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published In three 





•> ten 


1777— 1784. 



„ eighteen 





„ twenty 


1 801— 18 10. 



„ twenty 





„ twenty 





„ twenty-one 





„ twenty-two 





•„ twenty-fire 





ninth edition and eleven 

supplementary volume*, 




published in twenty-nine v 



1910— 1911. 

Cepyripfct, U dp United Seat** ot America* 191a 


The Eacydofwdia Briuanica Company. 

I'.A. .'! 

Jt 1 3 


.c ..'i .', 


A.»fc* - 

A. CO. 


A. ft. 

A. Go.* 

A. 0.0. 




A. So, 





Adolfo Bartoli .(1833-1894).. 

Formerly Professor of Literature at the Istituto di stud auperiori at Florence. " 
Author of Storia deUa leiUratura Italiana; Ac 

A&guste Boudinkon, D.D., D.CX. . 

Professor of Canon Law at the Catholic University of Paris, Honorary Canon of ' 
Paris. Editor of the Canonist* contemporain. 

literature (in part). 

Index 1 librorum Prohi- 

Arthur Ernest Cowley, M.A., Lrrr.D. 

Sub-Librarian of the Bodleian Library, Oxford. Fellow of Magdalen College. 

/ Dm GaMroI; 
t Inscriptions: 


(«» pattf. • 

Albert Charles Lewis Gotthilf Gunther.M.A., M.D., PkJD.. F.R.S. f 

Keeper of Zoological Department, British Museum, 1 875-1895. Gold Medallist, I 
Royal Society, 1878. Author of Catalogues of Colubrine Snakes, Boirachia SaUentiaA Ichthyojofy 
and Fishes in the British Museum*, Reptiles of British India; Fishes of Zambar; 
Reports on the u Challenger " Fishes; &c I 

Rev. Alfred Ernest Garvte, M.A., D.D. f ^ Mll4-i 

Principal of New College, Hampstead. Member of. the Board of Theology and the J immontMtyj 
Board of Philosophy, London University. Author of Studies in the inner Life\ Insptxatioo. 
of Jesus; *c *» ., 

Augustus Edward Hough Love, M.A., D.Sc, F.R.S. f 

Sedleian Professor of Natural Philosophy in the University of Oxford. Hon. J 
Fellow of Queen's College, Oxford ; formerly Fellow of St John's College, Cambridge. 1 
Secretary to the London Mathematical Society. I 

Alexander Francis Chamberlain, A.M., Ph.D. [ ■ » 

Assistant Professor of Anthropology, Clark University, Worcester, Massachusetts. J tm^an« North Amarttafc 
Member of American Antiquarian Society; Hon. Member of American Folk-lore | 
Society. Author of The Chhd and Childhood in Folk Thought I 

Major Arthur George Frederick Griffiths (d. 1908). 

H.M. Inspector of Prisons, 1878-1896. Author of The Chronicles of Newgate; 
Secrets of the Prison House; Ac 

Sir Archibald Geixxe, LL.D. 

See the; biographical article, Gsikib, Silt A. 
Rev. Alexander Gordon, M.A. 

Lecturer on Church History in the University of Manchester* 
Sis Alfred George Greenhill, M.A., F.R.S. 

Formerly Professor of Mathematics in the Ordnance College, Woolwich. , Author J n „j«-,i U ii..-i- 

of Differential and Integral Calculus with Applications; Hydrostatics; botes on\ *9™M*MX0toM. 

Dynamics; &c I 

. Sn A. Houtum*Schindler, CLE. f f . faMtl , • AmmA 

General in the Persian Army. Author of Eastern Persian Ink ^Wanto (m part). 

Agnes Mary Clerke. 

" article. Clerke. A. M. 1 ohhpib* vhsbsubsjsi 

Ibis; Icterus. 

bak-Anbi (in part). 

Ignanodon. • G 

See the biographical article, Clerke, A. M. 

Alfred Newton, F.R.S. 

Sea the biographical article, Newton, Alfred. 

Albrecht Socin, Ph.D. (i 844-1 809). 

Formerly Professor of Semitic Philology in the Universities of Leipzig and Tubingen. " 

Author of Atabische Crammatih; Ac. 
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. f r MMM 4.i ^«ism. -» 

ftrorir SchoU, of S, John'. Coltep. Orforf. . B«on SchoU, of Gra /. l*{HSSd?Sll«i.' 

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 Boohs 
and BiHiographica. Joint-editor of The Library. Chief Editor of the " Globe " 
■ Chanter* 

Alexander Wood Renton, M. A., LL.B. > tneuneiy, i*w on * -r .• 

Puisne Judge of the Supreme Court of Ceylon. Editor of Encyclopaedia of the' - ~ - ' .. .1 .- 

• Lam of England. 

1 A complete list, showing all individual contributors, appears in the final volume. 



C. BLHa. 
















Cbailes Francis Atkinson. /infantry; 

Formerly Scholar of Queen's College, Oxford. Captain, 1st City of London (Royal 1 tt M n M m Wan. 
Fusilier*). Author of The Wilderness and Cold Harbour. L Mmmm mm * 

Colonel Charles Grant. S India- Castum* 

Formerly Inspector of Military Education in India. , ^.vwum. 

Carlton Huntley Hayes, A.M., Ph.D. ' f mmmmm 

Assistant Professor of History at Columbia University, New Yodc Char, Memberl lanooent V., VOL 
of the American Historical AsSocaUiin. ^,7 ^ 

Conway Lloyd Morgan, LL,D., F-R5. 

Professor of Psychology at the University of Bristol. Principal of University College, 
Bristol, 1 887-1909. 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, 190ft. Author of 
Bent* Urn Navitaton The Dawn of Modem Geography;**. 

Carlo Salvioni. 

Professor of Classical and Romance Languages, University of Milan. 

Charlton Thoma* Lewis, Ph.D. U*34~i9»4>« 

Formerly Lecturer on Life Insurance, Harvard and Columbia Universities, and on 
• Principles of Insurance. Cornell University. Author of History of Germany; Essays; 
Addmems; &c 

Cecil Weatherly. 

Formerly Scholar of Oueen's College, Oxford. Barruter-at-Law, Inner Temple. 

. Duncan Black Magdonald, MA, DJD. 

Professor of Semitic Languages, Hartford Theological Seminary, U.S.A. Atfthor . 
of Development of Musltm Theology, Jurisprudence and Constitutional Theory; 
Selection from Ibn Khaldum; Religious Attitude and Life in Islam; &c 
Daym George Hogarxh, MA. 

Keeper of the Ashmolean Museum, Oxford. Fellow of Magdalen College, Oxford. Ionia (hi fcvxV 
Fellow of the British Academy. Excavated at Paphos, »««*• w»'»«*i« »«~» »•«* * - v r ^ i ' 

1903; Ephesus, 1 904- 1905; Assiut, 1906-1 007 ; Direct 
1897-1900; Director, Creua Exploration Fund, 1899. 

David Hannay. 

Formerly British Vice-Consul at Barcelona. Author of Short History of Royal 
Nary, 1217-1688 ; Life of Emilio Castelar ; &c 

Donald Francis Tovky. 

Author of Essays in Musical Analysis; comprising The Classical Concerto, The] Instrumentation* 
Goldberg Variations, and analyses of many other classical works. 

Dugald Sutherland MacColl, M.A., IXD. f 

Keeperof the National Gallery of British Art (TatsCallery). Lecturer on the History J Imnrankmlsm. 
of Art, University College, London; Fellow of University College, London. | T ' 

Author of Nineteenth Century Art; &c I 

EDWARD A0KEO MlNCHIN, M.A., F.Z.S. Psx-a.™^ 

Professor of Protozoology in the University of London. formerly Fellow of Merton J HjuTOmMull*; 
~' ' *" ~ * - 1.1 Hydro**. 

IntaUigenoa In Animals. 

Ibn Batata (in pari); 

« I UaJiaa Uwuci (m pvu\ 
Intnranoa (in pari). 

Infant Schools. 

; Naucratis, 1899 and' u, nr i- 
;.k <^.k^i „♦ aVi.. n . ISauTin. 

1903; Ephesus, 1 904- 1905; Assiut, 1906-1907 ; Director, British School at Athens, 

College, Oxford ; and Lecturer on Comparative Anatomy in the University of Oxford. 
Author of " Sponges and Spororoa " tn Lanltescer's Treatise on Zoology; Ac. 

Ernest Barker. M.A. 

Fellow and Lecturer in Modem History, St John's College, Oxford. 
" " r and Tutor of Merton College. Craven Scholar, 189$. 


Formerly 1 Imperial Chamber. 

Edwin Bramwell, M.B., F.R.C.P., F.R.S. (Edin.). 
Assistant Physician, Royal Infirmary, Edinburgh. 


fatt pari). 

Right Rev. Edward Cuthbert Butler, O.S.B., D.LrrT. f 

Abbot of Downside Abbey, Bath. Author of " The Lausiac History of Pallftdfas " i Imitation of 
in Cambridge Texts and Studies. { 


Edmund Crosby Quiggin, M.A, 

Fellow, Lecturer in Modern History, and Monro Lecturer in Cdtic, GonviUe and 

Caius College, Cambridge. 
Edward FOurbrother Strange. 

Assistant Keeper, Victoria and Albert Museum, South Kensington. Member' of , 

Council, Japan Society. Author of numerous works on art subjects. Joint-editor 

of BeiTs* Cathedral'' Series. 

Lady Dilke. 

See the biographical article: Dilke, Sir C. W., Bart. 

Emtum) Cosse, LL.D. 

S*e Ue biographical article, Gosse, Edmund. 

Emjl Hubner. 

See the biographical article, HOrnrr, Emil. ' 

Sit Edward Herbert Bunbury, Bart., M.A.. F.R.G.S. (d. 1805). f 

M.P. for Bury St Edmunds, 1847-1853. Author of a History of Ancient Geography; < lonja (in Pari), 
65c . • . I • 

Ellis Hovell Mimns, M.A. f 

Lecturer mod Assistant Librarian, and formerly Fellow, Pembroke Col lege, Cambridge < Iaxyftt; 
University Lecturer ia Palaeography. \, 

Edward Henry Palmer, M.A. 

See the biographical article, Palmer, E. H. 

Mud: Early History. 

Illustration: Technical 


f Hnjrftns, Sir Constantljn: 
I Ibsen; WyL 

I InsaripUoni: Latin (ws party. 

•(ibn Khaldun (in pari). 


B. S* Emkund Xnscht, 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; Ac Editor 
of Journal of the Society of Dyers and Cokntrists. 

B. Lb H. Thx 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 Cpllege. . Author of Manual 
of Greek Historical Inscriptions ; &c 


Inscription*: Greek 
(in pari). 




F.J. H. Fbanos John Haverjield, M.A., LLD , F.S.A. f 

Camden Professor of Ancient History in the University of Oxford. FeBow of _ . . , . _. . 

Brasenose College. Fellow of the British Academy. Formerly Censor, Student, i ICMUeld SBitt. 
Tutor and Librarian of Christ Church, Oxford. Ford's Lecturer. 1906-4907. I 
Author of Monographs on Roman History, especially Roman Britain; Ac [ 

F. LL 0. : Francis .Llewellyn Griffith, M.A., Ph.D., F.S:A. f 

Reader in Egyptology, Oxford Unfversity. Editor of the Archaeological Survey J Hvksos* *•*■ 
and Archaeological Reports of the Egypt Exploration Fund. Fellow of Imperial | ^ ' ; 
Gtrmai) Archaeological Institute. 

F. F« # Frederick Peterson. M.D., Ph.D. 

.T * 

DEWCic Peterson, M.D., Ph.D. . ' ffnaanltw* WastiLd 

Professor of Psychiatry, Columbia University. President of New Yoric State i ^wi-S ' 

Commission in Lunacy, 1902-1906. Author of Mental Diseases: &c I ereonmm. 

F. 8. P. Francis Samuel Phtuuck, A.M., Ph.D. ( indaMndaiiM. 

Formerly Fellow of Nebraska State University, and Scholar and Resident Fellow of \ nSTlMrTSIIi *f 
Harvard University. ^Member of American Historical Association. •{ AJfWMisjPsi ot. 

F.Wa. Francis Watt, M.A. J f Inn »nd Innkitptr. 

Barrister-at-Law, Middle Templet Author of Law's Lumber Room. \ * ■•*»■■■»»• . 

F. W. R.* Frederick William Rodler, ISO., F.G.S. f 

Curator and Librarian of the Museum of Practical Geology, London, 1879-1902. «{ Hyacinth: IoHta. 
President of the Geologists' Association, 1 887-1 889. L 

F. Y. P, . Fjkpwhck York Powell, D.C.L., LL.D! J fcthud: History, ind" 

See the biographical article, Powell, Frederick YdRK. \ ^ nc ^ tia Uterature. 

G. A. B. Qwmst A.. Boulencer, F.R.S.. D.Sc* Ph.D« , . f 

In charge of the collections of Reptiles and Fishes, Department of Zoology, British \ Ichihyalofy (m peri). 
Museum. Vice-President of the Zoological Society of London. { 

i of Linguistic Survey 

,_ .,._. ., - -, 1909. Vice-President 

of the Royal Asiatic Society.. , Formerly Fellow of Calcutta University. Author 
of The Languages of India ; &c.' 


Grenvtlle Ab 
Director of 
of Science 1 


Sir George. C 
See the bio 


George Fran< 
Assistant i 
Sources f^r 1 

G.O. Co. 

George Gorb 
Birlcbeck L 
of Medieval 


George Herb 
Professor 01 
their Siructu, 

lado-Ajyan Uncuifw. 

T C. 
eft • 


0. L A. G ^ A S?of L o^e L iangdoni of Italy. Profe«or of Comparative dammar at thej Itlltoll tan*** (« ***>. 

University of Milan. Author of Coddce Isuvndcse; Ac. 
G. J. George Jameson, C.M.G., M.A. , 

Formerly Consul-General at Shanghai, and Consul and Judge of the Supreme Court, ^ Hwang HO. 



G. K. Gustav Krugek. Ph.D. 

Professor of Church History in the University of Giessen. Author of Das PapsUkvm ; 

G. P. If. Gsorgb Prrctval Mudce, A.R.C.S., F.Z.S. 

Lecturer on Biology, London Hospital Mt ... 

Medicine for Women, University of London. Author of A Text Book of Zoology ; 

G. W. K. Very Rev. George William Kitchjn, M.A., D.D., F.S.A. 

Dean of Durham, and Warden of the University of Durham. Hon. Student of \ Hntton, Ulrieh Ton* 
Christ Church, Oxford. Fellow of King's College, London. Dean of Winchester. 
1883-1694. Author of A History of France; &c 

ribn 'AbdRabbnU; 

orgb; Peroval Mudce, A.R.C.S., F.Z.S. fc fm mmAmmgtm mmA t^u,^ 

Lecturer on Biology, London Hospital Medical College, and London School of i in«W»H0H Ud iDOOMton. 
Medicine for Women, University of London. Author of A Text Book of Zoology; &c. I 

of J I 
ter. I 

F. T. Rev. OwrwTHES 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; Ac 

lbs 'Aiftbt; Ibn AUtfr; 
Ibn DuraJd; Ibn FaxadT; 
Ibn FirW; Ibn Haxm; 
Ibn Hlshain; Ibn Isbaq; 
Ibn Jubair; Ibn KhaMfin 

(in parfc 
Ibn KhalBkln; 
Ibn Qutalba; Ibn ga'd; 
Ibn Tnfall; Ibn Usaibi'a; 
Ibrahim Al-MausOL 

IL Ch. Hugh Chisholm, M.A. _ 

.... 1 Irw| ■tj M s 4 .-tj Bt |t 4 

m Chisholm, M.A. f 

Formerly Scholar of Corpus Christi College, Oxford. Editor the lit* edition -{ I 

of the Encyclopaedia Briiannica; Co-edkor of the 10th edition. L 

Sir Henry Creswicke Rawunson, Bart., K.C.B. /irfabaa: TUstorv 

See the biographical article, Rawlinson, Sir Henry Creswiceb. I ^' 

H.L.H. Harriet L,HEBmawr, M.D„ (Bnix.) L.R.C.P.I., L.R.C.SX {intestinal Obstruction, 

H. M. H. Henry Marion Howe, A.M., LL.D. -f^- — a «_• 
Professor of Metallurgy, Columbia University. Author of Metallurgy of Sleet; &c\ "° 11 infl ifceL 

H. H. D. Henry Newton Dickson, M.A., D.Se., F.R.G.S. f 

' "■'.."■■ " ~ 4 

H. 0. Hermann Oelsner, M.A., PilD. 

Professor of Geography, University College, Reading. Author of Elementary \ Indtfttt Ooean. 
Meteorology; Papers on Oceanography; &c 

Tayiorian Professor of the Romance Languages in University of Oxford. Member J ttalisn Literature (in starA. 
of Couadi of the Philological Society. Author of A History of Provemcai Literature; | 1 * UM ""**""• v*» p* 9 * 

H. St SfarsY Sturt, M.A. J induction. 

Author of Idola Theatri; The Idea of a Free Church; and Personal Idealism. I 

H. T. A. Rev. Herbert Thomas Andrews. f 

Professor of New Testament Exegesis, New College, London, Author of the 4 1— ** ** , 
- . " Commentary on Acta " in the Westminster Mew Testament; Handbook on the * 
Apocryphal Books in the " Century Bible." <* 

H.Y. .Sir H>nry Yule, K.C.S.I., C.B. S w. ^^^^ ,,. . A . 

See the biographical article. Yule, Sir Henry. I™ 1 BuVaM <** parti. 

I. A. Israel Abrahams, M.A. f «j. ^ 

Reader in Talmudic and Rabbinic Literature in the University of Cambridge. J «■ TlMUli; 
Formerly President, Jewish Historical Society in England. Author of A Short " 
History of Jewish Literature; Jewish Life in the Middle Ages; Ac 

J. A. F. John Ambrose Fleming, M.A., F.R.S., D.Sc. f 

Pender Professor of Electrical Engineering In the University of London. Fellow I 

** " of University College, London, Formerly Fellow of St John's College, Cambridge, -j I 

and Lecturer on Appfied Mechanics in the University. Author of Magnets and I 

Electric Currents. [ 

J. Ba. James Burgess. CLE., LL.D., F.R.S.(£din.). F.R.G.S.. Hon.A.R.1.B.A. f ' 

Foraterly Director General of Archaeological Survey of India. Author of Arckaeo-) - -. _ 

logical Survey of Western- India, Editor of Fergusson's History of India* Archu\ *■»» Anummn* 
lecture, ■ I 

J. B. T. Sir John Batty Tuxe, Kt., M.D., F.R.S.(EdiiL), D.Sc, LL.D. f tgwm%m * m t . -_* 

President of the Neurological Society of the United Kingdom. Medical Director J "J*"™ lwl F***)', 
; • t • of New Saughton Hall Asylum, Edinburgh. M.P. for the Universities of Edinburgh I Insanity: Medical. 
and St Andrews, 1900-1910. I 

AJ. C. H. Right Rev. John Cuthbert Hedley, O.S.B., D.D. T immaMilsJe 

A R.C. Bishop of Newport. Author of The Holy Eucharist; &c \ uam *» um » 

J. C Van D. John Charles Van Dyes. f 

Professor of the History of Art, Rutgers College, New Brunswick, N.J. Formerly . T nnA M Gaom. 
Editor of The Studio and Art Review. Author of Art for Art's Sake; History of *"«■»»«•«**• 
Painting ; Old English Masters; &c I 


X C W. James Clauds Webster. J»« m » * _» 

Barrlster-at-Law, Middle Temple. \ lnM °* <&«*• 

1. D. B. James David Bourchier, M.A^ F.R.G.S. 

King'* College, Cambridge. Co 

Commander of the Orders of P „ 

Greece, and Officer of the Order of St Alexander of Bulgaria. 

J. F. P. 1 John Faitheull Fleet, CLE. Ph.D. 

Commissioner of Central and Southe 
of Inscriptions of the Early Gupta Kings; &c 

J. F.-K. James FrrrMAURiCE-KELLY, Lirr.D , F.R.Hist.S. 

_ _____ _, _ . . _. Correspondent of The Times in South-Eastern Europe. J t-nt^n bi*iwU 

Commander of the Orders of Prince Danilo of Montenegro and of the Saviour of ] wnmu ■■■•»• 
Greece, and Officer of the Order of St Alexander of Bulgaria. I 

in Faitheoll Fleet, CLE. Ph.D. [______. 

Commissioner of Central and Southern Divisions of Bombay, 1891-1897. Author "j iBSeripUoitS : Indian. 
of Inscriptions 0/ the Early Gupta Kings ; Ac. I 

Gilmour Professor of Spanish Language and Literature, Liverpool University. I . 

._ _, ">ridge University. FeRow of the British Academy, i W*» '• *. de. 

Ichthyology (in pari). 

Norman McCoII Lecturer, Cambridge University. FeRow 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 

J. 0. K. John Graham Kerr, M.A., F.R.S. 

Regius Professor of Zoology In the University of Glasgow. Formerly Demonstrator 
in Animal Morphology in the University of Cambridge. Fellow of Christ's College. 
Cambridge, 1808-1904. Walaingham Medallist, 1898. Neill Pruemen, Royal 
Society of Edinburgh, 1904. 

J. 0. Se_ Sir Tames George Scott. K.C.I.E. [ 

Superintendent and Political Officer, Southern Shan States. Author of Burma, i Imwaddy. 
4 Handbook; The Upper Burma Gazetteer; &c I 

J. H. A. H. John Henry Arthur Hart, M.A. S Hyraums. 

Fellow, Theological Lecturer and Librarian, St John's College, Cambridge. I 

J. H. Ma. John Hens* Mutrhead, M.A , LL.D. f 

Professor of Philosophy in the University of Birmingham. Author of Elements i Idealism. 
of Ethics ; Philosophy and Life; &c Editor of Library of Philosophy. I 

J. H. Be. Vhry Rev. John Henri. Bernard. M.A., D.D.. D.CL. 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'] ™«lfl» Cllttrcn OL 
Hymnorum ; &c L 

J. H. faol H. Jacobus Henricus van't Hoef, LL.D., D.Sc., D.M. f 

See the biographical article van't Hofp, Jacobus Henricus. 

J. L. M. John Lynton Myres, M.A., F.S.A.. F.R.G.S, 

Wykeham Professor of Ancient History in . , . , 

Gladstone Professor of Greek and Lecturer in Ancient Geography, University of 

Wykeham Professor of Ancient rfistory in the University of Oxford. Formerly J _v___4._._.,. i,___i_____ 
Gladstone Professor of Greek and Lecturer in Ancient Geography, University of 1 "•""»» IOMtM. 
Liverpool. Lecturer in Classical Archaeology in University of Oxford* I 

1. Mn. 

John Macpherson, M.D. /insanity: Medical {in Port). 

Formerly InspectoT-General of Hospitals, Bengal. \ v **coko* \m fart} . 

J.M. A.deL. Jean Marie Antoine de Lanessan. /._____. .__ ._ .. 

See the biographical article, Lanessan, J. M. A. de. \ Indo-Cbina, French (i» pari). 

SometimeScholar of Queen's College, Oxford. Lecturer jn Classics, East London 1 

J. M. H. John Malcolm Mitchell. 

Sometime Scholar of Quel _,_, , 

College (University of London). Joint^editor of Grote's History of Greece. 

J. P. B. Jean Paul Hifpolyte Emmanuel Adh£mar Esmein. f 

Professor of Law in the University of Paris. Officer of the Legion of Honour. J »-#.-,•--* 
Member of the Institute of France. Author of Cows tUmentaire d'histoire du droit 1 ""W" 1 *" 1 * 
francois;&c L 

I. P. Fi. Rev. John Punnett Peters, Ph.D., D.D. f 

* , Canon Residentiary , Cathedral of New York, Formerly Professor of Hebrew in | 

the University of Pennsylvania. Director of the University Expedition to Baby- S Irak-Arabl (in Part). 
Ionia, 1888-1895. Author of Nippur, or Explorations and Adwenium on the \ 
Euphrates. I 

J. 8. BL John Sutherland Black, M.A.. LL.D. f 

Assistant Editor of the Qth edition of the Encyclopaedia Britannka. Joint-editor ■< Hoss. John, 
of the Encyclopaedia Bibitca. [ 

J. 8. Co, James Sutherland Cotton, M.A. f India * Geography and 

Editor of the Imperial Caeetteer of India. Hon. Secretary of Ae Egyptian Explore- J Statistics (in part) 
tion Fond. Formerly Fellow and Lecturer of Queen's College, Oxford. Author! History (in part)' 
t* India; Ac I Inflow. 

J. 8. F. John Smith Flett, D.Sc, F.G.S. r 

Petrographer to the Geological Survey." Formerly Lecturer on Petrology in Edin- J .*____, «_. 

burgh University. Neffl Medallist of the Royal Society of Edinburgh. Bigsbyl "MOlomne. 
Medallist of the Geological Society of London. ' L 

J. T. Be. John Thomas Bealby. f 

Joint-author of Stanford's Europe. Formerly Editor of the Scotch Geographical \ Irkutsk (in harfl. 
Magazine. . Translator of Sven Hedin's Through Asia, Central Asia and met; &c [****"* Km *""'• 

J. V. # Jules Viard. r 

Archivist at the National Archives, Paris. Officer of Public Instruction. Author \ Ttnfrtni of Bawia. 
0/ La Prance sous Philippe VI. de Vahis; Ac [ 

Jdc W, John Westlake, K.C., LL.D. 

Professor of International Law, Cambridge. 1888-190& One of the Members for the f 
United Kingdom of International Court of Arbitration under the Hague Convention, 
1900-1906. Bencher of Lincoln's Inn. Author of A Treatise on Private International i 
Law, or the Conflict of Laws; Chapters on the Principles of International Law, pt. L J 
" Peace," pt. ii. " War." I 




L. Count Lftoow, Litt.D. (Oxon.), Ph.D» (Prague), F.R.G.S. f 

Chamberlain of H.M. the Emperor of Austria, King of Bohemia. Hod. Member | 
of the Royal Society of Literature. Member of the Bohemian Academy; &C.4 Hussites. 
Author of Bohemia, a Historical Sketch: The Historians of Bohemia (Itehester I 
Lecture, Oxford, 1904) ; The Life and Times of John Hut; Ac. |_ 

L. C. B. Lewis Campbell Bruce. M.D., F.R.C.P. f insanity: Medical (in oarXS 

Author of Studies in Clinical Psychiatry. l^^' Meawu v» t™*- 



of jl 

L. J. S. Leonard James Spencer, MA. 

Assistant in Department of Mineralogy, British Museum. Formerly Scholar of J HvMrsDienA* IhnMilfo 
Sidney Sussex College, Cambridge, and Harkness Scholar. Editor of the Altncra- l nw,ww ™' umwuw. 
logical Magazine. 

L. T. D. Sir Lewis Tonna Dibdin, M.A., D.C L.. F.S. A. 

Dean of the Arches; Master of the Faculties; and First Church Estates Commissioner. -\ Incense: Ritual Use. 
. Bencher of Lincoln's Ion. Author of Monastuism in England; &c 

M. Ha. 


M. 0. B. C. 


0. J. R. H. 

:ork. Author of " Protozoa " in Cam- ] Infusoria. 
is scientific journals. 

v of Pennsylvania,' U.S.A. Author of \ Ishtar. 

rsity. Lecturer in Creek at Birmingham 

ollege, Cambridge. University Lecturer 
languages Tripos and the Theological 

Isaao «f Anfloch. 

olar, 1 90 1. Assistant Secretary of the J Ireland: Geography. 

P. A. Paul Daniel Alphandery. r 

Professor of the History of Dogma, Ecole pratique dea haute* eludes, Sorbonne, i--_i-i#i-«, 
Paris. Author of Us liUs morale* the* U$ keterodoxes latines au debut du XUI: 1 InaunuolL 
sikh;. [ 

P. A. K. Prince Peter Alexeivitch Kropotktn. f.. ,.,. ... 

Sec the biographical article, Kropotkin, Prince P. A. ^ UMUmm U* fart). 

P. CM. Peter Chalmers Mitchell, M.A., F.R.S., F.2.S., D.Sc., LL.D. r 

Secretary to the Zoological Society of London. University Demonstrator in | u 

Comparative Anatomy and Assistant to Lipacre Professor at Oxford, 1 888-1891. J Hybridism. 
Examiner in Zoology to the University of London, 1903. ' Author of Outlines f 
of Biology i &c. i ' 

P. GL Peter Giles, MA., LL.D , Lrrr.D. 

Fellow and Classical Lecturer of Emmanuel College, Cambridge, and University . 
Reader in Comparative Philology. Formerly Secretary of the Cambridge Phili- ' 
logical Society. Author of Manual of Comparative Philology, flee. 



P. Sm. Preserved Smth. Ph.D. J innocent L, n. 

Rufus B. Kellogg Fellow, Amherst College, Amherst, Mass. \ 

R. The Right Hon. Lord Rayleigh. 

.eich, 3rd Baron. t * 

austeh, M.A., F.S. A. 


See the biographical article. Rayleigh, 3rd Baron. { l&tsfttiwiea of Light 

R. A. S. M. Robert Alexander Stewart Macauster, MA., F.S.A. 

St John's College, Cambridge. Director of Excavations for the Palestine Explora- 
tion Fund. 

R. Ba. Richard Bagwell, M.A., LL.D. 

Commissioner of National Education for Ireland. Author of Ireland under the 
Tudor s; Ireland under the Stuarts. 

Ireland: Modern History. 

R. C. J. Sir Richard Claverhousr Jebb, D.C.L., LL.D. t . t f 

See the biographical article* J mb, Sir Richard Clavbrhoosk. \ l *"* ut » Wxnto*. 

R. 0. Richard Gasnett. LL.D. 

See the biographical article, GarnbtT, Richard. 

R. H. C. Rev. Robert Henry Charles, M.A.. DJ)., D.Litt. 

Grlnfield Lecturer, and Lecturer in Biblical Studies, Oxford. Fellow of the British 
Academy. . Formerly Professor of Biblical Greek. Trinity Collegsv Dublin. Author 
of Critical History of the Doctrine of a Future Life ; Booh of JubUees ; &c 

R. L.* ^ Richard Lydekxer, F.R.S., F.Z.S., F.G.S. 

Irrlng, WiihJngtoiL 
Isaiah, Ascension of. 

Member of the Staff of the Geological Survey of India 1 874-1 863. Author of Color OT*MM**» 
logues of Fossil Mammals, Reptiles and Birds in the British Museum; The Deer ofi Ibex {in part); 
aU Lands; Ac.* [ Ifttfrl; Inseottvoi 

Phene Spiers', F.S.A., F.R.I.B.A. , 

Formerly Master of the Architectural School, Royal Academy, London. Past I " 

President of Architectural Association. Associate and.Feliow of King's College, J rfirMatlirni 
London. Corresponding Member of the Institute of France. Editor of Fergusson's | n #^*«n». 
History of Architecture. Author df ArehxUcturix East and West; &c. [ 















Robert Seymour Conway, M.A., D.Lrrr.(Cantab.). 

Professor of Latin and Indo-European Philology In the University of Manchecter, 
Formerly Professor of Latin in University College, Cardiff; and Fellow of Gonville 
and Caiurf College, Cambridge. Author of The Italic Dialects, 

The Right Hon. the Earl of $elborne. 

See the biographical article, Sslbornb, 1st Earl or, 

Roland Truslovx, M.A. 

Formerly Scholar of Christ Church, Oxford. Dean, Fellow and Lecturer in Classics 
«t Worcester College, Oxford. 

Stanley Arthur Cook, MA 

Lecturer in Hebrew and Syriac, and formerly Fellow, Gonvffle atid Cams College, 

r Palestine Exploration Fund . Author of Glossary of Aramaic 

Inscriptions; The Law of Masts ami me Cade of Hammurabi; Critical NtUs on Old 

Cambridge. Editor for I 

Siofus BiAnqal. , r - 

Ubrerian c* the Unrverslry<rf Copenhagen! ' ' - ■' 

Thomas Ashb*, M.A., DXitt. (Oxon.). ... , ■ * 

Director of British School of Archaeology at Rome. Formerly Scholar of Christ 
Church, Oxford. Craven Fellow, 1807. Conjngtoa t Prizeman. J9p6._>jetnber 
of the Imperial German Archaeological Institute. 

THomas Allan Ingram. M.A., LL.D. 
Trinity College, Dublin. 

Sir Thomas Barclay, M.P. 

Member of the Institute of International Law.' Member of the Supreme Council 
of the Congo Free State. Officer of the Legion of. Honour. Author of Problems 
of International Practice and Diplomacy; &c M.P. for Blackburn, 191a 

Rev. Thomas Fowler, M.A., D.D., LL.D. (1813-1004). 

President of Corpus Christ! College, Oxford. 1 881-1004. Honorary Fellow of 
Lincoln College. Professor of Logic. 1873-1888. Vtce-Chancellor of the University 
of Oxford, 1 899-1901 . Author of Elements of Deductive Logic ; Elements of Inductive 
Logic; Locke ("English Men of Letters "); Shaftesbury and Hutckeson (" English 
Philosophers );Aa , 

Theodore Freyunghuysen Collier, PhJX 

Assistant Professor of History, Williams College, Wniiamstown, Mass., U.SA 

Colonel Sir Thomas Hungerpord Holdios, K.C.M.G., K.C.I.E., Hon.D.Sc. 
'Superintendent, Frontier Surveys, India, 1892-1898. Gold Medallist, R.G.S., 
London, 1887. Author of The Indian Borderland; The Countries of the King's 
Award; India. Tibet; &c 

Rev. Thomas Kelly Cheyne, D.D. 

See the biographical article, Cbbynb, T. K 

Thorvaldur Thoroodsen~ 

Icelandic 'Expert and Explorer. Honorary Professor in the University of Copenhagen. 
Author of History of Icelandic Geography; Geological Map of Iceland; &c 

Rev. William Augustus Brevoort Coolidge, MA., F.R.G.S., Ph.D. (Bern). 
Fellow of Magdalen College, Oxford. Professor of English History, St David's 
College, Lampeter, 1 880-1881. Author of Guide du Haul Dauphini; The Range 
of the Tbdi; Guide to Grindehtold; Guide to Switserland; The Alps in Nature and %n 
History; &c Editor of The Alpine Journal, 1880-1881 ; &c 

Walter Alison Phillips, M.A. 

Formerly Exhibitioner of Merton College and Senior Scholar of St John's "College, 
Oxford. Author of Modern Europe; &c 

William T Cawthorne Unwln, LL.D.," F.R.S., MJnst.CE., M Jnst.M.E., 
Emeritus Professor, Central Technical College, City and Guilds of London Institute. 
Author of Wrought Iron Bridges and Roofs; Treatise on Hydraulics; Ac 

William Fetlden Crates, M.A. 

Barrister-at-Law, Inner Temple.' Lecturer on Criminal Law, King's College, 
London. Editor of Archbold's Criminal Pleading (23rd edition). 

William Fleetwood Sheppard. M.A. 

Senior Examiner in the Board ot Education, London. Formerly Fellow of Trinity 
College, Cambridge. Senior Wrangler, 1884. 

William Garnett, M.A., D.C.L. 

Educational Adviser to the London County Council. Formerly Fellow and Lecturer 
of St John's College, Cambridge. Principal and Professor of Mathematics, Durham 
College of Science, Newcastle-os-Tyne. Author of Elementary Dynamics; &c 

William Gow, M.A., Ph.D. 

Secretary of the British and Foreign Marine Insurance Co. Ltd., Liverpool Lecturer 
on Marine Insurance at University College, Liverpool Author of Marine Insurance : 

Sir William Henry Flower, F.R.S. 

See the biographical article, Flower, Sir W. H. 

W. Haldane Porter. 

Barrister-at-Law, Middle Temple, 

Ignvtam; IovQae. 

Indo-CMna, French 

(in part). 

feafcufe Rcvnt ZdUrVTe. i 

iHtenunHa Uranas; bchla. 


(in part). 

International Law. 

Hntohaton, Pianeta 

(in pari). 


Iceland: Geography and 

Hyeres; Innsbrvok; 
Interlaken; Iseo, Lake of; 
here (River); 
tain (Deportment). 

Innoooni LTL, IV. 



Insnranee: Marine. 

Ibex (tsi pa$i). 

Ireland: Statistics at 




W. R.So. 






Snt William Markby. K.C.I.E. 

See the biographical article, Miltn, 6» William. 

William McDoucall, MA. 

Wilde Reader in Mental Philotophy in the University of Oxford. Formerly Fellow 

oC St John's College, Cambridge. 
Wallace Martin Lindsay, MA, Lnr.D., LL.D. 

Professor of Humanity, University of St Andrews, 
lerly Fellow of Jesus Cotte ~ ' * * "' 

tions; The Latin Language; Ac. 

Snt William Mitchell Ramsay, Litt.D., D.C.L. 

See the biographical article, Ramsay, Sir W. Mitchell. 

{ Indian Uw. 

Fellow of the British Adademy. 


Inscriptions; Latin (m pad). 


William Ritchie Sorley, M.A., Lrrr.D., LL.D. r 

Professor of Moral Philosophy in the Umrerdty of Cambridge. Fellow of King's J T« 
College, Cambridge, Fellow of the British Academy. Fotmerty Fellow of Trinity 1 wn w tona i. 
College. Author of The Ethics of Naturalism; The Interpretation of Evolution; &cl . 

fin William Turner Thtselton-Dyer, F.R£., K.CM-Gu, CLE., D.Sa, UJ>., 
Ph.D.,F.L.S. h . ' ,, „ 

Hon. Student of Christ Church, Oxford. Director, Royal Botanic Gardens, Kew,: Hu-Lw 
1885-1905. Botanical Adviser to Secretary of State for Colonies, 1902-1906. ****"*• 
Joint-author of Flora of Middles** Editor of Flora Capensee and Flora of Tropical 

William Watson, D.Sc7f.R.S.7A.R.CS. 

Assistant Professor of Physics, Royal College of Science, London. Vice-President 
of the Physical Society. Author of A Text Booh of Practical Physics; Ac 

Snt William Wilson Hunter. 

Sat the biographical article. Hunter, Sir Wu-Uam Wilson. 

India: History 
Geography ai 
iin part). 

<*• Part); 
yd Sfntittin 

principal unsigned articles 


















Inoomt Tax. 








Indian M ntlny. 





International, The. 





HUSBAND, properly the " head of a household," but now 
chiefly used in the sense of a man legally joined by marriage to 
a woman, his " wife "; the legal relations between them are 
treated below under Husband and Wife. The word appears 
in 0. Eng. as hasbonda, answering to the Old Norwegian 
k&sbdndi, and means the owner or freeholder of a hus, or house. 
The last part of the word still survives in " bondage " and " bond- 
man," and is derived from bua, to dwell, which, like Lat. colere, 
means also to till or cultivate, and to have a household. " Wife," 
in O. Eng. vrij, appears in all Teutonic languages except Gothic; 
cf. Ger. Wtib, Dutch vrijf, &c, and meant originally simply 
a femate, " woman " itself being derived from vrifman, the 
pronunciation of the plural wimmen still preserving the original *. 
Many derivations of " wife " have been given; thus it has been 
connected with the root of " weave," with the Gothic waibjan, 
to fold or wrap up, referring to the entangling clothes worn 
by a woman, and also with the root of vibrare, to tremble. 
These are all merely guesses, and the ultimate history of the 
word is lost. It does not appear outside Teutonic languages. 
Parallel to " husband " is " housewife/' the woman managing 
a household. The earlier husvrif was pronounced hussif, and 
this pronunciation survives in the application of the word to 
a small case containing scissors, needles and pins, cottons, &c. 
From this form also derives " hussy," now only used in a, de- 
preciatory sense of a light, impertinent girl. Beyond the meaning 
of a husband as a married man, the word appears in connexion 
witb agriculture, in " husbandry " and " husbandman." Accord- 
ing to some authorities " husbandman " meant originally in 
the north of England a bolder of a- " husbandland," a manorial 
tenant who held two ox-gangs or virgates, and ranked next 
below the yeoman (see J. C Atkinson in Notes and Queries, 
6th series, vol. xii., and E. Bateson, History of Northumberland^ 
ii., tSoj). From the idea of the manager of a household, 
•• husband " was in use transferred to the manager of an estate, 
and the title was held by certain officials, especially in the great 
trading companies. Thus the " husband " of the East India 
Company looked after the interests of the company at the 
custom-house. The word in this sense is practically obsolete, 
but it still appears in " ship's husband," an agent of the owners 
of a strip who looks to the proper equipping of the vessel, and her 
repairs, procures and adjusts freights, keeps the accounts, makes 

charter-parties and sets generally as manager of the ship's 
employment. Where such an agent is himself one of the owners 
of the vessel, the name of " managing owner " is used. The 
"ship's husband" or "managing owner" must register his 
name and address at the port of registry (Merchant Shipping 
Act 1894, § 59). From the use of " husband " for a good and 
thrifty manager of a household, the verb " to husband " means 
to economize, to lay up a store,' to save. 

