as that written at the foot of p. 325. By the middle of the 17th century many mathematicians could perform integrations. Very many particular results had Integra- been obtained, and applications of them had been tiott before made to the quadrature of the circle and other conic the integral sections, and to various problems concerning the us ' lengths of curves, the areas they enclose, the volumes and superficial areas of solids, and centres of gravity. A systematic account of the methods then in use was given, along with much that was original on his part, by Blaise Pascal in his Leltres de A mos Deltonville sur quelques-unes de ses inventions en giometrie (1659). 16. The problem of maxima and minima and the problem of tangents had also by the same time been effectively solved. Fermat' s Oresme in the 14th century knew that at a point where methods of the ordinate of a curve is a maximum or a minimum Dffieren- it s variation from point to point of the curve is slowest ; ind Kepler in the Stereometria doliorum remarked that at the places where the ordinate passes from a smaller value to the greatest value and then again to a smaller value, its variation becomes insensible. Fermat in 1629 was in possession of a method which he then communicated to one Despagnet of Bordeaux, and which he referred to in a letter to Roberval of 1636. He communicated it to Rene Descartes early in 1638 on receiving a copy of Descartes's Gecmetrie (1637), and with it he sent to Descartes an account of his methods for solving the problem of tangents and for determining centres of gravity. Fermat's method for maxima and minima is essentially our method. Expressed in a more modern notation, what he did was to begin by connecting the ordinate y and the abscissa x of a point of a curve by an equation which holds at all points of the curve, then to subtract the value of y in terms of x from the value ob- tained by substituting x+E for x, then to divide the difference by E, to put E=o in the quotient, and to equate the quotient to zero. Thus he differentiated with respect to x and equated the differential coefficient to zero. Fermat's method for solving the problem of tangents may be explained as follows: — Let (x, y) be the coordinates of a point P of a curve, (x', y'), those of a neighbouring point P' on the tangent at P, and let MM' = E (fig. 6). From the similarity of the triangles P'TM', PTM we have y':A-E = y :A, where A denotes the subtangent TM. The point P' being near the curve, we may substitute in the equation of the curve x — E for x and (yA — yE)/A for y. The equation of the curve is approximately satisfied. If it is taken to be satisfied exactly, the result is an equation of the form tb(x, y. A, E)=o, the left-hand member of which is divisible by E. Omitting the factor E, and putting E=o in the remaining factor, we have an equation which gives A. In this problem of tangents also Fermat found the required result by a process equivalent to differentiation. . Fermat gave several examples of the application of his method ; among them was one in which he showed that he could differ- entiate very complicated irrational functions. For such functions his method was to begin by obtaining a rational equation. In rationalizing equations Fermat, in other writings, used the device of introducing new variables, but he did not use this device to simplify the process of differentiation. Some of his results were published by Pierre Herigone in his Supple- mentum cursus mathematici (1642). His communication to Descartes was not published in full until after his death (Fermat, Opera varia, 1679). Methods similar to Fermat's were devised by Ren6 de Sluse (1652) for tangents, and by Johannes Hudde (1658) for maxima and minima. Other methods for the solution of the problem of tangents were devised by Roberval and Torricelli, and published almost simultaneously in 1644. These methods were founded upon the composition of motions, the theory of which had been taught by Galileo (1638), and, less completely, by Roberval (1636). Roberval and Torricelli could construct the tangents of many curves, but they did not arrive at Fermat's artifice. This artifice is that which we have noted in §10 as the fundamental artifice of the infinitesimal calculus. 17. Among the comparatively few mathematicians who before 1665 could perform differentiations was Isaac Barrow. In his book entitled Lectiones opticae et geometricae, Barrow's written apparently in 1663, 1664, and published in Differ- 1669, 1670, he gave a method of tangents like that ^ntiai of Roberval and Torricelli, compounding two velocities """xte- in the directions of the axes of x and y to obtain a resultant along the tangent to a curve. In an appendix to this book he gave another method which differs from Fermat's in the introduc- tion of a differential equivalent to our dy as well as dx. Two neighbouring ordinates PM and QN of a curve (fig. 7) are regarded as containing an inde- finitely small {indefinite parwm) arc, and PR is drawn parallel to the axis of x. The tangent PT at P is regarded as identical with the secant PQ, and the position of the tangent is determined by the similarity of the triangles PTM, PQR. The increments QR, PR of the ordinate and abscissa are denoted by a and e; and the ratio of a to e is determined by substituting x-\-e for x and y-\-a for y in the equation of the curve, rejecting all terms which are of order higher than the first in a and e, and omitting the terms which do not contain a or e. This process is equivalent to differentiation. Barrow appears to have invented it himself, but to have put it into his book at Newton's request. The triangle PQR is some- times called " Barrow's differential triangle." The reciprocal relation between differentiation and integration (§6) was first observed explicitly by Barrow in the book cited above. If the quadrature of a curve y =/(*) is known, so that the „ , area up to the ordinate x is given by F(x), the curve y arrows ^ y = F(x) can be drawn, and Barrow showed that the theorem' 7 subtangent of this curve is measured by the ratio of its ordinate to the ordinate of the original curve. The curve y = F(*) is often called the " quadratrix " of the original curve; and the result has been called " Barrow's inversion-theorem." He did not use it as we do for the determination of quadratures, or indefinite, integrals, but for the solution of problems of the kind which were then called " inverse problems of tangents." In these problems it was sought to determine a curve from some property of its tangent, e.g. the property that the subtangent is proportional to the square of the abscissa. Such problems are now classed under "differentiaL equations." When Barrow wrote, quadratures were familiar and differentiation unfamiliar, just as hyperbolas were trusted while logarithms were strange. The functional notation was not invented till long afterwards (see Function), and the want of it is felt in read- ing all the mathematics of the 17th century. 18. The great secret which afterwards came to be called the " infinitesimal calculus " was almost discovered by Fermat, and still more nearly by Barrow. Barrow went farther than Fermat in the theory of differentiation, though not in the practice, for he compared two increments; he went farther in the theory of integration, for he obtained the inversion- theorem. The great discovery seems to consist partly in the Fig. 7. 54° INFINITESIMAL CALCULUS [HISTORY Nature of the dis- covery called the Infini- tesimal Calculus, recognition of the fact that differentiation, known to be a useful process, could always be performed, at least for the functions then known, and partly in the recognition of the fact that the inversion-theorem could be applied to problems of quadrature. By these steps the problem of tangents could be solved once for all, and the operation of integration, as we call it, could be rendered systematic. A further step was necessary in order that the discovery, once made, should become accessible to mathematicians in general; and this step was the introduction of a suitable notation. The definite abandonment of the old tentative methods of in- tegration in favour of the method in which this operation is regarded as the inverse of differentiation was especi- ally the work of Isaac Newton; the precise formulation of simple rules for the process of differentiation in each special case, and the introduction of the notation which has proved to be the best, were especially the work of Gottfried Wilhelm Leibnitz. This statement remains true although Newton invented a systematic notation, and practised differentia- tion by rules equivalent to those of Leibnitz, before Leibnitz had begun to work upon the subject, and Leibnitz effected integrations by the method of recognizing differential coefficients before he had had any opportunity of becoming acquainted with Newton's methods. iq. Newton was Barrow's pupil, and he knew to start with in 1664 all that Barrow knew, and that was practically all that was known about the subject at that time. His lavesttea- 0Tl &nal thinking on the subject dates from the year tlons. of the great plague (1665-1666), and it issued in the invention of the " Calculus of Fluxions," the principles and methods of which were developed by him in three tracts entitled De analysi per aequationes numero terminorum infinitas, Melhodus fluxionum el serierum infinitarum, and De quad- ratura curvarum. None of these was published until long after they were written. The Analysis per aequationes was composed in 1666, but not printed until 1711, when it was published by William Jones. The Methodus fluxionum was composed in 1671 but not printed till 1736, nine years after Newton's death, when an English translation was published by John Colson. In Horsley's edition of Newton's works it bears the title Geometria analytica. The Quadratura appears to have been composed in 1676, but was first printed in 1704 as an appendix to Newton's Opticks. 20. The tract De Analysi per aequationes . . . was sent by Newton to Barrow, who sent it to John Collins with a request that N , it might be made known. One way of making it known method 0/ wou '3 have been to print it in the Philosophical Trans- _^ ri actions of the Royal Society, but this course was not adopted. Collins made a copy of the tract and sent it to Lord Brouncker, but neither of them brought it before the Royal Society. The tract contains a general proof of Barrow's inversion-theorem which is the same in principle as that in § 6 above. In this proof and elsewhere in the tract a notation is introduced for the momentary increment (momentum) of the abscissa or area of a curve; this " moment " is evidently meant to represent a moment of time, the abscissa representing time, and it is effectively the same as our differential element — the thing that Fermat had denoted by E, and Barrow by e, in the case of the abscissa. Newton denoted the moment of the abscissa by o, that of the area z by ov. He used the letter v for the ordinate y, thus suggesting that his curve is a velocity- time graph such as Galileo had used. Newton gave the formula for the area of a curve u = x m (»t=t=-l) in the form z = x m+l j(m~\-l). In the proof he transformed this formula to the form z" = c n x p , where n and p are positive integers, substituted x+o for x and z+ov for z, and expanded by the binomial theorem for a positive integral exponent, thus obtaining the relation z"-|-nz" -1 0i>-f- . . . = c n (x p +px p ~ 1 o-\- . . .), from which he deduced the relation by omitting the equal terms z*> and c"x p and dividing the remaining terms by 0, tacitly putting = after division. This relation is the same as v = x m . Newton pointed out that, conversely, from the relation v=x m the relation z-=x m+l /(m + 1 ) follows. He applied his formula to the quadrature of curves whose ordinates can be expressed as the sum of a finite number of terms of the form ax m ; and gave examples of its application to curves in which the ordinate is expressed by an infinite series, using for this purpose the binomial theorem for negative and fractional exponents, that is to say, the expansion of (1 +x)" in an infinite series of powers of x. This theorem he had discovered; but he did not in this tract state it in a general form or give any proof of it. He pointed out, however, how it may be used for the solution of equations by means of infinite series. He observed also that all questions concerning lengths of curves, volumes en- closed by surfaces, and centres of gravity, can be formulated as problems of quadratures, and can thus be solved either in finite terms or by means of infinite series. In the Quadratura (1676) the method of integration which is founded upon the inversion- theorem was carried out systematically. Among other results there given is the quadrature of curves expressed by equations of the form y = x n (a+bx m )i'; this has passed into text-books under the title " integration of binomial differentials " (see § 49). Newton announced the result in letters to Collins and Oldenburg of 1676. 21. In the Methodus fluxionum (1671) Newton introduced his characteristic notation. He regarded variable quantities as gener- ated by the motion of a point, or line, or plane, and called N , the generated quantity a " fluent " and its rate of genera- ^/,°do/ tion a "fluxion." The fluxion of a fluent x is represented T. ,° by x, and its moment, or " infinitely " small increment accruing in an " infinitely " short time, is represented by vo. The problems of the calculus are stated to be (i.) to find the velocity at any time when the distance traversed is given; (ii.) to find the distance traversed when the velocity is given. The first of these leads to differentiation. In any rational equation containing x and y the expressions x+xo and y+yo are to be substituted for * and y, the resulting equation is to be divided by 0, and afterwards is to be omitted. In the case of irrational functions, or rational functions which are not integral, new variables are introduced in such a way as to make the equations contain rational integral terms only. Thus Newton's rules of differentiation would be in our notation the rules (i.), (ii.), (v.)of § 11, together with the particular result which we write dx" dx = mx m ~ l , (m integral). a result which Newton obtained by expanding {x-\-xo) m by the binomial theorem. The second problem is the problem of integra- tion, and Newton's method for solving it was the method of series founded upon the particular result which we write ( x m dx = - I 1 Publica- tion of the Fluxions! Notation. may be w + i" Newton added applications of his methods to maxima and minima, tangents and curvature. In a letter to Collins of date 1672 Newton stated that he had certain methods, and he described certain results which he had found by using them. These methods and results are those which are to be found in the Methodus fluxionum; but the letter makes no mention of fluxions and fluents or of the character- istic notation. The rule for tangents is said in the letter to be analogous to de Sluse's, but to be applicable to equations that con- tain irrational terms. 22. Newton gave the fluxional notation also in the tract De Quadratura curvarum (1676), and he there added to it notation for the higher differential coefficients and for indefinite integrals, as we call them. Just as x, y, z, . . . are fluents of which x, y, z, '. . . are the fluxions, so X, y, z, . . . can be treated as fluents of which the fluxions may be denoted by X, y, S, . . . In like manner the fluxions of these may be denoted by x, y, 2, . . and so on. Again x, y, z, . . regarded as fluxions of which the fluents may be denoted by x, j/ ; i, and these again as fluxions of other quantities denoted by S, y", z, . . . and so on. No use was made of the notation x, x, . . . in the course of the tract. The first publication of the fluxional notation was made by Wallis in the second edition of his Algebra (1693) in the form of extracts from communications made to him by Newton in 1692. In this account of the method the symbols 0, x, x, . . . occur, but not the symbols x, x, . . . Wallis's treatise also contains Newton's formulation of the problems of the calculus in the words DaUi aequatione fluentes quotcumque quanlitates involvente fluxiones invenire el vice versa (" an equation containing any number of fluent quantities being given, to find their fluxions and vice versa "). In the Philosophiae naturalis principia mathematica (1687), commonly called the " Principia," the words " fluxion " and " moment " occur in a lemma in the second book ; but the notation which is character- istic of the calculus of fluxions is nowhere used. 23. It is difficult to account for the fragmentary manner of publication of the Fluxional Calculus and for the long delays which took place. At the time (167 1) when Newton composed the Methodus fluxionum he contemplated bringing out an edition of Gerhard Kinckhuysen's treatise on algebra and prefixing his tract to this treatise. In the same year his " Theory of Light and Colours " was published in the Philosophical Transactions, and the opposition which it excited led to the abandonment of Retarded Publica- tion of the method ot Fluxions. HISTORY] INFINITESIMAL CALCULUS 54- 1 the project with regard to fluxions. In 1680 Collins sought the assistance of the Royal Society for the publication of the tract, and this was granted in 1682. Yet it remained unpublished. The reason is unknown; but it is known that about 1670, 1680, Newton took up again the studies in natural philosophy which he had intermitted for several years, and that in 1684 he wrote the tract De motu which was in some sense a first draft of the Principia, and it may be conjectured that the fluxions were held over until the Principia should be finished. There is also reason to think that Newton had become dissatisfied with the arguments about infinitesimals on which his calculus was based. In the preface to the De quadratura curvarum (1704), in which he describes this tract as something which he once wrote ('' olim scripsi ") he says that there is no necessity to intro- duce into the method of fluxions any argument about infinitely small quantities; and in the Principia (1687) he adopted instead of the method of fluxions a new method, that of " Prime and Ultimate Ratios." By the aid of this method it is possible, as Newton knew, and as was afterwards seen by others, to found the calculus of fluxions on an irreproachable method of limits. For the purpose of explaining his discoveries in dynamics and astronomy Newton used the method of limits only, without the notation of fluxions, and he presented all his results and demonstrations in a geometrical form. There is no doubt that he arrived at most of his theorems in the first instance by using the method of fluxions. Further evidence of Newton's dis- satisfaction with arguments about infinitely small quantities is furnished by his tract Methodus diferentialis, published in 17 1 1 by William Jones, in which he laid the foundations of the " Calculus of Finite Differences." 24. Leibnitz, unlike Newton, was practically a self-taught mathematician. He seems to have been first attracted to mathematics as a means of symbolical expression, and course of on tne occas i° n of his first visit to London, early in discovery, r 673, he learnt about the doctrine of infinite series which James Gregory, Nicolaus Mercator, Lord Brouncker and others, besides Newton, had used in their in- vestigations. It appears that he did not on this occasion become acquainted with Collins, or see Newton's Analysis per aequa- tiones, but he purchased Barrow's Lectiones. On returning to Paris he made the acquaintance of Huygens, who recommended him to read Descartes' Geometric He also read Pascal's Lettres de Dettonville, Gregory of St Vincent's Opus geomelricum, Cavalieri's Indivisibles and the Synopsis geometrica of Honore Fabri, a book which is practically a commentary on Cavalieri; it would never have had any importance but for the influence which it had on Leibnitz's thinking at this critical period. In August of this year (1673) he was at work upon the problem of tangents, and he appears to have made out the nature of the solution— the method involved in Barrow's differential triangle — for himself by the aid of a diagram drawn by Pascal in a demon- station of the formula for the area of a spherical surface. He saw that the problem of the relation between the differences of neighbouring ordinates and the ordinates themselves was the important problem, and then that the solution of this problem was to be effected by quadratures. Unlike Newton, who arrived at differentiation and tangents through integration and areas, Leibnitz proceeded from tangents to quadratures. When he turned his attention to quadratures and indivisibles, and realized the nature of the process of finding areas by summing ' infinitesimal " rectangles, he proposed to replace the rectangles by triangles having a common vertex, and obtained by this method the result which we write t*- = i-5+{-*+ • • • In 1074 he sent an account of his method, called " transmutation," along with this result to Huygens, and early in 1675 he sent it to Henry Oldenburg, secretary of the Royal Society, with inquiries as to Newton's discoveries in regard to quadratures. In October of 1675 he had begun to devise a symbolical notation for quadratures, starting from Cavalieri's indivisibles. At first he proposed to use the word omnia as an abbreviation for Cavalieri's "sum of all the lines," thus writing omnia y for chat which we write " fydx," but within a day or two he wrote " fy." He regarded the symbol " /" as representing an opera- tion which raises the dimensions of the subject of operation — a line becoming an area by the operation — and he devised his symbol " d " to represent the inverse operation, by which the dimensions are diminished. He observed that, whereas " / " represents " sum," " d " represents " difference." His notation appears to have been practically settled before the end of 1675, for in November he wrote fydy = %y 2 , just as we do now. 25. In July of 1676 Leibnitz received an answer to his inquiry in regard to Newton's methods in a letter written by Newton to Oldenburg. In this letter Newton gave a general corres- statement of the binomial theorem and many results poadeace relating to series. He stated that by means of such otNew series he could find areas and lengths of curves, centres *?".?"? of gravity and volumes and surfaces of solids, but, as this would take too long to describe, he would illustrate it by examples. He gave no proofs. Leibnitz replied in August, stating some results which he had obtained, and which, as it seemed, could not be obtained easily by the method of series, and he asked for further information. Newton replied in a long letter to Oldenburg of the 24th of October 1676. In this letter he gave a much fuller account of his binomial theorem and indicated a method of proof. Further he gave a number of results relating to quadratures; they were afterwards printed in the tract De quadratura curvarum. He gave many other results relating to the computation of natural logarithms and other calculations in which series could be used. He gave a general statement, similar to that in the letter to Collins, as to the kind of problems relating to tangents, maxima and minima, &c, which he could solve by his method, but he concealed his formulation of the calculus in an anagram of transposed letters. The solution of the anagram was given eleven years later in the Principia in the words we have quoted from Wallis's Algebra. In neither of the letters to Oldenburg does the characteristic notation of the fluxional calculus occur, and the words " fluxion " and " fluent " occur only in anagrams of transposed letters. The letter of October 1676 was not despatched until May 1677, and Leibnitz answered it in June of that year. In October 1676 Leibnitz was in London, where he made the acquaintance of Collins and read the Analysis per aequationes, and it seems to have been supposed afterwards that he then read Newton's letter of October 1676, but he left London before Oldenburg received this letter. In his answer of June 1677 Leibnitz gave Newton a candid account of his differential calculus, nearly in the form in which he afterwards published it, and explained how he used it for quadratures and inverse problems of tangents. Newton never replied. 26. In the Acta eruditorum of 1684 Leibnitz published a short memoir entitled Nova methodus pro maximis et minimis, itemque tangentibus, quae nee fractas nee irrationales Leibnitz's quantitates moratur, el singulare pro illis calculi genus. Differ- In this memoir the differential dx of a variable x, entiat considered as the abscissa of a point of a curve, is said Ca/cu/us - to be an arbitrary quantity, and the differential dy of a related variable y, considered as the ordinate of the point, is defined as a quantity which has to dx the ratio of the ordinate to the subtangent, and rules are given for operating with differentials. These are the rules for forming the differential of a constant, a sum (or difference), a product, a quotient, a power (or root). They are equivalent to our rules (i.)-(iv.) of § 1 1 and the particular result d(x m )=mx m ~ 1 dx. The rule for a function of a function is not stated explicitly but is illustrated by examples in which new variables are intro- duced, in much the same way as in Newton's Methodus fluxionum. In connexion with the problem of maxima and minima, it is noted that the differential of y is positive or negative according as y increases or decreases when * increases, and the discrimina- tion of maxima from minima depends upon the sigh of ddy, the differential of dy. In connexion with the problem of tangents the differentials are said to be proportional to the momentary "542 INFINITESIMAL CALCULUS [HISTORY increments of the abscissa and ordinate. A tangent is defined as a line joining two " infinitely " near points of a curve, and the " infinitely " small distances (e.g., the distance between the feet of the ordinates of such points) are said to be expressible by means of thedifferentials(e.g.,(*) =lim.i_oA" n f/(a;+«fe) - n f{(x + (n- i)h\ + n (n- 1) 2! f{x + (n-2)h\ ■■ + (-! )"/(*)} (ii.) As in the case of relation (i.) the limit expressed by the right-hand m ,T r£ ? ay e x' s t although some or all of the derived functions / (*),/ 0) /'"-"(x) do not exist. Corresponding to the rule iii. of § 1 1 we have the rule for forming the nth differential coefficient of a product in the form ^M = a ^!?_L M ^ d^H -|_?^LZI) {x)\dxY, in which dx is the (arbitrary) differential of x. YVhen d/dx is regarded as a single symbol of operation the symbol J .dx represents the inverse operation. If the former is denoted "Y u > the latter may be denoted by D" 1 . D" means that the operation D is to be performed n times in succession • s y mboIs D » that the operation of forming the indefinite integral "f ODera - is to be performed n times in succession. Leibnitz's course of thought (§ 24) naturally led him to inquire after an inter- pretation of D". where n is not an integer. For an account of the researches to which this inquiry gave rise, reference may be made to the article by A. Voss in Ency. d. math. Wiss. Bd. ii. A, 2 (Leipzig \?°9>- The matter is referred to as " fractional "or " generalized" differentiation. 36. After the formation of differential coefficients the most im- portant theorem of the differential calculus is the theorem of inter- mediate value (" theorem of mean value," " theorem of finite incre- ments," " Rolle's theorem," are other names for it). This theorem may be explained as follows: Let A, B be two points of a curve }'=/(x) (fig. 9)- Then there is a point P between A and B at which the tangent is parallel to the secant AB. This theorem is expressed analytically in the statement that if /'(*) is continuous between a and b, there is a value xi of x between a and b which has the pro- perty expressed by the equation The value x, can be expressed in the form a+0(b — a) where is a number between o and 1. A slightly more general theorem was given by Cauchy (1821) to the effect that, if /'(*) and F'(x) are continuous between x = a and x - 0, then there is a number 8 between o and 1 which has the property expressed by the equation F(ft)-F(fl) _ F'!a+9(6-a)| Kb) -/(a) f \a+B(b -a)] • The theorem expressed by the relation (i.) was first noted by Rolle (i 690) for the case where /(x) is a rational integral function which vanishes when x = a and also when x = b. The general theorem was given by Lagrange (1797). Its fundamental importance was first recognized by Cauchy (1823). It may be observed here that the theorem ot integral calculus expressed by the equation Fig. (i.) F(6)-F(o) = j F'(x)dx follows at once from the definition of an integral and the theorem of intermediate value. The theorem of intermediate value may be generalized in the statement that, if /(*) and all its differential coefficients up to the nth inclusive are continuous in the interval betweenx = a andx = 6 then there ts a number between o and 1 which has the property expressed by the equation H y Kfi)=Ka) + (b-a)f'(a) + (b ^f"(a)+...+ (x) and \p(x) both . . t vanish at x = a, the fraction (x)J\^(x) may have a finite mlaate limit at a. This limit is described as the limit of an forms. " indeterminate form." Such indeterminate forms were considered first by de l'Hospital (1696) to whom the problem of evaluating the limit presented itself in the form of tracing the curve y = (x)/\j/{x) near the ordinate x = a, when the curves y=(x) and y=, $, chosen so that P and Q have the same abscissa. The value of the ordinate of the corre- sponding point R of the compound curve is given by the ratio of the ordinates PM, QM. De l'Hospital treated PM and QM as " infinitesimal,'' so that the equations PM :AM =*'(o) and QM :AM =^'(a) could FlG - I0 - be assumed to hold, and he arrived at the result that the " true value " of (a)/^(a) is $' '(a) jrj/' (a) . It can be proved rigorously that, if 4>'(x) does not vanish at x = a, while tj>(a) =0 and ^(a) =0, then Km '(q) x=a t{x) ^»- It can be proved further if that m {x) and ^"(*) are the differential coefficients of lowest order of (x) andi/' (x) which do not vanish at x = a, and if m = n, then — — \x 2 2 2! _R? r 4 I §3y6_ -I 2 2! 4! 6! and they are connected with the sums of powers of the reciprocals of the natural numbers by equations of the type B„ = (2n)! The function Gi 4-J-+JL4- 2 2! iB,*™- 2 -. /o(o) + -Z* n=2 L^T dy~>- \My)\"h- lim.. has been called Bernoulli's function of the rath order by J. L. Raabe (Crelle's J. f. Math. Bd. xlii., 1851). Bernoulli's numbers and functions are of especial importance in the calculus of finite differ- ences (see the article by D. Seliwanoff in Ency. d. math. Wiss. Bd. i., E., 1901). When x is given in terms of y by means of a power series of the form x=y(C +C 1 y+C 1 f+...) (C *o) =>/o(y), say, there arises the problem of expressing y as a power series in x. This problem is that of reversion of series. It can be shown that provided the absolute value of x is not too great, 4>(x) _ #*(a) n the limit is zero; but if m(x)/\l/(x) " becomes infinite " at x = a. If the value of the function at x =0 is not assigned by the definition of the function, the function does not exist at x — a, and the meaning of the statement that it " becomes infinite " is that it has no finite limit. The state- ment does not mean that the function has a value which we call infinity. There is no such value (see Function). Such indeterminate forms as that described above are said to be of the form 0/0. Other indeterminate forms are presented in the form o X =0 , or i 00 , or °o /» , or 00 - 00 . The most notable of the forms i 00 is lim.x=o(i -hx) 1 /*, which is e. The case in which (x) and f(x) both tend to become infinite at x = a is reducible to the case in which both the functions tend to become infinite when x is increased indefinitely. If 4>'(x) and \(/'(x) have determinate finite limits when x is increased indefinitely, while (x) and ^(.x) are determinately (positively or negatively) infinite, we have the result expressed by the equation Urn _ ^W - K-»»'W '*-"><)/{x) lim.^^f (*)' For the meaning of the statement that (x) and \j/(x) are determinately infinite reference may be made to the article Function. The evalua- tion of forms of the type =0 /» leads to a scale of increasing " in- finities," each being infinite in comparison with the preceding. Such a scale is log x, .. .x, x 2 , . . .x n ,. . .e x , .. .x"; each of the limits expressed by such forms as lim.x=» 4>(x)/il/(x), where (x) precedes ^(x) in the scale, is zero. The construction of such scales, along with the problem of constructing a complete scale, was discussed in numerous writings by Paul du Bois-Reymond (see in particular, Math. Ann. Bd. xi., 1877). For the general problem of indeterminate forms reference may be made to the article by A. Pringsheim in Ency. d. math. Wiss. Bd. ii., A. 1 (1899"). Forms of the type 0/0 presented themselves to early writers on analytical geometry in connexion with the determination of the tangents at a double point of a curve; forms of the type 00/00 presented themselves in like manner in connexion with the deter- mination of asymptotes of curves. The evaluation of limits has innumerable applications in all parts of analysis. Cauchy's Analyse algebrique (1821) was an epoch-making treatise on limits. If a function (x) becomes infinite at x — a, and another function \l/{x) also becomes infinite at x=a in such a way that (x)li/(x) has a finite limit C, we say that 4>(x) and (x) =C<(>(x)+ct>\(x), where \\m.x-ai(x)l\l'(x)=o, and thus 4>i(x) is of a lower order than 4>{x)\ it may be finite or infinite at x = a. If it is finite, we describe C(x) 546 INFINITESIMAL CALCULUS [OUTLINES dlfferea tlatlon. as the " infinite part " of 4>(x). The resolution of a function which becomes infinite into an infinite part and a finite part can often be effected by taking the infinite part to be infinite of the same order as one of the functions in the scale written above, or in some more comprehensive scale. This resolution is the inverse of the process of evaluating an indeterminate form of the type oo — oo . For example lim. I=0 {(e* — 1) _1 — x -1 } is finite and equal to =J, and the function (e 1 — 1) _1 — XT 1 can be expanded in a power series in x. 39. The nature of a function of two or more variables, and the meaning, to be attached to continuity and limits in respect of such functions, have been explained under FUNCTION. The Functions theorems of differential calculus which relate to such rt*M functions are in general the same whether the number varuo es. Q ^ yaj-jabJeg j s )- wo or anv g rea ter number, and it will generally be convenient to state the theorems for two variables. 40. Let u or / (*, y) denote a function of two variables x and y. If we regard y as constant, u or/becomes a function of one variable x, . and we may seek to differentiate it with respect to x. Partial jf t ^ e f unc t; on f x j s differentiable, the differential coefficient which is formed in . this way is called the " partial differential coefficient " of u or /with respect to x, and is denoted by gj or «£. The symbol " d " was appropriated for partial differentiation by C. G. J. Jacobi (1841). It had before been written indifferently with " d " as a symbol of differentiation. Euler had written " (-f-j " for the partial differential coefficient of f with respect to x. Sometimes it is desirable to put in evidence the variable which is treated as constant, and then the partial differential coefficient is written " (-£■ j " or " Iqz.) "• This course is often adopted by writers on Thermodynamics. Sometimes the symbols d or 3 are dropped, and the partial differential coefficient is denoted by Ui or f x . As a definition of the partial differential coefficient we have the formula dx llm -h-0 h In the same way we may form the partial differential coefficient with respect to y by treating xasa constant. The introduction of partial differential coefficients enables us to solve at once for a surface a problem analogous to the problem of tangents for a curve; and it also enables us to take the first step in the solution of the problem of maxima and minima for a function of several variables. If the equation of a surface is expressed in the form z=f(x, y), the direction cosines of the normal to the surface at any point are in the ratios -g- : ■?- : = 1. If / is a maximum or a minimum at (x, y), then dfldx and df/dy vanish at that point. In applications of the differential calculus to mathematical physics we are in general concerned with functions of three variables x, y, z, which represent the coordinates of a point; and then considerable importance attaches to partial differential coefficients which are formed by a particular rule. Let F(x, y, z) be the function, P a point (x, y, 2), P' a neighbouring point (x+Ax, y+Ay, z+Az), and let As be the length of PP'. The value of F(x, y, 2) at P may be denoted shortly by F(P). A limit of the same nature as a partial differential coefficient is expressed by the formula F(P')=F(P) lim. As-0 As in which As is diminished indefinitely by bringing P' up to P, and P' is supposed to approach P along a straight line, for example, the tangent to a curve or the normal to a surface. The limit in question is denoted by dF/dh, in which it is understood that h indicates a direction, that of PP'. If /, m, n are the direction cosines of the limiting direction of the line PP', supposed drawn from P to P', then 3F ,3F , 3F . 3F dh dx dy dz The operation of forming dF/dh is called "differentiation with respect to an axis " or " vector differentiation." 41. The most important theorem in regard to partial differential coefficients is the theorem of the total differential. We may write down the equation ££j _ +/(«. b+k)-f(a, b). Dlfferea- If /» > s a continuous function of x when x lies between a Hal. and a+h and y = b+k, and if further/, is a continuous function of y when y lies between b and d+k, there exist values of and rj which lie between o and I and have the properties expressed by the equations f(a+h, b+k) -f(a, b+k)=hf x {a+eh, b+k), f(a, b+k) -/(a, b)=kf y (a, b+r,k). Further, f z (a+eh, b+k) and f v (a, b+ijk) tend to the limits/, (0,6) ftnd /»(<% b) when h and h tend to zero, provided the differential coefficients/*,/,, are continuous at the point (a, b). Hence in this case the above equation can be written f{a+h, b+k)-f(a, b)=hMa, b)+kf a (a, b)+R, where R R Un H-o, - The theorem is applicable to functions of any number of variables and is generally known as Eider's theorem of homogeneous functions. 42. Many problems in which partial differential coefficients occur are simplified by the introduction of certain determinants called " Jacobians " or " functional determinants." They were introduced into Analysis by C. G.J. Jacobi Jacoblan *- {J. f. Math., Crelle, Bd. 22, 1841, p. 319). The Jacobian of «i, Ms, . . . u„ with respect to xi, xt, . . . x n is the determinant du\ dut dui 3*i dxt ' ' ' dx n du2 dut dui dx\ dxi " ' ' dx„ 3w» 3*i dUn dxi ' ' 3k, 'dx n in which the constituents of the rth row are the n partial differential coefficients of u, with respect to the n variables x. This determinant is expressed shortly by 3(«1, «2,. . ., «.) 3(*1, Xi,. . ., Xn)' Jacobians possess many properties analogous to those of ordinary differential coefficients, for example, the following: — 3 («i, d(xi, Xi,. 3(«i, ui,. Un) s , d(Xl, Xt, . . u„) X 3(«1, «2, 3 (yi, y 2 , ■ . *») . . «.)■ y») _. 3(mi, ui,. «n) *n)' x n ) are ■ ■ U n ) 3(yi, y%, ■ ■ ■ 1 y n ) *d(xi, x 2 , . . . ,'lx„) 3(*i, xi, If n functions («i, u 2 , . . . «„) of n variables (xi, x it . . . , not independent, but are connected by a relation /(«i, ui, . = 0, then 3(ttl, «2,. ■ ., Mn) _ 3(*1, X 2 , . . ., X n ) ' and, conversely, when this condition is satisfied identically the functions U\, u%, . . . , u n are not independent. 43. Partial differential coefficients of the second and higher orders can be formed in the same way as those of the first order. For example, when there are two variables x, y, the first partial derivatives dfldx and dfjdy are functions of * and y, which we may seek to differentiate partially with respect to x or y. The most important theorem in re- lation to partial differential coefficients of orders higher than the first is the theorem that the values of such coefficients do not depend upon the order in which the differentia- tions are performed. For example, we have the equation dx \dyj dy \dx) yu > This theorem is not true without limitation. The conditions for its validity have been investigated very completely by H. A. Schwarz (see his Ges. math. Abhandlungen, Bd. 2, Berlin, 1890, p. 275). It is a sufficient, though not a necessary, condition that all the differ- ential coefficients concerned should be continuous functions of x, y. In consequence of the relation (i.) the differential coefficients ex- pressed in the two members of this relation are written 3*/ ay 3*3y or 3y3;c- Inter- change ot order ot differen- tiations. OUTLINES] The differential coefficient INFINITESIMAL CALCULUS 547 B"f m which />+g+r = n, is formed by differentiating p times with respect to x, q times with respect to y, r times with respect to z, the differentiations being performed in any order. Abbreviated nota- tions are sometimes used in such forms as Differentials of higher orders are introduced by the defining equation (d d \ n dx-z — \-dy^-\ is developed by the binomial a d theorem in the same way as if dxj- and dy-~- were numbers, and [dxj \dy) / is replaced by- ^^^ - When there are more than two variables the multinomial theorem must be used instead of the binomial theorem. The problem of forming the second and higher differential co- efficients of implicit functions can be solved at once by means of partial differential coefficients, for example, if / (3c,y)=o is the equation denning jasa function of x, we have *2.(&.X"\ m i *L- 2 *L.*L.*L+(*£\ , 2L\. dx* \dy/ I \dy) dx* dx dy dxdy^\dx) dy i S The differential expression Xdx+Ydy, in which both X and Y are functions of the two variables x and y, is a total differential if there exists a function /of * and y which is such that a//a*=x, a//ay=Y. When this is the case we have the relation dYjdx = dX!dy. (ii.) Conversely, when this equation is satisfied there exists a function / which is such that df=Xdx+Ydy. The expression XAt-f-YJy in which X and Y are connected by the relation (ii.) is often described as a " perfect differential." The theory of the perfect differential can be extended to functions of n variables, and in this case there are Jn(»-i) such relations as (ii.). In the case of a function of two variables x, y an abbreviated notation is often adopted for differential coefficients. The function being denoted by z, we write , , dz dz d 2 z SPz d 2 z p, Q, r, S, I lor -r-> -r— > t-=> , , ) -r— ,. r * dx dy dx' dxdy dy 1 Partial differential coefficients of the second order are important in geometry as expressing the curvature of surfaces. When a surface is given by an equation of the formz=/(x, y), the lines of curvature are determined by the equation \(l+q 2 )s-pqt\ (d y y+\(l+q*)r-(l+p*)t}dxdy -{{i+p*)s-pqr}(dxy = o, and the principal radii of curvature are the values of R which satisfy the equation W(rt-s*) -R{ (i +q*)r-2pqs+(l +P"W (i +^+8 2 ) + U+P 2 +q 2 ) 2 = 0. 44. The problem of change of variables was first considered by Brook Taylor in his Methodus incrementorum. In the case con- Chantt of s *dered by Taylor y is expressed as a function of z, and z variables as a f unct ' on °f x < ano " lt ls desired to express the differ- ential coefficients of y with respect to x without eliminating z. The result can be obtained at once by the rules for differentiating a product and a function of a function. We have dy dy dz_ dx dz dx' d?y_ _ dy dh_ ,djy_ (dz\ 2 dx*~dz'dx* + dz?' \dx) ' d^y_dy d 3 z , cPv dz_ dH.dQ (dz\ 3 dx' ~dz'd~P +i dz 2 ' dx ' dx 2+ dz i ' \d~x) ' The introduction of partial differential coefficients enables us to deal with more general cases of change of variables than that con- sidered above. If u, v are new variables, and x, y are connected with them by equations of the type x=fi(u, v), y=Mu, v), (i.) while y is either an explicit or an implicit function of x, we have the problem of expressing the differential coefficients of various orders of y with respect to x in terms of the differential coefficients of v with respect to u. We have by the rule of the total differential. In the same way, by means of differentials of higher orders, we may express d 2 y/dx 2 , and so on. Equations such as (i.) may be interpreted as effecting & transfor- mation by which a point (w, vj is made to correspond to a point (x, y). The whole theory of transformations, and of functions, or differential expressions, which remain invariant under groups of transforma^ tions, has been studied exhaustively by Sophus Lie (see, in particular, his Theorie der Transformdtionsgruppen, Leipzig, 1888-1893). (See also Differential Equations and Groups). A more general problem of change of variables is presented when it is desired to express the partial differential coefficients of a function V with respect to x, y, . . . in terms of those with respect to u,v, . . ., where u, v, . . . are connected with x, y, . . .by any functional relations. WHen there are two variables x, y, and u, v are given functions of x, y, we have SV^SVdu , aVcto ; dx du dx dv dx dy dVdu,dVdv t du dy dv dy and the differential coefficients of higher orders are to be formed by repeated applications of the rule for differentiating a product and the rules of the type 1 d _du d , 5» 9 dx dxdu dxdv When x, y are given functions of «, v, . . . we have, instead of the above, such equations as av = ava£ , avay. du dx du dy du' and dVldx, dVjdy can be found by solving these equations, pro- vided the Jacobian d{x, y)ld(u, v) is not zero. The generalization of this method for the case of more than two variables need not detain us. In cases like that here considered it is sometimes more convenient not to regard the equations connecting x, y with u, v as effecting a point transformation, but to consider the loci « = const., u = const. as two " families " of curves. Then in any region of the plane of (x, y) in which the Jacobian d(x, y)/d{u,v) does not vanish or become infinite, any point {x, y) is uniquely determined by the values of « and v which belong to the curves of the two families that pass through the point. Such variables as u, v are then described as "(curvilinear coordinates " of the point. This method is applicable to any number of variables. When the loci «= const intersect each other at right angles, the variables are " orthogonal " curvilinear coordinates. Three-dimensional systems of such coordinates have important applications in mathematical physics. Reference may be made to G. Lam6, Lecons sur les coordonni.es curvilignes (Paris, 1 859) , and to G. Darboux, Lecons sur les coordonnees curvilignes et systimes orthogonaux (Paris, 1898). When such a coordinate as u is connected with x and y by a functional relation of the form j{x,y,u) =0 the curves « = const, are a family of curves, and this family may be such that no two curves of the family have a common point. When this is not the case the points in which a curve f(x, y,u) =0 is intersected by a curve f(x,y,u+ Am) =0 tend to limiting positions as Am is diminished indefinitely. The locus of these limiting positions is the " envelope " of the family, and in general it touches all the curves of the family. It is easy to see that, if u,v are the parameters of two families of curves which have envelopes, the Jacobian d(x, y)/d(«,i>) vanishes at all points on these envelopes. _ It is easy to see also that at any point wheie the reciprocal Jacobian d(u;v)/d(x, y) vanishes, a curve of the family u touches a curve of the family v. If three variables x, y, z are connected by a functional relation f(x, y, z) =0, one of them, z say, may be regarded as an implicit function of the other two, and the partial differential coefficients of z with respect to x and y can be formed by the rule of the total differ- ential. We have dx dx/ dz' dy dyj dz' and there is no difficulty in proceeding to express the higher differ- ential coefficients. There arises the problem of expressing the partial differential coefficients of x with respect to y and z in terms of those of z with respect to x and y. The problem is known as that of " changing the dependent variable." It is solved by applying the rule of the total differential. Similar considerations are applicable to all cases in which n variables are connected by fewer than n equations. 45. Taylor's theorem can be extended to functions of several variables. In the case of two variables the general for- Extension mula, with a remainder after n terms, can be written / Taylor's most simply in the form theorem. f(a+h, b+k) =/(o, b)+df(a, b) + ±d*f(a, b)+ . . 41= l%i+*k»!L\ I (tt+ttiL) dx Kdu^dvdu// \du^dvdu) in which + (^~77! d "~ , /(°. b) + ^»f(a+0h,b+0k), d-/(a,6)=[(^+*|)7(x,,)]_ | »-* 548 INFINITESIMAL CALCULUS [OUTLINES and Wa+ek, b+6k) = [ (h~+k§-^ "f(x, y)] ^ Plane curves. The last expression is the remainder after n terms, and in it 9 denotes some particular number between o and I. The results for three or more variables can be written in the same form. The ex- tension of Taylor's theorem was given by Lagrange (1797); the form written above is due to Cauchy (1823). For the validity of the theorem in this form it is necessary that all the differential co- efficients up to the nth should be continuous in a region bounded by x = a^k, y = b=*k. When all the differential coefficients, no matter how high the order, are continuous in such a region, the theorem leads to an expansion of the function in a multiple power series. Such expansions are just as important in analysis, geometry ^ind mechanics as expansions of functions of one variable. Among the problems which are solved by means of such expansions are the problem of maxima and minima for functions of more than one variable (see Maxima and Minima). 46. In treatises on the differential calculus much space is usually devoted to the differential geometry of curves and surfaces. A few remarks and results relating to the differential geometry of plane curves are set down here. (i.) If 4 1 denotes the angle which the radius vector drawn from the origin makes with the tangent to a curve at a point whose polar coordinates are r, 6 and if p denotes the perpendicular from the origin to the tangent, then cos \j/ = dr/ds, sin ip = rd8lds = pjr, where ds denotes the element of arc. The curve may be determined by an equation connecting p with r. (ii.) The locus of the foot of the perpendicular let fall from the origin upon the tangent to a curve at a point is called the pedal of the curve with respect to the origin. The angle 4> for the pedal is the same as the angle ^ for the curve. Hence the (p, r) equation of the pedal can be deduced. If the pedal is regarded as the primary curve, the curve of which it is the pedal is the " negative pedal " of the primary. We may have pedals of pedals and so on, also negative pedals of negative pedals and so on. Negative pedals are usually determined as envelopes. (iii.) If denotes the angle which the tangent at any point makes with a fixed line, we have (iv.) The " average curvature " of the arc As of a curve between two points is measured by the quotient (As I where the upright lines denote, as usual, that the absolute value of the included expression is to be taken, and f is the angle which the tangent makes with a fixed line, so that Atj> is the angle between the tangents (or normals) at the points. As one of the points moves up to coincidence with the other this average curvature tends to a limit which is the " curvature " of the curve at the point. It is denoted by \d± \ds Sometimes the upright lines are omitted and a rule of signs is given : — Let the arc s of the curve be measured from some point along the curve in a chosen sense, and let the normal be drawn towards that side to which the curve is concave; if the normal is directed towards the left of an observer looking along the tangent in the chosen sense of description the curvature is reckoned positive, in the contrary case negative. The differential d is often called the " angle of contingence." In the 14th century the size of the angle between a curve and its tangent seems to have been seriously debated, and the name " angle of contingence " was then given to the supposed angle. (v.) The curvature of a curve at a point is the same as that of a certain circle which touches the curve at the point, and the "radius of curvature" p is the radius of this circle. We have - =\-fi p \ds The centre of the circle is called the " centre of curvature "; it is the limiting position of the point of intersection of the normal at the point and the normal at a neighbouring point, when the second point moves up to coincidence with the first. If a circle is described to intersect the curve at the point P and at two other points, and one of these two points is moved up to coincidence with P, the circle touches the curve at the point P and meets it in another point ; the centre of the circle is then on the normal. As the third point now moves up to coincidence with P, the centre of the circle moves to the centre of curvature. The circle is then said to " osculate " the curve, or to have " contact of the second order " with it at P. (vi.) The following are formulae for the radius of curvature 1 '.+ then, as Q moves up to coincidence with P, the distance from P to the point of intersection of the normals at P and Q becomes greater than any distance that can be assigned. The equation which gives the abscissae of the points in which a straight line meets the curve being expressed in the form /(x) =0, the function /(*) has a factor {x—xo) 3 , where xo is the abscissa of the point of inflection P, and the line is the tangent at P. When the factor (x—xa) occurs (n + i) times in/(x), the curve is said to have " contact of the rath order " with the line. There is an obvious modification when the line is parallel to the axis of y. (viii.) The locus of the centres of curvature, or envelope of the normals, of a curve is called the " evolute." A curve which has a given curve as evolute is called an " involute " of the given curve. All the involutes are " parallel " curves, that is to say, they are such that one is derived from another by marking off a constant distance along the normal. The involutes are " orthogonal trajectories " of the tangents to the common evolute. (ix.) The equation of an algebraic curve of the rath degree can be expressed in the form ao+«i + «j+... +k«=o, where « is a constant, and u, is a homogeneous rational integral function of x, y of the rth degree. When the origin is on the curve, tto vanishes, and #1=0 represents the tangent at the origin. If U\ also vanishes, the origin is a double point and u% = o represents the tangents at the origin. If ut has distinct factors, or is of the form a(y— pix){y — ptx); the value of y on either branch of the curve can be expressed (for points sufficiently near the origin) in a power series, which is either pix+\q i x i + . . . , or p 2 x+iq 2 x i + . . ., where qi, . . . and qt, . . . are determined without ambiguity. If pi and pi are real the two branches have radii of curvature pi, pj determined by the formulae )" ? Si|, ^-|d+#i , )" , 9.| When pi and fa are imaginary the origin is the real point of inter- section of two imaginary branches. In the real figure of the curve it is an isolated point. If « 2 is a square, a(y—px) % , the origin is a cusp, and in general there is not a series for y in integral powers of x, which is valid in the neighbourhood of the origin. The further investigation of cusps and multiple points belongs rather to analytical geometry and the theory of algebraic functions than to differential calculus. (x.) When the equation of a curve is given in the form «o+«i + • • . +«n-i+Mn = o where the notation is the same as that in (ix.), the factors of #„ determine the directions of the asymptotes. If these factors are all real and distinct, there is an asymptote corresponding to each factor. If «„ = LiL 2 . . . L„, where Li, ... are linear in x, y, we may resolve u n -ilu„ into partial fractions according to the formula (dyyi-idhA \dx) \ dx*\ Jr\ I . , (Pp p=r rp\ = \f+d4? (vii.) The points at which the curvature vanishes are " points of inflection." If P is a point of inflection and Q a neighbouring point, ± = P+ Pl m„_i _Ai . A-2 . U n Li Li , An ■ + TZ' and then L^Ai =0, L 2 +A2 = o, ... are the equations of the asymp- totes. When a real factor of u n is repeated we may have two parallel asymptotes or we may have a " parabolic asymptote." Sometimes the parallel asymptotes coincide, as in the curve x'^+y 2 — a 2 ) =a 4 , where x = o is the only real asymptote. The whole theory of asymptotes belongs properly to analytical geometry and the theory of algebraic functions. 47. The formal definition of an integral, the theorem of the existence of the integral for certain classes of functions, a list of classes of " integrable " functions, extensions of the notion integral of integration to functions which become infinite or in- calculus. determinate, and to cases in which the limits of integra- tion become infinite, the definitions of multiple integrals, and the possibility of defining functions by means of definite integrals — all these matters have been considered in Function. The definition of integration has been explained in § 5 above, and the results of some of the simplest integrations have been given in § 12. A few theorems relating to integrations have been noted in §§ 34, 35, 36 above. 48. The chief methods for the evaluation of indefinite m e t Boa - s „f integrals are the method of integration by parts, and the integration. introduction of new variables. From the equation d(uv) =udv-fvdu we deduce the equation /u^-dx=uv — ( v-j- dx, dx J dx or, as it may be written I uwdx = u ( wdx — j -7- j I wdx f dx. This is the rule of " integration by parts." As an example we have I xe" x dx=x I — dx— (-- — 5) 1 J a J a \a a 2 / When we introduce a new variable 2 in place of x, by means of an equation giving x in terms of z, we express f(x) in terms ol a. Let 4>(z) denote the function of z into which f(x) is transformed. Then from the equation dx = -j-dz dz OUTLINES] we deduce the equation INFINITESIMAL CALCULUS 549 fnx)dx-faz)$£dz. Integra- tion to terms of element' ary func- tions. As an example, in the integral /V(i-* 2 )<2x put x = sin z; the integral becomes /cos z. cos zdz = j 5(1 +cos 2z)dz = j(s+§ sin 2z) = ^(z-f-sin z cos z). 49. The indefinite integrals of certain classes of functions can be expressed by means of a finite number of operations of addition or multiplication in terms of the so-called " elementary " functions. The elementary functions are rational alge- braic functions, implicit algebraic functions, exponentials and logarithms, trigonometrical and inverse circular functions. The following are among the classes of functions whose integrals involve the elementary functions only: (i.) all rational functions; (ii.) all irrational functions of the form /(x, y), where / denotes a rational algebraic function of x and y, and y is connected with x by an algebraic equation of the second degree; (hi.) all rational functions of sin x and cos x; (iv.) all rational functions of e x \ (v.) all rational integral functions of the variables x, e"', e 1 ", . . . sin mx, cos mx, sin nx, cos nx, ... in which a, b, . . . and m, n, . . . are any constants. The integration of a rational function is generally effected by resolving the function into partial fractions, the function being first expressed as the quotient of two rational integral functions. Corresponding to any simple root of the denominator there is a logarithmic term in the integral. If any of the roots of the denominator are repeated there are rational algebraic terms in the integral. The operation of re- solving a fraction into partial fractions requires a knowledge of the roots of the denominator, but the algebraic part of the integral can always be found without obtaining all the roots of the denominator. Reference may be made to C. Her'mite, Cours d'analyse, Paris, 1873. The integration of other functions, which can be integrated in terms of the elementary functions, can usually be effected by transforming the functions into rational functions, 'possibly after preliminary integrations by parts. In the case of rational functions of x and a radical of the form V (ax 2 +bx-\-c) the radical can be reduced by a linear substitution to one of the forms V (a 2 — x 2 ), V(x 2 — a 2 ), V (x 2 -|-a 2 ). The substitutions x — a sin 0, x — a sec 0, x = a tan 9 are then effective in the three cases. By these substitutions the subject of integration becomes a rational function of sin 8 and cos 0, and it can be reduced to a rational function of t by the substitution Ian \f) = t. There are many other substitutions by which such integrals can be determined. Sometimes we may have information as to the functional character of the integral without being able to determine it. For example, when the subject of integration is of the form (ax 4 +6x 3 -|-cx 2 -f dx+e)~l the integral cannot be expressed explicitly in terms of elementary functions. Such integrals lead to new functions (see Function). Methods of reduction and substitution for the evaluation of in- definite integrals occupy a considerable space in text-books of the integral calculus. In regard to the functional character of the integral reference may be made to G. H. Hardy's tract, The In- tegration of Functions of a Single Variable (Cambridge, 1905), and to the memoirs there quoted. A few results are added here (i.) f(x*+a)-hdx = \og\x + (x*+a)l}. /dx r~_>^ 1 t„~zj-^h*--L.r\ can k e evaluated by the substitution {x—p)yj {ax--\-2bx-\-c) x-p = l!z, andj , x _ p) »^< ax ? +2bx+c) entiating (11 — 1) times with respect to p. (Hx+K)'V Jv(y 2 - x 2 ) where A and B are constants, and Xi and X 2 are the two values of X for which (a — \a)x-+2(b — \0)x+c — \y is a perfect square (see A. G. Greenhill, A Chapter in the Integral Calculus, London, 1888). (iv.) jx m {ax' lJ \-V)'>dx, in which m, n, p are rational, can be reduced, by putting ax" = bt, to depend upon ff(.i+t)"dt. If p is an integer and q a fraction r!s, we put t = u*. If q is an integer and p = r/s we put i-\-t = u s . If p+q is an integer and p = r/s we put i+t = tu\ These integrals, called " binomial integrals," were investigated by Newton (De quadratura curvarum). (v.) ( -^— = log tan-, (vi.) ( — — =log (tan x+sec x). v ' J sin x s 2 x ' J cos x " (vii.) /e"sin (f>x + a)dx = (a 2 +6 2 )- I e aI [asin '(bx + a) — bcos(bx + a)\. (viii.) / sin m x cos" x dx can be reduced by differentiating a function of the form sin p x cos« x ; d_ sin x _ 1 , q sin 2 x _ 1 — q . q e ' S ' dxcos* x~ cos« _1 x cos'%~cos«"'i; cos'%' Hence C dx __ cos" x (re — 1) cos >s"~ l x n — 1 J c dx (ix.) P' 7 sin 2 «xrfx= p"cos*«fa:= ' ' 3 ' ' ' (2W-l) ■* (nan integer). Jo Jo 2.4...2W 2 X s ' (x.) I '"sin 2n+1 xdx= ( ^cos^^xdx = — 2-4--- 2 w / n&n integer). Jo Jo 2 c I^-L-tI s ' 1 ■ \ C dx (xi.) I 7 — ; rz J (i+ecosx)" ~3-5---(2re + i) n ; can be reduced by one of the substitutions „„o jl «+cos x , e+cos x cos = — : , cosh u = — ■ , I +e cos x i-\-e cos x of which the first or the second is to be employed according as e < or > 1 . 50. Among the integrals of transcendental functions Newtrans- which lead to new transcendental functions we may notice ceadents. ■log . /x , Wog X z logx'° r J _ K 2 called the " logarithmic integral," and denoted by " Li x," also the integrals / sin x x dx and called the " sine integral " and the " cosine integral," and denoted by " Si x " and " Ci x," also the integral y dx called the " error-function integral," and denoted by " Erf x." All these f unctions havebeen tabulated (seeTABLEs, Mathematical). 51. New functions can be introduced also by means of the definite integrals of functions of two or more variables with re- £ / er / an spect to one of the variables, the limits of integration integrals. being fixed. Prominent among such functions are the Beta and Gamma functions expressed by the equations B(l, m) = Cx'-Hi -xp-^x, T(n)= ( er'r-M J Hi. When n is a positive integer T(n + i)=n ! . The Beta function (or " Eulerian integral of the first kind ") is expressible in terms of Gamma functions (or " Eulerian integrals of the second kind ") by the formula B(l, m) .T{l+m) = T{l) .T{m). The Gamma function satisfies the difference equation r(x+i)=xr(x), and also the equation r(x).r(l — x) =71-/ sin (xx), with the particular result r(i)=Vir. The number -[^logrci+^.or-r'Ci), is called " Euler's constant," and is equal to the limit lim.„, 00 [(i + i-H + .--+^) -logn]; its value to 15 decimal places is 0-577 2I 5 664 901 532. The function log r(i+x) can be expanded in the series iogr(i+x) = jiog( a ^L-)-liogf±|+|i+r'(i)}* -KS 3 -i)* 3 -j(S 5 -i)*«-..., where 1 , 1 S2r.fi — I -f-; >2r+l ~T -j 2r- :+• and the series for log r(i +x) converges when x lies between — I and I. 52. Definite integrals can sometimes be evaluated when the limits of integration are some particular numbers, although the corresponding indefinite integrals cannot be found. Definite For example, we have the result Integrals. ( (i — x 2 )""J logxo>o), 5inu?r v " dx = Tr(,cotaw — cotbw), (ol), (iv.) ( x 2 .cos 2x.e~ l2 d.v- = — jC -1 Vjt, ./ o , \ f 1 1 — x 2 ax , T \y-)\ — ; — ii =logtan7T, I, (viii.)f°5!!l*iO*'^S' Line Integrals. /(« and is called a " repeated integral." The identification of a surface integral, such as fff(x, y)dxdy, with a repeated integral cannot always be made, but implies that the function satisfies certain conditions of continuity. In the same way volume integrals are usually evaluated by regarding them as repeated integrals, and a volume integral is written in the form ffff(x, y, z)dxdydz. Integrals such as surface and volume integrals are usually called " multiple integrals." Thus we have " double " integrals, " triple " integrals, and so on. In contradistinction to multiple integrals the ordinary integral of a function of one variable with respect to that variable is called a " simple integral. A more general type of surface integral may be defined by taking an arbitrary surface, with or without an edge. We suppose in the . first place that the surface is closed, or has no edge. We u ace mav mar j c a l ar g e number of points on the surface, and n egra s. ^ Taw t h e tangent planes at all these points. These tangent planes form a polyhedron having a large number of faces, one to each marked point; and we may choose the marked points so that all the linear dimensions of any face are less than some arbitrarily chosen length. We may devise a rule for increasing the number of marked points indefinitely and decreasing the lengths of all the edges of the polyhedra indefinitely. If the sum of the areas of the faces tends to a limit, this limit is the area of the surface. If we multiply the value of a function /at a point of the surface by the measure of the area of the corresponding face of the polyhedron, sum for all the faces, and pass to a limit as before, the result is a surface integral, and is written ssm- The extension to the case of an open surface bounded by an edge presents no difficulty. A line integral taken along a curve is defined in a similar way, and is written ffds where ds is the element of arc of the curve (§ 33). The direction cosines of the tangent of a curve are dx/ds, dy/ds, dz/ds, and line integrals usually present themselves in the form u ~ds^~ v ds^~ w ds) ds or S>(- w d xJ r l 'dy+u>dz). In like manner surface integrals usually present themselves in the form _ Jfte+mv+nftdS where /, m, n are the direction cosines of the normal to the surface drawn in a specified sense. The area of a bounded portion of the plane of (x, y) may be ex- pressed either as lf(xdy-ydx), or as ffdxdy, the former integral being a line integral taken round the boundary of the portion, and the latter a surface integral taken over the area within this boundary. In forming the line integral the boundary is supposed to be described in the positive sense, so that the included area is on the left hand. 53a. We have two theorems of transformation connect- Theorems ing volume integrals with surface integrals and surface of Qreen integrals with line integrals. The first theorem, called and " Green's theorem," is expressed by the equation Stokes. fJS (i+8+8) ^3*=//(«+«i+»f)•&-%) fe where the integral on the left is taken round the curve s in the chosen sense. When the axes are left-handed, we may either reverse the sense of I, m, n and maintain the formula, or retain the sense of I, m, n and change the sign of the right-hand member of the equation. For the validity of the theorems of Green and Stokes it is in general necessary that the functions involved should satisfy certain con- ditions of continuity. For example, in Green's theorem the differ- ential coefficients d£/dx, dy/dy, df/dz must be continuous within S. Further, there are restrictions upon the nature of the curves or surfaces involved. For example, Green's theorem, as here stated, applies only to simply-connected regions of space. The correction for multiply-connected regions is important in several physical theories. 54. The process of changing the variables in a multiple integral, such as a surface or volume integral, is divisible into two stages. "Tt is necessary in the first place to determine the differential element expressed by the product of the differentials of the ^" a "# e of first set of variables in terms of the differentials of the J arlaoles second set of variables. It is necessary in the second place fj a ... to determine the limits of integration which must be em- , " t . ployed when the integral in terms of the new variables is " egra ' evaluated as a repeated integral. The first part of the problem is solved at once by the introduction of the Jacobian. If the variables of one set are denoted by x^ x 2 , . . ., x„, and those of the other set by «i, Ui u„, we have the relation dx\dx%. . .dx„ = d(xi,x 2 , ,-%•„) d(u u u 2 ,. . . ,«„) diiidih. . .dun. 14 OUTLINES] INFINITESIMAL CALCULUS 55i In regard to the second stage of the process the limits of integration must be determined by the rule that the integration with respect to the second set of variables is to be taken through the same domain as the integration with respect to the first set. For example, when we have to integrate a function f{x, y) over the area within a circle given by x 2 +y' = a 2 , and we introduce polar coordinates so that x = r cos 9, y = r sin 9, we find that r is the value of the Jacobian, and that all points within or on the circle are given by a^r^O, 2k>9^ o, and we have (" dx (^ ^~ X2 \f(x,y)dy = | "drf "f(rcos$,rsm9)rd8. J -a J -> \a2-x2) JO J If we have to integrate over the area of a rectangle a ^x 5s o, b^y^o, and we transform to polar coordinates, the integral becomes the sum of two integrals, as follows: — f" given by the equations x — r sin 8 cos <£, y=r sin 8 sin 4>, z = r cos 9, and the equation of the surface is of the form r =/(0, ) , the area is expressed by the formula The surface integral of a function of (9, ) over the surface of a sphere r — const, can be expressed in the form and in a number of equivalent forms. The area of any portion of the plane is represented by the double integral where J denotes the above Jacobian, and the integration is taken through a suitable domain. When the boundary consists of portions of curves for which | =const., or r\ =const., the above is generally the simplest way of evaluating it. (vi.) The problem of " rectifying " a plane curve, or finding its length, is solved by evaluating the integral or, in polar coordinates, by evaluating the integral In both cases the integrals are line integrals taken along the curve. (vii.) When we use curvilinear coordinates {, 17 as in (v.) above, the length of any portion of a curve £ = const, is given by the integral H-ldr, taken between appropriate limits for 17. There is a similar formula for the arc of a curve tj = const. (viii.) The area of a surface z=f(x, y) can be expressed by the formula /J>+(!)'+(!)T^ />/; F(0, C w F(r, 8, )r 2 sin 0d8. (x.) Integrations of rational functions through the volume of an ellipsoid x 2 /a 2 +y 2 /b 2 +z l /c 2 = i are often effected by means of a general theorem due to Lejeune Dirichlet (1839), which is as follows: when the domain of integration is that given by the inequality ©* +©'•+- + ©)-*'■ where the o's and a's are positive, the value of the integral //■■■ *i» 1-1 . Xi'-i' 1 . . . dxidxi . . . 0102 . r(S r (a- :t(i+5!+^+...) \ aj a 2 / by} When the coordinates of the points of a surface are expressed as If, however, the object aimed at is an integration through the volume of an ellipsoid it is simpler to reduce the domain of integration to that within a sphere of radius unity by the transformation x = a£, y = bri, z = c{, and then to perform the integration through the sphere by transforming to polar coordinates as in (ix). 56. Methods of approximate integration began to be devised very early. Kepler's practical measurement of the focal sectors A OBrox i. of ellipses (1609) was an approximate integration, as also "f 1 . '. was the method for the quadrature of the hyperbola given *jj haul' by James Gregory in the appendix to his Exercitationes e f. geometricae (1668). In Newton's Methodus differentialis "* ' (171 1 ) the subject was taken up systematically. Newton's te ^ at ' "' object was to effect the approximate quadrature of a given curve by making a curve of the type y=0o+0ix+a.23c 2 + . . . +a«* n pass through the vertices of (71 + 1 ) equidistant ordinates of the given curve, and by taking the area of the new curve so determined as an approximation to the area of the given curve. In 1743 Thomas Simpson in his Mathematical Dissertations published a very con- venient rule, obtained by taking the vertices of three consecutive equidistant ordinates to be points on the same parabola. The distance between the extreme ordinates corresponding to the abscissae x = a and x = 6 is divided into 2» equal segments by ordinates yi, ys, ■ . -Vin-i, and the extreme ordinates are denoted by yo, yzn- The vertices of the ordinates y , J"i, y% lie on a parabola with its axis parallel to the axis of y, so do the vertices of the ordinates yi, y 3 , yt, and so on. The area is expressed approximately by the formula {(b-a)/6n}[yo+yz„+2(y2+yi+ . . . +y 2n -2)+4(j'i+3'3+ • • • +yin-i)], which is known as Simpson's rule. Since all simple integrals can be represented as areas such rules are applicable to approximate in- tegration in general. For the recent developments reference may be made to the article by A. Voss in Ency. d. Math. Wiss., Bd. II., A. 2 (1899), and to a monograph by B. P. Moors, Valeur approximative d'une integrate definie (Paris, 1905). Many instruments have been devised for registering mechanically the areas of closed curves and the values of integrals. The best known are perhaps the " planimeter " of J. Amsler (1854) and the " integraph " of Abdank-Abakanowicz (1882). Bibliography. — For historical questions relating to the subject th chief authority is M. Cantor, Geschichte d. Mathematik (3 Bde., Leipzig, 1894-1901). For particular matters, or special periods, the following may be mentioned: H. G. Zeuthen, Geschichte d. Math, im Altertum u. Miltelalter (Copenhagen, 1896) and Gesch. d. Math. im XVI. u. XVII. Jahrhundert (Leipzig, 1903); S. Horsley, Isaaci Newtoni opera quae exstant omnia (5 vols., London, 1779-1785); C. I. Gerhardt, Leibnizens math. Schriften (7 Bde., Leipzig, 1849- 1863) ; Joh. Bernoulli, Opera omnia (4 Bde., Lausanne and Geneva, 1742). Other writings of importance in the history of the subject 552 INFINITIVE— INFLUENZA are cited in the course of the article. A list of some of the more important treatises on the differential and integral calculus is ap- pended. The list has no pretensions to completeness ; in particular, most of the recent books in which the subject is presented in an elementary way for beginners or engineers are omitted.^L. Euler, Institutiones calculi differ -entialis (Petrop., 1755) and Institutiones calculi integralis (3 Bde., Petrop., 1768-1770); J. L. Lagrange, Lecons sur le calcul des fonctions (Paris, 1806, CEuvres, t. x.), and, Theorie des fonctions analyliques (Paris, 1797, 2nded., 1813, CEuvres, t. ix.) ; S. P. Lacroix, Traite de calcul diff. et de calcul int. (3 tt., Paris, 1808-1819). There have been numerous later editions; a translation by Herschel, Peacock and Babbage of an abbreviated edition of Lacroix's treatise was published at Cambridge in 1816. G. Peacock, Examples of the Differential and Integral Calculus (Cambridge, 1820); A. L. Cauchy, Resume des lecons . . . sur le calcul infinitesimale (Paris, 1823), and Lecons sur le calcul differentiel (Paris, 1829; CEuvres, ser. 2, t. iv.) ; F. Minding, Handbuchd. Diff.-u. Int.-Rechnung (Berlin, 1836); F. Moigno, Lecons sur le calcul diff. (4 tt., Paris, 1840-1861) ; A. de Morgan, Diff. and Int. Calc. (London, 1842); D. Gregory, Examples on' the Diff. and Int. Calc. (2 vols., Cambridge, 1841-1846) ; I. Todhunter, Treatise on the Diff. Calc. and Treatise on the Int. Calc. (London, 1852), numerous later editions; B. Price, Treatise on the Infinitesimal Calculus (2 vols., Oxford, 1854), numerous later editions; D. Bierens de Haan, Tables d'integrales definies (Amsterdam, 1858); M. Stegemann, Crundriss d. Diff.- u. Int.-Rechnung (2 Bde., Hanover, 1862) numerous later editions; J. Bertrand, Traite de calc. diff. et int. (2 tt., Paris, 1864-1870); J. A. Serret, Cours de calc. diff. et int. (2 tt., Paris, 1868, 2nd ed., 1880, German edition by Harnack, Leipzig, 1884-1886, later German editions by Bohlmann, 1896, and Scheffers,' 1906,1 incomplete) ; B.Williamson, Treatise on the Diff. Calc. (Dublin, 1872), and Treatise on the Int. Calc. (Dublin, 1874) numerous later editions of both; also the article " Infinitesimal Calculus " in the 9th ed. of the Ency. Brit.; C. Hermite, Cours d 'analyse (Paris, 1873); O. Schlomilch, Compendium d. hoheren Analysis (2 Bde., Leipzig, 1874) numerous later editions; J. Thomae, Einleitung in d. Theorie d. bestimmlen Integrate (Halle, 1875); R. Lipschitz, Lehrbuch d. Analysis (2 Bde., Bonn, 1877, 1880); A. Harnack, Elemente d. Diff.-u. Int.-Rechnung (Leipzig, 1882, Eng. trans, by Cathcart, London, 1891); M. Pasch, Einleitung in d. Diff.-u. Int.