HUSBAND AND WIPE, Law relatino to. For the modes 
in which the relation of husband and wife may be constituted 
and dissolved, see Marriage and Divorce. The present article 
will deal only with the effect of marriage on the legal position 
of the spouses. The person chiefly affected is the wife, who 
probably in all political systems becomes subject, in consequence 
of marriage, to some kind of disability. The most favourable 
system scarcely leaves her as free as an unmarried woman; ana 
the most unfavourable subjects her absolutely to the authority 
of her husband. In modern tiroes the effect of marriage on 
property is perhaps the most important of its consequences, 
and on this point the laws of different states show wide diversity 
of principles. 

The history of Roman law exhibits a transition from an 
extreme theory to its opposite. The position of the wife in the 
earliest Roman household was regulated by the law of Manus. 
She fell under the M hand " of her husband, — became one of his 
family, along with his sons and daughters, natural or adopted, 
and his slaves. The dominion which, so far as the children 
was concerned, was known as the patria potestas f vt*s t with 
reference to the wife, called the manus. The subject members 
of the family, whether wife or children, had, broadly speaking, 
ho rights of their own. If this institution implied the complete 
subjection of the wife to the husband, it also implied a much 
closer bond of union between them than we find in the later 
Roman law. The wife on ber husband's death succeeded, like 
the children, to freedom and a share of the inheritance. Menus, 
however, was not essential to a legal marriage; its restraints 
were irksome and unpopular, and in course of time it ceased 
to exist, leaving no equivalent protection of the stability of 
family life. The later Roman marriage left the spouses com- 
paratively independent of each other. The distance between 
the two modes of marriage may be estimated by the fact that, 



while under the former the wife was one of the husband's immediate 
heirs, under the latter she was called to the inheritance only 
after his kith and kin had been exhausted, and only in preference 
to the treasury. It seems doubtful how far she had, during 
the continuance of marriage, a legal right to enforce aliment 
from her husband, although if he neglected her she had the 
unsatisfactory remedy of an easy divorce. The law, in fact, pre- 
ferred to leave the parties to arrange their mutual rights and 
obligations by private contracts. Hence the importance of the law 
of settlements (Dotes). The Dos and the Donatio ante nupiias were 
settlements by or on behaH of the husband or wife, during (he 
continuance of the marriage, and the law seems to have looked 
with some jealousy on gifts made by one to the other in any 
less formal way, as possibly tainted with undue influence. During 
the marriage the husband had the administration of the property. 

The manus of the Roman law appears to be only one instance 
of an institution common to all primiUvc -societies. ,On the 
continent of Eufope after many centuries, luring which local 
usages were brought under the influence of principles derived 
from the Roman law, a theory of marriage became established, 
the leading feature of which is the community of goods between 
husband and wife. Describing the principle as it prevails in 
France, Story (Conflict of Laws, g i jefr says: u TTiis community 
or nuptial partnership (in the absence of any special contract) 
generally extends to all the movable property of the husband 
and wife, and to the fruits, income and revenue thereof. . . . 
It extends also to all immovable property of the husband and 
wife acquired during the marriage, but not to such immovable 
property as either possessed at the time of the marriage, or 
which came to them afterwards by title of succession or by gift. 

The propert; * ble 

to the debts $e; 

to the debts ly, 

or by the w he 

husband; an he 

family. ... he 

property of ige 

it without tl >se 

by will of m an 

he part wit is 

dissolved b) of 

bodyorsep . r , r „ of 

property the wife is entitled to the full control of her movable 
property, but cannot alien her immovable property, without 
her husband's consent or legal authority. On the death of 
either party the property is divided in equal moieties between 
the survivor and the heirs of the deceased. 

Lam of England.— The English common law as usual followed 
tts own course in dealing with this subject, and in no department 
were its rules more entirely insular and independent. The 
text writers all assumed two fundamental principles, which 
between them established a system of rights totally unlike that 
just described. Husband and wife were said to be one person in 
the eye of the law — unica persona, quia caro una ct sanguis units. 
Hence a man could not grant or give anything- to his wife, 
because she was himself, and if there were any compacts between 
them before marriage they were dissolved by the union of persons. 
Hence, too, the old rule of law, now greatly modified, that husband 
and wife could not be allowed to give evidence against each 
other, in any trial, civil or criminal. The unity, however, was 
one-sided only; It was the wife who was merged in the husband, 
not the husband in the wife. And when the theory did not 
apply, the disabilities of "coverture" suspended the active 
exercise of the wife's legal faculties. The old technical phraseology 
described husband and wife as baron and feme ; the rights of 
the husband were baronial rights. From one point of view the 
wife was merged in the husband, from another she was as one of 
his vassals. A curious example is the immunity of the wife in 
certain cases from punishment for crime committed in the 
presence and on the presumed coercion of the husband. " So 
great a favourite," says Blackstone, ** is the female sex of the 
laws of England." 

The application of these .principles with reference to the 
property of the wife, and her capacity to contract, may now be 
briefly traced. ■ 

The freehold property of the wife became vested in the husband 
and herself during the coverture, and he had the management 
and the profits. If the wife had been in actual possession at 
any time during the marriage of an estate of inheritance, and if 
there had been a child of the marriage capable of inheriting, 
then the husband became entitled on his wife's death to hold 
the estate for his own life as tenant by the curtesy of England 
(curiatitas). 1 Beyond this, however, the husband's rights did 
not extend, and the wife's heir at last succeeded to the inheritance. 
The wife could not part with her real estate without the concur- 
rence of the husband; and even so she must be examined 
apart from her husband, to ascertain whether she freely and 
voluntarily consented to the deed. 

JVith regard to pccsqnal property, it passed absolutely at 
common law to the husband. Specific thinn io the possession 
of the wife (chuses in possession) became the prOpeYly* of the 
husband at once; things not. in possession, but due and re- 
coverable from others (choses in action), might be recovered 
by the husband. A cftost in action not reduced into actual 
possession, when the marriage was dissolved by death, reverted 
to the wife if she was the survivor; if the husband survived 
he could obtain possession by taking out letters of administra- 
tion. . A chase in action was to be distinguished from a specific 
thing which, although the property of the wife, was for the 
time being in the bands of another. In the latter case the 
property was in the wife, and passed at once to the husband; 
in the former the wife had a mere jus in personam, which the 
husband might enforce if he chose, but which was still cap- 
able of reverting to the wife if the husband died without 
enforcing it. 

The chattels real of the wife (I.e., personal property, dependent 
on, and partaking of, the nature of realty, such as leaseholds) 
passed to the husband, subject to the wife's right of survivorship, 
unless barred by the husband by some act done during his life. 
A disposition by will did not bar the wife's interest; but any 
disposition inter vivos by the husband was valid and effective. 

The courts of equity, however, greatly modified the rules of 
the common law by the' introduction of the wife's separate 
estate, i.e. property settled to the wife for her separate use, 
independently of her husband. The principle seems to have 
been originally admitted in a case of actual separation, when 
a fund was given for the maintenance of the wife while living 
apart from her husband. And the conditions under which 
separate estate might be enjoyed had taken the Court of Chancery 
many generations to develop. No particular form of words was 
necessary to create a separate estate, and the intervention of 
trustees, though common, was not necessary. A' dear intention 
to deprive the husband of his common law rights was sufficient 
to do so. In such a Case a married woman was entitled to deal 
with her property as if she was unmarried, although the earlier 
decisions were in favour of requiring her binding engagements 
to be in writing or under seal. But it was afterwards held that 
any engagements, clearly made with reference to the separate 
estate, would bind that estate, exactly as if the woman had been 
a feme sole. Connected with the doctrine of separate use Vas 
the equitable contrivance of restraint on anticipation with' which 
rater legislation has not interfered, whereby property might be 
so settled to the separate use of a married woman that she could 
not, during coverture, alienate it or anticipate the income. 
No such restraint is recognized in the case of a man or of a. feme 
sole, and it depends entirely on the separate estate; and the 
separate estate has its existence only during coverture, so thai 
a woman to whom such an estate is given may dispose of it so 
long as she is unmarried, but becomes bound by the restraint as 
soon as she is married. In yet another way the court of Chancery 
interfered to protect the interests of married vfomen. When a 

1 Curtesy or courtesy has been explained by legal writers a* 
" arising by favour of the law of England." The word has nolhiag 
to do with courtesy in the sense of complaisance. 


husband sought the aid of that couW to get possession of his 
wife's ckoses in action, he was required to make a provision 
for her and her children out of the fund sought to be recovered. 
This is called the wife's equity to a settlement, and is said to be 
based on the original maxjm of Chancery jurisprudence, that 
" he who seeks equity must do equity." Two other property 
interests of minor importance are recognised. The wife's pin- 
money is a provision for the purchase of cbthes and ornaments 
suitable to her husband's station, but it is not an absolute 
gift to the separate use of the wife; and a wife surviving her 
husband cannot claim for more than one year's arrears of pin- 
money. Paraphernalia are jewels and other ornaments given 
to the wife by her husband for the purpose of being worn by her, 
but not as her separate property. The husband may dispose 
of them by act inter vivos but not by will, unless the will confers 
other benefits on the wife, in which case she must elect between 
the will and the parapbernana. She may also on the death 
of the husband claim ^paraphernalia, provided all creditors 
have been satisfied, her right being superior to that of any 

The corresponding interest of the wife in the property of the 
husband is much more meagre and illusory. Besides a general 
right to maintenance at her husband's expense, she has at common 
law a right to dower (q.v.) in her husband's lands, and to a pars 
rationabilis (third) of his personal estate, if he dies intestate. 
The former, which originally was a solid provision for widows, 
has by the ingenuity of conveyancers, as well as by positive 
enactment, been reduced to very slender dimensions. It may 
be destroyed by a mere declaration to that effect on the part 
of the husband, as well as by his conveyance of the land or by 
his will. 

The common practice of regulating the rights of husband', 
wife and children by marriage settlements obviates the hardships 
of the common law— at least for the women of the wealthier 
classes. The legislature by the Married Women's Property 
Acts of 1870, 1874, 1889 (which repealed and consolidated the acts 
of 1870 and 1874), 1803 and 1007 introduced very considerable 
changes. The chief provisions of the Married Women's Property 
Act 1882, which enormously improved the position of women 
unprotected by marriage settlement, are, shortly, that a married 
woman is capable of acquiring, holding and disposing of by will 
or otherwise, any real and personal property, In the same manner 
as if she were a feme sole, without the intervention of any trustee. 
The property of a woman married after the beginning of the 
act, whether belonging to her at the time of marriage or acquired 
after marriage, is held by her as a feme sole. -The same is the case 
with property acquired after the beginning of the act by a woman 
married before the act. After marriage a Woman remains HaWe 
for antenuptial debts and liabilities, and as between her and her 
husband, in the absence of contract to the contrary, her separate 
property is deemed primarily liable. The husband is only 
liable to the extent of property acquired from or throogh his 
wife. The act also contained provisions as to stock, invest mcnt> 
insurance, evidence and other matters. The effect of the act 
was to render obsolete, the law ar to what created a separate 
use or a reduction into possession of chases fn action, as to equity 
to a settlement, as to fraud on the husband's marital rights, 
and as to the inability of one of two married persons to give 
a gift to (he other. Also, in the case of a gift to a husband and 
wife in terms which would make them joint tenants if unmarried, 
they rto longer take as one person but as two. The act contained 
a special saving of existing and future settlements; a settlement 
being still necessary where it is desired to secure only the enjoy- 
ment of the income to the wife and to provide for children. 
The act by itself would enable the wife, without regard to family 
claims, instantly to part with the whole of any property which 
might come to her. Restraint on anticipation was preserved 
by the act, subject to the liability of such property for antenuptial 
debts, and to the power given by the Conveyancing Act 1881 
to bind a married woman's interest notwithstanding a clause 
of rest rain tv The Married Women's Properly Act of 1893 
repealed two clauses in the act of 1882, the exact bearing of 


(•3°5) placed beyond the husband • control As regards property 
accruing to the wife in Germany by succession, wilt or gift inter 
vivos, it is only separate property where the donor has deliberately 
stipulated exclusion of' the husband's right. 

In France it seemed mb if the system of community of property 
was ingrained in the institutions of the country. But a law of 1907 

has brought France into line with other countries. This law gives a 
married woman sole control over earnings from her personal work 
and savings therefrom. She can with such money acquire personalty 

or realty, over the former of which she has absolute control But 
if she abuses her rights by squandering her money or administering 
her property badly or imprudently the husband may apply to the 
court to have her freedom restricted. 

American Law. — In the Unit he 

common law theory of husband a in 

England, and legislation early t< ite 

equality between the sexes. E< its 

own way and selected its own tit of 

the existing law, so that the 1 >w 

exceedingly complicated and di of 

Domestic Relations) gives an ace tx 

different states to which rcferc ar 

system of Homestead Laws in m tt> 

and Exemption Laws) constitui he 

wife and family of the householder. 

HUSHI (Rumanian Husi), the capita! of the department 
of Falciu, Rumania; on a branch of the Jassy-Galatz railway, 
o m. W. of the river Pruth and the Russian frontier. Pop. 
(1000) 1 5*404, about one-fourth being Jews. Hushi is an episcopal 
see. The cathedral was built in 1491 by Stephen the Great of 
Moldavia. There are no important manufactures,. but a large 
fair is held annually in September for the sale of live-stock, 
and wine is produced in considerable quantities. Hushi is said 
to have been founded in the 1 5th century by a colony of Hussites, 
from whom its name is derived. The treaty of the Pruth between 
Russia and Turkey was signed here in 171 1. 
' HUSKISSON, WILLIAM (1770-1830), English statesman and 
financier, was descended from an old Staffordshire family of 
moderate fortune, and was born at Birch Moreton, Worcester- 
shire, on the nth of March 1770. Having been placed in his 
fourteenth year under the charge of his maternal great-uncle 
Dr Gem, physician to the English embassy at Paris, in 1783 
he passed his early years amidst a political fermentation which 
led him to take a deep interest in politics. Though he approved 
of the French Revolution, his sympathies were with the more 
moderate party, and he became a member of the " dub of 1789," 
instituted to support the new form of constitutional monarchy 
in opposition to 'the anarchical attempts of the Jacobins. He 
early displayed bis mastery of the principles of finance by a 
Piscours delivered in August 1790 before this society, in regard 
to the issue of assignats by the government. The Discours 
gained him considerable reputation, but as it failed in its purpose 
he withdrew from the society. In January 1 793 he was appointed 
by Dundas to an office created to direct the execution of the 
Aliens Act; and in the discharge of his delicate duties he mani- 
fested such ability that in 1795 he was appointed undersecretary 
at war. In the following year he entered parliament as member for 
Morpeth, but for a considerable period he took scarcely any part 
in the debates. In 1800 he inherited a fortune from Dr Gem. 
On the retirement of Pitt in 1801 he resigned office, and after 
contesting Dover unsuccessfully he withdrew for a time into 
private life. Having in 1804 been chosen to represent Liskeard, 
he was on the restoration of the Pitt ministry appointed secretary 
of the treasury, holding office till the dissolution of the ministry 
after the death of Pitt in January 1806. After being elected 
for Harwich in 1807, he accepted the same office under the duke 
of Portland, but he withdrew from the ministry along with 
Canning in 1809. In the following year he published a pamphlet 
on the currency system, which confirmed his reputation as the 
ablest financier of his time; but his free-trade principles did not 
accord with those of his party. In 181 2 he was returned for 
Chichester. When in 1814 he re-entered the public service, it 
was only as chief commissioner of woods and forests, but his 
influence was from this time very great in the commercial and 
financial legislation of the country. He took a prominent part 
in the corn-law debates of 1814 and 1815; and in 1819 he 
presented a memorandum to Lord Liverpool advocating a large 

reduction in the unfunded debt, and explaining a method Jot 
the resumption of cash payments, which was embodied in the 
act passed the same year. In 1821 he was a member of the 
committee appointed to inquire into the causes of the agricultural 
distress then prevailing, and the proposed relaxation of the corn 
laws embodied in the report was understood to have been chiefly 
due to his strenuous advocacy. In 1823 be was appointed 
president of the board of trade and treasurer of the navy, and 
shortly afterwards he received a seat in the cabinet. In the 
same year he was returned for Liverpool as successor to Canning, 
and as the only man who could reconcile the Tory merchants 
to a free trade policy. Among the more important legislative 
changes with which he was principally connected were a reform 
of the Navigation Acts, admitting other nations to aiull equality 
and reciprocity of shipping duties; the repeal of the labour laws; 
the introduction of a new sinking fund; the reduction of the 
duties on manufactures and on the importation of foreign goods, 
and the repeal of the quarantine .duties. In accordance with 
his suggestion Canning in 18*7 introduced a measure on the 
corn laws proposing the adoption of a sliding scale to regulate 
the amount of doty. A misapprehension between Huslusson 
and the duke of Wellington led to the duke proposing an amend* 
ment, the success of which caused the abandonment of the 
measure h^ the government . After the death of Canning in the 
same year Huskitson accepted the secretaryship of the colonies 
under Lord Goderkh, an office which he continued to hold in 
the new cabinet formed by the duke of Wellington in the following 
year. After succeeding with great difficulty in inducing the 
cabinet to agree to a compromise on the corn laws, Huskisson 
finally resigned office in May 1829 on account of a difference 
with his colleagues in regard to the disfranchisement of East 
Retford. On the 1 5th of September of the following year he was 
accidentally killed by a locomotive engine while present at the 
opening of the Liverpool and Manchester railway. 

See the Life of Huskisson, by J^ Wright (London, 1831). 

HUSS (or Hus), JOHN (c. 1373-1415), Bohemian, reformer and 
martyr, was born at Hussinece, 1 a market village at the foot of 
the Bbhmerwald, and not far from the Bavarian frontier, between 
1373 end -375. the exact date being uncertain. His parents 
appear to have been well-to-do Czechs of the peasant class. 
Of his early life nothing is recorded except that, notwithstanding 
the early loss of his father, he obtained a good elementary 
education, first at Hussinecz, and afterwards at the neighbouring 
town of Prachaticz. At, or only a very little beyond, the 
usual age he entered the recently (1348) founded university of 
Prague, where be, became bachelor of, arts in 1303, bachelor 
of theology in 1304, and master of arts in 1306. In 1308 
he was chosen by the Bohemian " nation " of the university 
to an examjnership for the bachelor's degree; in the 
same year he began to lecture also, and there is reason to 
believe that the philosophical writings of Wycliffe, with which 
he had been for some years acquainted, were his text-books. 
In October 1401 he was made dean of the philosophical faculty, 
and for the half-yearly period from October 140a to April 1403 
he held, the office of rector of the university. In 1402 also be 
was made rector or curate (capdlarius) of the Bethlehem chapel, 
which bad in 1391 been erected and endowed by some zealous 
citizens of Prague for the purpose of providing good popular 
preaching in the Bohemian tongue. This appoinment had 
a deep influence on the already vigorous religious life of Hus* 
himself; and one of the effects of the earnest and independent 
study of Scripture into which it led him was a profound conviction 
of (he great value not only of the philosophical but also of the 
theological writings of Wycliffe. 

This newly-formed sympathy with the English reformer did 
not, in the first instance at least, involve Huss in any conscious 
opposition to the established doctrines of Catholicism, or in 
any direct conflict with the authorities of the church; and for 

1 From which the name Huss, or more properly Hus, an abbrevia- 
tion adopted by himself about 1396, is derived. Prior to that date 
he was invariably known as Johann Hussy nee t, Hussinecz. Hu 
or de Hussyncc*. 


several years he continued to met la full accord with hb archbishop 
(Sbynjek, or Sbynko, of Hasenburg). Thus in 1405 he, with 
other two masters, was commissioned to examine into certain 
reputed miracles at Wusnack, near Wittenberg, which had 
caused that church to be made a resort of pilgrims from all parts 
of Europe. The result of their report was that all pilgrimage 
thither jfrom the province of Bohemia was prohibited by the 
archbishop on pain of excommunication, while Huss, with the 
full sanction of his superior, gave to the world his first published 
writing, entitled De Omni Sanguine Ckristi OarifccaSo, in which 
he declaimed in no measured terms against forged miracles and 
ecclesiastical greed, urging Christians at the same time to desist 
from looking for sensible signs of Christ's presence, but rather 
to seek Him in His enduring word* More than once also Huss, 
together with his friend Stanislaus of Znaim, was appointed 
to be synod preacher, and in this capacity he delivered at the 
provincial councils of Bohemia many faithful admonitions. 
As early as the 28th of May 1403, it is true, there had been held 
a university disputation about the new doctrines of Wycliffe, 
which had resulted in the condemnation el certain propositions 
presumed to be his; five years later (May 20, 1408) this decision 
had been refined into a declaration that these, forty-five in 
number, were not to be taught in any heretical, erroneous 
or offensive sense. But it was only slowly that the growing 
sympathy of Huss with Wycliffe unfavourably affected his 
relations with his colleagues in the priesthood. In 1408, however, 
the clergy of the city and archiepiscopal diocese of Prague laid 
before the archbishop a formal complaint against Huss, arising 
out of strong expressions with regard to clerical abuses of which 
he had made use in his public discourses; and the result was 
that, having been first deprived of his appointment as synodal 
preacher, he was, after a vain attempt to defend himself in 
writing, publicly forbidden the exercise of arty priestly function 
throughout the diocese. Simultaneously with these proceedings 
in Bohemia, negotiations had been going on for the removal of 
the long-continued papal schism, and it had become apparent 
that a satisfactory solution could only be secured if, as seemed 
not impossible, the supporters of the rival popes, Benedict X11I. 
and Gregory XII., could be induced, in view of the approaching 
council of Pisa, to pledge themselves to a strict neutrality. 
With this end King Wenceslaus of Bohemia had requested the 
co-operation of the archbishop and his clergy, and also the 
support of the university, in both instances unsuccessfully, 
although in the case of the latter the Bohemian " nation," with 
Huss at its head, had only been overborne by the votes of t£e 
Bavarians, Saxons and Poles. There followed an expression 
of nationalist and particularistic as opposed to ultramontane 
and also to German feeling, which undoubtedly was of supreme 
importance for the whole of the subsequent career of Huss. In 
compliance with this feeling a royal edict (January 18, 1409) 
was issued, by which, in alleged conformity with Paris usage, 
and with the original charter of the university, the Bohemian 
" nation " received three votes, while only one was allotted to 
the other three "nations" combined; whereupon all the 
foreigners, to the number of several thousands, almost im- 
mediately withdrew from Prague, an occurrence which led to 
the formation shortly afterwards of the university of Leipsig. 

It was a dangerous triumph for Huss; for his popularity 
at court and in the general community had been secured only 
it the price of clerical antipathy everywhere and of much German 
ill-will. Among the first results of the changed order of things 
were on the one hand the election of Huss (October 1409) to be 
again rector of the university, but on the other hand the appoint- 
ment by the archbishop of an inquisitor to inquire into charges 
[>f heretical teaching and inflammatory preaching brought 
against him. He had spoken disrespectfully of the church, it 
was said, had even hinted that AntichrisUfmght be found to 
be in Rome, had fomented in his preaching the quarrel between 
Bohemians and Germans, and had, notwithstanding all that 
lad passed, continued to speak of Wycliffe as both a pious man 
rod an orthodox teacher. The direct result of this investigation 
s not known, but it is impossible to disconnect from it the 

promulgation by Pope Alexander V., on the soth of December 
1409, of a butt which ordered the abjuration of all WydifHte 
heresies and the surrender of all his books, while at the same 
time— a measure specially levelled at the pulpit of Bethlehem 
chapel— all preaching was prohibited except in localities which 
had been by long usage set apart for that use. This decree, as 
soon as it was published in Prague (March 9, 1410), led to much 
popular agitation, and provoked an appeal by Huss to the 
pope's better informed judgment; the archbishop, however, 
resolutely insisted on carrying out his instructions, and in the 
following July caused to be publicly burned, in the courtyard 
of his own palace, upwards of 300 volumes of the writings of 
Wycliffe, while he pronounced solemn sentence of excommunica- 
tion against Huss and certain of his friends, who had. in the 
meantime again protested and appealed to the new pope 
(John XXIII.). Again the populace rose on behalf of their hero/ 
who, in his turn, strong in the conscientious conviction that " in 
the things which pertain to salvation God is to be obeyed rather 
than man," continued uninterruptedly to preach in the Bethlehem 
chapel, and in the university began publicly to defend the sc*» 
called heretical treatises of Wycliffe, while from king and queen, 
nobles and burghers, a petition was sent to Rome praying that 
the condemnation and prohibition in the bull of Alexander V. 
might be quashed. Negotiations were carried on for some months, 
but in vain; in March 14x1 the ban was anew pronounced upon 
Huss as a disobedient son of the church, while the magistrates 
and councillors of Prague who had favoured him were threatened 
with a Similar penalty in case of their giving him a contumacious 
support. Ultimately the whole city, which continued to harbour 
him, was laid 1 under interdict; yet he went on preaching, and 
masses were celebrated as usual, so that at the date of Archbishop 
Sbynko's death in September 141 r, it seemed as if the efforts of 
ecclesiastical authority had resulted in absolute failure. 

.The struggle, however, entered on a new phase with the 
appearance at Prague in May 1412 of the papal emissary charged 
with the proclamation of the papal bulls by which 4 religious 
war was decreed against the excommunicated King Ladislauf 
of Naples, and indulgence was promised to ail who should take 
port in it, on terms similar to those which had been enjoyed 
by the earlier crusader* to the Holy Land. By his bold wikt 
thorough-going opposition to this mode of procedure against 
Ladblaus, and still more by his doctrine that indulgence could 
never be sold without simony, and could not be lawfully granted 
by the church except on condition of genuine contrition and 
repentance, Huss at last isolated himself, not only from the 
archiepiscopal party under Albik of TJnitschow, but also from 
the theological faculty of the university, and especially front 
such men- as Stanislaus of Znaim and Stephen Palets, who until 
then had been his chief supporters. A popular demonstration, 
in which the papal bulls bad been paraded through the streets 
with crrcurflstances of peculiar ignominy and finally burnt, led 
to intervention by Wenceslaus on beharf of public order; three 
young men, for having openly asserted the unlawfulness of the 
papal indulgence after silence had been enjoined, were sentenced 
to death (June 14x2); the excommunication against Huss was 
renewed,- and the interdict again laid on* all places whfch should 
give him shelter — a measure which now began to be more strictly 
regarded by the clergy, so that in the following December 
Huss had no alternative but to yield to the express wish of the 
king by temporarily withdrawing from Prague. A provincial 
synod, held at the instance of Wenceslaus in February 1413, 
broke up without having reached any practical result; and 
a commission appointed shortly afterwards also failed to bring 
about a reconciliation between Huss and his adversaries. The 
so-called heretic meanwhile spent his time partly at Koaihradek, 
some 45 m. south of Prague, and partly at Krakowiu in 
the immediate neighbourhood of the capital, occasionally 
giving a course of open-air preaching, but finding his chief 
employment in maintaining that copious correspondence of 
which some precious fragments still are extant, and 'in the 
composition of the treatise, De Etdtsio, which subsequently 
furnished most of the material for the capital charges brought 



crowd. On bearing this news King Weaceskus was seised with 
an apoplectic fit, and died a few days afterwards. The death of 
the king resulted in renewed troubles in Prague and in almost 
all parts of Bohemia. Many Romanist*, mostly Germaas— 4or 
they had almost all remained faithful- to the papal cause— were 
expelled from the Bohemian cities. In Prague, in November 
X410, severe fighting took place between the Hussites and the 
mercenaries whom Queen Sophia (widow of Wenceslaus and 
regent after the death of her husband) had hurriedly collected. 
After a considerable part of the city had been destroyed a truce 
was concluded on the 13th of November. The nobles, who 
though favourable to the Hussite cause yet supported the 
regent, promised to act as mediators with Sigismund; while 
the* citizens of Prague consented to restore to the royal forces 
the castle of Vyiehrad, which had fallen into their hands. &£ka, 
who disapproved of this compromise, left Prague and retired 
toPlsen (Pflscn). Unable to maintain himself there he marched 
to southern Bohemia, and after defeating the Romanists at 
Sudomef— the first pitched battle of the Hussite wars— he 
arrived at Usti, one of the earliest meetingrplaces of the Hussite*. 
Not considering its situation sufficiently stsong, he moved to 
the neighbouring new settlement of the Hussites, to which the 
biblical- name of Tabor was given. Tabor soon became the 
centre of the advanced Hussites, who differed from the Utraquists 
by recognizing only two s ar i n menl s— Baptism and Communion — 
and by rejecting most of the ceremonial of the Roman Church. 
The ecclesiastical organisation of Tabor had a somewhat puritanic 
character, and the government was established on * thoroughly 
democratic basis. Four captains of the people (hejtmant) were 
elected, one of whom was 2iika; and a very strictly military 
discipline was instituted. 

Sigismund, king of the Romans, had, by the death of his 
brother Wenceslaus without isste, acquired a claim on the 
Bohemian crown; though it was then, and remained till much 
later, doubtful whether Bohemia was an hereditary or an elective 
monarchy. A firm adherent of the Church of Rome, Sigismund 
was successful in obtaining aid from the pope. Martin V. 
issued a bull on the 17th of March 1420 which proclaimed a 
crusade " for the destruction of the Wyeliffites, Hussites and all 
other heretics in Bohemia." The vast army of crusaders, with 
which were Sigismund and many German princes, and which 
consisted of adventurers attracted by the hope of pillage from 
afi parts of Europe, arrived before Prague on the 30th of June 
and immediately began the siege of the city, which had, hewever, 
soon to be abandoned (see Zi&ca, Johm). Negotiations took 
place for a settlement of the religious differences. The united 
Hussites formulated their demands in a statement known as 
the " articles of Prague." This document, the most important 
of 'the Hussite period, runs thus in the wording of the con* 
temporary chronicler, Laurence of Brezovaj— 

1 f. The word of God shall be preached and made known in the 
kingdom of Bohemia freely and in an orderly manner by the priest* 
of the Lord. ... 

IL The sacrament ef the moat Holy Eucharist shall be freely 
administered in the two kinds, that is bread and wine, to all the 
faithful in Christ who are not precluded by mortal sin— according 
to the word and disposition of Oor Saviour. 

HI. The secular power over riches and worldly goods which the 
deify possesses in contradiction to Christ's precept, to the prejudice 
of its office and to the detriment of the secular arm, shall be taken 
and withdrawn from it, and the clergy itself shall be brought back to 
the evangelical rule and an apostofic life such as that which Christ 
and his apostles led. . . . 

IV. All mortal sins, and in particular all public and other dis- 
orders, which are contrary to God's law, shall in every rank of life 
be duly and judiciously prohibited and destroyed by those whose 
office it is. 

These articles, which contain the essence of the Hussite doctrine, 
were rejected by Sigismund, mainly through the influence 
of the papal legates, who considered them prejudicial to the 
authority of the Roman see, Hostilities therefore continued. 
Though Sigismund had retired from Prague, the castles of 
Vyiehrad and Hradcany remained in possession of his troops. 
The cituens of Prague laid siege to the Vyiehrad, and towards 

the end of October (14*0) the garrison was on the point of 
capitulating through famine. Sigismund attempted to relieve 
the fortress, but was decisively defeated by the Hussites on 
the tst of November near the village of Pankrac The castles 
of Vysehrad and Hradcany now capitulated, and shortly after- 
wards almost all Bohemia fell into the hands of the Hussites. 
Internal troubles prevented them from availing themselves 
completely of their victory. At Prague a demagogue, the 
priest John of 2elivo, for a time obtained almost unlimited 
authority over the lower classes of the townsmen; and at 
Tabor a communistic movement (that of the so-called Adamites) 
was sternly suppressed by 2i2ka. Shortly afterwards a new 
crusade against the Hussites was undertaken. A large German 
army entered Bohemia, and in August 1421 laid siege to the 
town of Zatec (Saaz). The crusaders hoped to be joined in 
Bohemia by King Sigismund, but that prince was detained 
in Hungary. After an unsuccessful attempt to storm Zatec 
the crusaders retreated somewhat ingloriously, on bearing 
that the Hussite troops were approaching. Sigismund only 
arrived in Bohemia at the end of the year 1421. He took 
possession of the town of Kutna Horn (Kuttenberg), but was 
decisively defeated by 2i2ka at Nemecky Brod (Deutschbrod) 
on the 6th of* January 1422. Bohemia was now again for a 
time free from foreign intervention, but internal discord again 
broke out caused partly by theological strife, partly by the 
ambition of agitators. John of Zelivo was on the 9th of March 
1422 arrested by the town council of Prague and decapitated. 
There were troubles at Tabor also, where a more advanced 
party opposed Ziika's authority. Bohemia obtained a temporary 
respite when, in 1422, Prince Sigismund Korybutovic' of Poland 
became for a short time ruler of the country. His authority 
was recognized by the Utraquist nobles, the citizens of Prague, 
and the more moderate Taborites, including 2i2ka* Korybutovic, 
however, remained but a short time in Bohemia; after his 
departure civil war broke out, the Taborites opposing in arms 
the more moderate Utraquists, who at this period are also 
called by the chroniclers the " Praguers," as Prague was their 
principal stronghold. On the 27th of April 1423, 2i£ka now 
again leading, the Taborites defeated at Horic the Utraquist 
army under Cenek of Wartemberg; shortly afterwards an 
armistice was concluded at Konopist. 

Papal influence had meanwhile succeeded in calling forth 
a new crusade against Bohemia, but it resulted in complete failure. 
In spite of the endeavours of their rulers, the Slavs of Poland 
and Lithuania did not wish to attack the kindred Bohemians; 
the Germans were prevented by internal discord from taking 
joint action against the Hussites; and the king of Denmark, 
who had landed in Germany with a large force intending to 
take part in the crusade, soon returned to his own country. 
Free for a time from foreign aggression, the Hussites invaded 
Moravia, where a large part of the population favoured their 
creed; but, again paralysed by dissensions, soon returned 
to Bohemia. The city of KoniggxaU (Kralove Hradec), which 
had been under Utraquist rule, espoused the doctrine of Tabor, 
and called 2i£ka to its aid. After several military successes 
gained by 2iika (g.v.) in 1435 and the following year, a treaty 
of peace between the Hussites was concluded on the 13th of 
September *4M at liben, a village near Prague, now part of 
that dty. 

In 1426 the Hussites were again attacked by foreign enemies 
In June of that year their forces, led by Prokop the Great — 
who took the command of the Taborites shortly after 2iika's 
death in October 1424— and Sigismund Korybutovic, who had 
returned to Bohemia, signally defeated the Germans at Aussig 
(Usti nad Labem). After this great victory,, and another at 
Tachau in 1437, the Hussites repeatedly invaded Germany, 
though they made no attempt to occupy permanently any part 
of the country. 

The almost uninterrupted series of victories of the Hussites 
now rendered vain all hope of subduing them by force of arms. 
Moreover, the conspicuously democratic character of the Hussite 
movement caused the German princes, who. were afraid that 


such view* might extend to their own countries, to desire peace. 
Many Hussites* particularly the Utraquist clergy, were also in 
favour of peace. Negotiations for this purpose were to take 
place at the oecumenical council which bad been summoned to 
meet at Basel on the 3rd of March 143 f. The Roman see re- 
luctantly consented to the presence of heretics at this council, 
but indignantly rejected the suggestion of the Hussites that 
members of t he Greek Church, and representatives of all Christian 
creeds, should also be present. Before definitely giving its consent 
to peace negotiations, the Roman Church determined on making 
a last efbrt to reduce the Hussites to subjection. On the j si 
el August 143 1 a large army of crusaders, under Frederick, 
margrave of Brandenburg, whom Cardinal Ccsarini accompanied 
as papal legate, crossed the Bohemian frontier; on the 14th 
of August it reached the town of Domailice (Tauss); but on 
the arrival of the Hussite army under Prokop the crusaders 
immediately took to flight, almost without offering resistance. 

On the 15th of October the members of the council, who had 
already assembled at Basel, issued a formal invitation to the 
Husskes to take part in its deliberations. Prolonged negotiations 
ensued; but finally a Hussite embassy, led by Prokop and 
including John of Rokycan, the Taborite bishop Nicolas of 
Pethfimov, the " English Hussite," Peter Payne and many 
others, arrived at Basel on the 4th of January 1433. It was 
found impossible to arrive at an agreement. Negotiations 
were not, however, broken off; and a change in the political 
situation of Bohemia finally resulted in a settlement. In 1434 
war again broke out between the Utraquists and the Taborites. 
On the 30th of May of that year the Taborite army, led by Prokop 
the Great and Prokop the Less, who both fell in the battle, 
was totally defeated and almost annihilated at Lipan. The 
moderate party thus obtained the upper hand; and it formulated 
its demands in a document which was finally accepted by the 
Church of Rome in a slightly modified form, and which is known 
as " the compacts." The compacts, mainly founded on the 
articles of Prague, declare that:— 

1. The Holy Sacrament is to be given freely in both kinds to all 
Christians in Bohemia and Moravia, and to those elsewhere who 
adhere to the faith of these two countries. 

a. All mortal sins shall be punished and extirpated by those whose 
office it is so to do. 

3. The word of God is to be freely and truthfully preached by the 
priests of the Lord, and by worthy deacons. 

4. The priests in the time of the law of grace shall claim no owner- 
ship of worldly possessions. 

On the 5th of July 1436 the compacts were formally accepted 
and signed at Iglau, in Moravia, by King Sigismund, by the 
Hussite delegates, and by the representatives of the Roman 
Church. The last-named, however, refused to recognize as 
archbishop of Prague, John of Rokycan, who had been elected 
to that dignity by the estates of Bohemia. The Utraquist 
creed, frequently varying in its details, continued to be that 
of the established church of Bohemia till all non-Roman religious 
services were prohibited shortly after the battle of the White 
Mountain in 1620. The Taborite party never recovered from 
its defeat at Lipan, and after the town of Tabor had been captured 
by George of Podebrad in 1452 Utraquist religious worship was 
established there. The Bohemian brethren, whose intellectual 
originator was Peter Chelttcky, hut whose actual founders 
were Brother Gregory, a nephew of Archbishop Rokycan, 
and Michael, curate of Zamberk, to a certain extent continued 
the Taborite traditions, and in the 15th and 16th centuries 
included most of the strongest opponents of Rome in Bohemia. 
J. A. Komensky (Comenius), a member of the brotherhood, 
claimed for the members of his church that they were the genuine 
inheritors of the doctrines of Hus. After the beginning of the 
German Reformation many Utraquists adopted to a large 
extent the doctrines of Luther and Calvin; and in 1567 obtained 
the repeal of the compacts, which no longer seemed sufficiently 
far-reaching From the end of the 16th century the inheritors 
of the Hussite tradition in Bohemia were included in the more 
general name of " Protestants u borne by the adherents of the 

An histories of Bohemia devote a large amount of space to tht 
Hussite movement. See Count Lflttow, Bohemia: an Historical 
Sketch (London, 1806); Palacky, Geukbhte ton B6hmen\ Bach* 
mann, Cesckiehte Bdkmens; L. Krumsnel, Gtxhukt* der bokmisckm 
Reformation (Gocha, 1866) and Utraqmsten und Tahoriten (Goths, 
1871); Ernest Denis, Huss et la guerre des Hussites (Paris, 1S7B); 
H. Toman, llusilski Vdldnicivi (Prague. 1898). (L.) 

HUSTING (0. Eng. hasting, from Old Norwegian hOsthing); 
the " thing " or " ting," i.e. assembly, of the household of 
personal (ollowprs or retainers of a king, earl or chief, contrasted 
with the " folkmoot, ,r the assembly of the whole people. "Thing'J 
meant an inanimate object, the ordinary meaning at the present 
day, also a cause or suit, and an assembly; a similar develop- 
ment of meaning is found in the Latin res. The word still 
appears in the names of the legislative assemblies of Norway j 
the Storthing and of Iceland, the AHhing. "Husting," or 
more usually in the plural " hustings," was the name ofa court 
of the city of London. This court was formerly the county 
court for the city and was held before the lord mayor, the 
sheriffs and aldermen, for pleas of land, common pleas and 
appeals from the sheriffs. It had probate jurisdiction and wills 
were registered. All this jurisdiction has long been obsolete, 
but the court still sits occasionally for registering gifts made to 
the city. The charter of Canute (1032) contains a reference 
to " hustings " weights, which points to the early establishment 
of the court. It is doubtful whether courts of this name were 
held in other towns, but John Cowell (1 554-161 1) in his Inter- 
preter (1601) s.v., "Hustings," says that according to Fleta there 
were such courts at Winchester, York, Lincoln, Sheppey and 
elsewhere, but the passage from Fleta, as the New English 
Dictionary points out, does not necessarily imply this (11. Iv. 
II abet ctiam Rex curiam in civiiatibus . . . et in locis . . . 
sicut in Hustingis London* Winlon, &V.). The ordinary use 
of " hustings " at the present day for the platform from which 
a candidate soeaks at a parliamentary or other election, or 
more widely for * political candidate's election campaign, is 
derived from the application of the word, first to the platform 
in the Guildhall on which the London court was held, ancLncxt 
to that from which the public nomination of candidates for a 
parliamentary election was formerly made, and from which 
the candidate addressed the electors. The Ballot Act of 1872 
did away with this public declaration of the nomination. 

HUSUM . a town in the Prussian province of Sch les wig -Hoist e in, 
in. a fertile district 2) m. inland from the North Sea, on the 
canalized Husumer Au, which forms its harbour and roadstead, 
09 m. N.W. from Hamburg on a branch line from T6nning. 
Pop. (1900) 8268. It has steam communication with the 
North Frisian Islands (Nordstrand, Fohr and Sylt), and is a 
port for the cattle trade with England. Besides a duc|I palace 
and park, it possesses an Evangelical church and a gymnasium. 
Cattle markets are held weekly, and in them, as also in cereals, 
a lively export trade is done. There are also extensive oyster 
fisheries, the property of the state, the yield during the season 
being very considerable. Husum is the birthplace of Johann 
Gcorg Forchhammer (1 704-1865), the mineralogist, Peter 
Wilhclm Forchhammer (1801-1894), the archaeologist, and 
Theodore Storm (1817-1888), the poet, to the last of whom a 
monument has been erected here. 

Husum is first mentioned in 1252, and Its first church was 
built in 1431- Wisby rights were granted it in 1582, and in 
1603 it received municipal privileges from the duke of Hoist ein. 
It suffered greatly from inundations in 1634 and 171 7. 

See Christiansen, Die Geschichte Husttms (Husum. 1003): and 
Heontngsen, Das Stiflunfsbuch der Stadt Husum (Husum, 1004). 

HUTCHESON, FRANCIS -(1694-1746), English philosopher, 
was born on the 8th of August 1694. His birthplace was probably 
the townland of Drumalig, in the parish of Saint field and county 
of Down, Ireland. 1 Though the family had sprung from Ayrshire, 
in Scotland, both bis father and grandfather were ministers 
of dissenting congregations in the north of Ireland. Hutcheson 
was educated partly by his grandfather, partly at an academy, 
where according to his biographer, Dr Leechman, he was taught 
1 See Belfast Magazine for August 1813. 



"the ordinary scholastic philosophy which was in vogue in 
those days." In 1710 he entered the university of Glasgow, 
where he spent six years, at first in the study of philosophy, 
classics and general literature, and afterwards in the study 
of theology. On quitting the university, he returned to the 
north of Ireland, and received a licence to preach. When, 
however, he was about to enter upon the pastorate of a small 
dissenting congregation he changed his plans on the advice 
of a friend and opened a private academy in Dublin. In Dublin 
his literary attainments gained him the friendship of many 
prominent inhabitants. Among these was Archbishop King 
(author of the De origfne malt), who resisted all attempts to 
prosecute Hutcheson in the archbishop's court for keeping a 
school without the episcopal licence. Hutcheson's relations 
with the clergy of the Established Church, especially with the 
archbishops of Armagh and Dublin, Hugh Boulter (167 2- 1742) 
and William King (16 50-1 729}, seem to have been most cordial, 
and his biographer, in speaking of " the inclination of his friends 
to serve him, the schemes proposed to him for obtaining pro- 
motion," &c, probably refers to some offers of preferment, on 
condition of his accepting episcopal ordination. _ These offers, 
however, were unavailing. 

While residing in Dublin, Hutcheson published anonymously 
the four essays by which he is best known, namely, the Inquiry 
concerning Beauty ; Order, Harmony and Design, the Inquiry con- 
cerning Moral Good and Evil, in 1725, the Essay on the Nature 
and Conduct of the Passions and Affections and Illustrations 
upon the Moral Sense, in 1728. The alterations and additions 
made in the second edition of these Essays were published in a 
separate form in 1726. To the period of his Dublin residence 
are also to be referred the Thoughts on Laughter (a criticism of 
Hobbes) and the Observations on the Fable of the Bees, being 
in all six letters contributed to Hibernicus' Letters, a periodical 
which appeared in Dublin (1725-1727, 2nd cd. 1754). At the end 
of the same period occurred the controversy in the. London 
Journal with Gilbert Burnet (probably the second son of Dr 
Gilbert Burnet, bishop of Salisbury), on the " True Foundation 
of Virtue or Moral Goodness." All these letters were collected 
Jn one volume (Glasgow, 1772). 

In 1729 Hutcheson succeeded his old master, Gershom 
Carmichael, in the chair of moral philosophy in the university 
of Glasgow. It is curious that up to this time all his essays 
and letters had been published anonymously, though their 
authorship appears to have been well known. In 1730 he 
entered on the duties of his office, delivering an inaugural lecture 
(afterwards published), De naturali hominum socialitate. 
It was a great relief to him after the drudgery of school work 
to secure leisure for his favourite studies; "non levi igitur 
laetitia commovebar cum almam matrem Academiam me, 
suum olim alumnum, in libertatem asseruisse audivcram." 
Yet the works on which Hutcheson's reputation rests had 
already been published. 

The remainder of his life he devoted to his professorial 
duties. His reputation as a teacher attracted many young 
men, belonging to dissenting families, from England and Ireland,, 
and he enjoyed a well-deserved popularity among both his 
pupils and his colleagues. Though somewhat quick-tempered, 
he was remarkable for his warm feelings and generous impulses. 
He was accused in 1738 before the Glasgow presbytery for 
" following two false and dangerous doctrines: first, that the 
standard of moral goodness was the promotion of the happiness 
of others; and second, that we could have a knowledge of good 
and evil without and prior to a knowledge of God" (Rae, Life ; 
of Adam Smith, 189s). The accusation seems to have had no 

In addition to the works named, the following were published 
during Hutcheson's lifetime: a pamphlet entitled Considerations 
on Patronage (1735); PhUosophiae moralis instituiio com- 
fendiaria, ethices et jurisprudentiae naturalis elementa continens, 
lib. Hi. (Glasgow, 1742); Metaphysioae synopsis ontologiom 
et pneumatologiam complectens (Glasgow, 1742). The last 
work was published anonymously. After his death, his son, 

Frauds Hut cheson (c 173*- 1773), author of a number of 
popular songs (e.g. u As Colin one evening," " Jolly Bacchus/' 
" Where Weeping Yews "), published much the longest, though 
by no means the most interesting, of his works, A System 0/ 
Moral Philosophy, in Three Books (2 vols., London, 1755). To this 
is prefixed a life of the author, by Dr Wtlb'am Leechman (1706- 
1785), professor of divinity in the university of Glasgow. The 
only remaining work assigned to Hutcheson is a small treatise on 
Logic (Glasgow, 1 764). Thiscompenditsm, together with the Com- 
pendium of Metaphysics, was republished at Strasbourg in 172a. 

Thus Hutcheson dealt with metaphysics, logic and ethics, 
His importance is, however, due almost entirely to his ethical 
writings, and among these primarily to the four essays and the 
letters published during his residence in Dublin. His Standpoint 
has & negative and & positive aspect; he is in strong opposition 
to Thomas Hobbes and Bernard de Mandeville, and in funds- 
mental agreement with Shaftesbury (Anthony Ashley Cooper, 
3rd earl of Shaftesbury), whost name he very property coupled 
with his own on the title-page of the first two essays. There 
are no two names, perhaps, in the history of English moral 
philosophy, which stand in a closer connexion. The analogy 
drawn between beauty and virtue, the functions assigned to 
the moral sense, the position that the benevolent feelings form 
an original and irreducible part of our nature, and the unhesitating 
adoption of the principle that the test of virtuous action is Us 
tendency to promote the general welfare are obvious and funda- 
mental points of agreement between the two authors. 

I. Jj^ic*.— According to Hutcheson, man has a variety of senses, 
internal as well as external, reflex as well as direct, the general 
definition of a sense being " any determination of our minds to receive 
ideas independently on our will, and to have perceptions of pleasure 
and pain (Essay on the Nature and Conduct of the Passions, sect. 1). 
He does not attempt to give an exhaustive enumeration of these 
" senses," but, in various parts of his works, he specifies, besides the 
five external senses commonly recognized (which, he rightly hints, 
might be added to), — (1) consciousness, by which each man has a 
perception of himself and of all that is going on in bis own mind 
(Metoph. Syn. pars i. cap. 2); (2) the sense of beauty (sometimes 
called specifically " an internal sense ") ; (3) a public sense, or sensus 
communis, "a determination to be pleased with the happiness of 
others and to be uneasy at their misery M ; (4) the moral sense, or 
"■ moral sense of beauty in actions and affections, by which we 
perceive virtue or vice, in ourselves or others " ; (5) a sense of honour, 
or praise and blame, " which makes the approbation or gratitude of 
others the necessary occasion of pleasure, and their dislike, con- 
demnation or resentment of injuries done by us the occasion of that 
uneasy sensation caned shame"; (6) a sense of the ridiculous. It 
is plain, as the author confesses, that there may be " other percep- 
tions, distinct from all these classes," and, in fact, there seems to be 
no limit to the number of u senses " in which a psychological division 
of this kind might result. 

Of these " senses " that which plays the most iniportant part in 
Hutcheson's ethical system is the " moral sense." It is this which 
pronounces immediately on the character of actions and affections, 
approving those which are virtuous, and disapproving those which 
arc vicious. " His principal design," he says in the preface to the 
two first treatises, " is to show that human nature was not left quite 
indifferent in the affair of virtue, to form to itself observations con- 
cerning the advantage or disadvantage of actions, and accordingly to 
regulate its conduct. The weakness of our reason, and the avocations 
arising from the infirmity and necessities of our nature, are so great 
that very few men could ever have formed those long deductions of 
reasons which show some actions to be in the whole advantageous 
to the agent, and their contraries pernicious. The Author of nature 
has much better furnished us for a virtuous conduct than oar 
moralists seem to imagine, by almost as quick and powerful instruc- 
tions as we have for the preservation of our bodies. He has made 
virtue a lovely form, to excite our pursuit of it, and has given us 
strong affections to be the springs of each virtuous action." Passing 
over the appeal to final causes involved in this and similar passages, 
as well as the assumption that the " moral sense " has had no growth 
or history, but was '' implanted " in man exactly in the condition ia 
which it is now to be found among the more civilized races, an 
assumption common to the systems of both Hutcheson and Butler, 
it may be remarked that this use of the term " sense " has a tendency 
to obscure the real nature of the process which goes on in an act of 
moral judgment. For, as is so clearly established by Hume, this act 
really consists of two parts: one an act of deliberation, more or less 
prolonged, resulting in an intellectual judgment : the other a reflex 
feeling, probably instantaneous, of satisfaction at actirjns which we 
denominate good, of dissatisfaction at those which we denominate bad. 
By the intellectual part of this process we refer the action or habit 
to a certain class; but no sooner is the intellectual process corop^ -1 


than there is excited in us a feeling similar to that which myriad* of 
actions and habits of the same class, or deemed to be of the same 
class, have excited in us on former occasions. Now, supposing the 
latter part of this process to be instantaneous, uniform and exempt 
from error, the former certainly is not. All mankind may, apart from 
their selfish interests, approve that which is virtuous or makes for 
the general good, but surely they entertain the most widely divergent 
opinions, and, in fact, frequently arrive at directly opposite con- 
clusions as to particular actions and habits. This obvious distinction 
is undoubtedly recognized by Hutcheson in his analysis of the mental 
process preceding moral action, nor does he invariably ignore it, 
even when treating of the moral approbation or disapprobation which 
is subsequent on action. None the less, it remains true that 
Hutcheson, both by his phraseology, and by the language in which he 
describes the process of moral approbation, has done much to favour 
that loose, popular view of morality which, ignoring the necessity of 
deliberation and reflection, encourages hasty resolves and unpre- 
meditated judgments. The term " moral sense " (which, it may be 
iad air ....... . — 

noticed, had already been employed by Shaftesbury, not only, as Dr 
Whewell appears to intimate, in the margin, but also in the text of his 
Inquiry), if invariably coupled with the term " moral judgment," 
would be open to little objection; but, taken alone, as designating 
the complex process of moral approbation, it is liable to lead not 
only to serious misapprehension but to grave practical errors. For, 
if each mans decisions am solely the result of an immediate intuition 
of the moral sense, why be at any pains to test, correct or review 
them? Or why educate a faculty whose decisions are infallible? 
And how do we account for differences in the moral decisions of 
different societies, and the observable changes in a man's own 
views? The expression has, in fact, the fault of most metaphorical 
terms: it leads to aa exaggeration of the truth which it is intruded 
to suggest. 

But though Hutcheson usually describes the moral faculty aa 
acting instinctively and immediately, he does not, like Butler, con- 
found the moral faculty with the moral standard. The test or 
criterion of right action is with Hutcheson, as with Shaftesbury, its 
tendency to promote the. general welfare of mankind. He thus 
anticipates the utilitarianism of Bentham — and not only in principle, 
but even in the use of the phrase " the greatest happiness for the 
greatest number " (Inquiry concerning Moral Good and Eml, sect. 3). 

It is curious that Hutcheson did not realize the inconsistency of 
this external criterion with his fundamental ethical principle. In- 
tuition has no possible connexion with an empirical calculation of 
results, and Hutcheson in adopting such a criterion practically 
denies his fundamental assumption. 

As connected with Hutcheson's virtual adoption of the utilitarian 
standard may be noticed a kind of moral algebra, proposed for the 
purpose of computing the morality of actions. This calculus 
occurs in the inquiry toncerning Moral Good and Evil, sect. 3. 

The most distinctive of Hutcheson's ethical doctrines still remaining 
Id be noticed is what has been called the " benevolent theory " of 
morals. Hobbcs had maintained that all our actions, how- 
ever disguised under apparent sympathy, have their roots in 
self-love. Hutcheson not only maintains that benevolence 
is the sole and direct source of many of our actions, but, by a not un- 
natural recoil, that it is the only source of those actions of which, on 
reflection, we approve. Consistently with this position, actions which 
flow from self-love only ace pronounced to be morally indifferent. 
But surely, by the common consent of civilized men, prudence, 
temperance, cleanliness, industry, self-respect and, in general, the 
" personal virtues," are .regarded, and rightly regarded, as fitting 
objects of moral approbation. This consideration could hardly escape 
any author, however wedded to his own system, and Hutcheson 
attempts to extricate himself from the difficulty by laying down the 
position that a man may justly regard himself as a part of the rational 
system, and may thus be. in part, an object of his own benevo- 
lence " (Ibid.), — a curious abuse of terms, which really concedes the 
Question at issue. Moreover, he acknowledges that, though self-love 
does not merit approbation, neither, except in its extreme forms, does 
k merit condemnation, indeed the satisfaction of the dictates of self- 
love is one. of the very conditions of the preservation of society. To 
press home the inconsistencies involved in these various statements 
would be a superfluous task. 

The vexed question of liberty and necessity appears to be carefully 
avoided in Hutcheson's professedly ethical works. But, in the 
Synopsis metaphysicae, he touches on it in three places, briefly 
stating both sides of the question, but evidently inclining to that 
which he designates as the opinion of the Stoics in opposition to 
what he designates as the opinion of the Peripatetics. This is 
substantially the same as the doctrine propounded by Hobbes and 
Locke (to the latter of whom Hutcheson refers in a note), namely, 
that our will is determined by motives in conjunction with our 
general character and habit of mind, and that the only true liberty 
is the liberty of acting as we will, not the liberty of willing as we will. 
Though, however, his leaning is clear, he carefully avoids dogmatiz- 
ing, and deprecates the angry controversies to which the speculations 
on this subject had given rise. 

It is easy to trace the influence of Hutcheson's ethical theories on 
the systems of Hume and Adam Smith. The prominence given by 
these writers to the analysis of moral action ami moral approbation. 


with the attempt to discriminate the respective provinces) of the 
reason and the emotions in these processes, is undoubtedly doe to the 
influence of Hutcheson. To a study of the writings of Shaftesbury 
and Hutcheson we might, probably, in large measure, attribute the 
unequivocal adoption of the utilitarian standard by Hume, and, if 
this be the case, the name of Hutcheson connects itself, through 
Hume, with the names of Priestley, Paley and Bentham. Butler's 
Sermons appeared in 1726, the year after the publication of 
Hutcheson s two first essays, and the parallelism between the 
" conscience " of the one writer and the " moral sense " of the othef 
is, at least, worthy of remark. 

II. Menial Philosophy.— In the sphere of mental philosophy and 
logic Hutcheson's contributions are by no means to important or 
original as in that of moral philosophy. They are interesting mainly 
as a link between Locke and the Scottish school. In the former 
subject the influence of Locke is apparent throughout. AH the main 
outlines of Locke's philosophy seem, at first sight, to be accepted as a 
matter of course. Thus, in stating his theory of the moral sense, 
Hutcheson is peculiarly careful to repudiate the doctrine of innate 
ideas (see, for instance, Inquiry concemmg Moral Good and Evil, sect. 
1 ad fa, and sect. 4; and compare Synopsis Metaphysieae, pars i. 
cap. 2). At the same time he shows more discrimination than does 
Locke in distinguishing between the two uses of this expression, and 
between the legitimate and illegitimate form of the doctrine (Syn. 
Metaph. pars i. cap. 2). All our ideas are, as by Locke, referred to 
external or internal sense, or, in other words, to sensation and re- 
flection (see, for instance, Syn. Metaph. pars i. cap. 1 ; Logicae 
Compend, pars 1. cap. 1 : System of Moral Philosophy, bk. i. ch. l). 
It is, however, a most important modification of Locke's doctrine. 
and one which connects Hutcheson's mental philosophy with that of 
Reid, when he states that the ideas of extension, figure, motion and 
rest "are more property ideas accompanying the sensations of sight 
and touch than the sensations of either of these senses "; that the 
idea of self accompanies every thought, and that the ideas of 
number, duration and existence accompany every other idea what- 
soever (see Essay on the Nature and Conduct of the Passions, sect. i. 
art. 1; Syn. Metafih. pars L cap. 1, pars ii. cap. 1; Hamilton on 
Reid, p. 124, note). Other important points In which Hutcheson 
follows the lead of Locke are his depreciation of the importance of 
the so-called laws of thought, his distinction between the primary and 
secondary qualities of bodies, the position that we cannot know the 
inmost essences of things (" intimae rerum naturae rive essentiae "), 
though they excite various ideas in us, and the assumption that ex- 
ternal things are known only through the medium of ideas (Syn. 
Metaph. pars 1. cap. 1), though, at the same time, we are assured 
of the existence of an external world corresponding to these ideas. 
Hutcheson attempts to account for our assurance of the reality of 
an external world by referring it to a natural instinct (Syn. Metaph. 
pars i. cap. l). Of the correspondence or similitude between our ideas 
of the primary qualities of things and the things themselves God 
alone can be assigned as the cause. This similitude has been effected 
by Him through a law of nature* " Haec prima qualitatum prima- 
narunt perccptio, sive mentis actio quaedam dve passio dicatur. non 
alia similitudinis aut coftvenientiae inter ejusmodi ideas et res ipsas 
causa assignari posse videtur, quam ipse Deus, qui certa naturae lege 
hoc erheit, ut notion**, quae rebus praesentibus excitantur, sint tpsis 
similes, aut saltern earum habitudines, si non veras quantitates, 
depingant " (pars ii. cap. 1). Locke does speak of God " annexing " 
certain ideas to certain motions of bodies; but nowhere does he 
propound a theory so definite as that here propounded by Hutcheson, 
which reminds us at least as much of the speculations of Malebranche 
as of those of Locke. 

Amongst the more important points in which Hutcheson diverges 
from Locke is his account of the idea of personal identity, which he 
appears to have regarded as made known to us directly by conscious- 
ness. The distinction between body and mind, corpus or materia and 
res cogitans, is more emphatically accentuated by Hutcheson than 
by Locke. Generally, he speaks as if we had a direct consciousness 
of mind as distinct from body (see, for instance, Syn. Metaph. pars it 
cap. 3), though, in the posthumous work on Moral Philosophy, be 
expressly states that we Know mind as we know body " by qualities 
immediately perceived though the substance of both be unknown " 
(bk. i. ch. i\ The distinction between perception proper and sensa- 
tion proper, which occurs by implication though it is not explicitly 
worked out (see Hamilton s Lectures on Metaphysics, Lect. 24; 
Hamilton's edition of DugaU Stewarts Works, r. 420), the 
imperfection of the ordinary division of the external senses into five 
classes, the limitation of consciousness to a special mental faculty 
(severely criticized in Sir W. Hamilton's Lectures on Metaphysics, 
Lect. xiu) and the disposition to refer on disputed questions of philo- 
sophy not so much to formal arguments as to the testimony of con- 
sciousness and our natural instincts are also amongst the points fn 
which Hutcheson supplemented or departed from the philosophy of 
Locke. The last point can hardly fail to suggest the " common- 
sense philosophy " of Reid. 

Thus, in estimating Hutcheson's position, we find that in particular 
questions he stands nearer to Locke, but in the general spirit of his 
philosophy he seems to approach mora closely to his Scottish suc- 
1 The short Compendium of Logic, which is more original than such 



works usually are, is remarkable chiefly for the Urge proportion of 

Bychological matter which it contains. In these parts ot the book 
utcheson mainly follows Locke. The technicalities of the subject 
are passed lightly over, and the book is readable. It may be specially 
noticed that he distinguishes between the mental result and its verbal 
expression [idea — term; judgment — proposition), that he constantly 
employs the word " idea," and that he defines logical truth as " con- 
venientia signorum cum rebus significatis " (or propositionis con- 
venientia cum rebus ipsts," Sy*. Metaph. pars i. cap 3), thus im- 
plicitly repudiating a merely formal view of logic. 

III. Aesthetics. — Hutchcson may further be regarded as one of 
•the earliest modern writers on aesthetics. His speculations on this 
subject are contained in the Inquiry concerning Beduty, Order, 
Harmony and Design, the first of the two treatises published in 1725. 
He maintains that we are endowed with a special sense by which we 
perceive beauty, harmony and proportion. This is a reflex sense, 
because it presupposes the action of the external senses of sight and 
hearing. It may be called an internal sense, both in order to dis» 
tinguisb its perceptions from the mere perceptions of sight and 
hearing, and because " in some other affairs, where our external senses 
are not much concerned, we discern a sort of beauty, very like in 
many respects to that observed in sensible objects, and accompanied 
with like pleasure" {Inquiry, &c, sect. 1). The latter reason leads 
him to call attention to the beauty perceived in universal troths, in the 
operations of general causes and in moral principles and action*. 
Thas, the analogy between beauty and virtue, which was so favourite 
a topic with Shaftesbury, is prominent in the writings of Hutchcson 
also. Scattered up and down the treatise there are many important 
and interesting observations which our limits prevent us from 
noticing. m But to the student of mental philosophy it may be 
specially interesting to remark that Hutcheson both applies the 
principle of association to explain our ideas of beauty and also sets 
limits to its application, insisting on there being " a natural power 
of perception or sense of beauty in objects, antecedent to all custom, 
education, or example" (see Inquiry, 6Yc, sects. 6, 7; Hamilton's 
Lectures on Metaphysics, Lcct. 44 ad fin.). 

Hutchcson's writings naturally gave rise to much controversy. 
To say nothing of minor opponents, such as " Philaretus " (Gilbert 
Burnet, already alluded to). Dr John Balguy (1686-1748), pre- 
bendary of Salisbury, the author of two tracts on " The Foundation 
of Moral Goodness, and Dr John Taylor (1604- J 761) of Norwich, a 
minister of considerable reputation in his time (author of An Examina- 
tion of the Scheme of Morality advanced by Dr Hutcheson}, the essays 
appear to have suggested, by antagonism, at least two works which 
hold a permanent place in the literature of English ethics— Butler's 
Dissertation on the Nature of Virtu*, and Richard Price's Treatise of 
Moral Good and Evil (1757). la this latter work the author main- 
tains, in opposition to Hutcheson, that actions are in themselves right 
or wrong, that right and wrong are simple ideas incapable of analysis, 
and that these ideas are perceived immediately by, the understand- 
ing. We thus see that, not only directly but also through the replies 
which it called forth t the system of Hutcheson, or at least the system 
of Hutchcson combined with that of Shaftesbury, contributed, .in 
large measure, to the formation and development of some of the most 
important of the modern schools of ethics (see especially art. Ethics). 

Authorities. — Notices of Hutcheson occur in most histories, both 
of general philosophy and of moral philosophy, as, for instance, in 
pt. vii. of Adam Smith's Theory of Moral Sentiments; Mackintosh's 
Progress of Ethical Philosophy; Cousin, Ccmrs d'histoire de la 
pktlosophie morale du XVI1P siicle; WhewelTs Lectures on the 
History of Moral Philosophy in England; A. Bain's Mental and Moral 
Science; Noah Porter's Appendix to the English translation of 
Ueberwcg's History of Philosophy; Sir Leslie Stephen's History of 
English Thought in the Eighteenth Century, &c. See also Martioeau. 
Types of Ethical Theory (London, 190a); W. R. Scott, Francis 
Hutcheson (Cambridge, 1000); Albee, History of English Utilitarian- 
ism (London, 1902) ; T. Fowler, Shaftesbury and Hutcheson (London, 
1882); J. McCosh, Scottish Philosophy (New York, 1874). Of Dr 
Leechman's Biography of Hutcheson we have already spoken. 
I, Veitch gives an interesting account of his professorial work in 
Glasgow, Mind, ii. 209-2 J 2. (T. F.; X.) 

HUTCHINSON, ANNE (c. 1600-1643), American religious 
enthusiast, leader of the " Antinomians " in New England, 
was born in Lincolnshire, England, about 1600. She was the 
daughter of a clergyman named Francis Marbury, and, according 
to tradition, was a cousin of John Dryderi. She married William 
Hutchinson, and in 1634 emigrated to Boston, Massachusetts, 
as a follower and admirer of the Rev. John Cotton. Her orthodoxy 
was suspected and for a time she was not admitted to the church, 
but soon she organized meetings among the Boston women, 
among whom her exceptional ability and her services as a nurse 
had given her great influence; and at these meetings "she dis- 
cussed and commented upon recent sermons and gave expression 
to her own theological views. The meetings became increasingly 
popular, and were soon attended not only by the women but 

even by some of the ministers and magistrates, including Governor 
Henry Vane. At these meetings she asserted that she, Cotton 
and her brother-in-law, the Rev. John Wheelwright— whom 
she was trying to make second " teacher " in the Boston church- 
were under a "covenant of grace," that they had a special 
inspiration, a " peculiar indwelling of the Holy Ghost," whereas 
the Rev. John Wilson, the pastor of the Boston church, and 
the other ministers of the colony were under a " covenant of 
works." Anne Hutchinson was, in fact, voicing a protest against 
the legalism of the Massachusetts Puritans, and was also striking 
at the authority of the clergy in an intensely theocratic community. 
In such a community a theological controversy inevitably 
was carried into secular politics, and the entire colony was 
divided. into factions. Mrs Hutchinson was supported by 
Governor Vane, Cotton, Wheelwright and the great majority of 
the Boston church; opposed to her were Deputy-Governor John 
Wintinrop, Wilson and all of the country magistrates and 
churches. At a general fast, held late in January 1637, Wheel- 
wright preached a sermon which was taken as a criticism of 
Wilson and his friends. The strength of the parties was tested 
at the General Court of Election of May 1637, when Winthrop 
defeated Vane for the governorship. Cotton recanted, Vane re- 
turned to England in disgust, Wheelwright was tried and banished 
and the rank and file either followed Cotton in making sub- 
mission or suffered various minor punishments. Mrs Hutchinson 
was. tried (November 1637) by the General Court chiefly for 
"traducing the ministers," and was sentenced to banjshmcnl; 
later, in March 1638, she was tried before the Boston church 
and was formally excommunicated. With William Coddington 
(d. 1678), John Clarke and others, she established a settlement 
on tbe island of Aquidneck (now Rhode Island) in 1^38. Four 
years later, after the death of her husband, she settled on Long 
Island Sound near what is now New Rochelle, Westchester 
county, New York, and was killed in an Indian rising in August 
1643, an event regarded in Massachusetts as a manifestation 
of Divine Providence. Anne Hutchinson and her followers 
were called " Antinomians," probably more as a term of reproach 
than with any special reference to her doctrinal theories; and 
the controversy in which she was involved is known as the 
" Antinomian Controversy." 

See C. F. Adams, Antinomianism in the Colony of Massachusetts 
Bay, vol. xfv. of the Prince Society Publications (Boston, 1894); 
and Three Episodes of Massachusetts History (Boston and New York, 

HUTCHINSON. JOHN (1615-1664). Puritan soldier, son of 
Sir Thomas Hutchinson of Owthorpe, Nottinghamshire, and 
of Margaret, daughter of Sir John Byron of Newstead, was 
baptized on the iSth of September 1615, He was educated at 
Nottingham and Lincoln schools and at Peterhouse, Cambridge, 
and in 1637 he entered Lincoln's Inn. On the outbreak of the 
great Rebellion he took the side of the Parliament, and was 
made in 1643 governor of Nottingham Castle, which he defended 
against external attacks and interna] divisions, till the triumph 
of the parliamentary cause. He was chosen member for 
Nottinghamshire in March 1646, took the side of the Independents, 
opposed the offers of the king at Newport, and signed the death- 
warrant. Though a member at first of the council of state, be 
disapproved of the subsequent political conduct of Cromwell 
and took no further part in politics during the lifetime of the 
protector. He resumed his seat in the recalled Long Parliament 
in May 1650, and followed Monk in opposing Lambert, bebeving 
that the former intended to maintain the commonwealth. 
He was returned to the Convention Parliament for Nottingham 
but expelled on the oth of June 1660, and while not excepted 
from the Act of Indemnity was declared incapable of holding 
public office. In October 1663, however, he was arrested upon 
suspicion of being concerned in the Yorkshire plot, and after 
a rigorous confinement in the Tower of London, of which he 
published an account (reprinted in the Harleian MtueUany, 
vol. iii.), and in Sandown Castle, Kent, he died on the 11th of 
September 1664. His career draws its chief interest from the 
Life by his wife, Lucy, daughter of Sir AUen Apsley, written 


alter the death of her husband bdt not published till 1806 (since 
often reprinted), a work not only valuable for the picture which 
it gives of the man and of the time in which he lived, but for 
the simple beauty of its style, and the nafvetfc with which the 
writer records her sentiments and opinions, and details the 
incidents of her private life. 

Sec the edition of Lucy Hutchinson's Memoirs of Ike Life of Colonel 
Hutchinson by C. H. Firth (1885) ; Brit. Mus. Add. MSS. 25,901 (a 
fragment of the Life), also Add. MSS. 19, 333, l 6 .*47 *• 5« • Nofes 
and Queries, 7, ser. Hi. 25, viii. 422; Monks Contemporaries, by 

HUTCHINSON, JOHN (1674-1737), English theological writer, 
was born at Spennithorne, Yorkshire, in 1674. He served as 
steward in several families of position, latterly in that of the 
duke of Somerset, who ultimately obtained for him the post 
of riding purveyor to the master of the horse, a sinecure worth 
about £200 a year. In 1700 he became acquainted with Dr 
John Woodward (1665-1728) physician to the duke and author 
of a work entitled The Natural History of the Earth, to whom he 
entrusted a large number of fossils of his own collecting, along 
with a mass of manuscript notes, for arrangement and publication. 
A misunderstanding as to the manner in which these should 
be dealt with was the immediate occasion of the publication 
by Hutchinson in 1724 of Moses's Principia, part i., In which 
Woodward's Natural History was bitterly ridiculed, his conduct 
with regard to the mineralogical specimens not obscurely 
characterized, and a refutation of the Newtonian doctrine of 
gravitation seriously attempted. It was followed by part ii. 
in 1727, and by various other works, including Moses's Sine 
Principle, 1730; The Confusion of Tongues and Trinity oj the 
Gentiles, 1731; Power Essential and Mechanical, or what power 
belongs to Cod' and what to his creatures, in which the design of 
Sir I. Newton and Dr Samuel Clarke is laid open, 1732; Glory or 
Gravity, 1733; The Religion of Satan, or Antichrist Delineated, 
1736. He taught that the Bible contained the elements not only 
of true religion but also of all rational philosophy. He held 
that the Hebrew must be read without points, and his interpreta- 
tion rested largely on fanciful symbolism. Bishop George Home 
of Norwich was during some of his earlier years an avowed 
Hutchinsonian; and William Jones of Nayland continued to 
be so to the end of his life. 

A complete edition of his publications, edited by Robert Spearman 
and Julius Bate, appeared in 1748 (12 vols.); an* Abstract of these 
followed io 1753; and a Supplement, with Life by Spearman pre* 
fated, in 1765. 

« HUTCHINSON. SIR JONATHAN (182*- ), English surgeon 
and pathologist, was bom on the 23rd of July 1828 at Selby, 
Yorkshire, his parents belonging to the -Society of Friends! 
He entered St Bartholomew's Hospital, became a member of the 
Royal College pi Surgeons in 1850 (F.R.C.S. 1862), and rapidly 
gained reputation as a skilful operator and a scientific inquirer. 
He was president of the Hunterian Society in 1869 and 1870, 
professor of surgery and pathology at the College of Surgeons 
from 1877 to 188a, president of the Pathological Society, 1870- 
1880, of the Ophthalmological Society, 1883, of the Neurological 
Society, 1887, of the Medical Society, 1890, and of the Royal 
Medical and Chirtzrgtcal En 1804-1896. In 1889 he was president 
of the Royal College of Surgeons. He- was a member of two 
Royal Commissions, that of 1881 to inquire into the provision 
for smallpox and fever cases in the London hospitals, and that 
of 1880-1896 on vaccination and leprosy. He also acted as 
honorary secretary to the Sydenham Society. His activity 
in the came of scientific surgery and in advancing the study 
of the natural sciences was unwearying. His lectures on neuro- 
pathogenesis, gout, leprosy, diseases of the tongue, &c, were full 
of original observation; out his principal work was connected 
with the study of syphilis, on which he became the first living 
authority. He was the founder of the London Polyclinic or 
Postgraduate School of Medicine; and both in his native town 
of Selby and at Haslemere, Surrey, he started (about 1800) 
educational museums for popular instruction in natural history. 
He published several volumes on his own subjects, was editor of 
the quarterly Archives of Surgery, and was given the Hon. LL.D, 


degree by both Glasgow and Cambridge. After his retirement 
from active consultative work he continued to take great interest 
in the question of leprosy, asserting the existence of a definite 
connexion between this disease and the eating of salted- fish. 
He received a knighthood in 1908% 

HUTCHINSON, THOMAS (1711-1780), the last royal governor 
of the province of Massachusetts, son of a wealthy merchant 
of Boston, Mass., was born there on the oth of September 17x1. 
He graduated at Harvard In 1727, then became an apprentice 
in his father's counting-room, and for several years devoted 
himself to business. In 1737 he began his public career as a 
member of the Boston Board of Selectmen, and a few weeks 
later he was elected to the General Court of Massachusetts Bay, 
of which he was a member until 1740 and again from 174a to 
1749, serving as speaker in 1747, 1748 and 1749. He con* 
sistently contended for a sound financial system, and vigorously 
opposed the operations of' the " Land Bank " and the issue of 
pernicious bills of credit. In 1748 he carried through the 
General-Court a bill providing for the cancellation and redemption 
of the outstanding paper currency. Hutchinson went to England 
in 1 740 'as the representative of Massachusetts in a boundary 
dispute with New Hampshire. He was a member of the Massa- 
chusetts Council from 1749 to 1756, was appointed judge of 
probate in 175* and was chief justice of the superior court of 
the province from 1761 to 1769, was lieutenant-governor from 
1758 to 1 77 1, acting as governor in the latter two years, and 
from 1771 to 1774 was governor. In 1754 he was a delegate 
from Massachusetts to the Albany Convention ,and, with Franklin, 
was a member of the committee appointed to draw up a plan of 
union. -Though h* recognized the legality of the Stamp Act 
of 1765, be considered the measure inexpedient and impolitic 
and urged its repeal, but his attitude was misunderstood; he 
was considered by many to have instigated the passage of the 
Act, and in August 1765 a mob sacked his Boston residence 
and destroyed many valuable manuscripts and documents. 
He was acting governor at the time of the " Boston Massacre " 
in 1770, and was virtually forced by the citizens of Boston, 
under the leadership of Samuel Adams, to order the temoval 
of the British troops from' the town. Throughout the pre* 
Revolutionary disturbances in Massachusetts he was the re* 
pnresentative of the British ministry, and though he disapproved 
of some of the ministerial measures he felt impelled to enforce 
them and necessarily incurred the hostility of the Whig or 
Patriot element. In 1774, upon the appointment of General 
Thomas Gage as military governor he went to England, and 
acted as an adviser to George III. and the British ministry 
on American affairs, uniformly counselling moderation. He 
died at Brompton, now part of London, on the 3rd of June 

He wrote A Brief Statement of the Claim of the Colonies (1764}? * 
Collection of Original Papers retntue to the History of Massachusetts 
Bay. (»7.69), reprinted at The Hutchinson Papers by the Prince 
Society in 1865; and a judicious, accurate and very valuable History 
of the Provinee of Massachusetts Bay (vol. i., 1764, vol. ii., 1767, and 
vol. Hi., 1828). His Diary and Letters, with an Account of hu Ad- 
ministration, was published at Boston in 1884-1886. 

See James K. Hosroer's Life of Thomas Hutchinson (Boston. 1896). 
and a biographical chapter in John Fiske's Essays Historical and 
Literary (New York, 1002). For an estimate of Hutchinson as an 
historian, see M. C. Tyler's Literary History of the American Revolu- 
tion (New York, 1897). 

HUTCHINSON, a city and the county-seat of Reno county, 
Kansas, U.S.A., in the broad bottom-land on the N. side of 
the Arkansas river. Pop. (tooo) 9379, of whom 414 were 
foreign-born and 44s negroes; (1910 census) 16464. It 
is served by the Atchison, Topeka & Santa Fe, the Missouri 
Pacific and the Chicago, Rock Island & Pacific railways. The 
principal public buildings are the Federal building and the county 
court bouse. The city has a public library, and an industrial 
reformatory is maintained here by the state. -Hutchinson is 
situated in a stock-raising, fruit-growing and farming region 
(the principal products of which are wheat, Indian corn and 
fodder), with which it has a considerable wholesale trade. An 
enormous- deposit of rock salt underlies the city and its vicinity, 


and Hutchinson's principal industry is the manufacture (by 
the open-pan and grainer processes) and the shipping of salt; 
the city has one of the largest salt plants in the world. Among 
the other manufactures are flour, creamery products, soda- 
ash, straw-board, planing-mill products and packed meats. 
Natural gas is largely used as a factory fuel The city's factory 
product was valued at $2,031,048 in. 1005, an increase of 31-8% 
since 1900. Hutchinson was chartered as a dty in 187 1. 

BUTTON, PHIUPP VON (c. 1 Si 1-1546), German knight, 
was a relative of Ulrica von Hutten and passed some of his 
early years at the court of the emperor Charles V. Later he 
joined the band of adventurers which under Georg Hohermuth, 
or George of Spires, sailed to Venezuela,, or Venosala as Hutten 
calls it, with the object of conquering and exploiting this land in 
the interests of the Augsburg family of Welser. The party 
landed at Coro in February 1535 and Hutten accompanied 
Hohermuth on his long and toilsome expedition into the interior 
in search of treasure. After the death of Hohermuth in December 
154a he became captain-general of Venezuela. Soon after this 
event he vanished into the interior, returning after five years 
of wandering to find that a Spaniard, Juan de Caravazil, or 
Caravajil, had been appointed governor in his absence. With 
his travelling companion, Bartholomew Welser the younger, 
he was seised by Caravazil in April 1546 and the two were 
afterwards put to death. 

Hutten left some letters, and also a narrative of the earlier part of 
his adventures, this Zeilung^aus India Junkkcr PkUipps von Hutten 
being published in 1785. 

HUTTEN, ULRICH VON (1488-1523), was born on the 21st of 
April 1488, at the castle of Steckclberg, near. Fulda, in Hesse. 
Like Erasmus or Pirckheimer, he was one of those men who 
form the bridge between Humanists and Reformers. He lived 
with both, sympathized with both, though he died before the 
Reformation had time fully to develop. His life may be divided 
into four parts:— his youth and cloister-life (1488-1504); his 
wanderings in pursuit of knowledge (1 504-1515); Jus strife 
with Ulrica of Wurttemberg (1515-15x0); and his connexion 
with the Reformation (1510-1523). Each of these periods 
had its own special antagonism, which coloured Hutten'a career; 
in the first, his horror of dull monastic routine; in the second, 
the ill-treatment he met with at Greifswald; in the third, the 
crime of Duke Ulrica ; in the fourth, his disgust with Rome 
and with Erasmus. He was the eldest son of a poor and not 
undistinguished knightly family. As he was mean of stature 
and sickly his father destined him for the cloister, and he was 
sent to the Benedictine house at Fulda; the thirst for learning 
there seized on him, and in 1505 he fled from the monastic life, 
and won his freedom with the sacrifice of his worldly prospects, 
and at the cost of incurring his father's undying anger. From 
the Fulda cloister he went first to Cologne, next to Erfurt, and then 
to Frankfort-on-O^cr on the opening in 1506 of the new university 
of that town. For a time he was in Leipzig, and in 1 508 we find 
him a shipwrecked beggar on the Pomeranian. coast In 1509 
the university of Greifswald welcomed him, but here too those 
who at first received him kindly became his foes; the sensitive 
ill-regulated youth, who took the liberties of genius, wearied 
his burgher patrons; they could not brook the poet's airs and 
vanity, and ill -timed assertions of his higher rank. Wherefore 
he left Greifswald, and as he went was robbed of clothes and 
books, his only baggage, by the servants of has late friends; 
in the dead of winter, Half starved, frozen, penniless, he reached 
Rostock. Here again the Humanists received him gladly, 
and under their protection he wrote against his Greifswald 
patrons, thus beginning the long list of his satires and fierce 
attacks on personal or pubjic foes. Rostock could not hold 
him long; he wandered on to Wittenberg and Leipzig, and 
thence to Vienna, where hejioped to win the emperor Maximilian's 
favour by an, elaborate national poem on the war with Venice. 
But neither Maximilian nor the university of Vienna would 
lift a hand for him, and be passed into Iujy, where, at Pavia, 
he sojourned throughout 15x1 and part of 1519. In the latter 
year his studies were interrupted by war; in. the siege of Pavia 

by papal troops and Swiss, he was plundered by both sides; 
and escaped, sick and penniless, to Bologna; on his recovery 
he even took service as a private soldier in the emperor's army. 