-Rechnung (Leipzig, 1882); Genocchi and Pcano, Calcolo differenziale (Turin, 1884, German edition by Bohlmann and Schepp, Leipzig, 1898, 1899); H. Laurent, Traite d 'analyse (7 tt., Paris, 1885-1891); J. Edwards, Elementary Treatise on the Diff. Calc. (London, 1886), several later editions; A. G. Greenhill, Diff. and Int. Calc. (London, 1886, 2nd ed., 1891); E. Picard, Traite d 'analyse (3 tt., Paris, 1891-1896); O. Stolz, Crund- zilge d. Diff.- u. Int.-Rechnung (3 Bde., Leipzig, 1893-1899); C. Jordan, Cours d'analyse (3 tt., Paris, 1893-1896); L. Kronecker, Vorlesungen ii. d. Theorie d. einfachen u. vielfachen Integrate (Leipzig, 1894); J. Perry, The Calculus for Engineers (London, 1897); H. Lamb, An Elementary Course of Infinitesimal Calculus (Cambridge, 1897) ; G. A. Gibson, An Elementary Treatise on the Calculus (London, 1901) ; E. Goursat, Cours d'analyse mathematique (2 tt., Paris, 1902- 1905) ; C.-J. de la Vallee Poussin, Cours d'analyse infinitesimale (2 tt., Louvain and Paris, 1903-1906) ; A. E. H. Love, Elements of the Diff. and Int. Calc. (Cambridge, 1909) ; W. H. Young, The Funda- mental Theorems of the Diff. Calc. (Cambridge, 1910). A resume' of the infinitesimal calculus is given in the articles "Diff.-u. Int-Rech- nung " by A. Voss, and " Bestimmte Integrale " by G. Brunei in Ency. d. math. Wiss. (Bde. ii. A. 2, and ii. A. 3, Leipzig, 1899, 1900). Many questions of principle are discussed exhaustively by E. W. Hobson, The Theory of Functions of a Real Variable (Cambridge, 1907). (A. E. H.L.) INFINITIVE, a form of the verb, properly a noun with verbal functions, but usually taken as a mood (see Grammar). The Latin grammarians gave it the name of infinitus or infinilivus modus, i.e. indefinite, unlimited mood, as not having definite persons or numbers. INFLEXION (from Lat. inflectere, to bend), the action of bending inwards, or turning towards oneself, or the condition of being bent or curved. In optics, the term " inflexion " was used by Newton for what is now known as " diffraction of light " (q.v.). For inflexion in geometry see Curve. Inflexion when used of the voice, in speaking or singing, indicates a change in tone, pitch or expression. In grammar (q.v.) inflexion indicates the changes which a word undergoes to bring it into correct relations with the other words with which it is used. In English grammar nouns, pronouns, adjectives (in their degrees of comparison), verbs and adverbs are inflected. Some gram- marians, however, regard the inflexions of adverbs more as an actual change in word-formation. INFLUENCE (Late Lat. influentia, from influere, to flow in), word whose principal modern meaning is that of power, control or action affecting others, exercised either covertly or without visible means or direct physical agency. It is one of those numerous terms of astrology (q.v.) which have established themselves in current language. From the stars was supposed to flow an ethereal stream which affected the course of events on the earth and the fortunes and characters of men. For the law as to " undue influence " see Contract. INFLUENZA (syn. "grip," la grippe), a term applied to an infectious febrile disorder due to a specific bacillus, characterized specially by catarrh of the respiratory passages and alimentary canal, and occurring mostly as an epidemic. The Italians in the 1 7th century ascribed it to the influence of the stars, and hence the name " influenza." The French name grippe came into use in 1743, and those of petite poste and petit courier in 1762, while general became another synonym in 1780. Apparently the scourge was common; in 1403 and 1557 the sittings of the Paris law courts had to be suspended through it, and in 1427 sermons had to be abandoned through the coughing and sneezing; in 1510 masses could not be sung. Epidemics occurred in 1580, 1676, 1703, 1732 and 1737, and their cessation was supposed to be connected with earthquakes and volcanic eruptions. The disease is referred to in the works of the ancient physicians, and accurate descriptions of it have been given by medical writers during the last three centuries. These various accounts agree substantially in their narration of the phenomena and course of the disease, and influenza has in all times been regarded as fulfilling all the conditions of an epidemic in its sudden invasion, and rapid and extensive spread. Among the chief epidemics were those of 1762, 1782, 1787, 1803, 1833, 1837 and 1847. It appeared in fleets at sea away from all communication with land, and to such an extent as to disable them temporarily for service. This happened in 1782 in the case of the squadron of Admiral Richard Kempenfelt (1718-1782), which had to return to England from the coast of France in consequence of influenza attacking his crews. Like cholera and plague, influenza reappeared in the last quarter of the 19th century, after an interval of many years, in epidemic or rather pandemic form. After the year 1848, in which 7963 deaths were directly attributed to influenza in England and Wales, the disease continued prevalent until i860, with distinct but minor epidemic exacerbations in 1851, 1855 and 1858; during the next decade the mortality dropped rapidly though not steadily, and the diminution continued down to the year 1889, in which only 55 deaths were ascribed to this cause. It is not clear whether the disease ever disappears wholly, and the deaths registered in 1889 are the lowest recorded in any year since the registrar-general's returns began. Occasionally local outbreaks of illness resembling epidemic influenza have been observed during the period of abeyance, as in Norfolk in 1878 and in Yorkshire in 1887; but whether such outbreaks and the so-called " sporadic " cases are nosologically identical with epidemic influenza is open to doubt. The relation seems rather to be similar to that between Asiatic cholera and " cholera nostras." Individual cases may be indistinguishable, but as a factor in the public health the difference between sporadic and epidemic influenza is as great and unmistakable as that between the two forms of cholera. This fact, which had been forgotten by some since 1847 and never learnt by others, was brought home forcibly to all by the visitation of 1889. According to the exhaustive report drawn up by Dr H. Franklin Parsons for the Local Government Board, the earliest appearances were observed in May 1889, and three localities are mentioned as affected at the same time, all widely separated from each other — namely, Bokhara in Central Asia, Athabasca in the north-west Territories of Canada and Greenland. About the middle of October it was reported at Tomsk in Siberia, and by the end of the month at St Petersburg. During November Russia became generally affected, and cases were noticed in Paris, Berlin, Vienna, London and Jamaica (?). In December epidemic influenza became established over the whole of Europe, along the Mediterranean, in Egypt and over a large area in the United States. It appeared in several towns in England, beginning with Portsmouth, but did not become generally INFLUENZA 553 epidemic until the commencement of the new year. In London the full onset of unmistakable influenza dated from the ist of January 1890. Everywhere it seems to have exhibited the same explosive character when once fully established. In St Petersburg, out of a government staff of 260 men, 220 were taken ill in one night, the 15th of November. During January 1890 the epidemic reached its height in London, and appeared in a large number of towns throughout the British Islands, though it was less prevalent in the north and north-west than in the south. January witnessed a great extension of the disease in Germany, Holland, Switzerland, Austria-Hungary, Italy, Spain and Portugal; but in Russia, Scandinavia and France it was already declining. The period of greatest activity in Europe was the latter half of December and the earlier half of January, with the change of the year for a central point. Other parts of the world affected in January 1890 were Cape Town, Canada, the United States generally, Algiers, Tunis, Cairo, Corsica, Sardinia, Sicily, Honolulu, Mexico, the West Indies and Montevideo. In February the provincial towns of England were most severely affected, the death-rate rising to 27-4, but in London it fell from 28-1 to 21-2, and for Europe generally the back of the epidemic was broken. At the same time, however, it appeared in Ceylon, Penang, Japan, Hong Kong and India; also in West Africa, attacking Sierra Leone, and Gambia in the middle of the month; and finally in the west, where Newfoundland and Buenos Aires were invaded. In March influenza became widely epidemic in India, particularly in Bengal and Bombay, and made its appearance in Australia and New Zealand. In April and May it was epidemic all over Australasia, in Central America, Brazil, Peru, Arabia and Burma. During the summer and autumn it reached a number of isolated islands, such as Iceland, St Heiena, Mauritius and Reunion. Towards the close of the year it was reported from Yunnan in the interior of China, from the Shire Highlands in Central Africa, Shoa in Abyssinia, and Gilgit in Kashmir. In the course of fifteen months, beginning with its undoubted appearance in Siberia in October 1889, it had traversed the entire globe. The localities attacked by influenza in 1889-1890 appear in no case to have suffered severely for more than a month or six weeks. Thus in Europe and North America generally the visita- tion had come to an end in the first quarter of 1890. The earliest signs of an epidemic revival on a large scale occurred in March i8gi, in the United States and the north of England. It was reported from Chicago and other large towns in the central states, whence it spread eastwards, reaching New York about the end of March. In England it began in the Yorkshire towns, particularly in Hull, and also independently in South Wales. In London influenza became epidemic for the second time about the end of April, and soon afterwards was widely distributed in England and Wales. The large towns in the north, together with London and Wales, suffered much more heavily in mortality than in the previous attack, but the south-west of England, Scotland and Ireland escaped with comparatively little sickness. The same may be said of the European continent generally, except parts of Russia, Scandinavia and perhaps the north of Germany. This second epidemic coincided with the spring and early summer; it had subsided in London by the end of June. The experience of Sheffield is interesting. In 1890 the attack, contrary to general experience, had been undecided, lingering and mild; in 1891 it was very sudden and extremely severe, the death-rate rising to 73-4 during the month of April, and subsiding with equal rapidity. During the third quarter of the year, while Europe was free, the antipodes had their second attack, which was more severe than the first. As in England, it reversed the previous order of things, beginning in the provinces and spreading thence to the capital towns. The last quarter of the year was signalized by another recrudescence in Europe, which reached its height during the winter. All parts, including Great Britain, were severely affected. In England those parts which had borne the brunt of the epidemic in the early part of the year escaped. In fact, these two revivals may be regarded as one, temporarily interrupted by the summer quarter. The recrudescence at the end of 1891 lasted through mid-winter, and in many places, notably in London, it only reached its height in January 1892, subsiding slowly and irregularly in February and March. Brighton suffered with exceptional severity. The continent of Europe seems to have been similarly affected. In Italy the notifications of influenza were as follow: 1891 — ■ January to October, o; November, 30; December, 6461: 1892— January, 84,543; February, 55,352; March, 28,046; April, 7962; May, 1468; June, 223. Other parts of the world affected were the West Indies, Tunis, Egypt, Sudan, Cape Town Teheran, Tongking and China. In August 1892 influenza was reported from Peru, and later in the year from various places in Europe. A fourth recrudescence, but of a milder character, occurred in Great Britain in the spring of 1893, and a fifth in the following winter, but the year 1894 was freer from influenza than any since 1890. In 1895 another extensive epidemic took place. In 189O influenza seemed to have spent its strength, but there was an increased prevalence of the disease in 1897, which was repeated on a larger scale in 1898, and again in 1899, when 12,417 deaths were recorded in England and Wales. This was the highest death-rate since 1892. After this the death-rate declined to half that amount and remained there with the slight upward variations until 1907, in which the total death-rate was 9257. The experience of other countries has been very similar; they have all been subjected to periodical revivals of epidemic influenza at irregular intervals and of varying intensity since its reappearance in 1889, but there has been a general though not a steady decline in its activity and potency. Its behaviour is, in short, quite in keeping with the experience of 1847-1860, though the later visitation appears to have been more violent and more fatal than the former. Its diffusion was also more rapid and probably more extensive. The foregoing general summary may be supplemented by some further details of the incidence in Great Britain. The number of deaths directly attributed to influenza, and the death- rates per million in each year in England and Wales, are as follow: — Death-rates Year. Deaths. per million. Year. Deaths. per million. 1890 4.523 157 1899 12,417 389 1891 16,686 574 1900 16,245 504 1892 15.737 534 1901 5,666 174 1893 9,669 325 1902 7.366 223 1894 6,625 220 1903 6,322 189 1895 12,880 424 1904 5.694 168 1896 3.753 122 1905 6,953 204 1897 6,088 196 1906 6,310 183 1898 10,405 33i 1907 9.257 265 It is interesting to compare these figures with the corresponding ones for the previous visitation: — Year. Deaths. Death-rates | per million. Year. Deaths. Death-rates per million. 1847 1848 1849 1850 1851 4,881 7.963 1,611 1,380 2,152 285 460 ! 02 78 120 1852 1853 1854 1855 1.359 1,789 1,061 3.568 76 99 58 193 The two sets of figures are not strictly comparable, because, during the first period, notification of the cause of death was no£ compulsory; but it seems clear that the later wave was much the more deadly. The average annual death-rate for the nine years is 320 in the one case against 162 in the other, or as nearly as possible double. In both epidemic periods the second year was far more fatal than the first, and in both a marked revival took place in the ninth year; in both also an intermediate recrudescence occurred, in the fifth year in one case, in the sixth in the other. The chief point of difference is the sudden and marked drop in 1849-1850, against a persistent high mortality in 1892-1893, especially in 1892, which was nearly as fatal as 554 INFLUENZA To make the significance of these epidemic figures clear, it should be added that in the intervening period 1861-1889 the average annual death-rate from influenza was only fifteen, and in the ten years immediately preceding the 1890 outbreak it was only three. Moreover, in epidemic influenza, the mortality directly attributed to that disease is only a fraction of that actually caused by it. For instance, in January 1890 the deaths from influenza in London were 304, while the excess of deaths from respiratory diseases was 1454 and from all causes 1958 above the average. We have seen above that the mortality was far greater in the second epidemic year than in the first, and this applies to all parts of England, and to rural as well as to urban communities, as the following table shows: — Deaths from Influenza. 1890. 1891. 24 Great Towns over 80,000 population . 35 Towns between 20,000 and 80,000 21 Towns between 10,000 and 20,000 85 Rural Sanitary Districts 624 439 186 46 62 317 2302 2417 765 196 196 841 In spite of these figures, it appears that the 1890 attack, which was in general much more sudden in its onset than that of 1891, also caused a great deal more sickness. More people were " down with influenza," though fewer died. For instance, the number of persons treated at the Middlesex Hospital in the two months' winter epidemic of 1890 was 1279; in the far more fatal three months' spring epidemic of 1891 it was only 726. One explanation of this discrepancy between the incidence of sickness and mortality is that in the second attack, which was more protracted and more insidious, the stress of the disease -fell more upon the lungs. Another is that its comparative mildness, combined with the time of year, in itself proved dangerous, because it tempted people to disregard the illness, whereas in the first epidemic they were too ill to resist. On the whole, rural districts showed a higher death-rate than towns, and small towns a higher one than large ones in both years. This is explained by the age distribution in such localities; influenza being particu- larly fatal to aged people, though no age is exempt. Certain counties were much more severely affected than others. The eastern counties, namely, Essex, Suffolk and Norfolk, together with Hampshire and one or two others, escaped lightly in both years; the western counties, namely, North and South Wales, with the adjoining counties of Monmouth, Hereford and Shrop- shire, suffered heavily in both years. It will be convenient to discuss seriatim the various points of interest on which light has been thrown by the experience described above. The bacteriology of influenza is discussed in the article on Parasitic Diseases. The disease is often called " Russian " influenza, and its origin in 1889 suggests that the name may have some foundation in fact. A writer, who saw the epidemic break out in Bokhara, is quoted by him to the following effect: — " The summer of 1888 was exceptionally hot and dry, and was followed by a bitterly cold winter and a rainy spring. The dried- up earth was full of cracks and holes from drought and sub- sequent frost, so that the spring rains formed ponds in these holes, inundated the new railway cuttings, and turned the country into a perfect marsh. When the hot weather set in the water gave off poisonous exhalations, rendering malaria general." On account of the severe winter, the people were enfeebled from lack of nourishment, and when influenza broke out suddenly they died in large numbers. Europeans were very severely affected. Russians, hurrying home, carried the disease westwards, and caravans passing eastwards took it into Siberia. There is a striking similarity in the conditions described to those observed in connexion with outbreaks of other diseases, particularly typhoid fever and diphtheria, which have occurred on the super- vention of heavy rain after a dry period, causing cracks and fissures in the earth. Assuming the existence of a living poison in the ground, we can easily understand that under certain conditions, such as an exceptionally dry season, it may develop exceptional properties and then be driven out by the subsequent rains, causing a violent outbreak of illness. Some such explana- tion is required to account for the periodical occurrence of epidemic and pandemic diffusions starting from an endemic centre. We may suppose that a micro-organism of peculiar robustness and virulence is bred and brought into activity by a combination of favourable conditions, and is then disseminated more or less widely according to its " staying power," by human agency. Whether central Asia is an endemic centre for influenza or not there is no evidence, but the disease seems to be more often prevalent in the Russian Empire than elsewhere. Ex- tensive outbreaks occurred there in 1886 and 1887, and it is certain that the 1889 wave was active in Siberia at an earlier date than in Europe, and that it moved eastwards. The hypo- thesis that it originated in China is unsupported by evidence. But whatever may be the truth with regard to origin, the dis- semination of influenza by human agency must be held to be proved. This is the most important addition to our knowledge of the subject contributed by recent research. The upshot of the inquiry by Dr Parsons was to negative all theories of atmo- spheric influence, and to establish the conclusion that the disease was " propagated mainly, perhaps entirely, by human inter- course." He found that it prevailed independently of climate, season and weather; that it moved in a contrary direction to the prevailing winds; that it travelled along the lines of human intercourse, and not faster than human beings can travel; that in 1889 it travelled much faster than in previous epidemics, when the means of loco- motion were very inferior; that it appeared first in capital towns, seaports and frontier towns, and only affected country district? later; that it never commenced suddenly with a large number of cases in a place previously free from disease, but that epidemic manifestations were generally preceded for some days or weeks by scattered cases ; that conveyance of infection by individuals and its introduction into fresh places had been observed in many instances; that persons brought much into contact with others were generally the first to suffer; that persons brought together in large numbers in enclosed spaces suffered more in proportion than others, and that the rapidity and extent of the outbreak in institutions corresponded with the massing together of the inmates. These conclusions, based upon the 1889-1890 epidemic, have been confirmed by subsequent experience, especially in regard to the complete independence of season and weather shown by influenza. It has appeared and disappeared at all seasons and in all weathers and only popular ignorance continues to ascribe its behaviour to atmospheric conditions. In Europe, however, it has prevailed more often in winter than in summer, which may be due to the greater susceptibility of persons in winter, or, more probably, to the fact that they congregate more in buildings and are less in the open air during that part of the year. No doubt is any longer entertained of its infectious character, though the degree of infectivity appears to vary considerably. Many cases have been recorded of individuals introducing it into houses, and of all or most of the other inmates then taking it from the first case. Difficulties in preventing the spread of infection are due to (1) the shortness of the period of incubation, (2) the disease being infectious in the earliest stages before the nature of the illness is recognized, (3) the milder varieties being equally infectious with the severe attacks, and the patient going to work and spreading the infection, (4) the diagnosis often being difficult, influenza being possibly confused with ordinary catarrhal attacks, typhoid fever and other diseases. Domestic animals seem to be free from any suspicion of being liable to human influenza. Sanitary conditions, other than overcrowding, do not appear to exercise any influence on the spread of influenza. Influenza has been shown to be an acute specific fever having nothing whatever to do with a " bad cold." There may be some inflammation of the respiratory passages, and then symptoms of catarrh are present, but that is not necessarily the case, and in some epidemics such symptoms are quite I exceptional. This had been recognized by various writers INFLUENZA 555 before the 1889 visitation, but it had not been generally realized, as it has been since, and some medical authorities, who persisted in regarding influenza as essentially a " catarrhal " affection, were chiefly to blame for a widespread and tenacious popular fallacy. Leichtenstern, in his masterly article in Nothnagel's Handbuch, divides the disease as follows: — (1) Epidemic influenza vera caused by Pfeiffer's bacillus; (2) Endemic-epidemic influenza vera, which occurs several years after a pandemic and is caused by the same bacillus; (3) Endemic influenza nostras or catarrhal fever, called la grippe, and bearing the same relation to true influenza as cholera nostras does to Asiatic cholera. The " period of incubation " is one to four days. Susceptibility varies greatly, but the conditions that influence it are matters of conjecture only. It appears that the inhabitants of Great Britain are less susceptible than those of many other countries. Dr Parsons gives the following list, showing the proportion of the population estimated to have been attacked in the 1889- 1890 epidemic in different localities: — Place. Per cent. Place. Per cent. St Petersburg . Berlin Nuremberg Grand-Duchy of Hesse Grand-Duchy, other Districts .... Heligoland .... Budapest .... 50 33 67 25-30 50-75 50 50 Portugal Belgrade Antwerp Gaeta .... Massachusetts . Peking .... St Louis (Mauritius) 90 30-40 33 33 50-77 39 50 67 In and about London he reckoned roughly from a number of returns that the proportion was about 12I % among those employed out of doors and 25% among those in offices, &c. The proportion among the troops in the Home District was 9'3%- The General Post Office made the highest return with 33 '6%, which is accounted for partly by the enormous number of persons massed together in the same room in more than one department, and partly by the facilities for obtaining medical advice, which would tend to bring very light cases, unnoticed elsewhere, upon the record. No public service was seriously disorganized in England by sickness in the same manner as on the continent of Europe. Some individuals appear to be totally immune; others take the disease over and over again, deriving no immunity, but apparently greater susceptibility from previous attacks. The symptoms were thus described by Dr Bruce Low from observations made in St Thomas's Hospital, London, in January 1890: — The invasion is sudden; the patients can generally tell the time when they developed the disease; e.g. acute pains in the back and loins came on quite suddenly while they were at work or walking in the street, or in the case of a medical student, while playing cards, rendering him unable to continue the game. A workman wheeling a barrow had to put it down and leave it ; and an omnibus driver was unable to pull up his horses. This sudden onset is often accom- panied by vertigo and nausea, and sometimes actual vomiting of bilious matter. There are pains in the limbs and general sense of aching all over; frontal headache of special severity; pains in the eyeballs, increased by the slightest movement of the eyes; shiver- ing; general feeling of misery and weakness, and great depression of spirits, many patients, both men and women, giving way to weeping; nervous restlessness; inability to sleep, and occasionally delirium. In some cases catarrhal symptoms develop, such as running at the eyes, which are sometimes injected on the second day ; sneezing and sore throat; and epistaxis, swelling of the parotid and submaxillary glands, tonsilitis, and spitting of bright blood from the pharynx may occur. There is a hard, dry cough of a paroxysmal kind, worst at night. There is often tenderness of the spleen, which is almost always found enlarged, and this persists after the acute symptoms have passed. The temperature is high at the onset of the disease. In the first twenty-four hours its range is from 100° F. in mild cases to 105° in severe cases. Dr J. S. Bristowe gave the following description of the illness during the same epidemic: — The chief symptoms of influenza are, coldness along the back, with shivering, which may continue off and on for two or three days ; severe pain in the head and eyes, often with tenderness in the eyes and pain in moving them; pains in the ears; pains in the small of the back; pains in the limbs, for the most part in the fleshy portions, but also in the bones and joints, and even in the fingers and toes; and febrile temperature,'which may in the early period rise to 104 or 105 F. At the same time the patient feels excessively ill and prostrate, is apt to suffer from nausea or sickness and diarrhoea, and is for the most part restless, though often (and especially in the case of children and those advanced in age) drowsy. ... In ordinary mild cases the above symptoms are the only important ones which present themselves, and the patient may recover in the course of three or four days. He may even have it so mildly that, although feeling very ill, he is able to go about his ordinary work. In some cases the patients have additionally some dryness or soreness of the throat, or some stiffness and discharge from the nose, which may be accom- panied by slight bleeding. And in some cases, for the most part in the course of a few days, and at a time when the patient seems to be convalescent, he begins to suffer from wheezing in the chest, cough, and perhaps a little shortness of breath, and before long spits mucus in which are contained pellets streaked or tinged with blood. . . . Another complication is diarrhoea. Another is a roseolous spotty rash. . . . Influenza is by no means necessarily attended with the catarrhal symptoms which the general public have been taught to regard as its distinctive signs, and in a very large proportion of cases no catarrhal condition whatever becomes developed at any time. Several writers have distinguished four main varieties of the disease — namely, (1) nervous, (2)gastro-intestinal, (3)respiratory, (4) febrile, a form chiefly found in children. Clifford Allbutt says, " Influenza simulates other diseases." Many forms are of typhoid or comatose types. Cardiac attacks are common, not from organic disease but from the direct poisoning of the heart muscle by influenza. Perhaps the most marked feature of influenza, and certainly the one which victims have learned to dread most, is the prolonged debility and nervous depression that frequently follow an attack. It was remarked by Nothnagel that " Influenza produces a specific nervous toxin which by its action on the cortex produces psychoses." In the Paris epidemic of 1890 the suicides increased 25%, a large proportion of the excess being attributed to nervous prostration caused by the disease. Dr Rawes, medical superintendent of St Luke's hospital, says that of insanities traceable to influenza melancholia is twice as frequent as all other forms ^f insanity put together. Other common after-effects are neuralgia, dyspepsia, insomnia, weakness or loss of the special senses, particularly taste and smell, abdominal pains, sore throat, rheumatism and muscular weakness. The feature most dangerous to life is the special liability of patients to inflammation of the lungs. This affection must be regarded as a complication rather than an integral part of the illness. The following diagram gives the annual death-rate per million in England and Wales, and is taken from an article by Dr Arthur Newsholme in The Practitioner (January 1907). The deaths directly attributed to influenza are few in propor- tion to the number of cases. In the milder forms it offers hardly any danger to life if reasonable care be taken, but in the severer forms it is a fairly fatal disease. In eight London hospitals the case-mortality among in-patients in the 1890 outbreak was 34-5 per 1000; among all patients treated it was i-6 per 1000. In the army it was rather less. The infectious character of influenza having been determined, suggestions were made for its administrative control on the familiar lines of notification, isolation and disinfection, but this has not hitherto been found practicable. In March 1895, however, the Local Government Board issued a memorandum recommend- ing the adoption of the following precautions wherever they can be carried out: — 1 . The sick should be separated from the healthy. This is especially important in the case of first attacks in a locality or a household. 2. The sputa of the sick should, especially in the acute stage of the disease, be received into vessels containing disinfectants. Infected articles and rooms should be cleansed and disinfected. 3. When influenza threatens, unnecessary assemblages of persons should be avoided. 4. Buildings and rooms in which many people necessarily con- gregate should be efficiently aerated and cleansed during the intervals of occupation. 556 IN FORMA PAUPERIS— INFORMER There is no routine treatment for influenza except bed. In all cases bed is advisable, because of the danger of lung complica- tions, and in mild ones it is sufficient. Severer ones must be treated according to the symptoms. Quinine has been much used. Modern " anti-pyretic " drugs have also been extensively employed, and when applied with discretion they may be useful, but patients are not advised to prescribe them for them- selves. Sir Wm. Broadbent in a note on the prophylaxis of influenza recommends quinine in a dose of two grains every morning, and remarks: " I have had opportunities of obtaining extraordinary evidence of its protective power. In a large public school it was ordered to be taken every morning. Some of the boys in the school were home boarders, and it was found that while 300 200 too the boarders at the school took the quinine in the presence | of a master every morning, there were scarcely any cases of influenza among them, although the home boarders suffered nearly as much as before." He continues, " In a large girls' school near London the same thing was ordered, and the girls and mistresses took their morning dose but the servants were forgotten. The result was that scarcely any girl or mistress suffered while the servants were all down with influenza." The liability to contract influenza, and the danger of an attack if contracted, are increased by depressing conditions, such as exposure to cold and to fatigue, whether mental or physical. Attention should, therefore, be paid to all measures tending to the maintenance of health. Persons who are attacked by influenza should at once seek rest, warmth and medical treatment, and they should bear in mind that the risk of relapse, with serious complications, constitutes a chief danger of the disease. In addition to the ordinary text-books, see the series of articles by experts on different aspects in The Practitioner (London) for January 1907. IN FORMA PAUPERIS (Latin, " in the character of pauper "), the legal phrase for a method of bringing or defending a case in court on the part of persons without means. By an English statute of 1495 (n Hen. VII. c. 12), any poor person having cause of action was entitled to have a writ according to the nature of the case, without paying the fees thereon. The statute of 1495 was repealed by the Statute Law Revision and Civil Procedure Act 1883, but its provisions, as well as the chancery practice were incorporated into one code and embodied in the rules of the Supreme Court (O. xvi. rr. 22-31). Now any person may be admitted to sue as a pauper, on proof that he is not worth £25, his wearing apparel and the subject matter of the cause or matter excepted. He must lay his case before counsel for opinion, and counsel's opinion thereon, with an affidavit of the party suing that the case contains a full and true statement of all the material facts to the best of his knowledge and belief, must be produced before the proper officers to whom the applica- tion is made. A person who desires to defend as a pauper must enter an appearance to a writ in the ordinary way and afterwards apply for an order to defend as a pauper. Where a person is admitted to sue or defend as a pauper, counsel and solicitor may be assigned to him, and such counsel and solicitor are not at liberty to refuse assistance unless there is some good reason for refusing. If any person admitted to sue or defend as a pauper agrees to pay fees to any person for the conduct of his business he will be dispaupered. Costs ordered to be paid to a pauper are taxed as in other cases. Appeals to the House of Lords in formd pauperis were regulated by the Appeal (Forma Pauperis) Act 1893, which gave the House of Lords power to refuse a petition for leave to sue. INFORMATION (from Lat. informare, to give shape or form to, to represent, describe), the communication of knowledge; in English law, a proceeding on behalf of the crown against a subject otherwise than by indict- ment. A criminal information is a proceeding in the King's bench by the attorney-general without the intervention of a grand jury. The attorney-general, or, in his absence, the solicitor-general, has a right ex officio to file a criminal information in respect of any in- dictments, but not for treason, felonies or misprision of treason. It is, however, seldom exercised, except in cases which might be described as " enormous misdemeanours," such as those peculiarly tending to disturb or endanger the king's government, e.g. sedi- tions, obstructing the king's officers in the execution of their duties, &c. In the form of the proceedings the attorney-general is said to " come into the court of our lord the king before the king himself at Westminster, and gives the court there to under- stand and be informed that, &c." Then follows the statement of the offence as in an indictment. The information is filed in the crown office without the leave of the court. An information may also be filed at the instance of a private prosecutor for misdemeanours not affecting the government, but being peculiarly flagrant and pernicious. Thus criminal informations have been granted for bribing or attempting to bribe public functionaries, and for aggravated libels on public or private persons. Leave to file an information is obtained after an application to show cause, founded on a sworn statement of the material facts of the case. Certain suits might also be filed in Chancery by way of informa- tion in the name of the attorney-general, but this species of information was superseded by Order 1, rule 1 of the Rules of the Supreme Court, 1883, under which they are instituted in the ordinary way. Informations in the Court of Exchequer in revenue cases, also filed by the attorney-general, are still resorted to (see A.-G. v. Williamson, 1889, 60 L.T. 930). INFORMER, in a general sense, one who communicates information. The term is applied to a person who prosecutes in any of the courts of law those who break any law or penal statute. Such a person is called a common informer when he furnishes evidence on criminal trials or prosecutes for breaches of penal laws solely for the purpose of obtaining the penalty I recovered, or a share of it. An action by a common informer INFUSORIA is termed a popular or qui tarn action, because it is brought by a person qui tarn pro domino rege quam pro se ipso sequitur. A suit by an informermust be brought within a year of the offence, unless a specific time is prescribed by the statute. The term informer is also used of an accomplice in crime who turns what is called " king's evidence " (see Accomplice). In Scotland, informer is the term applied to the party who. in criminal proceedings, sets the lord advocate in motion. INFUSORIA, the name given by Biitschli (following O F Ledermiiller, 1763) to a group of Protozoa. The name arose 3 557 Fig. i. Ciliata Opalinopsis sepiolae, Foett.: a parasitic i_i „i, ^„- 1 .11 ,--,- Holotrichous mouthless Ciliate from the liver of the Squid, a, branched meganucleus; b, vacuoles (non-con- tractile). 2. A similar specimen treated with picro- carmine, showing a remarkably branched and twisted meganucleus (a), in place of several nuclei. 3. Anoplophrya naidos, Duj.; a mouth- less Holotrichous Ciliate parasitic in the worm Nais. a, the large axial meganucleus; b, contractile vacuoles. 4. Anoplophrya prolifera, C. and L.; from the intestine of Clitellio. Remark- able for the adhesion of incomplete fission-products in a metameric series, a, meganucleus. 5. Amphileptus gigas, C. and L. (Gymno- stomaceae). b, contractile vacuoles; c, trichocysts (see fig. 2); d, mega- nucleus; e. pharynx. 6. 7. Prorodon niveus, Ehr. (Gymno- stomaceae). a, meganucleus; b, contractile vacuole; c, pharynx with horny cuticular lining. 6. The fasciculate cuticle of the pharynx isolated. 13- 14. 15- 16. Trachelitis ovum, Ehr. (Gymnosto- maceae); showing the reticulate arrangement of the endosarc, b, contractile vacuoles; c, the cuticle- lined pharynx. 10,^ 11, 12. Icthyophthirius multifilius, Fouquet (Gymnostomaceae). Free individual and successive stages of division to form spores, a, mega- nucleus; b, contractile vacuoles. " Didinium nasutum, Mull. (Gymno- stomaceae). The pharynx is everted and has seized a Paramecium as food, a, meganucleus; b, contrac- tile vacuole; c, everted pharynx. Euplotes charon, Miill. (Mypotrich- aceae); lateral view of the animal when using its great cirrhi, x, as ambulatory organs. Euplotes harpa, Stein (Hvpotrich- aceac); /;, mouth; x, cirrhi. ' Nyctotherus cordiformis, Stein (a Heterotriceae), parasitic in the intes- tine of the Frog; 0, meganucleus; b, contractile vacuole; c, food par- ticle; d, anus; e, heterotrichous band of membranelles; /, pharynx; i, small cilia. from the procedure adopted by the older microscopists to obtain animalcules. Infusions of most varied organic substances were prepared (hay and pepper being perhaps the favourite ones), the method of obtaining them including maceration and decoction, as well as infusion in the strict sense; they were then allowed to decompose in the air, so that various living beings developed therein. As classified by C. G. Ehrenberg m his monumema! f-.thsionstierrhen ais vnllkommmr Orcanis- men, they included (1) Desmids, Diatoms and Schizomycetes now regarded as essentially Plant Protista or Protophytes; (2)^ Sarcodina (excluding Foraminifera, as well as Radiolaria' which were only as yet known by their skeletons, and termed Polycystina), and (3) Rotifers, as well as (4) Flagellates and Infusoria in our present sense. F. Dujardin in his Histoire des zoophytes (1841) gave nearly as liberal an interpretation to the name; while C. T. Van Siebold (1845) narrowed it to its present limits save for the admission of several Flagellate families. O. Biitschli limited the group by removing the Flagel- l lata, Dinoflagellata and Cystoflagellata (g.u.)under the name of " Mastigophora " proposed earlier by R. M. Diesing (1865). We now define it thus: — Protozoa bounded by a permanent plasmic pellicle and consequently of definite form, never using pseudopodia for locomotion or ingestion, provided (at least in the young state) with 'a numerous cilia or organs derived from cilia and equipped with a double nuclear apparatus: the larger (mega-) nucleus usually dividing by con- striction, and disappearing during conjugation: the smaller (micro-) nucleus (sometimes multiple) dividing by mitosis, and entering into conjugation and giving rise to the cycle of nuclei both large and small of the race succeeding conjugation. Thus defined, the Infusoria fall into two groups: — (1) Ciliata, with cilia or organs derived from cilia throughout their lives, provided with a single permanent mouth (absent in the parasitic Opalinopsidae) flush with the body or at the base of an oral depression, and taking in food by active swallowing or by ciliary action: (2) Suc- toria, rarely ciliated except in the young state, if and taking in their food by suction through pro- ■y trusible hollow tentacles, usually numerous. The pellicle of the Infusoria is stronger and more permanent than in many Protozoa, and sometimes assumes the character of a mail of hard plates, closely fitting ; but even in this case it undergoes solution soon after death. It is continuous with a firm ecto- sarc, highly differentiated in the Ciliata, and in both groups free from coarse movable granules. The endosarc is semifluid and rich in granules mostly reserve " in nature, often showing proteid or fat reactions. One or more contractile vacuoles are pre- sent in some of the marine and all the freshwater species, and open to the surface by pores of perma- nent position: a system of canals in the deeper layers of the ectoplasm is sometimes connected with the vacucle. The body is often provided with not- hing external formations " stalk " and " theca " (or lonca ). The character of the nuclear apparatus excludes two groups both parasitic and mouthless: (1) the I richonymphidae, with a single nucleus of Leidy parasitic in Insects, especially Termites; (2) the Upahmdae, with several (often numerous) uniform nuclei, parasitic in the gut of Batrachia, &c, and producing i-nuclear zoospores which conjugate. Both these families we unite into a group of Pseudo- cihata, which may be referred to the Flagellata (q.v.). Lankester in the last edition of this Encyclo- paedia called attention to the doubtful position of Upahna, and Delage and Herouard placed Tricho- nymphidae among Flagellates. The theca_or shell is present in some pelagic species (fig. 111. 3, 5) and in many of the attached species, notably among the Peritricha (fig. iii. 21 22, 25, 26) and Suctoria (fig. viii. 11); and is found in some tree-swimming forms (fig. iii. 3, 5); it is usually chitinous, and forms a cup into which the animal protruded when at its utmost elongation, can retract itself In Metacmeta mystacina it has several distinct slits (pylomes) for the passage of tufts of tentacles. In Stentor it is ge atinous • and in the Dictyocystids it is beautifully latticed. ' in S.frW? ls T usu a U X s ?hd' and expanded at the base into a disk in buctona. In Pentnchaceae fig. iii. 8-22, 25, 26), the onlv ituJl™? W i th a Stalk ' i f, gr0W8 ?° r Some tim « after i?s formation^ and on fission two new stalks continue the old one, so as to form a tl'^'tfn 1 C . 0l< T„ (fig - iH l I , 8) - - In V r ticdla < fi S- ;ii - »■ » ' Tc.) the stalk is hollow and elastic, and attached to it along a spiral is a mouth ; h, 558 INFUSORIA prolongation of the ectosarc containing a bundle of myonemes, so that by the contractions of the bundle the stalk is pulled down into a corkscrew spiral, and on the relaxation of the muscle the elasticity of the hollow stalk straightens it out. On fission the stalk may become branched, as the solid one of Epistylis and Opercularia (fig. iii. 20) ; and the myoneme also in the tubular stem of Zoothaminum; or the branch-myoneme for the one offspring may be inserted laterally on that for the other in Car- chesium (fig. iii. 18). In several tubicolous Peritrichaceae there is some arrangement for closing their tubes. In Thuricola (fig. iii. 25-26) there is a valve which opens by the pressure of the animal on its protrusion, and closes automatically by elasticity on retraction. In Lagenophrys the animal adheres to the cup a little below the open- ing, so that its withdrawal closes the cup : at the adherent part the body mass is hardened, and so differentiated as to suggest the frame of the mouth of a purse. In Pyxicola (fig. iii. 21-22) the animal bears some way down the body a hardened shield (" operculum ") which closes the mouth of the shell on retraction. The cytoplasm of the Infusoria is very susceptible to injuries; and when cut or torn, unless the pellicle contracts rapidly to enclose the wounded surface, the substance of the body swells up, becoming frothy, with bubbles which rapidly enlarge and finally burst; the cell thus disintegrates, leaving only a few granules to mark where it was. This phenomenon, observed by Dujardin, is called " dif- fluence." The contractile vacuole appears to be one of the means by which diffluence is avoided in cells with no strong wall to resist the L-JB tf^i Fig. ii. * Surface view of Paramecium, showing the disposition of the cilia in longitudinal rows. a, mega-; b, micro-nucleus; c, junction of ecto- and en- dosarc; D, pellicle; E, endo- sarc ; /, cilia (much too numerous and crowded) ; g, trichocysts; g', same with thread; /z, discharged; i, pharynx, its undulating membrane not shown ; k, food granules collecting into a bolus; /, m, n, o, food vacuoles, their contents being digested as they pass in the endosarc along the path indicated by the arrows. 3, Outline showing contractile vacuoles in commencing diastole, surrounded by five afferent canals. 4-7 Successive stages of diastole of contractile vacuole. absorption of water in excess: for after growing in size for some time, its walls contract suddenly, and its contents are expelled to the outside by a pore, which is, like the anus, usually invisible, but permanent in position. The contractile vacuole may be single or multiple; it may receive the contents of a canal, or of a system of canals, which only become visible at the moment of the contraction of the vacuole (fig. ii. 4-7), giving liquid time to accumulate in them, or when the vacuole is acting sluggishly or imperfectly, as in the approach of asphyxia (fig. ii. 3). Besides this function, since the system passes a large quantity of water from without through the substance of the cell, it must needs act as a means of respiration and excretion. In all Peritrichaceae it opens to the vestibule, and in some of them it discharges through an intervening reservoir, curiously recalling the arrangements in the Flagellate Euglenaceae. The nuclear apparatus consists of two parts, the meganucleus, and themicronucleusormicronuclei (fig. iii. \j d, iv. 1). The meganucleus alone regarded and described as " the nucleus " by older observers is always single, subject to a few reservations. It is most frequently oval, .and then is indented by the micronucleus; but it may be lobed, the lobes lying far apart and connected by a -slender bridge or monili- form, or horseshoe-shaped (Peritrichaceae). It often contains darker inclusions, like nucleoles. It has been shown, more especially by Gruber, that many Ciliata are multinucleate, and do not possess merely a single meganucleus and a micronucleus. In Oxytricha the nuclei are large and numerous (about forty), scattered through the protoplasm, whilst in other cases the nucleus is so finely divided as to appear like a powder diffused uniformly through the medullary protoplasm (Trachelocerca) . Carmine staining, after treatment with absolute alcohol, has led to this remarkable discovery. The condition described by Foettinger in his Opalinopsis (fig. i. 1,2) is an example of this pulverization of the nucleus. The condition of pulverization had led in some cases to a total failure to detect any nucleus in the living animal, and it was only by the use of reagents that the actual state of the case was revealed. Before fission, whatever be its habitual character, it condenses, becomes oval, and divides by constriction ; and though it usually is then fibrillated, only in a few cases does it approach the typical mitotic condition. The micronucleus described by older writers as the " nucleolus " or " paranucleus " (" endoplastule " of Huxley), may be single or multiple. When the meganucleus is bilobed there are always two micronuclei, and at least one is found next to every enlargement of the moniliform meganucleus. In the fission of the Infusoria, every micronucleus divides by a true mitotic process, during which, however, its wall remains intact. From their relative sizes the meganucleus would appear to discharge during cell-life, exclusively, the functions of the nucleus in ordinary cells. Since in conjugation, however, the meganucleus degenerates and is in great part either digested or excreted as waste matter, while the new nuclear apparatus in both exconjugates arises, as we shall see, from a conjugation-nucleus of exclusively micronuclear origin, we infer that the micronucleus has for its function the carrying on of the nuclear functions of the race from one fission cycle to the next from which the meganucleus is excluded. Fission is the ordinary mode of reproduction in the Infusoria, and is usually transverse, but oblique in Stentor, &c, as in Flagellata, longitudinal in Peritrichaceae; in some cases it is always more or less unequal owing to the differentiation of the body, and conse- quently it must be followed by a regeneration of the missing organs in either daughter-cell. In some cases it becomes very uneven, affording every transition to budding, which process assumes especial importance in the Suctoria. Multiple fission (brood-formation or sporulation) is exceptional in Infusoria, and when it occurs the broods rarely exceed four or eight — another difference from Flagellata. The nuclear processes during conjugation suggest the phylogenetic loss of a process of multiple fission into active gametes. As noted, in_ fission the meganucleus divides by direct constriction; each micronucleus by a mode of mitosis. The process of fission is subject in its activity to the influences of nutrition and temperature, slacken- ing as the food supply becomes inadequate or as the temperature recedes from the optimum for the process. Moreover, if the descendants of a single animal be raised, it is found that the rapidity of fission, other conditions being the same, varies periodically, under- going periods of depression, which may be followed by either (1) spontaneous recovery, (2) recovery under stimulating food, (3) recovery through conjugation, or (4) the death of the cycle, which would have ensued if 2 or 3 had been omitted at an earlier stage, but which ultimately seems inevitable, even the induction of conjugation failing to restore it. These physiological conditions were first studied by E. Maupas, librarian to the city of Algiers, in his pioneering work in the later 'eighties, and have been confirmed and extended by later observers, among whom we may especially cite G. N. Calkins. Syngamy, usually termed conjugation or " karyogamy," is of exceptional character in the majority of this group — the Peri- trichaceae alone evincing an approximation to the usual typical process of the permanent fusion of two cells (pairing-cells or gametes), cytoplasm to cytoplasm, nucleus to nucleus, to form a new cell (coupled cell, zygote). This process was elucidated by E. Maupas in 1889, and his results, eagerly questioned and repeatedly tested, have been confirmed in every fact and in every generalization of importance. Previously all that had been definitely made out was that under certain undetermined conditions a fit of pairing two and two occurred among the animals of the same species in a culture or in a locality in the open; that after a union prolonged over hours, and sometimes even days, the mates separated; that during the union the mega- nucleus underwent changes of a degenerative character; and that the micronucleus underwent repeated divisions, and that from the offspring of the micronuclei the new nuclear apparatus was evolved for each mate. Maupas discovered the biological conditions leading to conjugation: (1) the presence of individuals belonging to distinct stocks; (2) their belonging to a generation sufficiently removed from previous conjugation, but not too far removed therefrom; ^3) a deficiency of food. He also showed that during conjugation a " migratory " nucleus, the offspring of the divisions of the micro- nucleus, passes from either mate to the other, while its sister nucleus remains ' stationary "; and that reciprocal fusion of the migratory nucleus of the one mate with the stationary nucleus of the other takes place to form a zygote nucleus in either mate ; and that from these zygote nuclei in each by division, at least two nuclei are formed, the one of which enlarges to form a meganucleus, while the other remains small as the first micronucleus of the new reorganized animal, which now separates as an " exconjugate " (fig. iv). More- over, if pairing be prevented, or be not induced, the individuals produced by successive fissions become gradually weaker, their nuclear apparatus degenerates, and finally they cannot be induced INFUSORIA 559 under suitable conditions to pair normally, so that the cycle becomes extinct by senile decay. In Peritrichaceae the gametes are of unequal sizes (fig. iii. II, 12), the smaller being formed by brood fissions (4 or 8) ; syngamy is here permanent, not temporary, the smaller (male) being absorbed into the body of the larger (female) ; and there are only two nuclei that pair. Thus we have a derived binary sexual process, comparable to that of ordinary bisexual organisms '*. Fig. iii. — Ciliata: 1, 2, Heterotrichaceae ; 3-7, 23-24, Oligotrichaceac ; 8-22, 25, 26, Peritrichaceae. 1 , Spirostomumambiguum,Ehr. ; on its left side oral groove and wreath of membra nel- lae; a, moniliform mega- nucleus; b, position of con- tractile vacuole. 2, Group of Stentor polvmor- plius, O. F. Muller; the twisted end of the peri- stome indicating the posi- tion of the mouth. 3, Tintinntis lagenula, CI. and L., in free shell. 4, Strombidinm claparedii, S. Kent. 5, Shell of Codonellacampanella, Haeck. 6, 7, Torquatella typica, Lank. (= Strombidium according to Batschli); p, oral tube seen through peristomial wreath of apparently coal- escent membranellae. X, Basal, and 9. side (inverted) views of Trichodina pedi- cidus, Ehr. ; a, mega- nucleus; c, basal collar and ring of hooks; d, mouth; contractile vacuole and oral tube seen by transparency in 8. 10, Spirochona gatnmipara, Stein; a, meganuclcus; g, bud. 11, 12, Vorticella 'microstoma, Ehr.; d, formation of a brood of 8 microgametes c by multiple fission; 6, contr. vacuole. Same sp. in binary fission; a, meganucleus. V. nebulifera, Ehr.; bud swimming away by 13. 14. ■ an d * ne spiral line the curve described by describing the base. ^ e anterior end ; the clear circles are the On any irritation', contractile vacuoles on the dorsal side. (1) the motion is arrested, (2) the animal reverses its cilia and swims backwards, (3) it swerves outwards away from the axis so" as to make a larger angle with it, and (4) then swims forwards along a new axis of progression, to which it is inclined at the same angle as to the previous axis (figs, vi., vii.). In this way it alters its axis of progression when it finds itself under conditions of stirhulation. Thus a Paramecium coming into a region relatively too cold, too hot, or too poor in C0 2 or in nutriment, alters its direction of swimming; in this way individuals come to assemble in crowds where food is abundant, or even where there is a slight excess of C0 2 . This reaction may lead to fatal results ; if a solution of corrosive sublimate (Mercuric chloride) diffuses towards thehinder end of the animal faster than it progresses, the stimulus affecting the hinder end first, the axis of progression is altered so as to bring the INFUSORIA 5-6 1 animal after a few changes into a region where the solution is strong enough to kill it. This " motile reaction," first noted by H. S. Jennings, is the explanation of the general reactions of minute swimming animals to most stimuli of whatever character, including light ; the practical working out is, as he terms it, a method of " trial and error." The action, however, of a current of electricity is dis- tinctly and immediately directive; but such a stimulus is not to be found in nature. The motile reaction in the Hypotrichaceae which crawl or dart in a straight line is somewhat different, the swerve being a simple turn to the right hand — i.e. away from the mouth. Parasitism in the Infusoria is by no means so important as among Flagellates. Ichthyophthirius alone causes epidemics among Fishes, and Balantidium coli has been observed in intestinal disease in Man. The Isotricheae, among Aspirotrichaceae and the Ophryoscolecidae among Heterotrichaceae are found in abundance in the stomachs of Ruminants, and are believed to play a part in the digestion of cellu- iose, and thus to be rather commensals than parasites. A large number of attached species are epizoic commensals, some very indifferent in choice of their host, others particular not only in the species they infest, but also in the special organs to which they adhere. This is notably the case with the shelled Peritrichaceae. Lichnophora and Trichodina (fig. iii. 8, 9) among Peritrichaceae are capable of locomotion by their permanent posterior wreath or of attaching themselves by the sucker which surrounds it; Kerona polyporum glides habitually over the body of Hydra, as does Tricho- dina pediculus. Several Suctoria are endoparasitic in Ciliata, and their occurrence led to the view that they represented stages in the life-history of these. Again, we find in the endosarc of certain Ciliates green nucleated cells, which have a cellulose envelope and multiply by fission inside or outside the animal. They are symbiotic Algae, or possibly the resting state of a Chlamydomonadine Flagellate (Carterial) , and have received the name Zoochlorella. They are of constant occurrence in Paramecium bursaria, frequent in Stentor polymorphus and S. igneus, and Ophrydium versatile, and a few other species, which become infected by swallowing them. Classification. Order I. — Section A. — Gymnostomaceae. Mouth habitually closed ; swallowing an active process ; cilia (or membranelles) uniform, usually distributed evenly over the body; form variable, sometimes of circular transverse section. Section B. — Trichostomata. Mouth permanently open against the endosarc, provided with I or 2 undulating membranes often prolonged into an inturned pharynx; ingestion by action of oral ciliary apparatus. Order 2. — Subsection (a). — Aspirotrichaceae. Cilia nearly uni- form, not associated with cirrhi or membranelles, nor forming a peristomial wreath. Form usually flattened, mouth unilateral. (N.B. — Orders 1, 2 are sometimes united into the single order Holotrichaceae.) Subsection (b). — Spirotricha. Wreath of distinct mem- branelles — or of cilia fused at the base — enclosing a peristomial area and leading into the mouth. §§ i. — Wreath of separate membranelles. Order 3. — Heterotrichaceae; body covered with fine uniform cilia, usually circular in transverse section. Order 4. — Oligotrichaceae; body covering partial or wholly absent ; transverse section usually circular. Drder 5. — Hypotrichaceae; body flattened; body cilia repre- sented chiefly by stiff cirrhi in ventral rows, and fine motion- less dorsal sensory hairs. Order 6. — §§ ii. — Peritrichaceae. Peristomial ciliary wreath, spiral, of cilia united at the base; posterior wreath circular of long membranelles; body circular in section, cylindrical, taper, or bell-shaped. Illustrative Genera (selected). 1. Gymnostomaceae. (a) Ciliation general or not confined to one surface. Coleps Ehr., with pellicle locclly hardened into mailed plates; Trachelocerca Ehr.; Prorodon Ehr. (fig. i. 6, 7); Trachelius Ehr., with branching endosarc (fig. i. 8) ; Lacrymaria Ehr. (fig. i. 5), body produced into a long neck with terminal mouth surrounded by offensive trichocysts; DUeptus Duj., of similar form, but anterior process, blind, preoral; Ichthyophthirius Fouquet (fig. i. 9-12), cilia represented by two girdles of membranellae ; Didinium St. (fig. i. 13), cilia in tufts, surface with numerous tentacles each with a strong terminal trichocyst; Actinobolus Stein, body with one adoral tentacle; Ileonema Stokes, (b) Cilia confined to dorsal surface. Chilodon Ehr.; Loxodes Ehr., body flattened, ciliated on one side only, endosarc as in Trachelius; Dysteria Huxley, with the dorsal surface hardened and hinged along the median line into a bivalve shell, ciliated only on ventral surface, with a protrusible foot-like process, and a complex pharyngeal armature, (c) Cilia restricted to a single equatorial girdle, strong (probably membra- nelles) ; Mesodinium, mouth 4-lobed. 2. Aspirotrichaceae. Paramecium Hill (fig. ii. 1-3) ; Ophryoglena Ehr. ; Colpoda O. F. Muller; Colpidium St.; Lembus Cohn, with posterior strong cilium for springing; Leucophrys St.; Urocentrum Nitsch, bare, with polar and equatorial zones and a posterior tuft of long cilia; Opalinopsis Foetlinger (fig. i. 1, 2); Anoplopkyra St. (fig. i. 3, 4). (The last two parasitic mouthless genera are placed here doubtfully.) 3. Heterotrichaceae. (a) Wreath spiral; Stentor Oken. (fig. iii. 2), oval when free, trumpet-shaped when attached by pseudopods at apex, and then often secreting a gelatinous tube; Blepharisma Pcrty, sometimes parasitic in Heliozoa; Spirostomum Ehr., cylindri- cal, up to 1" in length; (b) Wreath straight, often oblique; Nycto- therus Leidy, parasitic anus always visible; Balantidium CI. and L., parasitic (B. coli in man) ; Bursaria, O.F.M., hollowed into an oval pouch, with the wreath inside. 4. Oligotrichaeceae. Tintinnus Schranck (fig. iii. 3) ; Trichodin- opsis CI. and L. ; . Codonella Haeck. (fig. iii. 5) ; Strombidium CI. and L. (fig. iii. 4), including Torquatella Lank. (fig. iii. 6, 7), according to Biitschli; Halteria Duj., with an equatorial girdle of stiff bristle-like cilia; Caenomorpha Perty (fig. iii. 23, 24); Ophryo- scolex St., with straight digestive cavity, and visible anus, parasitic in Ruminants. 5. Hypotrichaceae. Stylonychia Ehr.; Oxytricha Ehr.; Euplotes Ehr. (fig. i. 14, 15); Kerona Ehr. (epizoic on Hydra). 6. Peritrichaceae. I. Peristomial wreath projecting when ex- panded above a circular contractile collar-like rim. (a) Fam. Urceolaridae : posterior wreath permanently present around sucker-like base. Trichodina Ehr. (fig. iii. 8, 9), epizoic on Hydra; Lichnophora CI. and L. ; Cyclochaeta Hatchett Jackson; Cerda CI. and L. ; Scyphidia Duj. (b) Fam. Vorticellidae = Bell Animalcules: posterior wreath temporarily present, shed after fixation. Subfam. I. Vorticellinae animals naked, (i.) Solitary; Vorticella Linn. (fig. iii. 11-17), stalk hollow with spiral muscle; Pyxidiunt S. Kent, stalk non-contractile, (ii.) Forming colonies by budding on a branched stalk: Carchesium Ehr., hollow branches and muscles discontinuous; Zoothamnium. Ehr., branched hollow stem and muscle continuous through colony; Epislylis Ehr., stalk rigid — (the animal body in these three genera has the same characters as Vorticella) — Campanella Goldf., stalked like Epistylis, wreath of many turns (nematocysts sometimes present) (fig. iii. 19) ; Oper- cularia, stalk of Epistylis, disk supporting wreath obconical, collar very high (fig. iii. 20). Subfam. 2. Vaginicolinae ; body enclosed in a firm theca: Vaginicola Lam., shell simple, sessile; Thuricola St. Wright, shell sessile, with a valve opening inwards (fig. iii. 25-26) ; Cothurnia Ehr., shell stalked, simple; Pyxicola S. Kent, shell stalked, closed by an infraperistomial opercular thickening on the body (fig. iii. 21-22). Subfam. 3. Shells gelatinous; those of the colony aggregatec into a floating spheroidal mass several inches in diameter Ophrydium Bory, O. versatile contains Zoochlorella, which secretes oxygen, and the gas-bubbles float the colonies like green lumps o? jelly. 2. Peristomial wreath, not protrusible, surrounded by a very high usually spiral collar. Fam. Spirochonina. Spirochona St. (fig. iii. 10) ; Kentrochona Rompel; both genera epizoic on gills, &c, of small Crustacea. Suctoria. — These are distinguished from Ciliata by their possession of hollow tentacles (one only in Rhyncketa, fig. viii. 1, and Urnula) through which they ingest food, and by not possess- ing cilia, except in the young stage. Fission approximately equal is very rare. Usually it is unequal, or if nearly equal one of the halves remains attached, and the other, as an embryo or gemmule, develops cilia and swims off to attach itself else- where; Sphaerophrya (fig. viii. 2-6) alone, often occurring as an endoparasite in Ciliata, may be free, tentaculate and unattached. The ectosarc is usually provided with a firm pellicle which shows a peculiar radiate " milling " in optical section, so fine that its true nature is difficult to make out ; it may be due to radial rods, regularly imbedded, or may be the expression of radial vacuoles. The tentacles vary in many respects, but are always retractile. They are tubes covered by an extension of the pellicle; this is invaginated into the body round the base of the tentacle as a sheath, and then evaginated to form the outer layer of the tentacle itself, over which it is frequently raised into a spiral ridge, which may be traced down into the part sunk and ensheathed within the body: in Choanophrya, where the tentacles are largest, the pellicle is further continued into the interior of the tentacle. The tentacles are always pierced by a central canal opening at the apex, which may be (1) enlarged into a terrfiinal capitate sucker, (2) slightly flared, (3) truncate and closed in the resting state to become widely opened into a funnel, or (4) pointed. The tentacles are always capable of being waved from side to side, or turned in a definite direction for the reception or prehension of food; in Khyncheta, the movements of the long single tentacle recall those of an elephant's trunk, only they are more extensive and more varied. In the majority of cases the food consists of Ciliata : and the contents of the prey may be seen passing down the canal of the sucker beyond where it becomes free from the general surface. In Choanophrya the food appears to consist of the debris of the prey of the carnivorous host {Cyclops), which is sucked into the wide funnel-shaped mouths of the tentacles — by what mechanism is 562 INFUSORIA Fig. viii. — Suctoria (in all a, meganucleus ; b, contractile vacuole). 1, Rhyncheta cyclopum, Zenker; only a single tentacle and that suctorial; epizoic on Cyclops. 2, Sphaerophrya urostylae,MsLU- pas; normal adult; para- sitic in Ciliate Urostyla. 3, The same dividing by trans- verse fission, the anterior moiety with temporarily developed cilia. 4, 5, 6, Sphaerophrya stentorea, Maupas. Parasitic in Slentor, and at one time mistaken for its young. 7, Trichophrya epistylidis, CI. and L. 8, Hemiophrya Hertwig. six buds, which a gemmipara, Example with into each of branch of the meganucleus a is extended. 9, The same species, showing the two kinds of tentacles (the suctorial and the pointed), and two contrac- tile vacuoles b. 10, Ciliated embryo of Podophrya steinii, CI. and L. 1 1 , A cineta grandis, Saville Kent ; showing pedunculated cup, and animal with two bunches of entirely suc- torial tentacles. 12, Sphaerophrya magna, Mau- pas. It has seized with its tentacles, and is in the act of sucking out the juices of six examples of the Ciliate Colpoda par- vifrons. 13, Podophrya elongata, CI. and unknown. The endosarc is full of food-granules and reserve-granules (oil, colouring matter and proteid). The meganucleus and the micronucleus are both usually single, but in Dendrosoma (fig. viii. 20), of which the body is branched, and the meganucleus with it, there are numerous micronuclei. In most cases the micronucleus has not been recorded, though from the similarity of conjugation, and its presence in most cases of fission and budding that have been accurately described, we may infer that it is always present. In unequal fission the meganucleus sends a process into the bud, while the micronucleus divides as in Ciliata. The bud may be nearly equal to the remains of the original animal, or much smaller, and in that case a depression surrounds it which may deepen so as to form a brood-cavity, either communicating by a mere " birth-pore " with the outside or entirely closed. In some cases the budding is multiple vfig- viii. 8), and a large number of buds are formed and liberated at the same time. In all cases the bud escapes without tentacles, and possesses a characteristic supply of cilia, whose arrangement is constant for the species. In some cases an adult may withdraw its tentacles, moult its pellicle and develop an equipment of cilia and swim away: this is the case with Dendrocometes, parasitic on Gammarus, when its host moults. The numerous species of Suctoria, often so abundant on various species of Cyclops, are not found on the other fresh-water Copepoda, Diaptomus and Canthocamptus, belonging indeed to other families. Again, these Suctoria affect different positions, those found on the antennae not being present on the mouth parts; the ventral part of the thorax has another set ; and the inside of the pleural fold another. Rhyncheta occupies the front of the " couplers " or median down- growths uniting the coxopodites of the swimming legs, and Choano- phrya settles in the immediate neighbourhood of the mouth, preferably on the epistoma, labrum and metastomatic region, but also on the adoral appendages and in rare cases extends, when the settlement is extensive, to the bases of the two pairs of antennae; while distinct species of Podophrya settle on the antennae, the front of the thorax and the inside of the pleural folds. Dendrocometes is common on the gills of the freshwater shrimp (Amphipod) Gammarus and Stylocometes on the gills and gill-covers of the Isopod Asellus, the water-slater. The independence of the Acinetaria was threatened by the erroneous view of Stein that they were phases in the life- history of Vorticellidae. Small parasitic forms {Sphaerophrya) were also regarded erroneously as the " acinetiform young " of Ciliata. They now must be regarded as an extreme modification of the Protozoon series, in which the differentiation of organs in a unicellular animal reaches its highest point. Principal Genera. 1. Unstalked simple forms. Urnula CI. and L., permanently ciliate ; Rhyncheta Zenker (fig. viii. 1 ) , on the limb couplers of Cyclops ; Sphaerophrya CI. and L. (fig. viii. 2-6, 12), endoparasitic in Ciliata and formerly taken for embryos thereof, never attached; Tricho- phrya CI. and L. (fig. viii. 7), of similar habits, but temporarily attached, sessile. 2. Stalked simple forms; Podophrya Ehr. (fig. viii. 10, 13, 16), tentacles all knobbed or flared; Ephelota Strethill Wright, tentacles all pointed; Hemiophrya S. Kent (fig. viii. 8, 9, 14), tentacles of both kinds; Choanophrya Hartog, tentacles thick, truncate, very retrac- tile, when expanded opening into funnels for aspiration of floating prey, never for attachment — epizoic on antero-ventral parts of Cyclops. 3. Cupped forms; Solenophrya CI. and L., cup sessile; Acineta Ehr., cup stalked; Acinetopsis Butschli, like Acineta, but the cup flattened, closed distally with only slit-like apertures (" pylomes ") for the bundles of tentacles; Podocyathus, like Acineta, but with pointed as well as knobbed tentacles. 4. Tentacles in bundles at the tips of one or more processes or branches of the body. Ophryodendron CI. and L., tentaculiferous process single (fig. viii. 21); Dendrocometes Stein (fig. viii. 15), body rounded, processes repeatedly branched, epizoic on gills of Gammarus pulex; Dendrosoma Ehr. (fig. viii. 17-20), body freely branched from a basal attached stolon, meganucleus branching with the body. Bibliography. — (a) Infusoria in the widest sense: C. E. Ehren- berg. Die Infusionstierchen als vollkommene Organismen (1838); F. Dujardin, Zoophytes infusoires (1841). (b) Infusoria, including Mastigophora : M. Perty, Zur Kenntniss Kleinster Lebensformen (1852); E. Claparede and J. Lachmann, Htudes sur les infusoires 14, Hemiophrya benedenii, Fraip. ; the suctorial ten- tacles retracted. 15, Dendrocometes paradoxus, Stein. Parasitic on Gam- marus pulex; captured prey. 16, A single tentacle of Podo- phrya. R. Hertwig. 17-20, Dendrosoma radians, Ehr. : — 17, free-swimming cili- ated embryo. 1 8, Earliest fixed condition of the embryo. 19, Later stage, a single tentaculiferous process now developed. 20, Adult colony; c, en- closed ciliated embryos; d, branching stolon; e, more minute reproductive (?) bodies. 21, Ophryodendron pedicettatum, Hincks. INGEBORG— INGEMANN 563 *' les Rhitopodes (1858-1861); F. von Stein, Der Organismus der Infusionstiere (1 859-1 883) ; W. Saville Kent, A Manual of the Infusoria, including a description of all known Flagellate, Ciliate ind Tentaculiferous Protozoa (1880-1882). (c) Infusoria, as limited by Butschli. O. Biitschli, Bronn's Tierreich, vol. i. Protozoa, pt. 3 Infusoria (1887-1889), the most complete work existing, but without specific diagnoses; S. J. Hickson, " The Infusoria " in Lankester's Treatise on Zoology, vol. i. fasc. 2 (1903), a general account, well illustrated, with a diagnosis of all genera. See also Delage and Herouard, Traite de Zoologie concrete, vol. i. " La Cellule et les Protozoaires " (1896), with an illustrated conspectus of the genera; E. Maupas, " Recherches expenmentales sur la multiplication des Infusoires cilies," Arch. zool. exp. vi. (1888); and " Le Rajeunisse- ment karyogomique chez les Cilies," ib. vii. (1889); R. Sand, £tude monographique sur le groupe des Infusoires tentaculiferes (Suctoria), (1899), with diagnoses of species; A. Lang, Lehrb. der vergleich, Anatomie der wirbellosen Tiere, vol. i. " Protozoa " (1901) (a view of comparative anatomy, physiology and bionomics) ; Marcus Hartog, " Protozoa," in Cambridge Natural History, i. (1906) ; H. S. Jennings, Contributions to the Study of the Behaviour of Lower Organisms (1904) ; G. N. Calkins, " Studies on the Life History of Protozoa " (Life cycle of Paramecium), I. Arch. Entw. xv. (1902), II. Arch. Prot. i. (1902), III. Biol. Bull. iii. (1902), IV. /. Exp. Zool. i. (1904). Numerous papers dealing especially with advances in structural knowledge have appeared in the Archiv fur Protistenkunde, founded by F. Schaudinn in (902. (M. Ha.) INGEBORG [Ingeburge, Ingelburge, Ingelborg, Isem- burge, Dan. Ingib/org] (c. 1176-1237 or 1238), queen of France, was the daughter of Valdemar I., king of Denmark. She married in 1 193 Philip II. Augustus, king of France, but on the day after his marriage the king took a sudden aversion to her, and wished to obtain a separation. During almost twenty years he strained every effort to obtain from the church the declaration of nullity of his marriage. The council of Compiegne acceded to his wish on the 5th of November 1193, but the popes Celestine III. and Innocent III. successively took up the defence of the unfortunate queen. Philip, having married Agnes of Meran in June 1 196, was excommunicated, and as he remained obdurate, the kingdom was placed under an interdict. Agnes was finally sent away, but Ingeborg, shut up in the chateau of Etampes, had to undergo all sorts of privations and vexations. The king attempted to. induce her to solicit a divorce herself, or to enter a convent. At last, however (1213), hoping perhaps to justify by his wife's claims his pretensions to England, Philip was reconciled with Ingeborg, whose life from henceforth was devoted to religion. She survived him more than fourteen years, passing the greater part of the time in the priory of St Jean at Corbeil, which she had founded. See Robert Davidson, Philip II. August von Vranhreich und Ingeborg (Stuttgart, 1888); and E. Michael, " Zur Geschichte der Konigin Ingelborg " in the Zeitschrift fur Katholische Theologie (1890). INGELHEIM (Ober-Ingelheim and Nieder-Ingelheim), the name of two contiguous market-towns of Germany, in the grand-duchy of Hesse-Darmstadt, on the Selz, near its confluence with the Rhine, 9 m.W.N.W. of Mainz on the railway to Coblenz. Ober-Ingelheim, formerly an imperial town, is still surrounded by walls. It has an Evangelical church with painted windows representing scenes in the life of Charlemagne, a Roman Catholic church and a synagogue. Its chief industry is the manufacture of red wine. Pop. (1900) 3402. Nieder-Ingelheim has an Evangelical and a Roman Catholic church, and, in addition to wine, manufactories of paper, chemicals, cement and malt. Pop. 3435- Nieder-Ingelheim is, according to one tradition, the birthplace of Charlemagne, and it possesses the ruins of an old palace built by that emperor between 768 and 774. The building contained one hundred marble pillars, and was also adorned with sculptures and mosaics sent from Ravenna by Pope Adrian I. It was extended by Frederick Barbarossa, and was burned down in 1 2 70, being restored by the emperor Charles IV. in 1354. Having passed into the possession of the elector palatine of the Rhine, the building suffered much damage during a war in 1462, the Thirty Years' War, and the French invasion in 1689. Only few remains of it are now standing; but of the pillars, several are in Paris, one is in the museum at Wiesbaden and another on the Schillerplatz in Mainz. Inside its boundaries there is the restored Remigius Kirche, apparently dating from the time of Frederick I. See Hilz, Der Reichspalast zu Ingelheim (Ober-Ingelheim, 1868); and Clemen, " Der Karolingische Kaiserpalast zu Ingelheim," in Westdeutsche Zeitschrift, Band ix. (Trier, 1890). INGELOW, JEAN (1820-1897), English poet and novelist, was born at Boston, in Lincolnshire, on the 17th of March 1820. She was the daughter of William Ingelow, a banker of that town. As a girl she contributed verses and tales to the magazines under the pseudonym of " Orris," but her first (anonymous) volume, A Rhyming Chronicle of Incidents and Feelings, did not appear until her thirtieth year. This Tennyson said had " very charming things " in it, and he declared he should " like to know " the author, who was later admitted to his friendship. Miss Ingelow followed this book of verse in 1851 with a story, Allerton and Dreux, but it was the publication of her Poems in 1863 which suddenly raised her to the rank of a popular writer. They ran rapidly through numerous editions, were set to music, and sung in every drawing-room, and in America obtained an even greater hold upon public estimation. In 1867 she published The Story of Doom and other Poems, and then gave up verse for a while and became industrious as a novelist. Of the Skelligs appeared in 1872, Fated to be Free in 1873, Sarah de Berenger in 1880, and John Jerome in 1886. She also wrote Studies for Stories (1864), Stories told to a Child (1865), Mopsa the Fairy (1869), and other excellent stories for children. Her third series of Poems was published in 1885. She resided for the last years of her life in Kensington, and somewhat outlived her popularity as a poet. She died on the 20th of July 1S97. Her poems, which were collected in one volume in 1898, have often the genuine ballad note, and as a writer of songs she was exceed- ingly successful. " Sailing beyond Seas " and " When Sparrows build " in Supper at the Mill were deservedly among the most popular songs of the day; but they share, with the rest of her work, the faults of affectation and stilted phraseology. Her best-known poem was the " High Tide on the Coast of Lincoln- shire," which reached the highest level of excellence. The blemishes of her style were cleverly indicated in a well-known parody of Calverley's; a false archaism and a deliberate assump- tion of unfamiliar and unnecessary synonyms for simple objects were among the most vicious of her mannerisms. She wrote, however, in verse with a sweetness which her sentiment and her hea r t inspired, and in prose she displayed feeling for character and the gift of narrative; while a delicate underlying tenderness is never wanting in either medium to her sometimes tortured expression. Miss Ingelow was a woman of frank and hospitable manners, with a look of the Lady Bountiful of a country parish. She had nothing of the professional authoress or the " literary lady" about her, and, as with characteristic simplicity she was accustomed to say, was no great reader. Her temperament was rather that of the improvisatore than of the professional author or artist. INGEMANN, BERNHARD SEVERIN (1 789-1 862), Danish poet and novelist, was born at Torkildstrup, in the island of Falster, on the 28th of May 1789. He was educated at the grammar school at Slagelse, and entered the university of Copenhagen in 1806. His studies were interrupted by the English invasion, and or. the first night of the bombardment of the city Ingemann stood with the young poet Blicher on the walls, while the shells whistled past them, and comrades were killed on either side. All his early and unpublished writings were destroyed when the English burned the town. In i8fr he published his first volume of poems, and in 181 2 his second, followed in 1813 by a book of lyrics entitled Procne and in 1814 the verse romance, The Black Knights. In 181 5 he published two tragedies, Masaniello and Blanca, i'ollowed by The Voice in the Desert, The Shepherd of Tolosa, and other romantic plays. After a variety of publications, all very successful, he travelled in 1818 to Italy. At Rome he wrote The Liberation of Tasso, and returned in 1819 to Copenhagen. In 1820 he began to display his real power in a volume of delightful tales. In 1821 his dramatic career closed with the production of an unsuccessful 5^4 INGERSOLL— INGLEFIELD comedy, Magnetism in a Barber's Shop. In 1822 the poet was nominated lector in Danish language and literature at Soro College, and he now married. Valdemar the Great and his Men, an historical epic, appeared in 1824. The next few years were occupied with his best and most durable work, his four great national and historical novels of Valdemar Seier, 1826; Erik Mcnvcd's Childhood, 1828; King Erik, 1833; and Prince Otto of Denmark, 1835. He then returned to epic poetry in Queen Margaret, 1836, and in a cycle of romances, Holger Danske, 1837. His later writings consist of religious and sentimental lyrics, epic poems, novels, short stories in prose, and fairy tales. His last publication was The Apple oj Gold, 1856. In 1846 Ingemann was nominated director of Sorb' College, a post from which he retired in 1849. He died on the 24th of February 1862. Inge- mann enjoyed during his lifetime a popularity unapproached even by that of Ohlenschlager. His boundless facility and fecundity, his sentimentality, his religious melancholy, his direct appeal to the domestic affections, gave him instant access to the ear of the public. His novels are better than his poems; of the former the best are those which are directly modelled on the manner of Sir Walter Scott. As a dramatist he outlived his reputation, and his unwieldy epics are now little read. Ingemann's works were collected in 41 vols, at Copenhagen (1843-1865). His autobiography was edited by Galskjot in 1862; his correspondence by V. Heise (1879-1881); and his letters to Grundtvig by S. Grundtvig (1882). See also H. Schwanenfliigel, Ingemanns Liv og Digtning (1886); and Georg Brandes, Essays (1889). INGERSOLL, ROBERT GREEN (1833-1899), American lawyer and lecturer, was born in Dresden, New York, on the 1 ith of August 1833. His father was a Congregational minister, who removed to Wisconsin in 1843 and to Illinois in 1845. Robert, who had received a good common-school education, was admitted to the bar in 1854, and practised law with success in Illinois. Late in 1861, during the Civil War, he organized a cavalry regiment, of which he was colonel, until captured at Lexington, Tennessee, on the 18th of December 1862, by the Confederate cavalry under General N. B. Forrest. He was paroled, waited in vain to be exchanged, and in June 1863 resigned from the service. He was attorney-general of Illinois in 1867-1869, and in 1876 his speech in the Republican National Convention, naming James G. Blaine for the Presidential candidate, won him a national reputation as a public speaker. As a lawyer he distinguished himself particularly as counsel for the defendants in the " Star-Route Fraud " trials. He was most widely known, however, for his public lectures attacking the Bible, and his anti-Christian views were an obstacle to his political advancement. Ingersoll was an eloquent rhetorician rather than a logical reasoner. He died at Dobbs Ferry, N.Y., on the 21st of July 1899. His principal lectures and speeches were published under the titles: The Gods and Other Lectures (1876); Some Mistakes of Moses (1879); Prose Poems (1884); Great Speeches (1887). His lectures, entitled " The Bible," " Ghosts," and " Foundations of Faith," attracted particular attention. His complete works were published in 12 vols, in New York in 1900. INGERSOLL, a town and port of entry of Oxford county, Ontario, Canada, 19 m. E. of London, on the river Thames and the Grand Trunk and Canadian Pacific railways. Pop. (1901) 4572. The principal manufactures are agricultural imple- ments, furniture, pianos and screws. There is a large export trade in cheese and farm produce. INGHAM, CHARLES CROMWELL (1796-1863), American artist, was born in Dublin, Ireland. He was a pupil of the Dublin Academy, emigrated to the United States at the age of twenty- one, and immediately became identified with the art life of that country, being one of the founders of the National Academy of New York in 1826 and its vice-president from 1845 to 1850. He painted portraits of the reigning beauties of New York and acquired considerable reputation, continuing to practise his profession until his death, in New York, on the 10th of December 186 v INGHIRAMI, the name of an Italian noble family of Volterra. The following are its most important members: Tommaso Inghirami (1470-1516), a humanist, is best known for his Latin orations, seven of which were published in 1777. His success in the part of Phaedra in a presentation of Seneca's Hippolytus (or Phaedra) led to his being generally known as Fedra. He received high honours from Alexander VI., Leo X. and Maximilian I. Francesco Inghirami (1772-1846), a distinguished archaeo- logist, fought in the French wars (1799), and afterwards devoted himself especially to the study of Etruscan antiquities. He founded a college at Fiesole and collected, though without critical insight, a mass of valuable material in his Monumenti etruschi (10 vols., 1820-1827), Galleria omerica (3 vols., 1829-1851), Pitture di vasifittili (1831-1837), Museo etrusco chiusino (2 vols., 1833), and the incomplete Sloria della Toscana (1841-1845): these works were elaborately illustrated. His brother, Giovanni Inghirami (1779-1851), was an astronomer of repute. He was professor of astronomy at the Institute founded by Ximenes in Florence and published beside a number of text-books EJJemeridi dell' occultazione delle piccole slelle sotto la lima (1809-1830): EJfemeridi di Venese e Giove all' uso de' naviganti (1821-1824); Tavole astronomichi universali portatili ( 1 8 1 1 ) ; . Base trigonometrica m isurata in Toscana ( 1 8 1 8) ; Carta topografica e geometrica della Toscana (1830). INGLEBY, CLEMENT MANSFIELD (1823-1886), English Shakespearian scholar, was born at Edgbaston, Birmingham, on the 29th of October 1823, the son of a solicitor. After taking his degree at Trinity College, Cambridge, he entered his father's office, eventually becoming a partner. In 1859 ne abandoned the law and left Birmingham to live near London. He contri- buted articles on literary, scientific and other subjects to various magazines, but from 1874 devoted himself almost entirely to Shakespearian literature. His first work in this field had been an exposure of the manipulations of John Payne Collier, entitled The Shakespeare Fabrications (1859); his work as a commentator began with The Still Lion (1874), enlarged in the following year into Shakespeare Hermeneutics. In this book many of the then existing difficulties of Shakespeare's text were explained. In the same year (1875) he published the Centurie of Prayse, a collection of references to Shakespeare and his works between 1592 and 1692. His Shakespeare: the Man and the Book was published in 1877-1881; he also wrote Shakespeare's Bones (1882), in which he suggested the disinterment of Shakespeare's bones and an examination of his skull. This suggestion, though not due to vulgar curiosity, was regarded, however, by public opinion as sacrilegious. He died on the 26th of September 1886, at Ilford, Essex. Although Ingleby's reputation now rests solely on his works on Shakespeare, he wrote on many other subjects. He was the author of hand-books on metaphysic and logic, and made some contributions to the study of natural science. He was at one time vice-president of the New Shakspere Society, and one of the original trustees of the " Birthplace." INGLEFIELD, SIR EDWARD AUGUSTUS (1820-1894), British admiral and explorer, was born at Cheltenham, on the 27th of March 1820, and educated at the Royal Naval College, Portsmouth. His father was Rear-Admiral Samuel Hood Inglefield (1783-1848), and his grandfather Captain John Nicholson Inglefield (1748-1828), who served with Lord Hood against the French. The boy went to sea when fourteen, took part in the naval operations on the Syrian Coast in 1840, and in 1845 was promoted to the rank of commander for gallant conduot at Obligado. In 1832 he commanded Lady Franklin's yacht " Isabel " on her cruise to Smith Sound, and his narrative of the expedition was published under the title of A Summer Search for Sir John Franklin (1853). He received the gold medal of the Royal Geographical Society on his return. and was given command of the " Phoenix," in which he made three trips to the Arctic, bringing home part of the Belcher Arctic expedition in 1834. In that year he was again sent out on the last attempt made by the Admiralty to find Sir John Franklin. I11 the Crimean War Captain Inglefield took part in (he siege INGLE-NOOK— INGRAM, J. K. S^S of Sevastopol. He was knighted in 1877, and nominated a Knight Commander of the Bath ten years later. He was pro- moted admiral in 1879. Besides being an excellent marine artist, he was the inventor of the hydraulic steering gear and the Inglefield anchor. He died on the 5th of September 1894. His son, Captain Edward Fitzmaurice Inglefield (b. 1861), became secretary of Lloyds in 1906. Sir Edward Inglefield's brother, Rear-Admiral V. O. Inglefield, was the father of Rear-Admiral Frederick Samuel Inglefield (b. 1854), director of naval intelli- gence in 1902-1904, and of two other sons distinguished as soldiers. INGLE-NOOK (from Lat. igniculus, dim. of ignis, fire), a corner or seat by the fireside, within the chimney-breast. The open Tudor or Jacobean fire-place was often wide enough to admit of a wooden settle being placed at each end of the embrasure of which it occupied the centre, and yet far enough away not to be inconveniently hot. This was one of the means by which the builder sought to avoid the draughts which must have been extremely frequent in old houses. English literature is full of references, appreciatory or regretful, to the cosy ingle-nook that was killed by the adoption of small grates. Modern English and American architects are, however, fond of devising them in houses designed on ancient models, and owners of old buildings frequently remove the modern grates and restore the original arrangement. INGLIS, SIR JOHN EARDLEY WILMOT (1814-1862), British major-general, was born in Nova Scotia on the 15th of November 1814. His father was the third, and his grandfather the first, bishop of that colony. In 1833 he joined the 32nd Foot, in which all his regimental service was passed. In 1837 he saw active service in Canada, and in 1848-1849 in the Punjab, being in command at the storming of Mooltan and at the battle of Gujrat. In 1857, on the outbreak of the Indian Mutiny, he was in command of his regiment at Lucknow. Sir Henry Lawrence being mortally wounded during the siege of the residency, Inglis took command of the garrison, and maintained a successful defence for 87 days against an overwhelming force. He was promoted to major-general and made K.C.B. After further active service in India, he was, in i860, given command of the British troops in the Ionian Islands. He died at Hamburg on the 27th of September 1862. INGLIS, SIR WILLIAM (1764-1835), British soldier, was born in 1764, a member of an old Roxburghshire family. He entered the army in 1781. After ten years in America he served in Flanders, and in 1796 took part in the capture of St Lucia. In 1809 he commanded a brigade in the Peninsula, taking part in the battle of Busaco (1810) and the first siege of Badajoz. At Albuera his regiment, the 57th, occupied a most important position, and was exposed to a deadly fire. " Die hard! Fifty- Seventh,'' cried Inglis, '" Die hard ! " The regiment's answer has gone down to history. Out of a total strength of 579, 23 officers and 415 rank and file were killed and wounded. Inglis himself was wounded. On recovering, he saw further Peninsular service. In two engagements his horse was shot under him. His services were rewarded by the thanks of parliament and in 1825 he became lieutenant-general, and was made a K.C.B. After holding the governorships of Kinsale and Cork, he was, in 1830, appointed colonel of the 57th. He died at Ramsgate on the 29th of November 1835. INGOLSTADT, a fortified town of Germany, in the kingdom of Bavaria, on the left bank of the Danube at its confluence with the Schutter, 52 m. north of Munich, at the junction of the main lines of railway, Munich, Bamberg and Regensburg- Augsburg. Pop. (1900) 22,207. The principal buildings are the old palace of the dukes of Bavaria-Ingolstadt, now used as an arsenal; the new palace on the Danube; the remains of the earliest Jesuits' college in Germany, founded in 1555; the former university buildings, now a school; the theatre; the large Gothic Frauenkirche, founded in 1425, with two massive towers, containing several interesting monuments, among them the tomb of Dr Eck, Luther's opponent; the Franciscan convent and nunnery; and several other churches and hospitals. Ingol- stadt possesses several technical and other schools. In 1472 a university was founded in the town by the Bavarian duke, Louis the Rich, which at the end of the 16th century was attended by 4000 students. In 1800 it was removed toLandshut, whence it was transferred to Munich in 1826. Its newer public buildings include an Evangelical church, a civil hospital, an arsenal and an orphanage. The industries are cannon-founding, manufacture of gunpowder and cloth, and brewing. Ingolstadt, known as Aureatum or Chrysopolis, was a royal villa in the beginning of the 9th century, and received its charter of civic incorporation before 1255. After that date it grew in importance, and became the capital of a dukedom which merged in that of Bavaria-Munich. The fortifications, erected in 1539, were put to the test during the contests of the Reformation period and in the Thirty Years' War. Gustavus Adolphus vainly besieged Ingolstadt in 1632, when Tilly, to whom there is a monument in the Frauenkirche, lay mortally wounded within the walls. In the War of the Spanish Succession it was besieged by the margrave of Baden in 1704. In 1743 it was surrendered by the French to the Austrians, and in 1800, after three months' siege, the French, under General Moreau, took the town, and dis- mantled the fortifications. They were rebuilt on a much larger scale under King Louis I., and since 1870 Ingolstadt has ranked as a fortress of the first class. In 1872 even more important fortifications were constructed, which include tetes-de-pont with round towers of massive masonry, and the redoubt Tilly on the right bank of the river. Sec Gerstner, Geschichte der Stadt Ingolstadt (Munich, 1853); and Prantl, Geschichte der Ludwig Maximilians Universitat (Munich, 1872). INGOT, originally a mould for the casting of metals, but now a mass of metal cast in a mould, and particularly the small bars of the precious metals, cast in the shape of an oblong brick or wedge with slightly sloping sides, in which form gold and silver are handled as bullion at the Bank of England and the Mint. Ingots of varying sizes and shapes are cast of other metals, and " ingot-steel " and " ingot-iron " are technical terms in the manufacture of iron and steel (see Iron and Steel) . The word is obscure in origin. It occurs in Chaucer (" The Canon's Yeoman's Tale ") as a term of alchemy, in the original sense of a mould for casting metal, and, as the New English Dictionary points out, an English origin for such a term is unlikely. It may, however, be derived from in and the O. Eng. geotan to pour; cf. Ger. giessen and Einguss, a mould. The Fr. lingol, with the second English meaning only, has been taken as the origin of " ingot " and derived from the Lat. lingua, tongue — with a supposed reference to the shape. This deriva- tion is wrong, and French etymologists have now accepted the English origin for the word, lingot having coalesced from V ingot. INGRAM, JAMES (1774-1850), English antiquarian and Anglo-Saxon scholar, was born near Salisbury on the 21st of December 1774. He was educated at Warminster and Winchester schools and at Trinity College, Oxford, of which he became a fellow in 1803. From 1803 to 1808 he was Rawlinsonian professor of Anglo-Saxon at Oxford, and in 1824 was made President of Trinity College and D.D. His time, however, was principally spent in antiquarian research, and especially in the study (*' Anglo-Saxon, in which field he was the pre-eminent scholar of his time. He published in 1823 an edition of the Saxon Chronicle. His other works include admirable Memorials of Oxford (1832-1837), and The Church in the Middle Centuries (1842). He died on the 5th of September 1850. INGRAM, JOHN KELLS (1823-1907), Irish scholar and economist, was born in Co. Donegal, Ireland, on the 7th of July 1823. Educated at Newry School and Trinity College, Dublin, he was elected a fellow of his college in 184&. He held the professorship of Oratory and English Literature in Dublin University from 1852 to 1866, when he became regius professor of Greek. ' In 1879 he was appointed librarian. Ingram was remarkable for his versatility. In his undergraduate days he had written the well-known poem " Who fears to speak of Ninety- eight ? " and his Sonnets and other Poems (1900) reveal the 5 66 INGRES poetic sense. He contributed many important papers to mathe- matical societies on geometrical analysis, and did much useful work in advancing the science of classical etymology, notably in his Creek and Latin Etymology in England, The Etymology oj Liddell and Scott. His philosophical works include Outlines oj the History oj Religion (1900), Human Nature and Morals according to A. Comle (1901), Practical Morals (1904), and the Final Transition (1905). He contributed to the 9th edition of the Encyclopaedia Britannica an historical and biographical article on political economy, which was translated into nearly every European language. His History oj Slavery and Serjdom was also written for the 9th edition of the Encyclopaedia Britan- nica. He died in Dublin on the 18th of May 1907. INGRES, JEAN AUGUSTE DOMINIQUE (1780-1867), French painter, was born at Montauban, on the 29th of August 1780. His father, for whom he entertained the most tender and respectful affection, has described himself as sculpteur en pldlre; he was, however, equally ready to execute every other kind of decorative work, and now and again eked out his living by taking portraits or obtained an engagement as a violin-player. He brought up his son to command the same varied resources, but in consequence of certain early successes — the lad's performance of a concerto of Viotti's was applauded at the theatre of Toulouse — his attention was directed chiefly to the study of music. At Toulouse, to which place his father had removed from Montauban in 1792, Ingres had, however, received lessons from Joseph Roques, a painter whom he quitted at the end of a few months to become a pupil of M. Vigan, professor at the academy of fine arts in the same town. From Vigan, Ingres, whose vocation became day by day more distinctly evident, passed to M. Briant, a landscape-painter who insisted that his pupil was specially gifted by nature to follow the same line as himself. For a while Ingres obeyed, but he had been thoroughly aroused and en- lightened as to his own objects and desires by the sight of a copy of Raphael's " Madonna della Sedia," and, having ended his con- nexion with Briant, he started for Paris, where he arrived about the close of 1 796. He was then admitted to the studio of David, for whose lofty standard and severe principles he always retained a profound appreciation. Ingres, after four years of devoted study, during which (1800) he obtained the second place in the yearly competition, finally carried off the Grand Prix (1801). The work thus rewarded — the " Ambassadors of Agamemnon in the Tent of Achilles " (Ecole des Beaux Arts) — was admired by Flaxman so much as to give umbrage to David, and was succeeded in the following year (1802) by the execution of a " Girl after Bathing," and a woman's portrait; in 1804 Ingres exhibited " Portrait of the First Consul " (Musee de Liege), and portraits of his father and himself; these were followed in 1806 by " Portrait of the Emperor " (luvalides), and portraits of M, Mme, and Mile Riviere (the first two now in the Louvre). These and various minor works were executed in Paris (for it was not until 1809 that the state of public affairs admitted of the re-establishment of the Academy of France at Rome), and they produced a disturbing impression on the public. It was clear that the artist was some one who must be counted with; his talent, the purity of his line, and his power of literal rendering were generally acknowledged; but he was reproached with a desire to be singular and extraordinary. " Ingres," writes Frau v. Hastfer (Leben und Kunst in Paris, 1806) " wird nach Italien gehen, und dort wird er vielleicht vergessen dass er zu etwas Grossem geboren ist, und wird eben darum ein hohes Ziel erreichen." In this spirit, also, Chaussard violently attacked his " Portrait of the Emperor " {Pausanias Francais, 1806), nor did the portraits of the Riviere family escape. The points on which Chaussard justly lays stress are the strange discordances of colour — such as the blue of the cushion against which Mme Riviere leans, and the want of the relief and warmth of life, but he omits to touch on that grasp of his subject as a whole, shown in the portraits of both husband and wife, which already evidences the strength and sincerity of the passionless point of view which marks all Ingres's best productions. The very year after his arrival in Rome (1808) Ingres produced " Oedipus and the Sphinx " (Louvre; lithographed by Sudre, engraved by Gaillard), a work which- proved him in the full possession of his mature powers, and began the" Venus Anadyomene " (Collection Rieset; engraving by Pollet), completed forty years later, and exhibited in 1855. These works were followed by some of his best portraits, that of M. Bochet (Louvre), and that of Mme la Comtesse de Tournon, mother of the prefect of the department of the Tiber; in 1811 he finished "Jupiter and Thetis," an immense canvas now in the Musee of Aix; in 1812 " Romulus and Acron " (Ecole des Beaux Arts), and " Virgil reading the Aeneid " — a composition very different from the version of it which has become popular through the engraving executed by Pradier in 1832. The original work, executed for a bedchamber in the Villa Aldobrandini-Miollis, contained neither the figures of Maecenas and Agrippa nor the statue of Marcellus; and Ingres, who had obtained possession of it during his second stay in Rome, intended to complete it with the additions made for engraving. But he never got beyond the stage of preparation, and the picture left by him, together with various other studies and sketches, to the Musee of his native town, remains half destroyed by the process meant for its regeneration. The " Virgil " was followed by the " Betrothal of Raphael," a small painting, now lost, executed for Queen Caroline of Naples; " Don Pedro of Toledo Kissing the Sword of Henry IV." (Collec- tion Deymie; Montauban), exhibited at the Salon of 1814, together with the " Chapelle Sistine " (Collection Legentil; lithographed by Sudre), and the " Grande Odalisque" (Collection Seilliere; lithographed by Sudre). In 18 15 Ingres executed " Raphael and the Fornarina " (Collection MmeN.de Rothschild; engraved by Pradier); in 1816 " Aretin " and the " Envoy of Charles V." (Collection Schroth), and " Aretin and Tintoret " (Collection Schroth); in 1817 the "Death of Leonardo" (engraved by Richomme) and " Henry IV. Playing with his Children " (engraved by Richomme), both of which works were commissions from M. le Comte de Blacas, then ambassador of France at the Vatican. " Roger and Angelique " (Louvre; lithographed by Sudre), and " Francesca di Rimini " (Musee of Angers; lithographed by Aubry Lecomte), were completed in 1819, and followed in 1820 by " Christ giving the Keys to Peter " (Louvre). In 181 s, also, Ingres had made many projects for treating a subject from the life of the celebrated duke of Alva, a commission from the family, but a loathing for " cet horrible homme " grew upon him, and finally he abandoned the- task and entered in his diary — " J'etais force par la necessite de peindre un pareil tableau; Dieu a voulu qu'il restat en ebauche." During all these years Ingres's reputation in France did not increase. The interest which his " Chapelle Sistine " had aroused at the Salon of 18T4 soon died away; not only was the public indifferent, but amongst his brother artists Ingres found scant recognition. The strict classicists looked upon him as a renegade, and strangely enough Delacroix and other pupils of Guerin — the leaders of that romantic movement for which Ingres, throughout his long life, always expressed the deepest abhorrence — alone seem to have been sensible of his merits. The weight of poverty, too, was hard to bear. In 1813 Ingres had married; his marriage had been arranged for him with a young woman who came in a business-like way from Montauban, on the strength of the representations of her friends in Rome. Mme Ingres speedily acquired a faith in her husband which enabled her to combat with heroic courage and patience the difficulties which beset their common existence, and which were increased by their removal to Florence. There Bartolini, an old friend, had hoped that Ingres might have materially bettered his position, and that he might have aroused the Florentine school — a weak offshoot from that of David — to a sense of its own shortcomings. These expecta- tions were disappointed. The good offices of Bartolini, and of one or two other persons, could only alleviate the miseries of this stay in a town where Ingres was all but deprived of the means of gaining daily bread by the making of those small portraits for the execution of which, in Rome, his pencil had been constantly in request. Before his departure he had, however, been commissioned to paint for M. de Pastoret the " Entry of INGRESS— INHAMBANE S 6 7 Charles V. into Paris," and M. de Pastoret now obtained an order for Ingres from the Administration of Fine Arts; he was directed to treat the " Vceu de Louis XIII." for the cathedral of Montauban. This work, exhibited at the Salon of 1824, met with universal approbation: even those sworn to observe the un- adulterated precepts of David found only admiration for the " Vceu de Louis XIII." On his return Ingres was received at Montauban with enthusiastic homage, and found himself celebrated throughout France. In the following year (1825) he was elected to the Institute, and his fame was further extended in 1826 by the publication of Sudre's lithograph of the " Grande Odalisque," which, having been scorned by artists and- critics alike in 1819, now became widely popular. A second commission from the government called forth the " Apotheosis of Homer," which, replaced by a copy in the decoration of the ceiling for which it was designed, now hangs in the galleries of the second storey of the Louvre. From this date up till 1834 the studio of Ingres was thronged, as once had been thronged the studio of David, and he was a recognized chef d'ecole. Whilst he taught with despotic authority and admirable wisdom, he steadily worked; and when in 1834 he produced his great canvas of the "Martyrdom of Saint Symphorien " (cathedral of Autun; lithographed by Trichot-Garneri), it was with angry disgust and resentment that he found his work received with the same doubt and indifference, if not the same hostility, as had met his earlier ventures. The suffrages of his pupils, and of one or two men — like Decamps — of undoubted ability, could not soften the sense of injury. Ingres resolved to work no longer for the public, and gladly availed himself of the opportunity to return to Rome, as director of the ficole de France, in the room of Horace Vernet. There he executed " La Vierge a 1'Hostie " (Imperial collections, St Petersburg), " Stratonice," " Portrait of Cherubini " (Louvre), and the " Petite Odalisque " for M. Marcotte, the faithful admirer for whom, in 1814, Ingres had painted the " Chapelle Sistine." The " Stratonice," executed for the duke of Orleans, had been exhibited at the Palais Royal for several days after its arrival in France, and the beauty of the composition produced so favourable an impression that, on his return to Paris in 1841, Ingres found himself received with all the deference that he felt to be his due. A portrait of the purchaser of " Stratonice " was one of the first works executed after his return; and Ingres shortly afterwards began the decora- tions of the great hall in the Chateau de Dampierre, which, unfortunately for the reputation of the painter, were begun with an ardour which gradually slackened, until in 1849 Ingres, having been further discouraged by the loss of his faithful and courageous wife, abandoned all hope of their completion, and the contract with the due de Luynes was finally cancelled. A minor work, " Jupiter and Antiope," marks the year 1851, but Ingres's next considerable undertaking (1853) was the " Apotheosis of Napoleon I.," painted for the ceiling of a hall in the Hotel de Ville; " Jeanne d'Arc " (Louvre) appeared in 1854; and in 1855 Ingres consented to rescind the resolution, more or less strictly kept since i834,in favour of the International Exhibition, where a room was reserved for his works. Prince Napoleon, president of the jury, proposed an exceptional recom- pense for their author, and obtained from the emperor Ingres's nomination as grand officer of the Legion of Honour. With renewed confidence Ingres now took up and completed one of his most charming productions — "La Source" (Louvre), a figure of which he had painted the torso in 1823, and which seen with other works in London (1862) there renewed the general sentiment of admiration, and procured him, from the imperial government, the dignity of senator. After the completion of " La Source," the principal works produced by Ingres were with one or two exceptions (" Moliere " and " Louis XIV.," presented to the Theatre Francais, 1858; " Le Bain Turc," 1859), of a religious character; " La Vierge de 1'Adoption," 1858 (painted for Mile Roland-Gosselin), was followed by " La Vierge Couronnee " (painted for Mme la Baronne de Larinthie) and ''La Vierge aux Enfans " (Collection Blanc); in 1859 these were followed by repetitions of " La Vierge a 1'Hostie "; and in 1862 Ingres completed " Christ and the Doctors " (Musee Montauban), a work commissioned many years before by Queen Marie Amelie for the chapel of Bizy. On the 17th of January 1867 Ingres died in his eighty-eighth year, having preserved his faculties in wonderful perfection to the last. For a moment only — at the time of the execution of the " Bain Turc," which Prince Napoleon was fain to exchange for an early portrait of the master by himself — Ingres's powers had seemed to fail, but he recovered, and showed in his last years the vigour which marked his early maturity. It is, however, to be noted that the " Saint Symphorien " exhibited in 1834 closes the list of the works on which his reputation wili chiefly rest; for " La Source," which at first sight seems to be an exception, was painted, all but the head and the extremities, in 182 1 ; and from those who knew the work well in its incomplete state we learn that the after-painting, necessary to fuse new and old, lacked the vigour, the precision, and the something like touch which distinguished the original execution of the torso. Touch was not, indeed, at any time a means of expression on which Ingres seriously calculated; his constant employment of local tint, in mass but faintly modelled in light by half tones, forbade recourse to the shifting effects of colour and light on which the Romantic school depended in indicating those fleeting aspects of things which they rejoiced to put on canvas; — their methods would have disturbed the calculations of an art wholly based on form and line. Except in his " Sistine Chapel," and one or two slighter pieces, Ingres kept himself free from any preoccupation as to depth and force of colour and tone; driven, probably by the excesses of the Romantic movement into an attitude of stricter protest, " ce que Ton sait " he would repeat, " il faut le savoir l'epee a la main." Ingres left himself therefore, in dealing with crowded compositions, such as the " Apotheosis of Homer " and the " Martyrdom of Saint Symphorien," without the means of producing the necessary unity of effect which had been employed in due measure — as the Stanze of the Vatican bear witness — by the very master whom he most deeply reverr enced. Thus it came to pass that in subjects of one or two figures Ingres showed to the greatest advantage: in " Oedipus," in the " Girl after Bathing," the " Odalisque " and " La Source " — subjects only animated by the consciousness of perfect physical well-being — we find Ingres at his best. One hesitates to put " Roger and Angelique " upon this list, for though the female figure shows the finest qualities of Ingres's work, — deep study of nature in her purest forms, perfect sincerity of intention and power of mastering an ideal conception — yet side by side with these the effigy of Roger on his hippogriff bears witness that from the passionless point of view, which was Ingres's birthright, the weird creatures of the fancy cannot be seen. A graphic account of " Ingres, sa vie et ses travaux," and a complete catalogue of his works, were published by M. Delaborde in 1870, and dedicated to Mme Ingres, nee Ramel, Ingres's devoted second wife, whom he married in 1852. Allusions to the painter's early days will be found in Delecluze's Louis David; and amongst less important notices may be cited that by Theophile Silvestre in his series of living artists. Most of Ingres's important works are engraved in the collection brought out by Magimel. (E. F. S. D.) INGRESS (Lat. ingressus, going in), entrance as opposed to exit or egress; in astronomy, the apparent entrance of a smaller body upon the disk of a larger one, as it passes between the latter and the observer; in this sense it is applied especially to the beginning of a transit of a satellite of Jupiter over the disk of the planet. INHAMBANE, a seaport of Portuguese East Africa in 23 50' S., 35° 25' E. The town, which enjoys a reputation for healthiness, is finely situated on the bank of a river of the same name which empties into a bay also called Inhambane. Next to Mozambique Inhambane, which dates from the middle of the 16th century, is architecturally the most important town in Portuguese East Africa. The chief buildings are the fort, churches and mosque. The principal church is built with stone and marble brought from Portugal. The population, about 4000 in 1909, is of a motley character: Portuguese and other Europeans, Arabs, Banyans, half-castes and negroes. Its commerce was formerly 5 68 INHERITANCE mostly in ivory and slaves. In 1834 Inhambane was taken and all its inhabitants save ten killed by a Zulu horde under Manikusa (see Gaz aland). It was not until towards the close of the 19th century that the trade of the town revived. The value of ex- ports and imports in 1907 was about £150,000. The chief exports are wax, rubber, mafureira and other nuts, mealies and sugar. Cotton goods and cheap wines (for consumption by natives) are the principal imports. The harbour, about 9 m. long by 5 wide, accommodates vessels drawing 10 to 12 ft. of water. The depth of water over the bar varies from 17 to 28 ft., and large vessels discharge into and load from lighters. Inhambane is the natural port for the extensive and fertile district between the Limpopo and Sabi rivers. This region is the best recruiting ground for labourers in the Rand gold mines. Mineral oils have been found within a short distance of the port. INHERITANCE. In English law, inheritance, heir and other kindred words have a meaning very different from that of the Latin hacres, from which they are derived. In Roman law the heir or heirs represented the entire legal personality of the deceased — his universum jus. In English law the heir is simply the person on whom the real property of the deceased devolves by operation of law if he dies intestate. He has nothing to do as heir with the personal property; he is not appointed by will; and except in the case of coparceners he is a single individual. The Roman haeres takes the whole estate; his appointment may or may not be by testament; and more persons than one may be associated together as heirs. The devolution of an inheritance in England is now regulated by the rules of descent, as altered by the Inheritance Act 1833, amended by the Law of Property Amendment Act 1859. 1. The first rule is that inheritance shall descend to the issue of the last " purchaser." A purchaser in law means one who acquires an estate otherwise than by descent, e.g. by will, by gratuitous gift, or by purchase in the ordinary meaning of the word. This rule is one of the changes introduced by the Inheritance Act, which further provides that " the person last entitled to the land shall be considered the purchaser thereof unless it be proved that he inherited the same." Under the earlier law descent was traced from the last person who had " seisin " or feudal possession, and it was occasionally a trouble- some question whether the heir or person entitled had ever, in fact, acquired such possession. Now the only inquiry is into title, and each person entitled is presumed to be in by purchase unless he is proved to be in by descent, so that the stock of descent is the last person entitled who cannot be shown to have inherited. 2. The male is admitted before the female. 3. Among males of equal degree in consanguinity to the purchaser, the elder excludes the younger; but females of the same degree take together as " coparceners." 4. Lineal descendants take the place of their ancestor. Thus an eldest son dying and leaving issue would be represented by such issue, who would exclude their father's brothers and sister's. 5. If there are no lineal descen- dants of the purchaser, the next to inherit is his nearest lineal ancestor. This is a rule introduced by the Inheritance Act. Under the former law inheritance never went to an ancestor — collaterals, however remote of the person last seized being pre- ferred even to his father. Various explanations have been given of this seemingly anomalous rule — Bracton and Blackstone being content to say that it rests on the law of nature, by which heavy bodies gravitate downwards. Another explanation is that estates were granted to be descendible in the same way as an ancient inheritance, which having passed from father to son ex necessitate went to collaterals on failure of issue of the person last seized. 6. The sixth rule is thus expressed by Joshua Williams in his treatise on The Law of Real Property: — " The father and all the male paternal ancestors of the purchaser and their descendants shall be admitted before any of the female paternal ancestors or their heirs; all the female paternal ancestors and their heirs before the mother or any of the maternal ancestors or her or their descendants ; and the mother and all the male maternal ancestors and her and their descendants before any of the female maternal ancestors or their heirs." 7. Kinsmen of the half-blood may be heirs; such kinsmen shall inherit next after a kinsman in the same degree of the whole blood, and after the issue of such kinsman where the common ancestor is a male and next after the common ancestor where such ancestor is a female. The admission of kinsmen of the half- blood into the chain of descent is an alteration made by the Inheritance Act. Formerly a relative, however nearly connected in blood with the purchaser through one only and not both parents, could never inherit — a half-brother for example. 8. In the admission of female paternal ancestors, the mother of the more remote male paternal ancestor and her heirs shall be preferred to the mother of the less remote male paternal and her heirs; and, in the case of female maternal ancestors, the mother of the more remote male maternal ancestor shall be preferred to the mother of a less remote male maternal ancestor. This rule, following the opinion of Blackstone, settles a point much disputed by text-writers, although its importance was little more than theoretical. 9. When there shall be a total failure of heirs of the purchaser, or when any lands shall be descendible as if an ancestor had been the purchaser thereof, and there shall be a total failure of the heirs of such ancestor, then and in every such case the descent shall be traced from the person last entitled to the land as if he had been the purchaser thereof. This rule is enacted by the Law of Property Amendment Act 1859. It would apply to such a case as the following: Purchaser dies intestate, leaving a son and no other relations, and the son in turn dies intestate; the son's relations through his mother are now admitted by this rule. If the purchaser is illegitimate, his only relations must necessarily be his own issue. Failing heirs of all kinds, the lands of an intestate purchaser, not alienated by him, would revert by " escheat " to the next immediate lord of the fee, who would generally be the crown. If an intermediate lordship could be proved to exist between the crown and the tenant in fee simple, such intermediate lord would have the escheat. But escheat is a matter of rare occurrence. The above rules apply to all freehold land whether the estate therein of the intestate is legal or equitable. Before 1884, if a sole trustee had the legal estate in realty, and his cestui que trust died intestate and without heirs, the land escheated to the trustee. This distinction was abolished by the Intestate Estates Act 1884. The descent of an estate in tail would be ascertained by such of the foregoing rules as are not inapplicable to it. By the form of the entail the estate descends to the "issue" of the person to whom the estate was given in tail — in other words, the last purchaser. The preceding rules after the fourth, being intended for the ascertainment of heirs other than those by lineal descent, would therefore not apply; and a special limitation in the entail, such as to heirs male or female only, would render unnecessary some of the others. When the entail has been barred, the estate descends according to these rules. In copyhold estates descent, like other incidents thereof, is regulated by the custom of each particular manor; e.g. the youngest son may exclude the elder sons. How far the Inheritance Act applies to such estates has been seriously disputed. It has been held in one case (Muggleton v. Barnett) that the Inheritance Act, which orders descent to be traced from the last purchaser, does not override a manorial custom to trace descent from the person last seized, but this position has been -controverted on the ground that the act itself includes the case of customary holdings. Husband and wife do not stand in the rank of heir to each othef . Their interests in each other's real property, are secured by courtesy and dower. The personal property of a person dying intestate devolves according to an entirely different set of rules (see Intestacy). In Scotland the rules of descent differ from the above in several particulars. Descent is traced, as in England before the Inheri- tance Act, to the person last seized. The first to succeed are the lineal descendants of the deceased, and the rules of primogeniture, preference of males to females, equal succession of females (heirs- portioners), and representation of ancestors are generally the same as in English law. Next to the lineal descendants, and failing them, INHIBITION— INITIATION 569 come the brothers and sisters, and their issue as collaterals. Failing collaterals, the inheritance ascends to the father and his relations, to the entire exclusion of the mother and her relations. Even when the estate has descended from mother to son, it can never revert to the maternal line. As to succession of brothers, a distinction must be taken between an estate of heritage and an estate of conquest. Conquest is where the deceased has acquired the land otherwise than as heir, and corresponds to the English term purchase in the technical sense explained. Heritage is land acquired by deceased as heir. The distinction is important only in the case when the heir of the deceased is to be sought among his brothers; when the descent is lineal, conquest and heritage go to the same person. And when the brothers are younger than the deceased, both conquest and heritage go to the brother (or his issue) next in order of age. But when the deceased leaves an elder and a younger brother (or their issues), the elder brother takes the conquest, the younger takes the heritage. Again, when there are several elder brothers, the one next in age to the deceased takes the conquest before the more remote, and when there are several younger brothers, the one next to the deceased takes the heritage before the more remote. When heritage of the deceased goes to an elder brother (as might happen in certain eventualities), the younger of the elder brothers is preferred. The position of the father, after the brothers and sisters of the deceased, will be noticed as an important point of difference from the English axioms; so also is the total exclusion of the mother and the maternal line. As between brothers and sisters the half-blood only succeeds after the full blood. Half-blood is either consanguinean, as between children by the same father, or uterine, as between children having the same mother. The half-blood uterine is excluded altogether. Half-blood consanguinean succeeds thus: if the issue is by a former marriage, the youngest brother (being nearest to the deceased of the consan- guinean) succeeds first; if by a later marriage than that from which the deceased has sprung, the eldest succeeds first. United Stales. — American law has borrowed its rules of descent considerably more from the civil law than the common law. "The 118 novel of Justinian has a striking resemblance to American law in giving the succession of estates to all legitimate children without distinction and disregarding all considerations of primogeniture. There is one particular in which the American law differs from that of Justinian, that while generally in this country lineal descendants if they stand in an equal degree from the common ancestor share equally per capita, under the Roman law regard was had to the right of representation, each lineal branch of descendants taking only the portion which their parent would have taken had he been living, the division being per stirpes and not per capita. But in some of the states the rule of the Roman law in this respect has been adopted and retained. Among these are Rhode Island, New Jersey, North and South Carolina, Alabama and Louisiana " (3 Washburn's Real Property, pp. 408, 409; 4 Kent's Cornm. p. 375). When such lineal descendants stand in unequal degrees of consanguinity the inheritance is per stirpes and not per capita {In re Prote, 1907; 104, X.Y. Supplement 581). This is the rule in practically all the states. But as in no two states or territories are the rules of descent identical, the only safe guides are the statutes and decisions of the particular state in which the land to be inherited is situated. The law of primogeniture as understood in England is generally abolished throughout the United States, and male and female relatives inherit equally. In some states, as in Massachusetts, relatives of the half-blood inherit equally with those of the whole-blood of the same degree; in others, like Maryland, they can inherit only in case none of whole-blood exist. In some of the states the English rule that natural children have no inheritable blood has been greatly modified. In Louisiana, if duly acknowledged, they may inherit from both father and mother in the absence of lawful issue. Degrees of kindred in the United States generally are computed accord- ing to the civil law, i.e. by adding together the number of degrees between each of the two persons whose relationship is to be ascertained and the common ancestor. Thus, relation- ship between two brothers is in the second degree; between uncle and nephew in the third degree; between cousins, in the fourth, &c. In a few states such degrees are computed according to the common law, i.e. by counting from the common ancestor to the most remote descendant of the two from him — thus, brothers would be related in the first degree, uncle and nephew in the second, &c. In most states representation amongst collaterals is restricted — in some to the descendants of brothers and sisters, in others to their children cnly. In some states, e.g. in California, Louisiana and Texas, the law of " community property " of husband and wife prevails. This is derived from the French and Spanish law existing in the territories out of which those states were formed, as the result of theconquestof Mexico by Spain and the colonizing of Louisiana by France. The foundation idea is an equal division at death of either party of all property acquired during their marriage except by gift, devise or descent. In general the husband has the control and management thereof during the marriage, and either survivor has the administra- tion of the moiety of the one deceased. There is a conflict in the laws in such states as to the exact definition and as to whether or not the gains or profits of such property are to be deemed separate property or community property [ Succession of Dielman (Louisiana, 1907), 43 Southern Rep. 972]. INHIBITION (from Lat. inhibere, to restrain, prevent), an act of restraint or prohibition, an English legal term, particularly used in ecclesiastical law, for a writ from a superior to an inferior court, suspending proceedings in a case under appeal, also for the suspension of a jurisdiction of a bishop's court on the visita- tion of an archbishop, and for that of an archdeacon on the visitation of a bishop. It is more particularly applied to a form of ecclesiastical censure, suspending an offending clergyman from the performance of any service of the Church, or other spiritual duty, for the purpose of enforcing obedience to a monition or order of the bishop or judge. Such inhibitions are at the discre- tion of the ordinary if he considers that scandal might arise from the performance of spiritual duties by the offender (Church Discipline Act i860, re-enacted by the Clergy Discipline Act 1892, sect. 10). By the Sequestration Act 1871, sect. 5, similar powers of inhibition are given where a sequestration remains in force for more than six months, and also, by the Benefices Act 1898, in cases where a commission reports that the ecclesiastical duties of a benefice are inadequately performed through the negligence of the incumbent. INISFAIL, a poetical name for Ireland. It is derived from Paul or Lia-fail, the celebrated stone, identified in Irish legend with the stone on which the patriarch Jacob slept when he dreamed of the heavenly ladder. The Lia-fail was supposed to have been brought to Ireland by the Dedannans and set up at Tara as the " inauguration stone " of the Irish kings; it was subsequently removed to Scone where it became the coronation stone of the Scottish kings, until it was taken by James VI. of Scotland to Westminster and placed under the coronation chair in the Abbey, where it has since remained. Inisfail was thus the island of the Fail, the island whose monarchs were crowned at Tara on the sacred inauguration stone. INITIALS (Lat. initialis, of or belonging to a beginning, iniiium), the first letters of names. In legal and formal docu- ments it is usually the practice in appending a signature to write the name in full. But this is by no means necessary, even in cases where a signature is expressly required by statute. It has been held that it is sufficient if a person affixes to a document the usual form in which he signs his name, with the intent that it shall be treated as his signature. So, signature by initials is a good signature within the Statute of Frauds {Phillimore v. Barry, 1818, 1 Camp. 513), and also under the Wills Act 1837 {In re Blewitt, 1880, 5 P.D. 116). INITIATION (Lat. initium, beginning, entrance, from inire, to go in), the process of formally entering, and especially the rite of admission into, some office, or religious or secret society, &c. Among nearly all primitive races initiatory rites of a bloody character were and are common. The savage pays homage to strength, and the purpose of his initiatory rites is to test physical vigour, self-control and the power of enduring pain. Initiation is sometimes religious, sometimes social, but in primitive society it has always the same character. Thus, in Whydah (West Africa) the young girls consecrated to the worship of the serpent, " the brides of the Serpent," had figures of flowers and animals burnt into their skins with hot irons; while in the neighbouring Yorubaland the power of enduring a sound thrashing is the qualification for the throne. In no country was the practice of initiatory rites more general than in the Americas. The Colombian Indians compelled their would-be chief to submit to terrible tests. He had first to bear severe beatings without a murmur. Then, placed in a hammock with his hands tied, INJECTOR— INJUNCTION 57o venomous ants were placed on his naked body. Finally a fire was lit beneath him. All this he had to bear without flinching. In ancient Mexico there were several orders of chivalry, entry into which was only permitted after brutal initiation. The nose of the candidate was pierced with an eagle's talon or a pointed bene, and he was expected to dig knives into his body. In Peru the young Inca princes had to fast and live for weeks without sleep. Among the North American Indians initiatory rites were universal. The Mandans held a feast at which the young " braves " supported the weight of their bodies on pieces of wood skewered through the muscles of shoulders, breasts and arms. With the Sioux, to become a medicine-man, it was necessary to submit to the ordeal known as " looking at the sun." The sufferer, nearly naked, was bound on the earth by cords passed through holes made in the pectoral muscles. With bow and arrow in hand, he lay in this position all day gazing at the sun. Around him his friends gathered to applaud his courage. Religious brotherhoods of antiquity, too, were to be entered only after long and complicated initiation. But here the char- acter of the ordeal is rather moral than physical. Such were the rites of admission to the Mysteries of Isis and Eleusis. Secret societies of all ages have been characterized by more or less elaborate initiation. That of the Femgerichte, the famous medieval German secret tribunal, took place at night in a cave, the neophyte kneeling and making oath of blind obedience. Imitations of such tests are perpetuated to-day in freemasonry; while the Mafia, the Camorra, the Clan-na-Gael, the Molly Maguires, the Ku-Klux lUan, are among more recent secret associations which have maintained the old idea of initiation. INJECTOR (from Lat. injicere, to throw in), an appliance for supplying steam-boilers with water, and especially used with locomotive boilers. It was invented by the French engineer H. V. Giffard in 1858, and presents the paradox that by the pressure of the steam in the boiler, or even, as in the case of the exhaust steam injector, by steam at a much lower pressure, water is forced into the boiler against that pressure. A dia- grammatic section illustrating its construc- tion is shown in figure. Steam enters at A and blows through the annular orifice C, the size of which can be regulated by a valve not shown in the figure. The feed water flows in at B and meeting the steam at C causes it to condense. Hence a vacuum is produced at C, and consequently the water rushes in with great velocity and streams down the combining cone D, its velocity being augmented by the impact of steam on the back of the column. In the lower part of the nozzle E the stream expands; it therefore loses velocity and, by a well-known hydrodynamic principle, gains pressure, until at the bottom the pressure is so great that it is able to enter the boiler through a check valve which opens only in the direction of the stream. An overflow pipe F, by providing a channel through which steam and water may escape before the stream has acquired sufficient energy to force its way into the boiler, allows the injector to start into action. Means are also pro- vided for regulating the amount of water admitted between D and C. In the exhaust-steam injector, which works with steam from the exhaust of non-condensing engines, the steam orifice is larger in proportion to other parts than in injectors working with boiler steam, and the steam supply more liberal. In self-starting injectors an arrangement is provided which permits free overflow until the injector starts into action, when the openings are automatically adjusted to suit delivery into the boiler. INJUNCTION (from Lat. injungere, to fasten, or attach to, to lay a burden or charge on, to enjoin), a term- meaning generally a command, and in English law the name for a judicial process whereby a party is required to refrain from doing a particular thing according to the exigency of the writ. Formerly it was a remedy peculiar to the court of chancery, and was one of the instruments by which the jurisdiction of that court was established in cases over which the courts of common law were entitled to exercise control. The court of chancery did not presume to interfere with the action of the courts, but, by direct- ing an injunction to the person whom it wished to restrain from following a particular remedy at common law, it effected the same purpose indirectly. Under the present constitution of the judicature, the injunction is now equally available in all the divisions of the high court of justice, and it can no longer be used to prevent an action in any of them from proceeding in the ordinary course. Although an injunction is properly a restraining order, there are instances in which, under the form of a prohibition, a positive order to do something is virtually expressed. Thus in a case of nuisance an injunction was obtained to restrain the defendant from preventing water from flowing in such regular quantities as it had ordinarily done before the day on which the nuisance commenced. But generally, if the relief prayed for is to compel something to be done, it cannot be obtained by injunction, although it may be expressed in the form of a prohibition — as in the case in which it was sought to prevent a person from discontinuing to keep a house as an inn. The injunction was used to stay proceedings in other courts " wherever a party by fraud, accident, mistake or otherwise had obtained an advantage in proceeding in a court of ordinary jurisdiction, which must necessarily make that court an instrument of injustice." As the injunction operates personally on the defendant, it may be used to prevent applications to foreign judicatures; but it is not used to prevent applications to parliament, or tc the legis- lature of any foreign country, unless such applications be in breach of some agreement, and relate to matters of private interest. In so far as an injunction is used to prohibit acts, it may be founded either on an alleged contract or on a right independent of contract. The jurisdiction of the court to prevent breaches of contract has been described as supplemental to its power of compelling specific performance; i.e. if the court has power to compel a person to perform a contract, it will interfere to prevent him from doing anything in violation of it. But even when it is not within the power of the court to compel specific performance, it may interfere by injunction; thus, e.g. in the case of an agreement of a singer to perform at the plaintiff's theatre and at no other, the court, although it could not compel her to sing, could by injunction prevent her from singing elsewhere in breach of her agreement. An injunction may as a general rule be obtained to prevent acts which are violations of legal rights, except when the same may be adequately remedied by an action for damages at law. Thus the court will interfere by injunction to prevent waste, or the destruction by a limited owner, such as a tenant for life, of things forming part of the inheritance. Injunctions may also be obtained to prevent the continuance of nuisances, public or private, the infringement of patents, copyrights and trade marks. Trespass might also in certain cases be prevented by injunction. Under the Common Law Procedure Act of 1854, and by other statutes in special cases, a limited power of injunc- tion was conferred on the courts of common law. But the Judicature Act, by which all the superior courts of common law and chancery were consolidated, enacts that an injunction may be granted by an interlocutory order of the court in all cases in which it shall appear to be just or convenient; . . . and, if an injunction is asked either before or at or after the hear- ing of any cause or matter, to prevent any threatened or appre- hended waste or trespass, such injunction may be granted whether the person against whom it is sought is or is not in possession under any claim of title or otherwise, or if not in possession does or does not claim to do the act sought to be restrained under colour of any title, and whether the estates claimed are legal or equitable. An injunction obtained on interlocutory application during the progress of an action is superseded by the trial. It may be continued either provisionally or permanently. In the latter case the injunction is said to be perpetual. The distinction INK 57i between " special " and " common " injunctions — the latter being obtained as of course — is now abolished in English law. In the courts of the United States the writ of injunction remains purely an equitable remedy. It may be issued at the instance of the president to prevent any organized obstruction to inter-state commerce or to the passage of the mails (in re Debs, 158 United States Reports, 564). Temporary restraining orders may be issued, ex parte, pending an application for a temporary injunction. In the state courts temporary injunc- tions are often issued, ex parte, subject to the defendant's right to move immediately for their dissolution. Generally, however, notice of an application for a temporary injunction is required. For the analogous practice in Scots law see Interdict. INK (from Late Lat. encaustum, Gr. tyKamrov, the purple ink used by Greek and Roman emperors, from eyKalav, to burn in), in its widest signification, a substance employed for producing graphic tracings, inscriptions, or impressions on paper or similar materials. The term includes two distinct conditions of pigment or colouring matter: the one fluid, and prepared for use with a pen or brush, as writing ink; the other a glutinous adhesive mass, printing ink, used for transferring to paper impressions from types, engraved plates and similar surfaces. The ancient Egyptians prepared and used inks (Flinders Petrie discovered a papyrus bearing written characters as old as 2500 B.C.), and in China the invention of an ink is assigned to Tien-Tcheu, who lived between 2697 B.C. and 2597 B.C. These early inks were prepared from charcoal or soot mixed with gum, glue or varnish. Sepia (q.v.), the black pigment secreted by the cuttle-fish, was used as a writing fluid by the Romans. The iron-gall ink, i.e. an ink prepared from an iron salt and tannin, appears to have been first described by the monk Theophilus, who lived in the nth century a.d., although Pliny, in the 1st century a.d., was acquainted with the blackening of paper containing green vitrioi by immersion in an infusion of nut-galls. Iron-gall inks, prepared by mixing extracts of galls, barks, &c, with green vitriol, subsequently came into common use, and in the 16th century recipes for their preparation were given in domestic encyclopaedias. Their scientific investigation was first made by William Lewis in 1748. The earlier iron-inks were essentially a suspension of the pigment in water. In the early part of the 19th century the firm of Stephens introduced the first of the so-called blue-black inks under the name of " Stephens' writing fluid." Solutions of green vitriol and tannin, coloured by indigo and logwood, were prepared, which wrote with a blue tint and blackened on exposure, this change being due to the production of the pigment within the pores of the paper. The " alizarine " inks, patented by Leonhardi in 1856, are similar inks with the addition of a little madder. The application of aniline colours to ink manufacture in England dates from Croc's patent of 1861. Writing Inks. — Writing inks are fluid substances which contain colouring matter either in solution or in suspension, and com- monly partly in both conditions. They may be prepared in all shades of colour, and contain almost every pigment which can be dissolved or suspended in a suitable medium. The most important of all varieties is black ink, after which red and blue are most commonly employed. Apart from colour there are special qualities which recommend certain inks for limited applications, such as marking inks, ineradicable ink, sympathetic ink, &c. A good writing ink for ordinary purposes should continue limpid, and flow freely and uniformly from the pen; it should not throw down a thick sludgy deposit on exposure to the air; nor should a coating of mould form on its surface. It should yield distinctly legible characters immediately on writing, not fading with age; and the fluid ought to penetrate into the paper without spreading, so that the characters will neither wash out nor be readily removed by erasure. Further, it is desirable that ink should be non-poisonous, that it should as little as possible corrode steel pens, that characters traced in it should dry readily on the application of blotting paper without smearing, and that the writing should not present a glossy, varnished appearance. Tannin Inks. — These inks are prepared from galls, or other sources of tannin, and a salt of iron, with the addition of some agglutinant . in the case of the so-called oxidized inks, or a colouring matter in the case of unoxidized inks. Such mixtures form the staple black inks of commerce; they are essentially an insoluble iron gallate in extremely fine division held in suspension in water or a soluble compound dissolved in water. On long exposure to air, as in inkstands, or otherwise, tannin inks gradually become thick and ropy, depositing a slimy sediment. This change on exposure is inevitable, resulting from the gradual oxidation of the ferrous compound, and it can only be retarded by permitting access of air to as small surfaces as possible. The inks also have a tendency to become mouldy, an evil which may be obviated by the use of a minute proportion of carbolic acid; or salicylic acid may be used. The essential ingredients of ordinary black ink are — first, tannin-yielding bodies, for which Aleppo or Chinese galls are the most eligible materials; second, a salt of iron, ferrous sulphate (green vitriol) being alone employed; and third, a gummy or mucilaginous agent to keep in suspension the insoluble tinctorial matter of the ink. For ink-making the tannin has first to be transformed into gallic acid. In the case of Aleppo galls this change takes place by fermentation when the solution of the galls is exposed to the air, the tannin splitting up into gallic acid and sugar. Chinese galls do not contain the ferment necessary for inducing this change; and to induce the process yeast must be added to their solution. To prepare a solution of Aleppo galls for ink-making, the galls are coarsely powdered, and intimately mixed with chopped straw. This mixture is thrown into a narrow deep oak vat, provided with a perforated false bottom, and having a tap at the bottom for drawing off liquid. Over the mixture is poured lukewarm water, which, percolating down, extracts and carries with it the tannin of the galls. The solution is drawn off and repeatedly run through the mixture to extract the whole of the tannin, the water used being in such proportion to the galls as will produce as nearly as possible a solution having 5% of tannin. The object of using straw in the extraction process is to maintain the porosity of the mixture, as powdered galls treated alone become so slimy with mucilaginous extract that liquid fails to percolate the mass. For each litre of the 5 % solution about 45 grammes of the iron salt are used, or about 100 parts of tannin for 90 parts of crystallized green vitriol. These ingredients when first mixed form a clear solution, but on their exposure to the air oxidation occurs, and an insoluble blue-black ferrosoferric gallate in extremely fine division, suspended in a coloured solution of ferrous gallate, is formed. To keep the insoluble portion suspended, a mucilaginous agent is employed, and those most available are gum Senegal and gum arabic. An ink so prepared develops its intensity of colour only after some exposure; and after it has partly sunk into the paper it becomes oxidized there, and so mordanted into the fibre. As the first faintness of the characters is a disadvantage, it is a common practice to add some adventitious colouring matter to give immediate distinctness, and for that purpose either extract of logwood or a solution of indigo is used. When logwood extract is employed, a smaller proportion of extract of galls is required, logwood itself containing a large percentage of tannin. For making an unoxidized or blue-black ink indigo is dissolved in strong sulphuric acid, and the ferrous sulphate, instead of being used direct, is prepared by placing in this indigo solution a proper quantity of scrap iron. To free the solution from excess of uncombined acid, chalk or powdered limestone is added, whereby the free acid is fixed and a deposit of sulphate of lime formed. A solution so prepared, mixed with a tannin solution, yields a very limpid sea-green writing fluid, and as all the constituents remain in solution, no gum or other suspending medium is necessary. In consequence the ink flows freely, is easily dried and is free from the glossy appearance which arises through the use of gum. 572 INK China ink or Indian ink is the form in which ink was earliest prepared, and in which it is still used in China and Japan for writing with small brushes instead of pens. It is extensively used by architects, engineers and artists generally, and for various special uses. China ink is prepared in the form of sticks and cakes, which are rubbed down in water for use. It consists essentially of lamp-black in very fine condition, baked up with a glutinous substance; and the finer Oriental kinds are delicately perfumed. The following description of the manufacture as conducted in Japan is from a native source: — " The body of the ink is soot obtained from pine wood or rosin, and lamp-black from sesamum oil for the finest sort. This is mixed with liquid glue made of ox-skin. This operation is effected in a large round copper bowl, formed of two spherical vessels, placed I in. apart, so that the space between can be filled up with hot water to prevent the glue from hardening during the time it is being mixed by hand with the lamp-black. The cakes are formed in wooden moulds, and dried between paper and ashes. Camphor, or a peculiar mixture of scents which comes from China, and a small quantity of carthamine (the red colouring substance of safflower), are added to the best kinds for improving the colour as well as for scenting the ink. There is a great difference both in price and in quality of the various kinds of ink, the finest article being rather costly." It is said that the size used in Chinese kinds is of vegetable origin. Logwood Ink. — Under the name of chrome ink a black ink was discovered by Runge, which held out the promise of cheap- ness combined with many excellent qualities. It is prepared by dissolving 15 parts of extract of logwood in 900 parts of water, to which 4 parts of crystallized sodium carbonate' are added. A further solution of 1 part of potassium chromate (not bichromate) in 100 parts of water is prepared, and is added very gradually to the other solution with constant agitation. The ink so obtained possesses an intense blue-black colour, flows freely and dries readily, is neutral in reaction and hence does not corrode steel pens, and adheres to and sinks into paper so that manuscripts written with it may be freely washed with a sponge without danger of smearing or spreading. It forms a good copying ink, and it possesses all the qualities essential to the best ink; but on exposure to air it very readily undergoes decomposition, the colouring matter separating in broad flakes, which swim in a clear menstruum. It is affirmed by Viedt that this drawback may be overcome by the use of soda, a method first suggested by Bottger. Logwood forms the principal ingredient in various other black inks used, especially as copying ink. A very strong decoction of logwood or a strong solution of the extract with ammonium- alum yields a violet ink which darkens slowly on exposure. Such an ink is costly, on account of the concentrated condition in which the logwood must be used. If, however, a metallic salt is introduced, a serviceable ink is obtained with the expendi- ture of much less logwood. Either sulphate of copper or sulphate of iron may be used, but the former, which produces a pleasing blue-black colour, is to be preferred. The following is the formula most highly recommended for this ink. A clear solution of 20 kilos of extract of logwood in 200 litres of water is obtained, to which is added, with agitation, 10 kilos of ammonium-alum dissolved in 20 litres of boiling water. The solution is acidified with 0-2 kilo of sulphuric acid, which has the effect of preventing any deposit, and finally there is added a solution of 15 kilos of sulphate of copper dissolved in 20 litres of water. This compound is exposed to the air for a few days to allow the colour to develop by oxidation, after which it is stored in well-corked bottles. The acid condition of this ink has a corrosive influence on steel pens; in all other respects it is a most valuable writing fluid. Aniline Inks. — Solutions of aniline dye-stuffs in water are widely used as inks, especially coloured varieties. They are usually fugitive. Nigrosine is a black ink, which, although not producing a black so intense as common ink, possesses various advantages. Being perfectly neutral, it does not attack pens; it can easily be kept of a proper consistency by making up with water; and its colour is not injuriously affected by the action of acids. Its ready flow from stylographic pens led to the name " stylographic ink." Other aniline inks are mentioned below. Copying Ink. — Ink which yields by means of pressure an im- pression, on a sheet of damped tissue paper, of characters written in it is called copying ink. Any ink soluble in water, or which retains a certain degree of solubility, may be used as copying ink. Runge's chrome ink, being a soluble compound, is, therefore, so available; and the other logwood inks as well as the ordinary ferrous gallate inks contain also soluble con- stituents, and are essentially soluble till they are oxidized in and on the paper after exposure to the air. To render these available as copying inks it is necessary to add to them a sub- stance which will retard the oxidizing effect of the air for some time. For this purpose the bodies most serviceable are gum arabic or Senegal, with glycerin, dextrin or sugar, which last, however, renders the ink sticky. These substances act by forming a kind of glaze or varnish over the surface of the ink which excludes the air. At the same time when the damp sheet of tissue paper is applied to the writing, they dissolve and allow a portion of the yet soluble ink to be absorbed by the moistened tissue. As copying ink has to yield two or more impressions, it is necessary that it should be made stronger, i.e. that it should contain more pigment or body than common ink. It, therefore, is prepared with from 30 to 40% less of water than non-copying kinds; but otherwise, except in the presence of the ingredients above mentioned, the inks are the same. Copying ink pencils consist of a base of graphite and kaolin impregnated with a very strong solution of an aniline colour, pressed into sticks and dried. Red Ink. — The pigment most commonly employed as the basis of red ink is Brazil-wood. Such an ink is prepared by adding to a strong decoction of the wood a proportion of stannous chloride (tin spirits), and thickening the resulting fluid with gum arabic. In some instances alum and cream of tartar are used instead of the stannous chloride. Cochineal is also employed as the tinctorial basis of red ink; but, while the resulting fluid is much more brilliant than that obtained from Brazil- wood, it is not so permanent. A very brilliant red ink may be prepared by dissolving carmine in a solution of ammonia, but this preparation must be kept in closely stoppered bottles. A useful red ink may also be made by dissolving the rosein of Brook, Simpson and Spiller in water, in the proportion of 1 to from 1 50 to 200 parts. Blue Ink. — For the production of blue ink the pigment principally used is Prussian blue. It is first digested for two or three days with either strong hydrochloric acid, sulphuric acid or nitric acid, the digested mass is next very largely diluted with water, and after settling the supernatant liquid is siphoned away from the sediment. This sediment is repeatedly washed, till all traces of iron and free acid disappear from the water used, after which it is dried and mixed with oxalic acid in the proportion of 8 parts of Prussian blue to 1 of the acid, and in this condition the material is ready for dissolving in water to the degree of colour intensity necessary. An aniline blue ink may be prepared by dissolving 1 part of bleu de Paris in from 200 to 250 parts of water. Marking Ink. — The ink so called, used principally for marking linen, is composed of a salt of silver, usually the nitrate, dissolved in water and ammonia, with a little provisional colouring matter and gum for thickening. The colour resulting from the silver salt is developed by heat and light; and the stain it makes, although exceedingly obstinate, gradually becomes a faint brownish-yellow. The following yields a good marking ink. Equal parts of nitrate of silver and dry tartaric acid arc triturated in a mortar, and treated with water, when a reaction takes place, resulting in the formation of tartrate of silver and the liberation of nitric acid. The acid is neutralized, and at the same time the silver tartrate is dissolved by the addition of ammonia, and this solution with colouring matter and gum forms the ink, which may be used with an ordinary steel pen. Many vegetable juices, e g. of Coriana thymifolia, Semecarpus INKERMAN, BATTLE OF 57 3 ynacardinm. Anacardium occidentale (Cashew), are inks of this type- Gold and silver inks are writing fluids in which gold and silver, or imitations of these metals, are suspended in a state of fine division. In place of gold, Dutch leaf or mosaic gold is frequently substituted, and bronze powders are used for preparing a similar kind of ink. The metallic foil is first carefully triturated into a fine paste with honey, after which it is boiled in water containing a little alkali, and then repeatedly washed in hot water and dried at a gentle heat. A solution is prepared consisting of i part of pure gum arabic and i part of soluble potash glass in 4 parts of distilled water, into which the requisite quantity of the metallic powder prepared is introduced. Owing to the superior covering nature of pure gold, less of the metal is required than is necessary in the case of silver and other foils. In general 1 part of foil to 3 or 4 parts of solution is sufficient. The metallic lustre of writing done with this solution may be greatly heightened by gently polishing with a burnishing point. Another gold ink depends upon the formation of purple of Cassius; the linen is mordanted with stannous chloride, and the gold applied as a gummy solution of the chloride. Indelible or incorrodible ink is the name given to various combinations of lamp-black or other carbonaceous material with resinous substances used for writing which is exposed to the weather or to the action of strong acids or alkaline solutions. An ink having great resisting powers may be conveniently prepared by rubbing down Indian ink in common ink till the mixture flows easily from the pen. Other combinations have more the character of coloured varnishes. Sympathetic inks are preparations used for forming characters which only become visible on the application of heat or of some chemical reagent. Many chemicals which form in themselves colourless solutions, but which develop colour under the influence of reagents, may be used as sympathetic ink, but they are of little practical utility. Characters written in a weak solution of galls develop a dark colour on being treated with a solution of copperas; or, vice versa, the writing may be done in copperas and developed by the galls solution. Writing done in various preparations develops colour on heating which fades as the paper cools. Among such substances are solutions of the chlorides of cobalt and of nickel. Very dilute solutions of the mineral acids and of common salt and a solution of equal parts of sulphate of copper and sal-ammoniac act similarly. Writing with rice water and developing with iodine was a device much used during the Indian Mutiny. Printing Inks. — Printing inks are essentially mixtures of a pigment and a varnish. The varnish is prepared from linseed oil, rosin and soap; the oil must be as old as possible; the rosin may be black or amber; and the soap, which is indispensable since it causes the ink to adhere uniformly to the type and also to leave the type clean after taking an impression, is yellow, or turpentine soap for dark inks, and curd soap for light inks. The varnish is prepared as follows: The oil is carefully heated until it " strings " properly, i.e. a drop removed from the vessel on a rod, when placed upon a plate and the rod drawn away, forms a thread about •]. in. long. The rosin is carefully and slowly added and the mixture well stirred. The soap is then stirred in. The ink is prepared by mixing the varnish with the pigment, and grindingthe massto impalpablefinenesseither inalevigating mill or by a stone and muller. For black ink, lamp-black mixed with a little indigo or Prussian blue is the pigment employed; for wood engravings it may be mixed with ivory black, and for copper plates with ivory or Frankfurt black; for lithographic reproductions Taris black is used. Red inks are made with carmine or cochineal; red lead is used in cheap inks, but it rapidly blackens. Blue inks are made with indigo or Prussian blue; yellow with lead chromate or yellow ochre; green is made by mixing yellow and blue; and* purple by mixing red and blue. Sec C. A. Mitchell and T. C. Hepworth, Inks, their Composition and Manufacture (1904); S. Lehncr, Ink Manufacture (190?); A. K. Gouilion, linrres et cirages (1906) ; L. E. Ande*- Schr'ih-, Kopicr- Httd amlerc Tinlcn (1906). INKERMAN, BATTLE OF, fought on the 5th of November 1854 between a portion of the Allied English and French army besieging Sevastopol and a B ussian army under Prince Menshikov (see Crimean War). This battle derives its name from a ruin on the northern bank of the river Tchernaya near its mouth, but it was fought some distance away, on a nameless ridge (styled Mount Inkerman after the event) between the Tchernaya and the Careenage Ravine, which latter marked the right of the siege- works directed against Sevastopol itself. Part of this ridge, called Home Ridge and culminating in a knoll, was occupied by the British, while farther to the south, facing the battleground of Balaklava, a corps under General Bosquet was posted to cover the rear of the besiegers against attacks from the direction of Traktir Bridge. The Russians arranged for a combined attack on ii|g-f INKERMAN txv- — ■iST^fi. ■■■• NVV.v'J ..... , . , camp-' \V.i l -k\ LIQHVV"vX CAMRJ m -y Jim , GUARDS Jh-f-A) BRIGADE CAMPf.'