This dark period lasted no long time; in 1514 he was again 
in Germany, where, thanks to his poetic gifts and the friendship 
of Eitelwolf von Stein (d. 1515), he won the favour of the elector 
of Mainz, Archbishop Albert of Brandenburg. Here high 
dreams of a learned career rose on him; Mainz should be made 
the metropolis of a grand Humanist movement, the centre of 
good style and literary form. But the murder in 1515 of his 
relative Hans von Hutten by Ulricb, duke of Wurttemberg, 
changed the whole course of his life; satire, chief refuge of the 
weak, became Hut ten's weapon; with one hand he took his 
part in the famous Epistolac obscurorum virorum, and with 
the other launched scathing letters, eloquent Ciceronian orations, 
or biting satires against the duke. Though the emperor was 
too lazy and indifferent to smite a great prince, he took Hutten 
under his protection and bestowed on him the honour of a 
laureate crown in 15 17. Hutten, who had meanwhile revisited 
Italy, again attached himself to the electoral court at Mainz; 
and he was there when in 15 18 his friend Pirckheimer wrote, 
urging him to abandon the court and dedicate himself to letters. 
We have the poet's long reply, in an epistle on his " way of life,** 
an amusing mixture of earnestness and vanity, self-satisfaction 
and satire; he tells his friend that his career is just begun, 
that he has had twelve years of wandering, and will now enjoy 
himself a while in patriotic literary work; that he has by no 
means deserted the humancr studies, but carries with him 
a little library of standard books. Pirckheimer in his burgher 
life may Have case and even luxury; he, a knight of the empire, 
how can he condescend to obscurity?. He must abide where 
he can shine. 

In 15x9 he issued, in one volume his attacks on Duke Ulrich, 
and then, drawing sword, took part in the private war which 
overthrew that prince; in this affair he became intimate with 
Franz von Sickingen, the champion of the knightly order 
(Ritterstand). Hutten now warmly and openly espoused the 
Lutheran cause, but he was. at the same time mixed up in the 
attempt of the " Ritterstand " to assert itself as the militia 
of the empire against the independence of the German princes. 
Soon after this time he discovered at Fulda a copy of the mani- 
festo of the emperor Henry IV. against Hildcbrand, and published 
it with comments as an attack on the papal claims over Germany. 
He hoped thereby to interest the new emperor Charles V. r and 
the higher orders in the empire; in behalf of German* lttetttes; 
but the appeal failed. . What Luther had achieved by Speaking 
to cities and common folk in homely phrase, because he touched 
heart and conscience, that the far finer weapons of Hutten failed 
to effect, because he triod to touch the more cultivated sympathies 
and dormant patriotism of princes and bishops, nobles and 
knights. And so he at once gained an undying name in the 
republic of letters and ruined his own career. He showed that 
the artificial verse-making of the Humanists could be connected 
with the new outburst of genuine German poetry. The Minne- 
singer was gone; the new national singer, a Luther or a Ham 
Sachs, was heralded by the stirring lines of Hutten's pen. These 
have in them a splendid natural swing and ring, strong and 
patriotic, though unfortunately addressed to knight and lands* 
knecht rather than to the German people. 

The poet's high dream of a knightly national regeneration 
had a rude awakening. The attack on the papacy, and Luther's 
vast and sudden popularity, frightened Elector Albert, who 
dismissed Hutten from his court. Hoping for imperial favour, 
be betook himself to Charles V.; but that young prince would 
have none of him. So he returned to his friends, and they 
rejoiced greatly to see bin) still alive; for Pope Leo X. had 
ordered him to be arrested ^nd sent to Rome, and assassins 
dogged his steps. He now attached himself more closely to 
Franz von Sickingen and the knightly movement. This also 
came to a disastrous end in the capture of the Ebernberg, and 
Sickingen'* death; the higher nobles had triumphed; the 
archbishop* avenged themselves on Lutheranisni as interpreted 


hy the knightly order. With Sicklhgen Hutten also finally fell. 
He fled to Bawl, where Erasmus refused to see him, both for 
fear of his loathsome diseases, and also because the beggared 
knight was sure to borrow money from him. A paper war 
consequently broke oat between the two Humanists, which 
embittered Hutten's last days, and stained the memory of 
Erasmus. From Basel Ulrieh dragged himself to Mulhausen; 
and when the vengeance trf Erasmus drove him thence, he went 
to Zurich. There 'the large, heart of Zwingh* welcomed him; 
he helped him with mosey, and found him a quiet refuge with 
the pastor of the little isle of Ufnau on the Zurich lake. There 
the frail and worn-out poet, writing swift satire to the end, died 
at the end of August or beginning of September 1523 at the 
age of thirty-five. He left behind him some debts due to com* 
passionate friends; he did not even own a single book, and 
all fris goods amounted to the clothes on his back, a bundle 
of letters, and that valiant pen which had fought so many 
a sharp battle, and had won for the poor knight-errant a sure 
place in the annals of literature. 

Ulrieh von Hutten is one of those men of genius at whom 
propriety is shocked, and whom the mean-spirited avoid. Yet 
through his short and buffeted life he was befriended, with 
wonderful charity and patience, by the chief leaders of the 
Humanist movement. For, in spite of his irritable vanity, 
his immoral life and habits, his odious diseases', his painful 
restlessness, Hutten had much in him that strong men could 
love. He passionately loved the truth, and was ever open 
to all good influences. He was a patriot, whose soul soared 
to ideal schemes and a grand Utopian restoration of his country. 
In spile of all, his was a frank and noble nature; his faults chiefly 
the faults of genius Ul-controUed, and of a life cast in the eventful 
changes of an age of novelty. A swarm of writings issued from 
his pen; at first the smooth elegance of his Latin prose and verse 
seemed strangely to miss hm real character; he was the Cicero 
and Ovid of Germany before he became its Lucian. 

His chief works were his Art versificandi (131 1) ; the Nemo (1518); 
a work on the Morbus Cautcus (1519); the volume of StcckcTberg 
complaints against Duke Ulrieh (including his four Ciceronian 
Orations, his Letters and the PhalarUmus) also in 1519; the Vadismus 
(1520); and the controversy with Erasmus at the end of bis life. 
Besides these were many admirable poems in Latin and German. 
It is not known with certainty how far Hutten was the parent of the 
celebrated Epistolae obscurorum virorum, that famous satire on 
monastic ignorance as represented by the theologians of Cologne 
with which the friends of Reuchlin defended him. At first the 
cloister-world, not discerning its irony, welcomed the work as a 
defence of their position; though their eyes were soon opened by 
the favour with which the learned world received it. The Epistolae 
were eagerly bought up; the first part (41 letters) appeared at the 
end of 1515; early in 1516 there was a second edition; later in 1516 
a third, with an appendix of seven letters; in 1^17 appeared the 
second part (6a letters), to which a fresh appendi* of eight letters 
was subjoined soon after. In 1909 the Latin text of the Epistolae 
with an English translation waspubiished try F» G. Stokes. Hutten, 
in a letter addressed to Robert Crocus, denial that he was the author 
of the book, but there is no doubt as to his connexion with it. 
Erasmus was of opinion, that there were three authors, of whom 
Crotus Ruhianus was the originator of the idea, and Hutten a chief 
contributor. D. F. Strauss, who dedicates to the subject a chapter 
of his admirable work on Hutten, concludes that he had no share in 
the first part, but that his hand is clearly visible In the second part, 
which he attribute* in the main to him. To him is due the more 
serious and severe tone of that Utter portion of the satire* See 
W. Brecht, Die Verfasur der Epistolae obscurorum virorum (190$), 

For a complete catalogue of the writings of Hutten, see E. Hocking's 
Index Bibliographicus Hutlenianus (1858). Bdcking is also the editor 
of the complete edition of Hutten's works (7 vols., 1859-1862). A 
•election of Hutten's German writings, edited by G. Bailee, appeared 
in 1 891. Cp. & SzamatoUki, Hutkm deutsche Schri/Un (1801). 
The best biography (though it is also somewhat of a political 
pamphlet) is that or D. F. Strauss {Vlrtch von Hulien, 1857 J 
4tb ed., 1878; English translation by G. St urge, 1874). with 
which may be compared the older monographs by A. Wagenseil 
(1823). A. Burck (1846) and I. Zeller (Paris, 1849). See also 
J. Deckert, Ulrieh von anttens Lcbtn und Wirken. Eine hisloriscke 
Shine (1901). , (G. W. K.) 

BUTTER, LEOsfHARD (1563-1616), German Lutheran 
theologkm, was born at Nellingcn near Ulm in January 1563. 
From 1562 he studied at the fuuversitie* of Suassburg, Leipzig, 


Heidelberg and Jena. In 1504 he began to give theological 
lectures at Jena, and in 1596 accepted a call as professor of 
theology at Wittenberg, where he died on the 23rd of October 
16 1 6. Huttcr was a stern champion of Lutheran orthodoxy, 
as set down in the confessions and embodied in his own 
Compendium loeorum theologicorum (1610; reprinted 1863), 
being so faithful to his master as to win the title of " Luther 

In reply to Rudolf Hospinian's Concordia JKscors (1607), he wrote 
a work, rich in historical material but one-sided In its apologetics, 
Concordia concors (161 a), defending the formula of Concord, which 
he regarded as inspired. His Irenuum vere ckristianum is directed 
against David Parcus (1548-1622), professor priraariusat Heidelberg, 
who in Irenicum sive de uniene et synodo Evangelicorum (1614) had 
pleaded for a reconciliation of Lutheram'sm and Calvinism; hts 
Calvinista aulopclilicus (1610} was written against the "damnable 
Calvinism " which was becoming prevalent in, Holstein and Branden- 
burg. Another work, based on the formula of Concord, was entitled, 
Loc* communes theologici. 

HUTTON, CHARLES (1737-1823), English mathematician, 
was born at Newcastle-on-Tyne on the 14th of August 1737. 
He was educated in a school at Jesmond, kept by Mr Ivison, 
a clergyman of the church of England. There is reason to believe, 
on the evidence of two pay-bills, that for a short time in 1755 
and 1756 Hutton worked in Old Long Benton colliery; at any 
rate, on Ivison 's promotion to a living, Hutton succeeded to 
the Jesmond school, whence, in consequence of increasing pupils, 
he removed to Stote's Hall. While he taught during the day 
at Stote's Hall, he studied mathematics in the evening at a 
school in Newcastle. In 1760 he married, and began tuition 
on a larger scale in Newcastle, where he had among his pupils 
John Scott, afterwards Lord Eldon, chancellor of England. 
In 1764 he published his first work, The Schoolmaster's Guide, 
or a Complete System of Practical Arithmetic, which in J770 
was followed by his treatise on Mensuration both in Theory and 
Practice. In 1772 appeared a tract on The Principles oj Bridges ; 
suggested by the destruction of Newcastle bridge by a high 
flood on the 17th of November 1771. In 1773 he was appointed 
professor of mathematics at the Royal Military Academy. 
Woolwich, and in the following year be was elected F.R.S. and 
reported on Nevil Maskelyne's determination of the mean density 
and mass of the earth from measurements taken in 1774-1776 at 
Mount Schiehalh'on m Perthshire. This account appeared in the 
Philosophical Transactions for 1778, was afterwards reprinted 
in the second volume of his Tracts on Mathematical and Philo- 
sophical Subjects, and procured for Hutton the degree of LL.D. 
from the university of Edinburgh. He was elected foreign 
secretary to the Royal Society in 1779, but his resignation in 
1783 was brought about by the president Sir Joseph Banks, 
whose behaviour to the mathematical section of the society 
was somewhat high-handed (see Kippis's Observations on the 
late Contests in' the Royal Society, London, 1784). After his 
Tables of the Products and Powers of Numbers, 1781, and his 
Mathematical Tables, 1785, he issued, for the use of the Royal 
Military Academy, in 1787 Elements of Conic Sections, and in 1 798 
his Course of Mathematics. His Mathematical and Philosophical 
Dictionary, a valuable .contribution to scientific biography, 
was published in 1795 (2nd ed., 181 5), and the four volumes of 
Recreations in Mathematics and Natural Philosophy, mostly a 
translation from the French, in 1803. One of the most laborious 
of his works was the abridgment, in conjunction with G. Shaw 
and R. Pearson, of the Philosophical Transactions. This under- 
taking, the mathematical and scientific parts of which fell to 
Mutton's share, was completed in J809, and filled eighteen 
volumes quarto. His name first appears in the Ladies' Diary 
(a poetical and mathematical almanac which was begun in 
1704, and lasted till 1871) in 1764; ten years later he was 
appointed editor of the almanac, a post which he retained till 
1817. Previously he had begun a small periodical, MisceUanea 
Malhemdtica, which extended only to thirteen numbers; subse- 
quently he published in five volumes The Diarian Miscellany, 
which contained large extracts from the Diary. He resigned 
his professorship in 1607, and died on the 27th of January 1823. 

See John Bruce, Charles Hutton (Newcastle, 1823). 



HTJTTOM, JAMES (1726-1797), Scottish geologist, was bora 
in Edinburgh on the 3rd of June 1726. Educated at the high 
school and university of his native city, be acquired while a 
student a passionate love of scientific inquiry. He was ap- 
prenticed to a lawyer, but his employer advised that a more 
congenial profession should be chosen for him. The young 
apprentice chose medicine as being nearest akin to his favourite 
pursuit of chemistry. He studied for three years at Edinburgh, 
and completed his medical education in Paris, returning by 
the Low Countries, and taking his degree of doctor of medicine 
at Leiden in 1749. Finding, however, that there seemed hardly 
any opening for him, he abandoned the medical profession, 
ana, having inherited a small property in Berwickshire from 
his father, resolved to devote himself to agriculture. He then 
went to Norfolk to learn the practical work of fanning, and 
subsequently travelled in Holland, Belgium and the north 
of France. During these years he began to study the surface 
of the earth, gradually shaping in his mind the problem 
to which he afterwards devoted bis energies. In the summer 
of 1754 he established himself on his own farm in Berwickshire, 
where he resided for fourteen years, and where he introduced 
the most improved forms of husbandry. As the farm was 
brought into excellent order, and as its management, becoming 
more easy, grew less interesting, he was induced to let it, and 
establish himself for the rest of his life in Edinburgh. This took 
place about the year 1768. He was unmarried, and from this 
period until his death in 1797 he lived with his three sisters. 
Surrounded by congenial literary and scientific friends he 
devoted himself to research. 

At that time geology in any proper sense of the term did 
not exist. Mineralogy, however, had made considerable progress. 
But Hutton had conceived larger ideas than were entertained 
by the mineralogists of his day. He desired to trace back . the 
origin of the various minerals and rocks, and thus to arrive 
at some clear understanding of the history of the earth. For 
many years he continued to study the subject. At last, in the 
spring of the year 1785, he communicated his views to the 
recently established Royal Society of Edinburgh in a paper 
entitled Theory of the Earth, or an Investigation of the Laws 
Observable in the Composition, Dissolution and Restoration of 
Land upon the Globe. In this remarkable work the doctrine 
is expounded that geology is not cosmogony, but murt confine 
itself to the study of the materials of the earth; that everywhere 
evidence may be seen that the present rocks of the earth's 
surface have been in great part formed out of the waste of older 
rocks ; that these materials having been laid down under the 
sea were there consolidated under great pressure, and were 
subsequently disrupted and upheaved by the expansive power 
of subterranean heat; that during these convulsions veins 
and masses of molten rock were injected into the rents of the 
dislocated strata; that every portion of the upraised land, 
as soon as exposed to the atmosphere, is subject to decay; and 
that this decay must tend to advance until the whole of the 
land has been worn away and bid down on the sea-floor, whence 
future upheavals will once more raise the consolidated sediments 
into new land. In some of these broad and bold generalizations 
Hutton was anticipated by the Italian geologists; but to him 
belongs the credit of having first perceived their mutual relations, 
and combined them in a luminous coherent theory based upon 

It was not merely the earth to which Hutton directed his 
attention. He had long studied the changes of the atmosphere. 
The same volume in which his Theory oj the Earth appeared 
contained also a Theory of Rain, which was read to the Royal 
Society of Edinburgh in 1784. He contended that the amount 
of moisture Which the air can retain in solution increases with 
augmentation of temperature, and, therefore, that on the 
mixture of two masses of air of different temperatures a portion 
of the moisture must be condensed and appear in visible form. 
He investigated the available data regarding rainfall and climate 
in different regions of the globe, and came to the conclusion 
that the rainfall is everywhere regulated by the humidity of the 

air on the one bond) tnd the causes which promote mixturea 
of different aerial currents in the higher atmosphere on 
the other. 

The vigour and versatility of his genius may be understood 
from the variety of works which, during his thirty yean' residence 
in Edinburgh, be gave to the world. In 1793 be published a 
quarto volume entitled Dissertations on different Subjects in 
Natural Philosophy, in which he discussed the nature of matter, 
fluidity, cohesion, light, heat and electricity. Some of these 
subjects were further illustrated by him in papers read before 
the. Royal Society of Edinburgh.. He did not restrain himself 
within the domain of physics, but boldly marched into that of 
metaphysics, publishing three quarto volumes with the title 
A n Investigation of the Principles of Knowledge, and of the Progress 
of Reason-*-from Sense to Science and Philosophy. In this work 
he developed the idea, that the external world, as conceived 
by us, is the creation of our own minds influenced by impressions 
from without, that there is no resemblance between our picture 
of the outer world and the reality, yet that the impression 
produced upon our minds, being constant and consistent, become 
as much realities to us as if they precisely resembled things 
actually existing, and, therefore, that our moral conduct must 
remain the same as if our ideas perfectly corresponded to the 
causes producing them. His closing years were devoted to the 
extension and republication of his Theory of the Earth, of which 
two volumes appeared in 1795. A third volume, necessary 
to complete the work, was left by him in manuscript, and is 
referred to by his biographer John Play fair. A portion of the 
MS. of this volume, which had been fciven to the Geological 
Society of London by Leonard Horner, was published by the 
Society in 1809, under the editorship of Sir A. Geikie. The 
rest of the manuscript appears to be lost. Soon afterwards 
Hutton set to work to collect and systematise his numerous 
writings on husbandry, which he proposed to publish under 
the title of Elements of Agriculture. He bad nearly completed 
this labour when an incurable disease brought his active career 
to a dose on the 26th of March 1797. 

It is by his Theory of (he Earth that Hutton witl be remembered 
with reverence while geology continues to be cultivated. The 
author's style, however, being somewhat heavy and obscure, the 
book did not attract during his lifetime so much attention as it de- 
served. Happily for science Hutton numbered among his friends 
John Playfair (q.v.), professor of mathematics in the university of 
Edinburgh, whose enthusiasm for the spread of Mutton's doctrine 
was combined with a rare gift of graceful and luminous exposition. 
Five years after Hutton's death he published a volume, Itlustrvtions 
of the Hutton tan Theory of the Earth, in which he gave an admirable 
sumntary of that theory, with numerous additional illustrations and 
arguments. This work is nistly regarded as one of the classical con- 
tributions to geological literature. To its influence much of the 
sound progress of British geology must be ascrbed. In the year 
180$ a biographical account of Hutton, written by Playfair, was 

Cublishcd in vol. v. of the Transactions of the Royal Society of JSrfw- 
Kit*. (A. Gb.) 

HOTTON, RICHARD HOLT (1826-1897), English writer 
and theologian, son of Joseph Hutton, Unitarian minister at 
Leeds, was born at Leeds on the and of June i8a6. His family 
removed to London in 1835, and he was educated at University 
College School and University College, where he began a lifelong 
friendship with Walter Bagchot, of whose works he afterwards 
was the editor; he took the degree in 1845, being awarded the 
gold medal for philosophy. Meanwhile he had also stwfied 
for short periods at Heidelberg and Berlin, and ra 1847 he entered 
Manchester New College with the idea of becoming a minister 
like his father, and studied there tinder James Martineau. 
He did not, however, succeed in obtaining a call to any church, 
and for some Httle time his future was unsettled. He married 
in 1851 his cousin, Anne Roscoe, and became joint-editor with 
J. L. Sanford of the Inquirer, the principal Unitarian organ. 
But his innovations and his unconventional views about stereo- 
typed Unitarian doctrines caused alarm, and in r8sj he resigned. 
His health had broken down, and he visited the West Indies, 
where his wife died of yellow fever. In 1855 Hutton and Bagebot 
became joint-editors of the National JUtUw, a new monthly, 
and conducted it for ten years. During this time HvUoa's 
theological views, influenced largely by Coleridge, and more 


» 7 

directly by F. W. Robertson and F. D. Maurice, gradually 
approached more and more to those of the Church of England, 
which be ultimately joined. His interest in theology was 
profound, and he brought to it a spirituality of outlook and 
an aptitude for metaphysical inquiry and exposition which 
added a singular attraction to his writings. In x86i he joined 
Meredith Townsend as joint-editor and part proprietor of the 
Spectator, then a well-known liberal weekly, which, however, 
was not remunerative from the business point of view. Hutton 
took charge of the literary side of the paper, and by degrees 
his own articles became and remained up to the last one of the 
best-known features of serious and thoughtful English journalism. 
The Special*, which gradually became a prosperous, property, 
was his pulpit, in which unwearyingly he gave expression to 
his views* particularly on literary, religious, and philosophical 
subjects, in opposition to the agnostic and rationalistic opinions 
(hen current in, intellectual circles, as popularized by Huxley. 
A man of fearless honesty, quick and catholic sympathies, broad 
culture, and many friends in intellectual and religious circles, 
he became one of the most influential journalists of the day, 
his fine character and conscience earning universal respect and 
confidence. He was an original member of the Metaphysical 
Society (i860). , He was an anti-vivisectionist, and a membet 
of the royal commission (1875) on that subject In 1858 he 
had married Eliza Roscpe, a cousin of his first wife; she died 
early in 1807, and Hut ton's own death followed on the 9th of 
September of the same year. 

Among his other publications may be mentioned Essays, Theo- 
logical and Literary^ ( 1 871 ; revised 1888), and Criticisms on Con- 
temporary Thought and Thinkers (1894); and his opinions may be 
studied compendiously in the selections from his Spectator articles 
published in 1899 under the title of Aspects of Rdi&ous and Scientific 

HUXLEY. THOMAS HENRY (1825-1895), English biologist, 
was born on the 4th of May 1825 at Ealing, where his father, 
George Huxley, was senior assistant-master in the school of 
Dr Nicholas. This was an establishment of repute, and is at 
any rate remarkable for having produced two men with so 
little in common in after life as Huxley and Cardinal Newman. 
The cardinal's brother, Francis William, had been " captain " 
of the school in 182 1. Huxley was a seventh child (as his father 
had also been), and the youngest who survived infancy. Of 
Huxley's ancestry no more is ascertainable than in the case 
of most middle-class families. He himself thought it sprang 
from the Cheshire Huxley* of Huxley Hall. Different branches 
migrated south, one, now extinct, reaching London, where its 
members were apparently engaged in commerce, They estab- 
lished themselves for four generations at Wyre Hall, near 
Edmonton, and one was knighted by Charles II. Huxley describes 
his paternal race as " mainly Iberian mongrels, with a good 
dash of Norman and a little Saxon." l From his father he thought 
he derived little except a quick temper and the artistic faculty 
which proved of great service to him and reappeared in an even 
more striking degree in his daughter, the Hon. Mrs Collier. 
" Mentally and physically," he wrote, "lama piece of my 
mother." Her maiden name was Rachel Withers. " She came 
of Wiltshire people," he adds, and describes her as" a typical 
example of the Iberian variety." He tells us that " her most 
distinguishing characteristic was, rapidity of thought. . . That 
peculiarity has been passed on to me in full strength " (Essays, i. 
4). One of the not least striking facts in Huxley's life is that 
of education in the formal sense he received none. " I had 
two years of a pandemonium of a school (between eight and 
ten), and after that neither help nor sympathy in any intellectual 
direction till I reached manhood " (Life, ii. 145). Aftej the 
death of Dr Nicholas the Ealing school broke up, and Huxley's 
father returned about 1835 t° bis native town, Coventry, where 
he had obtained a small appointment. Huxley was left to 
his own devices; few histories of boyhood could offer any 
parallel. At twelve he was sitting up in bed to read Hutton 's 
Geology. His great desire was to be a mechanical engineer; 
it ended in his devotion to " the mechanical engineering of living 
1 Nature, Ixtfi. 127. 

xrv 1* 

machines." Hfc curiosity in this direction was nearly fatajfc 
a post-mortem he was taken to between thirteen and fourteen, 
was followed by an illness which seems to have been the starting' 
point of the ill-health which pursued him all through life. At 
fifteen he devoured Sir William Hamilton's Logic, and thus 
acquired the taste for metaphysics, which he cultivated to the 
end. At seventeen he came under the influence of Thomas 
Carlyle's writings. Fifty years later he wrote: " To make 
things clear and get rid of cant and shows of all sorts. This 
was the lesson I learnt from Carlyle's books when I was a boy, 
and it has stuck by me all my life " (Life, ii. 268). Incidentally 
they led him to begin to learn German; he had already acquired 
French. At seventeen Huxley, with his elder brother James, 
commenced regular medical studies at Charing Cross Hospital, 
where they had both obtained scholarships. He studied under 
Wharton Jones, a physiologist who never seems to have attained 
the reputation he deserved. Huxley said of him: " I do not 
jfjiow that I ever felt so much respect for a teacher before or 
since " (Life, i. 20). At twenty he passed his first M.B. examina- 
tion at the University of London, winning the gold medal for 
anatomy and physiology; W. H, Ransom, tie well-known 
Nottingham physician, obtaining the exhibition. In 1845 
be published, at the suggestion of Wharton Jones, his first 
scientific paper, demonstrating the existence of a hitherto 
unrecognized layer in the inner sheath of hairs, a layer that 
has been known since as " Huxley's layer." 

Something had to be done for a livelihood, and at the sugges- 
tion of a fellow-student, Mr (afterwards Sir Joseph) Fayrer, he 
applied for an appointment in the navy. He passed the necessary 
examination, and at the same time obtained the qualification ojf 
the Royal College of Surgeons. He was " entered on the books 
of Nelson's old ship, the * Victory,' for duty at Haslar Hospital." 
Its chief, Sir John Richardson, who was a well-known Arctic 
explorer and naturalist, recognized Huxley's ability, and prop 
cured for him the post of surgeon to H.M.S. " Rattlesnake," 
about to start for surveying work in Torres Strait. The com- 
mander, Captain Owen Stanley, was a son of the bishop of 
Norwich and brother of Dean Stanley, and wished for an officer 
with some scientific knowledge. Besides Huxley the " Rattle- 
snake " also carried a naturalist by profession, John Macgillivray, 
who, however, beyond a dull narrative of the expedition, ac- 
complished nothing. The " Rattlesnake " left England on the 
3rd of December 1846, and was ordered home after the lamented 
death of Captain Stanley at Sydney, to be paid off at Chatham 
on the 9th of November 185a The tropical seas teem with 
delicate surface-life, and to the study of this Huxley devoted 
himself with unremitting devotion. At that time no known 
methods existed by which it could be preserved for study in 
museums at home. He gathered a magnificent harvest in 
the almost unreaped field, and the conclusions be drew from 
it were the beginning of the revolution in zoological science 
which be lived to see accomplished. 

Baron Cuviex (1 769-1832), whose classification still held 
its ground, had divided the animal kingdom into four great 
embranchemenls. Each of these corresponded to an independent 
archetype, of which the " idea " had existed in the mind of 
the Creator. There was no other connexion between these 
classes, and the " ideas " which animated them were, as far 
as one can see, arbitrary. Cuvicr's groups, without their 
theoretical. basis, were accepted by K. E. von Baer (1792-1876), 
The " idea " of the group, or archetype, admitted of endless 
variation within it; but this was subordinate to essential 
conformity with the archetype, and hence Cuvier deduced the 
important principle of the " correlation of parts," of which 
he made such conspicuous use in palaeontological reconstruction. 
Meanwhile the " Naturphilosophen," with J. W. Goethe (1740- 
1852) and L. Oken (1779-1851), bad in effect grasped the under- 
lying principle of correlation, and so far anticipated evolution 
by asserting the possibility of deriving specialized from simpler 
structures. Though they were still hampered by idealistic 
conceptions, they established morphology. Cuvicr's four great 
groups were Vertebrata, Mollusca, Articulata and Radiata T 



It was amongst the members of the last class that Huxley found 
most material ready to his hand in the seas of the tropics. It 
included organisms of the most varied kind, with nothing more 
in common than that their parts were more or less distributed 
round a centre. Huxley sent home "communication after 
communication to the Linnean Society," then a somewhat 
somnolent body, "with the same result as that obtained by 
Noah when he sent, the raven out of the ark " {Essays, i. 13). 
His important paper, On the Anatomy and the Affinities of the 
Family of Medusae, met with a better fate. It was communicated 
by the bishop of Norwich to the Royal Society, and printed 
by it in the Philosophical Transactions in 1849. Huxley 
united, with the Medusae, the Hydroid and Sertularian polyps, 
to form a class to which he subsequently gave the name of 
Hydrozoa. This alone was no inconsiderable feat for a young 
surgeon who had only had the training of the medical school 
But the ground on which it was done has led to far-reaching 
theoretical developments. Huxley realized that something 
more than superficial characters were necessary in determining 
the affinities of animal organisms. He found that all the members 
of the class consisted of two membranes enclosing a central 
cavity or stomach. This is characteristic of what are now 
called the Coelcnterata. All animals higher than these have 
been termed Coelomata; they possess a distinct body-cavity 
in addition to the stomach. Huxley went further than this, 
and the most profound suggestion in his paper is the comparison 
of the two layers with those which appear in the germ of the 
higher animals. The consequences which have flowed from 
this prophetic generalization of the ectoderm and endoderm are 
familiar to every student of evolution. The conclusion was 
the more remarkable as at the time he was not merely free 
from any evolutionary belief, but actually rejected it. The 
value of Huxley's work was immediately recognized. On 
returning to England in 1850 he was elected a Fellow of the Royal 
Society. In the following year, at the age of twenty-six, he not 
merely received the Royal medal, but was elected on the council. 
With absolutely no aid from any one he had placed himself 
in the front rank of English scientific men. He secured the 
friendship of Sir J. D. Hooker and John Tyndall, who remained 
his lifelong friends. The Admiralty retained him as a nominal 
assistant-surgeon, in order that he might work up the observations 
he had made during the voyage of the " Rattlesnake." He was 
thus enabled to produce various important memoirs, especially 
those on certain Ascidians, in which he solved the problem 
of Appendictdaria — an organism whose place in the animal 
kingdom Johannes Mil lie r had found himself wholly unable 
to assign — and on the morphology of the Cephalous Mollusca. 

Richard Owen, then the leading comparative anatomist in 
Great Britain, was a disciple of Cuvier, and adopted largely from 
him the deductive explanation of anatomical fact from idealistic 
conceptions. He superadded the evolutionary theories of 
Okcn, which were equally idealistic, but were altogether re- 
pugnant to Cuvier. Huxley would have none of either. Imbued 
with the methods of von Baer and Johannes Muller, his methods 
were purely inductive. He would not hazard any statement 
beyond what the facts revealed. He retained, however, as has 
been done by his successors, the use of archetypes, though they 
no longer represented fundamental " ideas " but generalizations 
of the essential points of structure common to the individuals 
of each class. He had not wholly freed himself, however, from 
archetypal trammels. " The doctrine," he says, " that every 
natural group is organized after a "definite archetype . . . seems 
to roe as important for zoology as the doctrine of definite pro- 
portions for chemistry." This was in 1853. He further stated: 
" There is no progression from a lower to a higher type, but 
merely a more or less complete evolution of one type " {Phil, 
Trans., 1853, p. 63). As Chalmers Mitchell points out, this state* 
ment is of great historical interest. Huxley definitely uses the word 
" evolution," and admits its existence within the great groups. 
He had not, however, rid himself of the notion that the archetype 
was a property inherent in the group. Herbert Spencer, whose 
acquaintance he made in 1852, was unable to convert him to 

evolution in its widest sense {Life, i. 168). He could not bring 
himself to acceptance of the theory-owing, no doubt, to his 
rooted aversion from & priori reasoning— without a mechanical 
conception of its mode of operation.* In his first interview 
with Darwin, which seems to have been about the same time, 
he expressed bis belief " in the sharpness of the lines of demarca- 
tion between natural groups," and was received with a h um orou s 
smile {Life, L 169). 

The naval medical service exists for practical purposes. It 
is not surprising, therefore, that after his three years' noraJnai 
employment Huxley was ordered on active service. Though 
without private means of any kind, he resigned.' The navy, 
however, retains the credit of having started his scientific career 
as well as that of Hooker and Darwin. Huxley was now thrown 
on his own resources, the immediate prospects of whieh were 
slender enough. As a matter of fact, he 1 had not to wail many 
months. His friend, Edward Forties; was appointed to die chaw 
of natural history in Edinburgh, and in July 1854 he succeeded 
him as lecturer at the School of Mines and as naturalist to the 
Geological Survey in the- following year. The latter post he 
hesitated at first to accept, as he "did not care for fossils'* 
{Essays, i. 15). In 1855 he married Miss H. A. Heathorn, whose 
acquaintance he had made in Sydney. They were engaged 
when Huxley could offer nothing but the future promise of his 
ability. The confidence of his devoted helpmate was not mis- 
placed, and her affection sustained him to the end, alter she 
had seen him the recipient of every honour which English science 
could bestow. His most important research belonging to this 
period was the Croonian Lecture delivered before the Royal 
Society in 1858 on " The Theory of the Vertebrate Skull." 
In this he completely and finally demolished, by applying as 
before the inductive method, the idealistic, if in some degree 
evolutionary, views of its origin Which Owen had derived from 
Goethe and Okcn. This finally disposed of the " archetype," 
and may be said once for all to have liberated the English 
anatomical school from the deductive- met hod. 

In 1859 The Origin of Species was published. This was a 
momentous event in the history of science, and not least for 
Huxley. Hitherto he had turned a deaf ear to evolution. " 1 
took my stand," he says, *' upon two grounds: firstly, that . . 
the evidence in favour of transmutation was wholly insufficient; 
and secondly, tha,t no suggestion respecting the causes of the 
transmutation assumed, which bad been made, was in any 
way adequate to explain the phenomena " {Life, i. 168). Huxley 
had studied Lamarck " attentively," but to no purpose. Sir 
Charles Lyell " was the chief agent in smoothing the road for 
Darwin. For consistent uniformitariahism postulates evolution 
as much in the organic as in the inorganic world " (I.e.) ; and 
Huxley found in Darwin what he had failed to find in Lamarck, 
an intelligible hypothesis good enough as a working basis. Yet 
with the transparent candour which was characteristic of him. 
he never to the end of his life concealed the fact that he thought 
it wanting in rigorous proof. Darwin, however, was a naturalist; 
Huxley was not. He says: "lam afraid there is very little 
of the genuine naturalist in me. I never collected anything, 
and species-work was always a burden to me; what I cared 
for was the architectural and engineering part of the business n 
{Essays, i. 7). But the solution of the problem of organic evolu- 
tion must work upwards from the initial stages, and it is precisely 
for the study of these that " species-work " is necessary. Darwin, 
by observing the peculiarities in the distribution of the plants 
which he had collected in the Galapagos, was started on the 
path that led to his theory. Anatomical research had only 
so far led to transcendental hypothesis, though in Huxley's 
hands it had cleared the decks of that lumber. He quotes with 
approval Darwin's remark that " no one has a right to examine 
the question of spedes who has not minutely described many " 
(Essays, li. 283). The rigorous proof which Huxley demanded 
was the production of species sterile to one another by selective 
breeding (Life, i. 103). But this was a misconception of the 
question. Sterility is a physiological character, and the specific 
differences which the theory undertook to account for are 



morphological; there is no necessary nexus between the two. 
Huxley, however, fell that he had at last a secure grip of evolution. 
He warned Darwin: " 1 will stop at no point as long as clear 
reasoning will carry me further" (Life, i. 172). Owen, who 
had some evolutionary tendencies, was at first favourably 
disposed to Darwin's theory, and even claimed that he had to 
some extent anticipated it in his own writings. But Darwin, 
though he did not thrust it into the foreground, never flinched 
from recognizing that man could not be excluded from his theory. 
" Light will be thrown on the origin of man and his history " 
{Origin, ed. i. 488) . Owen could not face the wrath of fashionable 
orthodoxy. In his Rede Lecture he endeavoured to save the 
position by asserting that man was clearly marked off from all 
other animals by the anatomical structure of bis brain. This 
was actually inconsistent with known facts, and was effectually 
refuted by Huxley in various papers and lectures, summed up in 
1863 in M an's Place in Nature This " monkey damnification " Of 
mankind was too much even for the " veracity " of Carlyle, who 
is said to have never forgiven it. Huxley had not the smallest 
respect for authority as a basis for belief, scientific or other- 
wise. He held that scientific men were morally bound " to try all 
things and hold fast to that which is good " (Life, ii. 161). Called 
upon in 1862, in the absence of the president, to deliver the presi- 
dential address to the Geological Society, he disposed once for all 
ot one of the principles accepted by geologists, that similar fossils 
in distinct regions indicated that the strata containing them 
were contemporary. All that could*. be concluded, he pointed 
out, was that the general order of succession was the same. 
In 1854 Huxley had refused the post of palaeontologist to the 
Geological Survey; but the fossils for which he then said that 
he " did not care " soon acquired importance in his eyes, as 
supplying evidence for the support of the evolutionary theory. 
The thirty-one years during which he occupied the chair of 
natural history at the School of Mines were largely occupied 
with palaeontological research. Numerous memoirs on fossil 
fishes established many far-reaching morphological facts. The 
study of fossil reptiles led to his demonstrating, in the course 
of lectures on birds, delivered at the College of Surgeons in 1867, 
the fundamental affinity of the two groups which he united 
under the title of Sauropsida. An incidental result of the same 
course was his proposed rearrangement of the zoological regions 
into which P. L. Sclater had •divided the world in 1857. Huxley 
anticipated, to a large extent, the results at which botanists have 
since arrived: he proposed as primary divisions, Arctogaea — 
to include the land areas of the northern hemisphere — and 
Notogaea for the remainder. Successive waves of life originated 
in and spread from the northern area, the survivors of the more 
ancient types finding successively a refuge in the south. Though 
Huxley had accepted the Darwinian theory- as a working 
hypothesis, he never succeeded in firmly grasping it in detail. 
He thought " evolution might conceivably have taken place 
without the development of groups possessing the characters 
of species" (Essays, v. 41). His palaeontological researches 
ultimately led him to dispense with Darwin. In 1892 he wrote: 
" The doctrine of evolution is no speculation, but a generalization 
of certain facts . . . classed by biologists under the heads 
of Embryology and of Palaeontology " {Essays, v. 42). Earlier 
in 1 88 1 he had asserted even more emphatically that if the 
hypothesis of evolution " had not existed, the palaeontologist 
would have had to invent it * (Essays , iv. 44). 