/Vr-i Emeiy W«!kcr sc. the ridge above-mentioned by part of Menshikov's army (i6,oco) and a corps (19,000) that was to issue from Sevastopol. This attack was to have, beside its own field artillery, the support of fifty-four heavy guns, and the Russian left wing on the Balaklava battleground was to keep Bosquet occupied. If successful, the attack on the ridge was to be the signal for a general attack all along the line. It was apparently intended by Menshikov -t}jat the column from the field army should attack the position from the north, and that the Sevastopol column should ad- vance along the west side of the Careenage Ravine.. But he only appointed a commander to take charge of both columns at the last moment, and the want of a clear understanding as to what was to be done militated against success from the first. General Soimonov, with the Sevastopol column, after assembling his troops before dawn on the 5th, led them on to the upland east of Careenage Ravine, while the field army column, under General Pavlov, crossed the Tchernaya near its mouth, almost at right angles to Soimonov's line of advance. 574 INLAYING The British troops on or near the ground were the 2nd Division, 3000, encamped on the ridge; Codrington's brigade of the Light Division, 1400, on the slopes west of the Careenage Ravine; and the Guards' brigade, 1350, about f- m. in rear of the 2nd Division camp. No other forces, French or British, were within 2 m. except another part of Sir George Brown's Light Division. A mist overhung the field and the hillsides were slippery with mud. Soimonov, with his whole force deployed in a normal attack formation (three lines of battalion columns covered by a few hundred skirmishers) pushed forward along the ridge (6 a.m.) without waiting for Pavlov or for Dannenberg, the officer appointed to command the whole force. Shell Hill, guarded only by a picquet, was seized at once. The heavy guns that had been brought from the fortress were placed in position on this hill, and opened fire (7 a.m.) on the knoll, 1400 yds. to the S., behind which the 2nd Division was encamped. The Russian infantry halted for the guns to prepare the way, and the heavy projectiles both swept the crest of the British knoll and destroyed the camp in rear. But already General Pennefather, commanding the division, had pushed forward one body of his infantry after another down the forward slope, near the foot of which they encountered the Russians in great force. On his side, Soimonov had been compelled to break up his regular lines of columns at the narrowest part of the ridge and to push his battalions forward a few at a time. This and the broken character of the ground made the battle even in the beginning a melee. The obscurity of the mist, which had at first allowed the big battalions to approach unobserved, now favoured the weaker side. Soimonov himself, however, formed up some qooo men, who drove back the British left wing — for the whole of Pennefather's force at the time was no more than 3600 men. But the right wing, not as yet attacked, either by Soimonov or by Pavlov, held on to its positions on the forward slope, and a column of Russian sailors and marines, who had been placed under Soimonov's command and had moved up the Careenage Ravine to turn the British left, were caught, just as they emerged on to the plateau in rear of Pennefather's line, between two bodies of British troops hurrying to the scene of action. On the front, too, the Russian attack came to a standstill and ebbed, for Soimonov's overcrowded battalions jostled one another and dissolved on the narrow and broken plateau. Soimonov himself was killed, and the disciplined confidence and steady volleys of the defenders dominated the chaotic elan of the Russians. Thus 3300 defenders were able to repulse and even to " expunge from the battlefield " the whole of the Sevastopol column, except that portion of it which drifted away to its left and joined Pavlov. This stage of the battle had lasted about forty minutes. But, brilliant as was this overture, it is the second stage of the battle that gives it its epic interest. The first attack made by Pavlov's advanced guard, aided by parts of Soimonov's corps, was relatively slight, but General Dannenberg now arrived on the field, and arranged for an assault on the British centre and right, to be delivered by 10,000 men (half his intact forces) chiefly by way of the Quarry Ravine, the attack to be prepared by the guns on Shell Hill. Pennefather had been reinforced by the Guards' brigade and a few smaller units. Not the least extraordinary feature of the battle that followed is the part played by a sangar of stones at the head of Quarry Ravine and a small battery, called the Sandbag Battery, made as a temporary emplacement for two heavy guns a few days before. The guns had done their work and been sent back whence they came. Nevertheless these two insignificant works, as points to hold and lines to defend on an otherwise featureless battlefield, became the centres of gravity of the battle. The sangar at first fell into the hands of the Russians, but they were soon ejected, and small British detachments reoccupied and held it, while the various Russian attacks flowed up and past it and ebbed back into the Quarry Ravine. Possession of the Sandbag Battery was far more fiercely contested. The right wing was defended by some 700 men of the 2nd Division, who were reinforced by 1300 of the Guards. The line of defence adjacent to the battery looked downhill for about 300 yds., giving a clear field of fire for the new Enfield rifle the English carried; but a sharp break in the slope beyond that range gave the assailants plenty of " dead ground " on which to form up. For a time, therefore, the battle was a series of attacks, delivered with great fierceness by the main body of Pavlov's corps, the repulse of each being followed by the disappearance of the assailants. But the arrival of part of the British 4th Division under Sir George Cathcart gave the impulse for a counter-attack. Most of the division indeed had to be used to patch up the weaker parts of the line, but Cathcart himself with about 400 men worked his way along the lower and steeper part of the eastern slope so as to take the assailants of the battery in flank. He had not proceeded far, however, when a body of Russians moving higher up descended upon the small British corps and scattered it, Cathcart himself being killed. Other counter-strokes that his arrival had inspired were at the same time made from different parts of the defensive front, and had the effect of breaking up what was a solid line into a number of disconnected bands, each fighting for its life in the midst of the enemy. The crest of the position was laid open and parts of the Russian right wing seized it. But they were flung back to the lower slopes of the Quarry Ravine by the leading French regiment sent by Bosquet. This regiment was quickly followed by others. The last great assault was delivered with more pre- cision, if with less fury than the others, and had Dannenberg chosen to employ the 9000 bayonets of his reserve, who stood idle throughout the day, to support the 6000 half-spent troops who made the attack, it would probably have been successful. * As it was, supported by the heavy guns on Shell Hill, the assailants, though no longer more than slightly superior in numbers, carried not only the sangar, but part of the crest line of the allied position. But they were driven back into the Quarry Ravine, and, relieving the exhausted British, the French took up the defence along the edge of the ravine, which, though still not without severe fighting, they maintained till the close of the battle. Inkerman, however, was not a drawn battle. The allied field artillery, reinforced by two long 18-pr. guns of the British siege train and assisted by the bold advance of two French "horse-artillery batteries which galloped down the forward slope and engaged the Russians at close range, gained the upper hand. Last of all, the dominant guns on Shell Hill thus silenced, the resolute advance of a handful of British infantry decided the day, and the Russians retreated. The final shots were fired about 1.30 p.m. The total British force engaged was 8500, of whom 2357 were killed and wounded. The French lost 939 out of about 7000 who came on to the field, though not all these were engaged. The Russians are said to have lost 1 1 ,000 out of about 42,000 present. The percentage (27-7) of loss sustained by the British is sufficient evidence of the intensity of the conflict, and provides a convincing answer to certain writers who have represented the battle as chiefly a French affair. On the other hand, the reproaches addressed by some British writers to General Bosquet for not promptly supporting the troops at Inker- man with his whole strength are equally unjustifiable, for apparently Sir George Brown and Sir George Cathcart both declined his first offers of support, and he had Prince Gorchakov with at least 20,000 Russians in his own immediate front. He would therefore have risked the failure of his own mission in order to take part in a battle where his intervention was not, so far as he could tell, of vital importance. When Lord Raglan definitely asked him for support, he gave it willingly and eagerly, sending his troops up at the double, and it must be remembered that several British divisions took no part in the action for the same reason that actuated Bosquet. But, in spite of the seemingly inevitable controversies attendant on an " allied " battle, it is now generally admitted that, as a " soldiers' battle," Inkerman is scarcely to be surpassed in modern history. INLAYING, a method of ornamentation, by incrusting or otherwise inserting in one material a substance or substances differing therefrom in colour or nature. The art is practised in the fabrication of furniture and artistic objects in all varieties of wood, metal, shell, ivory and coloured and hard stone, and in compound substances; and the combinations, styles and varieties of effect a're exceedingly numerous. Several special classes of inlaying may be here enumerated and defined, details INMAN— INN AND INNKEEPER 575 regarding most of which will be found under their separate headings. In the ornamental treatment of metal surfaces Niello decoration, applied to silver and gold, is an ancient and much-practised species of inlaying. It consists in filling up engraved designs with a composition of silver, copper, lead and sulphur incorporated by heat. The composition is black, and the finished work has the appearance of a drawing in black on a metallic plate. An art, analogous in effect, called bidri, from Bider in the Deccan, is practised in India. In bidri work the ground is an alloy of zinc, with small proportions of copper and lead, in which shallow patterns and devices are traced, and filled up with thin plates of silver. When the surface has been evened and smoothed, the bidri ground is stained a permanent black by a paste the chief ingredients of which are sal-ammoniac and nitre, leaving a pleasing contrast of bright metallic silver in a dead black ground. The inlaying of gold wire in iron or steel is known as Damascening (q.v.). It has been very largely practised in Persia and India for the ornamentation of arms and armour, being known in the latter country as Kuft work or Kuftgari. In Kashmir, vessels of copper and brass are very effectively inlaid with tin — an art which, like many other decorative arts, appears to have originated in Persia. In the ornamental inlaying of metal surfaces the Japanese display the most extraordinary skill and perfection of workmanship. In the inlaying of their fine bronzes they use principally gold and silver, but for large articles and also for common cast hollow ware commoner metals and alloys are employed. In inlaying bronzes they generally hollow out and somewhat undercut the design, into which the ornamenting metal, usually in the form of wire, is laid and hammered over. Frequently the lacquer work of the Japanese is inlaid with mother-of-pearl and other substances, in the same manner as is practised in ornamenting lacquered papier-mach6 among Western communities. The Japanese also practise the various methods of inlaying referred to under Damascening. The term Mosaic (q.v.) is generally applied to inlaid work in hard stones, marble and glass, but the most important class of mosaics — those which consist of innumer- able small separate pieces — do not properly come under the head of inlaying. Inlaid mosaics are those in which coloured designs are inserted in spaces cut in a solid ground or basis, such as the modern Florentine mosaic, which consists of thin veneers of precious coloured stones set in slabs of marble. The Taj Mahal at Agra is an example of inlaid mosaic in white marble, and the art, carried to that city by a French artist, is still practised by native workmen. Pietra dura is a fine variety of inlaid mosaic in which hard and expensive stones — agate, cornelian, amethyst and the like — are used in relief. Certain kinds of enamel might also be included among the varieties of inlaying. (See also Marquetry -and Bombay Furniture.) INMAN, HENRY (1801-1846), American artist, was born in Utica, New York, on the 20th of October 1801. Apprenticed to the painter John W. Jarvis at the age of fourteen, he left him after seven years and set up for himself, painting portraits, genre and landscape. He was one of the organizers of the National Academy of Design in New York and its first vice- president (from 1826 until 1832). As a portrait painter he was highly successful both in New York and Philadelphia, and going to England in 1844, he had for sitters the Lord Chancellor (Cottenham), the poet Wordsworth, Doctor Chalmers, Lord Macaulay and others. His American sitters included President Van Buren and Chief Justice Marshall. He died in New York City on the 17th of January 1846. INN, a river of Europe, an important right bank tributary of the Danube. It rises at an elevation of 7800 ft., in a small lake under the Piz Longhino, in the Swiss canton of the Grisons. After flowing for a distance of 55 m., through the Engadine it leaves Swiss territory at Martinsbruck and enters Austria. It next plunges through the deep ravine of Finstermiinz, and, continuing in the main a north-easterly direction, receives at Landeck the Rosanna. Hence its course becomes more rapid, until, after swirling through the narrow and romantic Oberinnthal, it enters the broader and pastoral Unterinnthal. It next passes Innsbruck and from Hall, a few miles lower down, begins to be navigable for barges. At Kufstein, down to which point it has still pursued a north-easterly direction, it breaks through the north Tirol limestone formation, and, now keeping a northerly course, enters at Rosenheim the Bavarian high plateau. Its bed is now broad, studded with islands and enclosed by high banks. Its chief tributaries on this last portion of its course are the Alz and the Salzach, and at Passau, 309 m. from its source, it joins the Danube, which river down to that point it equals in length and far exceeds in volume of water. Its rapid current does not permit of extensive navigation, but timber rafts are floated down from above Innsbruck. See Greinz, Eine Wanderung dutch das Unterinntal (Stuttgart, 1902). INN and INNKEEPER. An inn is a house where travellers are fed and lodged for reward. A distinction has been drawn between tavern, inn and hotel, the tavern supplying food and drink, the hotel lodging, the inn both; but this is fanciful. "Hotel" now means "inn," and "inn" is often applied to a mere public-house, whilst " tavern " is less used. " Inn," still the legal and best, as it is the oldest, is a form of the word " in " or " within." This sense is retained in the case of the English legal societies still known as Inns or Court (q.v.). In the Bible " inn " means " lodging-place for the night." Hospitality has always been a sacred duty in the East. The pilgrim or the traveller claims it as a right. But some routes were crowded, as that from Bagdad to Babylon. On these, khans (in or near a town) and caravanserais (in waste places) were erected at the expense of the benevolent. They consisted of a square building surrounded by a high wall; on the roof there was a terrace and over the gateway a tower; inside, was a large court surrounded by compartments in which was some rude provision for the animals and baggage of the traveller as well as for himself. The latter purchased his own food where he chose, and had to "do for himself." In some such place Jesus was born. Tavern is mentioned once in Scripture (Acts xxviii. 15) where it is said the brethren from Rome met Paul at "the Three Taverns." This was a station on the Appian Way, referred to also in Cicero's Letters (Ad Alt. ii. 12). So, in modern London, stations are called " Elephant and Castle," or " Bricklayers' Arms," from adjacent houses of entertainment. Among the Greeks inns and innkeepers were held in low repute. The houses were bad and those who kept them had a bad name. A self-respecting Greek entered them as seldom as possible; if he travelled he relied on the hospitality of friends. In Rome under the emperors some- thing akin to the modern inn grew up. There is, however, scarcely any mention of such institutions in the capital as distin- guished from mere wine-shops or eating-houses. Ambassadors were lodged in apartments at the expense of the state. But along the great roads that radiated from Rome there were inns. Horace's account of his journey to Brundisium (Sat. i. 5), that brilliant picture of contemporary travel, tells us of their existence, and the very name of the Three Taverns shows that there was sufficient custom to support a knot of these institutions at one place. Under the Roman law, the innkeeper was answer- able for the property of his guests unless the damage was due to damnum fatale or vis major, in modern language the act of God or the king's enemies. He was also liable for damage done by his servant or his slave or other inhabitant of the house. In the middle ages hospitality was still regarded as a duty, and provision for travellers was regularly made in the monasteries.' People of rank were admitted to the house itself, others sought the guest-chamber, which sometimes stood (as at Battle Abbey) outside the precincts. It consisted of a hall, round which were sleeping-rooms, though the floor of the hall itself was often utilized. Again, hospitality was rarely denied at the castle or country house. The knight supped with his host at the dais or upper part of the great hall, and retired with him into his own apartment. His followers, or the meaner strangers, sat lower down at meat, and after the tables had been removed stretched themselves to rest upon the floor. In desolate parts hospices 57^ INN AND INNKEEPER were erected for the accommodation of pilgrims. Such existed in the Alps and on all the great roads to the Holy Land or to famous shrines, notably to that of Canterbury. The still impres- sive remains of the Travellers' Hospital at Maidstone, founded by Archbishop Boniface in 1260, give an idea of the extent of such places. The mention of Canterbury recalls two inns celebrated by Chaucer. The pilgrims started from the" Tabard " at Southwark under the charge of Harry Baily the host, and they put up at the " Checquers of the Hope," in Mercery Lane, Canterbury. It is easy to infer that, as time went on, the meagre hospitality of the monastery or the hospice was not sufficient for an increasing middle class, and that the want was met by the development of the mere ale-house into the inn. The " ale-house," to give it the old English name, was always in evidence, and even in pre-Reformation days was a favourite subject for the satirist. In Langland's Piers the Plowman and in Skelton's Elynour Rummynge we have contemporary pictures of ale-houses of the 14th and 16th centuries, but the Tabard is quite a modern inn, with a table d'hote supper, a sign, a landlord (" right a mery man ") and a reckoning! It has been conjectured (Larwood and Hotten, History of Signboards, 1874) that the inn sign was taken or imitated from that displayed on the town houses or inns of noblemen and prelates. The innkeeper alone of tradesmen retains his individual sign. The inn shared with the tavern the long projecting pole garnished with branches. These poles had become of such inordinate length in London that in 1375 they were restricted to 7 ft. But the inn of those times was still a simple affair. In each room there were several beds, the price of which the prudent traveller inquired beforehand. Extortion was frequent, though it was forbidden by a statute of Edward III. The fare was simple ; bread, meat and beer, with fish on Fridays. The tavern senti- ment is strong in Elizabethan literature. The " Boar's Head " in Eastcheap is inseparably connected with Sir John Falstaff and Dame Quickly. " Shall I not take mine ease in mine Inn? " (1 Henry IV., Act iii. sc. 3) is well-nigh the most famous word of the famous knight. A passage in Holinshed's Chronicle (1587, i. 246) explains the inner meaning of this. He assures us that the inns of England are not as those of other lands. Abroad the guest is under the tyranny of the host, but in England your inn is as your own house; in your chamber you can do what you will, and the host is rather your servant than your master. The " Mermaid " in Bread Street is associated with the memory of many wits and poets — Raleigh, Shakespeare, Beaumont, Fletcher, Ben Jonson — who frequented it and praised it. Shenstone's lines as to " the warmest welcome at an inn " vent a common but rather cheap cynicism. Doctor Johnson was a great frequenter of inns and was outspoken in praise and blame. In the time immediately preceding railways the inn, which was also a post-house where the public coach as well as that of the private traveller changed horses, was a place of much importance. We have it presented over and over again in the pages of Dickens. The " Maypole " in Barnaby Rudge may be singled out for mention; it survives at Chigwell, Essex, as the " King's Head." The effect of railways was to multiply hotels in great centres and gradually increase their size till we have the huge structures so plentiful to-day. The bicycle and later the motor car, through the enormous traffic they caused on the country roads, have restored the old wayside inns to more than their former prosperity. In Scotland a statute (1424) of James I. ordained inns for man and beast, with food and drink at reasonable prices, in each borough, and a subsequent act prohibited lodging in privs'.e houses in places where there were inns, under a penalty of 40s. But for centuries the Scots inn was a poor affair. The Clachan of Aberfoyle in Rob Roy, kept by the widow MacAlpine, was probably typical. In St Ronan's Well Scott gives the more pleasing picture of the Cleikum Inn, kept by the delightful Meg Dods, and mention should be made of St Mary's Cottage, with its hostess Tibby Shiels, the scene of one of the Nodes Ambro- sianae, with memories not merely of Scott but of Christopher North and the Ettrick Shepherd. Burns had much to do with inns and taverns. If Poosie Nancie's, where the Jolly Beggars held wild revel, is long vanished, the Globe at Dumfries still exists, a fair sample of an inn of the period. As late as 184 1 Dickens, writing to John Foster during his first visit to Scotland, describes the Highland inns as very poor affairs, " a mere knot of little outhouses " he says of one; and even in Queen Victoria's Leaves from the Journal of Our Life in the Highlands the inn is described as invariably small and unassuming. Thus the development of hotels in Scotland did not begin much before the middle of the 19th century. In America the first hotel mentioned in New York is " Kriger's Tavern " about 1642, replaced in 1703 by the " King's Arms." When the town came to be English a proclamation was issued regulating the inns. Meals were not to cost more than 8d. or beer 2d. per quart. Law Relating to Innkeepers. — Whether any special building is an inn is a question of fact. A temperance hotel is an inn, but a mere public-house is not. An innkeeper is bound to receive, lodge and feed travellers if he has accommodation, if they are able and willing to pay, and are not obviously objection- able. If he refuse he is liable at common law to indictment, or an action will lie against him at the suit of the would-be guest. Under the Army Act soldiers of all kinds may be billeted on the innkeeper, even beyond his power to provide in his own house; he must find accommodation for them elsewhere. An innkeeper must keep the goods and chattels of his guest in safety, unless they are destroyed by the act of God or the king's enemies. Under this last the king's rebellious subjects are not included. He is not liable for goods stolen or destroyed by the companion of the guest or through the guest's own negligence. There are two theories as to the origin of this common law liability of the innkeeper: (1) it was a survival of the liability of the common trader, or (2) specially imposed from the nature of his calling. Old English law held him to some extent suspect. The traveller amongst strangers seemed forlorn and unprotected, and con- spiracy with thieves was dreaded. In modern times the landlord's responsibilities were cut down by the Innkeepers Liability Act 1 863 . He is not liable (save for horses and other live animals with their gear and carriages) to a greater extent than £30, unless the loss is caused by the default or neglect of himself or his servants, or the goods have been formally deposited with him. He must conspicuously exhibit a copy of the material parts of the act. The innkeeper may contract himself out of his common law obligation, and, apart from negligence, he is not liable for injury to the person or clothes of his guest. In return for these responsibilities the law gives him a lien over his guest's goods till his bill be paid. This is a particular and not a general lien. It attaches only to the special goods brought by the guest to the inn, and housed by the innkeeper with him. When several guests go together, the lien extends to all their goods. The innkeeper is only bound to take ordinary care of goods thus held, but he cannot use them or charge for their house-room. By the custom of London and Exeter, " when a horse eats out the price of his head," namely, when the cost of keep exceeds value, the host may have him as his own. By the Innkeepers Act 1878, if goods have been kept for six weeks they may be advertised and then sold after the interval of a month. Although an advertisement in a London paper is directed, this act (it would seem) applies to Scotland (J.A.Fleming, in Green's Encyclopaedia of the Law of Scotland, vi. 363). In that country the law is. generally the same as in England, though it has been held that the innkeeper is not responsible for loss by accidental fire. Nor is his refusal to receive a guest a criminal offence. In the United States the common law follows that of England, though laws of the various states have diminished the liability of the innkeeper in much the same fashion as in England. Innkeepers as retailers of intoxicating liquors are subject to the provisions of the Licensing Laws. See Angus, Bible Handbook (new ed., 1904) ; Beckmann's In- ventions, tr. by Johnson (1846); Jusserand, Les Anglais au moyen Age (1884); Liebenau, Das Gasthof- und Wirtshauswesen der Schweie INNERLEITHEN— INNOCENT (POPES) 577 in alterer Zeit (1891); Kempt, Convivial Caledonia (1893); F. W. Hackwood, Inns, Ales and Drinking Customs of Old England (1909) ; Jelf and Hurst, The Law of Innkeepers (1904). English and Roman law are compared in Pymar's Law of Innkeepers (1892). For Scots law, see Bell's Principles. An American treatise is S. H. Wandell, Law of Inns, Hotels and Boarding Houses (1888). (F. Wa.) INNERLEITHEN, a police burgh and health resort of Peebles- shire, Scotland, on Leithen Water, near its junction with the Tweed, 65 m. S.E. of Peebles by the North British railway. Pop. (iqoi) 2181. In olden times it seems to have been known as Hornehuntersland, and to have been mentioned as early as 1 1 59, when a son of Malcolm IV. (the Maiden) was drowned in i. pool of the Tweed, close to Leithenfoot. Its chief industry is the manufacture of tweeds and fine yarns, which, together with the fame of its medicinal springs, brought the burgh into promin- ence towards the end of the 18th century. The spa, alleged to be the St Ronan's well of Scott's novel of that name, has a pump-room, baths, &c. The saline waters are useful in minor cases of dyspepsia and liver complaints. The town is flanked on the W. by the hill fort of Caerlee (400 ft. long) and on the E. by that of the Pirn (350 ft. long). Farther E., close to the village of Walkerburn, are Purvis Hill terraces, a remarkable series of earthen banks, from 50 ft. to more than 100 ft. wide, and with a length varying up to 900 ft., the origin and purpose of which are unknown. Traquair House, or Palace, on the right bank of the Tweed, is believed to be the oldest inhabited house in Scotland, the most ancient portion dating from the 10th century, and including a remnant of the castle. It was largely added to by Sir John Stewart, first earl of Traquair (d. 1659) and is a good example of the Scottish Baronial mansion with high-pitched roof and turreted angles. To the west of the house was the arbour which formed the " bush aboon Traquair " of the songs by Robert Crawford (d. 1733) and John Campbell Shairp, its site being indicated by a few birch trees. James Nicol (1769-1819), the poet, was minister of Traquair, and his son James Nicol (1810-1879), the geologist and professor of natural history in Aberdeen University, was born in the manse. INNESS, GEORGE (1825-1894), American landscape painter, was born near Newburgh, N.Y., on the 1st of May 1825. Before he was five years of age his parents had moved to New York and afterwards to Newark, N.J., in which latter city his boyhood was passed. He would not " take education " at the town academy, nor was he a success as a greengrocer's boy. He had a strong bent towards art, and his parents finally placed him with a drawing-master named Barker. At sixteen he went to New York to study engraving, but soon returned to Newark, where he continued sketching and painting after his own initiative. In 1843 he was again in New York, and is said to have passed a month in Gignoux's studio. But he was too impetuous, too independent in thought, to accept teaching; and, besides, the knowledge of his teachers must have been limited. Practically he was self-taught, and always remained a student. In 1851 he went to Europe, and in Italy got his first glimpse of real art. He was there two years, and imbibed some traditions of the classic landscape. In 1854 he went to France, and there studied the Barbizon painters, whom he greatly admired, especially Daubigny and Rousseau. After his return to America he opened a studio in New York, then went to Medfield, Mass., where he resided for five years. A pastoral landscape near this town inspired the characteristic painting " The Medfield Meadows." Again he went abroad and spent six years in Europe. He came back to New York in 1876, and lived there, or near there, until the year of his death, which took place at Bridge of Allan on the 3rd of August 1894 while he was travelling in Scotland. He was a National Academician, a member of the Society of American Artists, and had received many honours at home and abroad. He was married twice, his son, George Inness (b. 1854), being also a painter. Inness was emphatically a man of temperament, of moods, enthusiasms, convictions. He was fond of speculation and experiment in metaphysics and religion, as in poetry and art. Swedenborgianism, symbolism, socialism, appealed to him as they might to a mystic or an idealist. He aspired to the perfect unities, and was impatient of structural foundations. This was Jtiv. 19 his attitude towards painting. He sought the sentiment, the light, air, and colour of nature, but was put out by nature's forms. How to subordinate form without causing weakness was his problem, as it was Corot's. His early education gave him no great technical facility, so that he never was satisfied with his achievement. He worked over his pictures incessantly, retouching with paint, pencil, coal, ink — anything that would give the desired effect — yet never content with them. In his latter days it was almost impossible to get a picture away from him, and after his death his studio was found to be full of experi- mental canvases. He was a very uneven painter, and his experiments were not always successful. His was an original — a distinctly American — mind in art. . Most of his American subjects were taken from New York state, New Jersey and New England. His point of view was his own. At his best he was often excellent in poetic sentiment, and superb in light, air and colour. He had several styles: at first he was somewhat grandiloquent in Roman scenes, but sombre in colour; then under French influence his brush grew looser, as in the " Grey Lowering Day "; finally he broke out in full colour and light, as in the " Niagara " and the last " Delaware Water-Gap." Some of his pictures are in American museums, but most of them are in private hands. (J. C. Van D.) INNOCENT (Innocentius), the name of thirteen popes and one anti-pope. Innocent L, pope from 402 to 417, was the son of Pope Anastasius I. It was during his papacy that the siege of Rome by Alaric (408) took place, when, according to a doubtful anecdote of Zosimus, the ravages of plague and famine were so frightful, and help seemed so far off, that pyons over St Bonaventura. His bulls are in the Turin collection (:S 5 9). See F. Gregorovius, Rome in the Middle Ages, vol. 5, trans, by Mrs G. \V. Hamilton (London, 1900-1902); A. Potthast, Regesta pontif. Roman, vol. ii. (Berlin, 1875); E. Bourgeois, Le Bienheureux Innocent V (Paris, 1899); J. E. Borel, Notice biogr. sur Pierre de Tarentaise (Chambery, 1890); P. J. Bethaz, Pierre des Cours de la Salle, pape sous le nom Innocent V (Augustae, 1891); L. Carboni, De Innoceniio V. Romano pontifice (1894). (C. H. Ha.) Innocent VI. (Etienne Aubert), pope from the 18th of December 1352 to the 12th of September 1362, was born at Mons in Limousin. He became professor of civil law at Toulouse and subsequently chief judge of the city. Having taken orders, he was raised to the see of Noyon and translated in 1340 to that of Clermont. In 1342 he was made cardinal-priest of Sti Giovanni e Paolo, and ten years later cardinal-bishop .of Ostia and Velletri, grand penitentiary, and administrator of the bishopric of Avignon. On the death of Clement VI., the cardinals made a solemn agreement imposing obligations, mainly in favour of the college as a whole, on whichever of their number should be elected pope. Aubert was one of the minority who signed the agreement with the reservation that in so doing he would not violate any law, and was elected pope on this understanding; not long after his accession he declared the agreement null and void, as infringing the divinely-bestowed power of the papacy. Innocent was one of the best Avignon popes and filled with reforming zeal; he revoked the reservations and commendations of his predecessor and prohibited pluralities; urged upon the higher clergy the duty of residence in their sees, and diminished the luxury of the papal court. Largely through the influence of Petrarch, whom he called to Avignon, he released Cola di Rienzo, who had been sent a prisoner in August 1352 from Prague to Avignon, and used the latter to assist Cardinal Albornoz, vicar- general of the States of the Church, in tranquillizing Italy and restoring the papal power at Rome. Innocent caused Charles IV. to be crowned emperor at Rome in 1355, but protested against the famous " Golden Bull " of the following year, which pro- hibited papal interference in German royal elections. He renewed the ban against Peter the Cruel of Castile, and interfered in vain against Peter IV. of Aragon. He made peace between Venice and Genoa, and in 1360 arranged the treaty of Bretigny between France and England. In the last years of his pontificate he was busied with preparations for a crusade and for the reunion of Christendom, and sent to Constantinople the celebrated Carmelite monk, Peter Thomas, to negotiate with the claimants to the Greek throne. He instituted in 1354 the festival of the Holy Lance. Innocent was a strong and earnest man of monastic temperament, but not altogether free from nepotism. He was succeeded by Urban V. The chief sources for the life of Innocent VI. are in Baiuzius, Vila? } J np. Avenion. vol. i. (Paris, 1693); Magnum bullari't Komanum, vol. iv. (Turin, 1859); E. Werunsky, Excerpt a ex registris Clementis VI. et Innoceiitii VI. (Innsbruck, 1885). See also I.. Pa: lor History of Ike Popes, vol. i. trans, by F. I. Antrobus (London, 1899); F. Gregorovius, Rome in the Middle Ages, vol. 6, trans, by Mrs G. W. Hamilton (London, 1900-1902); D. Cerri, Innocenzo Papa VI (Turin, 1873); J. B. Christophe, Histoire de la papaule pendant le XIV" siecle, vol. 2 (Paris, 1853); M. Souchon, Die Papstwahlen (Brunswick, 1888); G. Daumet, Innocent VI et Blanche de Bourbon (Paris, 1899); E. Werunsky, Gesch. Kaiser Karls IV. (Innsbruck, 1892). There is an excellent article by M. Naumann in Hauck's Realencyklopddie, 3rd ed. (C. H. Ha.) Innocent VII. (Cosimo dei Migliorati), pope from the 17th of October 1404 to the 6th of November 1406, was born of middle- class parentage at Sulmona in the Abruzzi in 1339. On account of his knowledge of civil and canon law, he was made papal vice-chamberlain and archbishop of Ravenna by Urban VI., and appointed by Boniface IX. cardinal priest of Sta Croce in Gerusalemme, bishop of Bologna, and papal legate to England. He was unanimously chosen to succeed Boniface, after each of the cardinals had solemnly bound himself to employ all lawful means for the restoration of the church's unity in the event of his election, and even, if necessary, to resign the papal dignity. The election was opposed at Rome by a considerable party, but peace was maintained by the aid of Ladislaus of Naples, in return for which Innocent made a promise, inconsistent with his previous oath, not to come to terms with the antipope Benedict XIII. , except on condition that he should recognize the claims of Ladislaus to Naples. Innocent issued at the close of 1404 a summons for a general council to heal the schism, and it was not the pope's fault that the council never assembled, for the Romans rose in arms to secure an extension of their liberties, and finally maddened by the murder of some of their leaders by the pope's nephew, Ludovico dei Migliorati, they compelled Innocent to take refuge at Viterbo (6th of August 1405). The Romans, recognizing later the pope's innocence of the outrage, made their submission to him in January 1406. He returned to Rome in March, and, by bull of the 1st of September, restored the city's decayed university. Innocent was extolled by contemporaries as a lover of peace and honesty, but he was without energy, guilty of nepotism, and showed no favour to the proposal that he as well as the antipope should resign. He died on the 6th of November 1406 and was succeeded by Gregory XII. See L. Pastor, History of the Popes, vol. i., trans, by F. I. Antrobus (London, 1899) ; M. Creighton, History of the Papacy, vol. i. (London, 1899); N. Valois, La France et le grand,, schisme d' Occident (Paris, 1896-1902); Louis Gayet, Le Grand Schisme d 'Occident (Paris, 1898); J. Loserth, Geschichte des spdteren Mittelalters (1903); Theodorici de Nyem, De schismate libri tres, ed. by G. Erler (Leipzig, 1890); K. J. von Hefele, Conciliengeschichte, Bd. 6, 2nd ed. ; J. von Haller, Papsttum m. Ktrchenreform (Berlin, 1903). (C. H. Ha.) Innocent VIII. (Giovanni Battista Cibo), pope from the 29th of August 1484 to the 25th of July 1492, successor of Sixtus IV., was born at Genoa (1432), the son of Arano Cibo, who under Calixtus III. had been a senator of Rome. His youth, spent at the Neapolitan court, was far from blameless, and it is not certain that he was married to the mother of his numerous family. He later took orders, and, through the favour of Cardinal Calandrini, half-brother of Nicholas V., obtained from Paul II. the bishopric of Savona. Sixtus IV. translated him to the see of Molfetta, and in T473 created him cardinal-priest of Sta Balbina, subsequently of Sta Cecilia. As pope, he addressed a fruitless summons to Christendom to unite in a crusade against the infidels, and concluded in 1489 a treaty with Bayezid II., agreeing in consideration of an annual payment of 40,000 ducats and the gift of the Holy Lance, to detain the sultan's fugitive brother Jem in close confinement in the Vatican. Innocent excommunicated and deposed Ferdinand, king of Naples, by bull of the nth of September 1489, for refusal to pay the papal dues, and gave his kingdom to Charles VIII. of France, but in 1492 restored Ferdinand to favour. He declared (i486) Henry VII. to be lawful king of England by the threefold right of conquest, inheritance and popular choice, and approved his marriage with Elizabeth, the daughter of Edward IV. Innocent, like his predecessor, hated heresy, and in the bull Snmmis desidcrantcs (5th of December 1484) he instigated very severe measures against magicians and witches in Germany; he 5 8 2 INNOCENT (POPES) prohibited (i486) on pain of excommunication the reading of the propositions of Pico della Mirandola; he appointed (1487) T. Torquemada to be grand inquisitor of Spain; and he offered plenary indulgence to all who would engage in a crusade against the VValdenses. He took the first steps towards the canonization of Queen Margaret of Scotland, and sent missionaries under Portuguese auspices to the Congo. An important event of his pontificate was the capture of Granada (2nd of January 1492), which was celebrated at Rome with great rejoicing and for which Innocent gave to Ferdinand of Aragon the title of " Catholic Majesty." Innocent was genial, skilled in flattery, and popular with the Romans, but he lacked talent and relied on the stronger will of Cardinal della Rovere, afterwards Julius II. His Curia was notoriously corrupt, and he himself openly practised nepotism in favour of his children, concerning whom the epigram is quoted: " Octo nocens pueros genuit, totidemque puellas: — Hunc merito poterit dicere Roma patrem." Thus he gave to his un- deserving son Franceschetto several towns near Rome and married him to the daughter of Lorenzo de' Medici. Innocent died on the 25th of July 1492, and was succeeded by Alexander VI. The sources for the life of Innocent VIII. are to be found in L. Muratori, Rerum Italicarum Scriptores, vol. 3, and in Raynaldus, a. 1484-1492. See also L. Pastor, History of the Popes, vol. 5, trans, by F. I. Antrobus (London, 1898); M. Creighton, History of the Papacy, vol. 4 (London, 1901); F. Gregorovius, Rome in the Middle Ages, vol. 7, trans, by Mrs. G. W. Hamilton (London, 1900-1902); T. Hagen, Die Papstwahlen von 1484 u. 14Q2 (Brizen, 1885); S. Riezler, Die Hexenprozesse (1896); G. Viani, Memorie della famiglia Cybo (Pisa, 1808) ;F. Serdonati, Vitaefatti d'Innocenzo VIII. (Milan, 1829). (C. H. Ha.) Innocent IX. (Giovanni Antonio Fachinetti) was born in 1 5 19. He filled the offices of apostolic vicar of Avignon, legate at the council of Trent, nuncio to Venice, and president of the Inquisition. He became cardinal in 1583; and under the invalid Gregory XIV. assumed almost the entire conduct of affairs. His election to the papacy, on the 29th of October 1 591. was brought about by Philip II., who profited little by it, however, inasmuch as Innocent soon succumbed to age and feebleness, dying on the 30th of December 1591. See Ciaconius, Vitae et res gestae summorum Pontiff. Rom. (Rome, 1601-1602); Cicarella, continuator of Platina, De Vitis Pontiff. Row. (both contemporaries of Innocent) ; Ranke, Popes (Eng. trans., Austin), ii. 233 sq. (all brief accounts). (T. F. C.) Innocent X. (Giovanni Battista Pamfili) was born in Rome on the 6th of May 1574, served successively as auditor of the Rota, nuncio to Naples, legate apostolic to Spain, was made cardinal in 1627, and succeeded Urban VIII. as pope on the 15th of September 1644. Throughout his pontificate Innocent was completely dominated by his sister-in-law, Donna Olimpia Maidalchini, a woman of masculine spirit. There is no reason to credit the scandalous reports of an illicit attachment. Never- theless, the influence of Donna Olimpia was baneful; and she made herself thoroughly detested for her inordinate ambition and rapacity. Urban VIII. had been French in his sympathies; but the papacy now shifted to the side of the Habsburgs, and there remained for nearly fifty years. Evidences of the change were numerous: Innocent promoted pro-Spanish cardinals; attacked the Barberini, proteges of Mazarin, and sequestered their possessions; aided in quieting an insurrection in Naples, fomented by the duke of Guise; and refused to recognize the independence of Portugal, then at war with Spain. As a reward he obtained from Spain and Naples the recognition of ecclesi- astical immunity. In 1649 Castro, which Urban VIII. had failed to take, was wrested from the Farnese and annexed to the Papal States. The most worthy efforts of Innocent were directed to the reform of monastic discipline (1652). His condemnation of Jansenism (1653) was met with the denial of papal infallibility in matters of fact, and the controversy entered upon a new phase (see Jansenism) . Although the pontificate of Innocent witnessed the conversion of many Protestant princes, the most notable being Queen Christina of Sweden, the papacy had nevertheless suffered a perceptible decline in prestige; it counted for little in the negotiations at Munster, and its solemn protest against the peace of Westphalia was entirely ignored. Innocent died on the 7th of January 1655, and was succeeded by Alexander VII. For contemporary lives of Innocent see Oldoin, continuator of Ciaconius, Vitae et res gestae summorum Pontiff. Rom. ; and Palazzi, Gesta Pontiff. Rom. (Venice, 1687-1688) iv. 570 sqq. ; Ciampi's Innoc. X. Pamfili, et la sua Corte (Rome, 1878), gives a very full account of the period. Gualdus' (pseud, of Gregorio Leti ; v. bibliog. note, art. " Sixtus V.") Vita de Donna Olimpia Maidalchina (1666) is gossipy and untrustworthy; Capranica's Donna Olympia Pamfili (Milan, '875, 3rd ed.) is fanciful and historically of no value. See also Ranke, Popes (Eng. trans., Austin), iii. 40 sqq. ; v. Reumont, Gesch. der Stadt Rom. iii. 2, p. 623 sqq. ; Brosch, Gesch. des Kirchenstaaies (1880) i. 409 sqq.; and the extended bibliography in Herzog-Hauck, Realencyklopddie, s.v. " Innocenz X." (T. F. C.) Innocent XI. (Benedetto Odescalchi), pope from 1676 to 1689, was born at Como on the 16th of May 161 1. He studied law in Rome and Naples, entered the Curia under Urban VIII. (his alleged military service seems to be questionable), and became successively protonotary, president of the Apostolic Chamber, governor of Macerate and commissary of Ancona. Innocent X. made him a cardinal (1647), legate to Ferrara, and, in 1650, bishop of Novara. His simple and blameless life, his conscientious discharge of duty, and his devotion to the needs of the poor had won for him such a name that, despite the opposition of France, he was chosen to succeed Clement X. on the 21st of September 1676. He at once applied himself to moral and administrative reform; declared against nepotism, intro- duced economy, abolished sinecures, wiped out the deficit (at the same time reducing rents), closed the gaming-houses, and issued a number of sumptuary ordinances. He held monks strictly to the performance of their vows; took care to satisfy himself of the fitness of candidates for bishoprics; enjoined regular catechetical instruction, greater simplicity in preaching, and greater reverence in worship. The moral teaching of the Jesuits incurred his condemnation (1679) (see Liguori), an act which the society never forgave, and which it partially revenged by forcing, through the Inquisition, the condemnation of the quietistic doctrines of Molinos (1687), for which Innocent entertained some sympathy (see Molinos). The pontificate of Innocent fell within an important period in European politics, and he himself played no insignificant role. His protest against Louis XIV.'s extended claim to regalian rights called forth the famous Declaration of Gallican Liberties by a subservient French synod under the lead of Bossuet (1682), which the pope met by refusing to confirm Louis's clerical appoint- ments. His determination to restrict the ambassadorial right of asylum, which had been grossly abused, was resented by Louis, who defied him in his own capital, seized the papal territory of Avignon, and talked loudly of a schism, without, however, shaking the pope in his resolution. The preponderance of France Innocent regarded as a menace to Europe. He opposed Louis's candidate for the electorate of Cologne (1688), approved the League of Augsburg, acquiesced in the designs of the Protestant William of Orange, even in his supplanting James II., whom, although a Roman Catholic, he distrusted as a tool of Louis. The great object of Innocent's desire was the repulse of the Turks, and his unwearying efforts to that end entitled him to share in the glory of relieving Vienna (1683). Innocent died on the 12th of August 1689, lamented by his subjects. His character and life were such as to suggest the propriety of canonization, but hostile influences have defeated every move in that direction. The life of Innocent has been frequently written. See Guarnacci, Vitae et res gestae Pontiff. Rom. (Rome, 1751), i. 105 sqq.; Palazzi, Gesta Pontiff. Rom. (Venice, 1690) ; also the lives by Albrizzi (Rome, 1695); Buonamici (Rome, 1776); and Immich (Berlin, 1900). Particular phases of Innocent's activity have been treated by Michaud, Louis XIV. et J««oc.XT.(Paris,i882sqq.,4vols.); Dubruel, La Correspond. . . . du Card. Carlo Pio, &c. (see Rev. des quest, hist. lxxv. (1904) 602 sqq.); and Gerin, in Rev. des quest, hist., 1876, 1878, 1886. For correspondence of Innocent see Colombo, Notizie biogr. e lettere di P. Innoc. XI. (Turin, 1878); and Berthier, Innoc. PP. XI. Epp. ad Principes (Rome, 1890 sqq.). An extended biblio- graphv may be found in Herzog-Hauck, Realencyklopddie, s.v. " Innocenz XI." (T. F. C.) INNOCENTS' DAY— INNSBRUCK 583 Innocent XII. (Antonio Pignatelli), pope from 1691 to 1700 in succession to Alexander VIII., was born in Naples on the 13th of March 1615, was educated at the Jesuit College in Rome, entered upon his official career at the age of twenty, and became vice-Jegate of Urbino, governor of Perugia, and nuncio to Tuscany, to Poland and to Austria. He was made cardinal and archbishop of Naples by Innocent XI., whose pontificate he took as a model for his own, which began on the 12th of July 1691. Full of reforming zeal, he issued ordinances against begging, extravagance and gambling; forbade judges to accept presents from suitors; built new courts of justice; prohibited the sale of offices, maintaining the financial equilibrium by reducing expenses; and, an almost revolutionary step, struck at the root of nepotism, in a bull of 1692 ordaining that thenceforth no pope should grant estates, offices or revenues to any relative. Innocent likewise put an end to the strained relations that had existed between France and the Holy See for nearly fifty years. He adjusted the difficulties over the regalia, and obtained from the French bishops the virtual repudiation of the Declaration of Gallican Liberties. He confirmed the bull of Alexander VIII. against Jansenism (1696); and, in 1699, under pressure from Louis XIV., condemned certain of Fenelon's doctrines which Bossuet had denounced as quietistic (see Fenelon). When the question of the Spanish succession was being agitated he advised Charles II. to make his will in favour of the duke of Anjou. Innocent died, on the eve of the great conflict, on the 27th of September 1700. Moderate, benevolent, just, Innocent was one of the best popes of the modern age. See Guarnacci, Vilae et res gestae Pontiff. Rom. (Rome, 1751), i. 389 sqq.; Ranke, Popes (Eng. trans., Austin), iii. 186 sqq.; v. Reumont, Gesch. der Stadt Rom. iii. 2, p. 640 sqq.; and the Bullarium Innoc. XII. (Rome, 1697). (T. F. C.) Innocent XIII. (Michele Angelo Conti), pope from 1721 to 1724, was the son of the duke of Poli, and a member of a family that had produced several popes, among them Innocent III., was born in Rome on the 13th of May 1655, served as nuncio in Switzerland, and, for a much longer time, in Portugal, was made cardinal and bishop of Osimo and Viterbo by Clement XL, whom he succeeded on the 8th of May 1721. One of his first acts was to invest the emperor Charles VI. with Naples (1722); but against the imperial investiture of Don Carlos with Parma and Piacenza he protested, albeit in vain. He recognized the Pretender, "James III.," and promised him subsidies conditional upon the re-establishment of Roman Catholicism in England. Moved by deep-seated distrust of the Jesuits and by their continued practice of " Accommodation," despite express papal prohibition (see Clement XL), Innocent forbade the Order to receive new members in China, and was said to have meditated its suppression. This encouraged the French Jansenist bishops to press for the revocation of the bull Unigenitus; but the pope commanded its unreserved acceptance. He weakly yielded to pressure and bestowed the cardinal's hat upon the corrupt and debauched Dubois. Innocent died on the 7th of March 1724, and was succeeded by Benedict XIII. See Guarnacci, Vitae et res gestae Pontiff. Rom. (Rome, 1751), ii. 137 sqq., 381 sqq.; Sandini, Vitae Pontiff. Rom. (Padua, 1739); M. v. Mayer, Die Papstwahl Innocenz XIII. (Vienna, 1874); Michaud, "La Fin du Clement XI. et le commencement du pontificat d'Innocent XIII." in the Internal. Theol. Zeitschr. v. 42 sqq., 304 sqq. (T. F. C.) INNOCENTS' DAY, or Childermas, a festival celebrated in the Latin church on the 28th of December, and in the Greek church on the 29th (O.S.) in memory of the massacre of the children by Herod. The Church early regarded these little ones as the first martyrs. It is uncertain when the day was first kept as a saint's day. At first it seems to have been absorbed into the celebration of the Epiphany, but by the 5th century it was kept as a separate festival. In Rome it was a day of fasting and mourning. In the middle ages the festival was the occasion. for much indulgence to the children. The boy-bishop (q.v.), whose tenure of office lasted till Childermas, had his last exercise of authority then, the day being one of the series of days which were known as the Feast of Fools. Parents temporarily abdicated authority, and in nunneries and monasteries the youngest nun and monk were for the twenty-four hours allowed to masquerade as abbess and abbot. These mockeries of religion were con- demned by the Council of Basel (1431); but though shorn of its extravagances the day is still observed as a feast day and merry- making for children in Catholic countries, and particularly as an occasion for practical joking like an April Fool's Day. In Spanish-America when such a joke has been played, the phrase equivalent to "You April fool!" is Que la inocencia le valga! May your innocence protect you! The society of Lincoln's Inn specially celebrated Childermas, annually electing a " king of the Cockneys." Innocents' Day was ever accounted unlucky. Nothing was begun and no marriages took place then. Louis XL prohibited all state business. The coronation of Edward IV., fixed for a Sunday, was postponed till the Monday when it was found the Sunday fell on the 28th of December. In rural England it was deemed unlucky to do housework, put on new clothes or pare the nails. At various places in Gloucestershire, Somerset and Worcestershire muffled peals were rung (Notes and Queries, 1st series, vol. viii. p. 617). In Northampton the festival was called " Dyzemas Day" (possibly from Gr. Sw- " ill " and "mass "), and there is a proverb "What is begun on Dyzemas will never be finished." The Irish call the day La Croasta na bliana, " the cross day of the year," or Diar dasin darg, " blood Thursday," and many legends attach to it (Notes and Queries, 4th series, vol. xii. p. 185). In medieval England the children were reminded of the mournfulness of the day by being whipped in bed on Innocents' morning. This custom survived to the 17th century. INNSBRUCK, the capital of the Austrian province of Tirol, and one of the most beautifully situated towns in Europe. In 1900 the population was 26,866 (with a garrison of about 2000 men), mainly German-speaking and Romanist. Built at a height of 1880 ft., in a wide plain formed by the middle valley of the Inn and on the right bank of that river, it is surrounded by lofty mountains that seem to overhang the town. It occupies a strong military position (its commercial and industrial import- ance is now but secondary) at the junction of the great highway from Germany to Italy over the Brenner Pass, by which it is by rail 1095 m. from Munich and 174I m. from Verona, with that from Bregenz in the Vorarlberg, distant 122 m., by rail under the Arlberg Pass. It takes its name from its position, close to the chief bridge over the Inn. It is the seat of the supreme judicial court of the Tirol, the Diet of which meets in the Landhaus. The streets are broad, there are several open places and the houses are handsome, many of those in the old town dating from the 17th and 18th centuries, and being adorned with frescoes, while the arcades beneath are used as shops. The principal monument is the Franciscan or Court church (1553-1563). In it is the magnificent 16th-century cenotaph (his body is elsewhere) of the emperor Maximilian (d. 1519), who, as count of the Tirol from 1490 onwards, was much beloved by his subjects. It represents the emperor kneeling in prayer on a gigantic marble sarcophagus, surrounded by twenty-eight colossal bronze statues of mourners, of which twenty-three figure ancestors, relatives or contemporaries of Maximilian, while five represent his favourite heroes of antiquity — among these five are the two finest statues (both by Peter Vischer of Nuremberg), those of King Arthur of Britain and of Theodoric, the Ostrogothic king. On the sides of the sarcophagus are twenty-four marble reliefs, depicting the principal events in the life of Maximilian, nearly all by Alexander Colin of Malines, while the general design of the whole monument is attributed to Gilg Sesselschreiber, the court painter. In one of the aisles of the same church is the Silver Chapel, so called from a silver Madonna and silver bas-reliefs on the altar; it contains the tombs of Archduke Ferdinand, count of the Tirol (d. 1595) and his non-royal wife, Philippine Welser of Augsburg (d. 1580), whose happy married life spent close by is one of the most romantic episodes in Tirolese history. In the other aisle are the tombs, with monuments, of the heroes of the War of Independence of 1809, Hofer, Haspinger and Speckbacher. It was in this church. 5*4 INNS OF COURT that Queen Christina of Sweden, daughter of Gustavus Adolphus, abjured Protestantism, in 1655. There are also several other churches and convents, among the latter the first founded (1593) in Germany by the Capuchins. The university of Innsbruck was formally founded in 1677, and refounded (after two periods of suspension, 1 782-1 792 and 1810-1826) in 1826. It is attended by about 1000 students and has a large staff of professors, the theological faculty being controlled by the Jesuits. It has a library of 176,000 books, and 1049 MSS. The University or Jesuit church dates from the early 17th century. The Ferdinandeum is the provincial museum (founded in 1823, though the present building is later). The house known as the Goldne Dachl has its roof covered with gilded copper tiles; it was built about 1425, by Frederick, count of the Tirol, nicknamed " with the empty pockets," but the balcony and gilded roof were added in 1500 by the emperor Maximilian. Among the other monuments of Innsbruck may be mentioned the Pillar of St Anne, erected in 1706 to com- memorate the repulse of the French and the Bavarians in 1703; the Triumphal Arch, built in 1765, on the occasion of the marriage of the future emperor Leopold II. with the Infanta Maria Louisa of Spain; and a fountain, with a bronze statue of Archduke Leopold V., set up in 1863-1877, in memory of the five-hundredth anniversary of the union of the Tirol with Austria. The Roman station of Veldidena was succeeded by the Pre- monstratensian abbey of Wilten, both serving to guard the important strategical bridge over the Inn. In 1180 the count of Andechs (the local lord) moved the market-place over to the right bank of the river (where is the convent), and in 1187 we first hear of the town by its present name. Between 1233 and 1235 it was fortified, and a castle built for the lord. But it was only about 1420 that Archduke Frederick IV. (" with the empty pockets ") built himself a new castle in Innsbruck, which then replaced Meran as the capital of Tirol. The county of Tirol was generally held by a cadet line of the Austrian house, the count being almost an independent ruler. But the last princeling of this kind died in 1665, since which date Innsbruck and Tirol have been governed from Vienna. In 1552 Maurice of Saxony surprised and nearly took Innsbruck, almost capturing the emperor Charles V. himself, who escaped owing to a mutiny among Maurice's troops. In the patriotic warof 1809, Innsbruck played a great part and suffered much, while in 1848, at the time of the revolution in Vienna, it joyfully received the emperor Ferdinand. ' (W. A. B. C.) INNS OF COURT. The Inns of Court and Chancery are voluntary non-corporate legal societies seated in London, having their origin about the end of the 13th and the commencement of the 14th century. Dugdale (Origines Juridiciales) states that the learned in English law were anciently persons in holy orders, the justices of the king's court being bishops, abbots and the like. But in 1 207 the clergy were prohibited by canon from acting in the temporal courts. The result proving prejudicial to the interests of the community, a commission of inquiry was issued by Edward I. (1290), and this was followed up (1292) by a second commission, which among other things directed that students " apt and eager" should be brought from the provinces and placed in proximity to the courts of law now fixed by Magna Carta at Westminster (see Inn). These' students were accordingly located in what became known as the Inns of Court and Chancery, the latter designated by Fortescue ( De Laudibus) as " the earliest settled places for students of the law," the germ of what Sir Edward Coke subsequently spoke of as our English juridical university. In these Inns of Court and Chancery, thus con- stituted, and corresponding to the ordinary college, the students, according to Fortescue, not only studied the laws and divinity, but further learned to dance, sing and play instrumental music, " so that these hostels, being nurseries or seminaries of the court, were therefore called Inns of Court." Stow in his Survey (1598) says: "There is in and about this city a whole university, as it were, of students, practisers or pleaders and judges of the laws of this realm"; and he goes on to enumerate the several societies, fourteen in number, then existing, corresponding nearly with those recognized in the present day, of which the Inns of Court, properly so-called, are and always have been four, namely Lincoln's Inn, the Inner Temple, the Middle Temple and Gray's Inn. To these were originally attached as subordinate Inns of Chancery, Furnival's Inn, Thavie's Inn (to Lincoln's Inn), Clifford's Inn, Clement's Inn (to the Inner Temple), New Inn (to the Middle Temple), Staple's Inn, Barnard's Inn (to Gray's Inn), but they were cut adrift by the older Inns and by the middle of the 18th century had ceased to have any legal character (vide infra) . In addition to these may be specified Serjeant's Inn, a society composed solely of serjeants-at-law, which ceased to exist in 1877. Besides the Inns of Chancery above enumerated, there were others, such as Lyon's Inn, which was pulled down in 1868, and Scrope's Inn and Chester or Strand Inn, spoken of by Stow, which have long been removed, and the societies to which they belonged have disappeared. The four Inns of Court stand on a footing of complete equality, no priority being conceded to or claimed by one inn over another. Their jurisdictions and privileges are equal, and upon affairs of common interest the benchers of the four inns meet in conference. From the earliest times there has been an interchange of fellowship between the four houses; nevertheless the Middle Temple and Lincoln's Inn, and the Inner Temple and Gray's Inn, have maintained a closer alliance. The members of an Inn of Court consist of benchers, barristers and students. The benchers are the senior members of the society, who are invested with the government of the body to which they belong. They are more formally designated " masters of the bench," are self-elected and unrestricted as to numbers. Usually a member of an inn, on attaining the rank of king's counsel, is invited to the bench. Other members of long standing are also occasionally chosen, but no member by becoming a king's counsel or by seniority of standing acquires the right of being nominated a bencher. The benchers vary in number from twenty in Gray's Inn to seventy and upwards in Lincoln's Inn and the Inner Temple. The powers of the benchers are practically without limit within their respective societies; their duties, however, are restricted to the superintendence and management of the concerns of the inn, the admission of candi- dates as students, the calling of them to the bar and the exercise of discipline generally over the members. The meetings of the benchers are variously denominated a " parliament " in the Inner and Middle Temples, a " pension " in Gray's Inn and a " council " in Lincoln's Inn. The judges of the superior courts are the visitors of the inns, and to them alone can an appeal be had when either of the societies refuses to call a member to the bar, or to reinstate in his privileges a barrister who has been disbarred for misconduct. The presiding or chief officer is the treasurer, one of the benchers, who is elected annually to that dignity. Other benchers fulfil the duties of master of the library, master of the walks or gardens, dean of the chapel and so forth, while others are readers, whose functions are referred to below. The usages of the different inns varied somewhat formerly in regard both to the term of probationary studentship enforced and to the procedure involved in a " call " to the bar by which the student is converted into the barrister. In the present day the entrance examination, the course of study and the examina- tions to be passed on the completion of the curriculum are identical and common to all the inns (see English Law). When once called to the bar, no hindrance beyond professional etiquette limits a barrister's freedom of action; so also members may on application to the benchers, and on payment of arrears of dues (if any), leave the society to which they belong, and thus cease altogether to be members of the bar likewise. A member of an Inn of Court retains his name on the lists of his inn for life by means of a small annual payment varying from £1 to £5. which at one or two of the inns is compounded for by a fixed sum taken at the call to the bar. The ceremony of the " call " varies in detail at the different inns. It takes place after dinner (before dinner at the Middle Temple, which is the only inn at which students are called in INNS OF COURT 585 their wigs and gowns), in the "parliament," "pension" or " council " chamber of the benchers. The benchers sit at a table round which are ranged the students to be called. Each candidate being provided with a glass of wine, the treasurer or senior bencher addresses them and the senior student briefly replies. " Call Parties " are also generally held by the new barristers; at the Middle Temple they are allowed in hall. During the reign of Edward III. the Inns of Court and Chancery, based on the collegiate principle, prospered under the supervision and protection of the crown. In 1381 Wat Tyler invaded the Temple, and in the succeeding century (1450) Jack Cade meditated pulling down the Inns of Court and killing the lawyers. It would appear, moreover, that the inmates of the inns were themselves at times disorderly and in conflict with the citizens. Fortescue (c. 1464) describing these societies thus speaks of them: " There belong to the law ten lesser inns, which are called the Inns of Chancery, in each of which there are one hundred students at least, and in some a far greater number, though not constantly residing. After the students have made some progress here they are admitted to the Inns of Court. Of these there are four, in the least frequented of which there are about two hundred students. The discipline is excellent, and the mode of study well adapted for proficiency." This system had probably existed for two centuries before Fortescue wrote, and continued to be enforced down to the time of Sir Thomas More (1498), of Chief Justice Dyer (1537) and of Sir Edward Coke (1571). By the' time of Sir Matthew Hale (1629) the custom for law students to be first entered to an Inn of Chancery before being admitted to an Inn of Court had become obsolete, and thenceforth the Inns of Chancery have been abandoned to the attorneys. Stow in his Survey succinctly points out the course of reading enforced at the end of the 16th century. He says that the Inns of Court were replenished partly by students coming from the Inns of Chancery, who went thither from the universities and sometimes immediately from grammar schools; and, having spent some time in studying the first elements of the law, and having performed the exercises called " bolts," " moots " and " putting of cases," they proceeded to be admitted to, and become students in, one of the Inns of Court. Here continuing for the space of seven years or thereabouts, they frequented readings and other learned exercises, whereby, growing ripe in the knowledge of the laws, they were, by the general consent either of the benchers or of the readers, called to the degree of barrister, and so enabled to practise in chambers and at the bar. This ample provision for legal study continued with more or less vigour down to nearly the commencement of the 1 8th century. A languor similar to that which affected the church and the universities then gradually supervened, until the fulfilment of the merest forms sufficed to confer the dignity of advocate and pleader. This was maintained until about 1845, when steps were taken for reviving and extending the ancient discipline and course of study, bringing them into harmony with modern ideas and requirements. The fees payable vary slightly at the different inns, but average about £150. This sum covers all expenses from admission to an inn to the call at the bar, but the addition of tutorial and other expenses may augment the cost of a barrister's legal education to £400 or £500. The period of study prior to call must not be less than twelve terms, equivalent to about three years. Solicitors, however, may be called without keeping any terms if they have been in practice for not fewer than five consecutive years. It has been seen that the studies pursued in ancient times were conducted by means of " readings," " moots " and " bolts." The readings were deemed of vital importance, and were delivered in the halls with much ceremony; they were frequently regarded as authorities and cited as such at Westminster in argument. Some statute or section of a statute was selected for analysis and explanation, and its relation to the common law pointed out. Many of these readings, dating back to Edward I., are extant, and well illustrate the importance of the subjects and the exhaustive and learned manner in which they were treated. The function o( " reader " involved the holder in very weighty expenses, chiefly by reason of the profuse hospitality dispensed — a constant and splendid table being kept during the three weeks and three days over which the readings extended, to which were invited the nobility, judges, bishops, the officers of state and sometimes the king himself. In 1688 the readers were paid £200 for their reading, but by that time the office had become a sinecure. In the present day the readership is purely honorary and without duties. The privilege formerly assumed by the reader of calling to the bar was taken away in 1664 by an order of the lord chancellor and the judges. Moots were exercises of the nature of formal arguments on points of law raised by the students and conducted under the supervision of a bencher and two barristers sitting as judges in the halls of the inns. Bolls were of an analogous character, though deemed inferior to moots. In the early history of the inns discrimination was exercised in regard to the social status of candidates for admission to them. Sir John Feme, a writer of the 16th century, referred to by Dugdale, states that none were admitted into the houses of court except they were gentlemen of blood. So also Pliny, writing in the 1 st century of the Christian era (Letters, ii. 14) , says that before his day young men even of the highest families of Rome were not admitted to practice except upon the introduction of some man of consular rank. But he goes on to add that all barriers were then broken down, everything being open to everybody — a remark applicable to the bar of England and elsewhere in the present day. It may here be noted that no dignity or title confers any rank at the bar. A privy councillor, a peer's son, a baronet, the speaker of the House of Commons or a knight — all rank at the bar merely according to their legal precedence. Formerly orders were frequently issued both by the benchers and by the crown on the subject of the dress, manners, morals and religious observances of students and members. Although some semblance of a collegiate discipline is still maintained, this is restricted to the dining in hall, where many ancient usages survive, and to the closing of the gates of the inns at night. Each inn maintains a chapel, with the accompaniment of preachers and other clergy, the services being those of the Church of England. The Inner and the Middle Temple have joint use of the Temple church. The office of preacher is usually filled by an ecclesiastic chosen by the benchers. The principal ecclesiastic of the Temple church is, however, constituted by letters patent by the crown without episcopal institution or induction, enjoying, nevertheless, no authority independently of the benchers. He bears the title of Master of the Temple. It has already been stated, on the authority of Fortescue, that the students of the Inns of Court learned to dance, sing and play instrumental music; and those accomplishments found expression in the " masques " and " revels " for which the societies formerly distinguished themselves, especially the Inner Temple and Gray's Inn. These entertainments were of great antiquity and much magnificence, involving very considerable expense. Evelyn (Diary) speaks of the revels at the Middle Temple as an old and riotous custom, having relation neither to virtue nor to policy. The last revel appears to have been held at the Inner Temple in 1734, to mark the occasion of the elevation of Lord Chancellor Talbot to the woolsack. The plays and masques performed were sometimes repeated elsewhere than in the hall of the inn, especially before the sovereign at court. A master of the revels was appointed, commonly desig- nated Lord of Misrule. There is abundant information as to the scope and nature of these entertainments: one of the festivals is minutely described by Gerard Leigh in his Accedence of Armorie" 161 2; and a tradition ascribes the first performance of Shake- speare's Twelfth Night to a revel held in the Middle Temple hall in February 1601. The hospitality of the inns now finds expres- sion mainly in the " Grand Day," held once in each of the four terms, when it is customary for the judges and other distinguished visitors to dine with the benchers (who sit apart from the barristers and students on a dais in some state), and " Readers' Feast," on both which occasions extra commons and wine are served to the members attending. But the old customs also found some renewal in the shape of balls, concerts, garden-parties 5 86 INNS OF COURT and other entertainments. In 1887 there was a revival (the first since the 17th century) of the Masque of Flowers at both the Inner Temple and Gray's Inn. The Royal Horticultural Society's annual exhibition of flowers and fruit is held in May in the Temple Gardens. Plays are also occasionally performed in the Temple, Robert Browning's Sordello being acted in 1902 by a company of amateurs, most of whom were either members of the bar or connected with the legal profession. The Inner and the Middle Temple, so far as their history can be traced, have always been separate societies. Fortescue, writing between 1461 and 1470, makes no allusion to a previous junction of the two inns. Dugdale (1671) speaks of the Temple as having been one society, and states that the students so increased in number that at length they divided, becoming the Inner and Middle Temple respectively. He does not, however, give any authority for this statement, or furnish the date of the division. The first trustworthy mention of the Temple as an inn of court is found in the Paston Letters, where, under date November 1440, the Inner Temple is spoken of as a college, as is also subsequently the Middle Temple. The Temple had been the seat in England of the Knights Templars, on whose suppression in 1312 it passed with other of their possessions to the crown, and after an interval of some years to the Knights Hospitallers of St John of Jerusalem, who in the reign of Edward III. demised the mansion and its surroundings to certain professors of the common law who came from Thavie's Inn. Notwithstanding the destruction of the muniments of the Temple by fire or by popular commotion, sufficient testimony is attainable to show that in the reigns of Edward III. and Richard II. the Temple had become the residence of the legal communities which have since maintained there a permanent footing. The two societies continued as tenants to the Knights Hospitallers of St John until the dissolution of the order in 1539; they then became the lessees of the crown, and so remained until 1609, when James I. made a grant by letters patent of the premises in perpetuity to the benchers of the respective societies on a yearly payment by each of £10, a payment bought up in the reign of Charles II. In this grant the two inns are described as " the Inner and the Middle Temple or New Temple," and as " being two out of those four colleges the most famous of all Europe " for the study of the law. Excepting the church, nothing remains of the edifices belonging to the Knights Templars, the present buildings having been almost wholly erected since the reign of Queen Elizabeth or since the Great Fire, in which the major part of the Inner Temple perished. The church has been in the joint occupation of the Inner and Middle Temple from time immemorial — the former taking the southern and the latter the northern half. The round portion of the church was consecrated in 1 185, the nave or choir in 1240. It is the largest and most complete of the four remaining round churches in England, and is built on the plan of the church of the Holy Sepulchre at Jerusalem. Narrowly escaping the ravages of the fire of 1666, this beautiful building is one of the most perfect specimens of early Gothic architecture in England. In former times the lawyers awaited their clients for consultation in the Round Church, as similarly the serjeants-at-Law were accustomed to resort to St Paul's Cathedral, where each Serjeant had a pillar assigned him. The Inner Temple, comprehending a hall, parliament chamber, library and other buildings, occupies the site of the ancient mansion of the Knights Templars, built about the year 1240, and has from time to time been more or less rebuilt and extended, the present handsome range of buildings, including a new dining hall, being completed in 1870. The library owes its existence to William Petyt, keeper of the Tower Records in the time of Queen Anne, who was also a benefactor to the library of the Middle Temple. The greatest addition by gift was made by the Baron F. Maseres in 1825. The number of volumes now in the library is 37,000. Of the Inns of Chancery belonging to the Inner Temple Clifford's Inn was anciently the town residence of the Barons Clifford, and was demised in 1345 to a body of students of the law. It was the most important of the Inns of Chancery, and numbered among its members Coke and Selden. At its dinners a table was specially set aside for the " Kentish Mess," though it is not clear what connexion there was between the Inn and the county of Kent. It was governed by a Crincipal and twelve rulers. Clement's Inn was an Inn of Chancery efore the reign of Edward IV., taking its name from the parish church of St Clement Danes, to which it had formerly belonged. Clement's Inn was the inn of Shakespeare's Master Shallow, and was the Shepherd's Inn of Thackeray's Pendennis. The buildings of Clifford's Inn survive (1910), but of Clement's Inn there are left but a few fragments. The Middle Temple possesses in its hall one of the most stately of existing Elizabethan buildings. Commenced in 1562, under the auspices of Edmund Plowden, then treasurer, it was not com- pleted until 1572, the richly carved screen at the east end in the style of the Renaissance being put up in 1575. The belief that the screen was constructed of timber taken from ships of the Spanish Armada (1588) is baseless. The hall, which has been preserved unaltered, has been the scene of numerous historic incidents, notably the enter- tainments given within its walls to regal and other personages from Queen Elizabeth downwards. The library, which contains about 28,000 volumes, dates from 1641, when Robert Ashley, a member of the society, bequeathed his collection of books in ail classes of literature to the inn, together with a large sum of money; other benefactors were Ashmole (the antiquary), William Petyt (a bene- factor of the Inner Temple) and Lord Stowell. From 1711 to 1826 the library was greatly neglected ; and many of the most scarce and valu- able books were lost. The present handsome library building, which stands apart from the hall, was completed in 1861, the prince of Wales (afterwards Edward VII.) attending the inauguration cere- mony on October 31st of that year, and becoming a member and bencher of the society on the occasion. He afterwards held the office of treasurer (1882). The MSS. in the collection are few and of no special value. In civil, canon and international law, as also in divinity and ecclesiastical history, the library is very rich; it contains also some curious works on witchcraft and demonology. There was but one Inn of Chancery connected with the Middle Temple, that of New Inn, which, according to Dugdale, was formed by a society of students previously settled at St George's Inn, situated near St Sepulchre s Church without Newgate; but the date of this transfer is not known. The buildings have now been pulled down. Lincoln' slnn stands on the site partly of an episcopal palace erected in the time of Henry III. by Ralph Nevill, bishop of Chichester and chancellor of England, and partly of a religious house, called Black Friars House, in Holborn. In the reign of Edward II., Henry Lacy, earl of Lincoln, possessed the place, which from him acquired the name of Lincoln's Inn, probably becoming an Inn of Court soon after his death (in 13 10), though of its existence as a place of legal study there is little authentic record until the time of Henry VI. (1424), to which date the existing muniments reach back. The fee simple of the inn would appear to have remained vested in the see of Chichester; and it was not until 1580 that the society which for centuries had occupied the inn as tenants acquired the absolute ownership of it. The old hall, built about 1506, still remains, but has given place to a modern structure designed by Philip Hardwick, R.A., which, along with the buildings containing the library, was completed in 1845, Queen Victoria attending the inauguration ceremony (October 13). The chapel, built after the designs of Inigo Jones, was consecrated in 1623. The library — as a collection of law books the most complete in the country — owes its foundation to a bequest of John Nethersale, a member of the society, in 1497, and is the oldest of the existing libraries in London. Various entries in the records of the inn relate to the library, and notably in 1608, when an effort was made to extend the collection, and the first appointment of a master of the library (an office now held in annual rotation by each bencher) was made. The library has been much enriched by donations and by the acquisition by purchase of collec- tion* of books on special subjects. It includes also an extensive ana valuable series of MSS., the whole comprehending 50,000 volumes. The prince of Wales (George V.), a bencher of the society, filled the office of treasurer in 1904. The Inns of Chancery affiliated to Lincoln's Inn were Thavie's Inn and Furnival's Inn. Thavie's Inn was a residence of students of the law in the time of Edward III., and is mentioned by Fortescue as having been one of the lesser houses of Lincoln's Inn for some centuries. It thus continued down to 1769, when the inn was sold by the benchers, and thenceforth it ceased to have any character as a place of legal education. Furnival's Inn became the resort of students about the year 1406, and was pur- chased by the society of Lincoln's Inn in 1547. It was governed by a principal and twelve antients. In 1817 the Inn was rebuilt, but from that date it ceased to exist as a legal community and is now demolished. The exact date of Gray's Inn becoming the residence of lawyers is not known, though it was so occupied before the year 1370. The inn stands upon the site of the manor of Portpoole, belonging in ancient times to the dean and chapter of St Paul's, but subsequently the property of the family of Grey de Wilton and eventually of the crown, from which a grant of the manor or inn was obtained, many years since discharged from any rent or payment. The hall of the inn is of handsome design, similar to the Middle Temple hall in its general character and arrangements, and was completed about the year 1560. The chapel, of much earlier date than the hall, has, notwithstanding its antiquity, little to recommend it to notice, being small and insignificant, and lacking architectural features of any kind. The library, including about 13,000 volumes, contains a small but important collection of MSS. and missals, and also some valuable works on divinity. Little is known of the origin or early history of the library, though mention is incidentally made of it in the society's records in the 16th and 17th centuries. The gardens, laid out about J597) it is believed under the auspices of the lord chancellor Bacon, at that time treasurer of the society, continue to this day as then planned, though with some curtailment owing to the erection of additional buildings. Among many curious customs maintained in this inn is that of drinking a toast on grand days " to the glorious, pious and immortal memory of Queen Elizabeth." Of the special circumstances originating this display of loyalty there is no record. The Inns of Chancery connected with Gray's Inn are Staple and Barnard's Inns. Staple Inn was an Inn of Chancery in the reign of Henry V., and is probably of yet earlier date. Readings and moots were observed here with regularity. Sir Simpnds d'Ewes mentions attending a moot in February 1624. The /nn, with its INNUENDO— INQUISITION 587 picturesque Elizabethan front, faces Holborn. It was sold by the antients in 1884 for £68,000. It is in a very good state of preservation, and it is the intention of the purchasers, the Prudential Assurance Company, to preserve it as a memorial of vanishing London. Bar- nard's Inn, anciently designated Mackworth Inn, was an Inn of Chancery in the reign of Henry VI. It was bequeathed by him to the dean and chapter of Lincoln. It is now the property of the Mercer's Company and is used as a school. The King's Inns, Dublin, the legal school in Ireland, corresponds closely to the English Inns of Court, and is in many respects in unison with them in its regulations with regard to the admission of students into the society, and to the degree of barrister-at-law, as also in the scope of the examinations enforced. Formerly it was necessary to keep a number of terms at one of the Inns in London — the stipulation dating as far back as 1542 (33 Henry VIII. c. 3). Down to 1866 the course of education pursued at the King's Inns differed from the English Inns of Court in that candidates for admission to the legal profession as attorneys and solicitors carried on their studies with those studying for the higher grade of the bar in the same building under a professor specially appointed for this purpose, — herein following the usage anciently prevailing in the Inns of Chancery in London. This arrangement was put an end to by the Attorneys and Solicitors Act (Ireland) 1866. The origin of the King's Inns may be traced to the reign of Edward I., when a legal society designated Collett's Inn was established without the walls of the city; it was destroyed by an insurrectionary band. In the reign of Edward III. Sir Robert Preston, chief baron of the exchequer, gave up his resi- dence within the city to the legal body, which then took the name of Preston's Inn. In 1542 the land and buildings known as Preston's Inn were restored to the family of the original donor, and in the same year Henry VIII. granted the monastery of Friars Preachers for the use of the professors of the law in Ireland. The legal body removed to the new site, and thenceforward were known by the name of the King's Inns. Possession of this property having been resumed by the government in 1 742 , and the present Four Courts erected thereon, a plot of ground at the top of Henrietta Street was purchased by the society, and the existing hall built in'the year 1800. The library, numbering over 50,000 volumes, with a few MSS., is housed in build- ings specially provided in the year 1 831, and is open, not only to the members of the society, but also to strangers. The collection comprises all kinds of literature. It is based principally upon a purchase made in 1787 of the large and valuable library of Mr Justice Robinson, and is maintained chiefly by an annual payment made from the Consolidated Fund to the society in lieu of the right to receive copyright works which was conferred by an Act of 1801, but abrogated in 1836. In discipline and professional etiquette the members of the bar in Ireland differ little from their English brethren. The same style of costume is enforced, the same gradations of rank — attorney-general, solicitor-general, king's counsel and ordinary barristers — being found. There are also serjeants-at-law limited, however, to three in number, and designated 1st, 2nd and 3rd Serjeant. The King's Inns do not provide chambers for business purposes; there is consequently no aggregation of counsel in certain localities, as is the case in London in the Inns of Court and their immediate vicinity. The corporation known as the Faculty of Advocates in Edinburgh corresponds with the Inns of Court in London and the King's Inns in Dublin (see Advocates, Faculty of). Authorities. — Fortescue, De laudibus legum Angliae, by A. Amos (1825); Dugdale, Origines juridicales (2nd ed., 1671); History and Antiquities of the Four Inns of Court, &c. (1780, 2nd ed.) ; Foss, Judges of F.ngland (1848-1864, 9 vols.); Herbert, Antiquities of the Inns of Court (1804); Pearce, History of the Inns of Court (1848); Report of the Commissioners appointed to inquire into the Inns of Court and Chancery, 1855; Ball, Student's Guide to the Bar (1878); Stow, Survey of London and Westminster, by Strype (1754- 1755) ; Nichols, Progresses of Elizabeth and James I. ; Lane, Student's Guide through Lincoln's Inn (2nd ed., 1805) ; Spilsbury, Lincoln's Inn, with an Account of the Library (2nd ed., 1873); Douthwaite, Notes illustrative of the History and Antiquities of Gray's Inn (1876), and Gray's Inn, its History and Associations (1886); Paston Letters (1872); Law Magazine, 1859-1860; Quarterly Review, October, 187 1 ; Cowcl, Law Dictionary (1727); Duhigg, History of the King's Inns in Ireland (1806); Mackay, Practice of the Court of Session (1879); Bellot, The Inner and Middle Temple (1902); Inderwick, The King's Peace (1895); Fletcher, The Pension Book of Gray's Inn (1901); Loftie, The Inns of Court (1895); Hope, Chronicles of an Old Inn (Gray's Inn) (1887); A Calendar of the Inner Temple Records fed. F. A. Inderwick, 3 vols.). (J. C. W.) INNUENDO (Latin for " by nodding," from innuere, to indicate by nodding), an insinuation, suggestion, in prima facie innocent words, of something defamatory or disparaging of a person. The word appears in legal documents in Medieval Latin, to explain, in parenthesis, that to which a preceding word refers; thus, " he, innuendo, the plaintiff, is a thief." The word is still found in pleadings in actions for libel and slander. The innuendo, in the plaintiffs statement of claim, is an averment that words written or spoken by the defendant, though prima facie not actionable, have, in fact, a defamatory meaning, which is specifically set out (see Libel and Slander). INOUYE, KAORU, Marquess (1835- ), Japanese states- man, was born in 1835, a samurai of the Choshu fief. He was a bosom friend of his fellow-clansman Prince Ito, and the two youths visited England in 1863, serving as common sailors during the voyage. At that time all travel abroad was forbidden on pain of death, but the veto did not prove deterrent in the face of a rapidly growing conviction that, as a matter of self- protection, Japan must assimilate the essentials of Western civilization. Shortly after the departure of Inouye and Ito, the Choshu fief, having fired upon foreign vessels passing the strait of Shimonoseki, was menaced by war with the Yedo government or with the insulted powers, and Inouye and Ito, on receipt of this news, hastened home hoping to avert the catastrophe. They repaired to the British legation in Yedo and begged that the allied squadron, then about to sail for Shimonoseki to call Choshu to account, should be delayed that they might have an opportunity of advising the fief to make timely submission. Not only was this request complied with, but a British frigate was detailed to carry the two men to Shimonoseki, and, pending her departure, the British legation assisted them to lie perdu. Their mission proved futile, however, and Inouye was subse- quently waylaid by a party of conservative samurai, who left him covered with wounds. This experience did not modify his liberal views, and, by the time of the Restoration in 1867, he had earned a high reputation as a leader of progress and an able statesman. Finance and foreign affairs were supposed to be the spheres specially suited to his genius, but his name is not associated with any signal practical success in either, though his counsels were always highly valued by his sovereign and his country alike. As minister of foreign affairs he conducted the long and abortive negotiations for treaty revision between 1883 and 1886, and in 1885 he was raised to the peerage with the title of count, being one of the first group of Meiji statesmen whose services were thus rewarded. Prior to his permanent retirement from office in 1898, he held the portfolios of foreign affairs, finance, home affairs, and agriculture and commerce, and throughout the war with Russia he attended all important state councils, by order of the emperor, being also specially designated adviser to the minister of finance. In 1907 he was raised to the rank of marquess. His name will go down in his country's history as one of the five Meiji statesmen, namely, Princes Ito and Yamagata, Marquesses Inouye and Matsukata and Count Okuma. INOWRAZLAW, the Polish form of the German Jung-Breslau, by which the place was formerly known, a town in the Prussian province of Posen, situated on an eminence in the most ferule part of the province, 21 m. S.W. of Thorn. Pop. (1900) 26,141. Iron-founding, the manufacture of machinery and chemicals, and an active trade in cattle and country produce are carried on. In the vicinity are important salt works and a sulphur mine, and since 1876 a brine bath has been within the town. Inowrazlaw is mentioned as early as 1185, and in 1772 it passed to Prussia. INQUEST (O. Fr. enqueste, modern enquete, from Lat.inquisitum, inquirere, to inquire), an inquiry, particularly a formal legal inquiry into facts. The word is now chiefly confined to the inquiry held by a coroner and jury into the causes of certain deaths, in matters of treasure trove, and, in the city of London, in cases of fires (see Coroner). Formerly the term was applie'd to many formal and official inquiries for fixing prices, &c. INQUISITION, THE (Lat. inquisitio, an inquiry), the name given to the atclesiastical jurisdiction dealing both in the middle ages and in modern times with the detection and punl . punishment of heretics and all persons guilty of any mea t „/ offence against Catholic orthodoxy. It is incorrect heresy to say that the Inquisition made its appearance ia ihe in the isth century complete in all its principles and . * < " n f t^ til i* c t u . Empire. organs. It was the result 01, or rather one step in, a process of evolution, the beginnings of which are to be traced back to the origins of Christianity. St Paul (1 Tim 5 88 INQUISITION i. 20) " delivered unto Satan " Hymenaeus and Alexander, " that they might learn not to blaspheme." The penalty of death by stoning inflicted by the book of Deuteronomy upon those who deserted the true faith (Deut. xiii. 6-9, xvii. 1-6) is thus reduced to a purely spiritual excommunication. During the first three centuries of the Church there is no trace of any persecution, and the earlier Fathers, especially Origen and Lactantius, reject the idea of it. Constantine, by the edict of Milan (313), inaugurated an era of official tolerance, but from the time of Yalentinian I. and Theodosius I. onwards, laws against heretics began to appear, and increased with astonishing regularity and rapidity. We can count sixty-eight distributed over fifty-two years; heretics are subjected to exile or confiscation, disqualified from inheriting property, and even, in the case of a few groups of Manichaeans and Donatists, condemned to death; but it should be noticed that these penalties apply only to the outward manifestations of heresy, and not, as in the middle ages, to crimes of conscience. Within the Church, of the S St Optatus alone {De schismate Donalistarum, lib. iii. Fathers. cap. iii.) approved of this violent repression of the Donatist heresy; St Augustine only admitted a lemperata sever ilas, such as scourging, fines or exile, and at the end of the 4th century the condemnation of the Spanish heretic Priscillian, who was put to death in 385 by order of the emperor Maximus, gave rise to a keen controversy. St Martin of Tours, St Ambrose and St Leo vigorously attacked the Spanish bishops who had obtained the condemnation of Priscillian. St John Chrysostom considered that a heretic should be deprived of the liberty of speech and that assemblies organized by heretics should be dissolved, but declared that " to put a heretic to death would be to introduce upon earth an inexpiable crime." From in the the 6th to the 9th century the heterodox, with the early exception of the Manichaean sects in certain places, Middle W ere hardly subjected to persecution. They were, ges ' moreover, rare and generally isolated, for groups of sectaries only began to appear to any extent at the time of the earliest appearances of Catharism. However, at the end of the 10th century, the disciples of Vilgard, a heretic of Ravenna, were destroyed in Italy and Sardinia, according to Glaber, jcrro et incendio, probably by assimilation to the Manichaeans. Perhaps this was the precedent for the punish- ment of the thirteen Cathari who were burnt at Orleans in 1022 by order of King Robert, a sentence which has been commonly quoted as the first action of the " secular arm " (or lay power) against heresy in the West during the middle ages. However that may be. after 1022 there were numerous cases of the execu- tion of heretics, either by burning or strangling, in France, Italy, the Empire and England. Up till about 1200 it is not quite easy to determine what part w T as taken by the Church and its bishops and doctors in this series of executions. At Orleans the people, supported by the Crown, were responsible for the death of the heretics; the historians give only the faintest indica- tions of any direct intervention of the clergy, except perhaps for the examination of doctrine. At Goslar (1051-1052) the pro- ceedings were the same. At Asti (1034) the bishop's name appears side by side with those of the other lords who attacked the Cathari, but it seems clear that it was not he who hadthechief voice in their execution; at Milan, it was again the civil magis- trates, and this time against the wish of the archbishop — who gave the heretics the choice between the adoration of the cross and death. At Soissons (1114) the mob, distrusting the weakness of the clergy, took advantage of their bishop's absence to burn heretics at the stake. It was also the mob who, infuriated at seeing him destroy and burn crosses, burnt the heiresiarch Peter of Bruis (c. 1 140). At Liege (1144) the bishop saved from the flames certain persons whom the faithful were attempting to burn. At Cologne (1163) the archbishop was less successful, and the mob put the heretics to death Without even a trial. The condemnation of Arnold of Brescia was entirely political, though he was denounced as a heretic to the secular arm by Bernard of Clairvaux, and his execution was the act of I he prefect of Rome (1155). At Yczckiy, on the contrary (1167). the heretics were burnt after ecclesiastical judgment had been pronounced by the abbot and several bishops. From n 83 to 1206 Hugh, bishop of Auxerre, took upon himself the discre- tionary power of exiling, dispossessing or burning heretics, while about the same time William of the White Hands, arch- bishop of Reims, in concert with Philip, count of Flanders, stamped out heresy from his diocese by fire. There was a similar unanimity between the lay and ecclesiastical authorities in the famous condemnation of the disciples of Amalric of Bena, who were burnt at Paris in 1209 by order of Philip Augustus after an ecclesiastical inquiry and judgment. The theory in these matters was at first as uncertain as the practice; in the nth century one bishop only, Theodwin of cnntll t- Liege (d. 1075), affirms the necessity for the punishment ingvlews of heretics by the secular arm (1050). His predecessor, as to the Wazo, bishop of Liege from 1041 to 1044, had expressly puoish- condemned any capital punishment and advised the meat IlCFCSV* bishop of Chalons to resort to peaceful conversion. In the 1 2th century Peter the Cantor 1 protested against the death penalty, admitting at the most imprisonment. It was imprisonment again, or exile, but not death, which the German abbot Gerhoh of Reichersperg (1003-1169) demanded in the case of Arnold of Brescia, and in dealing with the heretics of Cologne, St Bernard, who cannot be accused of leniency where heterodoxy was concerned, recommended pacific refutation, followed by excommunication or prison, but never the death penalty (see Bernard, St, of Clairvaux) . In the councils, too, it is clear that the appeal to the secular arm was equally guarded: at Reims (1049) excommunication church alone is decreed against heretics; and when, as at Councils. Toulouse (1119) and the Lateran council (1139), it is laid down that heretics, in addition to excommunication, should be dealt with per poleslates extents, or when, as at the council. of Reims (1148), the secular princes are forbidden to support or harbour heretics, there is never any suggestion of capital punishment. But it must be noticed that from the opening years of the 12th century date the beginnings influence of a decided evolution in the canon law, continuing up of the to the time of Innocent III., which substituted for Caaon arbitrary decisions according to circumstances an Law. organized and particularized legislation, in which judgment was given secundum canonicas et legitimas sanctiones. Anselm of Lucca and the Panormia attributed to Ivo of Chartres reproduced word for word under the rubric De edicto imperatorum in dampna- lionem hoereticorum, law 5 of the title De hereticis of Justinian's code, which pronounces the sentence of death against the Manichaeans; and we should remember that the Cathari, and in general all heretics in the West in the nth and 12th centuries were considered by contemporary theologians as Manichaeans. Gratian in the Dccretum proclaims the views of St Augustine (exile and fines). Certain of his commentators (2 pars Caus. xxiii.), and notably Rufinus Johannes Teutonicus, and the anonymous glossator (in Uguccio's Great Summa of The the Decretum) declare that impenitent heretics may, Council or even should, be punished by death. As early as of r °«"*, 1163, the council of Tours suggested to the ecclesiastical authorities definite penalties to be inflicted on heretics, namely, imprisonment and loss of all their property. Pope Alexander III., who had attended the council of Tours of 1 163, re- Definition newed at the Lateran council (1179) the decisions which of the had already been made with regard to the heterodox procedure in the south of France, and at Verona in ir84 uader Pope Lucius III., in concert with the emperor aadtne Frederick Barbarossa, took still more severe measures: Emperor obstinate heretics were to be excommunicated, and Frederick then handed over to the secular arm, which would '• inflict a suitable penalty. The emperor, on his side, laid them under the imperial ban (exile, confiscation, demolition of their houses, infamia, loss of civil rights, disqualification from 1 Pierre de Beauvoisis (?), choir-master (grand-chantre) of the university of Paris (1184), bishop of Tournai (1191), of Paris (1196); 1 died a;, a Cistercian in 1107. He was beatified. INQUISITION 589 Innocent III. tar In- quisition. public offices, &c). The usage, then, was already quite clear; but the death penalty had not as yet been demanded leaa1tr! h or inflated. Possibly it was Count Raymond V. of Toulouse, in whose territories heretics abounded, who in 1 194 enacted a law threatening them with the penalty of death; but the authenticity of this act has been questioned. It was more probably Peter II. of Aragon who was the first to decree, in 1107, the punishment of death by burning against the heretics who should not have left his kingdom within a given time. But it was Innocent III. who gave the most powerful impetus to the anti-heretical movement in the secular world by his frequent exhortations (beginning in 1198) to the secular princes (letters of March 25th, 1199, and September 22nd, 1207). As a jurist he henceforward assimilated the crime of high treason against God to that of high treason against temporal rulers, and admitted all the terrible consequences of this assimilation. It is therefore incorrect to believe that the Inquisition arose out of, and at the time of, the crusade against the Albigenses. These executions en tnasse certainly created a definitive ton*"' precedent for violent repression, but there was still Crusade. no regular organization: the council of Toulouse, Soregu- held in November 1229 by the Roman legate after the treaty of peace, attempted to organize one, and constituted itself the tribunal. But the procedure was still uncertain; in the north, from 1200 to 1222, at Paris (execu- tion of the disciples of Amalric of Bena), at Strassburg, Cambrai, Troyes and Besangon executions took place, after trials in which the bishops were the judges, the exercise of the secular power being based on vague phrases in the decrees of Louis VIII. (that heretics be punished animadversione debita), or in those of Louis IX., ordering his baillis or barons to do to them quod debebunt. The emperor Frederick II. denned his jurisprudence more clearly: from 1220 to 1239, supported by Pope Emperor Honorius III., and above all by Gregory IX., he Frederick established against the heretics of the Empire in "• general a legislation in which the penalties of death, banishment and confiscation of property were formulated so clearly as to be henceforth incontestable. Gregory IX. felt his influence, and also that of the Dominican Guala, Gregory ... IX. creates bishop of Brescia, who had subjected his episcopal the moo- town to the full rigour of the imperial laws. The pope "I".'"' no longer hesitated as to the principle or the degree of repression; but introduced new methods of inquiry and judgment: he created out of the material furnished him by the mendicant orders, and especially the Dominicans, who were more disciplined than the rest and better theologians, the monastic inquisition, which was more elastic, more constant in its activities and more numerous than the inquisition by legate, and better disciplined than the episcopal inquisition. In November 1232 the Dominican Alberic went round Lombardy with the title of Inquisitor haerelicae pravitatis. In 1231 a similar commission was given to the Dominicans of Friesach and to the terrible Conrad of Marburg, whose zeal in Germany even exceeded the pope's wishes. In 1233 Gregory IX. addressed a letter to the bishops in the south of France, in which he announced his intention of employing the preaching friars in future for the discovery and repression of heresy. The inquisition was now regularly instituted, but its juris- prudence was elaborated by successive additions or limitations, by the force of custom and the detailed prescriptions Beginnings ^Aded by the papal constitutions. The pope's com- auisttion rnissioners " in the matter of heresy " at first travelled from place to place. On arriving in a district they addressed its inhabitants, called upon them to confess, if they were heretics, or to denounce those whom they knew to be heretics: a " time of grace " was opened, during which those who freely confessed were dispensed from all penalties, or only given a secret and very light penance; while those whose heresy had been openly manifested were exempted from the penalties of death and perpetual imprisonment. But this time The Domi- nicans. could not exceed one month. After that began the inquisition. As soon as their mission was at an end, and heresy was considered to be stamped out, the inquisitors left the country. Later, inquisitorial districts were formed. The seat of the Inquisition in each district was the monastery of toi" 1 ^ 1 ' the order (Dominican or Franciscan) to which the districts. inquisitors for that part belonged. There was never any special court or prison: the munis (prison) was lent to the Inquisition by the ecclesiastical or secular authorities. The maintenance of the prisoners and the duty of providing the prison fell in principle upon the bishops (council of Toulouse, 1229), but they tried to evade it. The kings of France, and in particular Louis VIII., granted subsidies to the _, i„ a ui- inquisitors. For each district the inquisitors were sitorsand chosen by the provincials of their order, approved their or rejected by the pope, and removable by him only. «"*'"" Their discretionary powers were absolute. They conducted their interrogations before two persons (laymen or ecclesiastics) and only pronounced their sentence after consulta- tion with leading men in the district {communicato bonorum virorum consilio). This was the only protection for the accused. It was in vain that the civil lawyers tried to proye that the secular authorities had a right to see the documents bearing on the case; the Inquisition always succeeded in setting aside these claims. The share taken in the proceedings by the bishops, the accused or their representatives, though admitted in principle, was as a rule merely illusory. The Inquisition had in addition to these boni viri certain other lay assistant officials, its sworn notaries, messengers and familiars, all of whom were closely bound to it. Bernard Guy (Bernardus Guidonis), 1 one of the earliest and most complete exponents of the theory of the Inquisition, admits distinctly that in its procedure multa sunt Ppocetfure specialia. The procedure was secret and in the of the highest degree arbitrary, proceeding sine strcpilu et Inqulsi- figiira judkii, its object being to ascertain not so t!oa ' much particular offences as tendencies: the murderers of the inquisitor Peter Martyr 2 were tried, not as assassins, but as guilty of heresy and adversaries of the Inquisition; and on the other hand, external acts of piety and verbal professions of faith were held of no value. Moreover the Inquisition was not bound by the ordinary rules of procedure in its inquiries: the accused was surprised by a sudden summons, and as a rule imprisoned on suspicion. All the accused were presumed to be guilty, the judge being at the same time the accuser. Absence was naturally considered as contumacy, and only increased the presumption of guilt by seeming to admit it. The accused had the right to demand a written account of the offences attributed to him (capitula accusationis) , but the names of the witnesses were withheld from him (Innocent IV.; bulls Cum negocium and Licet sicut accepimus) , he did not know who had denounced him, nor what weight was attached by the judges to the denunciations made against him. The utmost that was allowed him was the unsatisfactory privilege of the recusationes divinatrices, i.e. at his first examination he was asked for the names of any enemies of whom he knew, and the causes of their enmity. Heretics or persons deprived of civil rights (infames) were admitted as witnesses in cases of heresy. Women, children or slaves could be witnesses for the prosecution, but not for the defence, and cases are even to be found in which the witnesses were only ten years of age. Langhino Ugolini states that a witness who should retract his hostile evidence should be punished for false witness; but that his evidence should be retained, and have its full effect on the sentence. No witness might refuse to give evidence, under pain of being considered guilty of heresy. The prosecution went on in the utmost secrecy. The accused swore that he would tell the whole truth, and was bound to denounce all those 1 He was born c. 1261, was a Dominican at Limoges in 1279, succes- sively prior of Albi (1294), Carcassonne (1297), Castres (1301) and Limoges (1305), inquisitor at Toulouse (1307), bishop of Tuy (1323) and of Lodeve (1325). He died in 1 33 1. 2 Peter, a Dominican, born at Verona, was murdered near Milan in 1252 and canonized in 1253. 59° INQUISITION Use of torture. who were partners of his heresy, or whom he knew or suspected to be heretics. If he confessed, and denounced his accomplices, relatives or friends, he was " reconciled " with the Church, and had to suffer only the humiliating penalties prescribed by the canon law. If further examination proved necessary, it was continued by various methods. Bernardus Guidonis enumerates many ways of obtaining confessions, sometimes by means of moral subterfuges, but sometimes also by a process of weakening the physical strength. And as a last expedient torture was resorted to. The Church was originally opposed to torture, and the canon law did not admit confessions extorted by that means; but by the bull Ad extir- panda (1252) Innocent IV. approved its use for the discovery of heresy, and Urban IV. confirmed this usage, which had its origin in secular legislation (cf. the Veronese Code of 1228, and Sicilian Constitution of Frederick II. in 1231). In 1312 excessive cruelty had to be suppressed by the council of Vienna. Canonic- ally the torture could only be applied once, but it might be " continued." The next step was the torture of witnesses, a practice which was left to the discretion of the inquisitors. Moreover, all confessions or depositions extorted in the torture- cha-mber had subsequently to be " freely " confirmed. The confession was always considered as voluntary. The procedure was of course not litigious; any lawyer defending the accused would have been held guilty of heresy. The inquiry might last a long time, for it was interrupted or resumed according to the discretion of the judges, who disposed matters so as to obtain as many confessions or denunciations as possible. After the different phases of the examination, the accused were divided into two categories: (1) those who had confessed and abjured, (2) those who had not confessed and were consequently convicted of heresy. There was a third class, by no means the least numerous, namely, those who having previously confessed and abjured had relapsed into error. Next came the moment of the sentence: " there was never any case of an acquittal pure and simple " (H. C. Lea). The formula for full and complete acquittal given by Bernardus Guidonis in his Practica, should, he says, never or very rarely be employed. The sentences were solemnly pronounced on a Sunday, in a church or public place, in the presence of the inquisitors, their auxiliaries, the meats.' bishops, the secular magistrates and the people. This was the sermo generalis (see Auto da rf). The accused who had confessed were reconciled, and the penalties were then pronounced; these were, in order of severity, penances, fasting, prayers, pilgrimages (Palestine, St James of Compostella, Canterbury, &c), public scourging, the compulsory wearing on the breast or back of crosses of yellow felt sewn on to the clothes or sometimes of tongues of red, letters, &c. These were the poenaeconfusibiles (humiliating). The inquisitors eventually acquired the right of inflicting fines at discretion. In 1244 and 1 25 1 Innocent IV. reproved them for their exactions. All these minor penalties could be commuted for payments in money in the same way as absolution from the crusader's vow, and the council of Vienna tried to put an end to these extortions. Beyond these minor penalties came the severer ones of imprison- ment for a period of time, perpetual imprisonment and imprison- ment of various degrees of severity (murus largus, murus strictus vel strictissimus) . The murus strictus consisted in the deepest dungeon, with single or double fetters, and " the bread and water of affliction "; but the severity of the prison regime varied very much. The murus largus, especially for a rich prisoner, amounted to a fairly mild imprisonment, but the mortality among those confined in the murus strictus became so high that Clement V. ordered an inquiry to be made into the prison regime in Langue- doc, in spite of Bernard Guy's protest against the investiga- tion as likely to diminish the prestige of the inquisitors. After the sentences had been pronounced, the obstinate heretics and renegades were for the last time called upon to submit and to confess and abjure. If they consented, they were received as penitents, and condemned on the spot to perpetual imprisonment; if they did not consent, they were handed over to the secular arm. When the heretic was handed over to the secular arm, the agents of the secular power were recommended to punish him debita animadversione, and the form of recommending him to mercy was gone through. But, as M. Vacandard „„ says, "If the secular judges had thought fit to take lag over this formula literally, they would soon have been to the brought back to a recognition of the true state of secular affairs by excommunication." In effect, handing over to the secular arm was equivalent to a sentence of death, and of death by fire. The Dominican Jacob Sprenger, provincial of his order in Germany (1494) and inquisitor, does not hesitate to speak of the victims quas incincrari jecimus (" whom we [the inquisitors] caused to be burnt to ashes "). But we must accept the conclusions of H.C. Lea and Vacandard that compara- tively few people suffered at the stake in the medieval Inquisition. Between 1308 and 1323, Bernard Guy, who cannot be accused of inactivity, only handed over to the secular arm 42 persons, out of 930 who were convicted of heresy. From the point of view of jurisprudence of the Inquisition, the confiscation of the condemned man's property by the ecclesiastical and secular powers is only the accompani- pj.„i s fc_ ment to the more severe penalties of perpetual im- mentby prisonment or death; but from the point of view of confisca- te economic history the importance of the confisca- tloD ' of tion is supreme. The practice originated in the Roman law, and all secular princes had already, in their own interest, recognized it as lawful (Frederick Barbarossa, Decree of Verona; Louis VIII., ordinances of 1226, 1229; Louis IX., ordinance of 1234; Raymond VII. of Toulouse, &c). In the kingdom of France there was a special official, the procureur des encours (confiscation in the matter of heresy), whose duty it was to collect the personal property of the heretics, and to incorporate their landed estates in the royal domain; in Languedoc crying abuses arose, especially under the reign of Alphonse of Poitiers. Soon the papacy managed to gain a share ^ "*® of the spoils, even outside the states of the Church, system. as is shown by the bulls ad extirpanda of Innocent IV. and Alexander IV., and henceforward the inquisitors had, in varying proportions, a direct interest in these spoliations. In Spain this division only applied to the property of the clergy and vassals of the Church, but in France, Italy and Germany, the property of all those convicted of heresy was shared between the lay and ecclesiastical authorities. Venice alone decided that all the receipts of the Holy Office should be handed over in full to the state. Clement V., in his attempted reform and regularization of inquisitorial procedure, endeavoured to reduce the confiscations to a fairly reasonable minimum, and in 1337- 1338 a series of papal inquiries was held into this financial aspect of the matter. The Assize of Clarendon, the Constitutions of Frederick II. (1232) and of Count Raymond of Toulouse (1234) had also come to a joint decision with the councils on this question. King Charles V. of France prevailed upon the papacy to abolish this regulation (1378). Confiscation was, indeed, most profitable to the secular princes, and there is no doubt that the hope of considerable gain was what induced many princes to uphold the inquisitorial administration, especially in the days of the decay of faith. The an a po iui- resistance of the south of France to the Capetian calim- monarchs was to a large extent broken owing to the portance decimation of the bourgeoisie by the Inquisition s ystem , and their impoverishment by the extortions of the encours. The same was the case in certain of the Italian re- publics; while in districts such as the north of France, wHe*e heretics were both poor and few and far between, the Inquisition did not easily take root, nor did it prove very profitable. These confiscations, the importance of which in the political and economic history of the middle ages was first shown fully by H. C. Lea, were a constant source of uncertainty in transactions of all kinds; there was, for instance, always a risk in entering into a contract in a place where the existence of heretics was suspected, since any contract entered into with a heretic was void in itself. Nor was there any more security in the trans- mission of inheritances for posthumous trials were frequent; INQUISITION 59i the Liber senlentiarum inquisitionis of Bernardus Guidonis (1307-1,323) records sentences pronounced after death against Sq persons during a period of 15 years. But not only was their property confiscated and their heirs disinherited; they were subject to still further penalties. Frederick II. extended to heresy the application of the Roman law disqualifying from holding office, and even included under its operation the children and grandchildren of the guilty man. Alexander IV. and Boniface VIII. lightened the severity of this law, and removed certain disqualifications, notably in the case of ecclesiastical offices and property. Among other accessory penalties, we must notice the con- demnation of books. There were many precedents for this: Constantine had had the Arian writings burnt, ^ationot Theodosius IL and Valentinian III. those of the books. Nestorians and Manichaeans, Justinian the Talmud. In 1 2 10 were burnt the books of David of Dinant and the Periphyseon of Aristotle. In 1255 the De periculis novis- simorum temporum of William of St Amour 1 was burnt by order of Pope Alexander IV., and from 1248 to 13 19 was pronounced a series of condemnations of the Talmud. Nicholas Eymerich (c. 1320-1399), the Spanish inquisitor, demanded from Pope Gregory XI. the condemnation of Raymond Lully's books, and in 1376 obtained it, but before long the Lullists returned into favour with the pope and Eymerich was banished. This rebuff suffered by an inquisitor shows how uncertain the censure of books still was, even in a country where in less than two centuries' time it was to become one of the chief spheres of inquisitorial activity. The definite object of the Inquisition was the prosecution of heresy; but its sphere of action was gradually extended by the theologians and casuists until sorcery and magic ranked with dogmatic heresy. The council of Valence Sorcery and magic (1248) dealt with sorcerers as well as sacrilegious per- sons, but did not treat them as heretics. Alexander IV. went further, declaring that divination and sorcery should only come within the competence of the inquisitor when they directly affected the unity or faith of the Church (9th December 1257; cf. bull Quod super nonnullis, 10th January 1260). Cases of simple sorcery were left to be dealt with by the ordinary judges. The distinction was very subtle, but it was not tampered with until 1451, at which date Nicholas V. gave the inquisitor Hugues Lenoir the cognizance of cases of divination, even when the crime did not savour of heresy. In dealing with such a subtle question, great variations had naturally arisen in practice, and the repression of sorcery was carried on jointly by the inquisitors, the bishops and the secular courts. John XXII., in consequence of a perfect epidemic of sorcery about 1320, handed over to the inquisitors for a time (1320-1333) all cases of crimes involving magic; but this measure was temporary and exceptional and only confirms the rule. There were various occasions during the middle ages when men's minds became infatuated, and it seemed as if the scourge of magic were likely entirely to destroy the Catholic faith; and during such times, morbidly infected with fear and the spirit of persecu- tion, the ecclesiastical judges regained all their prestige. One of these crises culminated in the affair of the "Vauderie" 2 of Arras (1459), in which twelve unfortunates perished at the stake; and there were similar occurrences at the same period in Dauphine and Gascony; of this nature again was the violent persecution in the Germanic countries begun by the bull Summis desiderantes of Innocent VIII. (5th December 1484), in the course of which the two authors of the Malleus maieficorum, the inquisitors Sprenger and Institoris (Heinrich Kramer), distinguished themselves as much by their knowledge of theoreti- cal demonology as by their zeal as persecutors. In France 1 Guillaume de St Amour (d. 1272), named after his birthplace in the Jura, was canon of Beauvais and rector of the university of Paris. He was conspicuous as the mouthpiece of the secular clergy in their attacks on the mendicant orders, the Dominicans in particular. 2 The name of vauderie, i.e. the Vaudois or Waldensian heresy, had come to be used of witchcraft. the secular authority was not long in claiming and obtaining jurisdiction over sorcerers (parlement of Paris, 1374), and as early as 1378 the university of Paris gave judgment in a case of demonology. Those unfortunates who were charged with sorcery gained, however, nothing by this change of jurisdiction, for they were invariably put to death. The inquisitors could not take proceedings against Jews as such. They might profess their religion and observe its rites without being in a state of heresy; they were only rheia- heretic when they attacked the Christian faith or quisHioa community, made proselytes, or returned to Judaism «»<* the after being converted. Further, those who practised Jews - usury were " suspected of not holding very orthodox doctrine as to theft " (Vacandard), and on this account the Inquisition gained a hold on them. Pope Martin V. (6th November 1419) authorized inquisitors to take proceedings against usurers. But these are merely extensions of competence resulting from the works of the casuists; the Inquisition was primarily the instrument for the repression of all kinds of breaches Treatment of orthodoxy. Its work in this capacity we will now of heresy describe in outline for each of the great countries of '" the medieval Christendom. England, whether before or varlo " s after the establishment of the Inquisition, had but few trials for heresy and, particularist in this as in all her religious activity, judged them according to her own discipline, without asking Rome for laws or special judges. In 1166, a Ensiand few heretics having been apprehended, Henry II. called a council at Oxford and summoned them to appear before it; they all confessed, and were condemned to be scourged, branded on the face with the mark of a key, and expelled from the country, and by the 21st article of the Assize of Clarendon the king forbade any one to harbour on their lands or in the house any " of that sect of renegades who had been excommunicated at Oxford. " Any one offending against this law was to be " at the king's mercy " and his house was to be " carried outside the town and burnt." The sheriffs were obliged to swear observance of this law and to require a similar oath from all barons' stewards, knights and free tenants. This was the first civil law against heresy since the end of the Roman empire, and preceded the famous rescripts of Frederick II. against sectaries in the 13th century. It should, however, be noted that the political acts of Henry II. and Frederick II. drew down the most explicit condemnation of the church. Orthodoxy remained almost unimpaired in England up till the time of Wycliffe. Apparently neither the Catharist, Waldensian nor Pantheistic heresies gained any footing in Great Britain. The affair of the Templars in France, which was quite political, was repeated in England: Clement V. having ordered their arrest, Edward II. , after much hesitation, gave orders to the sheriffs to execute it and then decided that the ecclesiastical law should be applied. The papal inquisitors sent to England met with a bad reception, and the pope was obliged to forbid them to use torture, which was contrary to the laws of the kingdom. It was found impossible to establish the Templars' guilt and only canonical penalties were inflicted on them. The rising of the Lollards having alarmed both the church and the state, the article De haeretico comburendo was established by statute in 1401, and gained a melancholy notoriety during the religious struggles of the 16th century; it seems to have been not so much a measure for the safeguarding of dogma as a violent assertion of the secular absolutism. It was not till 1676 that Charles II. caused it to be abrogated, and obtained a decision that in cases of atheism, blasphemy, heresy, schism and other religious offences, the ecclesiastical courts should be confined to the penalties of excommunication, removal from office, degradation and other ecclesiastical means of censure, to the exclusion of the death penalty. Scotland was much later than England in giving up persecution and blood- Scotland shed; and so late as 1696 a student of medicine aged eighteen and named Aikenhead was accused of heresy and hanged at Edinburgh. In Ireland Richard de Lederede or Ledred, a Franciscan and bishop of Ossory, in 1324 prosecuted on suspicion of heresy and for sorcery a certain Dame Alice 59 2 INQUISITION Kettle or Kyteler and her accomplices, Petronilla of Meath and her daughter Bassilla, who were accused of holding " nightly Ireland. conference with a spirit called Robert Artisson, to whom she sacrificed in the high way nine red cocks and nine peacocks' eyes." The lady had powerful connexions, and her brother-in-law, Arnold le Powre, seneschal of Kilkenny, even went so far as to imprison the bishop. But in spite of the refusalof the secular authorities to co-operate with him, the bishop was strong enough to force them in 1325 to burn some of the accused. Dame Kettle herself, however, who had been cited to appear at Dublin before the dean of St Patrick's, escaped with the assistance of some of the nobles to England. Mean- while the bishop, who had attempted to involve Arnold le Powre in the same charge, became involved in a quarrel with the administrators of the English government in Ireland; counter charges were brought against him, he was excommunicated by his metropolitan, Alexander de Bicknor, archbishop of Dublin; and in defiance of the king's commands, after pub- lishing counter charges against the archbishop, he appealed to Rome and left the country. In 1335 Benedict XII. wrote to Edward III. deploring the absence of any inquisition in the king's dominions, and exhorting him to lend the aid of the secular arm in repressing heresy. Archbishop Alexander, who in 1347 was denounced as an abettor of heresy, died in 1349, and his successor was ordered to chastise those heretics who had taken refuge in the diocese from Richard de Lederede's violence, and whom his predecessor had protected. Finally, in 1354, Richard de Lederede himself was allowed to return to his diocese, where his zeal for persecution does not, however, seem to have found much further scope. He died in 1360. '" The scene of the activities of the monastic Inquisition in France lay chiefly in the south. The repression of the Albigensian France. heresy (see Albigenses) went on even when its importance had quite disappeared. The chronicle of the inquisitor Guilhem Pelhisso (d. 1268) shows us the most tragic episodes of the reign of terror which wasted Languedoc for a century. Guillaume Arnaud, Peter Cella, Bernard of Caux. Jean de St Pierre, Nicholas of Abbeville, Foulques de St Georges, were the chief of the inquisitors who played the part of absolute dictators, burning at the stake, attacking both the living and the dead, confiscating their property and land, and enclosing the inhabitants both of the towns and the country in a network of suspicion and denunciation. The secular authorities were of the utmost assistance to them in this task; owing to the confiscations, the crown had too direct an interest in the success of the inquisitorial trials not to connive at all their abuses. Under the regency of Alphonse of Poitiers Languedoc was regularly laid under contribution by the procureur des cncours. There were frequent attempts at retaliation, directed for the most part against the inquisitors, and isolated attacks were made on Dominicans. In 1234-123 5 there were regular risings of the people at Albi and Narbonne, which forced the inquisitors to retreat. In 1235 the inquisitors were driven out of Toulouse. These risings were followed by terrible measures of repression, which, in turn, led to violent outbreaks on the part of the relatives, friends or compatriots of the sufferers. During the night of the 28th or 29th of May 1242 the inquisitors and their agents were massacred at the castle of Avignonet. This massacre led to a persecution which went on without opposition and almost without a lull for nearly fifty years. At the beginning of the 14th century the terrified people found a defender in the heroic Franciscan Bernard Delicieux. For a moment King Philip the Fair and Pope Clement V. seemed to interest themselves in the misfortunes of Languedoc, and the king of France sent down reformers; but they had no effect, their activity being restrained by the king himself, who was alarmed at a separatist movement which was arising in Languedoc. The work of repression which followed this moment of hope was carried out, between 1308 and 1323, by the inquisitor Bernard Guy, and completed the destruction of the Catharist heresy, the appearances of which after the middle of the 14th century became less and less frequent. Other heretics, for a time at least, took their place, namely the Spirituals, who had developed out of a branch of the Franciscans, and were remotely disciples of Joachim, abbot of Floris {q.v.), and whom their rigid rule of absolute poverty led, by a reaction against the cupidity of the ordinary ecclesiastics, to repudiate any hierarchy and to uphold the doctrines of Peter John de Oliva against the word of the pope. On the 17th of February 13 17 John XXII. con- demned all these irregular followers of St Francis, " jraticelli, fratres de paupere vita, bizochi or beghini," and the Inquisition of Languedoc was at once set in motion against them. Four spirituales were burnt at Marseilles in 1318, and soon the persecu- tion was extended to the Franciscan beguins or tcrtiarii, many people being burnt about 1320 at Narbonne, Lunel, Beziers, Carcassonne, &c. The persecution stopped for lack of an object, for the small groups of beguins were soon destroyed, and those of the Spirituales who were not sent to the stake or to prison were compelled by the papacy to enter other orders than the Franciscan. The Waldenses {q.v ) were more difficult to destroy: originally less dangerous to the church than the Cathari, they resisted longer, and their dispersal in scattered communities aided their long resistance. In the north of France the workings of the Inquisition were very intermittent; for there were fewer heretics there than in the south, and as they were poorer, there was less zeal on the part of the secular arm to persecute them. At its outset, how- ever, the Inquisition in the north of France was marked by a series of melancholy events: the inquisitor Robert le Bougre, formerly a Catharist, spent six years (1 233-1 239) in going through the Nivernais, Burgundy, Flanders and Champagne, burning at the stake in every place unfortunates whom he condemned without a judgment, supported as he was by the ecclesiastical authorities and by princes such as Theobald of Champagne. The pope was forced to put a check on his zeal, and, after an inquiry, condemned him to imprisonment for life. We know that there were inquisitors settled in lie de France, Orleanais, Touraine, Lorraine and Burgundy during the 12th century, but we know next to nothing of what they did. In the 14th century, the Flemish and German heresies of the Free Spirit made their appearance in France; in 13 10 a heretic named Marguerite Porette was burnt at Paris, and in 1373 another named Jeanne Daubenton, both of whom seem to have professed a kind of rudimentary pantheism, the latter being the head of a sect called the Turlupins. The Turlupins reappeared in 142 1 at Arras and Douai and were persecuted in a similar way. But in the 15th century, with the exception of a few condemnations aimed against the Hussites, the Inquisition acted but feebly against heresy, which, as in the famous case of the " Vauderie " of Arras, was often nothing but fairly ordinary sorcery. From the middle of the 14th century onward, the parlement had taken upon itself the right of hearing appeals from persons sentenced by the Inquisition. And the University again, by its faculty of theology, escaped the jurisdiction of the Inquisition. It was these two great bodies which at the time of the Re- formation took the place of the Inquisition in dealing with heresy. In Italy heresy not infrequently took on a social or political character; it was sometimes almost indistinguishable from the opposition of the Ghibellines or the communalist Itgl spirit of independence. Lombardy, besides a number of Cathari, contained a certain number of vaguely-defined sects against whom the efforts of the Apostolic Visitors sent by Innocent III. were not of much effect. From the very earliest days of the Inquisition, John of Vicenza, Roland of Cremona and Rassiero Sacchoni directed their persecutions against Lombardy, and especially against Milan. St Peter Martyr, who was conspicuous for his bigoted violence, was assassinated in 1252. On the 20th of March 1236 Alexander IV. ordered the provincial of the friar preachers of Lombardy to increase the number of inquisitors in that province from four to eight. At Florence both heresy and Ghibellinism were alike crushed by the terrible severities of Fra Ruggieri, and indulgences were promised to all who should aid in the extinction of heresy in INQUISITION 593 Tuscany. Certain districts revolted against this violence, which threatened to devastate Italy as it had devastated Provence; in 1277 Fra Corrado Pagano was killed on an expedi- tion against the heretics of the Vattelline, and two years after the people of Parma rose against the inquisitors. Besides, this reign of terror only raised to a furious pitch the passionate and independent piety of the Italian peoples. The body of a heretic, Armanno Ponzilupo, who was killed at Ferrara in 1269, was venerated by the people, and his mediation was even invoked, until the Inquisition had to suppress this cult. But it had a harder struggle against the successes of Gerard Legarelli, and especially Dolcino (see Apostolici), which only came to an end after a long and difficult trial of the adepts of the Messianist sect of Guglielma, some of whom belonged to the noble families of Lombardy. Up till the beginning of the 14th century, how- ever, the power of the Inquisition steadily increased, and at this period Zanghino Ugolini appeared as the most skilful exponent of its theory and procedure. About the same time Charles of Anjou introduced the Inquisition into the Two Sicilies, but it could rarely effect anything there; the religious cohesion of the country was weak, and refugees were sure of safe hiding, both Waldenses and Fraticelli being frequently harboured there. When Sicily passed into the hands of Peter III. of Aragon, moreover, it came into a position of open hostility to the Hoby See and became a refuge for heretics. Venice always preserved its autonomy as regards the repression of heresy; she was perfectly orthodox, but remained entirely independent of Rome; Innocent IV. sent inquisitors there, but the heretics continued actually to be subject to the secular tribunals. In 1288 a compromise was arrived at, and the papal Inquisition was admitted into the republic, but only on con- dition that it should remain under the control of the secular power; thus there was established a mixed regime which sur- vived till the last days of the Venetian state. In Savoy the Inquisition constantly carried on severe measures against the Waldenses of the Alps. During the 14th and 15th centuries there was an uninterrupted succession of trials. As regards the papal states, " it was in the nature of things that, by a confusion of the two personages, the pope should consider all opposition to him qua Italian prince as st f'" s resistance offered to the head of the church, i.e. to the Church. church " (Ch.V.Langlois). The Colonna had a personal animosity against the Gaetani ; therefore Boniface VIII., a Gaetauo, declared the Colonna to be heretics. Rienzi was accused of heresy for having questioned the temporal sovereignty of the pope at Rome. The Venetians, who in 1309 opposed the annexation of Ferrara by Clement V. to the detriment of the house of Este, were proclaimed heretics and placed under the ban of Christendom. Savonarola was attacked because he interfered with the policy of Alexander VI. at Florence. It was this same desire for the hegemony of Italy which inspired the attitude of the popes throughout the middle ages, causing them to excommunicate, apparently without reason so far as doctrine was concerned, the Visconti of Milan, the Delia Scala of Verona, the Maffredi of Faenza, &c, and prompting them to lay under an interdict or preach a crusade against certain rebellious great towns (Clement V. against Venice, John XXII. against Milan). Further, in each of the great cities of Lombardy and Tuscany, the papal party directed the local inquisition, and this power was rarely abused. In Germany heresies, especially of a mystical character, were numerous in the middle ages; some of them affected the mass Germany ot tne P eo P' c > an d led lo religious and social movements t of no little importance. The repression of heresy went on by fits and starts, and the Inquisition was never exercised so regularly in the Germanic as in certain of the Latin countries. At the outset of the 13th century persecutions of the Waldenses and Ortlibarii (followers of Ortlieb of Strassburg, c. 1200) took place at Strassburg; measures were taken locally until, in 1 231, Gregory IX. issued definite instructions to the German prelates with a view to a regular repression of heresy, and gave full powers to execute them to Conrad of Marburg. Certain nobles having offered him resistance, he preached a crusade against them, but died by the hand of an assassin. The council of Mainz (April 1234) dealt gently with Conrad's murderers, but severely with the false witnesses whom he had employed. Shortly before (February 1234), the diet of Frankfort had decided, in spite of the pope's injunctions, that the destruction of heresy should be entrusted to the ordinary magistrates. And besides, thanks to the struggle between the Empire and the papacy, the German prelates always limited the prerogatives of the papal Inquisition. Again, by the municipal laws of the north (Sachsenspiegel) the ecclesiastical jurisdiction in the matter of heresy was very much limited, while the Sckwaben Spiegel (municipal laws for southern Germany) does not seem to be aware of the existence of any inquisitional jurisdiction or procedure. When in the 14th century communities of Beghards developed with extraordinary rapidity, it was the episcopal authority, both at Cologne and Strassburg, which undertook to deal with these groups of sectaries, and at the very height of the conflict between the Empire and the papacy. Marsilius of Padua, the theoretical exponent of the imperial rights, attributes to the secular judge the right atid obligation to punish heresy, the priest's role being merely advisory. In 1353 Innocent VI. tried to implant the papal Inquisition in Germany once for all; its success was but short, and Urban V.'s attempt in 1362 succeeded little better, in spite of the fact that Charles IV. (edicts of Lucca, June 1369) gave him the support of the secular power. Towards 1372, however, Gregory XI. succeeded in regularizing the exercise of the powers of the papal inquisitors on German soil; and the latter, notably Kerlinger, Hetstede, &c, set to work to destroy the communities of the Beghards, to burn their books, to close those beguinages which were under suspicion, and to check by more or less violent means mystical epidemics such as those of the " flagellants," " dancers," &c. But these measures provoked angry protests from the people, the secular magistrates and even the bishops, so that Gregory XL, perceiving that he was face to face with the popular party, invited the bishops to control the inquiries of his own envoys. At the end of the 15th century the two inquisitions were acting con- currently. In Bohemia and the provinces subject to it the Waldenses had found their chosen country, and by the middle of the 13th century their propaganda was very flourishing. In Bohemia. 