From 1870 onwards he was more and more drawn away from 
scientific research by the claims of public duty. Some men 
yield the more readily to such demands, as their fulfilment 
is not unaccompanied by public esteem. But he felt, as he 
himself said of Joseph Priestley, " that he was a man and a 
citizen before he was a philosopher, and that the duties of the 
two former positions are at least as imperative as those of the 
latter " (Essays, iii. 13). From 186a to 1884 he served on no 
less than ten Royal Commissions, dealing in every case with 
subjects of great importance, and in many with, matters of the 
gravest moment to the community. He held and filled with 
invariable dignity and distinction more public positions than ' 

have perhaps ever fallen to the lot of a scientific man in England; 
From 187 1 to 1880 he was a secretary of the Royal Society. 
From 1 88 1 to 1885 he was president. For honours he cared 
little, though they were within his reach; it is said that he 
might have received a peerage. He accepted, however, in 1802, 
a Privy Counciilorship, at once the most democratic and the 
most aristocratic honour accessible to an English citizen. In 
1870 he was president of the British Association at Liverpool, and 
in the same year was elected a member of the newly constituted 
London School Board. He resigned the latter position in 
1872, but in the brief period during which he acted, probably 
more than any man, he left his mark on the foundations of 
national elementary education. He made war on the scholastic 
methods which wearied the mind in merely taxing the memory; 
the children were to be prepared to take their place worthily 
in the community. Physical training was the basis; domestic 
economy, at any rate for girls, was insisted upon, and for all 
some development of the aesthetic sense by means of drawing 
and singing. Reading, writing and arithmetic were the in* 
dispensable tools for acquiring knowledge, and intellectual 
discipline was to be gained through the rudiments of physical 
science. He insisted on the teaching of the Bible partly as a great, 
literary heritage, partly because he was " seriously perplexed 
to know by what practical measures the religious feeling, which 
is the essential basis of conduct, was to be kept up, in the present 
utterly chaotic state of opinion in these matters, without its 
use " (Essays, iii- 397). In 1872 the School of Mines was moved 
to South Kensington, and Huxley had, for the first time after 
eighteen years, those appliances for teaching beyond the 
lecture room, which to the lasting injury of the interests of 
biological science in Great Britain had been withheld from 
him by the short-sightedness of government. Huxley had 
only been able to bring his influence to bear upon his pupils 
by oral teaching, and bad had no opportunity by personal 
intercourse in the laboratory of forming a school. He was now 
able to organize a system of instruction for classes of elementary 
teachers in the general principles of biology, which indirectly 
affected the teaching of the subject throughout the country. 

The first symptoms of physical failure to meet the strain of 
the scientific and public duties demanded of him made some 
rest imperative, and he look a long holiday in Egypt. He still 
continued. for some years to occupy himself mainly with verte- 
brate morphology. But he seemed to find more interest and the 
necessary mental stimulus to exertion in lectures, public addresses 
and more or less controversial writings. His health, which 
had for a time been fairly restored, completely broke down 
again in 188$. la 1890 he removed from London to East' 
bourne, where after a painful illness be died on the 39th of 
June 1895. 

The latter years of Huxley's life were mainly occupied with con- 
tributions to periodical literature on subjects connected with philo- 
sophy and theology. The t effect produced by these on popular 
opinion was profound. This was partly due to his position as a 
man of science, partly to his obvious earnestness and sincerity, but 
in the main to his strenuous and attractive method of exposition. 
Such studies were not wholly new to him, as they had more or less 
engaged his thoughts from his earliest days. That his views exhibit 
f * * 'pment and are not wholly consistent was, 

1 ed, and for this reason it is not easy to 

1 onnected body of teaching. They may be 

I lost systematic form in the volume on Hum* 

titude to the problems of theology and 

1 illy that of scepticism. " \ am," he wrote,' 
:o deny the possibility of anything *' (Life , ft\' 
neficent demon " (Essays, ix. 56;. He was 

i avoid the accusation of Pyrrhonism iLife. ii. 

2 sm which he defined to express his position 
i yrrhonist Aphasia. The only approach to 

< mitted lay in the order of nature. "The 

< incy of the order of nature has become the 

< rn thought. . . . Whatever may be mah's 
1 is quite certain that every intelligent person 
fc-.^„ ...* M .w »..« ..*«.* his fortune upon the belief that the order off 
nature is constant, and that the chain ofriatural causation is never 
broken." He adds, however, that " it by no means necessarily 
follows that we are justified in expanding this generalization into the 
infinite past " (Essays, iv. 47, 48). This was little more than a pious 

ao HUY 

reservation, as evolution implies the principle of continuity (Jx. p. 55). 
Later he stated his belief even more absolutely: " If there is any- 
thing in the world which I do firmly believe in, it is the universal 
validitv of the law of causation, but Chat universality cannot be. 
proved by any amount of experience " {Essays, ix. 121). The 
assertion that " There is only one method by which intellectual truth 
can be reached, whether the 6ubject-matter of investigation belongs 
to the world of physics or to the world of consciousness " (Essays, ix. 
126) laid him open to the charge of materialism, which he vigorously 
repelled. His defence, when he rested it on the imperfection of the 
physical analysis of matter and force (Ac. p. 131), was irrelevant; he 
was on sounder ground when he contended with Berkeley " that our 
certain knowledge does not extend beyond our states of conscious* 
aess " (I.e. p. 130). " Legitimate materialism, that is, the extension 
of the conceptions and of the methods of physical science to the 
highest as well as to the lowest phenomena of vitality, is neither 
more nor less than a sort of shorthand idealism " (Essays, L 10$). 
While " the substance of matter is a metaphysical -unknown quality 
of the existence of which there is no proof . . . the non-existence of 
a substance of mind is equally arguable; . . . the result ... is the 
reduction of the All to co-existences and sequences of phenomena 
beneath and beyond which there is nothing cognoscible " (Essays, ix. 
06). Hume had defined a miracle as a violation of the laws' of 
nature/' Huxley refused to accept this. While, on the one hand, he 
insists that " the whole fabric of practical life is built upon our 
faith in its continuity " (Hume, p. 129), on the other " nobody 
can presume to sav what the order of nature must be "; this " knocks 
the bottom out of all a priori objections either to ordinary 'miracles' 
or to the efficacy of prayer " (Essays, v. 133). •' If by the term 
miracles we mean only extremely wonderful events, there can be no 
just ground for denying the possibility of their occurrence " (Hume, 
p. 134). Assuming the chemical elements to be aggregates of uniform 
primitive matter, he saw no more theoretical difficulty in water 
being turned into alcohol in the miracle at Cana, than in sugar 
undergoing a similar conversion (Essays, v. 81). The credibility of 
miracles with Huxley is a question of evidence. It may be remarked 
that a scientific explanation is destructive of the supernatural 
character of a miracle, and that the demand for evidence may be 
so framed as to preclude the credibility of any historical event. 
Throughout his life theology had a strong attraction, not without 
elements of repulsion, for Huxley. The circumstances of his early 
training, when Paley was the most interesting Sunday reading 
allowed him when a boy " (Life, ii. 57), probably had something to 
do with both. In i860 his beliefs were apparently theistic : " Science 
seems to me to teach in the highest and strongest manner the 
great truth which is embodied in toe Christian conception of entire 
surrender to the will of God " (l>ife* «• 219)- In 1885 he formulates 
"the perfect. ideal of religion" in a passage which has become 
almost famous: " In the 8th century B.C. in the heart of a world of 
idolatrous polytheists, the Hebrew prophets put forth a conception 
of religion which appears to be as wonderful an inspiration of genius 
as the art of Pheidias or the science of Aristotle. ' And what doth 
the Lord require of thee, but to do justly, and to love mercy, and to 
walk humbly with thy God ' " (Essays, iv. 161). Two years later he 
was writing: " That there is no evidence of the existence of such a 
being as the God of the theologians is true enough " (Life, ii. 162). 
He insisted, however, that "atheism is on purely philosophical 
*"* ally advanc 

(Ix.). His theism never really advanced 
Beyond the recognition of " the passionless impersonality of the 

grounds untenable 
nd the recogni 
own and unknowable, which science shows everywhere under- 
lying the thin veil of phenomena M (Life, i. 230). In other respects 
his personal creed was a kind of scientific Calvinism. There is an 

__j personal 

interesting; passage in an essay written in 1802, " An Apologetic 
Eirenicon/' which has not been republished, which illustrates this: 
" It is the secret of the superiority of the best theological teachers to 
the majority of their opponents that they substantially recognize 
these realities of things, however strange the forms in which they 
clothe their conceptions. The doctrines of predest ination, of original 
sin, of the innate depravity of man and the evil fate of the greater 
part of the race, of the primacy of Satan in this world, of the essential 
vileness of matter, of a malevolent Demiurgus subordinate to a 
benevolent Almighty, who has only lately revealed himself, faulty 
as they are, appear to me to be vastly nearer the truth than the 
' liberal ' popular illusions that babies arc all born good, and that the 
example of a corrupt society is responsible for their failure to remain 
so; that it is given to everybody to reach the ethical ideal if he will 
only try; that all partial evil is universal good, and other optimistic 
figments, such as that which represents " Providence ' under the 
guise of a paternal philanthropist, and bids us believe that everything 
will come right (according to our notions) at last." But his " slender 
definite creed,". R. H. Hutton, who was associated with him in 
the Metaphysical Society, thought — and no doubt rightly — in no 
respect " represented the cravings of his larger nature.* 

From 1880 onwards till the very end of his life, Huxley was 
continuously occupied in a controversial campaign against orthodox 
beliefs. As Professor W. F. R. Weldon justly said of his earlier 
polemics: " They were certainly among the principal agents in 
winning a larger measure of toleration lor the critical examination of 
fundamental beliefs, and for the free expression of honest reverent 
doubt." He threw Christianity overboard bodily and with little 

appreciation of its historic effect as a civilizing agency. He thought 
that " the exact nature of the teachings and the convictions of 
Jesus is extremely uncertain " (Essays, v. 348). " What we are 
usually pleased to call^religion nowadays is, for the most part. 

HeUenizcd Judaism" (Essays, iv. 162). His final analysis of what 
" since the second century, has assumed to itself the title of Orthodox 
Christianity " is a " varying compound of some of the best and 
some of the worst elements of Paganism and Judaism, moulded m 
practice by the innate character of certain people of the Wetter* 
world " (Essays, v. 142). He concludes " That this Christianity is 
doomed to fall is, to my mind, beyond a doubt; but its fall will 
neither be sudden nor speedy " (l.e.). He did not omit, however, 
to do justice to " the bright side of Christianity," and was deeply 
impressed with the life of Catherine of Siena. Failing Christianity, 
he thought that some other " hypostasis of men's hopes *' will arise 
(Essays, v. 254). His latest speculations on ethical problems are 
perhaps the least satisfactory of his writings. In 1892 he wrote: 
11 The moral sense is a very complex affair— dependent in part upon 
associations of pleasure and pain, approbation and disapprobation, 
formed by education in early youth, but in part also on an innate 
sense of moral beauty and ugliness (how originated need not be dis- 
cussed), which is possessed by some people in great strength, whue 
some are totally devoid of it (Life, ii. 305). This is an intuitional 
theory, and he compares the moral with the aesthetic sense, which he 
repeatedly declares to be intuitive; thus: " All the understanding 
in the world will neither increase nor diminish the force of the' 
intuition that this is beautiful and this is ugly " (Essays, ix. 80). la 
the Romanes Lecture delivered in 1894, in which this passage occurs, 
he defines " law and morals " to be restraints upon the struggle 
for existence between men in society." It follows that " the ethical 

f>rocess is in opposition to the cosmic process," to which the struggle 
or existence belongs (Essays, ix. 31). Apparently he thought that 
the moral sense in its origin was intuitional and in its development 
utilitarian. " Morality commenced with society " (Essays, v. 52). 
The " ethical process is the " gradual strengthening of the social 
bond " (Essays, ix. 35). " The cosmic process has no sort of relation 
to moral ends (Ix. p. 83) ; *' of moral purpose I see no trace in 
nature. That is an article of exclusive human manufacture " (Ufc 
ii. 268). The cosmic process Huxley identified with evil, and the 
ethical process with good ; the two axe in necessary conflict. " The 
reality at the bottom of the doctrine of original sin " is the " innate 
tendency to self-assertion " inherited by man from the cosmic order 
(Essays, ix. 27). " The actions we call sinful are part and parcel of 
the struggle for existence " (Life, ii. 282). " The prospect of attaining 
untroubled happiness " is an illusion " (Essays, ix. 44), and the 
cosmic process in the long run will get the best of the contest, and 
" resume its sway " when evolution enters on its downward course 
(Ix. p. 45). This approaches pure pessimism, and though in Husky's 
view the " pessimism of Schopenhauer is a nightmare ' (Essays, ix. 
200), his own philosophy of life is not distinguishable, and is often 
expressed in the same language. The cosmic order is obviously 
non-moral (Essays, ix. 197). That it is, as has been said, immoral 
is really meaningless. Pain and suffering are affections which 
imply a complex nervous organization, and we are not justified in 
projecting them into nature external to ourselves. Darwin and A. R. 
Wallace disagreed with Huxley in seeing rather the joyous than the 
suffering side of nature. Nor can it be assumed that the descending 
scale of evolution will reproduce the ascent, or that man will ever be 
conscious of his doom. 

As has been said, Huxley never thoroughly grasped the Darwinian 
principle. He thought transmutation may take place without 
transition " (Life, i. 173). In other words, that evolution is ac- 
complished by leaps and not by the accumulation of small variations. 
He recognized the " struggle for existence " but wt the gradual 
adjustment of the organism to its environment which is implied in 
" natural selection.** In highly civilized societies he thought that the 
former was at an end (Essays, ix. 36) and had been replaced by the 
" struggle for enjoyment " (ta> p- 40). But a consideration of the 
stationary population of France might have shown him that the 
effect in the one case may be as restrictive as in the other. So far 
from natural selection being. in abeyance under modern social 
conditions, " it is," as Professor Karl Pearson points out, " some- 
thing we run up against at once, almost as soon as we era mine a 
mortality table" (Biometrika, L 76). The inevitable conclusion, 
whether we like it or not, is that the future evolution of humanity is 
as much a part df the cosmic process as its past history, and Huxley's 
attempt to shut the door on it cannot be maintained scientifically. 

Authorities.— -Life and Letters of Thomas Henry Huxley, by his 
son Leonard Huxley (2 vols., 1900); Scientific Memoirs of T. H. 
Huxley (4 vols.. 1898-1901); Collected Essays by T. H. Huxley 
(9 vols., 1898); Thomas Henry Huxley, a Sketch of his Life and Work, 
by P. Chalmers Mitchell, M.A. (Oxon., looo); a critical study 
founded on careful research and of great value. (W. T. T.-D.) 

HUY (Lat. Hoiunt, and Flem. Hoey), a town of Belgium, 
on the right bank of the Meuse, at the point where it is joined 
by the Hoyoux. Pop. (1004), 14,164. It is 19 m. E. of Narnur 
and a trifle less west of Liege. Huy certainly dates from the 
7th century, and, according to some, was founded by the emperor 



Aatoamus in a.d. 148. Its situation is striking, with its grey 
citadel crowning a grey rock, and the fine collegiate church 
(with a 13th-century gateway) of Notre Dame built against it. 
The citadel is now used partly as a depot of military equipment 
and partly as a prison. The ruins are still shown of the abbey 
of Neumoustier founded by Peter the Hermit on his return 
from the first crusade. He was buried there in 1115, and a 
statue was erected to his memory in the abbey grounds in 
1858. Neumoustier was one of seventeen abbeys in this town 
alone dependent on the bishopric of Liege. Huy is surrounded 
by vineyards, and the bridge which crosses the Meuse at this 
point connects the fertile Hesbaye north of the river with the 
rocky and barren Condros south of it. 

HUYGEU8, CHBBTIAAN (1620-1695), Dutch mathematician, 
mechanician, astronomer and physicist, was born at the Hague 
on the 14th of April 16*9. He was the second son of Sir 
Constantijn Huygens. From his father he received the rudiments 
of his education, which was continued at Leiden under A. Vinnius 
and F van Schooten, and completed in the juridical school 
of Breda. His math e mati c al bent, however, soon diverted 
him from legal studies, and the perusal of some of bis earliest 
thffHTim enabled Descartes to predict his future greatness. In 
1649 he accompanied the mission of Henry, count of /Nassau; 
to Denmark, and in 1651 entered the lists of science as an assailant 
of the unsound system of quadratures adopted by Gregory of 
St Vincent. This first essay (Entasis guadratmae modi* 
Leiden, 1651) was quickly succeeded by his Tke*r**ata dt 
qmedratura ky per botes, ellipsis, el aHuH; while, in a treatise 
entitled Dt circuit magnUudtnt invent*, he made, three years 
later, the closest approximation so far obtained to the ratio 
of the circumference to the diameter of a circle. 

Another class of subjects was now to engage his attention. 
The improvement of the telescope was justly regarded as a 
tint qua rum for the advancement of astronomical knowledge. 
But the difficulties interposed by spherical and chromatic, 
aberration had arrested progress in that direction until, in 1655, 
Huygens, working with his brother Constantijn, hit upon a 
new method of grinding and polishing lenses. The immediate 
results of the clearer definition obtained were the detection 
of a satellite to Saturn (the sixth in order of distance from its 
primary), and the resolution into their true form of the abnormal 
appendages to that planet . Each discovery in turn was, according 
to the prevailing custom, announced to the learned world under 
the veil of an anagram — removed, in the case of the first, by the 
publication, early in 1656, of the little tract Dt Satumi luna 
obscrvalio mm; but retained, as regards the second, until 
1659, when in the System* Saturnism the varying appearanfes 
of the so-called " triple planet " were clearly explained as the 
phases of a ring inclined at an angle of 28 to the ecliptic Huygens 
was also in 1656 the first effective observer of the Orion nebula; 
he delineated the bright region still known by his name, and 
detected the multiple character of its nuclear star, His applica- 
tion of the pendulum to regulate the movement of clocks sprang 
from his experience of the need for an exact measure of time 
in observing the heavens. The invention dates from 1656; 
on the z6th of June 1657 Huygens presented his first " pendulum* 
dock " to the states-general; and the Eorohgium, containing 
a description of the requisite mechanism, was published in 

His reputation now became cosmopolitan. As early as 1655 
the university of Angers had distinguished him with an honorary 
degree of doctor of laws. In 1663, on the occasion of his second 
visit to England, he was elected a fellow of the Royal Society, 
and imparted to that body in January 1669 a clear and concise 
statement of the laws governing the collision of elastic bodies. 
Although these conclusions were arrived at independently, and, 
as it would seem, several years previous to their publication, 
they were in great measure anticipated by the communications 
on the same subject of John Wallis and Christopher Wren, 
made respectively in November and December 1668. 
' Huygens had before this time fixed bis abode in France* 
In 1 66s Colbert made to him on behalf of Louis XIV. an offer 

too tempting to be refused, and between the fbOowing year and 
1681 his residence in the philosophic seclusion of the Bibliotbeque 
du Roi was only interrupted by two short visits to his native 
country. His magnum opus dates from this period. The 
HaroUgium osciUatornm, published with a dedication to his. 
royal patron in 1673, contained original discoveries sufficient 
to have furnished materials for half a dozen striking disquisitions. 
His solution of the celebrated problem of the "centre of oscilla- 
tion" formed in itself an important event in the history of 
mechanics. Assuming as an axiom that the centre of gravity 
of any number of interdependent bodies cannot rise higher 
than the point from which it fell, he arrived, by anticipating 
in the particular case the general principle of the conservation 
of vis tba, at correct although not strictly demonstrated con- 
clusions. His treatment of the subject was the first successful 
attempt to deal with the dynamics of a system. The determina- 
tion of the true relation between the length of a pendulum 
and the* time of its oscillation; the invention of the theory of 
evolutes; the discovery, hence ensuing, that the cycloid is 
its own ©volute, and is strictly isochronous; the ingenious 
although practically inoperative idea of correcting the " circular 
error " of the pendulum by applying cydoidal cheeks to docks- 
were all contained in this remarkable treatise. The theorems 
on the composition of forces in circular motion with which it 
concluded formed the true prelude to Newton's Prindpia, and 
would alone suffice to establish the claim of Huygens to the 
highest rank among mechanical inventors. 

In 1 68 1 he finally severed his French connexions, and returned 
to Holland. The harsher measures which about that time 
began to be adopted towards his co-religionists in France are 
usually assigned as the motive of this step. He now devoted 
himself during six years to the production of lenses of enormous 
focal distance, which, mounted on high poles, and connected with 
the eye-piece by means of a cord, formed what were called " aerial 
telescopes." Three of his object-glasses, of respectively 123, 
180 and 3 10 ft. focal length, are in the possession of the Royal 
Society. He also succeeded in constructing an almost perfectly 
achromatic eye-piece, still known by his name. But his re- 
searches in physical optics constitute his chief 7 title-deed to 
immortality. Although Robert Hooke in 1668 and Ignace 
Fardies in 1672 had adopted a vibratory hypothesis of light, 
the, conception was a mere floating possibility until Huygens 
provided it with a -sure foundation. His powerful scientific 
imagination enabled him to realize that all the points of a wave- 
front originate partial waves, the aggregate effect of which is 
to reconstitute the primary disturbance at the subsequent stages 
of its advance, thus accomplishing its propagation; so that 
each primary undulation is the envelope of an indefinite number 
of secondary undulations. This resolution of the original wave 
is the well-known " Principle of Huygens," and by its means 
he was enabled to prove the fundamental laws of optics, and 
to assign the correct construction for the direction of the extra- 
ordinary ray in uniaxial crystals. These investigations, together 
with his discovery of the " wonderful phenomenon " of polariza- 
tion, are recorded in bis Traits dt U lumicrt t published at • 
Leiden in 1690, but composed in 1678. In the appended 
treatise Sur la Cause dt la pesanteur, he rejected gravitation as 
a universal quality of matter, although admitting the Newtonian 
theory of the planetary revolutions. From his views on centri- 
fugal force he deduced the oblate figure of the earth, estimating 
its compression, however, at little more than one-half its actual 

Huygens never married. He died at the Hague on the 8th 
of June 1695, bequeathing his manuscripts to the university 
of Leiden, and his considerable property to the sons of his 
younger brother. In character he was as estimable as he was 
brilliant in intellect Although, like most men of strong originative 
power, be assimilated with difficulty the ideas of others, his 
tardiness sprang rather from inability to depart from the track 
of his own methods than from reluctance to acknowledge the 
merits of his competitors. 

In addition to the works already mentioned, his C o sm otk t orot— 


a speculation concerning the inhabitants of the planets— was printed 
posthumously at the Hague in 1698, and appeared almost simultane- 
ously in an English translation. A volume entitled Opera posthuma 
(Leiden, 1703) contained his " Dioptrica," in which the ratio between 



HUYGENS. SIR C0N8TANTUH (1596-1687), Dutch poet 
and diplomatist, was born at the Hague on the ath of September 
1596. His father, Christiaan Huygens, was secretary to the 
state council, and a man of great political importance. At the 
baptism of the child, the city of Breda was one of his sponsors, 
and the admiral Justinus van Nassau the other. He was trained 
in every polite accomplishment, and before he was seven could 
speak French with fluency. He was taught Latin by Johannes 
Dedelus, and soon became a master of classic versification. 
He developed not only extraordinary intellectual gifts but 
great physical beauty and strength, and was one of the most 
accomplished athletes and gymnasts of his age; his skill in 
playing the lute and in the arts of painting and engraving 
attracted general attention before be began to develop his 
genius as a writer. In 16 16 he proceeded, with his elder brother, 
to the university of Leiden. He stayed there only one year, 
and in 1618 went to London with the English ambassador 
Dudley Carle ton; he remained in London for some months, 
and then went to Oxford, where he studied for some time in the 
Bodleian Library, and to Woodstock, Windsor and Cambridge; 
he was introduced at the English court, and played the lute 
before James I. The most interesting feature of this visit was 
the intimacy which sprang up between the young Dutch poet 
and Dr Donne, for whose genius Huygens preserved through 
life an unbounded admiration. He returned to Holland in 
company with the English contingent of the synod of Don, 
and in x6ig he proceeded to Venice in the -diplomatic service 
of his country; on his return he nearly lost his life by a foolhardy 
exploit, namely, the scaling of the topmost spire of Strassburg 
cathedral. In 162 1 he published one of his most weighty and 
popular poems, his Batava Tempt, and in the same year he 
proceeded again to London, as secretary to the ambassador, 
Wijngaerdan, but returned in three months. His third diplo- 
matic visit to England lasted longer, from the 5th of December 
162 1 to the 1st of March 1623. During his absence, his volume 
of satires, 7 Costelick Mai, dedicated to Jacob Cats, appeared 
at the Hague. In the autumn of 1622 he was knighted by 
James I. He published a large volume of miscellaneous poems 
in 1625 under the title of Otiorum libri sex; and in the same 
year he was appointed private secretary to the stadhokler. 

In 1617 Haygeas married Susanna van Baerle, and settled at 
the Hague; four sons and a daughter were born to them. In 
1630 Huygens was called to a seat in the privy council, and he 
continued to exercise political power with wisdom' and vigour 
for many years, under the title of the lord of Zuylichem. In 
1634 he is supposed to have completed his k>ng»talked-of version 
of the poems of Donne, fragments of which exist. In 1637 las 
wife died, and he immediately began to celebrate the virtues 
and pleasures of their married life in the remarkable didactic 
poem called Dapoerck, which was not published till long after- 
wards. From 1639 to 1641 he occupied himself by building 
a magnificent house and garden outside the Hague, and by 
celebrating their beauties in a poem entitled Hofwijck, which 
was published in 1653. in 1647 he wrote his beautiful poem 
of Oogtniroest or " Eye Consolation," to gratify his blind friend 
Lucretia van Trollo He made his solitary effort in the dramatic 
line in 1657, when he brought out his comedy of Trijntje C and is 
Klackt, which deals, in rather broad humour, with the adventures 
of the wife of a ship's captain at Zaandam. In 1658 he rearranged 
his poems, and issued them with many additions, under the 
title of Cotn Flowers. He proposed to the government that 
the present highway from the Hague to the sea at Scheveningtn 
should be constructed, and during his absence on a diplomatic 
mission to the French court in 1666 the road was made as a 
compliment to the venerable statesman, who expressed his 
gratitude in a descriptive poem entitled Zeestraei. Huygens 
edited his poems for the* last time in 1672, and died in his ninety* 
first year, on the 28th of March 1687. He was buried, with the 
pomp of a national funeral, in the church of St Jacob, on the 
4th of April. His second son , Christiaan, the eminent astronomer, 
is noticed separately. 

Constantiin Huygens is the most brilliant figure in Dutch literary 
history Other statesmen surpassed him in political influence, and 
at least two other poets surpassed him in the value and originality of 
their writings. But his figure was more dignified and splendid, his 
talents were more varied, and his general accomplishments more 
remarkable than those of any other person of his age, the greatest 
age in the history of the Netherlands. Huygens is the grand setpumr 
of the republic, the type of aristocratic oligarchy, the jewel and 
ornament of Dutch liberty. When we considerms imposing character 
and the positive value of his writings, we may well be surprised that 
he has not found a modern editor. It is a disgrace to Dutch scholar- 
ship that no complete collection of the writings of Huygens exists. 
His autobiography, De vita propria sermonum libri duo, did not see 
the light until 1817, and his remarkable poem, Cluyswtrck. was not 
printed until 1841. As a poet Huygens shows a finer sense of form 
than any other early Dutch writer: the language, in hit hands, 
becomes as flexible as Italian. His epistles and lighter pieces, in par- 
ticular, display his metrical ease and facility to perfection. (E. G.J 

HTJYSVANS, the nam* of four Flemish painters who matricu- 
lated in the Antwerp gild in the 17th century Cornells the 
elder, apprenticed in 1633, passed for a mastership in 1636. 
and remained obscure. Jacob, apprenticed to Frans Wouters 
in 1650, wandered to England towards the close of the reign 
of Charles II., and competed with Lely as a fashionable portrait 
painter He executed a portrait of the queen, Catherine o( 
Braganza, now in the national portrait gallery, and Horace 
Walpole assigns to him the likeness of Lady Bellasys, catalogued 
at Hampton Court as a work of Lely. His portrait of Iaaak 
Walton in the National Gallery shows a disposition to imitate 
the styles of Rubens and Van Dyke. According to most accounts 
he died in London in 1696. Jan Baptist Huysmans, born at 
Antwerp in 1654, matriculated in 1676-1677, and died there in 
1715-1716. He was younger brother to Cornells Huysmans 
the second, who was born at Antwerp in 1648, and educated 
by Caspar de Wit and Jacob van Artois. Of Jan Baptist little 
or nothing has been preserved, except that he registered numerous 
apprentices at Antwerp, and painted a landscape dated 1607 
now in the Brussels museum. Cornells the second is the only 
master of the name of Huysmans whose talent was largely 
acknowledged. J}t received lessons from two artists, one of 
whom was familiar with the Roman art of the Poussins, whilst 
the other inherited the scenic style of the school of Rubens. 
He combined the two in a rich, highly coloured, and usually 
effective style, which, however, was not free from monotony. 


Seldom attempting anything out woodside views with fancy 
backgrounds, half Italian, half Flemish, he painted with great 
facility, and left numerous examples behind. At the outset 
of his career he practised at Malines, where he married in x68«, 
and there too he entered into some business connexion with 
van der Meuten, for whom he painted some backgrounds. 
In 1706 be withdrew to Antwerp, where he resided till 1717, 
returning then to Malines, where he died on the 1st of June 

Though most of his pictures were composed for cabinets rather than 
churches, he sometimes emulated van Artois in the production of 
Urge sacred pieces, and for many years his " Christ on the Road to 
Emmaus adorned the choir of Notre Dame of Malines. In the 
gallery of Nantes, where three of his small landscapes are preserved, 
there hangs an " Investment of Luxembourg," by van der Meulen, of 
which he is known to have laid in the background. The national 
galleries of London and Edinburgh contain each one example of his 
skill. Blenheim, too, and other private galleries in England, possess 
one or more of his pictures, but most of his works, art on the 
European continent. 

HUYSMANS, JORIS KARL (1848-1007), French novelist, 
was bora at Paris on the 5th of February 1848. He belonged 
to a family of artists of Dutch extraction; he entered the 
ministry of the interior, and was pensioned after thirty years' 
service. His earliest venture in literature, Le Drageoir a Spices 
(1874), contained stories and short prose poems showing the 
influence of Baudelaire. Marthe (1876), the life of a courtesan, 
was published in Brussels, and Huysmans contributed a story, 
" Sac an dos," to Les Soirees de Midon, the collection of stories 
of the Franco-German war published by Zola. He then pro- 
duced a series of novels of everyday life, including Les Sours 
V atari (1870), En Menage (1881), and A vau-i'eau (1883), in which 
he outdid Zola in minute and uncompromising Teanam. He 
was influenced, however, more directly by Flaubert and the 
brothers de Goncourt than by Zola. In VArt modern* (1883) 
he gave a careful study of impressionism and in Certains (1889) 
a series of studies of contemporary artists. A Reborns (1884), 
the history of the morbid tastes of a decadent aristocrat, des 
Essdntes, created a literary sensation, its caricature of literary 
and artistic symbolism covering much of the real beliefs of the 
leaders of the aesthetic revolt. In Li-Bat Huysmans's most 
characteristic hero, Durtal, makes his appearance. Durtal 
is occupied in writing the life of Gilles de Rais; the insight 
he gains into Satanism is supplemented by modern Parisian 
students of the black art; but already there are signs of a 
leaning to religion in the sympathetic figures of the religious 
bell-ringer of Saint Sulpice and his wife. En Route (1895) relates 
the strange conversion of Durtal to mysticism and Catholicism 
in his retreat to La Trappe. In La Catkidrate (1808), Huysmans's 
symbolistic interpretation of the cathedral of Chartrcs, he 
develops his enthusiasm for the purity of Catholic ritual. The 
life of Saint* Lydmne de Schiedam (1001), an exposition of 
the value of suffering, gives further proof of his conversion; 
and LVbht (1003) describes Durtal's retreat to the Val des 
Saints, where he is attached as an oblate to a Benedictine 
monastery. Huysmans was nominated by Edmond de Gon- 
court as a member of the Academic des Goncourt. He died 
as a devout Catholic, after a long illness of cancer in the palate 
on the 13th of May 1007. Before his death he destroyed his 
unpublished MSS. His last book was Les Panics d* Lowdes 

See Arthur Symons, Studies in two Literatures (1807) and The 
Symbolist Movement in Literature (1899); Jean Lionnet in L Evolu- 
tion des idles (1903); Eugene Gilbert in trance et Belpque (1905); 
J. Sargeret in Les Grands converHs (1906). 

HUYSUM, JAN VAN (1682-174?), Dutch painter, was born 
at Amsterdam in 1682, and died in bis- native city on the 8th 
of February 1749. He was the son of Justus van Huysum, 
who is said to have "been expeditious in decorating doorways, 
screens and vases. A picture by this artist is preserved in 
the gallery of Brunswick, representing Orpheus and the Beasts 
in a wooded landscape, and here we have some explanation 
of his son's fondness for landscapes of a conventional and Arcadian 
kind; for Jan van Huysum, though skilled as a painter of still 
life, believed himself to possess the genius of a landscape painter. 


Half his pictures in public galleries are landscapes, views of 
imaginary lakes and harbours with impossible ruins and classic 
edifices, and woods of tall and motionless trees— the whole 
very glossy and smooth, and entirely lifeless. The earliest dated 
work of this kind is that of 1717, in the Louvre, a grove with 
maidens culling flowers near a tomb, ruins of a portico, and a 
distant palace oa the shores of a lake bounded by mountains. 

It b doubtful whether any artist ever surpassed van Huysum 
in representing fruit and flowers. It has been said that Ms 
fruit has no savour and his flowers have no perfume — in other 
words, that they axe hard and artificial— but this is scarcely 
true. In substance fruit and flower are delicate and finished 
imitations of nature in its more subtle varieties of matter. 
The fruit has an incomparable blush of down, the flowers have 
a perfect delicacy of tissue. Van Huysum, too, shows supreme 
art in relieving flowers of various colours against each- other, 
and often against a light and transparent background. He 
is always bright, sometimes even gaudy. Great taste and 
much grace and elegance are apparent in the arrangement of 
bouquets and fruit in vases adorned with bas reliefs or in baskets 
on marble tables. There is exquisite and faultless finish every- 
where. But what van Huysum has not is the breadth, the 
bold effectiveness, and the depth of thought of de Heem, from 
whom he descends through Abraham Mignon. 

Some of the finest of van Huysum's fruit and flower pieces have 
been in English private collections: those'of 1723 in the earl of 
Ellesmere's gallery, others of 1730-^1732 in the collections of Hope 
and Ashburton. One of the best examples is now m the National 
Gallery $1736-1737). No public museum has finer and more numer- 
ous specimens than the Louvre, which boasts of four landscapes and 
six panels with still life; then come Berlin and Amsterdam with four 
fruit and flower pieces; then St Petersburg, Munich, Hanover, 
D resde n, the Hague, Brunswick, Vienna, Carlsruheand Copenhagen. 

HWANG HO tHoANO HoJ, the second largest river in China. 
It is known to foreigners as the Yellow river — a name which 
is a literal translation of the Chinese. It rises among the Kuen- 
lun mountains in central Asia, its head-waters being in dose 
proximity to those of the Yangtsze-Kiang. It has a total 
length of about 2400 m. and drains an area of approximately 
400,000 sq. m. The main stream has its source in two lakes 
named Tsaring-nor and Oring-nor, lying about 35 N., 97° E., 
and after flowing with a south-easterly course it bends sharply 
to the north-west and north, entering China in the province 
of Kansuh in lat. 36 . After passing Lanchow-fu, the capital 
of this province, the river takes an immense sweep to the north 
and north-east, until It encounters the rugged barrier ranges 
that here run north and south through the provinces of Shansi 
and CbihlL By these ranges it is forced due south for 500 m., 
forming the boundary between the provinces of Shansi and 
Shensi, until it finds an outlet eastwards at Tung Jtwan — a 
pass which for centuries has been renowned as the gate of Asia, 
being indeed the sole commercial passage between central 
China and the West. At Tung Kwan the river is joined by its 
only considerable affluent in China proper, the Wei (Wei-ho), 
which drains the large province of Shensi, and the combined 
volume of water continues its way at first east and then north- 
east across the great plain to the sea. At low water in the winter 
season the discharge is only about 36,000 cub. ft. per second, 
whereas during the summer flood it reaches 116,000 ft. or more. 
The amount of sediment carried down is very large, though 
no accurate observations have been made. In the account 
pf Lord Macartney's embassy, which crossed the Yellow river 
in 1792, it was calculated to be 17,520 million cub. ft. a year, 
but this is considered very much over the mark. Two reasons, 
however, combine to render it probable that the sedimentary 
matter is very large in proportion to the volume of water: 
the first being the great fall, and the consequently rapid current 
over two-thirds of the river's course; the second that the 
drainage area is nearly alt covered with deposits of loess, which, 
being very friable, readily gives way before the rainfall and 
is washed down in large quantity. The ubiquity of this loess 
or yellow earth, as the Chinese call it, has in fact given its 
name both to the river which carries it in solution and to the 
sea (the Yellow Sea) into which it is discharged. It is calculated 



by Or Guppy (Journal of China Branch of Royal Anatic Soatty, 
voL xvL) that the sediment brought down by the three northern 
rivers of China, viz., the Yangtsze, the Hwang-bo and the 
Peiho, is 24,000 million cub. ft. per annum, and is sufficient 
to nil up the whole of the Yellow Sea and the Gulf of Pechili 
in the space of about 36,000 years. 

Unlike the Yangtsze, the Hwang-ho is of no practical value for 
navigation. The silt and sand form banks and bars at the mouth, 
the water is too shallow in winter and the current is too strong in 
summer, and, further, the bed of the river is continually shifting. 
It is this last feature which has earned for the river the name u China s 
sorrow." A» the silt-laden waters debouch from the rocky bed of the 
apper reaches on to the plains, the current slackens, and the' coarser 
detritus settles on the bottom. By degrees the bed rises, and the 
people build embankments to prevent the river from overflowing. 
As the bed rises the embankments must be raised too, until the stream 
is flowing many feet above the level of the surrounding country; 
As time goes on the situation becomes more and more dangerous; 
finally, a breach occurs, and the whole river pours over the country, 
carrying destruction and ruin with it. If the breach cannot be re- 
paired the river leaves its old channel entirely, and finds a new exit 
to the sea along the line of least resistance. Such in brief has been 
the story of the river since the dawn of Chinese history. At various 
tunes it has discharged its waters alternately on one side or the other 
of the great mass of mountains forming the promontory of Shantung, 
and by mouths as far apart from each other as 500 m. At each 
change it has worked havoc and disaster by covering the cultivated 
fields with 2 or 3 ft. of sand and mud. 

A great change in the river's course occurred in 1851, when a 
breach was made in the north embankment near Kaifengfu in Honan. 
At this point the river bed was some 25 ft. above the plain; the 
water consequently forsook the old channel entirely and poured over 
the level country, finally seizing on the bed of a small river called 
the Tsing, and thereby finding an exit to the sea. Since that time 
the new channel thus carved out has remained the proper course of 
the river, the old or southerly channel being left quite dry. It re- 
quired some fifteen or more years to repair damages from this out- 
break, and to confine the stream by new embankments. After that 
there was for a time comparative immunity from inundations, but 
in 1882 fresh outbursts again began. The most serious of all took 
place in 1887, when it appeared probable that there would be again a 
permanent change in the river's course. By dint of great exertions, 
however, the government succeeded in dosing the breach, though 
not till January 1889, and not until there had been immense destruc- 
tion of fife and property. The outbreak on this occasion occurred, as 
all the more serious outbreaks have done, in Honan, a few miles west 
of the city of Kaifengfu. The stream poured itself over the level and 
fertile country to the southwards, sweeping whole villages before 
it, and converting the plain into one vast lake. The area affected 
was not less than 50,000 sq. m. and the loss of life was computed at 
over one million. Since 1887 there have been a series of smaller 
outbreaks, mostly at points lower down and in the neighbourhood of 
Chinanfu, the capital of Shantung. These perpetually occurring 
disasters entail a heavy expense on the government; and from the 
mere pecuniary point of view it would well repay them to call in the 
best foreign engineering skill available, an expedient, however, which 
has not commended itself to the Chinese authorities. (G. J.) 

HWICCE, one of the kingdoms of Anglo-Saxon Britain. Its 
exact dimensions are unknown; they probably coincided with 
those of the old diocese of Worcester, the early bishops of 
which bore the title " Episcopus Hwicciorum." It would there- 
fore include Worcestershire, Gloucestershire except ihe Forest 
of Dean, the southern half of Warwickshire, and the neighbour- 
hood of Bath. The name Hwicce survives in Wychwood in 
Oxfordshire and Whichford in Warwickshire. These districts, 
or at all events the southern portion of them, were according 
to the Anglo-Saxon Chronicle, s.a. 577, originally conquered 
by the West Saxons under Ceawlin. In later times, however, 
the kingdom of the Hwicce appears to have been always subject 
to Mercian supremacy, and possibly it was separated from 
Wessex in the time of Edwin. The first kings of whom we read 
were two brothers, Eanhcre and Eanfrith, probably contempor- 
aries of Wulfhere. They were followed by a king named Osric, 
a contemporary of iEthelred, and he by a king Oshere. Oshere 
had three sons who reigned after him, /Ethelheard, iEthelweard 
and /Ethelric. The two last named appear to have been reigning 
in the year 706. At the beginning of Offa's reign we again find 
the kingdom ruled by three brothers, named Eanberht, Uhtred 
and Aldred, the two latter of whom lived until about 780. After 
them the title of king seems to have been given up. Their 
successor jEthelmund, who was killed in a campaign against 

Wessex in 80a. is des cri bed only as an earl* The district re- 
mained in possession of the rulers of Mercia until the fall of that 
kingdom. Together with the rest of English Mercia it submitted 
to King Alfred about 877-883 under Earl vEthelred, who possibly 
himself belonged to the Hwicce. No genealogy or list oi kingi 
has been preserved, and we do not know whether the dynasty 
was connected with that of Wessex or Mercia. 