1245 Innocent IV. ordered the bishops to prosecute them with the aid of the secular arm, and in 1257, at the request of King Premysl Ottokar II., Alexander IV. introduced the Inquisition into Bohemia. But from this date till 133 5 inquisi- torial missions succeeded one another without effecting any sensible diminution in the material and moral strength of the heresy. The Waldenses had been joined by other sectaries, the Luciferani, and especially the Brethren of the Free Spirit. It was in vain that the bishops of Bohemia and Silesia carried on during the second half of the 14th century an active campaign against heresy; the spirit of criticism which had arisen with regard to the morals, and even to the dogmas of the church, was already preparing the way for Hussitism. 1-' In the regions east of the Adriatic, Catharism, the first com- munities of which had very probably settled here, was supreme in the time of Innocent III. and Honorius III. The first Dominicans who established themselves in these parts £*?. had much to suffer from the aggression of those very states. heretics whom they had come to convert. Gregory XI . , implacable in his persecution of Catharism, preached a crusade against them in 1234, and Bosnia was laid waste by fire and sword. But in spite of these violent measures Catharism only gained strength in the churches of Bulgaria, Rumania, Slavonia and Dalmatia. In 1298 Boniface VIII. tried to organize the Inquisition there, but the project remained fruitless. The attempt was revived in 1323 by John XXII. with doubtful success. The persecutions undertaken in the 14th and 15th centuries merely resulted in binding the Cathari to the invading Turks, with whom they found more tolerance than with the Slav princes converted to Roman orthodoxy. 594 INQUISITION Spain. In Spain the papal Inquisition could gain no solid footing in the middle ages. Spain had been, in turn or simultaneously, Arian under the Visigoths, Catholic under the Hispano- Romans, Mussulman by conquest, and under a regime of religious peace Judaism had developed there. After the reconquest, and even at the height of the influence of the Cathari its heresies had been of quite minor importance. At the end of the 1 2th century Alphonso II. and Peter II. had on principle promulgated cruel edicts against heresy, but the persecution seemed to be dormant. By the bull Declinante of the 26th of May 1232 inquisitors were sent to Aragon by Gregory IX. on the request of Raymond of Penaforte, and by 1237-1238 the Inquisition was practically founded. But as early as 1233 King James I. had promulgated an edict against the heretics which quite openly put the Inquisition in a subaltern position, and secularized a great part of its activities. The people, more- over, showed great hostility _ towards it. The inquisitor Fray Pedro de Cadrayta was murdered by the mob, and in 1235 the Cortes, with the consent of King James, prohibited the use of inquisitorial procedure and of the torture, as constituting a violation of the Fueros, though they made no attempt to give effect to their prohibition. In Castile Alphonso the Wise had, by establishing in his Fuero Real and his Siete Partidas an entirely independent secular legislation with regard to heretics ( r 2 5 5 ), removed his kingdom from all papal interference. At the opening of the 14th century Castile and Portugal had still no Inquisition. But at that time in Spain orthodoxy was generally threatened only by a few Fraticelli and Waldenses, who were not numerous enough to call for active repression. The Spanish inquisitor Nicholas Eymerich, the author of the famous Direc- torium Inquisitorum, had rarely to exercise his functions during the whole of his long career (end of 14th century). It was not against heresy that the church had to direct its vigilance. A mutual tolerance between the different religions had in fact sprung up, even after the conquest; the Christians in the north recognized the Mahommedan and Jewish religions, and Alphonso VI. of Castile took the title of imperador de losdoscultos. But for a long time past both the decisions of councils and papal briefs had proclaimed their surprise and indignation at this ominous indifference. As early as 1077 the third council of Rome, and in 1081 Gregory VII., protested against the admission of Jews to public offices in Spain. Clement IV., in a brief of 1266, exhorted James I. of Aragon to expel the Moors from his dominions. In 1278 Nicholas III. blamed Peter III. for having made a truce with them. One of the canons of the council of Vienne (1311-1312) denounces as intolerable the fact that Mahommedan prayers were still proclaimed from the top of the mosques, and under the influence of this council the Spanish councils of Zamora (1313) and Valladolid (1322) came to decisions which soon led to violent measures against the Mudegares (Mussulmans of the old Christian provinces). Already in 12 10 massacres of Jews had taken place under the inspiration of Arnold of Narbonne, the papal legate; in 1276 fresh disturbances took place as a result of James I.'s refusal to obey the order of Clement IV., who had called upon him to expel the Jews from his dominions. In 1278 Nicholas IV. commanded the general of the Dominicans to send friars into all parts of the kingdom to work for the conversion of the Jews, and draw up lists of those who should refuse to be baptized. It was in vain that a few princes such as Peter III. or Ferdinand of Castile interfered; the Spanish clergy directed the persecution with ever increasing zeal. In the 14th century the massacres increased, and during the year 1391 whole towns were destroyed by fire and sword, while at Valencia eleven thousand forced baptisms took place. In the 15th century the persecution continued in the same way; it can only be said that the years 1449, 1462, 1470, 1473 were marked by the greatest bloodshed. Moreover, the Mudegares were also subjected to these baptisms and massacres en masse. From those, or the children of those who had escaped death by baptism, was formed the class of Conversos or Marranos, the latter name being confined to the converted Jews. This class was still further increased after the conquest of the kingdom of Granada and the completion of the conquest by Ferdinand and Isabella, and after the pacification of the kingdoms of Aragon and Valencia by Charles V. The Mahommedans and Jews in these parts were given the choice between conversion and exile. Being of an active nature, and desiring some immediate powers as a recompense for their moral sufferings, the Jewish or Mussul- man Conversos soon became rich and powerful. In addition to the hatred of the church, which feared that it might quickly become Islamized or Judaized in this country which had so little love for theology, hatred and jealousy arose also among laymen and especially in the rich and noble classes. Limpieza, i.e. purity of blood, and the fact of being an " old Christian " were made the conditions of holding offices. It is true, this mistrust had assumed a theological form even before the Mahom- medan conquest. As early as 633 the council of Toledo had declared heretics such converts, forced or voluntary, as returned to their old religion. When this principle was revived and, whether through secular jealousy, religious dislike or national pride, was applied to the Conversos, an essentially national Inquisition, directed against local heretics, was founded in Spain, and founded without the help of the papacy. It was created in 1480 by Ferdinand and Isabella. Sixtus IV. had wished the papal Inquisition to be established after the form and spirit of the middle ages; but Ferdinand, in his desire for centralization (his efforts in this direction had already led to the creation of the Holy Hermandad and the extension of the royal jurisdiction) wished to establish an inquisition which should be entirely Spanish, and entirely royal. Rome resisted, but at last gave way. Sixtus IV., Alexander VI., Innocent VIII., Julius II. and after them all the popes of the 16th century, saw in this secular attempt a great power in favour of orthodoxy, and approved it when established, and on seeing its constant activity. The Inquisition took advantage of this to claim an almost complete autonomy. The decisions of the Roman Congregation of the Index were only valid for Spain if the Holy Office of Madrid thought good to countersign them; consequently there were some books approved at Rome and proscribed in the peninsula, such as the Historia pelagiana of Cardinal Nores, and some which were forbidden at Rome and approved in the peninsula, such as the writings of Fathers Mateo Moya and Juan Bautista Poza. The Spanish Holy Office perceived long before Rome the dangers of mysticism, and already persecuted the mystics, the Alumbrados while Rome (impervious to Molinism) still favoured them. " During the last few centuries the church of Spain was at once the most orthodox and the most independent of the national churches " (Ch. V. Langlois). There was even a financial dispute between the Inquisition and the papacy, in which the Inquisition had the better of the argument; the Roman Penitentiary sold exemptions from penalties (involving loss of civil rights), such as prison, the galleys and wearing the sanbenito, and dispensations from the crime of Marrania (secret Judaism). The inquisitors tried to gain control of this sale, and at a much higher price, and were seconded in this by the kings of Spain, who saw that it was to their own interest. At first they tried a compromise; the unfortunate victims had to pay twice, to the pope and to the Inquisition. But the payment to the pope was held by the Inquisition to reduce too much its own share of the confiscated property, and the struggle continued throughout the first half of the 1 6th century, the Curia finally triumphing, thanks to the energy of Paul III. Since, however, the Inquisition continued to threaten the holders of papal dispensations, most of them found it prudent to demand a definite rehabilitation, in return for payments both to the king and the Inquisition. As a national institution the Inquisition had first of all the advantage of a very strong centralization and very rapid procedure, consisting as it did of an organization of local tribunals with a supreme council at Madrid, the Suprema. The grand inquisitor was ex officio president for life of the royal council of the Inquisition. It was the grand inquisitor, General Jimenez de Cisneros, who set in motion the inquisitorial tribunals of Seville, Cordova, Jaen, Toledo, Murcia, Valladolid and Calahorra. There was no such tribunal at Madrid till the time of Philip IV. The inquisitor- INQUISITION 595 general of Aragon established inquisitors at Saragossa, Barcelona, Valencia, Majorca, Sardinia, Sicily and Pampeluna (moved later to Calahorra) . From the very beginning.the papacy strengthened this organization by depriving the Spanish metropolitans, by the bull of the 25th of September 1487, of the right of receiving appeals from the decisions given jointly by the, bishops of the various dioceses, their suffragans and the apostolic inquisitors, and by investing the inquisitor-general with this right. And, more than this, Torquemada actually took proceedings against bishops, for example, the accusation of heresy against Don Pedro Aranda, bishop of Calahorra (1498); while the inquisitor Lucero prosecuted the first archbishop of Granada, Don Ferdi- nando de Talavera. Further, when once the Inquisition was closely allied to the crown, no Spaniard, whether clerk or layman, could escape its power. Even the Jesuits, though not till after 1660, were put under the authority of the Suprema. The highest nobles were kept constantly under observation; during the reigns of Charles III. and Charles IV. the duke of Almodovar, the count of Aranda, the great writer Campomanes, and the two ministers Melchior de Jovellanos and the count of Florida-Alanca, were attacked by the Suprema. But the descendants of Moors and Jews, though they were good Christians, or even nobles, were most held in suspicion. Even during the middle ages the descendants of the Paterenes were known, observed and de- nounced. In the eyes of the Inquisition the taint of heresy was even more indelible. A family into which a forced conversion or a mixed marriage had introduced Moorish or Jewish blood was almost entirely deprived of any chance of public office, and was bound, in order to disarm suspicion, to furnish agents or spies to the Holy Office. The Spaniards were very quick to accept the idea of the Inquisition to such an extent as to look upon heresy as a national scourge to be destroyed at all costs, and they consequently considered the Inquisition as a powerful and indispensable agent of public protection; it would be going too far to state that this conception is unknown to orthodox present-day historians of the Inquisition, and especially certain Spanish historians (cf. the preface to Menendez y Pelayo's Heterodoxos espafwles). As had happened among the Albigenses, commerce and industry were rapidly paralysed in Spain by this odious regime of suspicion, especially as the Converses, who inherited the industrial and commercial capacity of the Moors and Jews, represented one of the most active elements of the population. Besides, this system of wholesale confiscations might reduce a family to beggary in a single day, so that all transactions were liable to extraordinary risks. It was in vain that the counsellors of Charles V., and on several occasions the Cortes, demanded that the inquisitors and their countless agents should be appointed on a fixed system by the state; the state, and above all the Inquisition, refused to make any such change. The Inquisition preferred to draw its revenues from heresy, and this is not surprising if we think of the economic aspect of the Albigensian Inquisition; the system of encours was simply made general in Spain, and managed to exist there for three centuries. In the case of the Inquisition in Languedoc, there still remained the possibility of an appeal to the king, the inquisitors, or more rarely the pope, against these extortions; but there was nothing of the kind in Spain. The Inquisition and the Crown could refuse each other nothing, and appeals to the pope met with their united resistance. As early as the reign of Ferdinand certain rich Conversos who had bought letters of indulgence from the Holy See were nevertheless prosecuted by Ferdinand and Torquemadq, in spite of the protests of Sixtus IV. The papacy met with the most serious checks under the Bourbons. Philip V. forbade all his subjects to carry appeals to Rome, or to make public any papal briefs without the royal exequatur. The political aspect of the work and character of the Inquisi- tion has been very diversely estimated; it is a serious error to attribute to it, as has too often been done, extreme ideas of equality, or even to represent it as having favoured centralization and a royal absolutism to the same extent as the Inquisition of the 13th and 14th centuries in Languedoc. " It was a mere coincidence," says H. C. Lea," that the Inquisition and absolut- ism developed side by side in Spain." The Suprema did not attack all nobles as nobles; it attacked certain of them as Conversos, and the Spanish feudal nobles were sure enough of their limpieza to have nothing to fear from it. But it is undeni- able that it frequently tended to constitute a state within the state. At the time of their greatest power, the inquisitors paid no taxes, and gave no account of the confiscations which they effected; they claimed for themselves and their agents the right of bearing arms, and it is well known that their declared adversaries, or even those who blamed them in some respects, were without fail prosecuted for heresy. But that was not the limit to their pretensions. In 1574, under Philip II., there was an idea of instituting a military order, that of Santa Maria de la Espada Blanca, having as its head the grand inquisitor, and to him all the members of the order, i.e. all Spaniards distinguished by limpieza of blood, were to swear obedience in peace and in war. Moreover, they were to recognize his jurisdiction and give up to him the reversion of their property. Nine provinces had already consented, when Philip II. put a stop to this theocratic movement, which threatened his authority. It was, however, only the Bourbons, who had imbibed Gallican ideas, who by dint of perseverance managed to make the Inquisition subservient to the Crown, and Charles III., " the philosopher king," openly set limits to the privileges of the inquisitors. Napoleon, on his entry into Madrid (December 1808), at once suppressed the Inquisition, and the extraordinary general Cortes on the 12th of February 1813 declared it to be incompatible with the constitu- tion, in spite of the protests of Rome. Ferdinand VII. restored it (July 21, i8r4) on his return from exile, but it was impoverished and almost powerless. It was again abolished as a result of the Liberal revolution of 1820, was restored temporarily in 1823 after the French military intervention under the due d'Angouleme, and finally disappeared on the 15th of July 1834, when Queen Christina allied herself with the Liberals. " It was not, however, till the 8th of May 1869 that the principle of religious liberty was proclaimed in the peninsula; and even since then it has been limited by the constitution of 1876, which forbids the public celebration of dissident religions " (S. Reinach). In 1816 the pope abolished torture in all the tribunals of the Inquisition. It is a too frequent practice to represent as peculiar to the Spanish Inquisition modes of procedure in use for a long time in the inquisitorial tribunals of the rest of Europe. There are no special manuals, or practica, for the inquisitorial procedure in Spain; but the few distinctive characteristics of this procedure may be mentioned. The Suprema allowed the accused an advocate chosen from among the members or familiars of the Holy Office ; this privilege was obviously illusory, for the advocate was chosen and paid by the tribunal, and could only interview the accused in presence of an inquisitor and a secretary. The theological examination was a delicate and minute proceeding; the " quali- ficators of the Holy Office," special functionaries, whose equivalent can, however, easily be found in the medieval Inquisition, charged those books or speeches which had incurred " theological censures," with " slight, severe or violent " suspicion. There was no challenging of witnesses; on the contrary, witnesses who were objected to were allowed to give evidence on the most important points of the case. The torture, to the practice of which the Spanish Inquisition certainly added new refinements, was originally very much objected to by the Spaniards, and Alphonso X. prohibited it in Aragon; later, especially in the 15th, 16th and 17th centuries it was applied quite shamelessly on the least suspicion. But by the end of the 18th century, according to Llorente, it had not been employed for a long time; the fiscal, however, habitually demanded it, and the accused always went in dread of it. The punishment of death by burning was much more often employed by the Spanish than by the medieval Inquisition; about 2000 persons were burnt in Torquemada's day. Penitents were not always reconciled, as they were in the middle ages, but those condemned to be burnt were as a rule strangled previously. With the extension of the Spanish colonial empire the 59 6 INQUISITION Inquisition spread throughout it almost contemporaneously with Spanish the Catholic faith. Ferdinand IV. decreed the estab- Inquisl- tion. and Portu- lishment of the Inquisition in America, and Jimenes in icese 1516 appointed Juan Quevedo, bishop of Cuba, °" s ' inquisitor-general delegate with discretionary powers. Excesses having been committed by the agents of the Holy Office, Charles V. decreed (October 15, 1538) that only the European colonists should be subject to the jurisdiction of the Inquisition; but Philip II. increased the powers of the inquisitors' delegate and, in 1541, established on a permanent basis three new provinces of the Inquisition at Lima, Mexico and Cartagena. The first auto-da-fe took place at Mexico in 1574, the year in which Hernando Cortez died. The Inquisition of Portugal was no less careful to ensure the orthodoxy of the Portuguese colonies. An Inquisition of the East Indies was established at Goa, with jurisdiction over all the dominions of the king of Portugal beyond the Cape of Good Hope. Finally Philip II. even wished to establish an itinerant Inquisition, and at his request the pope created, by a brief of the 21st of July 1571, the " Inquisition of the galleys," or " of fleets and armies." After the expulsion of the Jews under Isabella the Catholic (1492), followed under Philip III. by that of the Moriscoes (1609), the Inquisition attacked especially Catholics descended activities fr° m infidels, the Marrancs and Converses, who were, of the not without reason, suspected of often practising in Spanish secret the rites of their ancestral religions. As late as 1 71 5 a secret association was discovered at Madrid, consisting of twenty families, having a rabbi and a synagogue. In 1727 a whole community of Moriscoes was denounced at Granada, and prosecuted with the utmost rigour. Again, a great number of people were denounced, sent to the galleys, or burnt, for having returned to their ancestral religion, on the flimsiest of evidence, such as making ablutions during the day time, abstaining from swine's flesh or wine, using henna, singing Moorish songs, or possessing Arabic manu- scripts. During the 16th and 17th centuries the Inquisition in Spain was directe.d against Protestantism. The inquisitor- general, Fernando de Valdes, archbishop of Seville, asked the pope to condemn the Lutherans to be burnt even if they were not backsliders, or wished to be reconciled, while in 1560 three foreign Protestants, two Englishmen and a Frenchman were burnt in defiance of all international law. But the Reformation never had enough supporters in Spain to occupy the attention of the Inquisition for long. After the Marrams the mystics of all kinds furnished the greatest number of victims to the terrible tribunal. Here again we should not lose sight of the tradition of the medieval Inquisition; the mysticism of the Beghards, the Brethren of the Free Spirit and the innumerable pantheist sects had been pitilessly persecuted by the inquisitors of Germany and France during the 14th and 15th centuries. The Illuminati (alumbrados), who were very much akin to the medieval sectaries, and the mystics of Castile and Aragon were ruthlessly examined, judged and executed. Not even the most famous persons could escape the suspicious zeal of the inquisitors Valdes and Melchior Cano. The writings of Luis de Granada were censured as containing cosas de alumbrados. St Ignatius de Loyola was twice imprisoned at the beginning of his career; St Theresa was accused of misconduct, and several times de- nounced; one of her works, Conceptos del amor divino, was prohibited by the Inquisition, and she was only saved by the personal influence of Philip II. Countless numbers of obscure visionaries, devotees both men and women, clerks and laymen, were accused of Illuminism and perished in the fires or the dungeons of the Inquisition. From its earliest appearance Molinosism was persecuted with almost equal rigour. Molinos himself was arrested and condemned to perpetual imprisonment (1685-1687), and during the 18th century, till 1781, several Molinosists were burnt. The Inquisition also attacked Jansenism, freemasonry (from 1738 onwards; cf. the bull In eminenti) and " philosophism," the learned naturalist Jose Clavigo y Faxarcho (1730-1806), the mathematician Benito Bails (1730-1797), the poet Tomas de Iriarte, the ministers Clavigo Ricla, Arjinda and others being prosecuted as " philosophers." Subject also to the tribunal of the Holy Office were bigamists, blasphemers, usurers, sodomites, priests who had married or broken the secrecy of the confessional, laymen who assumed ecclesiastical costume, &c. " In all these matters, though the Inquisition may have been indiscreet in meddling with affairs which did not concern it, it must be confessed that it was not cruel, and that it was always preferable to fall into the hands of the Inquisition rather than those of the secular judges, or even the Roman inquisitors " (S. Reinach). Apart from certain exceptional cruelties such as those of the Inquisition of Calahorra, perhaps the greatest number of executions of sorcerers took place in the colonies, in the Philippines and Mexico. In Spain the persecu- tion was only moderate; at certain times it disappeared almost completely, especially in the time of the clear-sighted inquisitor Salazar. Two features of the Spanish Inquisition are especially note- worthy: the prosecutions for " speeches suspected of heresy " and the censure of books. The great scholar Pedro de Lerma, who after fifty years at Paris (where he was dean of the faculty of theology) had returned to Spain as abbot of Compluto, was called upon in 1537 to abjure eleven " Erasmian " propositions, and was forced to return to Paris to die. Juan de Vergara and his brother were summoned before the Inquisition for favouring Erasmus and his writings, and detained several years before they were acquitted. Fray Alonso de Virues, chaplain to Charles V., was imprisoned on an absurd charge of depreciating the monastic state, and was only released by the pope at the instance of the emperor. Mateo Pascual, professor of theology at Alcala, who had in a public lecture expressed a doubt as to purgatory, suffered imprisonment and the confiscation of his goods. A similar fate befell Montemayor, Las Brozas and Luis de la Cadena. The censure of books was established in 1502 by Ferdinand and Isabella as a state institution. All books had to pass through the hands of the bishops; in 1521 the Inquisition took upon itself the examination of books suspected of Lutheran heresy. In 1554 Charles V. divided the responsibility for the censorship between the Royal Council, whose duty it was to grant or refuse the imprimatur to manuscripts and the Inquisition, which retained the right of prohibiting books which it judged to be pernicious; but after 1527 it also gave the licence to print. In 1547 the Suprema produced an Index of prohibited books, drawn up in 1546 by the university of Louvain; it was completed especially as regards Spanish books, in 1551, and several later editions were published. Moreover, the revisores de libros might present themselves in the name of the Holy Office in any private library or bookshop and confiscate prohibited books. In 1558 the penalty of death and confiscation of property was decreed against any' bookseller or individual who should keep in his possession condemned books. The censure of books was eventually abolished in 181 2. Bibliography. — A critical bibliography was drawn up by P. Fredericq in the preface to the French translation (1900) of H. C. Lea's important standard work : History of the Inquisition in the Middle Ages (3 vols., London, 1888). See also J. Havet, L'Heresie el le bras seculier au moyen age jusqu'au XIII" Steele in the CEuvres completes, vol. ii. (Paris, 1896) ; Ch. V. Langlois, L' Inquisition d'apris des travaux recents (Paris, 1901); Douais, V Inquisition (Paris, 1907); E. Vacandard, V Inquisition (Paris, 1907); Douais, Documents pour servir a Vhistoire de V inquisition dans le Languedoc (2 vols., Paris, 1 900) ; Dollinger, Beitrdge zur Sektengeschichte des Mittelaltets (2 vols., Munich, 1890. The second volume is composed of docu- ments) ; Molinier, V Inquisition dans le midi de la France au XIII' zl au XIV' siecle. Etude sur les sources de son histoire (Paris, 1880); P. Fredericq, Corpus documentorum inquisitionis haereticae pravitatis neerlandicae (1205-1525) (4 vols., Ghent, 1889-1900); Tanon, Histoire des tribunaux de V inquisition en France (Paris, 1893); Hansen, Inquisition, Hexenwahn und Hexenverfolgung (Munich, 1900) ; Llorente, Histoire critique de V inquisition d'Espagne (4 vols., Paris, 1818); H. C. Lea, History of the Inquisition of Spain (5 vols., London, 1905-1908); S. Reinach, articles on Lea's History of the Inquisition of Spain in the Revue critique (1906, 1907, 1908) and Cultes, mythes et religions (Paris, 1908), tome iii. (P. A.) INSANITY 597 Definition. INSANITY (from Lat. in, not, and sanus, sound), a generic term applied to certain morbid mental conditions produced by defect or disease of the brain. The synonyms in more or less frequent use are lunacy (from a supposed influence of the moon), mental disease, alienation, derangement, aberration, madness, unsoundness of mind. The term Psychiatry (faxy, mind, and larptla, treatment) is applied to the study and treatment of the condition. I. Medical and General There are many diseases of the general system productive of disturbance of the mental faculties, which, either on account of their transient nature, from their being associated with the course of a particular disease, or from their slight intensity, are not included under the head of insanity proper. From a strictly scientific point of view it cannot be doubted that the fever patient in his delirium, or the drunkard in his excitement or stupor, is insane; the brain of either being under the influence of a morbific agent or of a poison, the mental faculties are deranged; yet such derangements are regarded as functional disturbances, i.e. disturbances pro- duced by agencies which experience tells will, in the majority of cases, pass off within a given period without permanent results on the tissues of the organ. The comprehensive scientific view of the position is that all diseases of the nervous system, whether primary or secondary, congenital or acquired, should, in the words of Griesinger, be regarded as one inseparable whole, of which the so-called mental diseases comprise only a moderate proportion. However important it may be for the physician to keep this principle before him, it may be freely admitted that it cannot be carried out fully in practice, and that social considera- tions compel the medical profession and the public at large to draw an arbitrary line between such functional diseases of the nervous system as hysteria, hypochondriasis and delirium on the one hand, and such conditions as mania, melancholia, stupor and dementia on the other. All attempts at a short definition of the term " insanity " have proved unsatisfactory; perhaps the nearest approach to accuracy is attained by the rough statement that it is a symptom of disease of the brain inducing disordered mental symptoms — the term disease being used in its widest acceptance. But even this definition is at once too comprehensive, as under it might be included certain of the functional disturbances alluded to, and too exclusive, as it does not comprehend certain rare transitory forms. Still, taken over all, this may be accepted as the least defective short definition; and moreover it possesses the great practical advantage of keeping before the student the primary fact that insanity is the result of disease of the brain (see Brain, and Neuropathology), and that it is not a mere immaterial disorder of the intellect. In the earliest epochs of medicine the corporeal character of insanity was generally admitted, and it was not until the superstitious ignorance of the middle ages had obliterated the scientific, though by no means always accurate, deductions of the early writers, that any theory of its purely psychical character arose. At the present day it is unnecessary to combat such a theory, as it is universally accepted that the brain is the organ through which mental phenomena are manifested, and therefore that it is impossible to conceive of the existence of an insane mind in a healthy brain. On this basis insanity may be defined as consisting in morbid conditions of the brain, the results of defective formation or altered nutrition of its substance induced by local or general morbid processes, and characterized especially by non-development, obliteration, im- pairment or perversion of one or more of its psychical functions. Thus insanity is not a simple condition; it comprises a large number of diseased states of the brain, gathered under one popular term, on account of mental defect or aberration being the predominant symptom. The insanities are sharply divided into two great classes— the Congenital and the Acquired. Under the head of Congenital Insanity must be considered all cases in which, from whatever cause, brain development lias been arrested, with consequent Causation. impotentiality of development of the mental faculties; under that of Acquired Insanity all those in which the brain has been born healthy but has suffered from morbid processes affect- ing it primarily, or from diseased states of the general tjoo _ ' system implicating it secondarily. In studying the causation of these two great classes, it will be found that certain remote influences exist which are believed to be commonly predisposing; these will be considered as such, leaving the proximate or exciting causes until each class with its subdivisions comes under review. In most treatises on the subject will be found discussed the bearing which civilization, nationality, occupation, education, &c, have, or are supposed to have, on the production of insanity. Such discussions are as a rule eminently unsatisfactory, founded as they are on common observa- tion, broad generalizations, and very imperfect statistics. As they are for the most part negative in result, at the best almost entirely irrelevant to the present purpose, it is proposed merely to summarize shortly the general outcome of what has been arrived at by those authorities who have sought to assess the value to be attached to the influence exercised by such factors, without entering in any detail on the theories involved. The causes of insanity may be divided into (a) general, and (b) proximate. (a) General Causes. — i. Civilization. — Although insanity is by no means unknown amongst savage races, there can be no reasonable doubt that it is much more frequently developed in civilized com- munities; also that, as the former come under the influence of civilization, the percentage of lunacy is increased. This is in con- sonance with the observation of disease of whatever nature, and is dependent in the case of insanity on the wear and tear of nerve tissue involved in the struggle for existence, the physically de- pressing effects of pauperism, and on the abuse of alcoholic stimu- lants; each of which morbid factors falls to be considered separately as a proximate cause. In considering the influence of civilization upon the production of insanity, regard must be had to the more evolved ethical attitude towards disease in general which exists in civilized communities as well as to the more perfect recognition and registration of insanity. 2. Nationality. — In the face of the imperfect social statistics afforded by most European and American nations, and in their total absence or inaccessibility amongst the rest of mankind, it is impossible to adduce any trustworthy statement under this head. 3. Occupation. — There is nothing to prove that insanity is in any way connected with the prosecution of any trade or profession per se. Even if statistics existed (which they do not) showing the proportion of lunatics belonging to different occupations to the 1000 of the population, it is obvious that no accurate deduction quoad the influence of occupation could be drawn. 4. Education. — There is no evidence to show that education has any influence over either the production or the prevention of in- sanity. The general result of discussions on the above subjects has been the production of a series of arithmetical statements, which have either a misleading bearing or no bearing at all on the question. In the study of insanity statistics are of slight value from the scien- tific point of view, and are only valuable in its financial aspects. 5. Inheritance. — The hereditary transmission of a liability to mental disease must be reckoned as the most important among all predisposing causes of insanity. It is probably well within the mark to say that at least 50 % of the insane have a direct or colla- teral hereditary tendency towards insanity. The true significance of this factor cannot as yet be explained or described shortly and clearly, but it cannot be too definitely stated that it is not the insanity which is inherited, but only the predisposition to the manifestation of mental symptoms in the presence of a sufficient exciting cause. The most widely and generally accepted view of the exciting cause of insanity is that the predisposed brain readily breaks down under mental stress or bodily privations. There is, however, another view which has been recently advanced to the effect that the majority of mental diseases are secondary to bodily disorders, hereditary predisposition being the equally predisposing causal factor. There is probably truth in both these views, and such an admission accentuates the complexity of the factorship of heredity. If insanity can be induced by physical disorders, which must essentially be of the nature of toxic action or of mechanical agency which can alter or influence the functional powers of the brain, then it is probable that hereditary predisposition to insanity means, not only the transmission of an unstable nervous system, but also a constitution which is either peculiarly liable to the pro- duction of such toxic or poisonous substances, or incapable of effectively dealing with the toxins or poisonous substances normally formed during metabolic processes. Such a view broadens our conception of the factorship of hereditary transmission and offers 59 8 INSANITY [MEDICAL AND GENERAL explanation as to the manner in which insanity may appear in families previously free from the taint. Very frequently we find in the history of insane patients that although there may be no in- sanity in the family there are undoubted indications of nervous alongside of physical instability, the parental nervous defects taking the form of extreme nervousness, vagabondage, epilepsy, want of mental balance, inequality in mental development or endowment, extreme mental brilliancy in one direction associated with marked deficiency in others, the physical defects showing themselves in the form of insanity; liability to tubercular and rheumatic infections. The failure of constitutional power which allows of the invasion of the tubercle bacillus and the micrococcus rheumaticus in certain members of a family is apparently closely allied to that which favours the development of mental symptoms in others. 6. Consanguinity. — It has been strongly asserted that con- sanguineous marriage is a prolific source of nervous instability. There is considerable diversity of opinion on this subject; the genera! outcome of the investigations of many careful inquirers appears to be that the offspring of healthy cousins of a healthy stock is not more liable to nervous disease than that of unrelated parents, but that evil consequences follow where there is a strong tendency in the family to degeneration, not only in the direction of the original diathesis, but also towards instability of the nervous system. The objection to the marriage of blood relations does not arise from the bare fact of their relationship, but has its ground in the fear of their having a vicious variation of constitution, which, in their children, is prone to become intensified. There is sufficient evidence adducible to prove that close breeding is productive of degeneration ; and when the multiform functions of the nervous system are taken into account, it may almost be assumed, not only that it suffers concomitantly with other organs, but that it may also be the first to suffer independently. 7. Parental Weakness. — Of the other causes affecting the parents which appear to have an influence in engendering a predisposition to insanity in the offspring, the abuse of alcoholic stimulants and opiates, over-exertion of the mental faculties, advanced age and weak health may be cited. Great stress has been laid on the in- fluence exercised by the first of these conditions, and many extreme statements have been made regarding it. Such statements must be accepted with reserve, for, although there is reason for attaching considerable weight to the history of ancestral intemperance as a probable causating influence, it has been generally assumed as the proved cause by those who have treated of the subject, without reference to other agencies which may have acted in common with it, or quite independently of it. However unsatisfactory from a scientific point of view it may appear, the general statement must stand that whatever tends to lower the nervous energy of a parent may modify the development of the progeny. Constitutional tendency to nervous instability once established in a family may make itself felt in various directions — epilepsy, hysteria, hypo- chondriasis, neuralgia, certain forms of paralysis, insanity, eccen- tricity. It is asserted that exceptional genius in an individual member is a phenomenal indication. Confined to the question of insanity, the morbid inheritance may manifest itself in two direc- tions — in defective brain organization manifest from birth, or from the age at which its faculties are potential, i.e. congenital insanity ; or in the neurotic diathesis, which may be present in a brain to all appearance congenitally perfect, and may present itself merely by a tendency to break down under circumstances which would not affect a person of originally healthy constitution. 8. Periodic Influence. — The evolutional periods of puberty, adolescence, utero-gestation, the climacteric period and old age exercise an effect upon the nervous system. It may be freely admitted that the nexus between physiological processes and mental disturbances is, as regards certain of the periods, obscure, and that the causal relation is dependent more on induction than on demonstration; but it may be pleaded that it is not more obscure in respect of insanity than of many other diseases. The pathological difficulty obtains mostly in the relation of the earlier evolutional periods, puberty and adolescence, to insanity; in the others a physiologico-pathological nexus may be traced; but in regard to the former there is nothing to take hold of except the purely physiological process of development of the sexual function, the expansion of the intellectual powers, and rapid increase of the bulk of the body. Although in thoroughly stable subjects due provision is made for these evolutional processes, it is not difficult to conceive that in the nervously unstable a considerable risk is run by the brain in consequence of the strain laid on it. Between the adolescent and climacteric periods the constitution of the nervous, as of the other systems, becomes established, and disturbance is not likely to occur, except from some accidental circumstances apart from evolution. In the most healthily constituted individuals the " change of life " expresses itself by some Joss of vigour. The nourishing (trophesial) function becomes less active, and either various degrees of wasting occur or there is a tendency towards restitution in bulk of tissues by a less highly organized material. The most important instance of the latter tendency is fatty de- generation of muscle, to which the arterial system is very liable. In the mass of mankind those changes assume no pathological importance : the man or woman of middle life passes into advanced age without serious constitutional disturbance; on the other hand, there may be a break down of the system due to involutional changes in special organs, as, for instance, fatty degeneration of the heart. In all probability the insanity of. the climacteric period may be referred to two pathological conditions : it may depend on structural changes in the brain due to fatty degeneration of its arteries and cells, or it may be a secondary result of general systemic disturbance, as indicated by cessation of menstruation in the female and possibly by some analogous modification of the sexual function in men. The senile period brings with it further reduction of formative activity; all the tissues waste, and are liable to fatty and calcareous degeneration. Here again, the arteries of the brain are very generally implicated; atheroma in some degree is almost always present, but is by no means necessarily followed by insanity. The various and profound modifications of the system which attend the periods of utero-gestation, pregnancy and child-bearing do not leave the nervous centres unaffected. Most women are liable to slight changes of disposition and temper, morbid longings, strange likes and dislikes during pregnancy, more especially during the earlier months; but these are universally accepted as accompani- ments of the condition not involving any doubts as to sanity. But there are various factors at work in the system during pregnancy which have grave influence on the nervous system, more especially in those hereditarily predisposed, and in those gravid for the first time. There is modification of direction of the blood towards a new focus, and its quality is changed, as is shown by an increase of fibrin and water and a decrease of albumen. To such physical influences are superadded the discomfort and uneasiness of the situation, mental anxiety and anticipation of danger, and in the unmarried the horror of disgrace. In the puerperal (recently delivered) woman there are to be taken into pathological account, in addition to the dangers of sepsis, the various depressing influences of child-bed, its various accidents reducing vitality, the sudden return to ordinary physiological conditions, the rapid call for a new focus of nutrition, the translation as it were of the blood supply from the uterus to the mammae — all physical influences liable to affect the brain. These influences may act independently of moral shock; but, where this is coincident, there is a condition of the nervous system unprepared to resist its action. (6) Proximate Causes. — The proximate causes of insanity may be divided into (1) toxic agents, (2) mechanical injury to the brain, including apoplexies and tumours, and (3) arterial degeneration. 1. Toxic Agents. — The definite nature of the symptoms in the majority of the forms of acute insanity leave little reason to doubt that they result from an invasion of the system by toxins of various kinds. The symptoms referred to may be briefly indicated as follows: (i.) Pyrexia, or fever generally of an irregular type; (ii.) Hyperleucocytosis, or an increase of the white blood corpuscles, which is the chief method by which the animal organism protects itself against the noxious influence of micro-organisms and their toxins. In such cases as typhoid fever, which is caused by a bacillus, or Malta fever which is caused by a coccus, it is found that if the blood serum of the patient is mixed in vitro with a broth culture of the infecting organism in a dilution of I in 50, that the bacilli or the cocci, as the case may be, when examined microscopically, are seen to run into groups or clusters. The organisms are- said to be agglutinated, and the substance in the serum which produces this reaction is termed an agglutinine. In many of the forms of insanity which present the symptom of hyperleucocytosis there can also be demonstrated the fact that the blood serum of the patients contains agglutinines to certain members of a group of streptococci (so called on account of their tendency to grow in the form of a chain, (rTptirTos; (iii.) the rapid organic affection of the special nerve elements depending upon the virulence of the toxin, and the resist- ance of the individual to its influence; (iv.) the marked physical deterioration as indicated by emaciation and other changes in nutrition; (v.) the close analogy between the character of many of the mental symptoms, e.g. delirium, hallucinations or depression, and the symptoms produced artificially by the administration of certain poisonous drugs. The toxic substances which are generally believed to be associated with the causation of mental disorders may be divided into three great classes: (a) those which arise from the morbific products of metabolism within the body itself " auto-intcxicants " ; (b) those due to the invasion of the blood or tissues by micro-organisms; (c) organic or inorganic poisons introduced into the system volun- tarily or accidentally. (a) Auto-intoxication may be due to defective metabolism or to physiological instability, or to both combined. The results of defective metabolism are most clearly manifested in the mental symptoms which not infrequently accompany such diseases as gout, diabetes or obesity, all of which depend primarily upon a deficient chemical elaboration of the products of metabolism. The association of gout and rheumatism with nervous and mental diseases is historical, and the gravest forms of spinal and cerebral degeneration have been found in association with diabetes. Until the pathology of these affections is better understood we are not in a position to determine the nature of the toxins which appear to be the cause of these diseases and of their accompanying nervous MEDICAL AND GENERAL] INSANITY 599 symptoms. Physiological instability is usually manifested by neurotic persons under the strain of any unusual change in their environment. If, for instance, any material change in the food supply consisting either in a decrease of its quality or quantity, or in a failure to assimilate it properly, the nerve-cells become exhausted and irritable, sleep is diminished and a condition known as the delirium of collapse or exhaustion may supervene. An extreme instance of this condition is presented by the delirium occurring in shipwrecked persons, who having to take to the boats are suddenly deprived of food, water or both. Poisoning of the nervous system may also result from the defective action of special glands such as the thyroid, the liver or the kidneys. These conditions are specially exemplified in the mental disturbances which accompany exophthalmic goitre, uraemic poisoning, and the conditions of depression which are observed in jaundice and other forms of hepatic insufficiency. The results of modern research point to a growing belief in the frequency of infection of the nervous system from the hosts of micro-organisms which infest the alimentary tract. No definite or substantiated discoveries have as yet been formulated which would justify us in treating this source of infection as more than a highly probable causative influence. (6) When we turn, however, to the potentiality of infection by micro-organisms introduced from without into the system we are upon surer if not upon entirely definite ground. A special form of insanity called by Weber, who first described it, the delirium of collapse, was observed by him to follow certain infectious diseases such as typhus fever and pneumonia. In later years it has been frequently observed to follow attacks of influenza. Recently our views have broadened and we find that the delirium of collapse is an acute, confusional insanity which may arise without any previous febrile symptoms, and is in fact one of the common forms of acute insanity. The nature of the physical symptoms, the mental con- fusion and hallucinations which accompany it, as well as the fact that it frequently follows some other infective disease, leave no doubt as to its toxic origin. A similar and analogous condition is presented by incidence of general paralysis after a previous syphilitic infection. The symptoms of general paralysis coupled with the extensive and rapid degeneration of not only the nervous but of the whole of the body tissues point to a microbic disease of intense virulence which, though probably not syphilitic, is yet induced, and enhanced in its action by the previous devitalizing action of the syphilitic toxin. There is abundant evidence to show that emotions which powerfully affect the mind, if long continued, conduce towards a condition of metabolic change, which in its turn deleteriously affects the nervous system, and which may terminate in inducing a true toxic insanity. One of the best examples of insanity arising from micro-organisms is that form which occurs after childbirth, and which is known as puerperal mania. Other insanities may, it is true, arise at this period, but those which occur within the first fourteen days after parturition are generally of infective origin. The confusional nature of the mental symptoms, the delirium and the physical symptoms are sufficient indications of the analogy of this form of mental aberration with such other toxic forms of insanity as we find arising from septic wounds and which sometimes accompany the early toxic stages of virulent infectious diseases such as typhus, diphtheria or malignant scarlet fever. The infective origin of puerperal mania is undoubted, though, as yet, no special pathogenic organism has been isolated. Dr Douglas (Ed. Med. Journ., 1897, i. 413) found the staphylococcus pyogenes aureus present in the blood in one case; Jackman (quoted he. cit.) found the micrococcus pneumonial crouposae in one case; while Haultain (Ed. Med. Journ., 1897, ii. 131) found only the bacillus coli communis in the blood and secretions of several cases. From our experience of similar mental and physical symptoms produced as a result of septic wounds or which succeed surgical operations there seems to be no doubt that several forms of micro- cocci or streptococci of a virulent character are capable by means of the toxins they exude of causing acute delirium or mania of a confusional clinical type when introduced into the body. (c) Accidental and voluntary poisonings of the system which result in insanity are illustrated by the forms of insanity which follow phosphorus or lead poisoning and by Pellagra. The voluntary intoxication of the system by such drugs as morphia and alcohol will be treated of below. 2 and 3. Mechanical injuries to the brain arise from direct violence to the skull, from apoplectic hemorrhage or embolism, or from rapidly growing tumours, or from arterial degeneration. The forms of insanity may be divided into (I.) Congenital Mental Defect and (II.) Acquired Insanity. Forms of *• Congenital Mental Defect. — The morbid mental lasaalty. conditions which fall to be considered under this head are Idiocy (with its modification, Imbecility) and Cretinism (q.v.). Idiocy (from Gr. tStcorrjs, in its secondary meaning of a deprived person). In treating of idiocy it must be carefully borne in mind that we are dealing with mental phenomena dis- sociated for the most part from active bodily disease, and that, in whatever degree it may exist, we have to deal with Mfa _. a brain condition fixed by the pathological circum- ^ cy ' stances under which its possessor came into the world or by such as had been present before full cerebral activity could be developed, and the symptoms of which are not dependent on the intervention of any subsequent morbid process. From the earliest ages the term Amentia has been applied to this condition, in contradistinction to Dementia, the mental weakness following on acquired insanity. The causes of congenital idiocy may be divided into four classes: (1) hereditary predisposition, (2) constitutional con- ditions of one or both parents affecting the constitution of the infant, (3) injuries of the infant prior to or at birth, and (4) injuries or diseases affecting the infant head during infancy. All these classes of causes may act in two directions: they may produce either non-development or abnormal development of the cranial bones as evidenced by microcephalism, or by deformity of the head ; or they may induce a more subtle morbid condition of the constituent elements of the brain. As a rule, the pathological process is more easily traceable in the case of the last three classes than in the first. For instance, in the case of constitutional conditions of the parents we may have a history of syphilis, a disease which often leaves its traces on the bones of the skull; and in the third case congenital malformation of the brain may be produced by mechanical causes acting on the child in utero, such as an attempt to procure abortion, or deformities of the maternal pelvis rendering labour difficult and instrumental interference necessary. In such cases the bones of the skull may be injured; it is only fair, however, to say that more brains are saved than injured by instrumental interference. With regard to the fourth class, it is evident that the term congenital is not strictly applicable; but, as the period of life implicated is that prior to the potentiality of the manifestation of the in- tellectual powers, and as the result is identical with that of the other classes of causes, it is warrantable to connect it with them, on pathological principles more than as a mere matter of con- venience. Dr Ireland, in his work On Idiocy and Imbecility (1877), classifies idiots from the standpoint of pathology as follows: (1) Genetous idiocy: in this form, which he holds to be complete before birth, he believes the presumption of heredity to be stronger than in other forms; the vitality of the general system is stated to be lower than normal; the palate is arched and narrow, the teeth misshapen, irregular and prone to decay and the patient dwarfish in appearance; the head is generally unsym- metrical and the commissures occasionally atrophied; (2) Microcephalic idiocy, a term which explains itself; (3) Eclampsic idiocy, due to the effects of infantile convulsions; (4) Epileptic idiocy; (5) Hydrocephalic idiocy, a term which explains itself; (6) Paralytic idiocy, a rare form, due to the brain injury causing the paralysis; (7) Traumatic idiocy, a form produced by the third class of causes above mentioned; (8) Inflammatory idiocy; (9) Idiocy by deprivation of one or more of the special senses. The general conformation of the idiot is generally imperfect; he is sometimes deformed, but more frequently the frame is merely awkwardly put together, and he is usually of short stature. Only about one-fourth of all idiots have heads smaller than the average. Many cases are on record in which the cranial measurements exceed the average. It is the irregularity of development of the bones of the skull, especially at the base, which marks the condition. Cases, however, often present themselves in which the skull is perfect in form and size. In such the mischief has begun in the brain matter. The palate is often highly arched; hare-lip is not uncommon; in fact congenital defect or malformation of other organs than the brain is more commonly met with among idiots than in the general community. Of the special senses, hearing is most frequently affected. Sight is good, although co-ordination may be defective. Many are mute. On account of the mental dullness it is difficult to determine whether the senses of touch, taste and smell suffer 6oo INSANITY [MEDICAL AND GENERAL impairment; but the impression is that their acuteness is below the average. It is needless to attempt a description of the mental phenomena of idiots, which range between utter want of intelligence and mere weakness of intellect. The term Imbecility has been conventionally employed to indicate the less profound degrees of idiocy, but in point of fact no distinct line of demarcation can be drawn between the conditions. As the scale of imbeciles ascends it is found that the condition is evidenced not so much by obtuseness as by irregularity of intellectual development. This serves to mark the difference between the extreme stupidity of the lowest of the healthy and the highest forms of the morbidly deprived type. The two conditions do not merge gradually one into the other. Absolute stupidity and sottishness mark many cases of idiocy, but only in the lowest type, where no dubiety of opinion can exist as to its nature, and in a manner which can never be mistaken for the dulness of the man who is less talented than the average of mankind. Where in theory the morbid (in the sense of deprivation) and the healthy types might be supposed to approach each other, in practice we find that, in fact, no debatable ground exists. The uniformity of dulness of the former stands in marked opposition to the irregularity of mental conformation in the latter. Comparatively speaking, there are few idiots or imbeciles who are uniformly deprived of mental power; some may be utterly sottish, living a mere vegetable existence, but every one must have heard of the quaint and crafty sayings of manifest idiots, indicating the presence of no mean power of applied observation. In institutions for the treatment of idiots and imbeciles, children are found not only able to read and write, but even capable of applying the simpler rules of arithmetic. A man may possess a very considerable meed of receptive faculty and yet be idiotic in respect of the power of application ; he may be physically disabled from relation, and so be manifestly a deprived person, unfit to take a position in the world on the same platform as his fellows. Dr Ireland subdivides idiots, for the purpose of education, into five grades, the first comprising those who can neither speak nor understand speech, the second those who can understand a few easy words, the third those who can speak and can be taught to work, the fourth those who can be taught to read and write, and the fifth those who can read books for themselves. The treatment of idiocy and imbecility consists almost entirely of attention to hygiene and the building up of the enfeebled constitution, along with endeavours to develop what small amount of faculty exists by patiently applied educational in- fluences. The success which has attended this line of treatment in many public and private institutions has been very consider- able. It may be safely stated that most idiotic or imbecile children have a better chance of amelioration in asylums devoted to them than by any amount of care at home. In the class of idiots just spoken of, imperfect development of the intellectual faculties is the prominent feature, so prominent that it masks the arrest of potentiality of development of the moral sense, the absence of which, even if noticed, is regarded as relatively unimportant; but, in conducting the practical study of congenital idiots, a class presents itself in which the moral sense is wanting or deficient, whilst the intellectual powers are apparently up to the average. It is the custom of writers on the subject to speak of " intellectual " and " moral " idiots. The terms are convenient for clinical purposes, but the two conditions cannot be dissociated, and the terms therefore severally only imply a specially marked deprivation of intellect or of moral sense in a given case. The everyday observer has no difficulty in recognizing as a fact that deficiency in receptive capacity is evidence of imperfect cerebral development; but it is not so patent to him that the perception of right or wrong can be com- promised through the same cause, or to comprehend that loss of moral sense may result from disease. The same difficulty does not present itself to the pathologist; for, in the case of a child born under circumstances adverse to brain development, and in whom no process of education can develop an appreciation of what is right or wrong, although the intellectual faculties appear to be but slightly blunted, or not blunted at all, he cannot avoid connecting the physical peculiarity with the pathological evidence. The world is apt enough to refer any fault in intel- lectual development, manifested by imperfect receptivity, to a definite physical cause, and is willing to base opinion on com- paratively slight data; but it is not so ready to accept the theory of a pathological implication of the intellectual attributes concerned in the perception of the difference between right and wrong. Were, however, two cases pitted one against another — the first one of so-called intellectual, the second one of so-called moral idiocy — it would be found that, except as regards the psychical manifestations, the cases might be identical. In both there might be a family history of tendency to degeneration, a peculiar cranial conformation, a history of previous symptoms during infancy, and of a series of indications of mental in- capacities during adolescence, differing only in this, that in the first the prominent indication of mental weakness was inability to add two and two together, in the second the prominent feature was incapacity to distinguish right from wrong. What compli- cates the question of moral idiocy is that many of its subjects can, when an abstract proposition is placed before them, answer according to the dictates of morality, which they may have learnt by rote. If asked whether it is right or wrong to lie or steal they will say it is wrong; still, when they themselves are detected in either offence, there is an evident non-recognition of its concrete nature. The question of moral idiocy will alwavs be a moot one between the casuist and the pathologist; but, when the whole natural history of such cases is studied, there are points of differentiation between their morbid depravation and mere moral depravity. Family history, individual peculiarities, the general bizarre nature of the phenomena, remove such cases from the category of crime. Statistics. — According to the census returns of iqoi the to*-al number of persons described as idiots and imbeciles in England and. Wales was 48,882, the equality of the sexes being remarkabto, namely, 24,480 males and 24,402 females. Compared with the entire population the ratio is 1 idiot or imbecile to 665 persons, or 15 per 10,000 persons living. Whether the returns are defective, owing to the sensitiveness of persons who would desire to conceal the occurrence of idiocy in their families, we have no means of knowing; but such a feeling is no doubt likely to exist anions; those who look upon mental infirmity as humiliating, rather than, as one of the many physical evils which afflict humanity. Dr. Ire- land estimates that there is 1 idiot or imbecile to every 500 persons in countries that have a census. The following table shows the num- ber of idiots according to official retu r ns of the various countries : — Proportion Males. Females. Total. to 100,000 of Pop. England and Wales 24,480 24,402 48,882 150 Scotland ... 3.246 3.377 6,623 148 Ireland .... 2,946 2,270 5,216 117 France (including . 1 cretins) (1872) 20,456 H.677 35.133 97 Germany (1871) . — — 33,739 82 Sweden (1870) . . — — 1,632 38 Norway (1891) . . 1,357 1,074 2,43i 121 Denmark (1888-89). 2, 1 06 1,751 3,857 200 For the United States there are no later census figures than 1890 when the feeble-minded or idiotic were recorded as 95,571 (52,940 males and 42,631 females). In 1904 (Special Report of Bureau of Census, 1906) the "feeble-minded" were estimated at 150,000. The relative frequency of congenital and acquired insanity in various countries is shown in the following table, taken from Koch's statistics of insanity in Wurttemberg, which gives the number ol idiots to 100 lunatics: — Prussia . Bavaria . Saxony • 158 ■ 154 . 162 France .... Denmark . Sweden .... 66 58 22 Austria . Hungary . Canton of Bern . America . • 53 . 140 • "7 • 79 Norway. England and Wales Scotland Ireland .... 65 74 68 69 It is difficult to understand the wide divergence of these figures, except it be that in certain states, such as Prussia and Bavaria, dements have been taken along with aments and in others cretins. MEDICAL AND GENERAL] INSANITY 60 1 General symptoms. This cannot, however, apply to the case of France, which is stated to have only 66 idiots to every 100 lunatics. In many_ districts of France cretinism is common; it is practically unknown in England, where the proportion of idiots is stated as higher than in France; and it is rare in Prussia, which stands at 158 idiots to 100 lunatics. Manifestly imperfect as this table is, it shows how important an element idiocy is in social statistics ; few are aware that the number of idiots and that of lunatics approach so nearly. II. Acquired Insanity. — So far as the mental symptoms of acquired insanity are concerned, Pinel's ancient classification, into Mania, Melancholia and Dementia, is still applic- in^ntt a ^ e t0 ever y case, and although numberless classifica- tions have been advanced they are for the most part merely terminological variations. Classifications of the insanities based on pathology and etiology have been held out as a solution of the difficulty, but, so far, pathological observations have failed to fulfil this ideal, and no thoroughly satisfactory pathological classification has emerged from them. Classifications are after all matters of convenience; the following system admittedly is so: — Melancholia. Mania. Delusional Insanity. Katatonia. Hebephrenia. Traumatic Insanity. Insanity following upon arterial degeneration. Insanities associated or caused by: General Paralysis; Epilepsy. Insanities associated with or caused by Alcoholic and Drug intoxi- cation: Delirium Tremens, Chronic Alcoholic Insanity, Dip- somania, Morphinism. Senile Insanity. The general symptoms of acquired insanity group themselves naturally under two heads, the physical and the mental. The physical symptoms of mental disease generally, if not invariably, precede the onset of the mental symptoms, and the patient may complain of indefinite symptoms of malaise for weeks and months before it is suspected that the disorder is about to terminate in mental symptoms. The most general physical disorder common to the onset of all the insanities is the failure of nutrition, i.e. the patient rapidly and apparently without any apparent cause loses weight. Associated with this nutritional failure it is usual to have disturbances of the alimentary tract, such as loss of appetite, dyspepsia and obstinate constipation. During the prodromal stage of such conditions as mania and melancholia the digestive functions of the stomach and intestine are almost or completely in abeyance. To this implication of other systems consequent on impairment of the trophesial (nourishment- regulating) function of the brain can be traced a large number of the errors which exist as to the causation of idiopathic melan- cholia and mania. Very frequently this secondary condition is set down as the primary cause; the insanity is referred to derangements of the stomach or bowels, when in fact these are, concomitantly with the mental disturbance, results of the cerebral mischief. Doubtless these functional derangements exercise considerable influence on the progress of the case by assisting to deprave the general economy, and by producing depressing sensations in the region of the stomach. To them may probably be attributed, together with the apprehension of impending insanity, that phase of the disease spoken of by the older writers as the stadium melancholicum, which so frequently presents itself in incipient cases. The skin and its appendages — the hair and the nails — suffer in the general disorder of nutrition which accompanies all insanities. The skin may be abnormally dry and scurfy or moist and offensive. In acute insanities rashes are not uncommon, and in chronic conditions, especially conditions of depression, crops of papules occur on the face, chest and shoulders. The hair is generally dry, loses its lustre and becomes brittle. The nails become deformed and may exhibit either excessive and irregular or diminished grov.'th. Where there are grave nutritional disorders it is to be ex- pected that the chief excretions of the body should show de- partures from the state of health. In this article it is impossible to treat this subject fully, but it may suffice to say that in many states of depression there is a great deficiency in the excretion of the solids of the urine, particularly the nitrogenous waste pro- ducts of the body; while in conditions of excitement there is an excessive output of the nitrogenous waste products. It has lately been pointed out that in many forms of insanity indoxyl is present in the urine, a substance only present when putrefactive processes are taking place in the intestinal tract. The nervous system, both on the sensory and motor side, suffers very generally in all conditions of insanity. On the sensory side the special senses are most liable to disorder of their function, whereby false sense impressions arise which the patient from impairment of judgment is unable to correct, and hence arise the psychical symptoms known as hallucinations and delusions. Common sensibility is generally impaired. On the motor side, impairment of the muscular power is present in many cases of depression and in all cases of dementia. The incontinence of urine so frequently seen in dementia and in acute insanity complicated with the mental symptom of con- fusion depends partly on impairment of muscular power and partly on disorder of the sensory apparatus of the brain and spinal cord. The outstanding mental symptom in nearly all insanities, acute and recent or chronic, is the failure of the capacity of judgment and loss of self-control. In early acute insanities, however, the two chief symptoms which are most evident and easily noted are depression on the one hand and excitement or elevation on the other. Some distinction ought to be made between these two terms, excitement and elevation, which at present are used synonymously. Excitement is a mental state which may be and generally is associated with confusion and mental impair- ment, while elevation is an exaltation of the mental faculties, a condition in which there is no mental confusion, but rather an unrestrained and rapid succession of fleeting mental processes. The symptoms which most strongly appeal to the lay mind as conclusive evidence of mental disorder are hallucinations and delusions. Hallucinations are false sense impressions which occur without normal stimuli. The presence of hallucinations certainly indicates some functional disorder of the higher brain centres, but is not an evidence of insanity so long as the sufferer recognizes that the hallucinations are false sense impressions. So soon, however, as conduct is influenced by hallucinations, then the boundary line between sanity on the one hand and insanity on the other has been crossed. The most common hallucinations are those of sight and hearing. Delusions are not infrequently the result of hallucinations. If the hallucinations of a melancholic patient consist in hearing voices which make accusatory statements, delusions of sin and unworthiness frequently follow. Hallucinations of the senses of taste and smell are almost invariably associated with the delusion that the patient's food is being poisoned or that it consists of objectionable matter. On the other hand, many delusions are apparently the outcome of the patient's mental state. They may be pleasant or disagreeable according as the condition is one of elevation or depression. The intensity and quality of the delusions are largely influenced by the intelligence and education of the patient. An educated man, for instance, who suffers from sensory disturbances is much more ingenious in his explanations as to how these sensory disturbances result from electricity, marconigrams, X-rays, &c, which he believes are used by his enemies to annoy him, than an ignorant man suffering from the same abnormal sensations. Loss of self-control is char- acteristic of all forms of insanity. Normal self-control is so much a matter of race, age, the state of health, moral and physical up- bringing, that it is impossible to lay down any law whereby this mental quality can be gauged, or to determine when deficiency has passed from a normal to an abnormal state. In many cases of in- sanity there is no difficulty in appreciating the pathological nature of the deficiency, but there are others in which the conduct is other- - wise so rational that one is apt to attribute the deficiency to physio- logical rather than to pathological causes. Perversion of the moral sense is common to all the insanities, but is often the only symptom to be noticed in cases of imbecility and idiocy, and it as a rule may be the earliest symptom noticed in the early stages of the excitement of manic-depressive insanity and general paralysis. The tendency to commit suicide, which is so common among the insane and those predisposed to insanity, is especially prevalent in patients who suffer from depression, sleeplessness and delusions of persecution. Suicidal acts may be divided into accidental, im- pulsive and premeditated. The accidental suicides occur in patients who are partially or totally unconscious of their surroundings, and are generally the result of terrifying hallucinations, to escape 602 INSANITY [MEDICAL AND GENERAL from which the patient jumps through a window or runs blindly into water or some other danger. Impulsive suicides may be prompted by suddenly presented opportunities or means of self- destruction, such as the sight of water, fire, a knife, cord or poison. Premeditated suicides most frequently occur in states of long continued depression. Such patients frequently devote their attention to only one method of destruction and fail to avail them- selves of others equally practicable. As a rule the more educated the patient, the more ingenious and varied are the methods adopted to attain the desired result. The faculty of attention is variously affected in the subjects of insanity. In some the attention is entirely subjective, being occupied by sensations of misery, depression or sensory disturb- ances. In others the attention is objective, and attracted by every accidental sound or movement. In most of the early acute insanities the capacity of attention is wholly abolished, while in hebephrenia the stage of exhaustion which follows acute excitement, and the condition known as secondary dementia, loss of the power of at- tention is one of the most prominent symptoms. The memory for both recent and remote events is impaired or abolished in all acute insanities which are characterized by confusion and loss 01 impair- ment of consciousness. In the excited stage of manic-depressive insanity it is not uncommon tc find that the memory is abnormally active. Loss of memory for recent but net remote events is char- acteristic of chronic alcoholism and senility and even the early stage of general paralysis. Of all the functions of the brain that of sleep is the most liable to disorder in the insane. Sleeplessness is the earliest symptom in the onset of insanity ; it is universally present in all the acute forms, and the return of natural sleep is generally the first symptom of recovery. The causes of sleeplessness are very numerous, but in the majority of acute cases the sleeplessness is due to a state of toxaemia. The toxins act either directly on the brain cells producing a state of irritability incompatible with sleep, or indirectly, producing physical symptoms which of themselves alone are capable of preventing the condition of sleep These symptoms are high arterial tension and a rapid pulse-rate. The arterial tension of health ranges between no and 120 millimetres of mercury, and when sleep occurs the arterial tension falls and is rarely above 100 millimetres. In ob- servations conducted by Bruce (Scottish Medical and Surgical- Journal, August 1900) on cases of insanity suffering from sleepless- ness the arterial tension was found to be as high as 140 and 150 millimetres. When such sleep was obtained the tension always sank at once to no millimetres or even lower. In a few cases suffering from sleeplessness the arterial tension was found to be below 100 millimetres, accompanied by a rapid pulse-rate. When sleep set in, in these cases, no alteration was noted in the arterial tension, but the pulse was markedly diminished. Melancholia. — Melancholia is a general term applied to all forms of insanity in which the prevailing mental symptom is that of depression and dates back to the time of M f'*"' Hippocrates. Melancholic patients, however, differ very widely from one another in their mental symptoms, and as a consequence a perfectly unwarrantable series of sub- divisions have been invented according to the prominence of one cr other mental symptoms. Such terms as delusional melancholia, resistive melancholia, stuporose melancholia, suicidal melancholia, religious melancholia, &c. have so arisen; they are, however, more descriptive of individual cases than indicative of types of disease. So far as our present knowledge goes, at least three different and distinct disease conditions can be described under the general term melancholia. These are, acute melancholia, excited melancholia and the state of depression occurring in Folie circulaire or alternating insanity, a condition in which the patient is liable to suffer from alternating attacks of excite- ment and depression. Acute Melancholia is a disease of adult life and the decline of life. Women appear to be more liable to be attacked than men. Hereditary predisposition, mental worry, exhausting occupations, such as the sick-nursing of relatives, are the chief predisposing causes, while the direct exciting cause of the condi- tion is due to the accumulation in the tissues of waste products, which so load the blood as to act in a toxic manner on the cells and fibres of the brain. The onset of the disease is gradual and indefinite. The patient suffers from malaise, indigestion, constipation and irregular, rapid and forcible action of the heart. The urine become scanty and high coloured. The nervous symptoms are irritability, sleeplessness and a feeling of mental confusion. The actual onset of the acute mental symptoms may be sudden, and is not infrequently heralded by distressing hallucinations of hearing, together with a rise in the body temperature. In the fully developed disease the patient is flushed and the skin hot and dry; the temperature is usually raised 1° above the normal in the evening. The pulse is hard, rapid and often irregular. There is no desire for food, but dryness of the mouth and tongue promote a condition of thirst. The bowels are constipated. The urine is scanty and frequently contains large quantities of indoxyl. The blood shows no demonstrable de- parture from the normal. The patient is depressed, the face has a strained, anxious expression, while more or less mental confusion is always present. Typical cases suffer from dis- tressing aural hallucinations, and the function of sleep is in abeyance. Acute melancholia may terminate in recovery either gradually or by crises, or the condition may pass into chronicity, while in a small proportion of cases death occurs early in the attack from exhaustion and toxaemia. The acute stage of onset generally lasts for from two to three weeks, and within that period the patient may make a rapid and sudden recovery. The skin becomes moist and perspiration is often profuse. Large quantities of urine are excreted, which are laden with waste products. The pulse becomes soft and compressible, sleep returns, and the depression, mental confusion and hallucinations pass away. In the majority of untreated cases, however, recovery is much more gradual. At the end of two or three weeks from the onset cf the attack the patient gradually passes into a condition of comparative tranquillity. The skin becomes moister, the pulse less rapid, and probably the earliest symptom of improvement is return of sleep. Hallucinations accompanied by delusions persist often for weeks and months, but as the patient improves I physically the mental symptoms become less and less prominent. If the patient does not recover, the physical symptoms are those of mal-nutrition, together with chronic gastric and intestinal disorder. The skin is dull and earthy in appearance, the hair dry, the nails brittle and the heart's action weak and feeble. Mentally there is profound depression with delusions, and persistent or recurring attacks of hallucinations of hearing. When death occurs, it is usually preceded by a condition known as the " typhoid state." The patient rapidly passes into a state of extreme exhaustion, the tongue is dry and cracked, sordes form upon the teeth and lips, diarrhoea and congestion of the lungs rapidly supervene and terminate life. Treatment, — The patient in the early stage of the disease must be confined to bed and nursed by night as well as day. The food to begin with should be milk, diluted with hot water or aerated water, given frequently and in small quantities. The large intestine should be thoroughly cleared out by large enemata and kept empty by large normal saline enemata administered every second day. Sleep may be secured by lowering the blood pressure with half-grain doses of erythrol-tetra-nitrate. If a hypnotic is necessary, as it will be if the patient has had no natural sleep for two nights in succession, then a full dose of paraldehyde or veronal may be given at bed-time. Under this treatment the majority of cases, if treated early, improve rapidly. As the appetite returns great care must be taken that the patient does not suddenly resume a full ordinary dietary. A sudden return to a full dietary invariably means a relapse, which is often less amenable to treatment than the original attack. Toast should first be added to the milk, and this may be followed by milk puddings and farinaceous foods in small quantities. Any rise of temperature or increase of pulse-rate or tendency to sleeplessness should be regarded as a threatened relapse and treated accordingly. Excited Melancholia. — Excited melancholia is almost invariably a disease of old age or the decline of life, and it attacks men and women with equal frequency. Chronic gastric disorders, deficient food and sleep, unhealthy occupations and environments, together with worry and mental stress, are all more or less predisposing causes of the disease. The direct exciting cause or causes have not as yet been demonstrated, but there is no doubt that the disease is associated with, or caused by, a condition of bacterial toxaemia, analogous to the bacterial toxaemias of acute and chronic rheumatism. The onset of the disease is always gradual and is associated with mal-nutrition, loss of body weight, nervousness, depres- sion, loss of the capacity for work, sleeplessness and attacks of MEDICAL AND GENERAL] INSANITY 603 restlessness. These attacks of restlessness become more and more marked as self-control diminishes, and as the depression increases the disease passes the borderland of sanity. In the fully developed disease the appearance of the patient is typical. The expression is drawn, depressed, anxious or apprehensive. The skin is yellow and parchment like. The hair is often dry and stands out stiffly from the head. The hands are in constant movement, twisting and untwisting, picking the skin, pulling at the hair or tearing at the clothes. The patient moans continuously, or emits cries of grief and wanders aimlessly. Mentally the patient, although depressed, miserable and self- absorbed, is not confused. There is complete consciousness except during the height of a paroxysm of restlessness and de- pression, and the patient can talk and answer questions clearly and intelligently, but takes no interest in the environment. Some of the patients suffer from delusions, generally a sense of impending danger, but very few suffer from hallucinations. Physically there is loss of appetite, constipation and rapid heart action, a great increase in the number of the white blood corpuscles, particularly of the multinucleated cells which are frequently increased in bacterial infections. In the blood serum also there can be demonstrated the presence of agglutinines to certain members of the streptococci group. The course of the disease is prolonged and chronic. The acute symptoms tend to remit at regular intervals, the patient becoming more quiet and less demonstratively depressed; but as a rule these remissions are extremely temporary. Excited melancholia is a disease characterized by repeated relapses, and recoveries are rare in cases above the age of forty. Treatment. — There is no curative treatment for excited melan- cholia. The patient must be carefully nursed ; kept in bed during the exacerbations of the disease and treated with graduated doses of nepenthe or tincture of opium, to secure some amelioration of the acute symptoms. Careful dieting, tonics and baths are of benefit during the remissions of the disease, and in a few cases seem to promote recovery. Folle circulaire, or alternating insanity, was first described by Falret and Baillarger, and more recently Kraepelin has considerably widened the conception of this class of disease, which he describes under the term "manic-depressive insanity." Of the two terms (folie circulaire and manic-depressive insanity) the latter is the more correct. Folie circulaire implies that the disease invariably passes through a complete cycle, which descrip- tion is only applicable to very few of the cases. Manic-depressive insanity implies that the patient may either suffer from excite- ment or depression which do not necessarily succeed one another in any fixed order. As a matter of fact, the majority of patients who suffer from the disease either have marked excited attacks with little or no subsequent depression, or marked attacks of de- pression with a subsequent period of such slight exaltation as hardly to be distinguished from a state of health. Depression of the manic-depressive variety, therefore, may either precede or follow upon an attack of maniacal excitement, or it may be the chief and only obvious symptom of the disease and may recur again and again. The disease attacks men and women with equal frequency, and as a rule manifests itself either late in adolescence or during the decline of life. Hereditary predisposition has been proved to exist in over 50 % of cases, beyond which no definite predisposing cause is at present known. A considerable number of cases follow upon attacks of infective disease such as typhoid fever, scarlet fever or rheumatic fever. The actual exciting cause is probably an intestinal toxaemia of bacterial origin; at all events, mal-nutrition, gastric and intestinal symptoms not infrequently precede an attack, and the condition of the blood— the increase in number in the multinucleated white blood corpuscles and the presence of agglutinines to certain members of the streptococci group of bacteria — are symptoms which have been definitely demon- strated by Bruce in every case so far examined. If the depression is the sequel to an attack of excitement, the onset may be very sudden or it may be gradual. If, on the othei hand, the depression is not the sequel of excitement, the onset i.s very gradual and the patient complains of lassitude, incapacity for mental or physical work, loss of appetite, con- stipation and sleeplessness often for months before the case is recognized as one of insanity. In the fully developed disease the temperature is very rarely febrile, on the contrary it is rather subnormal in character. The stomach is disordered and the bowels confined. The urine is scanty, turbid and very liable to rapid decomposition. The heart's action is slow and feeble and the extremities become cold, blue and livid. In extreme cases gangrene of the lower extremities may occur, but in all there is a tendency to oedema of the extremities. The skin is greasy, often offensive, and the palms of the hands and the soles of the feet are sodden. Mentally there is simple depression, without, in the majority of cases, any implication of consciousness. Many patients pass through attack after attack without suffering from hallucinations or delusions, but in rare cases hallucinations of hearing and sight are present. Delusions of unworthiness and unpardonable sin are not uncommon, and if once expressed are liable to recur again during the course of each successive attack. The disease is prolonged and chronic in its course, and the condition of the patient varies but little from day to day. When the depression follows excitement, the patient as a rule becomes fat and flabby. On the other hand, if the illness commences with depression, the chief physical symptoms are mal-nutrition and loss of body weight, and the return to health is always preceded by a return of nutrition and a gain in body weight. The attacks may last from six months to two or three years. The intervals between attacks may last for only a few weeks or months or may extend over several years. During the interval the patient is not only capable of good mental work but may show capacity of a high order. In other words this form of mental disorder does not tend to produce dementia; the explanation probably being that between the attacks there is no toxaemia. Treatment. — There is no known curative treatment for the de- pression of manic-depressive insanity, but the depression, the sleeplessness and the gastric disorder are to some extent mitigated by common sense attention to the general health of the body. If the patient is thin and wasted, then treatment is best conducted in bed. The diet should be bland, consisting largely of milk, eggs and farinaceous food, given in small quantities and frequently. Defecation should be maintained by enemata, and the skin kept clean by daily warm baths. What is of much more importance is the fact that in some instances subsequent attacks can be prevented by impressing upon the patient the necessity for attending to the state of the bowels, and of discontinuing work when the slightest symptoms of an attack present themselves. If these symptoms are at all prominent, rest in bed is a wise precaution, butcher-meat should be discontinued from the dietary and a tonic of arsenic or quinine and acid prescribed. Mania. — The term mania, meaning pathological elevation or excitement, has, like the term melancholia, been applied to all varieties of morbid mental conditions in which M _„.. • - 1 Mania. the prevailing mental symptom is excitement or eleva- tion. As in melancholia so in mania various subdivisions have been invented, such as delusional mania, religious mania, homi- cidal mania, according to the special mental characteristics of each case, but such varieties are of accidental origin and cannot be held to be subdivisions. Under the term mania two distinct diseased conditions can be described, viz. acute mania, and the elevated stage of folie circu- laire or manic-depressive insanity. Acute Mania. — Acute mania is a disease which attacks both sexes at all ages, but its onset is most prevalent during adoles- cence and early adult life. Hereditary predisposition, physical and mental exhaustion, epileptic seizures and childbirth are all predisposing causes. The direct exciting cause or causes are un- known, but the physical symptoms suggest that the condition is one of acute toxaemia or poisoning, and the changes in the blood are such as are consequent on bacterial toxaemia. The onset is gradual in the large majority of cases. Histories of sudden outbursts of mania can rarely be relied on, as the illness is almost invariably preceded by loss of body weight, sleepless- ness, bad dreams, headaches and symptoms of general malaise, sometimes associated with depression. The actual onset of the mental symptoms themselves, however, are frequently sudden. 604 INSANITY [MEDICAL AND GENERAL A typical case of the fully developed disease is not easily mistaken. | sound mental health. A few cases die, exhausted by the acute- The patient is usually anaemic and thin, the expression of the face is unnatural, the eyes widely opened and bright; and there is great motor restlessness, the muscular movements being purposeless and inco-ordinate. This inco-ordination of movement affects not only the muscles of the limbs and trunk but also those of expression, so that the usual aspect of the face becomes entirely altered. The temperature is generally slightly febrile. The tongue and lips are cracked and dry through excessive shouting or speaking. There is often no desire for food or drink. The heart's action is rapid and forcible. The skin is soft and moist. The urine is scanty, turbid and loaded with urates. The white blood corpuscles per cubic millimetre of blood are markedly increased, and the blood serum contains agglutinines to certain strains of streptococci which are not present in healthy persons. Sensibility to pain is lost or much impaired. Such patients will swing and jerk a broken limb apparently unaware that it is broken. Sleep is absent or obtained in short snatches, and even when asleep the patient is often restless and talkative as if the disease processes were still active. Mentally the patient is excited, often wildly so, quite confused and unable to recognize time or place. Answers to questions may sometimes be elicited by repeated efforts to engage the attention of the patient. The speech is incoherent, and for all practical purposes the patient is mentally inaccessible. This state of acute excitement lasts usually for two or three weeks and gradually passes into a condition of chronic restlessness and noise, in which I the movements are more co-ordinate and purposeful. The con- fusion of the acute stage passes off and the attention can be more readily attracted but cannot be concentrated on any subject for any length of time. The patient will now recognize friends, but the affections are in abeyance and the memory is de- fective. The appetite becomes insatiable, but the patient does not necessarily gain in weight. This stage of subacute excitement may last for months, but as a rule favourable cases recover within six months from the onset of the disease. A recovering patient gradually gains weight, sleeps soundly at night and has periods of partial quiescence during the day, particularly in the morning after a good night's sleep. These lucid intervals become more and more prolonged and finally pass into a state of sanity. Some cases on the other hand, after the acute symptoms decline, remain confused, and this state of confusion may last for months; by some alienists it is described as secondary stupor. The symptoms detailed above are those typical of an attack such as is most frequently met with in adult cases. Acute mania, however, is a disease which presents itself in various forms. Adolescent cases, for instance, very commonly suffer from re- current attacks, and the recurrent form of the disease is also to be met with in adults. The recurrent form at the onset does not differ in symptoms from that already described, but the course of the attack is shorter and more acute, so that the patient after .one or two weeks of acute excitement rapidly improves, the mental symptoms pass off and the patient is apparently perfectly recovered. An examination of the blood, however, reveals the fact that the patient is still suffering from some disorder of the system, inasmuch as the white blood corpuscles remain increased above the average of health. Subsequent attacks of excitement come on without any obvious provocation. The pulse becomes fast and the face flushed. The patient frequently complains of fullness in the head, ringing in the ears and a loss of appetite. Sleeplessness is an invariable symptom. Self-control is generally lost suddenly, and the patient rapidly passes into a state of delirious excitement, to recover again, appar- ently, in the course of a few weeks. Recurrent mania might therefore be regarded as a prolonged toxaemia, complicated at intervals by outbursts of delirious excitement. Acute mania in the majority of cases ends in recovery. In the continuous attack the recovery is gradual. In the recurrent cases the intervals between attacks become longer and the attacks less severe until they finally cease. In such recovered cases very frequently a persistent increase in the number of the white blood corpuscles is found, persisting for a period of two or three years of apparently ness of the excitement and inability to obtain rest by the natural process of sleep. When death does occur in this way the patient almost invariably passes into the typhoid state. The residue of such cases become chronic, and chronicity almost invariably means subsequent dementia. The chronic stage of acute mania may be represented by a state of continuous subacute excitement in which the patient becomes dirty and destructive in habits and liable from time to time to exacerba- tions of the mental symptoms. Continuous observation of the blood made in such cases over a period extending for weeks reveals the fact that the leucocytosis, if represented in chart form, shows a regular sequence of events. Just prior to the onset of an exacerbation the leucocytosis is low. As the excitement increases in severity the leucocytosis curve rises, and just before improvement sets in there may be. a decided rise in the curve and then a subsequent fall; but this fall rarely reaches the normal line. In other cases, which pass into chronicity, a state of persistent delusion, rather than excitement, is the prevailing mental characteristic, and these cases may at recurrent intervals become noisy and dangerous. Treatment. — Acute mania can only be treated on general lines. During the acute stage of onset the patient should be placed in bed. If there is difficulty in inducing the patient to take a sufficient quantity of food, this difficulty can be got over by giving food in liquid form, milk, milk-tea, eggs beaten up in milk, meat juice and thin gruel, and it is always better to feed such a patient with small quantities given frequently. Cases of mania following childbirth are those which most urgently demand careful and frequent feeding, artificially administered if necessary. If there is any tendency to exhaustion, alcoholic stimulants are indicated, and in some cases strychnine, quinine and cardiac tonics are highly .beneficial. The bowels should be unloaded by large enemata or the use of saline purgatives. The continuous use of purgatives should as a rule be avoided, as they drain the system of fluids. On the other hand, trie administration of one large normal saline enema by supplying the tissues with fluids, and probably thereby diluting the toxins circulating in the system, gives considerable relief. A continuous warm bath frequently produces sleep and reduces excitement. The sleeplessness of acute mania is best treated bv warm baths wherever possible, and if a drug must be administered, then paraldehyde is the safest and most certain, unless the patient is also an alcoholic, when chloral and bromide is probably a better sedative. The Elevated Stage of Foiie Circulaire or Manic Depressive Insanity. — As previously mentioned in the description of the depressed stage of this mental disorder, the disease is equally prone to attack men and women, generally during late adolescence or in early adult life, and in a few cases first appears during the decline of life. Hereditary predisposition undoubtedly plays a large part as a predisposing cause, and after that is said it is difficult to assign any other definite predisposing causes and certainly no exciting causes. As in the stage of depression, so in the stage of excitement the first attack may closely follow upon typhoid fever, erysipelas or rheumatic fever. On the other hand many cases occur without any such antecedent disease. Another fact which has been commented upon is that these patients at the onset of an attack of excitement often appear to be in excellent physical health. The earliest symptoms of onset are moral rather than physical, The patient changes in character, generally for the worse. The sober man becomes intemperate. The steady man of business enters into foolish, reckless speculation. There is a tendency for the patient to seek the society of inferiors and to ignore the recognized conventionalities of life and decency. The dress becomes extravagant and vulgar and the speech loud, boastful and obscene. These symptoms may exist for a considerable period before some accidental circumstance or some more than usually extravagant departure from the laws and customs of civilization draws public attention to the condition of the patient. The symptoms of the fully developed disease differ in degree in different cases. The face is often flushed and the expression unnatural. There is constant restlessness, steady loss of body weight, and sleeplessness. In very acute attacks there are frequently symptoms of gastric disorder, while in other cases the appetite is enormous, gross and perverted. The leucocytosis is above that usually met with in health, and the increase in the MEDICAL AND GENERAL] INSANITY 605 early stages is due to the relative and absolute increase in the multinucleated or polymorphonuclear leucocytes. The hyper- leucocytosis is not, however, so high as it is in acute mania, and upon recovery taking place the leucocytosis always falls to normal. In the serum of over 80% of cases there are present agglutinines to certain strains of streptococci, which agglutinines are not present in the serum of healthy persons. The changes in the urine are those which one would expect to find in persons losing weight; the amount of nitrogenous output is in excess of the nitrogen ingested in the food. Mentally there is always exaltation rather than excitement, and when excitement is present it is never of a delirious nature, that is to say, the patient is cognizant of the surroundings, and the special senses are abnormally acute, particularly those of sight and hearing. Hallucinations and delusion are sometimes present, but many cases pass through several attacks without exhibiting either of these classes of symptoms. The patient is always garrulous and delighted to make any chance acquaint- ance the confidant of his most private affairs. The mood is sometimes expansive and benevolent, interruption in the flow of talk may suddenly change the subject of the conversation or the patient may with equal suddenness fly into a violent rage, use foul and obscene language, ending with loud laughter and protestations of eternal friendship. In other words the mental processes are easily stimulated and as easily diverted into other channels. The train of thought is, as it were, constantly being changed by accidental associations. Although consciousness is not impaired, the power of work is abolished as the attention cannot be directed continuously to any subject, and yet the patient may be capable of writing letters in which facts and fiction are most ingeniously blended. A typical case will pass through the emotions of joy, sorrow and rage in the course of a. few minutes. The memory is not impaired and is often hyper- acute. The speech may be rambling but is rarely incoherent. The course of the attack is in some cases short, lasting for from one to three weeks, while in others the condition lasts for years. The patient remains in a state of constant restlessness, both of body and mind, untidy or absurd in dress, noisy, amorous, vindictive, boisterously happy or virulently abusive. As time passes a change sets in. The patient sleeps better, begins today on flesh, the sudden mental fluctuations become less marked and finally disappear. Many of these patients remember every detail of their lives during the state of elevation, and many are acutely ashamed of their actions during this period of their illness. As a sequel to the attack of elevation there is usually an attack of depression, but this is not a necessary sequel. The majority of patients recover even after years. of illness, but the attacks are always liable to recur. Even recurrent attacks, however, leave behind them little if any mental impair- ment. Treatment. — General attention to the health of the body, and an abundance of nourishing food, and, where necessary, the use of sedatives such as bromide and sulphonal, sum up the treatment of the elevated stage of manic-depressive insanity. In Germany it is the custom to treat such cases in continuous warm baths, extending sometimes for weeks. The use of warm baths of several hours' duration has not proved satisfactory. Delusional Insanity. — Considerable confusion exists at the present day regarding the term delusional insanity. It is not correct to define the condition as a disease in which fixed delusions dominate the conduct and are the chief mental symptom present. Such a definition would include many chronic cases of melancholia and mania. All patients who suffer from attacks of acute insanity and who do not recover tend to become delusional, and any attempt to include and describe such cases in a group by them- selves and term them delusional insanity is inadmissible. The fact that delusional insanity has been described under such various terms as progressive systematized insanity, mania of persecution and grandeur, monomanias of persecution, unseen agency, grandeur and paranoia, indicates that the disease is obscure in its origin, probably passing through various stages, and in some instances having been confused with the terminal Delusional Insanity. stages of mania and melancholia. If this is admitted, then probably the best description of the disease is that given by V. Magnan under the term of "systematized delusional insanity," and it may be accepted that many cases conform very closely to Magnan's description. The disease occurs with equal frequency in men and women, and in the majority of cases commences during adolescence or early adult life. The universally accepted predisposing cause is hereditary predisposition. As to the exciting causes nothing is known beyond the fact that certain forms of disease, closely resembling delusional insanity, are apparently associated or caused by chronic alcoholism or occur as a sequel to syphilitic infection. In the vast majority of cases the onset is lost in obscurity, the patient only drawing attention to the diseased condition by insane conduct after the delusional state is definitely established. The friends of such persons frequently affirm that the patient has always been abnormal. However this may be, there is no doubt that in a few cases the onset is acute and closely resembles the onset of acute melancholia. The patient is depressed, confused, suffers from hallucinations of hearing and there are disturbances of the bodily health. There is generally mal-nutrition with dyspepsia and vague neuralgic pains, often referred to the heart and intestines. Even at this stage the patient may labour under delusions. These acute attacks are of short duration and the patient apparently recovers, but not uncommonly both hallucinations and delusions persist, although they may be concealed. The second or delusional stage sets in very gradually. This is the stage in which the patient most frequently comes under medical examination. The appearance is always peculiar and unhealthy. The manner is unnatural and may suggest a state of suspicion. The nutrition of the body is below par, and the patient frequently complains of indefinite symptoms of malaise referred to the heart and abdomen. The heart's action is often weak and irregular, but beyond these symptoms there are no special characteristic symptoms. Mentally there may be depression when the patient is sullen and uncommunicative. It will be found, however, that he always suffers from hallucinations. At first hallucinations of hearing are the most prominent, but later all the special senses may be implicated. These hallucinations constantly annoy the patient and are always more troublesome at night. Voices make accusa- tions through the walls, floors, roofs or door. Faces appear at the window and make grimaces. Poisonous gases are pumped into the room. Electricity, Rontgen rays and marconigrams play through the walls. The food is poisoned or consists of filth. In many cases symptoms of visceral discomfort are supposed to be the result of nightly surgical operations or sexual assaults. All these persecutions are ascribed to unknown persons or to some known person, sect or class. Under the influence of these sensory disturbances the patient may present symptoms of angry excite- ment, impulsive violence or of carefully-thought-out schemes of revenge; but the self-control may be such that although the symptoms are concealed the behaviour is peculiar and unreason- able. It is not uncommon to find that such patients can converse rationally and take an intelligent interest in their environments, but the implication of the capacity of judgment is at once apparent whenever the subject of the persecutions is touched upon. All cases of delusional insanity at this stage are dangerous and their actions are not to be depended upon. Assaults are common, houses are set on fire, threatening letters are written and accusa- tions are made which may lead to much worry and trouble before the true nature of the disease is realized. This, the second or persecutory stage of delusional insanity, may persist through life. The patient becomes gradually accustomed to the sensory disturbances, or possibly a certain amount of mental enfeeblement sets in which reduces the mental vigour. In other cases, the disease goes on to what Magnan calls the third stage or stage of grandiose delusions. The onset of this stage is in some cases gradual. The patient, while inveighing against the persecu- tions, hints at a possible cause. One man is an inventor and his enemies desire to deprive him of the results of his inventions. 6o6 INSANITY [MEDICAL AND GENERAL Another is the rightful heir to a peerage, of which he is to be deprived. Women frequently believe themselves to be abducted princesses or heirs to the throne. Others of both sexes, even more ambitious, assume divine attributes and proclaim them- selves Virgin Marys, Gabriels, Holy Ghosts and Messiahs. Cases are recorded in which the delusions of grandeur were of sudden onset, the patient going to bed persecuted and miserable and rising the following morning elated and grandiose. In this stage the hallucinations persist but appear to change in character and become pleasant. The king hears that arrangements are being made for his coronation and waits quietly for the event. The angel Gabriel sees visions in the heavens. The heirs and heiresses read of their prospective movements in the court columns of the daily papers and are much soothed thereby. In short, no delusion is too grotesque and absurd for such patients to believe and express. Cases of delusional insanity never become demented in the true sense of the word, but their mental state might be described as a dream in which an imaginary existence obliterates the experiences of their past lives. Treatment. — No treatment influences the course of the disease. During the stage of persecution such patients are a danger to them- selves, as they not infrequently commit suicide, and to their supposed persecutors, whom they frequently assault or otherwise annoy. Katatonia. — This disease, so called on account of the symptom of muscular spasm or rigidity which is present during certain of its stages, was first described and named by K. L. toaia. Kahlbaum in 1874. Many British alienists refuse to accept katatonia as a distinct disease, but as it has been accepted and further elaborated by such an authority as E. Kraepelin reference to it cannot be avoided. Katatonia attacks women more frequently than men, and is essentially a disease of adolescence, but typical cases occasionally occur in adults. Hereditary predisposition is present in over 50% of the cases and is the chief predisposing cause. Childbirth, worry, physical strain and mental shocks are all advanced as secondary predisposing causes. The disease is one of gradual onset, with loss of physical and mental energy. Probably the earliest mental symptom is the onset of aural hallucinations. For convenience of description the disease may be divided into (1) the stage of onset; (2) the stage of stupor; (3) the stage of excitement. The symptoms of the stage of onset are disorders of the alimentary tract, such as loss of appetite, vomiting after food and obstinate constipation. The pulse is rapid, irregular and intermittent. The skin varies between extreme dryness and drenching perspira- tions. In women the menstrual function is suppressed. At un- certain intervals the skeletal muscles are thrown into a condition of rigidity, but this symptom does not occur invariably. The instincts of cleanliness are in abeyance, owing to the mental state of the patient, and as a result these cases are inclined to be wet and dirty in their habits. Mentally there is great confusion, vivid hallucinations, which • apparently come on at intervals and are of a terrifying nature, for the patient often becomes frightened, endeavours to hide in corners or escape by a window or door. A very common history of such a case prior to admission is that the patient has attempted suicide by jumping out of a window, the attempt being in reality an un- conscious effort on the part of the patient to escape from some imaginary danger. During these attacks the skin pours with perspiration. The patient is oblivious to his surroundings and is mentally inaccessible. In the intervals between these attacks the patient may be conscious and capable of answering simple questions. This acute stage, in which sleep is abolished, lasts from a few days to four or six weeks and then, generally quite sud- denly, the patient passes into the state of stupor. In some cases a sharp febrile attack accompanies the onset of the stupor, while in others this symptom is absent; but in every case examined by Bruce during the acute stage there was an increase in the number of the white blood corpuscles, which, just prior to the onset of stupor, were sometimes enormously increased; the in- crease being entirely due to multiplication of the multinucleated or polymorphonuclear leucocytes. In the second or stuporose stage of the disease the symptoms are characteristic. The patient lies in a state of apparent placidity, generally with the eyes shut. Consciousness is never entirely abolished, and many of the patients give unmistakable evidence that they understand what is being said in their presence. Any effort at passive movement of a limb immediately sets up muscular resistance, and throughout this stage the sternomastoid and the abdominal muscles are more or less in a state of over-tension, which is increased to a condition of rigidity if the patient is interfered with in any way. This symptom of restiveness or negativism is one of the characteristics of the disease. The patient resists while being fed, washed, dressed and undressed, and even the normal stimuli which in a healthy man indicate that the bladder or rectum require to be emptied are resisted, so that the bladder may become distended and the lower bowel has to be emptied by enemata. The temperature is low, often subnormal, the pulse is small and weak, and the extremities cold and livid. This symptom is probably due in some part to spasm of the terminal arterioles. Mentally the symptoms are negative. Though conscious, the patient cannot be got to speak and apparently is oblivious to what is passing around. Upon recovery, however, these cases can often recount incidents which occurred to them during their illness, and may also state that they laboured under some delusion. Coincidently with the onset of the stupor sleep returns, and many cases sleep for the greater part of the twenty-four hours. The duration of the stuporose state is very variable. In some cases it lasts for weeks, in others for months or years, and may be the terminal stage of the disease, the patient gradually sinking into dementia or making a recovery. The third stage or stage of excitement comes on in many cases during the stage of stupor: the stages overlap; while in others a distinct interval of convalescence may intervene between the termination of the stupor and the onset of the excitement. The excitement is characterized by sudden impulsive actions, rhythmical repetition of words and sounds (verbigeration), and by rhythmical movements of the body or limbs, such as swaying the whole frame, nodding the head, swing- ing the arms, or walking in circles. The patient may be absolutely mute in this stage as in the stage of stupor. Others again are very noisy, singing, shouting or abusive. The speech is staccato in character and incoherent. Physically the patient, who often gains weight in the stage of stupor, again becomes thin and haggard in appearance owing to the incessant restlessness and sleeplessness which characterize the stage of excitement. The patient may, during the stage of onset, die through exhaustion, or accidentally and unconsciously commit suicide usually by leaping from a window. During the stuporose stage symptoms of tubercular disease of the lungs may commence. All the adolescent insane are peculiarly liable to contract and die from tubercular disease. Accidental suicide is also liable to occur during this stage. The stage of excitement, if at all prolonged, invariably ends in dementia. According to Kraepelin 13% of the cases recover, 27 make partial recoveries, and 60% become more or less demented. Treatment. — No treatment arrests or diverts the course of katatonia, and the acute symptoms of the disease as they arise must be treated on hospital principles. Hebephrenia. — This is a disease of adolescence (Gr. ^/Srjl which was first described by Hecker and Kahlbaum and more recently by Kraepelin and other foreign workers. Hebephrenia is not yet recognized by British alienists, phrenia. The descriptions ot the disease are indefinite and confusing, but there are some grounds for the belief that such an entity does exist, although it is probably more correct to say that as yet the symptoms are very imperfectly understood Hebephrenia is always a disease of adolescence and never occurs during adult life. It attacks women more frequently than men, and according to Kahlbaum hereditary predisposition to insanity is present in over 50% of the cases attacked. The onset of the disease is invariably associated with two symptoms. On the physical side an arrested or delayed development and on the mental a gradual failure of the power of attention and MEDICAL AND GENERAL] INSANITY 607 Traumatic Insanity. concentrated thought. The onset of the condition is always gradual and the symptoms which first attract attention are mental. The patient becomes restless, is unable to settle to work, becomes solitary and peculiar in habits and sometimes dissolute and mischievous. As the disease advances the patient becomes more and more enfeebled, laughs and mutters to himself and wanders aimlessly and without object. There is no natural curiosity, no interest in life and no desire for occupation. Later, delusions may appear and also hallucinations of hearing, and under their influence the patient may be impulsive and violent. Physically the subjects are always badly developed. The temperature is at times slightly elevated and at intervals the white blood corpuscles are markedly increased. The menstrual function in women is suppressed and both male and female cases are addicted to masturbation. According to Kraepelin 5% of the cases recover, 15% are so far relieved as to be able to live at home, but are mentally enfeebled, the remaining 80% become hopelessly demented. The patients who recover fre- quently show at the onset of their disease acute symptoms, such as mild excitement, slightly febrile temperature and quick pulse-rate. When recovery does take place there is marked improvement in development. The subjects of hebephrenia are peculiarly liable to tubercular infection and many die of phthisis. There is no special treatment for hebephrenia beyond attention to the general health. Insanity following upon Injuries to the Brain, or Apoplexies or Tumours or Arterial Degeneration, (a) Traumatic Insanity. — Insanity following blows on the head is divided into (1) the forms in which the insanity immedi- ately follows the accident ; (2) the form in which there is an intermediate prodromal stage characterized by strange conduct and alteration in disposition; and (3) in which the mental symptoms occur months or years after the accident, which can have at most but a remote pre- disposing causal relation to the insanity. The cases which immediately succeed injuries to the head are in all respects similar to confusional insanity after operations or after fevers. There is generally a noisy incoherent delirium, accompanied by hallucinations of sight or of hearing, and fleeting unsystematized delusions. The physical symptoms present all the features of severe nervous shock. In those cases in which there is an intervening prodromal condition, with altered character and disposition, there is usually a more or less severe accidental implication of the cortex cerebri, either by depression of bone or local hemorrhage, or meningitic sub-inflammatory local lesions. Most of the cases during the prodromal stage are sullen, morose or suspicious, and indifferent to their friends and surroundings. At the end of the prodromal stage there most usually occurs an attack of acute mania of a furious impulsive kind. The cases which for many years after injury are said to have remained sane will generally be found upon examination and inquiry to exhibit symptoms of hereditary degeneration or of acquired degeneracy, which may or may not be a consequence of the accident. The most common site of vascular lesion is one of the branches of the middle cerebral artery within the sylvian fissure, or of one of the smaller branches of the same artery which go directly to supply the chief basal ganglia. When an artery like the middle cerebral or one of its branches becomes either through rupture or blocking of its lumen, incapable of performing its function qf supplying nutrition to important cerebral areas, there ensues devitality of the nervous tissues, frequently followed by softening and chronic inflammation. It is these secondary changes which give rise to and maintain those peculiar mental aberrations known as post-apoplectic insanity. Various characteristic physical symptoms, depending upon the seat of the cerebral lesion, are met with in the course of this form of insanity. These consist of paraplegias, hemiplegias and muscular contractures. Speech defects are very common, being due either to the enfeebled mental condition, to paralysis of the nerve supplying the muscles of the face and tongue, or to aphasia caused by implication of those parts of the cortex which are intimately associated with the faculty of speech. Mental symptoms vary considerably in different cases and in accordance with the seat and extent of the lesion. There is almost always present, however, a certain degree of mental enfeeblement, accompanied by loss of memory and of judgment, often by mental confusion. Another very general mental symptom is the presence of emotionalism which leads the patient to be affected either to tears or to laughter upon trifling and inadequate occasions. Cerebral tumours do not necessarily produce insanity. Indeed it has been computed that not one half of the cases become insane. When insanity appears it is met with in all degrees varying from slight mental dulness up to complete dementia, and from mere moral perversion up to the most intense form of maniacal excitement. On the physical side the various symptoms of cerebral tumour such as coma, ataxia, paralysis, headache, vomiting, optic neuritis and epileptiform convulsions are met with. All forms of so-called moral changes and of changes of disposition are met with as mental symptoms and all the ordinary forms of insanity may occur in varying in- tensity; but by far the most common mental change occurring in connexion with cerebral tumour is a progressive enfeeble- ment of the intelligence, unattended with any more harmful symptoms than mental deterioration which ends in complete dementia. (b) Arterial Degeneration. — Arterial degeneration is a common cause of mental impairment, especially of that form j asan n y of mental affection known as " Early " dementia, due to It also predisposes to embolism and thrombosis, Arterial which often results in the paralytic and aphasic Degenera- groups of nerve disturbance, and which are always °°' accompanied by more or less marked interference with normal cerebral action. The commonest seat for atheroma of the cerebral vessels is the arteries at the base of the brain and their main branches, especi- ally the middle cerebral. As a general rule the other arteries of the cerebrum are not implicated to the same extent, although in a not inconsiderable number of cases of the disease all the arteries of the brain may participate in the change. When this is so, we obtain those definite symptoms of slowly advancing dementia commencing in late middle life and ending in complete dementia before the usual period for the appearance of senile dementia. The same appearances are met with in certain patients who have attained the age in which senile changes in the arteries are not unexpected. As a rule atheroma in the cerebral vessels is but a part of a general atheroma of all the arteries of the body. Atheroma is common after middle life and increases in frequency with age. The chief causes are syphilis, alcoholism, the gouty and rheumatic diatheses and above all Bright's disease of the kidneys. Perhaps certain forms of Bright's disease, owing to the tendency to raise the blood pressure, are of all causes the most common. It is not easy to say to what extent, alone, the arteriosclerosis is effectual in inducing the gradual failure of the mental powers, and to what extent it is assisted in its operation by the action on the brain-cells of the general toxic substances which give rise to the arterial atheroma. In any case there can be no question that the gradual mechanical diminution of the blood-supply to the cortex caused by the occlusion of the lumen of the arteries is a factor of great importance in the production of mental incapacity. General Paralysis of the Insane (syn. General Paralysis, dementia paralytica, progressive dementia) is a disease character- ized by symptoms of progressive degeneration of the central nervous system, more particularly of the motor p" er . a , centres. The disease is almost invariably fatal. Apparent recoveries do very occasionally occur, though this is denied by the majority of alienists. The disease is in every case associated with gradually advancing mental enfeeble- ment, and very frequently is complicated by attacks of mental disease. 6o8 INSANITY {MEDICAL AND GENERAL General paralysis, which is a very common disease, was first recognized in France; it was identified by J. E. D. Esquirol, and further described and elaborated by A. L. J. Bayle, Delaye and J. L. Calmeil, the latter giving it the name of paralysie generate des alienes. As first described by the earlier writers the disease was re- garded as being invariably associated with delusions of grandeur. At the present day this description does not apply to the majority of cases admitted into asylums. The change may be explained as being either due to an alteration in the type of the disease, or more probably the disease is better understood and more frequently diagnosed than formerly, the diagnosis being now entirely dependent on the physical and not on the mental symptoms. This latter may also be the explanation why general paralysis is much more common at the present day in British asylums than it was. The total death-rate from this disease in English and Scottish asylums rose from 1321 in 1894 to 1795 in 1904. General paralysis attacks men much more frequently than women, and occurs between the ages of 35 and 50 years. It is essentially a disease of town life. In asylums which draw their patients from country districts in Scotland and Ireland, the disease is rare, whereas in those which draw their population from large cities the disease is extremely common. Considerable diversity of opinion exists at present regarding the causation of general paralysis. Hereditary predisposition admittedly plays a very small part in its causation. There is, however, an almost universal agreement that the disease is essentially the result of toxaemia or poisoning, and that acquired or inherited syphilitic infection is an important predisposing factor. A history of syphilitic infection occurs in from 70 to 90% ofthe patients affected. At first it was held that general paralysis was a late syphilitic manifestation, but as it was found that no benefit followed the use of anti-syphilitic remedies the theory was advanced that general paralysis was a secondary auto-intoxication following upon syphilitic infection. The latest view is that the disease is a bacterial invasion, to which syphilis, alcoholism, excessive mental and physical strain, and a too exclusively nitrogenous diet, only act as predisposing causes. This latter theory has been recently advanced and elaborated by Ford Robertson and McRae of Edinburgh. Whatever the cause of general paralysis may be, the disease is essentially progressive in character, marked by frequent re- missions and so typical in its physical symptoms and pathology that we regard the bacterial theory with favour, although we are far from satisfied that the actual causative factor has as yet been discovered. For descriptive purposes the disease is most conveniently divided into three stages,— called respectively the first, second and third,— but it must be understood that no clear line of demarcation divides these stages from one another. The onset of general paralysis is slow and gradual, and the earliest symptoms may be either physical or mental. The disease may commence either in the brain itself or the spinal cord may be primarily the seat of lesion, the brain becoming affected secondarily. When the disease originates in the spinal cord the symptoms are similar to those of locomotor ataxia, and it is now, believed that general paralysis and locomotor ataxia are one and the same disease; in the one case the cord, in the other the brain, being the primary seat of lesion. The early physical symptoms are generally motor. The patient loses energy, readily becomes tired, and the capacity for finely co-ordinated motor acts, such as are required in playing games of skill, is impaired. Transient attacks of partial paralysis of a hand, arm, leg or one side of the body, or of the speech centre are not uncommon. In a few cases the special senses are affected early and the patient may complain of attacks of dimness of vision or impairment of hearing. Or the symptoms may be purely mental and affect the highest and most recently acquired attributes of man, the moral sense and the faculty of self-control. The patient then becomes irritable, bursts into violent passions over trifles, changes in character and dibits, frequently takes alcohol to excess and behaves in an extravagant, foolish manner. Theft is often committed in this stage and the thefts are characterized by an open, purposeless manner of commission. The memory is impaired and the patient is easily influenced by others, that is to say he becomes facile. In other cases a wild attack of sudden excitement, following upon a period of restlessness and sleeplessness may be the first symptom which attracts attention. Whatever the mode of onset the physical symptoms which characterize the disease come on sooner or later. The speech is slurred and the facial muscles lose their tone, giving the face a flattened expression. The muscular power is impaired, the gait is straddling and the patient sways on turning. All the muscles of the body, but particularly those of the tongue, upper lip and hands, which are most highly inner- vated, present the symptom of fine fibrillary tremors. The pupils become irregular in outline, often unequal in size and either one or both fail to react normally to the stimuli of light, or of accommodation for near or distant vision. As the disease advances there is greater excitability and a tendency to emotionalism. In classical cases the 'general exaltation of ideas becomes so great as to lead the patient to the commission of insanely extravagant acts, such as purchases of large numbers of useless articles, or of lands and houses far beyond his means, numerous indiscriminate proposals of marriage, the suggestion of utterly absurd commerical schemes, or attempts at feats beyond his physical powers. The mental symptoms," in short, are very similar to those of the elevated stage of manic- depressive insanity. Delusions of the wildest character may also be present. The patient may believe himself to be in possession of millions of money, to be unsurpassed in strength and agility, to be a great and overruling genius, and the recipient of the highest honours. This grandiose condition is by no means present in every case and is not in itself diagnostic of the disease. But mental facility, placid contentment, complete loss of judgment and affection for family and friends, with impaired memory, are symptoms universally present. As the disease advances the motor symptoms become more prominent. The patient has great' difficulty in writing, misses letters out of words, words out of sentences, and writes in a large laboured hand. The expression becomes fatuous. The speech is difficult and the facial muscles are thrown into marked tremors whenever any attempt at speech is made. The voice changes in timbre and becomes high-pitched and monotonous. The gait is weak and uncertain and the re- flexes are exaggerated. In the first stage the patient, through restlessness and sleeplessness, becomes thin and haggard. As the second stage approaches sleep returns, the patient lays on flesh and becomes puffy and unhealthy in appearance. The mental symptoms are marked by greater facility and enfeeblement, while the paralysis of all the muscles steadily advances. The patient is now peculiarly liable to what are called congestive seizures or epileptiform attacks. The temperature rises, the face becomes flushed and the skin moist. Twitchings are noticed in a hand or arm. These twitchings gradually spread until they may involve the whole body. The patient is now unconscious, bathed in perspiration, which is offensive. The bowels and bladder empty themselves reflexly or become distended, and bedsores are very liable to form over the heels, elbows and back. Congestive seizures frequently last for days and may prove fatal or, on the other hand, the patient may have recurrent attacks and finally die of exhaustion or some accidental disease, such as pneumonia. Jn the second stage of the disease the patient eats greedily, and-as the food is frequently swallowed unmasticated, choking is not an uncommon accident. The special senses of taste and smell are also much disordered. We have seen a case of general paralysis, in the second stage drink a glass of quinine and water under the impression that he was drinking whisky. The third stage of the disease is characterized by sleeplessness and rapid loss of body weight. Mentally the patient becomes quite demented. On the physical side the paralysis advances rapidly, so that the patient becomes bed-ridden and speechless. Death may occur as the result of exhaustion, or a congestive seizure, or of some intercurrent illness. MEDICAL AND GENERAL] INSANITY 6oq The duration of the disease is between eighteen months and three years, although it has been known to persist for seven. No curative measures have so far proved of any avail in the treatment of general paralysis. Insanity associated with Epilepsy. — The term " epileptic insanity," which has for many years been in common use, is now regarded as a misnomer. There is in short no insanity. sucri disease as epileptic insanity. A brain, however, which is so unstable as to exhibit the sudden discharges of nervous energy which are known as epileptic seizures, is prone to be attacked by insanity also, but there is no form of mental disease exclusively associated with epilepsy. Many epileptics suffer from the disease for a lifetime and never exhibit symptoms of insanity. The majority of patients, however, who suffer from epilepsy are liable to exhibit certain mental symptoms which are regarded as characteristic of the disease. Some suffer from recurrent attacks of depression, ill-humour and irritability, which may readily pass into violence under provocation. Others are emotionally fervid in religious observances, though sadly deficient in the practice of the religious life. A third class are liable to attacks of semi-consciousness which may either follow upon or take the place of a seizure, and during these attacks actions are performed automatically and without consciousness on the part of the patient. When epileptics do become insane the insanity is generally one of the forms of mania. Either the patient suffers from sudden furious attacks of excitement in which consciousness is entirely abolished, or the mania is of the type of the elevated stage of folie circulaire (manic-depressive insanity) and alternates with periods of deep depression. In the elevated period the patient shows exaggerated self-esteem, with passionate outbursts of anger, and periods of religious emotionalism. While in the stage of depression the patient is often actively suicidal. Epileptic patients who suffer from recurrent attacks of delirious mania are liable to certain nervous symptoms which indicate that not only are the motor centres in the brain damaged, but that the motor tracts in the spinal cord are also affected. The gait becomes awkward and laboured, the feet being lifted high off the ground and the legs thrown forward with a jerk. The tendon reflexes are at the same time exaggerated. These symptoms indicate descending degeneration of the motor tracts of the cord. If the mental attacks partake of the character of elevation or depression the mental functions suffer more than the motor. These patients, in course of time, become delusional, enfeebled and childish, and in some cases the enfeeblement ends in complete dementia of a very degraded type. Where insanity is superadded to epilepsy the prognosis is unfavourable. Insanity associated with or caused by Alcoholic and Drug Intoxication. — The true role of alcoholic indulgence in the production of insanity is at present very imperfectly insanity, understood. In many cases the alcoholism is merely a symptom of the mental disease — a result, not a cause. In others, alcohol seems to act purely as a predisposing factor, breaking down the resistance of the patient and disordering the metabolism to such an extent that bodily disorders are en- gendered which produce well-marked and easily recognized mental symptoms. In others, again, alcohol itself may possibly act as a direct toxin, disordering the functions of the brain. In the latter class may be included the nervous phenomena of drunkenness, which commence with excitement and confusion of ideas, and terminate in stupor with partial paralysis of all the muscles. Certain brains which, either through innate weakness or as the result of direct injury, have become peculiarly liable to toxic influences, under the influence of even moderate quan- tities of alcohol pass into a state closely resembling delirious mania, a state commonly spoken of as mania -a polu. Delirium Tremens. — Delirium tremens is the form of mental disorder most commonly associated with alcoholic indulgence in the lay mind. Considerable doubt exists, however, as to whether the disease is directly or secondarily the result of My, 20 alcoholic poisoning. Much evidence exists in favour of the latter supposition. Delirium tremens may occur in persons who have never presented the symptom of drunkenness, or it may occur weeks after the patient has ceased to drink alcohol, and in such cases the actual exciting cause of the disease may be some accidental complication, such as a severe accident, a surgical operation, or an attack of pneumonia or erysipelas. The early symptoms are always physical. The stomach is disordered. The desire for food is absent, and there may be abdominal pain and vomiting. The hands are tremulous, and the patient is unable to sleep. At this stage the disease may be checked by the administration of an aperient and some sedative such as bromide and chloral. The mental symptoms vary greatly in their severity. In a mild case one may talk to the patient for some time before discovering any mental abnormality, and then it will be found that confusion exists regarding his position and the identity of those around him, while the memory is also impaired for recent events. Hallucinations of sight and hearing may be present. The hallucinations of sight may be readily induced by pressure upon the eyeballs. If the symptoms are more acute they usually come on suddenly, generally during the evening or night. The patient becomes excited, suffers from vivid hallucinations of sight and hearing which produce great fear, and these hallucinations may be so engrossing as to render him quite oblivious to the environment. The hallucinations of sight are characterized by the false sense impressions taking the forms of animals or insects which surround or menace the patient. Visions may also appear in the form of flames, goblins or fairies. The hallucinations of hearing rarely consist of voices, but are more of the nature of whistlings, and ringings in the ears, shouts, groans or screams which seem to fill the air, or emanate from the walls or floors of the room. All the special senses may be affected, but sight and hearing are always implicated. Delirium tremens is a short-lived- disease, generally running its course in from four to five days. Recovery is always preceded by the return of the power of sleep. The patient must be carefully nursed and constantly watched, as homicidal and suicidal impulses are liable to occur under the terrifying influence of the hallucinations. The food should be concentrated and fluid, given frequently and in small quantities. Chronic Alcoholic Insanity. — Almost any mental disorder may be associated with chronic alcoholism, but the most characteristic mental symptoms are delusions of suspicion and persecution which resemble very closely those of the persecution stage of systematized delusional insanity. The appearance of the patient is bloated and heavy; the tongue is furred and tremulous, and symptoms of gastric and intestinal disorder are usually present. The gait is awkward and dragging, owing to the partial paralysis of the extensor muscles of the lower limbs. All the skeletal muscles are tremulous, particularly those of the tongue, lips and hands. The common sensibility of the skin is disordered so that the patient complains of sensory disturbances, such as tinglings and prickings of the skin, which may be interpreted as electric shocks. In some cases the mental symptoms may be concealed, but delusions and hallucinations, particularly hallucinations of sight and hearing, are very commonly present. The delusions are often directly the outcome of the physical state; the disordered stomach suggesting poisoning, and the disturbances of the special senses being interpreted as various forms of persecution. The patient hears voices shouting foul abuse at him; all his thoughts are read and repeated aloud; electric shocks are sent through him at night ; gases are pumped into his room. Sexual delusions are very common and frequently affect marital relations by arousing suspicions regarding the fidelity of wife or husband; or the delusions may be more gross and take the form of belief in actual attempts at sexual mutila- tions. The memory is always impaired. Patients who in addition to chronic alcoholism are also insane are always dangerous and liable to sudden and apparently causeless outbursts of violence. Dipsomania. — Dipsomania is a condition characterized by recurrent or periodic attacks of an irresistible cravine for 6io INSANITY [MEDICAL AND GENERAL stimulants. The general bodily condition has a great deal to do with the onset of the attack, that is to say, the patient is more liable to an attack when the bodily condition is low than when the health is good. The attacks may be frequent or recur at very long intervals. They generally last for a few weeks, and may be complicated by symptoms of excitement, delusions or hallucinations. Treatment consists in attention to the general health between attacks, with the use of such tonics as arsenic and strychnine. During the attack the patient should be confined to bed and treated with sedatives. Morphinism.— -The morphia habit is most commonly con- tracted by persons of a neurotic constitution. The mental symptoms associated with the disease may arise either as the result of an overdose, when the patient suffers from hallucinations, confusion and mild delirium, frequently associated with vomiting. On the other hand, mental symptoms very similar to those of delirium tremens may occur as the result of suddenly cutting off the supply of morphia in a patient addicted to the habit. Finally, chronic morphia intoxication produces mental symptons very similar to those of chronic alcoholism. This latter condition, characterized by delusions of persecution, mental enfeeblement and loss of memory, is hopelessly incurable. The patient is always thin and anaemic on account of digestive disturbances. There is weakness or slight paralysis of the lower limbs, and the skeletal muscles are tremulous. Treatment. — The quantity of the drug used must be gradually reduced until it is finally discontinued, and during treatment the patient must be confined to bed. Senile Insanity. — States of mental enfeeblement are always the result of failure of development or of structural changes in the cortical grey matter of the brain. If the enfeeble- lasaalty. me nt is due to failure of development or brain damage occurring in early life, it is spoken of as idiocy or imbecility. Every form of insanity which occurs after a certain period of life is apt to be regarded by some observers as senile, but although the failing mental power may colour the character of the symptoms it cannot be regarded as correct to designate, for instance, a recurrent form of mania as senile merely because it necessarily manifests itself in a subject who has lived into the senile period. On the other hand, many persons first suffer from mental derangement at an advanced period of life without at the same time manifesting any marked failure of mental power, while others only manifest their insanity as a result of the decay of their mental faculties. From this statement it will be seen that senile insanity is a complex of different conditions, some of them accompanied by dementia, others without dementia. Senile Dementia is distinguished occasionally Into " senile " properly so called, and " presenile " dementia, which supervenes at middle age or even- earlier. The occurrence of dementia is sometimes preceded by an acute hallucinatory phase, accompanied by mania or melancholia; but as a general rule, in the presenile cases, by neurasthenia, indifference, and mental apathy which extends to a disregard for the ordinary conventions and the means of subsistence. It has pithily been remarked that the age of a man is the age of his blood-vessels. The two conditions of senile and presenile dementia cannot therefore be separated scientifically. From a clinical point of view, however, the two are distinguishable in so far as their symptoms are concerned, for the presenile cases are more complete and the process of dementia achieves its consummation earlier and quicker, while in the senile the gradual disease of the arteries and the slow decay of the mental faculties offer a different background for the manifestation of mental symptoms. Moreover, the senile patients more frequently present symptoms of recurrent attacks of acute insanity, a more pronounced emotionalism, and a greater tendency to restlessness at night. The presenile cases, on the other hand, except at the commencement of their malady, are usually free from acute and troublesome symptoms and present chiefly an apathetic indif- ference and irresponsiveness on the mental side, and on the physical side a neurasthenic and enfeebled bodily state. In both conditions memory is greatly impaired. Added to senile dementia there is often found a condition of mania or melancholia or even of systematized delusional insanity. The chief symptoms of the maniacal attacks are the great motor restlessness and excitement, which are worst during the night time. Sleep is almost always seriously disturbed, and the patients rapidly become exhausted unless carefully nursed and tended. The actions of senile maniacs are often puerile and foolish, and they may exhibit impulses of a homicidal, suicidal or sexual character. The melancholic cases are also extremely restless, and their emotion is loudly expressed in an uncontrollable manner. They often have delusions of persecution. Their cries and groans have an automatic character, as if the patient, though compelled to utter them, did not experience the mental pain which he expressed. They also, many of them, eat their food ravenously, although a few obstinately refuse it. The senile delusional cases may manifest any of the classical forms of paranoia described above, but their delusions are of a rudimentary and unfinished type. The most common of all senile delusions is that they are being robbed. They therefore often hide their small valuables in corners and out-of-the-way places, and as their memories are very defective they are afterwards unable to find them. Others, who live alone, barricade their doors and try to prevent any one entering for fear of thieves. Delusions of ambition in senile subjects are usually of a very improbable and childish character. Hallucinations are generally present in the senile delusional cases. The treatment of senile insanity is from the medical point of view not hopeful; it resolves itself largely into instructions for careful nursing, suitable feeding, and the protection of the patient from all the physical dangers to which he may be exposed. Statistics. — The statistics of lunacy are merely of interest from a sociological point of view; for under that term are comprised all forms of insanity. It is needless to produce tables illustrative of the relative numbers of lunatics in the various countries of Europe, the systems of registration being so unequal in their working as to afford no trustworthy basis of comparison. Even in Great Britain, where the systems are more perfect than in any other country, the tables published in the Blue Books of the three countries can only be regarded as approximately correct, the difficulty of registering all cases of lunacy being insuperable. On the 1st of January 1907, according to the returns made to the offices of the Commissioners in Lunacy, the numbers of lunatics stood thus on the registers : — Males. Females. Totals. England and Wales . Scotland Gross total 57,176 8,594 12,254 66,812 8,999 11,300 123,988 17,593 23.554 78,024 87,111 165,135 These figures show the ratio of lunatics to 100,000 of the popula- tion to be 354 in England and Wales, 312 in Scotland, and 538 in Ireland. Numbers of Lunatics on the 1st of January of the years 1857-IQ07 inclusive, according to Returns made to the Offices of the Com- missioners in Lunacy for England and Wales, Scotland and Ireland. England Years. and Wales. Scotland. Ireland. 1858 5,823 1859 36,762 6,072 i860 38,058 6,273 1861 39,647 6,327 1862 41,129 6,398 8,055 1863 43.118 6,386 7,862 1864 44.795 6,422 8,272 1865 45.950 6,533 8,845 1866 47,648 6,73° 8,964 1867 49,086 6,888 8,962 1868 51,000 7,055 9,086 1869 53,177 7,3io 9,454 1870 54,713 7,571 10,082 1871 56,755 7,729 10,257 1872 58,640 7,849 10,767 1873 60,296 7,982 10,958 LEGAL ASPECTS] INSANITY 61 1 Years. England and Wales. Scotland. Ireland. 