See Bede, Hi&ria tubs, (edited by C. Plumraer) iv. 13 (Chdord. 
1896) ; W. de G. Birch, Cartularium Saxomcum, 43, 51, 76, 85, 1 16, J 17, 
122, 163, 187. 232, 233, 238 (Oxford, 1885-1889), CE. G. M. a) 

HYACIIITH (Gr. v4ju*9qi), also called Jacinth (through Ital. 
giadnto), one of the most popular of spring garden flowers. It 
was in cultivation prior to 1597, at which date it is mentioned 
by Gerard. Rea in 166s mentions several single and double 
varieties as -being then in English gardens, and Justice in 1754 
describes upwards of nfty single-flowered varieties, and nearly 
one hundred double-flowered ones, as a selection of the best from 
the catalogues of two then celebrated Dutch growers. One of 
the Dutch sorts, called La Reine de Feeunes, a single wMte, 
is said to have produced from thirty-four to thirty-eight flowers 
in a spike, and on its, first appearance to have sold for 50 guilders 
a bulb; while one called Overwtnnaar, or Conqueror, a double 
nkie, sold at first for; 100 guilders, Gloria Mundi for 500 guilders, 
and Koning Saloman for 600 guilders. Several sorts axe at 
that date mentioned as blooming well in water-glasses. Justice 
relates that he himself raised several very valuable doable- 
flowered kinds from seeds, which many of the sorts he describe? 
are noted for producing freely. 

The original of the cultivated hyacinth, Hyacinth** aritnlaUs, 
a native of Greece and Asia Minor, is by comparison an insigaafi. 
cant plant, bearing on a spike only a few small, narrow-lobed, 
washy blue flowers, reseznblmg in form those of our commoa 
bluebell. So great has been the improvement effected by the 
florists, and chiefly by the Dutch, that the modem hyacinth 
would scarcely be recognized as the descendant of the type above 
referred to, the spikes being long and dense, composed of a Urge 
number of flowers; the spikes produced by strong bulbs not 
unfrequently measure 6 to 9 in. in length and from 7 to 9 in. 
in circumference, with the flowers closely set on from bottom to 
top. Of late years much improvement has been effected in the 
size of the individual flowers and the breadth of their recurving 
lobes, as well as in securing increased brilliancy and depth of 

The peculiarities of the soil and climate of Holland are so very 
favourable to their production that Dutch florists have made a 
specialty of the growth of those and other bulbous-rooted flowers. 
Hundreds of acres are devoted to the growth of hyacinths is the 
vicinity of Haarlem, and bring in a revenue of several hundreds 
of thousands of pounds. Some notion of the vast number 
imported into England annually may be formed from the fact 
that, for the supply of flowering plants to Covent Garden, one 
market grower alone produces from 60,000 to 70,000 in pots 
under glass* their blooming period being accelerated by artificial 
heat, and extending from Christinas onwards until they bloom 
aaturaUy in the open ground. 

In the Spring flower garden few plants make a more effective 
display than the hyacinth. Dotted in clumps in the flower 
borders, and arranged in masses of well-contrasted colours in 
beds in the flower garden, there are no flowers which impart 
during their season— March and April— a gayer tone to the par- 
terre. The bulbs are rarely grown a second time, either for 
Indoor or outdoor culture, though with care they might be 
utilized for the latter purpose; and hence the enormous numbers 
which are procured each recurring year from Holland. 

The first hyacinths were single-flowered, but towards the dose 
of the 17th century double-flowered ones began to appear, and 
till a recent period these bulbs were the most esteemed. At 
the present time, however, the single-flowered sorts are tn the 
ascendant, as they produce more regular and symmetrical spikes 
Of blossom, the flowers being closely set and more or less horizontal 
in direction, while most of the double sorts have the bells distant 
and dependent, so that the spike is loose and bv comparison 



ineffective. For pot culture, mod for growth in water-abuses 
especially, the single-flowered aorta are greatly to be preferred. 
Few if any of the original hinds are now in cultivation, a success 
son of new and improved varieties having been raised, the 
demand for which is regulated in some respects by fashion. 

The hyacinth delights in a rich light sandy soiL The Dutch ta» 
corporate freely with their naturally light soil a compost consisting 
of one- third coarse sea or river sand, one-third rotten cow dune 
without litter and one-third leaf-mould. The soil thus renovated 
retains its qualities for six or seven years, but hyacinths are not 
planted upon the same place for two yean successively, intermediary 
crops of narcissus* crocus or tulips being taken. A good compost for 
hyacinths is sandy loam, decayed leaf-mouM, rotten cow dung and 
sharp sand in equal parts, the whole being collected and laid up in a 
heap and turned over occasionally. Well-drained beds made up of 
this soil, and refreshed with a portion of new compost annually, 
would grow the hyacinth to perfection. The best time to plant the 
bulbs is towards the end of September and during October; they 
should be arranged in rows, 6 to 8 in. asunder, there being four rows 
in each bed. The bulbs should be sunk about a to 6 in. deep, with a 
small .quantity of clean sand placed below and around each of them. 
The beds should be covered with decayed tan-bark, coco-nut fibre or 
half-rotten dung litter. As the flower-stems appear, they are tied to 
rigid but slender stakes to preserve them from accident. If the bulbs 
are at all prised, the stems should be broken off as soon as the flower- 
ing is over, so as not to exhaust the bulbs; the leaves, however, must 
be allowed to grow on till matured, but as soon as they assume a 
yellow colour, the bulbs are taken up, the leaves cut off near their 
base, and the bulbs laid out in a dry, airy, shady place to ripen, after 
which they are cleaned of loose earth and skin, ready for storing. 
It is the practice in Holland, about a month after the bloom, or when 
the tips of the leaves assume a withered appearance, to take up the 
bulbs, and to lay them sideways on the ground, covering them with 
an inch or two of earth. About three weeks later they are again 
taken up and cleaned. In the store-room they should be kept dry, 
well-aired and apart from each other. 

Few plants are better adapted than the hyacinth for pot culture 
as greenhouse decorative plants; and by the aid of forcing they may 
be had in bloom as early as Christmas. They flower fairly well in 
5-in. pots, the stronger bulbs in 6- in. pots. To bloom at Christmas, 
they should be potted early in September, in a compost resembling 
that already recommended for the open-air beds; and, to keep up a 
succession of bloom, others should be potted at intervals ofa lew 
weeks till the middle or end of November. The tops of the bulbs 
should be about level with the soil, and if a tittle sand is put im- 
mediately around them so much the.better. The pots should be set 
in an open place on a dry hard bed of ashes, and be covered over to a 
depth of 6 or 8 in. with the same material or with fibre or soH", and 
when the roots are well developed, which will take from six to eight 
weeks, they may be removed to a frame, and gradually exposed to 
,; -ht, and then placed in a forcing pit in a heat of from 6o to 70*. 

ben the flowers arc fairly open, they may be removed to the green- 
house or conservatory. 

The hyacinth may be very successfully grown in glasses for orna- 
ment in dwelling-houses. The glasses are filled to the neck with rain 
or even tap water, a few lumps of Charcoal being dropped into them. 
The bulbs are placed in the hollow provided for them, so that their 
base just touches the water. This may be done in September or 
October. They are then set in a dark cupboard for a few weeks till 
roots are freely produced, and then gradually exposed to light. The 
carry-flowering single white Roman hyacinth, a small-growing pure 
white variety, remarkable for its fragrance, is well adapted for 
forcing, as it can be had in bloom if required by November. For 
windows it grows well in the small glasses commonly used for 
crocuses; and for decorative purposes .should be planted about five 
bulbs in a 5-in. pot, or in pans holding a dosen each. If grown for 
cut flowers it can be planted thickly in boxes of any convenient size. 
It is highly esteemed during the winter months by florists. 

The Spanish hyacinth (H. amefhystinus) and H. azurtus are 
charming little bulbs for growing in masses in the rock garden or front 
of the ffower border. The •older botanists incUdedin the genus 
Hyacinthus species of Muscari, ScUia and other genera of bulbous 
Liliaceae, and the name of hyacinth is still popularly applied to 
several other bulbous plants. Thus Muscari batryoidts is the grape 
hyacinth, 6 in., blue or white, the handsomest; Mi. moschatum, the 
musk hyacinth, 10 in., has peculiar livid greenish-yellow flowers and 
a strong musky odour; M. comosum var. monsirosuvu, the feather 
hyacinth, bears sterile flowers broken up jnto a fcatherlike mass.; 
M. raccmosum, the starch hyacinth, is a native with deep blue plum- 
scented flowers. The Cape hyacinth is Galtonia candkans, a magnifi- 
cent border plant, 3-4 ft. high, with large drooping white beU-sbaped 
flowers; the star hyacinth, Scilla amoena; the Peruvian hyacinth 
or Cuban lily, £. peruviana, a native of the Mediterranean region, to 
which Linnaeus gave the species name peruviana on a mistaken 
assumption of its origin; the wild hyacinth or blue-bell, kriown 
variously as Endymton nonscribtum, Hyacinthus nonscriptus or 
Scilla nutans ; the wild hyacinth of western North Amercia, Camassia 
tscuUnta. JThey all flourish in good garden soil of a gritty nature. . 


. HYACINTH, or Jacinth, In mineralogy, a variety of rircon 
(q.p.) of yellowish red colour, used as a gem-stone. The hyacinth** 
of ancient writers most have been our sapphire, or blue corundum, 
while the hyacinth of modern mineralogists nay have been 
the stone, known ea lyncurium (Xirysovpior). The Hebrew 
word lakem, translated ligure in the Authorized Version (Ex. 
xxviii. 19), from the . Xtyhpup of the Septuagint, appears in 
the Revised Version as jacinth, but with a marginal alternative 
of amber. Both jacinth and amber may be reddish yellow, 
but their identification. is doubtful As our jacinth (zircon) 
ia not known in ancient Egyptian work, Professor Flinders 
Peine has suggested that the kshem may have been a yellow 
quart*, or perhaps agate. Some -old English writers describe 
the jacinth as yellow, whilst others refer, to it as a blue stone, 
and. the hyacinthus of some authorities seems undoubtedly to 
have been our sapphire. In Rev.- zx. so the .Revised Version 
retains the word jacinth, but gives sapphire as an alternative, j 
* Most of the gems known in trade as hyacinth are only garnets— 
generally the deep orange-brown hessonite or cinnamon-stone— 
and many of the antique engraved stones reputed hyacinth 
are probably garnets. The difference may be detected optically; 
since the garnet is singly and the hyacinth doubly refracting; 
moreover the specific gravity affords a simple means of diagnosis-, 
that of garnet being only about 3*7, whilst hyacinth may have 
a density as high as 4*7« Again, it was shown many years ago 
by Sir A. H. Church that most hyacinths, when examined by 
the spectroscope, show a series of dark absorption bands, due 
perhaps to the presence of some rare element such as uraniiua 
or erbium. 

.Hyacinth is not a common mineral. It occurs, with other 
zircons, in the gem-gravels of Ceylon, and very fine stones have: 
been found as pebbles at Mudgee in New South Wales. Crystals 
of zircon, with all the typical characters of hyacinth, occur at 
Expailly, Le Puy-en-Velay, in Central France, but they are not 
large,, enough for cutting. The stones which have been called 
Compostella hyacinths are simply ferruginous quarts from 
Santiago deConrpostella in Spain. (F.W.R.*) 

HYACINTHUS,' in Greek mythology, the youngest son of the 
Spartan king Amyclas, who reigned at Araydae (so Pausaniss) 
iii, 1. 3, iii. 19. 5; and ApoUodorus i. 3. 3, iii. 20. 3). Other 
stories make him son of Oebftlus, of Eurotas, or of fferus 
and the jiymph Clio (see Hyginus, Fobulae, 271; Lucian, Ve 
sallalione, 45* and Did. dear. 14).. According to the genera* 
story,. which, is probably late and composite, his great beauty 
attracted the love of Apollo, who killed him. accidentally when 
teaching him to throw the discus (quoit); others say that, 
Zephyrus (or Boreas) out of jealousy deflected the quoit so that 
it hit Hyacinthus on the head and killed him. According to the 
representation on the tomb at Arayclae (Pausanias, loc. cit.) 
Hyacinthus was translated into heaven with bis virgin sister 
Polyboca. Out of his blood there grew the flower known as 
the hyacinth, the petals of which were marked with the mournful 
exclamation AI, AI, " alas *' (cf. " that sanguine flower inscribed 
with woe ")• This Greek hyacinth cannot have been the flower 
which now, bears the name; it has been identified with a species 
of iris and with the larkspur (delphinium Aiacis), which appear 
to have the markings described. The Greek hyacinth was also 
said to have sprung from the blood of Ajax. Evidently the 
Greek authorities confused both the flowers and the traditions. 

The death of Hyacinthus was celebrated at Amydae by the 
second most important of Spartan festivals, the Hyadnthia, 
Which took place in the Spartan month Hecatoinbeus.' What 
month this was is not certain. Arguing from Xenophon {Hell. 
iv. 5) we get May; assuming that the Spartan Hecatoinbeus 
is the Attic Hecatombaion, we get July; or again it may be the 
Attic Sdropborion, June. At all events the Hyadnthia was an 
early summer festival. It lasted three days, and the rites 
gradually passed from mourning for Hyadnthus to rejoidngs' 

? *The word Is probably derived front an Indo-European root; 
meaning " youthful," found in Latin, Greek, English and Sanskrit. 
Some have suggested that the first two. letters are from tmn, to rain* 



in the majesty of Apollo, the god of light and warmth, and giver 
of the ripe fruits of the earth (see a passage from Polycratea, 
LaconicOy quoted by Athenaeus 139 o; criticized by L R. 
Farnell, Cults of the Greek States, iv. a66 foil.)- This festival is 
dearly connected with vegetation, and marks the passage from 
the youthful verdure of spring to the dry heat of summer and 
the ripening of the corn.' 

.The precise relation which Apollo bears to Hyadnthus h 
obscure. The fact that at Tarentum a Hyadnthus tomb is 
ascribed by Polybius to Apollo Hyadnthus (not Hyacinthius) 
has led some to think that the personalities are one, and that 
the hero is merely an emanation from the god; confirmation 
is sought in the Apolline appellation rsrpax*P, alleged by 
Hesychius to have been used in Laconia, and assumed to describe 
a composite figure of Apollo-Hyacinthus. Against this theory 
is the essential difference between the two figures. Hyadnthus 
is a chthonian vegetation god whose worshippers are afflicted 
and sorrowful; Apollo, though interested in vegetation, is never 
regarded as inhabiting the lower world, his death is not celebrated 
in any ritual, his worship is joyous and triumphant, and finally 
the Amyclean Apollo is specifically the god of war and song. 
Moreover, Pausanias describes the monument at Arayclae as 
consisting of a rude figure of Apollo standing on an altar-shaped 
base which formed the tomb of Hyadnthus. Into the latter 
offerings were put for the hero before gifts were made to the god. 

On the whole it is probable that Hyadnthus belongs originally 
to the pre-Dorian period, and that his story was appropriated 
and woven into their own Apollo myth by the conquering 
Dorians. Possibly he may be the apotheosis of a pre-Dorian 
king of Amydae. J. G. Frazer further suggests- that he may 
have been regarded as spending the winter months in the under- 
world and returning to earth in the spring when the " hyadnth *' 
blooms. In this case his festival represents perhaps both the 
Dorian conquest of Amydae and the death of spring before the 
ardent heat of the summer. sun, typified as usual by the discus 
(quoit) with which Apollo is said to have slain him. With the 
growth of the hyadnth from his blood should be compared the 
oriental stories of violets springing from the blood of Attis, and 
roses and anemones from that of Adonis. As a youthful vegeta- 
tion god, Hyadnthus may be compared with Linus and Scephrus, 
both of whom are connected with Apollo Agyieus. 

See L. R. Farnell, Cults of Ike Creek States, vol. iv. (1907), pp. 125 
foil., 264 foil.; X- G. Frazer, Adonis, Attis, Osiris (1906), bk. ii. 
ch, 7: S. Wide, Lakouiscke Kulte, p. 390; E. Rhode, Psyche, 
3rd ca. i. 137 foil.; Roschcr, Lexikon d. grieck. u. r6m. Myth., s.v. 
* Hyakinthos M (Grevc) ; L. Prcller, Grvuhische Mylhot. 4th cd. 
ii 248 foil. v a- M. M.) 

« HTADES ("the~ rainy~ones"), In Greek mythology, the 
daughters of Atlas and Aethra; their number varies between 
two and seven. As a reward for having brought up Zeus at 
Dodona and taken care of the infant Dionysus Hycs, whom they 
conveyed to Ino (sister of his mother Semdc) at Thebes when his 
life was threatened by Lycurgus, they were translated to heaven 
and placed among the stars (Hyginus, Poll, aslron. ii. 21). 
Another form of the story combines them with the Pleiades. 
According to this they were twdve (or fifteen) sisters, whose 
brother Hyas was killed by a snake while hunting in Libya 
(Ovid, Fasti,.v. 165; Hyginus, Fab. 192). They lamented him 
so bitterly .that Zeus, out of compassion/ changed them into 
stars --five into the Hyadcs, at the head of the constellation 
of the Bull, the remainder into the Pldades. Their name is 
derived from the fact that the rainy season commenced when 
they rose at the same time as the sun (May 7-21); the original 
conception of them is that of the fertilizing principle of moisture. 
The Romans derived the name, from vs (pig), and translated it 
by Suculae (Cicero, Do not. deorum, ii. 43). 

HYATT, ALPHEUS (1838-1002), American naturalist, was 
born .at Washington, D.C., on the 5th of April 1838. From 
1858 to 1862 he studied at Harvard, where he had Louis Agassiz 
for his master, and in 1863 he served as a. volunteer in the Civil 
War, attaining the rank of captain. In 1867 he was appointed 
curator of the Essex Institute at Salem, and .in 1870 became 
professor of zoology and palaeontology . at the Massachusetts 

Institute of Technology (resigned 1888), and custodian of the 
Boston Society of Natural History (curator in 1881). 'In 1886 
he was appointed assistant for palaeontology in the Cambridge 
museum of comparative anatomy, and in 1889 was attached 
to the United States Geological Survey as palaeontologist for 
the Trias and Jura. He was the chief founder of the American 
Society of Naturalists, of which he acted as first president ia 
1883, and he also took a leading part in establishing the marine 
biological laboratories at Annisquam and Woods Hole, Has*. 
He- died at Cambridge on the 15th of January 1902. 

" k-water Polysoa (1866); 
Ft paratope Zoology (1872): 

Rt -1 877) ; -Genera of Fossil 

Ct Origin of Cellular Tissue 

(1 nd Phytogeny of an «• 

au iction on Cephalopoda ia 

Ki his wdl-known study oa 

th Genesis of the Tertiary 

Sf cd in the Memoirs of the 

B< e was one of the founders 


HYBLA, the name of several cities in SidryT The best known 
historically, though its exact site is uncertain, is Hybla Major, 
near (or by some supposed to be identical with) Megara HybUea 
{q.v.): another Hybla, known as .Hybla Minor or Galeatis. is 
represented by the modern Patcrnd; while, the site of. Hybla 
Heraea is to be sought near Ragusa. 

HYBRIDISM. The Latin word hybrid*, hibriia or ibriaa 
has been assumed to be derived from the Greek &0p«r, an insult 
or outrage, and a hybrid or mongrel has been supposed to be 
an outrage on nature, an unnatural product. As a general rule 
animals and plants belonging to distinct spedes do not produce 
offspring when crossed with each other, and the. term hybrid 
has been employed for the .result of a fertile cross between 
individuals of different species, the word mongrel for the more 
common result of the crossing of distinct varieties. A closer 
scrutiny of the facts, however, makes the term hybridism less 
isolated and more vague. The words species and genus, and 
atill more subspedes and variety, do not correspond with clearly 
marked and sharply defined zoological categories, and no exact 
line can be drawn between the various kinds of crossings from 
those between individuals apparently identical to those belonging 
to genera universally recognized as distinct. Hybridism therefore 
grades into mongrelism, mongrelism into cross-breeding, and cross* 
breeding into normal pairing, and we can say little more than 
that the success of the union is the more unlikely or more un- 
natural the further apart the parents are in natural affinity. 

The interest in hybridism was for a long time chiefly of a 
practical nature, and was due to the fact that hybrids are often 
found to present characters somewhat different from those of 
either parent. The leading facts have been known in the case 
of the horse and ass from time immemorial. The earliest recorded 
observation of a hybrid plant is by J. G. Gmelin towards the end 
of the 17th century; the next is that of Thomas Fairchild, who 
in the second decade of the 18th century, produced the cross 
which is still grown in gardens under the name of " Fairchfld's 
Sweet William." Linnaeus made many experiments in the 
cross-fertilization of plants and produced several hybrids, but 
Joseph Gottlieb Kolreutcr (1733-1806) laid the first real founds- 
tion of our scientific knowledge of the subject. Later on Thomas 
Andrew Knight, a celebrated English horticulturist, devoted 
much successful labour to the improvement of fruit trees and 
vegetables by crossing. In the second quarter of the 10th 
century C. F. Gartner made and published the results of a number 
of experiments that had not been equalled by any earlier worker. 
Next came Charles Darwin, who first in the Origin of Spedes, 
and later in Cross and Self-Fertilisation of Plants, subjected the 
whole question to a critical examination, reviewed the known- 
facts and added many to them. 

. Darwin's conclusions were summed up by G. J. Romanes in the 
9th edition of this Encyclopaedia as follows : — 

1. The laws governing the production of hybrids are identical, or 
nearly identical, in the animal and vegetable kingdoms. • 

2. The sterility which so generally attends the crossing of two 
specific forms is to be distinguished as of two kinds, which, although 



. confounded by naturalist*, are In reality quite distinct. For 

rllity may obtain between the two parent species when first 

•H. or it may first assert itself in their hybrid progeny. In the 

r case the hybrids, although possibly produced without any 

- * r ance of infertility on the part of their parent aperies* neverthe- more or less infertile among themselves, and also with 

rs of either parent species. 

• he degree of both... kinds of infertility varies in the case of 
- nt species, and in that of their hybrid progeny, from absolute 

.' up to complete fertility. Thus, to take the case of plants, 
. • pollen from a plant of oae family is placed on the stigma of a 

• A a distinct family, it exerts no more influence than so much 
.nic dust. From this absolute zero of fertility, the pollen of 

at species, applied to the stigma of some one species of the same 

\ ields a perfect gradation in the number of seeds produced, up 

■*ly complete, or even quite complete, fertility: so, in hybrids 

«. ives, there are some which never have produced, and probably 

• ould produce, even with the pollen of the pure parents, a 
'Vrtile seed; but in some of these cases a first trace of fertility 

• >c detected, by the pollen of one of the pure parent species 

* the flower of the hybrid to wither earlier than, it otherwise 
have done; and the early withering of the flower is well 
to be a sign of incipient fertilization. From this extreme 

of sterility we have self-fertilized hybrids producing a greater 
1 ater number of seeds up to perfect fertility." 

• hough there is, as a rule, a certain parallelism, there is no 
fatten between the degree of sterility manifested by the 

species when crossed and that which is manifested by their 
progeny. There are many cases in which two pure species 
crossed with unusual facility, while the resulting hybrids ate 
ably sterile: and* contrariwise, there are species which can 
c crossed with extreme difficulty, though the hybrids, when 
v d. are very fertile. Even within the limits of the same genus, 
: ao opposite cases may occur. 

.hen two species are reciprocally crossed, • i\*V mate A with 
U, and male B with female -A, the degree of sterility often 
greatly in the two cases, . The sterility of the resulting hybrids 
<:uTer likewise. 

he degree of sterility of first crosses and df hybrids runs, to a 
.1 extent, parallel with the systematic affinity of the forms 
. are united. " For species belonging to distinct genera can 
, and those belonging to distinct families can never, be crossed. 
■ irallelism, however, is far from complete; for a multitude of 
y allied species will not unite, or unite with extreme difficulty, 
other species, widely different from each other, can be crossed 
perfect facility. Nor does the difficulty depend on ordinary 
uutional differences; for annual and perennial plants, decidu- 
and evergreen trees, plants flowering at different seasons, in- 
ing different stations, and naturally living under the most 
«ite climates, can often be crossed with ease. The difficulty or 
iity apparently depends exclusively on the sexual constitution of 
pedes which are crossed, or on their sexual elective affinity," 
i here are many new records, as to the production of hybrids, 
irticulturists have been extremely active and successful in 
c j- attempts to produce new flowers or new varieties of vege- 
Jes by seminal or graft-hybrids, and any florist's catalogue or 
•e account of any special plant, such as is to be found in Foster- 
dliar's Book of the Rose, is in great part a history of successful 
. bridixation. Much * special experimental work has been done 
> botanists, notably by de Vries, to the results of whose experi- 
ments we shall recur. • Experiments show clearly that the 
.btaining of hybrids is in many cases merely a matter of taking 
jufneient trouble, and the successful crossing of genera is not 
.nfrcquent. „ 

Focke, foe instance^Ites cases where hybrids were obtained 
between Brosska and Raphanus, Galium and Asptrulo, Campanula 
and PhyUuma, Verbascum and Celsia. Among animals, new records 
and new experiments are almost equally numerous. Boveri has 
crossed Echinus *microtuberculatus with Sphatrechhtus granulans. 
Thomas Hunt Morgan even obtained hybrids between Asterias, a 
starfish, and Arbacus, a sea-urchin, a crass aa remote as would be 
that between a fish and a mammal. Vernon got many hybrids by 
.of Slrongyloccntrolus thidus with the sperm of 

fertilizing the eggs 

Spkacrechinus granular is, 

series of experiments with.Leptdopterous insects, and has obtained a 

sperm — 

Stand fuss has carried on an enormous 

very large series of hybrids, .of which he has kept careful record. 
Lcpidoptcrists generally begin to suspect that many curious forms 
offered by dealers as new species are products got by crossing known 
species, Apello has succeeded with Tclcostean fish; Gebhardt and 
others with Amphibia. Elliot and Suchetet have studied carefully 
the question of hybridization occurring normally among, birds, and 
have got together a very large body of evidence. Among the cases 
cited by Elliot the most striking are that of the hybrid between 

Assam. St M. Podmore has produced successful cresses between the 
wood-pigeon (Columb* palumbus) and a domesticated variety of the 
rock pigeon (C. /ma). Among mammals noteworthy results have 
been obtained by Professor Cossar Ewart, who has bred nine zebra 
hybrids by rrnsmng mares of various sizes with a zebra stallion, and 
who has studied in addition three hybrids out of zebra mares, one 
sired by a donkey, the others by ponies. Crosses have been, made 
between the common rabbit (fiifpus cunicul. s) and the guinea-pig 
(Casta cobaya), and examples of the results have been exhibited in the 
Zoological Gardens of Sydney, New South Wales. The Camivorm 

„ easy to hybridize, and many successful experiments 
ve been made with animals in captivity. Karl. Hagenbcck of 


have be w ., „ , 

Hamburg has produced crosses between the lion {Felis leo) and the 
tiger (F. tigris). What was probably a " tri-hybrid " in which lion, 
leopard and jaguar were mingled was exhibited by a London show- 
man in 1006. Crosses between various species of the smaller cats 
have been fertile on many occasioaa. The black bear ( Urstts outer** 
coma) and the European brown bear (U. arctos) bred in the London 
Zoological Gardens in 1859, but the three cubs did not reach maturity. 
Hybrids between the brown bear and the grizzly-bear (U. korrioilu) 
have been produced in Cologne, whilst at Halle since 1874 a series of 
successful soarings of. polar (£/. marUimus) and brown bears have 
been made. Examples of these hybrid bears have been exhibited 
by the London Zoological Society. The London Zoological Society 
has also successfully mated several species of antelopes, for instance* 
the water-bucks Kokus tllipsiprymnus and K, unctuosus, and Selous '• 
antelope Idmnotrogus sdouri with JL grains, 
. The causes militating against the production of hybrids 
have also received considerable attention. Delagc, discussing 
the question, states that there is a general proportion between 
sexual attraction and zoological affinity, and in many cases 
hybrids are not naturally produced simply from absence of the 
stimulus to sexual ma ring, or because of preferential mating 
within the species or variety. £ In addition to differences of 
habit, temperament, time of maturity, and so forth, gross 
structural differences may make mating impossible. Thus 
Escherick contends that among insects the peculiar structure 
of the genital appendages makes cross-impregnation impossible, 
and there is reason to believe that the specific peculiarities 
of the modified sexual palps in .male spiders have a similar 

result. ... ~ 

The difficulties, however^ may not e*xist, or may be overcome by 
experiment, and frequently it is only careful management that is 
required to produce crossing. Thus it has been found that when 
the pollen of one species does not succeed in fertilizing the ovules 
of another species, yet the r e cip roc al cross may be successful; that 
is to say, the pollen of the second specks may fertilize the ovules 
of the first. H. M. Vernon, working with sea-urchins, found that the 
obtaining of hybrids depended on the relative maturity of the 
sexual products. The difficulties in crossing apparently may ex- 
tend to the chemiotaaic processes of the actual sexual cells. Thus 
when the spermatozoa ot an urchin were placed in a drop of sea- 
water containing ripe eggs of an urchin and of a starfish, the former 
eggs became surrounded by clusters of the male cells, while the latter 
appeared to exert little attraction for the alien germ-cells. Finally, 
when the actual impregnation of the egg is possible naturally, or has 
been secured by artificial means, the development of the hybrid may 
stop at an early stage. Thus hybrids between the urchin and the 
starfish, animals belonging to different classes, reached only the 
stage of the pluteus larva,*; A. D. Apello, experimenting with 
Teleostean fish, found that very often Impregnation and segmenta- 
tion occurred, but that the development broke down immediately 
afterwards. W. Gebhardt, crossing Rana escultnla with R. arvalis, 
found that the cleavage of the ovum was normal, but that ab- 
normality began with the gastrula, and that development soon 
stopped. In a very general fashion there appears' to be a parallel 
between the sooJogicalaffinity and the extent to which the incomplete 
development of the hybrid proceeds. 

As to the sterility of hybrids inter M, or with either of the 
parent forms, information is still wanted. Dclage, summing up 
the evidence in a general way, states that mongrels are more 
fertile and stronger than their parents, while hybrids are at 
least equally hardy but less fertile. While many of the hybrid 
products of horticulturists are certainly infertile, others appear 
to be indefinitely fertile. - 

Focke, it is true, states that the hybrids between Primula auruvta 
and P. hirsute are fertile for many generations, but not indefinitely 
so; but, while this may be true for the particular case, there seems 
no reason to doubt that many plant hybrids are quite fertile. In the 
case of animals the evidence is rather against fertility. Standfast* 
who has made experiments lasting, over many years, and who has 



kb one 
ry were 
e other 
t moths 
i fertile 
een the 
ick (A.. 
and the 
\\t inter 
bred at 
ies and 
with one another. 

Corncvin and Lesbre state that in 1 873 an Arab mule was fertilized 
in Africa by a stallion, and gave birth to female offspring which she 
suckled. All three were brought to the Jardtn d'Acclimatation in 
Paris, and there the mule had a second female colt to the same 
father, and subsequently two male colts in succession to an ass and 
to a stallion. The female progeny were fertilized, -but their offspring 
were feeble and died at birth, Cossar Ewart gives an account of a 
recent Indian case in which a female mule gave birth to a male colt. 
He points out, however, that many mistakes have been made about 
the breeding of hybrids, and is not altogether inclined to accept this 
supposed case; Very little has been published with regard to the 
most important question, as to the actual condition of the sexual 
organs and cells in hybrids. There does not appear to be gross 
anatomical defect to account for the infertility of hybrids, but 
microscopical examination in a large number of cases is wanted. 
Cossar Ewart, to whom indeed much of the most interesting recent 
work on hybrids is due, states that in male zebra-hybrids the sexual 
cells were immature, the tails of the spermatozoa being much shorter 
than those of the similar cells in stallions and zebras. He adds, 
however, that the male hybrids he examined .were ^roung, and might 
not have been sexually, mature. He examined microscopically- the 
ovary of a female zebra-hybrid and found one large and several small 
Graafian follicles, in all respects similar to those in a normal mare or 
female zebra. A careful study of the sexual organs in animal and 
plant hybrids is very much to De desired, but it may be said that so 
;ar as our present knowledge goes there is not to be expected any 
Obvious microscopical cause of the relative infertility of hybrids. 
f # The relative variability of hybrids has received considerable 
attention from many writers. Horticulturists, as Bateson has 
written, arc " aware of the great and striking variations which 
occur in so many Orders of plants when hybridization is effected." 
The phrase has been used " breaking the constitution of a 
plant " to indicate the effect produced in the offspring of a 
hybrid union, and the device is frequently used by those who are 
seeking for novelties to introduce on the market. It may be 
said generally that hybrids are variable, and that the products 
pf hybrids are still more variable. J. L. Bonhotc found extreme 
■variations amongst his hybrid ducks. Y. Delage states that 
in reciprocal crosses there is always a marked tendency for the 
-Offspring to resemble the male parents; he quotes from Huxley 
that the mule, whose male parent is an ass, is more like the ass, 
and that the hinny, whose male parent is a horse, is more like 
the horse. Standfuss found among Lepidoptera that males 
were produced much more often than females, and that these 
males paired jeadily. The freshly hatched larvae closely 
resembled the larvae of the female parent, but in the course of 
growth the resemblance to the male increased, the extent of the 
final approximation to the male depending on the relative 
phylogenetic age of the two parents, the parent of the older 
species being prepotent. In reciprocal pairing, he found that the 
male was able to transmit the characters of the parents in a 
higher degree. Cossar Ewart, in relation to zebra hybrid, has 
discussed the matter of resemblance to parents in very great 
detail, and fuller information must be sought in his writings. 
He shows that the wild parent is not necessarily prepotent, 
although many writers have urged that view. He described 
three hybrids bred out of a zebra mare by different horses, and 
found in all cases that the resemblance to the male' or horse 
parent was more profound. Similarly, zebra-donkey hybrids 
out of zebra mares bred in France and in Australia were in 
characters and disposition far more like the donkey parents. 
The results which he obtained in the hybrids which he bred 


from a zebra stalKon and different mothers were more variable; 
but there was rather a balance in favour of zebra disposition 
and against zebra shape and marking, 

14 Of the nine zebra-horse hybrids 1 have bred," be says, " only two 
in their make and. disposition take decidedly after the wild parent. 
As explained fully below, all the hybrids differ profoundly in the ptaa 
of their markings from the zebra, while in their ground colour they 
take after their respective- dams or the ancestors of their dams far 
more than after the- zebra — the hybrid out of the yellow and white 
Iceland pony, e.g. instead of being light in colour, as I anticipated, 
is for the most part of a dark dun colour, with but indistinct stripes. 
The hoofs, mane and tall of the hybrids are at the most intermediate, 
but this is perhaps partly owing to reversion towards the ancestors 
of these respective dams. In their disposition and habits they aB 
undoubtedly agree more with the wild sire." 

Ewart's experiments and bis discussion of them also throw 
important light on the general relation of hybrids to their 
parents. . He found that the coloration and pattern of his 
zebra hybrids resembled far more those of the Somali or Grevy's 
zebra than those of their sire— a BurchelPs zebra. In a general 
discussion of the stripings of horses, asses and zebras, he came 
to the conclusion that the Somali zebra represented the older 
type, and that therefore, his zebra hybrids furnished important 
evidence of the effect of crossing in producing reversion to 
ancestral type. The same subject has of course been discussed 
at length by Darwin, in relation to the cross-breeding of 
varieties of pigeons; but the modern experimentalists who 
are following the work of Mendel interpret reversion differently 
(see Mendelism). 

Graft-Hybridism, — It is well known that, when two varieties or 
allied species are grafted together, each retains its distinctive 
characters. But to this general, if not universal, rule there are on 
record several alleged exceptions, in which either the scion is said 
to have partaken of the qualities of the stock, the stock of the 
scion, or each to have affected the other. Supposing any of these 
influences (q have been exerted, the resulting product would 
deserve to be called a graft-hybrid. It is clearly a matter of 
great interest to ascertain whether such formation of hybrids by 
grafting is really possible; for, if even one instance of such 
formation could be unequivocally proved, it would show that 
sexual and asexual reproduction are essentially identical. 

The cases of alleged graft-hybridism are exceedingly few, con- 
sidering the enormous number of grafts that are made every year 
by horticulturists, and have been so made for centuries. Of these 
cases the most celebrated are those of Adam's laburnum (Cyiisu) 
Adami) and the bizzarria orange. Adam's laburnum is now 
flourishing in numerous places throughout Europe, all the trees 
having been raised as cuttings from the original graft, which was 
made by inserting a bud of the purple laburnum into a stock of 
the yellow. M. Adam, who made the graft, has left on record 
that from it there sprang the existing hybrid. There can be no 
question as to the truly hybrid character of the latter — all the 
peculiarities of both parent species being often blended in the 
same raceme, flower or even petal; but until the experiment shall 
have been successfully repeated there must always remain a 
strong suspicion that, notwithstanding the assertion and doubt- 
less the belief of M.. Adam, the hybrid arose as a cross in the 
ordinary way of seminal reproduction. Similarly, the bizzarria 
orange, which is unquestionably a hybrid between the bitter 
orange and the citron— since it presents the remarkable spectacle 
of these two different fruits blended into one— is stated by the 
gardener who first succeeded in producing it to have arisen as a 
graft-hybrid; but here again a similar doubt, similarly due to the 
need of corroboration, attaches to the statement. And the same 
remark applies to the still more wonderful case of the so-called 
trifacial orange, which blends three distinct kinds of fruit in one, 
and which is said to have been produced by artificially splitting 
and uniting the seeds taken from the three distinct species, the 
fruits of which now occur blended in the triple hybrid. 

The other instances of alleged graft-hybridism are too numer> 
ous to be here noticed in detail; they refer to jessamine, ash, 
hazel, vine, hyacinth, potato, beet and rose." Of these the cases 
of the vine, beet and rose are the strongest as evidence of graft- 
hybridization, from the fact that some of them, were produced 


la the result of careful experiments mad 
saperimentalists. On the whole, the ret 
Experiments, although so few in number, 
making out a strong case in favour of t 
hybridism. For it must always be remen 
ments of this kind, negative evidence, hov 
may be logically dissipated by a single p< 
. Theory tf Hybridism.— Charles Darw 
hybridism as an experimental side of bi 
from the bearing of the facts on the th 
species. It is obvious that although hyb 
possible as an exception to the general 
inter se, the exception is still more mini 
membcred that the hybrid progeny usuall 
of sterility. The main fads of hybridism < 
to the old doctrine that there are place 
the barriers of mutual sterility. The ar 
of species appears still stronger when tt 
species crossing is contrasted with the g 
crossing of natural and artificial varieti 
and afterwards G. J. Romanes, ahowei 
theory of natural selection did not require 
commingling of specific types, and that t 
suppose that the mutation of species shea 
mutual crossing. There existed more tl 
and this has been added to since, to sho' 
other species is no criterion of a species, 
exact parallel between the degree of affini 
their readiness to cross. The problem of 
than the explanation of the generally redu 
crosses as compared with the generally 
crosses between organisms slightly difterex 
and rejected the view that the inter-ste 
have been the result of natural selection. 

" At one time it appeared to me piofaabl 
Species, 6th ed. p. 2^7), " as it has to othi 
first crosses and of hybrids might have been 1 
the natural selection of slightly lessened dq 
like any other variation, spontaneously ap 
viduals of one variety when cros s e d with tl 
For it would clearly be advantageous to t* 
species if they could be kept from blending 
that, when man is selecting at the same t 
necessary that he should keep them separat 
may be remarked that species inhabiting di 
sterile when crossed; aow it could clearly ha' 
to such separated species to have been rendei 
consequently, this could not have been el 
selection; but it may perhaps be argued 
rendered sterile with some one compatrk 
specks would follow as a necessary contir 
place, it is almost as much opposed to the th< 
as to that of special creation, that in recij 
element of one form should have been renden 
second form, whilst at the same time the mal 
form is enabled freely to fertilise the first 
state of the reproductive system could hard! 
ous to either species." 

Darwin came to the conclusion that t 
species must be due to some principle 
natural selection. In his search for such 
together much evidence as to the instabili 
system, pointing out in particular how fr 
in captivity fail to breed, whereas somed 
been so modified by confinement as to be fe 
they are descended from species probat 
He was disposed to regard the phenomena 
as, so to speak, by-products of the proce 
Romanes afterwards developed his tb< 
selection, in which he supposed that the ap 
fertility within a species was the starting 
certain individuals by becoming fertile o 
along lines of. modification diverging from 
other members of the species. Physiolof 
would operate in the same fashion as | 
at a portion of a species separated on an i 



tobacco, sugar-cane, and fruits and garden produce in great 
variety. Silk, known ai tussnr t the. produce of a wild species 
ol worm, is utilised on a large scale. Lac, suitable for use as a 
resin or dye, gums and oils are found in great quantirirs Hides, 
raw and tanned, are articles of some importance in commerce. 
The principal exports are cotton, oil-seeds, country-clothes 
and hides; the imports are salt, grain, timber, European piece- 
goods and hardware. The mineral wealth of the state consists 
of coal, copper, iron, diamonds and gold; but the development 
of these resources has not hitherto been icty successful. The 
only coal mine now worked is the large one At Singarera~ with an 
annual out-turn of nearly half a million tons. This coal has 
enabled the nizam 'a guaranteed state railway to be worked so 
cheaply that it now returns a handsome profit to the state.' It 
also gives encouragement to much-needed schemes of railway 
extension, and to the erection of cotton presses and o£ spinning 
and weaving mills* The Hyderebad-Godavari railway (opened 
in iooi) traverses a rich cotton country, and cotton presses 
have been erected along the line. The currency of the state 
is based on the kali ukka, which contains approximately the 
same weight of silver as the British rupee, but its exchange 
value fell heavily after 1895, when free coinage ceased in the 
mint. In fooa, however* a new coin (the Mahbnbia rupee) 
was minted; the supply was regulated, and the rate of exchange 
became about n$« 100 British rupees. The state suffered from 
amine during 1900, the total number of persons in receipt of 
relief rising to nearly 500,000 in June of that year, The nizam 
met the demands for relief with great liberality. 

The nizam of Hyderabad is the principal Mahommedan ruler 
in India. The family was founded by Asaf Jab, a distinguished 
Turkoman soldier of the emperor Auraagzeb, who in 17 13 was 
appointed subahdar of the Deccan, with the title of nizam- 
ail-mulk (regulator of the state), but eventually threw off the 
control of the Delhi court. Azaf Jab's death in 1 748 was followed 
by an internecine struggle for the throne among his descendants, 
in which the British and the French took part. At one time 
the French nominee, Salabat Jang, established himself with 
the help of Bussy. But finally,, in 1761, when the British bad 
secured their predominance throughout southern India, Nizam 
Ali took his place and ruled till 1803. It was he who confirmed 
the grant of the Northern Circars in 1766, and joined in the two 
wars against Tippoo Sultan in 179a and 1709. The additions 
of territory which he acquired by these wars was afterwards 
(1800) ceded to the British, as payment for the subsidiary force 
which he had undertaken to maintain. By a later treaty in 
1853, the districts known as Berar were " assigned " to defray 
the cost of the Hyderabad contingent. In 1857 when the 
Mutiny broke out, the attitude of Hyderabad as the premier 
native state and the cynosure of the Mahommedans in India 
became a matter of extreme importance; but Afzul-ud-Dowla, 
the lather of the present ruler, and his famous minister, Sir 
Salar Jang, remained loyal to the British. An attack on the 
sestdency was repulsed, and the Hyderabad contingent displayed 
their loyalty in the field against the rebels. In 190a by a treaty 
made by Lord Curzon, Berar was leased in perpetuity to the 
British government, and the Hyderabad contingent was merged 
in the Indian army. The nizam Mir Mahbub Ali Khan Bahadur, 
Asaf Jan, a direct descendant of the famous nizam-ul-mulk, 
was born on the 18 in of August 1866. On the death of his 
father in 1869 be succeeded to the throne as a minor, and was 
invested with fuM powers in 1884. He is notable as the originator 
of the Imperial Service Troops, which now form the contribution 
of the native chiefs to the defence of India. On the occasion 
of the Panjdeh incident in 1885 he made an offer of money and 
men, and subsequently on the occasion of Queen Victoria's 
Jubilee in 1887 he offered 20 lakhs (£130,000) annually for three 
years for the purpose of frontier defence. It was finally decided 
that the native chiefs should maintain small but well-equipped 
bodies of infantry and cavalry for imperial defence. For many 
years past the Hyderabad finances were in a very unhealthy 
condition; the expenditure consistently outran the revenue, 
and the nobles, who held their tenure under an obsolete feudal 

system, vied with each other in ostentatious extravagance. 
But in 1 901, on the revision of the Berar agreement, the nizam 
received 25 lakhs (£167,000) a year for the rent of Berar, thus 
substituting a fixed for a fluctuating source of income, and 
a British financial adviser was appointed for the purpose of 
reorganizing the resources of the state. 

See S. H. Bilgrami and C. WUhnott, Historical and Dcscri+tm 
Sketch of the Ntiam's Dominions (Bombay, 1883-1884). 

HYDERABAD or Haidaeabad, capital of the above state, 
is situated on the right bank of the river Musi, a tributary of 
the Kistna, with Golconda to the west, and the residency and 
its bazaars and the British cantonment of Secunderabad to the 
north-east. It is the fourth largest city in India; pop. (1001) 
448,466, including suburbs and cantonment. The city itself is 
in shape a parallelogram, with an area of more than 2 sq. n. 
It was founded in 1589 by Mahommcd Kuli, fifth of the Kotb 
Shahi kings, of whose period several important buildings remain 
as monuments. The principal of these is the Chat Miner or 
Four Minarets (1591). The minarets rise from arches facing the 
cardinal points, and stand in the centre of the oity, with fov 
roads radiating from their base. The Ashur Khana (1594), a 
ceremonial building, the hospital, the Gosha Mahal palace and 
the Mecca mosque, a sombre building designed after a mosoat 
at Mecca, surrounding a paved quadrangle 360 ft. square, were 
the other principal buildings of the Kutb Shahi period, though 
the mosque was only completed in the time of Aurangzeb. The 
city proper is surrounded by a stone wall with thirteen gales, 
completed in the time of the first nizam, who made Hyderabad 
his capital. The suburbs, of which the most important b 
Chadarghat, extend over an additional area of 9 sq. m. There 
are several fine palaces built by various nizams, and the British 
residency is an imposing building in a large park on the left 
bank of the Musi, N.E. of the city. The bazaars surrounding it, 
and under its jurisdiction, are extremely picturesque and are 
thronged with natives from all parts of India. Four bridges 
crossed the Musi, the most notable of which was the Purana 
Pal, of 23 arches, built in 1593. On the 27th and '28th of 
September 1008, however, the Musi, swollen by torrential rainfall 
(during which 15 in. fell in 36 hours), rose in flood to a height of 
12 ft. above the bridges and swept them away. The damage 
done was widespread; several important buildings were involved, 
including the palace of Salar Jang and the Victoria zenana 
hospital, while the beautiful grounds of the residency were 
destroyed. A large and densely populated part of the city was 
wrecked, and thousands of lives were lost. The principal 
educational establishments are the Nizam college (first grade), 
engineering, law, medical, normal, industrial and Sanskrit 
schools, and a number of schools for Europeans and Eurasians. 
Hyderabad is an important centre of general trade, and there is a 
cotton mill in its vicinity. The city is supplied with water from 
two notable works, the Husain Sagar and the Mir Alan, both 
large lakes retained by great dams. Secunderabad, the British 
military cantonment, is situated 5} m. N. of the residency; 
it includes Bolaram, the former headquarters of the Hyderabad 

HYDER AU, or Haioa* 'Ail (c. 1722-1782), Indian ruler 
and commander. This Mahommedan soldier-adventurer, who, 
followed by his son Tippoo, became the most formidable Asiatic 
rival the British ever encountered in India, was the great-grandson 
of a fakir or wandering ascetic of Islam, who had found his way 
from the Punjab to Gulburga in the Deccan, and the second ssa 
of a ndik or chief constable at Budikota, near Kola* in Mysore. 
He was born in 1722, or according to other authorities 1717. 
An elder brother, who like himself was early turned out iau 
the world to seek his own fortune, rose to command a brigade 
in the Mysore army, while Hyder, who never learned to sead or 
write, passed the first years of his life aimlessly in sport aai 
sensuality, sometimes* however, acting as the agent of his brother, 
and meanwhile acquiring a useful familiarity with the tactia 
of the French when at the height of their reputation under 
Dupleix. He is said to have induced his brother to employ a 
Parsee to purchase artillery and small arms from the Bombay 



government, and to enrol some thirty sailors of (Efferent European 
nations as fanners, and a Urns credited with having been u the 
first Indian who formed a corps of sepoys armed with fire- 
locks and bayonets, and who had a train of artillery served by 
Europeans." At the siege of Devanhalli (1749) Hyder*s services 
attracted the attention of Nanjiraj, the minister of the raja of 
Mysore, and he at once received ah independent command; 
within the next twelve years his energy and ability had made 
him completely master of minister and raja alike, and ia every- 
thing but in name he was ruler of the kingdom. In 1763 the 
conquest of Kanara gave him possession of the treasures of 
Bednor, which he resolved to make the most splendid capital 
in India, under his own name, thenceforth changed from Hyder 
Naik into Hyder Ali Khan Bahadur; and in 1765 he retrieved 
previous defeat at the handeof the Mahrattas by the destruction 
o£ the Nairs or military caste of the Malabar coast, and the 
conquest of Calicut. Hyder Ali now began to occupy the 
serious attention of the Madras government, which in 1766 
entered Into an agreement with the niaam to furnish him with 
troops to be used against the common foe. But hardly had this 
alliance been formed when a secret arrangement was come to 
between the two Indian powers, the result of which was that 
Colonel Smith's small force was met with a united army of 
80,000 men and 100 guns* British dash and sepoy fidelity, 
however, prevailed, first in the battle of Chengam (September 3rd, 
1 767), and again still more remarkably in that of Timvannamalai 
(Trinomalai)* On the loss of bis recently made fleet and forts 
on the western coast, Hyder Ali now offered overtures for peace; 
on the rejection of these, bringing all bis resources and strategy 
into play, he forced Colonel Smith to raise the siege of Bangalore, 
and brought his army within 5 m. of Madras, The result was 
the' treaty of April 1769, providing for the mutual restitution 
of all conquests, and for mutual aid and alliance in defensive 
war; it was followed by a commercial treaty ia 1770 with the 
authorities of Bombay. Under these arrangements Hyder Ali, 
when defeated by the Mahrattas in 1772, claimed British assist- 
ance, but in vain; tbi* breach of faith stung him to fury, and 
thenceforward he and his son did not cease to thirst lor vengeance. 
His time came when in 1778 the British, on the declaration of 
war with France, resolved to drive the French out of India. 
The capture of Man* on the coast of Malabar in 1770, followed 
by tbe.annexation of lands belonging to a dependent of his own, 
gave him the needed pretext. Again master of all that the 
Mahrattas had taken from him, and with empire extended to the 
Kistna, he descended through the passes of the Ghats amid 
burning villages, reaching Conjeeveram, only 45 m. from Madras, 
unopposed. Not till the smoke was seen from St Thomas's 
Mount, where Sir Hector Munro commanded some 5300 troops, 
was any movement made; then, however, the British general 
sought to effect a junction with a smaller body under Colonel 
Baillie recalled from Guntur. The incapacity of these officers, 
notwithstanding the splendid courage of their men, resulted 
in the total destruction of BaiUie's force of a8oo (September 
the xoth, 1,780). Warren Hastings sent from Bengal Sir Eyre 
Coote, who, though repulsed at Chidambaram, defeated Hyder 
thrice successively in the battles of Porto Novo, Pollilur and 
Shohngarh, while Tippoo was forced to raise the siege of Wandi- 
wasb, and Vellore was provisioned. On the arrival of Lord 
Macartney as governor of Madras, the British fleet captured 
Negapatam, and forced Hyder Ali to confess that he could never 
ruin a power which had command of the sea, He had sent his 
son Tippoo to the west coast, to seek the assistance of the French 
fleet, when his death took place suddenly at Chit tux in December 

See L. B. Bowring, Haidar Ali and Tipu Sultan. " Rulers of India " 

trie* (1893). For the personal character and administration of 

Hyder Ali see the History f Hyder Naik. written by Mir Hussein Ali 

Khan Kirmani (translated from the Persian by Colonel Miles, and 

1 published by the Oriental Translation Fund), and the curious work 

written by M. Le Malt re de La Tour, commandant of his artillery 

{Histoire d'Hayder-Ali Khan, Paris, 1783) For the whole life and 

1 times see Wilks, Historical Sketches of the South of India (1810-1817) ; 

'■ Akchtson's Treaties, vol. v. (and ed., 1876); and Pearson, Memotrs 

«/£*•«/* (1834). 

HTD1A (or Smut, Nd»u, Ideso, Ac; anc Hydrea), an 
island of Greece, lying about 4 am. off the S.E. coast of Argelis 
in the Peloponnesus, and forming along with the neighbouring 
island of Dokos (Dhoko) the Bay of Hydra. Pop. about 6aoa> 
The greatest length from south-west to north-east is about 1 1 nv 
and the area is about ai sq. 1x14 but it is little better than a 
rocky and treeless ridge with hardly a patch or two of arable* 
sofl. Hence the epigram of Antonios Rrjezes to the queen of 
Greece: "The island produces prickly pears in abundance, 
splendid sea captains and excellent prime ministers.'* Tbe 
highest point, Mount Ere, so called (according to MiaoulesV 
from the Albanian word for wind, is roe& ft. high. The next in 
importance is known as the Prophet Bias, from tbe large convent 
oi that name on its summit. It was there that the patriot 
Theodoras Kolokotrones was imprisoned, and a, large pine tree 
is still called after him. The met that in former rimes the island 
was richly clad with woods is indicated by the name stall employed 
by the Turks, Tchamlaa^ the place of pines; but it is only in. 
some favoured spots that a, few trees' are. now to be sound. 
Tradition also has it that it was once a weU-Wateced islamt 
(hence the designation Hydrea), but the inhabitants are now 
wholly dependent on the rain supply, and they have sometimes 
had to bring water from the mainland. This lack of fountains 
is probably to be ascribed in part to the effect of earthquakes; 
which are not infrequent that of 2769 continued for six whole 
days. Hydra, the chief town, is built near the middle of the 
northern coast, on a very irregular site, consisting of three hills 
and tbe intervening ravines. From the sea its white and hand- 
some houses present a picturesque appearance, and its streets 
though narrow are dean and attractive. Besides the principal 
harbour, round which the town is bulk, there are three other 
ports on the north coast— Mandraki, Molo, Feaagis, but none 
of them is sufficiently sheltered. Almost all the population 
of the island is collected in tbe chief town, which is the seat of a 
bishop, and has a local court, numerous churches and a high 
school. Cotton and silk weaving, tanning and ahjpbmldmg 
are carried on, and there is a fairly active trade. 

Hydra was of no importance in ancient times. The only fact 
in its history is that the people of Hermioae <a city on the 
neighbouring mainland now known by the common name of 
Kastri) surrendered it to Samian refugees, and that from these 
the people of Troezen received it in trust. It appears to be com- 
pletely ignored by the Byzantine chroniclers. In 1580 it was 
chosen as a refuge by a body of Albanians from Kokkinyas in 
Troezenia; and other emigrants followed in 1590, i6a8, 1635, 
1640, fcc At tbe close of the 17th century the Hydriotes took 
part in the reviving commerce of the Peloponnesus; and in 
course of time they extended their range. About 1716 they 
began to build sakturia (of from xo to 15 tons burden), and to 
visit tbe islands of the Aegean; not long after they introduced 
tbe latinadika (40-50 tons), and sailed as far as Alexandria, 
Constantinople, Trieste and Venice; and by and by they 
ventured to France and even America. From the grain trade 
of south Russia more especially they derived great wealth. In 
18,13 there were about aa,ooo people in the island, and of these 
10,000 were seafarers At the time of the outbreak of the war of 
Greek independence the total population was 28,190, of whom 
16,460 were natives and the rest foreigners. One of their chief 
families, the Konduriotti, was worth £ a, 000,000. Into the 
struggle the Hydriotes flung themselves with rare enthusiasm 
and devotion, and the final deliverance of Greece was mainly 
due to the service rendered by their fleets. 

See POoqueviUe, Voy. da At Grlce, vol. vi.; Antonios Miaoolee, 
Tr*n*m* **t ffe rt>o0 Tipcs (Munich, 1834) : Id. Zrtwtvc* t*r*pU 
r£* yavMaxtuf it* rCtr w\olu* t2*rpL$r *$«**, "T6>at, lUritttfl *f*m 
(Nauplia, 1833); Id. 'loropU Hjt rjoov Tipat (Athens, 1874); G. D. 
Kriezes, 'Uropfa rft p+oov Ttpas (Patras, i860). 

HYDRA (watersnake) , in Greek legend, the offspring of Typhon 
and Echidna, a gigantic monster with nine heads (the number 
is variously given), the centre one being immortal Its haunt 
was a hill beneath a plane tree near the river Amymone, in the 
marshes of Lcrna by Argos. The destruction of this Leroacan 



hydra was one of the twelve " labours " of Heracles, which he 
accomplished with the assistance of Iolaus. Finding that as 
soon as one head was cut off two grew up in its place, they burnt 
out the roots with firebrands, and at last severed the immortal 
head from the body, and buried it under a mighty block of rock. 
The arrows dipped by Heracles in the poisonous blood or gall 
of .the monster ever afterwards inflicted fatal wounds. The 
generally accepted interpretation of the legend is that " the 
hydra denotes the damp, swampy ground of Lema with its 
numerous springs («0aXof, heads); its poison the miasmic 
vapours rising from the stagnant water, its death at the hands 
of Heracles the introduction of the culture and consequent 
purification of the soil " (Preller). A euhemeristic explanation 
is given by Palaephatus (39). An ancient king named Letnus 
occupied a small citadel named Hydra, which was defended 
by 50 bowmen. Heracles besieged the citadel and hurled 
firebrands at the garrison. As often as one of the defenders 
fell, two others at once stepped into his place. The citadel 
was finally taken with the assistance of the army of Iolaus and 
the garrison slain. 

See Hettod, Tkeoe., 313; Euripides, Hercules furens, 410; 
Pauaanlas U. 37; ApoUodorus ii. 5, 2: Diod. Sic iv. n ; Roscher's 
Lcxikon der Mytkologic. In the article Greek Art, fig. 20 represents 
the slaying of the Lcrnaean hydra by Heracles. 

HYDRA, in astronomy, a constellation of the southern 
hemisphere, mentioned by Eudoxus (4th century B.C.) and 
Aratus (3rd century B.C.), and catalogued by Ptolemy (27 stars), 
Tycho Brahe (19) and Hevelius (31). Interesting objects are: 
the nebula H. IV. 27 Hydro*, a planetary nebula, gaseous and 
whose light is about equal to an 8th magnitude star; e Hydro*, 
a beautiful triple star, composed of two yellow stars of the 4th 
and 6th magnitudes, and a blue star of the 7th magnitude; 
R. Hydra*, a long period (435 days) variable, the range in 
magnitude being from 4 to 9*71 and U. Hydra*, an irregularly 
variable, the range in magnitude being 4*5 to 6. 

HYDRACRYUC ACID (ethylene lactic add), CHjOH-CH^ 
COsH, an organic oxyadd prepared by acting with silver oxide and 
water on pModopropionic add, or from ethylene by the addition 
of hypochlorous add, the addition product being then treated 
with potassium cyanide and hydrorysed by an add. It may 
also be prepared by oxidising the trimethylene glycol obtained 
by the action of hydrobromk add on allylbromide. It is a 
syrupy liquid, which on distillation is resolved into water and 
the unsaturated acrylic add, CH»: CHCOjH. Chromic and 
nitric adds oxidize it to oxalic add and carbon dioxide. 
HydracryhTaldehyde, CHjOHCHrCHO, was obtained in 1904 
by J. U. Nef (Ann. 33s, p. 219) as a colourless oil by heating 
acrolein with water. Dilute alkalis convert it into crotonalde- 
hyde, CRVCH : CHCHO. 

HYDRANGEA, a popular flower, the plant to which the name 
ii most commonly applied being Hydrangea HorUnsia, a low 
deciduous shrub, producing rather large oval strongly-veined 
leaves in opposite pairs along the stem. It is terminated by 
a massive globular corymbose head of flowers, which remain a 
long period in an ornamental condition. The normal colour 
of the flowers, the majority of which have neither stamens nor 
pistil, is pink; but by the influence of sundry agents in the soil, 
such as alum or iron, they become changed to blue. There are 
numerous varieties, one of the most noteworthy being " Thomas 
Hogg " with pure white flowers. The part of the inflorescence 
which appears to be the flower is an exaggerated expansion of 
the sepals, the other parts being generally abortive. The perfect 
flowers are small, rarely produced in the species above referred 
to, but well illustrated by others, in which they occupy the inner 
parts of the corymb, the larger showy neuter flowers being 
produced at the circumference. 

There are upwards of thirty species, found chiefly In Japan, 
in the mountains of India, and in North America, and many of 
them are familiar in gardens. H. Hortensio (a speries long 
known in cultivation in China and Japan) is the most useful 
for decoration, as the head of flowers lasts long in a fresh state, 
and by the aid of forcing can be had for a considerable period 

for the or n a me ntation of the greenhouse and conservatory. 
Their natural flowering season is towards the end of the summer, 
but they may be had earlier by means of forcing. H. japonic* 
is another fine conservatory plant, with foliage and habit much 
resembling the last named, but this has flat corymbs of flowers, 
the central ones small and perfect, and the outer ones only 
enlarged and neuter. This also produces pink or blue flowers 
under the influence of different soils. 

The Japanese spedes of hydrangea are sufficiently hardy 
to grow in any tolerably favourable situation, but except in 
the most sheltered localities they seldom blossom to any degree 
of perfection in the open air, the head of blossom depending 
on the uninjured development of a well-ripened terminal bud, 
and this growth being frequently affected by late spring frosts. 
They are much more useful for pot*emkure indoors, and should 
be reared from cuttings of shoots having the terminal bud plump 
and prominent, pot in during summer, these developing a single 
head of flowers the succeeding summer. Somewhat larger 
plants may be had by nipping out the terminal bud and indutisg 
three or four shoots to start in its place, and these, being steadily 
developed and well ripened, should each yield its inflorescence 
in the following summer, that is* when two years old. Large 
plants grown in tubs and vases are fine subjects for large con- 
servatories, and useful for decorating terrace walks and similar 
places .during summer, being boused in winter, and started 
under glass in spring. 

Hydrangea paniadala vxt. grand i flora is a very handsome 
plant; the branched inflorescence under favourable drcum- 
stances is a yard or mote in length, and consists of large spreading 
masses of crowded white neuter flowers which completely conceal 
the few inconspicuous fertile ones. The plant attains a height 
of 8 to to ft. and when in flower late in summer and in autaroa 
is a very attractive object in the shrubbery. 

The Indian and American species, especially the latter, are 
quite hardy, and some of them are extremely effective. 

HYDRASTINB, C*H M NOt, an alkaloid found with berberine 
in the root of golden seal, Hydrastis canadensis, a plant indigenous 
to North America. It was discovered by Durand in 185 1, and 
its chemistry formed the subject of numerous communications 
by £. Schmidt and M. Freund (see Ann., 1892, 271, p. 311) 
who, aided by P. Fritsch (Ann., 1895, 286, p. 1), established 
its constitution. It is related to narcotine, which is metbory 
hydrastine- The root of golden seal is used in medicine under 
the name Hydrastis rhiaome, as a stomachic and nervine 

HYDRATE, in chemistry, a compound containing the elements 
of water in combination, more specifically, a compound contain- 
ing the monovalent hydroxyl or OH group. The first and more 
general definition include* substances containing water of 
crystallization, such salts are said to be bydrated, and when 
deprived of their water to be dehydrated or anhydrous. Com- 
pounds embraced by the second definition are more usually 
termed hydroxides, since at one time they were regarded as com- 
binations of an oxide with water, for example, calcium oxide or 
lime when slaked with water yielded caldum hydroxide, written 
formerly as CaO H 2 0. The general formulae of hydroxides 
are: M'-OH, M l KOH)», M» l (OH),, M^OHV,, &c, corresponding 
to the oxides M^O, M"0, Mi ,l, Oj, M*Oj, &c., the Roman index 
denoting the valency of the element. There is an important 
difference between non-metallic and metallic hydroxides; 
the former are invariably acids' (oryacids), the latter are more 
usually basic, although acidic metallic oxides yield acidic 
hydroxides. Elements exhibiting strong basigenic or oxygenic 
characters yield the most stable hydroxides; in other words, 
stable hydroxides are associated with dements belonging to the 
extreme groups of the periodic system, and unstable hydroxides 
with the central members. The most stable basic hydroxides 
are those of the alkali metals, vte. lithium, sodium, potassium, 
rubidium and caesium, and of the alkaline earth metals, vu- 
calcium, barium and strontium; the most stable acidic hydroxides 
are those of the elements placed in groups VB, VIB and VIIB 
of the periodic table. 



HYDRATJIJCS (Gr. titoo, water, and dtkh, a pipe), the branch 
of engineering science -which deals with the practical applications 
of the laws ol hydromechanics. 


S i. Properties of Fluids.— The fluids to which the laws of 
practical hydraulics relate are substances the parts of which 
possess very great mobility, or which offer a very small resistance 
to distortion independently of inertia. Under the general 
heading Hydromechanics a fluid is defined to be a substance 
which yields continually to the- slightest tangential stress, and 
hence m a fluid at rest there can bo no tangential stress. But, 
further, in fluids such as water, air, steam, far., to which the 
present division of the article relates, the tangential stresses 
that are called into action between contiguous portions during 
distortion or change of figure are always small compared with 
the' weight, inertia, pressure, &c. T which produce the visible 
motions it is the object of hydraulics to estimate. On the other 
hand, while a fluid passes easily from one form to another, it 
opposes considerable resistance to change of volume. 

It is easily deduced from the absence or smallness of the 
tangential stress that contiguous portions of fluid act on each 
other with a pressure which is exactly or very nearly normal 
to the interface which separates them. The stress must be a 
pressure, not a tension, or the parts would separate. Further, 
at any point in a fluid the pressure in all directions must be the 
same; or, in other words, the pressure on any small element 
of surface is independent of the orientation of the surface. 

§ 2. Fluids are divided into liquids, or incompressible fluids, 
and gases, or compressible fluids. Very great changes of pressure 
change the volume of liquids only by a small amount, and if 
the pressure on them is reduced to zero they do. not sensibly 
dilate. In gases or compressible fluids the volume alters sensibly 
for small changes of pressure, and if the pressure is indefinitely 
diminished they dilate without limit. 

In ordinary hydraulics, liquids are treated as absolutely 
incompressible. In dealing with gases the changes of volume 
which accompany changes j>f pressure must be taken into 
account.' _ . T — — 

| j. Viscous fluids are those in which change 'of form under a 
continued stress proceeds gradually and increases indefinitely. 
A very viscous fluid opposes great resistance to change of form 
in a short time, and yet may be deformed considerably by a 
small stress acting for a long period. A block of pitch is more 
easily splintered than indented by a hammer, but under the 
action ol the mere weight of its parts acting for a long enough 
time it flattens out and flows like a liquid. 

All actual fluids are viscous.' They oppose a resistance 
to the relative motion of their parts. This resistance diminishes 
with the velocity of the relative motion, and' becomes zero 
is a fluid the parts of which are relatively at rest. When, the 
relative motion of different parts of a fluid is small, the viscosity 
may be neglected 'without introducing important errors. On 
the other hand, where there is considerable relative motion, 
• I . _• ' the viscosity, may be cx- 
ff*™7^ pectcd to have an influence 
too great to be neglected. 

Measurement of Viscosity. 
Coefficient*/ Viscosity.— 
Suppose the plane no, ug. I 
of area «, to move with the 
p._ velocity V relatively to 'the 

• r 1<K *• surface cd and parallel to it. 

Let the space between be filled with liquid. The layers of liquid 
in contact with ab and cd adhere to them. The intermediate layers 
all offering an equal resistance to shearing or distortion, the rect- 
angle of fluid abed will take the form of the parallelogram a'b'cd. 
Further, the resistance to the motion of ab may be expressed in 
the form 

R-«*V, (i) 

where « is a coefficient the nature ol which remains to be deter- 

1 Except where other units are given, the units throughout this 
article are feet, pounds, pounds per sq. ft., feet per second. 


ah*, is, according to H. von 

If we suppose' the liquid between ab and cd divided into layers as 
shown in fig. 2, it will be clear that the stress R acts, at each dividing 
face, forward* in the direction of motion if we consider. the upper 
layer, backwards jf we consider the lower layer. Now suppose the 
original thickness of the layer T increased to »T; if the bounding 
plane in Its new position has the velocity nV, the shearing at each 
dividing face will be exactly the same as before, and the resistance 
must therefore be the same. Hence, 

R-^V). (a) 

Bat equations (i) and (2) may both be e xpress e d in one equation IT 
« and ■' are replaced by a constant varying inversely as the thickness 
of the layer. Putting «-«/T, kW/bT, 
or, for an indefinitely thin layer, 

R-WW (3) 

an expression first proposed by L. M. H. Navier. The coefficient p is 
termed the coefficient of viscosity. 

According to J. Clerk Maxwell, the value of n for air at •* Fahr. in 
pounds, when the velocities are expressed in feet per second, is 

n =0000 000 025 6(4(61 *+9) ; 
that is, the coefficient of viscosity is proportional to the absolute 

temperature and independent of the pr 

The value of » for water at 77* Fs 
Helmboltz and G. Piotrowski, 

c M""OOOOox88, m 

the units being the same as before. For water p decreases rapidly 
with increase of tem p er a ture. 

9 4- When a fluid flows in a very regular manner, asfor instance 
when it flows in a capillary tube, the velocities vary gradually 
at any moment from ; 

one point of the fluid L-i— * V— v 

to a neighbouring ,._ T L — ^iiiv.v-'.*::!::r:|' 

point. The layer ad- ; ; ,.L 1- • 

jacent to the sides of • • J_ ,.i 

the tube adheres to it ,V t ' : 

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 pipesand open 
channels there were a 
similar regularity of 

1 i 1 1'*'** lU v 

_Fic a; 

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 x metre radius, and Inclined at a slope 
of only o'oooi, would have a velocity of 187 metres per second,' 
the layer next the -boundary remaining' at rest. But before 
such a .djfference 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 oh the general velocities of translation at different points 
of the.fluid(oc what Boussinesq terms the mean local velocities^ 
but rather on the intensity at each point pf 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 T>y the viscosity of the fluid. 

Relation or Peessum, Density, ahx> Tsmfbratue* 
of Liquids 

I s- 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. • 

• Journal de M. LiouoiOe, t. xiii. (1868); Mimoirts de FAcadhrie 
des Sciences de rinstitut de France, t. joan., xaiv. (1877). 



I cob. ft. « 6-336 imp. gallon* - 7*481 U.S. gallons, 

r imp. gallon - 01605 cub. ft. *»i -200 U.S. gallons. 

1 US. gallon - 0*1537 cub. ft. -0-8333 »™P- gallon. 

1 litre « 0*2201 imp. gallon « 0*2641 U.S. gallon. 

Density of Water. — Water at 53° F. and ordinary pressure contains 
62-4 lb 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 $7-28 lb per cub. ft. (Leduc). 

i 6. Comfresstbtlity 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 tt> per 
sq. in., the compression is proportional to the pressure. The chief 
results of experiment are given in the following table. Let V* be 
the volume of a liquid in cubic feet under a pressure fa lb per sq. ft., 
and Vt its volume under a pressure fa. Then the cubical compres- 
sion is (Vt— Vi)/Vi, and the ratio of the increase of pressure 
ubic " 

and Vt its volume under a pressure fa. Then the cubical compres- 
sion is (Vt— Vi)/Vi, and the ratio of the increase of pressure 
fa— fa to the cubical compression is sensibly constant. That is; 
^-•^ *- X1 ' ,nT Vi) is constant. This constant is termed the 
. With the notation of the differential calculus, 

Elasticity of Volume of Liquids. 



and Sturm. 



Sea water . 










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 
9f Units. 

Density of Water at Different Temperatures. 






Density of 


1 cub. ft 

in ft. 

Dm* of 

Wcfcht of 

1 cob. ft 
























































































rt , , v 


































The weight per cubic foot has been calculated from the values of 
>, on the assumption that I cub. ft. of water at 39-2* Fahr. is 62.425 lb. 
"or ordinary calculations in hydraulics, the density of water (which 

will in future be designated by the symbol G) will be taken at 62-4 lb 
per cub. ft., which is its density at 53 ° Fahr. It may be noted also 
that ice at 32 • Fahr. contains 57-3 lb 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 r (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 A of the column is a measure of the pressure at the point 
P. Let « be the area of section of the pipe, a the height of the 
pressure column, p the intensity of pressure at P; then 


that is, h is the: height due to the pressure at p. The level 00 wOl 
be termed the free surface level corresponding to the pressure 
at P. 

Relation of Pressure, Temperature, and Density of Gases 
i 9. Relation of Pressure, Volume, Temperature and Density n 

Compressible F/«i45.-*-Certain problems on the flow of air and 

steam arc 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 of compres- 
sible fluids sof ar 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 

and Volume at Constant Temperature.— At constant te m per a t u re 

the product of the pressure p and volume V of a given quantity «i 

air is a constant (Boyle's law). 

Let fa be mean atmospheric pressure (21168 lb per sq. ft.). V» 

the volume of 1 lb of air at 32° Fahr. under the pressure p». Then 
poV e »262i4. (1) 

If Go is the weight per cubic foot of air in the same conditions, 

G»»i/Vo=2ii6-8/262i4-«-o8o75. (2) 

For any other pressure p, at which the volume of 1 lb is V and the 

weight per cubic foot is G, the temperature being 32* Fahr., 

£V-£/G«=262i4;orG-#262i4. (3) 

Change of Pressure or Volume 8* Change of Temperature. — Let p%, 
s Gt, as before be the pressure, the volume of a pound in cubic feet, 
id the weight of a cubic foot in pounds, at 32° Fahr. Let p. V, G 


and „ . .. _ . 

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, 

pV -p.V,(46o.6+/)/(46o.6+32) -poVWn. <«) 

where r, r» are the temperatures t and 3a* reckoned from the absolute 
zero, which, is — a6o*6* Fahr. : 

Fio. 3. 

If A" 

460-6* Fahr.; 
21 i6-8 r G«« -08075, T -460-6+32 -492-6, then 


Or quite generally p/C = Rr for all gases, if R is a constant varying 
inversely as the density of the gas at 32° F. For steam R —85'S. 

I 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 

.'(») 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. 

§ II. Steady and Unsteady, Uniform and Varying, Motion.— Then 
are two quite distinct ways of treating hydrodynamical questiocs. 
We may cither fix attention on a given mass of fluid and consider 
its changes of position and energy under the action of the atresss 
to which it is subjected, or we may have regard to a given socd 
portion of space, and consider the volume and energy of the ftsd 
entering and leaving that space. 


If, in folk 
constant ve 
energy of tl 
from point t 
If at a give 
with the s*i 
time, then \ 
if at the pc 

tends alway 
and it is the 
No river pre 
in rocky ch< 
during the i 
the flood. 1 
the conditio 
changes are 

As a-stre 
becomes pei 
are sometim 
is a definite 
less definite 
the stream I 

1 12. The 
motion of ti 
simplify hy 
assumed, an 

Motion tn 
is one in wl 




be the velocity of the fluid. Then the volume flowing through the 
surface A in unit time is ' 

Q-«V. (i) 

)tton is rectilinear, afl the particles at any instant in 
rill be found after one second in a similar surface A', 
f, and as each particle is followed by a continuous 
particles, the volume of flow is the right prism AA' 
t and length V. 

ion of motion makes an angle $ with the normal to 
> volume of flow is represented by an oblique prism 
d in that case 

If the velocity varies at different points of the surface, let the sur- 
face be divided into very smalt portions, for each of which the 


velocity may be 
v cos. a, the nor. 
volume of flow la 

Flo. 7. 

an constant. If dm is the area and *, or 

velocity fcr this element of the surface, the 


as the case may be. 

( 14. Principle of Continuity.-— U we consider any eomp 
bounded fixed space in a moving liquid initially and finally 
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 ail the boundaries, 

to be motic 
in deforming 
ince to the 

it is observi 
parts. Tot 
nay be con 
tections son 
Jiding on e 
is having di 
>r deduced 
ion to the r 

Stream Li 
n each (ami 
he stream, 
he stream 1 
ach repress 
icnts may; ! 
f the motic 
7cn termed 

3 lindanes, 
om momei 
/erage veU 
iries very 

in concen 
i velocity 
an veloci 
ual more 
? ht be 
\ 13. Volt 

If Ai, A« are tne areas of two normal cross sections of a stream, 
and Vi, Vi are the velocities of the stream at those sections, then 
from the prtrtcipf -' -^ , 


as the areas of the cross 
es, if at each section the 
varying slope the velocity 
b to see that in parts of 
n in parts of small crass 

that is, the norrr 
sections. This it 
velocity of the sti 
varies with the 1 
large cross sectic 
section. 4 

If we conceive a space ui a liquid bounded by normal sections at 
Ai. At and between A., A, by stream lines (fig. 8), then, as there 
is no flow across the stream lines, 

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, p* 
be the pressures, n, t* the velocities, Gi. d the weight per cubic foot 
of fluid, at cross sections of a stream of areas At, A* The volumes 
of inflow and outflow are 

Ai* and.Atsi, 
and, if the weights of these are the same. 

and hence, from (5a) § 9, if the temperature is constant, 

feAitt-feArf* (3) 



§ 15. Stream Inks.— The characteristic of a perfect fluid, that is, 
a fluid free from viscosity, b 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 
0/ the particles in different parts of the current, for the velocities 

1 ■ 

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 002 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 tines of a sheet of fluid passing a fairly 

Fig. 13. 


shipshape body such as a screwshait 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. 1 1 shows one of the 
earlier air-bubble experiments with a thicker sheet of water, la 
this case the stream lines break up behind the obstruction, forming 
an eddying wake. Fig. ta 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. JnsL Naval Arch. (1898); " Stream Lane Motion 
of a Viscous Fluid," Report of British Association (1898). 


| t6. 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 Squid 
in the vessel from which 
it flows. The difference 
of level K (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 a. From ordinary 
dynamics, the relation 
between the velocity and 
height of projection is 
given by the equation 

t-Vlf*. (I) 
As this velocity is nearly 
reached in the flow from 
well-formed orifices, it is 


Fig. 14. 

sometimes called the theoretical velocity of discharge, 
was first obtained by Torricelli. 

If the orifice is of a suitable conoidal form, the water issues is 
filaments normal to the plane of the orifice. Let « be the area sf 
the orifice, then the discharge per second must be, from eq. (1), 
Q *» <* ■» 0-/7gk nearly. (a) 

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 as oU 
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 * to the orifice, ve 
may say there are k ft. of head above the orifice. Still more genoaBy 
any mass of liquid k ft. above a horizontal plane may be said to have 
k 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-a, the quantity p/G may be tensed 
the pressure head at the orifice. Lastly, the velocity v is connected 

with H by the relation **/*£»*» so that ti'/ag may be termed the 
head due to the velocity v. 
§ 17. Coefficients of Vdocitjand JtatstefK*.— Asthe actual velocity 

of discharge differs from v^5» by a small quantity, let the 

•• -••-cVagl, (3) 

where e, 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 hekfet 
k causing outflow consists of two parts— one part *. ei r p rnr Vd 
effectively in producing the velocity of outflow, another K in ove> 
coming the resistances due to viscosity and friction. Let 

where «, Is a coefficient determined by experiment, and called the 
coefficient of resistance of the orifice. It is tolerably constant (or 
different heads with well-formed orifices. Then 

*-Vai*,-VI*t*/0+«r)l. (4) 


The relation between e, and c, (or any orifice U easily found:— 

«.-v|i/(i+*>|. fe) 

Cr-l/C.'-I. (50) 

rhus if c, «o«97, then. «r « 0*0628. That is, for auch an orifice about 
>i % of the head is expended in overcoming f actional resistances 
o flow. 

Coefficient of Contraction— Sharp-edf** Orifices in Plane Surfaces.— 
A'ben a jet issues from an aperture in a vessel, it may either spring 








Fig. 15. 

lear foom the inner edge of the orifice as at a or b (fig. J 5), or it 

nav adhere to the sides of the orifice as at c. The former condition 

till be found if the orifice is bevelled outwards as at a, so as to be 

harp edged, and it will also occur generally for a prismatic aperture 

ike b, provided the thickness of the plate in which the aperture is 

ormed is less than the diameter 

if the jet. But if the thickness 

s greater the condition shown 

it c will occur. 
When the discharge occurs \ 

ts at a or b, the filaments con- 

Trging towards the orifice , 

ontinue to converge beyond 

t, so that the section of the 

et where the filaments have 

>ecome parallel is smaller than 

he section of the orifice. The 

nertia of the filaments opposes 

udden change of direction 

»f motion at the edge of the 

•rifice, and the convergence 

ontinucs for a distance of 

bout half the diameter of the 

rifice beyond it. Let w be the 

rca of the orifice, and c** the area of the jet at the point where 

onvergence ceases; then c« is a coefficient to be determined experi- 
mentally for each kind of orifice, called the coefficient of contraction. 

Vhcri the orifice is a sharp-edged orifice in a plane surface, the 

alue of c, is on the average 0-64, or the section of the jet is very 

early five-eighths of the area of the orifice. 
Coefficient of Discharge. — In applying the general formula Q-w* 

:> a stream, it b assumed that the filaments have a common velocity 
v normal to the section 9. But if 
. the jet contracts, it is at the con- 
/'j tracted section of the jet that 
£/> the direction of motion is normal 
£Z to a transverse section of the 
Vs, jet. Hence the actual discharge 
r y when contraction occurs is 
£ Q«-<*»Xc«*»-««c v *V(2iA). 
==. or simply, if c-c^ 4 , 
=^ p.-«-V(af*>, 

s* where c is called the coefficient 
\^ of discharie. Thus for a sharp- 
•£ edged plane orifice *-007X 

Vy 0-64 -0'62. 