1874 60,027 8,069 11,326 1875 63.793 8,225 n,583 1876 64,916 8,509 n,777 1877 66,636 8,862 12,123 1878 68,538 9,097 12,380 1879 69,885 9,386 12.585 1880 7i,l9i 9,624 12,819 1881 73,H3 10,012 13,062 1882 74,842 io,355 13,444 1883 76,765 10,510 13,882 1884 78,528 io,739 14,088 1885 79,704 10,918 H,279 1886 80,156 11,187 14,590 1887 80,891 11,309 14,702 1888 82,643 11,609 15,263 1889 84,340 11,954 15,685 1890 86,067 12,302 16,159 1891 86,795 12,595 16,251 1892 87,848 12,799 16,688 1893 89,822 13,058 17,124 1894 92,067 13,300 17,276 1895 94,081 13,852 17,665 1896 96,446 , 14,093 18,357 1897 99,365 14,500 18,966 1898 101,972 14,906 19,590 1899 105,086 15,399 20,304 1900 106,611 15,663 20,863 1901 107,944 15,899 21,169 1902 110,713 16,288 21,630 1903 113,964 16,658 22,138 1904 "7,199 16,894 22,794 1905 119,829 17,241 22,996 1906 121,979 17,450 23,365 1907 123,988 17,593 23,554 There is thus an increased ratio in England and Wales of lunatics to the population (which in 1859 was 19,686,701, and in 1907 was estimated at 34,945,600) of 1 86-8 per 100,000 as against 354-8, and in Scotland of 15.7 as against 312 per 100,000. The Irish figures on the same basis have increased from 130-9 in 1862 to 538-1 in 1907. The publication of these figures has given rise to the question whether lunacy has actually become more prevalent during the last twenty years, whether there is real increase of the disease. There is a pretty general consent of all authorities that if there has been an increase it is very slight, and that the apparent increase is due, first to the improved systems of registration, and secondly (a far more powerful reason) to the increasing tendency among all classes, and especially among the poorer class, to recognize the less pro- nounced forms of mental disorder as being of the nature of insanity. Thirdly, the grant of four shillings per week which in 1876 was made by parliament from imperial sources for the maintenance of pauper lunatics has induced parochial authorities to regard as lunatics a large number of weak-minded paupers, and to force them into asylums in order to obtain the benefit of the grant and to relieve the rates. These views receive support from the fact that the increase of private patients, i.e. patients who are provided for out of their own funds or those of the family, has advanced in a vastly smaller ratio. In their case the increase, small as it is, can be accounted for by the growing disinclination on the part of the community to tolerate irregularities of conduct due to mental disease. And again, careful inquiry has failed to show a proportional increase of admissions into asylums of such well-marked forms as general paralysis, puerperal mania, &c. The main cause of the registered increase of lunatics is thus to be sought for in the improved registration, and parochial and family convenience. If there is an actual increase, and there is reason for believing that there is a slight actual increase, it is due to the tendency of the population to gravi- tate towards towns and cities, where the conditions of health are inferior to those of rural life, and where there is therefore a greater disposition to disease of all kinds. The futility of seeking for accurate figures bearing on the relative number of lunatics in other countries is illustrated by the tables set forth in a report by the United States Census Bureau. They show that the number of registered lunatics in 1903 was 150,151; in 1890, 74,028; and in 1880, 40,942. An attempt was made in 1890 to estimate the number of insane persons outside of hospitals, which was stated to be 32,457. In 1903 no such attempt was made, as it was admitted that so many sources of fallacy existed as to render it useless. Thus the mere statement that of every 100,000 of the population (calculated at 80,000,000) 186-2 were registered as insane is of no value. Bibliography. — The following are systematic works: Bucknill and Tuke, Psychological Medicine (4th edition, 1879); Griesinger, On Menial Diseases (New Sydenham Society, 1867); Maudsley, The Pathology of Mind (1895); Bevan Lewis, A Text-Book 0} Mental Diseases (1899); Clouston, Clinical Lectures on Mental Diseases (1892); Kraepelin, Psychiatrie (1893); Krafft-Ebing, Lehrbuch der Psychiatrie (J893); Regis, A Practical Manual oj Mental Medicine (London, 1895); Magnan, Lecons cliniques sur les maladies mentales (1897); Mendil, Leitfaden der Psychiatrie (1902); Mercier, A Text-Book of Insanity (1902) ; Lewis C. Bruce, Studies in Clinical Psychiatry (1906) ; Macpherson, Mental Affections (1899) ; Brower-Bannister, Practical Manual of Insanity (1902) ; Ford Robertson, Text-Book of Pathology in Relation to Mental Diseases (1900). (J. B. T.; J. Mn.; L. C. B.) II. Legal Aspects The effect of insanity upon responsibility and civil capacity has been recognized at an early period in every system of law. Roman Law. — In the Roman jurisprudence its consequences were very fully developed, and the provisions and terminology of that system have largely affected the subsequent legal treat- ment of the subject. Its leading principles were simple and well marked. The insane person having no intelligent will, and being thus incapable of consent or voluntary action, could acquire no right and incur no responsibility by his own acts (see Sohm's Inst. Roman Law, 3rd ed. pp. 216, 217, 219); his person and property were placed after inquiry by the magistrate under the control of a curator, who was empowered and bound to manage the property of the lunatic on his behalf (Sohm, p. 513; Hunter, Roman Law, pp. 732-735). The different terms by which the insane were known, such as demens, furiosus, fatuus, although no doubt signifying different types of insanity, did not in Roman law infer any difference of legal treatment. They were popular names, which all denoted the complete deprivation of reason. Medieval Law. — During the middle ages the insane were little protected. Their legal acts were annulled, and their property placed under control, but little or no attempt was made to supervise their personal treatment. In England the wardship of idiots and lunatics, which was annexed before the reign of Edward II. to the king's prerogative, had regard chiefly to the control of their lands and estates, and was only gradually elaborated into the systematic control of their persons and property now exercised under the jurisdiction in lunacy. Those whose means were insignificant were left to the care of their relations or to charity. In criminal law the plea of insanity was unavailing except in extreme cases. About the beginning of the 19th century a very considerable change commenced. The public attention was strongly attracted to the miserable condition of the insane incarcerated in asylums without any efficient check or inspection; and at the same time the medical knowledge of insanity entered on a new phase. The possibility and advantages of a better treatment of insanity were illustrated by eminent physicians, Philippe Pinel in France, H. Tuke in England, Bond, B. Rush and I. Ray in the United States; its physical origin became generally accepted; its mental phenomena were more carefully observed, and its relation was established to other mental conditions. Modern Law.— -From this period we date the commencement of legislation such as that known in England as the Lunacy Acts, which aimed at the regulation and control of all constraint applied to the insane. Hitherto, the criteria of insanity had been very rude, and the evidence was generally of a loose and popular character; but, whenever it was fully recognized that insanity was a disease with which physicians who had studied the subject were peculiarly conversant, expert evidence obtained increased importance, and from this time became prominent in every case. The newer medical views of insanity were thus brought intct contact with the old narrow conception of the law courts, and a controversy arose in the field of criminal law which in England, at least, still continues. Relations between Insanity and Law. — The fact of insanity may operate in law — (1) by excluding responsibility for crime; (2) by invalidating legal acts; (3) by affording ground for depriv- ing the insane person by a legal process of the control of his person and property; or (4) by affording ground for putting him under restraint. Legal Terminology. — Before proceeding, however, to deal with 6l2 INSANITY [LEGAL ASPECTS these matters in succession, it may be desirable to say something with regard to the chief legal terms respecting persons suffering under mental disabilities. The subject is now of less importance than formerly, because the modern tendency of the law is to determine the capacity or responsibility of a person alleged to be insane by considering it with reference to the particular matter or class of matters which brings his mental condition sub judice. But the literature of the law of lunacy cannot be clearly understood unless the distinctions between the different terms employed to describe the insane are kept in view. The term non compos mentis is as old as the statute De praerogativa regis (1325), and is used sometimes, as in that statute, to indi- cate a species contrasted with idiot, sometimes (e.g. in Co. Litt. 246 (b)) as a genus, and afterwards, chiefly in statutes relating to the insane, in connexion with the terms " idiot " and " lunatic " as a word cjusdem generis. The word " idiot " (Gr. Ibios, a private person, one who does not hold any public office, and ISioiT-rjs, an ignorant and illiterate person) appears in the statute De praerogativa regis as fatuus naturalis, and it is placed in contradistinction to non compos mentis. The " idiot " is defined by Sir E. Coke (4 Rep. 124 (6)) as one who from his nativity, by a perpetual infirmity, is non compos mentis, and Sir M. Hale (Pleas of the Crown, i. 29) describes idiocy as " fatuity a nativitate vel dementia naturalis." In early times various artificial criteria of idiocy were suggested. Fitzherbert's test was the capacity of the alleged idiot to count twenty pence, or tell his age, or who were his father and mother (De natura brevium, 233). Swinburne proposed as a criterion of capacity, inter alia, to measure a yard of cloth or name the days in the week ( Testaments, 42). Hale propounded the sounder view that " idiocy or not is a question of fact triable by jury and sometimes by inspection " (Pleas of the Crown, i. 29). The legal incidents of idiocy were at one time distinct in an important particular from those of lunacy. Under the statute De praerogativa regis the king was to have the rents and profits of an idiot's lands to his own use during the life of the idiot, subject merely to an obligation to provide him with necessaries. In the case of the lunatic the king was a trustee, holding his lands and tenements for his benefit and that of his family. It was on account of this difference in the legal con- sequences of the two states that on inquisitions distinct writs, one de idiota inqidrendo, the other de lunatico inquirendo, were framed for each of them. But juries avoided finding a verdict of idiocy wherever they could, and the writ de idiota inquirendo fell into desuetude. A further blow was struck at the distinction when it came to be recognized even by the legislature (see the Idiots Act 1886) that idiots are capable of being educated and trained, and it was practically abolished when the Lunacy Regulation Act 1862, in a provision reproduced in substance in the Lunacy Act 1890, limited the evidence admissible in proof of unsoundness of mind on an inquisition (without special leave of the Master trying the case) to a period of two years before the date of the inquiry, and raised a uniform issue, viz. the state of mind of the alleged lunatic at the time when the inquisition is held. The term " lunatic," derived from the Latin lima in con- sequence of the notion that the moon had an influence on mental disorders, 1 does not appear in the statute-book till the time of Henry VIII. (1541). Coke defines a lunatic as a " person who has sometimes his understanding and sometimes not, qui gaudet lueidis intcrvallis, and therefore he is called non compos mentis so long as he has not understanding " (Co. Litt. 247 (a), 4 Rep. 124 (h)). Hale defines " lunacy " as " interpolated " (i.e. inter- mittent) dementia accidentalis vel adventitia, whether total or (a description, it will be observed, of " partial insanity ") quoad hoc vel illud (Pleas of the Crown, i. 29). In modern times, the word " lunacy " has lost its former precise signification. It is employed sometimes in the strict sense, sometimes in contra- distinction to "idiocy" or "imbecility"; once at least — viz. in the Lunacy Act 1890 — as including " idiot "; and frequently 1 The word for " lunatic " in several other languages has a similar etymology. Cp. Ital. lunatico. Span, alunado, Gr. at\i)viaKos (epileptic) , Ger. mondsiichtig. in conjunction with the vague terms " unsound mind " (non-sane memory) and " insane." Section 116 of the Lunacy Act 1890 has by implication extended the meaning of the term lunacy so as to include for certain purposes the incapacity of a person to manage his affairs through mental infirmity arising from disease or age. " Imbecility " is a state of mental weakness " between the limits of absolute idiocy on the one hand and of perfect capacity on the other " (see 1 Haggard, Eccles. Rep. p. 401). 1. The Criminal Responsibility of the Insane. — The law as to the criminal responsibility of the insane has pursued in England a curious course of development. The views of Coke and Hale give the best exposition of it in the 17th century. Both were agreed that in criminal causes the act and wrong of a madman shall not be imputed to him; both distinguished, although in different language, between dementia naturalis (or a nativitate) and dementia accidentalis or adventitia; and the main points in which the writings of Hale mark an advance on those of Coke are in the elaboration by the former of the doctrine of " partial insanity," and his adoption of the level of understanding of a child of fourteen years of age as the test of responsibility in criminal cases (Pleas of the Crown, i. 29, 30; and see Co. 4 Rep. 124 (b)). In the 18th century a test, still more unsatisfactory than this " child of fourteen " theory, with its identification of " healthy immaturity " with " diseased maturity " (Steph. Hist. Crim. Law, ii. 15°), was prescribed. On the trial of Edward Arnold in 1723 for firing at and wounding Lord Onslow, Mr Justice Tracy told the jury that " a prisoner, in order to be acquitted on the ground of insanity, must be a man that is totally deprived of his understanding and memory, and doth not know what he is doing, no more than an infant, than a brute or wild beast." In the beginning of the 19th century a fresh statement of the test of criminal responsibility in mental disease was attempted. On the trial of Hadfield for shooting at George III. in Drury Lane Theatre on 15th May 1800, Lord Chief Justice Kenyon charged the jury in the following terms: " If a man is in a deranged state of mind at the time, he is not criminally answerable for his acts; but the material part of the case is whether at the very time when the act was committed the man's mind was sane." The practical effect of this ruling, had it been followed, would have been to make the question of the amen- ability of persons alleged to be insane to the criminal law very much one of fact, to be answered by juries according to the particular circumstances of each case, and without being aided or embarrassed by any rigid external standard. But in 181 2, on the trial of Bellingham for the murder of Mr Perceval, the First Lord of the Treasury, Sir James Mansfield propounded yet another criterion of criminal responsibility in mental disease, viz. whether a prisoner has, at the time of committing an offence, a sufficient degree of capacity to distinguish between good and evil. The objection to this doctrine consisted in the fact, to which- the writings of Continental and American jurists soon afterwards began to give prominence, that there are very many lunatics whose general ideas on the subject of right and wrong are quite unexceptionable, but who are yet unable, in con- sequence of delusions, to perceive the wrongness of particular acts. Sir James Mansfield's statement of the law was dis- credited in the case (4 State Tri. (n.s.) 847; 10 CI. and Fin. 200) of Daniel Macnaughton, who was tried in f on ^ s Case! March 1843, before Chief Justice Tindal, Mr Justice Williams and Mr Justice Coleridge, for the murder of Mr Drum- mond, the private secretary of Sir Robert Peel. Mr (afterwards Lord Chief Justice) Cockburn, who defended the prisoner, used Hale's doctrine of partial insanity as the foundation of the defence, and secured an acquittal, Chief Justice Tindal telling the jury that the question was whether Macnaughton was capable of distinguishing right from wrong with respect to the act with which he stood charged. This judicial approval of the doctrine of partial insanity formed the subject of an animated debate in the House of Lords, and in the end certain questions were put by that House to the judges, and answered by Chief Justice Tindal on behalf of all his colleagues except Mr Justice Maule, who gave LEGAL ASPECTS] INSANITY 613 independent replies. The answers to those questions are com- monly called " The Rules in Macnaughton's case," and they still nominally contain the law of England as to the criminal responsi- bility of the insane. The points affirmed by the Rules that must be noted here are the propositions that knowledge of the nature and quality of the particular criminal act, at the time of its com- mission, is the test of criminal responsibility, and that delusion is a valid exculpatory plea, when, and only when, the fancies of the insane person, if they had been facts, would have been so. The Rules in Macnaughton's case are open to serious criticism. They ignore, at least on a literal interpretation, those forms of mental disease which may, for the present purpose, be roughly grouped under the heading " moral insanity," and in which the moral faculties are more obviously deranged than the mental — the affections and the will, rather than the reason, being appar- ently disordered. The test propounded with reference to delu- sions has also been strenuously attacked by medical writers, and especially by Dr Maudsley in his work on Responsibility in Mental Disease, on the ground that it first assumes a man to have a delusion in regard to a particular subject, and then expects and requires him to reason sanely upon it. It may be pointed out, however, that in thus localizing the range of the immunity which insane delusion confers, the criminal law is merely following the course which, mutatis mutandis, the civil law has, with general acceptance, adopted in questions as to the contractual and testamentary capacity of the insane. The Rules in Macnaughton's case have, as regards moral insanity, undergone considerable modification. Soon after they were laid down, Sir (then Mr) James Fitz- James Stephen, in an article in the Juridical Papers, i. 67, on the policy of maintaining the existing law as to the criminal responsibility of the insane, foreshadowed the view which he subsequently propounded in his History of the Criminal Law, ii. 163, that no man wh(J was deprived by mental disease of the power of passing a fairly rational judg- ment on the moral character of an act could be said to " know " its nature and quality within the meaning of the Rules; and it has in recent years been found possible in practice so to manipu- late the test of the criminal responsibility which they prescribed as to afford protection to the accused in the by no means infre- quent cases of insanity which in its literal interpretation it would leave without excuse. In Scotland the Rules in Macnaughton's case are recognized, but, as in England, there is a tendency among judges to adopt a generous construction of them. Mental unsoundness in- sufficient to bar trial, or to exempt from punishment, may still, it is said, be present in a degree which is regarded as reducing the offence from a higher to a lower category, — a doctrine first practically applied in Scotland, it is believed, in 1867 by Lord Deas; and the fact that a prisoner is of weak or ill-regulated mind is often urged with success as a plea in mitigation of punish- ment. The Indian Penal Code (Act XLV. of i860, § 84) expressly adopts the English test of criminal responsibility, but the qualifi- cations noted in the case of Scotland have received some measure of judicial acceptance (see Mayne, Crim. Law Ind., 3rd ed., pp. 403-419; Nelson, Ind. Pen. Code, 3rd ed., pp. 135 et seq.). The Rules in Macnaughton's case have also been adopted in substance in those colonies which have codified the criminal law. The following typical references may be given: 55 and 56 Vict. (Can.) c. 29, § n; 57 Vict. (N.Z.), No. 56 of 1893, § 23; No. 101 of 1888 (St Lucia), § 50; No. 5 of 1876 (Gold Coast), § 49 (&); No. 2 of 1883, art. 77 (Ceylon); No. 4 of 1871, art. 84 (Straits Settlements). On the other hand, a departure towards a recogni- tion of " moral insanity " is made by the Queensland Criminal Code (No. 9 of 1899), § 27 of which provides that " a person is not criminally responsible for an act " if at the time of doing it " he is in such a state of mental disease ... as to deprive him ... of capacity to control his actions " : and the law has been defined in the same sense in the Cape of Good Hope in the case of Queen v. Hay (1899, 16 S.C.R. 290). The Rules were rapidly reproduced in the United States, but the modern trend of American judicial opinion is adverse to them (see Clevenger, Med. Jur. of Ins. p. 125; Parsons v. State (1887) 81 Ala. 577). On the Continent of Europe moral insanity and irresistible impulse are freely recognized as exculpatory pleas (see the French Code Penal, § 64; Belgian Code Penal, § 71; German Penal Code, § 51; Italian Penal Code, §§ 46, 47). Not only is insanity at the time of the commission of an offence a valid exculpatory plea, but supervening insanity stays the action of the criminal law at every stage from arrest up to punish- ment. High treason was formerly an exception, but the statute making it so (33 Hen. VIII. c. 20) was repealed in the time of Philip and Mary. The Home Secretary has power, under the Criminal Lunatics Act 1884 to order by warrant the removal of a prisoner, certified to be insane, to a lunatic asylum, before l trial or after trial, whether under sentence of death or not. Prisoners dealt with under these provisions are styled " Secretary of State's lunatics." On the other hand, a prisoner who on arraignment appears, or is found by the jury to be unfit to plead, or who is found " guilty but insane " at the time of committing the offence — a verdict substituted by the Trial of Lunatics Act 1883 for the old verdict of " acquitted on the ground of insanity," in the hope that the formal conviction recorded in the new finding might have a deterrent effect on the mentally unstable — is committed to a criminal lunatic asylum by the order of the judge trying the case, to be detained there " during the king's pleasure." Lunatics of this class are called " king's pleasure lunatics." There was no doubt at common law as to the power of the courts to order the detention of criminal lunatics in safe custody, but, prior to 1800, the practice was varying and uncertain. On the acquittal of Hadfield, however, in that year for the attempted murder of George III., a question arose as to the provision which was to be made for his detention, and the Criminal Lunatics Act 1800, part of which is still in force, was passed to affirm the law on the subject. The Criminal Lunatics Act contains provisions similar to those of the Lunacy Act 1890, as to the discharge (conditional or absolute) and transfer of criminal lunatics and the detention of persons becoming pauper lunatics. The expenses of the main- tenance of criminal lunatics are defrayed out of moneys provided by Parliament (Crim. Luns. Act 1884, and Hansard, 3rd series, vol. ccxc. p, 75; 139 Com. Jo. pp. 336, 340, 344). The Lunatics' Removal (India) Act 1851 provides for the removal to a criminal lunatic asylum in Great Britain of persons found guilty of crimes and offences in India, and acquitted on the ground of insanity. Similar provisions with regard to colonial criminaj lunatics are contained in the Colonial Prisoners' Removal Act 1884; and the policy of this statute has been followed by No 5. of 1894 (New South Wales), and Ordin. No 2 of 1895 (Falkland Islands). Indian law (see Act V. of 1898, §§ 464-475) and the laws of the colonies (the Cape Act No. 1 of 1897 is a typical example) as to the trial of lunatics are similar to the English. In Scotland all the criminal lunatics, except those who may have been removed to the ordinary asylums or have been discharged, are confined in the Criminal Asylum established at Perth in connexion with H.M.'s General Prison, and regulated by special acts (23 & 24 Vict. c. 105, and 40 & 41 Vict. c. 53). Provision similar to the English has been made for prisoners found insane as a bar to trial, or acquitted on the ground of insanity or becoming insane in con- finement. In New York, Michigan and other American states there are criminal lunatic asylums. Elsewhere insane criminals are apparently detained in state prisons, &c. The statutory rules as to the maintenance of criminal lunatic asylums, the treatment of the criminal insane, and the plea of insanity in criminal courts in America, closely resemble English practice. 1 It has sometimes been stated that this power, which ought clearly, in the interests alike of prisoners and of the public, to be exercised with caution, is in fact exerted in an unduly large number of cases. The following figures, taken from the respective volumes of the Criminal Judicial Statistics, show the number of criminal lunatics certified insane before trial. In 1884-1885, out of a total of 938 criminal lunatics, 169 were so certified; in 1885-1886, 149 out of 890; in 1889-1890, 108 out of 926; in 1S90-1891, 95 out of 900; in 1894, 78 out of 738; in 1895, 84 out of 757; in 1896, 88 out of 769; in 1897, 85 out of 764; in 1898, 17 out of 209; in 1899, 13 out of 159; in 1900, 12 out of 185; in 1901, 15 out of 205; in 1902, 7 out of 233; in 1903, II out of 229. 6l4. INSANITY [LEGAL ASPECTS The only special point In Continental law calling for notice is the system by which official experts report for the guidance of the tribunals on questions of alleged criminal irresponsibility (see, e.g., the German Code of Penal Procedure, § 293, and cp. § 81). 2. Insanity and Civil Capacity. — The law as to the civil capacity of the insane was for some time influenced in Great Britain by the view propounded by Lord Brougham in 1848 in the case of Waring v. Waring, and by Sir J. P. Wilde in a later case, raising the question of the validity of a marriage, that, as the mind is one and indivisible, the least disorder of its faculties was fatal to civil capacity. In the leading case of Banks v. Good- fellow in 1870, the court of queen's bench, in an elaborate judgment delivered by Chief Justice Cockburn, disapproved of this doctrine, and in effect laid down the principle that the question of capacity must be considered with strict reference to the act which has to be or has been done. Thus a certain degree of unsoundness of mind is not now, in the absence of undue influence, a bar to the formation of a valid marriage, if the party whose capacity is in question knew at the time of the marriage the nature of the engagement entered into (but see 51 Geo. III. c. 3 7 as to the marriage of lunatics so found by inquisition) . Again, a man whose mind is affected may make a valid will, if he possesses at the time of executing it a memory sufficiently active to recall the nature and extent of his property, the persons who have claims upon his bounty, and a judgment and will sufficiently free from the influence of morbid ideas or external control to determine the relative strength of those claims. So far has this rule been carried, that in 1893 probate was granted of the will of a lady who was a Chancery lunatic at the date of its execution, and died without the inquisition having been superseded. (Roe v. Nix, 1893, p. 55.) It is also now settled that the simple con- tract of a lunatic is voidable and not void, and is binding upon him, unless he can show that at the time of making it he was, to the knowledge of the other party, so insane as not to know what he was about. (Imperial Loan Co. v. Stone, 1892, 1 Q.B. 599.) The test established by Banks v. Goodfettow is applied also in a number of minor points in which civil capacity comes into question, e.g. competency of the insane as witnesses. The law implies, on the part of a lunatic, whether so found or no^, an obligation to pay a reasonable price for " necessaries " supplied to him; and the term " necessaries " means goods suitable to his condition in life and to his actual requirements at the time of sale and delivery, (Sale of Goods Act 1893). The question of the liability of an insane person for tort appears still to be undecided (see Pollock on Torts, 7th ed. p. 53 ; Clerk and Lindsell on Torts, 2nd ed. pp. 39, 40; Law Quart. Rev. vol. xiii. p. 325). Supervening insanity is no bar to proceedings by or against a lunatic husband or wife for divorce or separation for previous matrimonial offences. It does not avoid a marriage nor constitute per se a ground either for divorce or for judicial separation. But cruelty does not cease to be a cause of suit if it proceeds from disorderly affections or want of moral control falling short of positive insanity; and possibly even cruelty springing from intermittent or recurrent insanity might be held a ground for judicial separation, since in such case the party offended against cannot obtain protection by securing the per- manent confinement of the offending spouse. Whether insanity at the time when an alleged matrimonial offence was committed is a bar to a suit for divorce or separation is an open question; and in any event, in order that it may be so, the insanity must be of such a character as to have prevented the insane party from knowing the nature and consequences of the act at the time of its commission. The laws of Scotland, Ireland, India (see, e.g., Act IX. of 1872, § 12), the colonies and the United Statesare substantially identical with English law on the subject of the civil capacity of the insane. The German Civil Code (§1569) recognizes the lunacy of a spouse as a ground for divorce, but only where the malady continues during at least three years of the union, and has reached such a pitch that intellectual inter- course between the spouses is impossible, and that every prospect of a restoration of -such association is excluded. If one of the spouses obtains a divorce on the ground of the lunacy of the other the former has to allow alimony, just as a husband declared to be the sole guilty party in a divorce suit would have to do (§§ 1S85, 1578)- 3. The Jurisdiction in Lunacy. — In order to effect a change in the status of persons alleged to be of unsound mind, and to bring their persons and property under control, the aid of the juris- diction in lunacy must be invoked. Under the unrepealed statute De Praerogativa Regis (1325) the care and custody of lunatics belong to the Crown. But the Crown has, at least since the 1 6th century, exercised this branch of the prerogative by dele- gates, and principally through the Lord Chancellor — not as head of the Court of Chancery, but as the representative and delegate of the sovereign. Under the Lunacy Acts 1890 and 1891, the jurisdiction in lunacy is exercised first by the Lord Chancellor and such of the Lords Justices and other judges as may be invested with it by the sign-manual; and, secondly, by the two Masters in Lunacy, appointed by the Lord Chancellor, from members of the bar of at least ten years'^standing, whose duties include the holding of inquisitions and summary inquiries, and the making of most of the consequential orders dealing with the persons and estates of lunatics. County court judges may also exercise a limited jurisdiction in lunacy in the case of lunatics as to whom a reception order has been made, if their entire property is under £200 in value, and no relative or friend is willing to undertake the management of it; in partnership cases where the assets do not exceed £500; and upon application by the guardians of any union for payment of expenses incurred by them in relation to any lunatic. Persons of unsound mind are brought under the jurisdiction in lunacy either by an inquisition de lunatico inquirendo, or, in certain cases which will be adverted to below, by proceedings instituted under §116 of the Lunacy Act 1890, which is now the great practice section in the Lunacy Office. Prior to 1853 a special commission was issued to the Masters in each alleged case of lunacy. But by the Lunacy Regulation Act of that year a general commission was directed to the Masters, empowering them to proceed in each case in which the Lord Chancellor by order required an inquisition to be held. This procedure is still in force. A special commission would now be issued only where both Masters were personally interested in th,e subject of the inquiry, or for some other similar reason. An inquisition is ordered by the judge in lunacy (a term which does not, for this purpose, at present include the Masters, although this is one of the points in regard to which a change in the law has been suggested, on the petition generally of a near relative of the alleged lunatic. The inquiry is held before one of the Masters, and a jury may be summoned if the alleged lunatic, being within the jurisdiction, demands it, unless the judge is satisfied that he is not competent to form and express such a wish; and even in that case the Master has power to direct trial by jury if he thinks fit on consideration of the evidence. Where the alleged lunatic is not within the jurisdiction the trial must be by jury; and the judge in lunacy may direct this mode of trial to be adopted in any case whatever. A few points of general interest in connexion with inquisitions must be noted. In practice thirty-four jurors are summoned by the sheriff, and not more than twenty-four are empanelled. Twelve at least must concur in the verdict. Counsel for the petitioner ought to act in the judicial spirit expected from counsel for the prosecution in criminal cases. The issue to be determined on an inquisition is " whether or not the alleged lunatic is at the time of the inquisition of unsound mind, and incapable' of managing himself and his affairs " (a special verdict may, however, be found that the lunatic is capable of managing himself, although not his affairs, and that he is not dangerous to others) ; and without the direction of the person holding the inquisition, no evidence as to the lunatic's conduct at any time being more than two years before the inquisition is to be receivable. This limitation, both of the issue and of the evidence, was imposed with a view to preventing the recurrence of such cases as that of Mr Windham in 1861-1862, when the inquiry ranged over the whole life of an alleged lunatic, forty-eight witnesses being LEGAL ASPECTS] INSANITY 615 examined on behalf of the petitioners and ninety-one on behalf of the respondents, while the hearing lasted for thirty-four days. For the purpose of assisting the Master or jury in arriving at a decision, provision is made for the personal examination of the alleged lunatic by them on oath or otherwise, and either in open court or in private, as may be directed. The proceedings on inquisition are open to the public. When a person has been found lunatic by inquisition he becomes subject to the jurisdiction in lunacy, and remains so (unless he succeeds in setting aside the verdict by a " traverse " — a proceeding which ultimately comes before, and is determined by, the King's Bench Division in London or at the assizes) until his recovery, when the inquisition may be put an end to by a procedure technically known as " supersedeas," or by his death. The results of the inquisition are worked out in the Lunacy Office. The control of the estate, and, except where he was found incapable of managing his property only, of the person of the lunatic is entrusted to com- mittees of the estate and person, who are appointed by, and accountable to, the Master in Lunacy, and whose legal position corresponds roughly with that of the tutors and curators of the civil law. The committee of the estate in particular exercises over the property of the lunatic, with the sanction or by the order of the Master, very wide powers of management and administra- tion, including the raising of money by sale, charge or otherwise, to pay the lunatic's debts, or provide for his past or future main- tenance, charges for permanent improvements, the sale of any property belonging to the lunatic, the execution of powers vested in him and the performance of contracts relating to property. The alternative method of bringing a person of unsound mind under lunacy jurisdiction was created by §116 of the Lunacy Act 1890. The effect of that section briefly is to enable the Master, on a summons being taken out in his chambers and heard before him, to apply the powers of management and administration summarized in the last preceding paragraph, without any inquisition, to the following classes of cases: lunatics not so found by inquisition, for the protection or admini- stration of whose property any order was made under earlier acts; every person lawfully detained, within the jurisdiction of the English courts, as a lunatic, though not so found by inquisition; persons not coming within the foregoing categories who are " through mental infirmity arising from disease or age" incapable of managing their affairs; persons of unsound mind whose property does not exceed £2000 in value, or does not yield an annual income of more than £100; and criminal lunatics continuing insane and under confinement. In Scotland the insane are brought under the jurisdiction in lunacy by alternative methods, similar to the English inquisition and summary procedure, viz. " cognition," the trial taking place before the Lord President of the Court of Session, or any judge of that court to whom he may remit it, and a jury of twelve- see 31 & 32 Vict. c. 100, and Act of Sederunt of 3rd December 1868 — and an application to the Junior Lord Ordinary of the Court of Session or (43 & 44 Vict. c. 4, § 4) to the Sheriff Court, when the estate in question does not exceed £100 a year, for the appointment of a curator bonis or judicial factor. The powers of the Lord Chancellor of Ireland with regard to lunatics are generally similar to those of the English Chancellor (see the Lunacy Regulations (Ireland) Act 1871, 34 & 35 Vict, c. 22, and the Lunacy (Ireland) Act 1901, 1 Ed. VII. c. 17; also Colleson The Lunacy Regulation (Ireland) Act). The main feature of the French system is the provision made by the Civil Code (arts. 489-512) for the interdiction of an insane person by the Tribunal of First Instance, with a right of appeal to the Court of Appeal, after a preliminary inquiry and a report by a family council (arts. 407, 408), consisting of six blood relatives in as near a degree of relationship to the lunatic as possible, or, in default of such relatives, of six relatives by marriage. The family council is presided over by the Jvge de Paix of the district in which the lunatic is domiciled. This system is also in force in Mauritius. There arc provisions, it may be noted, in Scots law for the interdiction of lunatics, either voluntarily or judicially (sec Bell's Principles, § 2123). The German Civil Code provides for insane persons being made subject to guardianship (vormun- dung), on conditions similar to those of Scots and French law (see Civil Code, §§ 6, 104 (1896, 1906), 645-679). In the United States the fundamental procedure is an inquisition conducted on practically the same lines as in England. (Cf. Indiana, Rev. Stats. (1894) §§ 2715 et seq.; Missouri, Annot. Code (1892) §§ 2835 et seq.; New Mexico, General Laws (1880) c. 74 §§ 1 et seq.). 4. Asylum Administration.- — Asylum administration in England is now regulated by the Lunacy Acts 1890 and 1891. Receptacles for the insane are divisible into the following classes: (i.) Institutions for lunatics, including asylums, registered hospitals and licensed houses. The asylums are provided by counties or boroughs, or by union of counties or boroughs. Registered hospitals are hospitals holding certificates of registration from the Commissioners in Lunacy, where lunatics are received and supported wholly or partially by voluntary contributions or charitable bequests, or by applying the excess of the payments of some patients towards the maintenance of others. Licensed houses are houses licensed by the Commissioners, or, beyond their immediate jurisdiction, by justices; (ii.) Workhouses — see article Poor Law; (iii.) Houses in which patients are boarded out; (iv.) Private houses (unlicensed) in which not more than a single patient may be received. A person, not being a pauper or a lunatic so found by inquisition, cannot, in ordinary cases, be received and detained as a lunatic in any institution for the insane, except under a " reception order " made by a county court judge or stipendiary magistrate or specially appointed justice of the peace. The order is made on a petition presented by a relative or friend of the alleged lunatic, and supported by two medical certificates, and after a private hearing by the judicial authority. The detention of a lunatic is, however, justifiable at common law, if necessary for his safety or that of others; and the Lunacy Act 1890, borrowing from the lunacy law of Scotland, provides for the reception of a lunatic not a pauper into an asylum, where it is expedient for his welfare or the public safety that he should be confined without delay, upon an " urgency order," made if possible by a near relative and accompanied by one medical certificate. The urgency order only justifies detention for seven days (the curtailment of this period to four days is proposed), and before the expiration of that period the ordinary procedure must be followed. " Summary reception orders" may be made by justices otherwise than on petition. There are four classes of cases in which such orders may be made, viz. : (i.) lunatics (not paupers and not wandering at large) who are not under proper care and control, or are cruelly treated or neglected; (ii.) resident pauper lunatics; (iii.) lunatics, whether pauper or not, wandering at large; (iv.) lunatics in workhouses. (As to pauper lunatics generally, see article Poor Law.) A lunatic may also be received into an institution under an order by the Commissioners in Lunacy; and a lunatic so found by inquisition under an order signed by the committee of his person. The chief features of English asylum administration requiring notice are these. Mechanical restraint is to be applied only when necessary for surgical or medical purposes, or in order to prevent the lunatic from injuring himself or others. The privacy of the correspondence of lunatics with the Lord Chancellor, the Commissioners in Lunacy, &c, is secured. Provision is made for regular visits to patients by their relatives and friends. The employment of males for the custody of females is, except on occasions of urgency, prohibited. Pauper lunatics may be boarded out with relatives and friends. Elaborate provision is made for the official visitation of every class of receptacle for the insane. The duties of visitation are divided between the Com- missioners in Lunacy, the Chancery Visitors and various other visitors and visiting committees. There are ten Commissioners in Lunacy — four unpaid and six paid, three of the latter being barristers of not less than five years' standing at the date of appointment, and three medical. The Commissioners in Lunacy, who are appointed by the Lord Chancellor, visit every class of lunatics except persons so found by inquisition. These are 6i6 INSANITY [HOSPITAL TREATMENT visited by the Chancery Visitors. There are three Chancery Visitors, two medical and one legal (a barrister of at least five years' standing at the date of his appointment), who are appointed and removable by the Lord Chancellor. The Chancery Visitors (together with the Master in Lunacy) form a Board, and have offices in the Royal Courts of Justice. In addition to these two classes of visitors, every asylum has a Visiting Committee of not less than seven members, appointed by the local authority; and the justices of every county and quarter-sessions borough not within the immediate jurisdiction of the Commissioners in Lunacy annually appoint three or more of their number as visitors of licensed houses. Provision is made for the discharge of lunatics from asylums, &c, on recovery, or by habeas corpus, or by the various visiting authorities. Any person who considers himself to have been unjustly detained is entitled on discharge to obtain, free of expense, from the secretary to the Lunacy Commissioners a copy of the documents under which he was confined. The Irish [Lunacy Acts 1821-1890; Lunacy (Ireland) Act 1901] and Scottish [Lunacy Acts 1857 (20 & 21 Vict. c. 71), 1887 (50 & 51 Vict. c. 39)] asylum systems present no feature sufficiently different from the English to require separate notice, except that in Scotland " boarding out " is a regular, and not merely an incidental, part of asylum administration. The " boarding out " principle has, however, received its most extended and most successful application in the Gheel colony in Belgium. The patients, after a few days' preliminary observa- tion, are placed in families, and, except that they are under ultimate control by a superior commission, composed of the governor of the province, the Procureur du Roi and others, enjoy complete liberty indoors as well as out of doors. The patients are visited by nurses from the infirmary, to which they may be sent if they become seriously ill or unmanageable. They are encouraged to work. The accommodation provided for them is prescribed, and is to be of the same quality as that of the household in which they live. Clothing is provided by the administration. In the French (see laws of 30th June 1838 and 18th December 1839) and German {see Journal of Comparative Legislation, n.s. vol. i. at pp. 271, 272) asylum systems the main features of English administration are also reproduced. The lunacy laws of the British colonies have also closely followed English legislation (cf. Ontario, R.S. 1897, cc. 317, 318; Manitoba, R.S. 1902, c. 80; Victoria (No. 1113, 1890); New Zealand (No. 34 of 1882 and Amending Acts); Mauritius (No. 37 of 1858).' In America the different states of the Union have each their own lunacy legislation. The national government provides only for the insane of the army and navy, and for those residing in the District of Columbia and in Alaska. The various laws as to the reception, &c, of the insane into asylums closely resemble English procedure. But in several states the verdict of a jury finding lunacy is a necessary preliminary to the commitment of private patients (Kentucky, Act of 1883, c. 900, § 14; Mary- land, R.S. 1878, c. 53, § 21; Illinois, R.S. 1874, c. 85, § 22). Authorities. — The following works may be consulted: Collin- son on the Law of Lunatics and Idiots (2 vols., London, 1812); Shelford on the Law of Lunatics and Idiots (London, 1847). On all points relating to the history and development of the law these two treatises are invaluable. Pope on Lunacy (2nd ed., London, 1890); Archbold's Lunacy (4th ed., London, 1895); Elmer on Lunacy (7th ed., London, 1892); Wood Renton on Lunacy- (London and Edin- burgh, 1896); Fry's Lunacy Laws (3rd ed., London, 1890); Pitt- Lewis, Smith and Hawke, The Insane and the Law (London, 1895); Hack-Tuke, Dictionary of Psychological Medicine (London, 1892), and the bibliographies attached to the various legal articles in that work; Clevenger, Medical Jurisprudence of Insanity (2 vols., New York, 1899); Semelaigne, Les Alienistes francais (Paris 1849); Bertrand. Loi sur les alienes (Paris, 1872), presents a comparative view of English and foreign legislations. In forensic medicine the works of Taylor, Medical Jurisprudence (5th ed., London, 1905); Dixon Mann, Foreign Medicine and Toxicology (3rd ed., London, 1902) ; and Wharton and Stille, A Treatise on Medical Jurisprudence (Phila- delphia, 1873); Hamilton and Godkin, System of Legal Medicine (New York, 1895); are probably the English authorities in most common use. See also Casper and Liman, Praktisches Handbuch der gerichtlichen Medicin (Berlin, 6th ed., 1876); Tardieu, Etude medico-legale sur la folie (Paris, 1872); Legrand du Saulle, La Folie devant les tribunaux (Paris, 1864) ; Dubrac, Traite de jurisprudence mkdicale (Paris, 1894); Tourdes, Traite de medecine legale (Paris, 1897) I and especially Krafft-Ebing, Lehrbuch der gerichtlichen Psycho- pathologie (Stuttgart, 1899). (A. W. R.) III. Hospital Treatment The era of real hospitals for the insane began in the 19th century. There had been established here and there in different parts of the world, it is true, certain asylums or places of restraint before the beginning of the 19th century. We find mention in history of such a place established by monks at Jerusalem in the latter part of the 5th century. There is evidence that even earlier than this in Egypt and Greece the insane were treated as individuals suffering from disease. Egyptian priests employed not only music and the beautiful in nature and art as remedial agents in insanity, but recreation and occupation as well. A Greek physician protested against mechanical restraint in the care of the insane, and advocated kindly treatment, the use of music, and of some sorts of manual labour. But these ancient beneficent teachings were lost sight of during succeeding centuries. The prevailing idea of the pathology of insanity in Europe during the middle ages was that of demoniacal possession. The insane were not sick, but possessed of devils, and these devils were only to be exorcised by moral or spiritual agencies. Medieval therapeutics in insanity adapted itself to the etiology indicated. Torture and the cruellest forms of punishment were employed. The insane were regarded with abhorrence, and were frequently cast into chains and dungeons. Milder forms of mental disease were treated by other spiritual means — such as pilgrimages to the shrines of certain saints who were reputed to have particular skill and success in the exorcism of evil spirits. The shrine of St Dymphna at Gheel, in Belgium, was one of these, and seems to have originated in the 7th century, a shrine so famed that lunatics from all over Europe were brought thither for miraculous healing. The little town became a resort for hundreds of insane persons, and as long ago as the 17th century acquired the reputation, which still exists to this day, of a unique colony for the insane. At the present time the village of Gheel and its adjacent farming hamlets (with a population of some 13,000 souls) provides homes, board and care for nearly 2000 insane persons under medical and government supervision. Numerous other shrines and holy wells in various parts of Europe were resorted to by the mentally afflicted — such as Glen-na-Galt in Ireland, the well of St Winifred, St Nun's Pool, St Fillans, &c. At St Nun's the treatment consisted of plunging the patient backwards into the water and dragging him to and fro until mental excitement abated. Not only throughout the middle ages, but far down into the 17th century, demonology and witchcraft were regarded as the chief causes of insanity. And the insane were frequently tortured, scourged, and even burned to death. Until as late as the middle of the 18th century, mildly insane persons were cared for at shrines, or wandered homeless about the country. Such as were deemed a menace to the community were sent to ordinary prisons or chained in dungeons. Thus large numbers of lunatics accumulated in the prisons, and slowly there grew up a sort of distinction between them and criminals, which at length resulted in a separation of the two classes. In time many of the insane were sent to cloisters and monasteries, especially after these began to be abandoned by their former occupants. Thus " Bedlam " (Bethlehem Royal Hospital) was originally founded in 1247 as a priory for the brethren and sisters of the Order of the Star of Bethlehem. It is not known exactly when lunatics were first received into Bedlam, but some were there in 1403. Bedlarh was rebuilt as an asylum for the insane in 1676. In 181 5 a committee of the House of Commons, upon investiga- tion, found it in a disgraceful condition, the medical treatment being of the most antiquated sort, and actual inhumanity practised upon the patients. Similarly the Charenton Asylum, just outside Paris, near the park of Vincennes, was an old monastery which had been given over to the insane. Numerous HOSPITAL TREATMENT] INSANITY 617 like instances could be cited, but the interesting point to be borne in mind is, that with a general tendency to improvement in the condition of imbeciles upon public charge, idiots and insane persons came gradually to be separated from criminals and other paupers, and to be segregated. The process of segregation was, however, very slow. Even after it had been accomplished in the larger centres of civilization, the condition of these unfortunates in provincial districts remained the same. Furthermore, the transfer to asylums provided especially for them was not followed by any immediate improvement in the patients. Twenty-five years after Pinel had, in 1792, struck the chains from the lunatics huddled in the Salpetriere and Bicetre of Paris, and called upon the world to realize the horrible injustice done to this wretched and suffering class of humanity, a pupil of Pinel, Esquirol, wrote of the insane in France and all Europe: " These unfortunate people are treated worse than criminals, reduced to a condition worse than that of animals. I have seen them naked, covered" with rags, and having only straw to protect them against the cold moisture and the hard stones they lie upon; deprived of air, of water to quench thirst, and all the necessaries of life; given up to mere gaolers and left to their surveillance. I have seen them in their narrow and filthy cells, without light and air, fastened with chains in these dens in which one would not keep wild beasts. This I have seen in France, and the insane are every- where in Europe treated in the same way." It was not until 1838 that the insane in France were all transferred from small houses of detention, workhouses and prisons to asylums specially con- structed for this purpose. In Belgium, in the middle ages, the public executioner was ordered to expel from the towns, by flogging, the poor lunatics who were wandering about the streets. In 1804 the Code Napoleon " punished those who allowed the insane and mad criminals to run about free." In 1841 an investigation showed in Belgium thirty-seven establishments for the insane, only six of which were in good order. In fourteen of them chains and irons were still being used. In Germany, England and America, in 1 84 1, the condition of the insane was practically the same as in Belgium and France. These facts show that no great advance in the humane and scientific care of the insane was made till towards the middle of the 19th century. Only then did the actual metamorphosis t.f asylums for detention into hospitals for treatment begin to take place. Hand in hand with this progress there has grown, and still is growing, a tendency to subdivision and specialization of hospitals for this purpose. There are now hospitals for the acutely insane, others for the chronic insane, asylums for the criminal insane, institutions for the feeble-minded and idiots, and colonies for epileptics. There are public institutions for the poor, and well-appointed private retreats and homes for the rich. All these are presided over by the best of medical authorities, supervised by unsalaried boards of trustees or managers, and carefully inspected by Government lunacy com- missioners, or boards of charities — a contrast, indeed, to the gaols, shrines, holy wells, chains, tortures, monkish exorcisms, &c, of the past! The statistics of insanity have been fairly well established. The ratio of insane to normal population is about 1 to 300 among civilized peoples. This proportion varies within narrow limits in different races and countries. It is probable that intemperance in the use of alcohol and drugs, the spread of venereal diseases, and the over-stimulation in many directions induced by modern social conditions, have caused an increase of insanity in the 19th as compared with past centuries. The amount of such increase is probably very small, but on superficial examination might seem to be large, owing to the accumulation of the chronic insane and the constant upbuilding of asylums in new communities. The imperfections of census-taking in the past must also be taken into account. The modern hospital for the insane does credit to latter-day civilization. Physical restraint is no longer practised. The day of chains — even of wristlets, covered cribs and strait-jackets — ■ is past. Neat dormitories, cosy single rooms, and sitting- and dining-rooms please the eye. In the place of bare walls and floors and curtainless windows, are pictures, plants, rugs, birds, curtains, and in many asylums even the barred windows have been abolished. Some of the wards for milder patients have unlocked doors. Many patients are trusted alone about the grounds and on visits to neighbouring towns. An air of busy occupation is observed in sewing-rooms, schools, shops, in the fields and gardens, employment contributing not only to economy in administration, but to improvement in mental and physical conditions. The general progress of medical science in all directions has been manifested in the department of psychiatry by improved methods of treatment, in the way of sleep-producing and alleviating drugs, dietetics, physical culture, hydrotherapy and the like. There are few asylums now without pathological and clinical laboratories. While it is a far cry from the prisons and monasteries of the past to the modern hospital for the insane, it is still possible to trace a resemblance in many of our older asylums to their ancient prototypes, particularly in those asylums built upon the so-called corridor plan. Though each generation contributed something new, antecedent models were more or less adhered to. Progress in asylum architecture has hence advanced more slowly in countries where monasteries and cloisters abounded than in countries where fixed models did not exist. Architects have had a freer hand in America, Australia and Germany, and even in Great Britain, than in the Catholic countries of Europe. Germany approaches nearest to an ideal standard of provision for the insane. The highest and best idea which has yet been attained is that of small hospitals for the acutely insane in all cities of more than 50,000 inhabitants, and of colonies for the chronic insane in the rural districts adjacent to centres of population. The psychopathic hospital in the city gives easy and speedy access to persons taken suddenly ill with mental disease, aids in early diagnosis, places the patients within reach of the best specialists in all departments of medicine, and associated, as it should be, with a medical school or university, affords facilities not otherwise available for scientific research and for instruction in an important branch of medical learning. A feature of the psychopathic hospital should be the reception of patients for a reasonable period of time, as sufferers from disease, without the formality of legal commitment papers. Such papers are naturally required for the detention and restraint of the insane for long periods of time, but in the earlier stages they should be spared the stigma, delay and complicated procedure of commitment for at least ten days or two weeks, since in that time many may convalesce or recover, and in this way escape the public record of their infirmities, unavoidable by present judicial procedures. There should be associated with such hospitals for the acutely insane in cities out-door departments or dispensaries, to which patients may be brought in still earlier stages of mental disorder, at a period when early diagnosis and preventive therapeutics may have their best opportunities to attain good results. In Germany a psychopathic hospital now exists in every university town, under the name of Psychiatrische ivlinik. Colonies for the chronic insane are established in the country, but in the neighbourhood of the cities having psychopathic hospitals, to receive the overflow of the latter when the acute stage has passed. The true colony is constructed on the principle of a farming hamlet, without barracks, corridored buildings, or pavilions. It is similar in most respects to any agricultural community. The question here is one of humane care and' economical administration. Humane care includes medical supervision, agreeable home-life, recreation, and, above all things, regular manual and out-of-door occupation in garden, farm and dairy, in the quarry, clay-pit or well-ventilated shop. Employment for the patients is of immense remedial importance, and of great value from the standpoint of economical administra- tion. In the colony system the small cottage homes of the patients are grouped about the centres of industry. The workers in the farmstead live in small families about the farmstead group of buildings; the tillers of the soil adjacent to the fields, 6i8 INSCRIPTIONS meadows and gardens; the . brickmakers, quarry men and artizans in still other cottages in the neighbourhood of the scenes of their activities. In addition to these groups of cottages, which constitute the majority of the buildings in the village, an infirmary for bedridden, excited and crippled patients is required, and a small hospital for the sick. All the inhabitants of the colony are under medical supervision. A laboratory for scientific researches forms a highly important part of the equip- ment. The colony is not looked upon as a refuge for the incurable ; it is still a hospital for the sick, where treatment is carried on under the most humane and most suitable conditions, and wherein the precentage of recoveries will be larger than in asylums and hospitals as now conducted. In respect of the establishment of colonies for the insane upon the plan outlined here, Germany has, as in the case of the psychopathic hospital, led the world. It has been less difficult for that country to set the example, because she had fewer of the conditions of the past to fight, and with her the progress of medical science and of methods of instruction in all departments of medicine has been more pronounced and rapid. Among the German colonies for the insane, that at Alt- Scherbitz, near Leipzig, is the oldest and most successful, and is pre-eminent in its close approach to the ideal village or colony system. In 1899 Professor Kraeplin of Heidelberg stated (Psychialrie, 6th edition) that the effort was made everywhere in Germany to give the exterior of asylums, by segregation of the patients in separate home-like villas, rather the appearance of hamlets for working-people than prisons for the insane, and he said, further, that the whole question of the care of the insane had found solution in the colony system, the best and cheapest method of support. " I have myself," he writes, " had oppor- tunity to see patients, who had lived for years in a large closed asylum, improve in the most extraordinary manner under the influence of the freer movement and more independent occupa- tion of colony life." In America the colony scheme has been successfully adopted by the state of New York at the Craig Colony for Epileptics at Sonyea and elsewhere. That the tendency nowadays, even outside of Germany, in the direction of the ideal standard of provision for the insane is a growing one is manifested in all countries by a gradual disintegration of the former huge cloister-like abodes. More asylums are built on the pavilion plan. Many asylums have, as it were, thrown off detached cottages for the better care of certain patients. Some asylums have even established small agricultural colonies a few miles away from the parent plant, like a vine throwing out feelers. What is called the boarding-out system is an effort in a similar direction. Patients suffering from mild forms of insanity are boarded out in families in the country, either upon public or private charge. Gheel is an example of the boarding-out system practised on a large scale. But the ideal system is that of the psychopathic hospital and the colony for the insane. Authorities. — Sir J. B. Tuke, Dictionary of Psychological Medicine, (London and Philadelphia, 1892); W. P. Letchworth, The Insane in Foreign Countries (New York, 1889); Care and Treatment of Epileptics (New York, 1900); F. Peterson, Mental Diseases (Phila- delphia, 1899); " Annual Address to the American Medico-Psycho- logical Association," Proceedings (1899). (F. P.*) INSCRIPTIONS (from Lat. inscribere, to write upon), the general term for writings cut on stone or metal, the subject matter of epigraphy. See generally Writing and Pai.aeo- graphv. Under this heading it is convenient here to deal more specifically with four groups of ancient inscriptions, Semitic, Indian, Greek and Latin, but further information will be found in numerous separate articles on philological subjects. See especially Cuneiform. Babylonia and Assyria, Sumer, Behistcn, Egypt (Language and Writing), Ethiopia, Phoe- nicia, Arabia, Hittites, Sabaeans, Minaeans, Etruria, Aegean Civilization, Crete, Cyprus, Britain, Scandinavian Languages, Teutonic Languages, Central America: Archae- ology, &c. I. Semitic Inscriptions Excluding cuneiform (q.v.), the inscriptions known as Semitic are usually classed under two main heads as North and South Semitic. The former class includes Hebrew (with Moabite), Phoenician (with Punic and neo-Punic), and Aramaic (with Nabataean and Palmyrene). The South Semitic class includes the Minaean and Sabaean inscriptions of South Arabia, In most of these departments there has been a very large increase of material during recent years, some of which is of the highest historical and palaeographical importance. The North Semitic monuments have received the greater share of attention because of their more general interest in connexion with the history of surrounding countries. 1. North Semitic. — The earliest authority for any North Semitic language is that of the Tel-el-Amarna tablets (15th century B.C.) which contain certain " Canaanite glosses," 1 i.e. North Semitic words written in cuneiform characters. From these to the first inscription found in the North Semitic alphabet, there is an interval of about six centuries. The stele of Mesha, commonly called the Moabite Stone, was set up in the gth century B.C. to commemorate the success of Moab in shaking off the Israelitish rule. It is of great value, both historically as relating to events indicated in 2 Kings i. 1, iii. 5, &c, and linguistic- ally as exhibiting a language almost identical with Hebrew — that is to say, another form of the same Canaanitish language. It was discovered in 1868 by the German missionary, Klein, on the site of Dibon, intact, but was afterwards broken up by the Arabs. The fragments, 2 collected with great difficulty by Cfermont-Ganneau and others, are now in the Louvre. Its genuineness was contested by A. Lowy (Scottish Review, 1887; republished, Berlin, 1903) and recently again by G. Jahn (ap- pendix to Das Buch Daniel, Leipzig, 1004), but, although there are many difficulties connected with the text, its authenticity is generally admitted. Early Hebrew inscriptions are at present few and meagre, although it cannot be doubted that others would be found by excavating suitable sites. The most important is that discovered ih 1880 in the tunnel of the pool of Siloam, commemorating the piercing of the rock. It is generally believed to refer, to Hezekiah/s scheme for supplying Jerusalem with water (2 Kings xx. 20), and therefore to date from about 700 B.C. It consists of six lines in good Hebrew, and is the only early Hebrew inscrip- \ tion of any length. The character does not differ from that of the Moabite Stone, except in the slightly cursive tendency of its curved strokes, due no doubt to their having been traced for the stone-cutter by a scribe who was used to writing on parchment. There are also a few inscribed seals dating from before the Exile, some factory marks and an engraved capital at al-Amwas, which : last may, however, be Samaritan. Otherwise this character is only found (as the result of an archaizing tendency) on coins of the Hasmoneans, and, still later, on those of the first and second (Bar Kokhba's) revolts. The new Hebrew character, which developed into the modern square character, is first found in a name of five letters at "Araq- al-amtr, of the 2nd century B.C. Somewhat later, but probably of the 1st century B.C., is the tombstone of the B'ne Hezif (" Tomb of St James ") at Jerusalem. An inscription on a ruined synagogue at Kafr Bir'im, near Safed, perhaps of about a.d. 300, or earlier, shows the fully developed square character. Since the publication of the Corpus I riser. Sem. it has been customary to treat papyri along with inscriptions, and for palaeographical reasons it is convenient to do so. Hebrew papyri are few, all in square character and not of great interest. The longest, and probably the earliest (6th century a.d.), is one now in the Bodleian Library at Oxford, containing a private 1 See Winckler in Schrader's Keilinschr. Bibl. v. (Berlin, &c, 1896). 2 A nearly complete text has been made from these with the help of a squeeze taken before its destruction. See the handbooks mentioned feelfc»w. SEMITIC] INSCRIPTIONS 6ig letter l written in a character closely resembling that of the Kair Bir'im inscription. Other fragments were published by Steinschneider 2 (perhaps 8th century), and by D. H. Miiller and Kaufmann.' Hebrew inscriptions outside Palestine are the cursive graffiti in the catacombs at Venosa (2nd~sth century), the magical texts on Babylonian bowls (7th-8th century), and the numerous tomb- stones * in various parts of Europe, of all periods from the 6th century to the present time. The few Samaritan inscriptions in existence are neither early nor interesting. Closely related to the Hebrews, both politically and in language, were the Phoenicians in North Syria. Their monuments in Phoenicia itself are few and not earlier than the Persian period. The oldest yet found, dating probably from the 5th or 4th century B.C., is that of Yehaw-milk, king of Gebal (modern Jebel) or Byblus, where it was found. It records at some length the dedication of buildings, &c, to the goddess of Gebal. Of the 3rd century B.C. are the inscriptions on the sarcophagi of Tabnith and his son Eshmun'azar, kings of Sidon, and some records of other members of the same family, Bod-'ashtart and his son Yathan-milk, found in 1902 a short distance north of Sidon. Outside Phoenicia the inscriptions are numerous and widely scattered round the Mediterranean coasts, following the course of Phoenician trade. The earliest is that on some fragments Of three bronze bowls, dedicated to Baal of Lebanon, found in Cyprus. The character is like that of the Moabite Stone, and the date is probably the 8th century B.C., though some scholars would put it nearer to 1000 B.C. In the latter case, the Hiram, king of Sidon, mentioned in the inscriptions would be the same as Hiram, king of Tyre, in Solomon's time. Similar bowls (of about 700 B.C.) found at Nimrud sometimes bear the maker's name in Phoenician characters. Many monumental inscriptions have also been found in Cyprus, at Kition, Idalion, Tamassos, &c. They are chiefly votive, some dated in the 4th century, and some being perhaps as late as the 2nd century B.C., so that they afford valuable evidence as to the succession of the local kings. Several also are bilingual, and it was one of these which supplied George Smith with the clue to the Cypriote syllabic system of writing Greek. Similar memorials of Phoenician settlements were found at Athens (Piraeus), in Egypt, Sardinia, Malta and Gozo. Most interesting of all is the celebrated sacrificial tablet of Marseilles, giving an elaborate tariff of payments at or for the various offerings, and showing some striking analogies with the directions in the book of Leviticus. For the information it gives as to civil and priestly organization, it is the most important Phoenician text in exist- ence. It was probably brought from Carthage, where similar tariffs have been found. On the site of that important colony, and indeed throughout the parts of North Africa once subject to its rule, Punic inscriptions are, as might be expected, very numerous. By far the majority are votive tablets, probably belonging to the period between the 4th and the 2nd centuries B.C., many of them in a wonderfully perfect state of preservation. One of the most interesting, recently discovered, mentions a high-priestess who was head of the college of priests, and whose husband's family had been sujfetes for four generations. Later inscriptions, called neo-Punic, dating from the fall of Carthage to about the 1st century a.d., are written in a debased character and language differing in several respects from the earlier Punic, and presenting many difficulties. In Aramaic the earliest inscriptions are three found in 1890- 1891 at and near Zinjlrll in North-west Syria, dating from the 8th century B.C. Of these, one was set up by Panammu, king of Ya'dl, in honour of the god Hadad, and is inscribed on a 1 Published with other fragments in the Jew. Quart. Review, xvi. 1. 2 Zeitsch. f. Aegypt. Spr. (1879). These were the first specimens found. See also Erman and Krebs, Aus den Papyrus d. kgl. Mus. p. 290 (Berlin, 1899). 3 Mittheilungen . . . Rainer, i. 38 (Wien, 1886). 4 Those in France were collected by Schwab in Nouvelles archives, jrii. 3. See also Chwolson, Corpus Inscr. Hebr. (St Petersburg, 1882). statue of him, the other two were set up by Bar-rekub, son of Panammu, one in honour of his father and on his statue, the second commemorating the erection of his new house. They are remarkable as being engraved in relief, a peculiarity which has been thought to be due to " Hittite " influence. Otherwise the character resembles that of the Moabite Stone. The texts consist of 77 lines (not all legible), giving a good deal of informa- tion about an obscure place and period hitherto known only from cuneiform sources. The ornamentation is Assyrian in style, as also is that of the inscriptions of Nerab (near Aleppo), commemorative texts engraved on statues of priests, of about the 7th century. Of shorter inscriptions there is a long series from about the 8th century B.C., on bronze weights found at Nineveh (generally accompanied by an Assyrian version), and as "dockets" 6 to cuneiform contract-tablets, giving a brief indication of the contents. Aramaic, being the commercial language of the East, was naturally used for this purpose in business documents. For the same reason it is found in the 6th-4th centuries B.C. sporadic- ally in various regions, as in Cilicia, in Lycia 6 (with a Greek version), at Abydos (on a weight). At Taima also, in North Arabia, an important trading centre, besides shorter texts, a very interesting inscription of twenty-three lines was found, recording the foundation and endowment of a new temple, probably in the 5th century b.c. But by far the most extensive collection of early Aramaic texts comes from Egypt, where the language was used not only for trade purposes, as elsewhere, but also officially under the Persian rule. From Memphis there is a funeral inscription dated in the fourth year of Xerxes (482 B.C.), and a dedication on a bowl of about the same date. A stele recently published by de Vogti6 7 is dated 458 B.C. Another which is now at Carpentras in France (place of origin unknown) is probably not much later. At Elephantine and Assuan in Upper Egypt, a number of ostraka have been dug up, dating from the 5th century B.C. and onward, all difficult to read and explain, but interesting for the popular character of their contents, style and writing. There was a Jewish (or Israelitish 8 ) settle- ment there in the 5th century from which emanated most, if not all, of the papyrus documents edited in the C.I.S. Since the appearance of this part of the' Corpus, more papyri have come to light. One published by Euting 9 is dated 411 B.C. and is of historical interest, eleven others, 10 containing legaldocuments, mostly dated, were written between 471 and 411 B.C.; another (408 B.C.) is a petition to the governor of Jerusalem. 11 The fragments in the C.I.S. are in the same character and clearly belong to the same period. The language continued to be used in Egypt even in Ptolemaic times, as shown by a papyrus 12 (accounts) and ostrakon 13 containing Greek names, and belonging, to judge from the style of the writing, to the 3rd century B.C. The latest fragments u are of the 6th-8th century a.d., written in a fully developed square character. They are Jewish private letters, and do not prove anything as to the use of Aramaic in Egypt at that time. Nabataean inscriptions are very numerous. They are written in a peculiar, somewhat cursive character, derived from the square, and date from the 2nd century b.c. The earliest dated is of the year 40 B.C., the latest dated is of a.d. 95. The Nabataean kingdom proper had its centre at Petra ( = Sela in 2 Kings xiv. 7), which attained great importance as the emporium on the trade route between Arabia and the Persian Gulf on the 5 These have been collected by J. H. Stevenson, Babyl. and Assyr.. Contracts (New York, 1902). A more complete collection has been prepared by Professor A. T. Clay. 6 For the literature see Kalinka, Tituli Lyciae, No. 152 (Vienna, 1901). 7 Repertoire d'epigr. sent., No. 438. 8 So Bacher in /. Q. R. xix. 441. 9 In Mem. Acad, inscr. i re ser. xi. 397. See also Rip. d'ipigr. sem., for some smaller fragments, Nos. 244-248. 10 Sayce and Cowley, Aramaic Papyri (London, 1906). 11 Sachau, " Drei aram. Papyrusurkunden " Abh. d. kgl. Preuss. Akad. (Berlin, 1907). 12 See P.S.B.A. (1907), p. 260. la Sp