^ f 18. Experimental Determina- 
tion of c„ c t , and c— The co- 
efficient of contraction <« is 
r |C ,g directly determined by measur- 

* fng the dimensions 01 the jet. 

yr this purpose fixed screws of fine pitch (fte. 16) are convenient. 
>esc are set to touch the jet, and then the distance between them 
n be measured at leisure. 

The coefficient of velocity is determined directly by measuring 
e parabolic path of a horizontal jet. 

Let OX, OY-ffig. 17) be horizontal and vertical axes, the origin 
ing at the orifice. Let k be the head, and x, y the coordinates of 
xnnt A on the parabolic path of the jet. If v» is the velocity at 


the orifice, and t the time in which a particle moves from O to A. 
then ^ 

Eliminating t, 


w , m *.-*./v*(2t*W(xV4y*). 

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 oest determined by tank 
measurement of 
the flow from the 
given orifice in a 
suitable time. If 
Q is the discbarge 
measured in the 
tank per second, 

Measure mcnls of 

this kind though 

simple in principle 

are not free from 

some practical 

difficulties, and 

require much care. 

In fig. 18 is shown 

an arrangement of 

measuring tank. F10. 17. 

The orifice is fixed 

in the wall of the cistern A and discharges either into the waste 

channel BB, or into the measuring tank. There is a short trough 

on rollers C which when run i under the jet directs the discharge- 

into the tank, and when run back again allows the discharge to orop- 

Fig. 18. 

irge valve 
tank, the 
3 must be. 

the water , 
the same: 
1 such an 1 
ant is re- 
aver each 
in of the 
ogh each 

c 2 -c.(<<.A*W(*i/*t). 

1 10. Coefficients for BeUm&utks and Betlwuntthed Orifices.— If an 
e-ince U furnished with a mouthpiece exactly of the form of the 


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 - 1. It is often desirable to bellmouth 
the ends of pipes, to avoid the loss of head which occurs if ihis uj 




not done; and such a beOmouth nay also have the form of the con- 
tracted jet. Ftg. 19 6hows 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 sttch an orifice L. J. Weisbach found the following values of 
the coefficients with different heads. 

Head over orifice, in ft. » h 






Coefficient of velocity -c, . 
Coefficient of resistance »<v 






As there is no contraction after the jet issues from the orifice, 
c#«i,c—f»; and therefore 

Q -*«V (2gh) -*w \2gkKi -Hr». 

I 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 kte Hamilton 
Smith (Wiley & Sons, New York, lOTfl). 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- <r«V (2gk). 


measured to 

Centre of 


Diameters of Orifice. 








Values^* C. 
























































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. 

Bead la 

Farm of Orifice. 



Rectanmlar Ratio 

Rectangular Ratio 

of Side* 16:1. 
















*£ 5 





I 14 ' 








i 4 * 







The orifice was 0106 sq. in. area and the reductions were made 
with g 132-176 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 iProc* InsL 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 scr apers 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 A-0-0037J, 
where A is in feet and d m inches. 

Coefficients of Discharge from Circular Orifice*. 
Temperature 5/ to $s*. 

Head in 



Diameters of Orifices in Inches ((f)- 








** | 3 







Coefficients (c). 























The following table, compiled by J. T. Fanning {Treatise em Weto 
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 cult 
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 tie 

Coefficients 0} 

>f Discharge for Rectangular Orifices, Sharp-edged, 
in Vertical Plane Surfaces. «~«— 

Head to 
Centre of 










Ratio of Height to Width. 










•61 10 






•601 1 











f 21. Orifices with Edges of Sensible Thickness.— When the edges d 
the orifice are not bevelled outwards, but have a sensible thickness, 
the coefficient of discharge is somewhat altered. The fofbvu* 
table gives values of the coefficient of discharge for the arrangement* 
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 onfices were all 24 in. wide. 
The heads Were measured immediately over the orifice. In this esse, 

1 22. Partially Suppressed Contraction.— Since the contractioe of 
the jet is due to the convergence towards the orifice of the issue 
streams** wOl be diminished H for anyportibn of the edge cT3 
orifice the convergence is prevented. Thus, if an internal rim or 
border n applied to part of the edge of the orifice (fig. 31) the as- 
vereence for so much of the edge is suppressed. For such am 
G. Btdone found the following empirical formulae appKcable— 





erf deficients of Disdurte for Jtefettfatsr Vertical Orifices in Fit. 2 °- 


edge of 

Height of Orifice, H - A, in feet. 





in feet. 
















































071 1 









































































0-6! I 











For rectangalar orifices. 

c. -0-62(1 +Ori52«/p)i 
and for circular orifices, 

t ct «o-6a(i +0*1281*/*) ; 

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 <#, when the border extends over 
J. f or f of the whole perimeter-—* 


Rectangular Orifices. 

.Circular Orifices. 







For larger values of n(p the formulae are not applicable- C. R. 

Bornemann has shown, 
however, that these for- 
mulae for suppressed con- 
traction are not reliable. 
f 23. Imperfect Con- 
.— If ' " 

the sides of 

the vessel approach near 

to the edge of the orifice, 

tSJ they interfere with the 

£-4^2ht convergence of the streams 

I ^§P 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 corresponding 

Fie. 20. Fie. 21. 

vidth of the orifice. The coefficients of contraction for this case 
are imperfectly known. 

1 24. Orifices Furnished with Channels of DtwAmt*— 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). 


A, to feet 









• 84 

























I 25. Jnveesien of ike /«*.— When a jet isswas from a horiaontal 
orifice, or is of small sise compared with the head, it presents no 

A * 

of form. But if the orifice is in a vertical Star* 
are hot small compared with the head. 








it .nde^ce. . «fc. ol ^"^-- !«. -« ■«««* *. 

orifice. These were first investtgatt 


Fie. 24* 

subsequently H. C. Magnus (1 802-1 870) measuredjets from different 
orifices; and later Lord Rayleigh (Proc. Raj. Sec. xxix. 71) in- 
vestigated them anew. 

Fig. 23 shows some forms, the- upper figure giving the shape of 
the orifices, and the otiiera 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 K sides, forms ft sheets in planes 
perpendicular to the sides of the polygon. 

Bidonc 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 a t> a, (fig. 24) be two points in an orifice at depths k u At from 
the free surface. The filaments issuing at at, a t will have the different 

velocities V 2g hi and V 2gh t . 
Consequently they will 
tend to describe parabolic 
paths aic&i and a*b% 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 en Discharge of Orifices. — Professor 
W. 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 1 cm. in diameter with heads of about 
I to 1 J it. the coefficients were: — 

Temperature F. C. 

■&* :.::::: :§J 

For a conoidal or bell-mouthed orifice I cm. diameter the effect of 
temperature was greater.— 

Temperature F. . C. 

19V .... . . . 0-987 

!*>• .... V '. . 0.974 

oo* . 0-949 

an Increase in velocity of discharge of 4% when the temperature 
increased 130*. 

I. 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 a* 57° 
and 0-607 at 179° F., a very small difference. With a conoidal 
orifice the coefficient was 0961 at 55° and 0-981 at 170" F. The 
corresponding coefficients of resistance are 0-0828 and 0-0301, 
•bowing thai the resistance decreases to about half at the higher 

§ 27. Fire Hose Afassfw.— 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-io. 
nozzle; 0-082 for { in.; 0*972 for 1 in.; 6-976 for it in.; and 
097 1 for 1 1 in. The nozzles were fixed on a taper play-pipe, and the 
coefficient includes the resistance of this pipe lAmer. Sec. Civ. Eng. 
xxi., 1889). Other forms of nozzle were tried such as ring nozzka 
lor which the coefficient was 


1 28. The general equation of the steady motion of a fluid given 
under Hydrodynamics furnishes immediately three results as to the 
distribution of pre wu re in a stream which may here be assumed. 
1 (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 


ocjfcit channel tor instance, when the effect of eddies produced by the 
r o nghn tas o f the sides ia neglected, the pressu re at each point is 
simply the hydrostatic pressure due to the depth below the free 

(0) If the velocity of the fluid is very small, the distribution oi 
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 fairing 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 flnid at rest. 
Distribution of Energy in Incompressible Fluids. 

f 29. Application of Ike Principle 0/ the Conservation of Energy to 
Cases of Steam 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 ia 
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 OO be the free surface and XX any hor izonta l datum line. Let 
O O 

Fig. 25. 

« be the area of a normal cross section, t the velocity, p the intensity 
ofpressure, and a the elevation above XX, of the elementary stream 
AB at A, and «i, ft, Vi, % the same quantities at B. Suppose that 
in a short time I the mass of fluid initially occupying AB comes to 
A'B'. Their AA\ BB' are equal to vt, v\t, and the volumes of fluid 
AA', BB' are the equal inflow and outflow -Q*-fa*i -«!»»/. in the 
given time. If we suppose the filament AB surrounded by other 
filaments moving with not very different velocities, the frictions! 
or viscous resistance on its surface will be small enough to 
be neglected, and if the fluid ia 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 (s-Si). The work of the 
pressures on the ends, reckoning that at B negative, because it is 
opposite to the direction of motion, is (pwXtf)— (P»«*iX»iO» 
tylp—Pd' The change of kinetic energy in the time I to the differ* 
ence 01 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 GQtfg, and the change of 

this to the 

rfAA' and BB' is GQtfg, and the cfo 
* iPQtfg) (tffr-f/a). equating thi 


kinetic energy is therefore ( 

work done on the mass AB, 

~ ... G»-*>+&<^)-<CWl)Csr^-^). 

Dividing by GQf and rearranging the terms, 

or, as A and B are any two points, 

»*/af +p/G+s-constant - H. (a) 

Now v*l2g isthe head due to the velocity v, p/G is the head equivalent 
to the pressure, and s 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, s is 
easily seen to be the work in foot-pounds which would be done 
by l lb of fluid falling to the datum line, and similarly PfG and 
v*/2f 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 1 * *" 




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 OO is taken as the datum, and -A, —At are the depths of A 
and B measured down from the free surface, the equation takes the 

*to+P/G-h -n'to+fc/G-At; (3) 

or generally 

*/2g+pfG -A -constant. (3a) 

f 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 

Fig. 26. 

(| 8), having their lower ends accurately parallel to the direction of 
flow. In such tubes the water will rise to heights corresponding to 
the pressures at A and B. Hence b-p/G, and y-f./G. Conse- 
quently the tops of the pressure columns A' and B' will be at 
total heights 6+c-p/G+s and t'+e'-fr/G+si above the datum 
line XX. The difference of level of the pressure column tops, or 
the fall of free surface level between A and B, is therefore 

and this by equation (1), $ 29 is fa'-a*)^*;. 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 Hne of hvdrauhc 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 V B* drawn at H ft. above XX by the 
quantities a »P*/2f and a' =-riV2r. 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. Froude 

Kre some experimental illustrations of the principle of Bernoulli. 
remarked that it was a common but erroneous impression that 
a fluid exercises in a contracting pipe A C&g- 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 b commonly assumed that 
when passing through a contraction 

C, there is in the narrow neck an 

excess) ofpressure due to the squeezing together of the tiqutd 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 

chow the decrease of 
pressure at the contrac- 
> tion and increase of 
pressure at the enlarge- 
ment. The line abc in 
both, figures shows the 
C ______ variation of free surface 

level, supposing the pipe 

frictionlcss. In actual 

pipes, however, work is 

Fig. 27. expended in friction 

against the pipe; the 

total bead diminishes in proceeding along the pipe, and the free 

surface level is a line such as obtC\, 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. 

projected surface at 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 ot liquid parallel to the 

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 

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 
orifices. In the actual experiment there was 18 in. of head in the 
right and 20} in. of head in the left-hand cistern, so. that about 

Fie. 30. 1 

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. 

f 32. Venturi Meter. — An ingenious application of the variation 
of pressure and velocity in a converging ana diverging pipe has been 



Fie. 31. 

made by Gcmens Hcrschel in the construction of what he terms a 
Venturi Meter for measuring the flow in water mains. Suppose that, 
as in fig. 32, a contraction is made in a water main, the change of 
section being gradual to avoid the production of eddies. _The ratio p 



4 *e ««■» «**«mm ** A and B, that b at Inlet and throat, is in 
*•«■* ■ m i • to I to *o to I, and k very carefully determined by 
** -np i w r «4 Um sBrttr. Theft, if e and « are the velocities at A 
*** ** -*-#o. Let era a m re pipe* bo introduced at A, B and C, 
* iS. c 

Fig. 32. 

and let H.. H ; H, be the pressure heads at those points. Since the 
yejader at B m greater than at A the pressure will be less. Negjkct- 

ler »*Hr-H be termed the Venturi head, .then 

1 the velocity through the throat and the discharge of the 
1 be calculated if the areas at A and B are known and h 
sr—rml Thus if the diameters at A and B are 4 and 13 in., the 
arnmaae 12*57 and 113*1 tq. in-, and p-o, 

*s-V8i/8oV (2ga) -IKW7V (2«I»X 
I *e observed Venturi head is 12 ft., 

*- 28 ft. per sec, 
astf tfat discharge of the main is 

28X12-57-351 cub. ft. per tec 
React fee a simple observation of pressure difference, the flow in 
2fe IBM at any moment can be determined. Notice that the 
ir«wir-t height at C will be the same as at A except for a small loss 
a fee a* friction and eddying between A and B. To get the pressure 
« *^t throat very exactly Herschel surrounds it by an annular 
sjMace communicating with the throat by several small holes, 
wbsseSms formed in vulcanite to prevent corrosion. Though con- 
«r*aed to prevent eddying as much as possible there is some eddy 
In* TW main effect of this is to cause a loss of head between A 
<s*a C whkh may vary from a fraction of a foot to perhaps* ft. 

* -kWktt velocities at which a meter can be used. The eddying 
«»* asWts a little the Ventunhead k. Consequently an expen- 
«aa^ vtcacknt must be determined for each meter by tank measure- 
~ ~ w^T— of this co ef ficien t is, however, surprisingly smalL 
TtaSwWrlcticm. «-KU//(p^i)IV (***).. S»en herschel 

* ^ *TL Ir • from 0-97 to l-o for throat velocities varying from 
tsone varan u* 8 to 2g ft . per sec The 

meter ss extremely con* 
venient. At Staines reser- 
voirs these are two meters 
of this type on mains 04 in. 
in diameter. Herschel con- 
trived a teuurding arrange- 
ment which records the 
variation of flow from hour 
to hour and also toe total 
flow ia any given time. In 
Great Britain the meter is 
I conttructedby C. Kent, 

I m ho has made improvements 

w ^. InUt in the recording arrange- 

^-» " In the Deacon Waste 

v\V#-r Meter (fig. 33) a 
«i:ii»Ti-*t prinrijjie i» used. 
A 4i*k D, partly counter- 
babvjH try a weight, is 
•o^tirVd in the water flow* 
in* \\*w$i the main ia a 
rvo'^J ».».-«.W. The un- 
riw#^ l*k«»**l ».-i^M of the disk 

»t \..\<\*r*>A »/y the impact 
11 .fc.M*'**?* **•***""*"' '"•" ''**' kri*r*.but 
**»** "JJL,Mi«h* ' i " a ** r *» *•** ***» *» </**#*|u<w of 

* " 1 frvtt Lb» iU: vamtK« of ttrm is uv 

3^***' ^-euseand velocity 


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 denned, 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 AS, CD (fig. 34) be two consecutive stream lines, at present 
assumed to be in a vertical plane, and PQ a normal to these lines 




Fig. 34- 

making an angle o with the vertical. Let P, Q be two particles 
moving along these lines at a distance PQ-c&, and let s 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, 

Differentiating, we get 

for the increment of energy between Q and P. 
. <M »<fp/G +wfr/g+<fc cos +, (in) 

where the last term disappears if the motion is in a horizontal plane. 
Now imagine a small cylinder of section « described round PQ 
as an axis. This will be in equilibrium under the action of Ha 
centrifugal force, its weight and the pressure on its ends. But its 
volume is uds and its weight Outds. Hence, taking the components 
of the forces parallel to PQ— 

udp "GvWs/gp-Gw cos *ds, 
where p is the radius of curvature of the stream line at Q. Conse- 
quently, introducing these values in (1), 

m-*dslv-Hdv1g-(9[g){v/p+dvJds)ds. (2) 

f 34. Rectilinear Current. — Suppose the motion is in parallel 
straight stream lines (fig. 35) in a vertical plane. Then /> b infinite, 
and from eq. (2), § 33, 

Comparing this with (x) we see that 


/. z+p/G-constant; (3) 

or the pr e s sure varies hydrostatically as in a fluid at rest. For two 

plane, a is constant, and there- 
fore p is constant. 

Jcofttolcng Current. — Suppose 
water flowing radially between 
horizontal parallel planes, at 
a distance apart ■»*. Conceive 
two cylindrical sections of the 
current at radii r% and r», where 
the velocities are * and «*, and the pressures pi and pt- 
each cylindrical section of the current b toe 

Fig. 35- 



1 The following theorem is taken from a paper by J. H. ConeriD. 
" On the Distribution of Energy in a Mass of Fluid in Steady Motion,* 
Phil. Mat., February 1876. 


Tke velocity would be infinite at radius o, it the current could be 
conceived to extend to the axis. Now, if the motion it steady, 

K - PxlG +»,'/2« - PilG +p»V2f : 

-f*/G+Ti*i , /'i , ?£; 
(pr-pi)/G -t-i»(i-r,»/ri , )/2f ; (5) 

^/C-H-f,VWa|. 16) 

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-hyperbota of the form xv» -c*. 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 
of water, in which the stream lines are concentric circles, and in which 



Fie 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 proper 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 +»*/2£ - constant ; 


Consider two stream lines at radii r and r+dr (fig. 36). Then in 
(*)t I 33. m r and ds-dr, 


• ml/r, (8) 

precisely as in a radiating current; and hence the distribution 
of pressure is the same, and formulae 5 and 6 are applicable to this 

Fret Spiral Vortex. — As m a radiating and circular current the 
equations of motion are the same, they will also apply to a vortex 
in which the motion is compounded of these motions in any pro- 
portions, provided the radial component of the motion vanes in- 
versely as the radius as in a radial current, and the tangential 
component varies inversely as the radius as in a free vortex. Then 
the whole velocity at any point will be inversely proportional to 
the radius of the point, and the fluid will describe stream lines 
having a constant inclination to the radius drawn to the axis of the 
current. That is, the stream lines will be logarithmic spirals. 
When water is delivered from the circumference of a centrifugal 
pump or turbine into a chamber, it forms a free vortex of this kind. 
The water flows spirally outwards, its velocity diminishing and its 




wjr/v* — wrwr/^, 

P/C - aV/ag +constant. (9) 

Let ft, ft, si be the pressure, radius and velocity of one cylindrical 
section, pi, ft, t»i those of another; then -, 

(p*-Pi)fG - *(rf-rf)l2g - (*»*-ci«)/*f • (10) 

That is, the pressure increases from .within outwards in a curve 

Fie. 37. 

which in radial sections is a parabola, and surfaces of equal pressure 
are paraboloids of revolution (fig. 37). 

Dissipation of Hbad in Shock 
% 36. Relation of Pressure and Velocity in a Stream in Stmdjt 
Motion when Ike Changes 0/ Section of the Stream are Abrupt. — 
When a stream changes section abruptly, rotating eddies are formed 
which dissipate energy. The energy absorbed in producing rotation 
is at once abstracted from that effective in causing the, flow, and 
sooner or later it is wasted by frkrtional .resistances due to the rapid 
relative motion of the eddying parts of the fluid. In such cases the 
work thus expended internally in the fluid is too important to be 
neglected, ana the energy thus lost is commonly termed energy Jost 
in shock. Suppose fig. 38 to represent a stream having such* an 
abrupt change of section. Let AB, CD be normal aectjonaat points 
where ordinary stream line motion has not boen disturbed and 
where it has been re-established. Let w, p, » be the area of section, 
pressure and velocity at AB, and t*, Pi, Vi corresponding quantities 
at CD. Then if no work were expended internally , and assuming 
the stream horizontal, we should have 

ptGWto-pdG+*H*t (0 




But if work is expended in producing irregular eddying motion, the 
head at the section CD will be diminished^ 

Suppose the mass A BCD comes in « short time I to A'B'CD'. 
The resultant force parallel to the axis of the stream is 

where p« is put for the unknown pressure on the annular space 
between AB and EF. The impulse of that force is 

_. . . l/>u>+fc(«l-«>-fc-iW. 


If there is shock, 

pi!G-plG*9i{v r *)/ t . 

Hence the pressure head at CD in the second case is less than in the 
former by the quantity (p-ti)Vig. or, putting wtffi-wv, by the 

W*gKi-*MP. (4) 

.$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 



Fig. 39. 

and the pressure at those points may be take 

static pressure due to the depth from the fn 

Che area of the mouthpiece AB, w that of the contracted jet aa. 

u 1.. .4.- i... 

Suprose that in a short time i. the mass OOua comes to tae poattaan 
O'O a'a'j the impulse of the hotuonul 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 (or all other portions of the 
vertical surfaces of the mass, excepting the portion EF opposite the 
mouthpiece and the surface AoiB of the jet. On EF the pressure it 
j — _., jg p ressure due to the depth, that is. {P* +GJk;a 
lection AaaB of the jet, the horizontal resultant 
ual to the atmospheric pressure p, acting on the 
VB of the jet ; that is, the resultant pressure is 
-esultant horizontal force for the whole mass 
p.ftsGAa Its impulse in the time tisCkQt. 
.teady there is no change of momentum between 
change of horizontal momentum is, therefore, 
horizontal momentum lost in the space 0000* 
.pace aaa'a'. In the former space there is no 

e space aaa'a' is *rf; the mass of liquid in that 
Is CG/g)wtr*l. Equating impulse to 

space is (G/{)wrt ; its 
momentum gained, 


•*-2fA, and w/q* 

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 pi the vessel in 

.i_- ^*-- jrhood of the orifice is not so small that it can be 

The resultant horizontal pressure is therefore greater 

id the contraction is less. The experimental values of the 

f discharge for a re-entrant mouthpiece are 05140 

547 (Bidone), 05324 (Wcisbach). values which differ 

c theoretical value, 0-5. given above. 

rt/y of Filaments issuing in a Jet. — A jet is composed 

cms or elementary streams, which start into motion at 

in lhc a an 


m at the most con- 
tracted section of 
the jet, where the 

filaments have be» p|-. .^ 

come parallel and 

.exercise uniform mutual* pressure. Take the free surface AB for 
datum line, and let P\, V\. Ai, be the pressure, velocity and depth 
below datum at M; p. v, k, the corresponding quantities at a. 
Then § 29. cq. (31). 

v,V2t +A1/G-A. «*»/**. +PIG-H. (1) 

But at M. since the velocity is insensible* the pressure is the hydro- 
static pressure due to the depth; that is, Pi«*o. pi*pa+G*i. At 
f». P-P«. the atmospheric pressure round the jet. Hence, inserting 
these values, 

o+p,/C+AHk. -»Vaf +*/G-A; 

•V**-*; (2) 

or »-V(2«A)-8o25VA. (2«) 

That is. neglecting the viscosity of the fluid, the velocity of fila- 
ments at the contracted section of the jet is simply the velocity doe 
to the difference of level 
of the free surface in the 
reservoir and the orifice. 
If the orifice is small in 
dimensions compared with 
a, the filaments will all 
have nearly the same vel- 
ocity, and if A is measured 
to the centre of the orifice, 
the equation above gives 
the mean velocity of the 

Cast of a Submerged 
Ort/ue.— Let the orifice 
discharge below the level 
of the tail water. Then 
using the notation shown in fig. 41, we have at M, V| «o,*i ~Ga;+*j 
at m, p-Ght+f*. Inserting these values in (3). | 29, 
o+A,+p*/G-A, «t*/?jt +Ar-*i+p./G; 

v7*£-Ai-Aj«A. (3) 

Ftc. 41. 


where L is the difference of level of the head and tail water, aad may 

be termed the effective head producing flow. 

Case where ike Pressures are different on the Fret Surface and at 
^^^^^^^^^^^^^^^^_ A* Orifice.— Let the 

fluid flow from a vessel 
in which the pressure 
n f* into a vessel ia 
which the pressure is 
p, fig. 42- The pres- 
sure p* will produce the 
same effect as a layer 
of fluid of thickness 
pjG added to the head 
water; and the pres- 
sure p will produce 
the same effect aa a 
layer of thickness p/G 
added to the tail 
water. Hence the 
effective difference of 
level, or effective head 
producing flow* wiU 




Fig. a* 
and the velocity of discharge will be 

• -VUf|A.+(A,-*)/Cl|. (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-<«»-«W(2*A), (5) 

where «* is the area of the orifice, o» the area of the contracted 
section of the jet. and * the effective head measured to the centre of 
the orifice. If ft and u 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 orinccs. ana 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 ft is different 
for different filaments, and then the velocity of different filaments is 
not sensibly the same. 

Sim rut Omfices— Head Constant 
5 so. 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 rectangular con- 
tracted section with 
•vertical and horizon- 
tal sides. Let b (fig. 
43) be the breadth of 
the jet. At and h t 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 
p, c 4 , " of discharge VSfT 

riG ' 43 The discharge, per 

weond in this lamina is. therefore fry 4 *!* dk, and that of the whole' 
jet n therefore 


-i*Vi«l*i , -*i , |. (6) 

where the first factor on the right is a coefficient depending on the 
form of the orifice. 

Now an orifice producing a rectangular jet must itself be very 
approximately rectangular. Let B be the breadth, Hi, fcj f , the 
depths to the upper and lower edges of the orifice. Put 

Ktf-JA/BOtf-HA-e. (7) 

Then the discharge, in terms of the dimensions of the orifice, instead 
of ibose of the jet, is 

Q-fcBVSRHr'-HA. (8) 

tKc formula commonly given for the discharge of rectangular orifices. 
The coefficient c Is not, however, simply the coefficient of contraction, 
•he value of which is 


awl not that given in (7). It cannot be assumed, therefore, that e 

in equation (8) is constant, and in fact ii is found- to vary fox different 

values of B/H4 and B/H|. and must be ascertained experimentally. 

Relation between the Expressions (5) and (8). — For a rectangular 


orifice the area of the orifice is « « B(H» - H,), and thedepth meaaured 
to its centre » § (H t +Hi). Putting these values in (5), 

rr ,„v ^. >-«BvHt-Hi)VUKHi+lii)|. 
From (8) the discharge » 

u 1 u fc-fcBy5(H.*-H,«). 

Hence, for the same value of e in the two cases, 

, U m, Q2yQ»-« H « , - H '*M( H «- H »WI(H.+Hi)/2H. 

Let Hj/H a -<r t then 

Q,/Q, -0.9427 (I -**)/{ 1 -#V (1 +*))• (9) 

If Hi varies from o to 00, <r(=-Hi/Hj) varies from o to I. The 
following table gives values of the two estimates of the discharge 
for diffeeent values of : — 










I 000 

Hence it is obvious that, except for very small values of 0, the 
simpler equation (5) gives values sensibly identical with those of 
(8). When «<o-5 it is hatter to use equation (8) with values .of 
c determined experimentally for the particular proportions of onfice 
which arc in question. 

S 40. Large Jets having a Circular Section from Orifices in a Vertical 
Plane Surface.— Let fig. 44 represent the section of the jet, 00 being 

-J> , , r JL_ 

Fig. 44. 
the free surface level in the reservoir. The discharge through the 
horizontal strip aabb, of breadth oa«6, between the depths h\jrj 
•nd *4+y+dv, is 

The whole discharge of the jet is 


But»-dsin+; y-ld<i-cos*); rfv-ldsin+rf*. Let«-d/(»*i+d), 

Q-s*V (2g(mt+dh)\f\xnWi -.«*♦•>. 

From eq. (5). putting w-ir^/4, h-hi+dl*, r»i when d is the 
diameter of the jet and not that of the orifice* 

O/Qi -»/*/j «« W (1 ~« cos *\d*. 
For fti-oo,«-oand Q/Qiai; 

and for A, =0, « - 1 and Q/Qi -0-96. 

So that in this case also the difference between the simple 1 formula 
(5) and the formula above, in which the variation of head at different 
partsjof the orifice is taken into account, is very small. 

Notches and Weirs 
5 41, Notches. Weirs and Byevashes.—A, notch is aa orifice ex- 
tending up to the free surface level in the reservoir from which the 
discharge takes place. A weir is a structure over which the water 
flows, the discharge being: in the same conditions as for a notch. 
The formula of discharge for aa orifice of this kind is ordinarily 
deduced by putting Hi -o in the formula for the corresponding orifice, 
obtained as in the preceding section. Thus for a rectangular notch, 
put Hi -o in (8). Then 

Q-fcBVC2*)H«. (ii) 

where His put for the depth to the crest of the weir or the bottom 
of the notch. Fig. 45 shows the mode in which the discharge occurs 
in the case of a rectangular notch or weir with a level «rcst. As;the 
free surface level falls very sensibly near the notch* the head H 
should be measured at some distance back from the notch, at a 
point where the velocity of the water is very small. 

Since the area of the notch opening n BH, the above formula i« 
of the form 

where A is a factor depending on the form of the notch and expressing 
the ratio of the mean velocity of discharge to the velocity due to the 
depth H. 

1 42. Francis's Formula for Rectangular Notches.— The" jet dis- 
charged through a rectangular notch has a section smaller than BH. 
(a) because of the fall ofthe water surface from the point where H 


HYDRAULICS (discharge from orifices 

or, introducing a coefficient to allow for contraction, 

When a notch is used to gauge a stream of varying flow, the ratio 
B/H varies if the notch is rectangular, but ia obmum if the arte* 4s 
triangular. This led Professor James Thomson to suspect that the 
coefficient of dis- 
charge, c, would ' . « _ 

be much more T — : — : rr? — 

constant with \2^^^~ z i^zy I * *" 

different values V" ft~" 7 J i 

of H in a trian- V;:v..v.t7.*^ ,fc ~* ** 

gutar than in a \ / " & 

rectang u la r \ / k 

notch, and this \o/ J 

has been experi- \/ 1 

mentally shown *" •"""* *" ""* 

to be the case. Fie. 46. 

Hence a tnan- 

gular notch is more suitable for accurate gaugings than a rectangular 
notch. For a sharp-edged triangular -notch Professor J . Thorasoa 
found £-0-617. It will be seen, as in | 41. that since |BH is the 
area of section of the stream through the notch, the formula is 
again of the form 

where *-,*, it the ratio of the mean velocity in the notch tt> tat 
velocity at the depth H. It may easily be shown that for all notches 
the discharge can be expressed in this (orm. 

§ 44. Weir with a Broad Sloping Crest. Suppose a weir formed 
with a broad crest so sloped that the streams flowing over it have a 
movement sensibly rectilinear and uniform (fig. 47). Let the inner 
edge be so rounded as to prevent a crest contraction. Consider a 
filament aa', the point a being so far back from the weir that the 

o „ o 

„ k - " 

"1 ■ 

••* ::.v.v.*a:: 


Fie. 47. 

velocity of. approach is negligible. Let OO be the surface level in the 
reservoir, and let • be at a height A* below OO, and V above a'. 
Let ft be the distance from OO to the weir crest and e the thickness 
of the stream upon it. Neglecting atmospheric pressure, which has 
no influence, the pressure at a is GA"; at a' it is Gs. If r be the 
velocity at «', 

*f2t-h' +k'-t-h -e- r 


Theory does not furnish a value for e, but Q-»o for r— o and for 

r - A. Q has therefore a maximum for a value of e between o and •, 

obtained by equating dQfde to cero. This gives e • | A, and, inserting 

this value, 

Q-o&$ bhJljdT. 
as a maximum value of the discharge with the conditions assigned. 
Experiment shows that the actual discharge is very approximately 
equal to this maximum, and the formula is more legitimately ap- 
plicable to the discharge over broad-crested weirs and to cases such 
as the discharge with free upper surface through large masonry 

Coefficients for the Discharge over Weirs, derived from the Experiments of T. £. BlackwsU. When more than one experiment was made with the 
same head, and the results were pretty uniform, the resulting coefficients are marked, with an (•). The effect of the converging mtuf-heardi 
is very strongly marked. 

Heads ia 

Sharp Edge. 

Planks ■ in. thick, square 

on Crest. 

Crests j ft. wide 

bom still 
Water in 

S ft. long. 

10 ft. Ions . 

j ft. long 

6 ft long. 

.oft. long 

1 oft long. 

wing*- boards 

■akin* an angle 


j ft. tow, 

fall 1 in 1 8 

lali tin 12. 

6 fc!r 



Ullita il 

















•8o 3- 







•479 # 




•642 • 













602 * 


















































• 4 8o- 










•534 # 




. • 

1 The discharge per second varied from -461 to -665 cub. ft. "in two experiments. The coefficient ^435 is derived from the mean value. 




sluice openings than the ordinary weir formula for •harp-edged 
weirs. It should be remembered, however, that the friction on 
the sides and crest of the weir has been neglected, and that this 
tends to reduce a little the discharge. The formula is equivalent 
to the ordinary weir formula with c - 0*577. 

Sficial Cases of Discharge rmoii OtincM 

I 45. Cases t* which the Velocity of Approach needs to he taken 
mto Account. Rectangular Orifices and Notches. — In finding the 
velocity at the orifice in the preceding investigations, it has been 
assumed that die head h has been measured from the free surface 
of still water above the orifice. In many cases which occur in 

Eractice the channel of approach to an orifice or notch is not so 
irge, relatively to the stream through the orifice or notch, that the 
velocity in It can be disregarded. 

Let Jii, At (fig. 48) be the heads measured from the free surface to 
the top and bottom edges of a rectangular orifice, at a point in the 

Ftc. 48. 

channel of approach where the velocity b «. It is obvious that a 
fail of the free surface, 

has been somewhere expended in producing the velocity «, and 
hence the true heads measured in still water would have been «i+b 
and ht+ff. Consequently the discharge, allowing for the velocity 
of approach, is 

Q-W5((*.+v)»-(*i+v) ? ). (1) 

And for a rectangular notch for which A ( -o, the discharge is 

Q-k*VTgl(A, + ¥ )l-b*l. (2) 

In cases where « can be directly determined, these formulae give the 
discharge quite simply. When, however, u is only known as a 
function of the section of the stream in the channel of approach, they 
become complicated. Let Q be the sectional area of the channel 
where At and At are measured. Then u — Q/ Q and b •*Q7**f tf. 

This value introduced in the equations above woukT render them 
excessively cumbrous. In cases therefore where O only is known, 
it is best to proceed by approximation. Calculate an approximate 
value Q' of Q by the equation 

Then $ -Q^fff nearly. This value of h introduced in the equations 
above will give a second and much more approximate value of Q. 

I 46. Partially Submerged Rectangular Orifices and Notches. — 
When the tail water is above the lower but below the upper edge 
of the orifice, the flow in the two parts of the orifice, into which it 
is divided by the surface of the tail water, takes place under different 
conditions. A filament M ( fMi (fig. 49) in the upper part of the 
orifice issues with a head A' which may have any value between 

Fie. 49. 

ii and h. But a filament M3I** issuing In the lower part of the 
orifice has a velocity due to h'—h", or h, simply. In the upper part 
of the orifice the head is variable, in the lower constant If Qi. Q» 
are the discharges from the upper and lower parts of the orifice, 
© the width of the orifice, then 

















a-c-XAt-AWai* , 
In the case of a rectangular notch or weir, A1-0. Inserting this 
value, and adding the two portions of the discharge together, we get 
for a drowned weir 

Q -cWSi*C*»-A/3>. (4) 

where A is the difference of level of the head and tail water, and At 
is the head from the free surface above the weir to the weir crest 
(fifc 50). 

From some experiments by Messrs A. Ftelcy and F. P. Stearns 
(Trans. Am. Soc. C.E., 1883, p. 102) some values of the coefficient c 
can be reduced 

Ai/At c hjh* 




Ifvelodty of approach is taken into account, let ft be the head due 
to that velocity; then, adding b to each of the heads in the equations 
(3), and reducing, we get for a weir 

Q-cftV^iKAi+IXA+Wl-JCA+WI-ftlJ; (5) 

an equation which may be useful in estimating flood discharges. 

Bridge Piers and other Obstructions in Streams.— When the piers 
of a bridge are erected in a stream they create an obstruction to the 
flow of the stream, which 
causes a difference of surface- 
level above and below the 
pier (fig. 51). If it is 1 
sary to estimate this differ- 1 
ence of level, the flow 
between the piers may be 
treated as if it occurred over 
a drowned weir. But the 
value of c in this oase is 
imperfectly known. 

ft 47. Basin'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 Pouts et ChaussbcS 
(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 

Fig. 50. 

vuwjwmz z. 

this extends a channel 200 metres in length with a slope of 1 mm 
per metre. The channel is 2 metres wide with vcrticaf sides. The 
channels were constructed of concrete rendered with cement. The 
water levels were taken in chambers con s truc t ed 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 | 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 
I metre and 0-5 metre in length, the end contractions being sup- 
pressed in ail cases. Assuming the general formula 

Q-twttV(2f*). (0 



Bazin arrives at the following values of m :— 

Coefficients of Discharge of Standard Weir. 


Head A metres. 

Head * feet. 



- ,6 f 



















1 -476 



1 640 






0-434 « 


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 k+au*j2g 
where aba coefficient not very well ascertained. Then 
Q -,J(A+a«72«W (2 ? (*+«*«fo)) 
The original simple equation can be used if 
or very approximately, since ut/agk is small, 

m-j.(i+ia««/2gA). (3) 

Now if p is the height of the weir crest above the bottom of the 
canal (fig. 52), s*-Q//(p+A). 
n placing Q by its value 

-m'JA/(/>+A)|«, (4) 
so that (3) may be written 
^m-Mli+W^+W (5) 

a jaugings were made with 

55^^^^^^^^^^5^^7J^? weirs of 0-75, 0-50, 0-35, and 
Fig. 52. °' 2 4 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): — 

Values of m — 

-m(i +2-5mV2#*) 

Head A metres. 

Head A feet. 






An approximate formula for j* is: 

p =0-405+0-003/* (A in metres) 

M-0-405+O-OI/A (A 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 .- • 

. 1 to 1 


„ „ 




3 to 1 

Vertical weir .... 


Inclination down stream . 

. 3 to 1 


3 to 2 


1 to X 

1 10 

•t t» 

1 to a 


„ „ 

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 arc more complicated. So 
long as the head does not exceed a certain limit the sheet is detached 


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 b 
followed by a rapid, terminating in a standing wave. In the Utter 
case when the foot of the 
sheet is drowned the level--- 
of the tail water influences 
the discharge even if it is 
below the weir crest. 

Weirs with Flat Crests.— 
The water sheet may spring 

or ma l y ra adhere P w C tn n e ^xW^m^^^^^^Z^^TZt 
crest falling free beyond the Fig. 53. 

downstream edge. In the 

former case the condition is that of a sharr>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 »hcet 
is adherent the coefficient m depends on the ratio of the head A 
to the width of crest c (fig. 53), and is given by the equation 
w-mi [0-70+o*i85A/cl, 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 I +R/A nearly. 
The results are limited to R 
less than \ in. 

Drowned Weirs. — Let h 
(fig- 54) be the height of 
"icad water and A» that of 

_ _ Fio. 54. 

tail water above the weir crest. Then Bazin obtains as the approxi- 
mate formula for the coefficient of discharge 

w-1-05m.l1 +M.//>]v ((* - Ai)/A|, 
where as before n%\ 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. 
1 4$. Separating 
Weirs. — Many 
towns derive their 
water-supply from 
streams in high 
moorland 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, la 

Fig. 55. 

Plan of 
Cast Iron 

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 




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. Binnic 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. 

Jt may be assumed, probably with accuracy enough for practical 
purposes, that the particles describe the parabolas due to tne mean 
velocity of the water passing over the weir, that b, to a velocity 

where k 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 I 

*-!«<■. *-!V(a«A)l; 

.'. y-ft*V*. 

which gives the width x for any given difference of level y and head 

k, which the jet will just pass over the orifice. Set off aa vertically 














— J 

Fig. 57. 

and equal to }f on any scale; of horizontally and equal to I V igh). 
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 of give the parabolic path of the jet. 

Mouthpieces— Head Constant 

I 40. Cylindrical Mouthpieces.— When water issues from a short 
cylindrical pipe or mouthpiece of a length. at least equal to 1} 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 
came 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 be the area of the mouthpiece, w the area of 
the stream at the contracted section EF. Let v, p be the velocity 
and pressure at EF, and *t, pi the same quantities at GH. If the 
discharge is into the air, p t is equal to the atmospheric pressure p». 

The total head of any filament which goes to form the jet, taken 






the friction of the 

mouthpiece is allowed 

for. Hence, for mouthpieces of this kind, and for the section at 

fc«o*8a c,-i'Oo c-o-to, 
It is easy to see from the equations that the pressure p at EF is 
less than atmospheric pressure. Eliminating Pi, we get 

- (>.-/>)/$-«* nearly: (3) 

or p-fto-|G*!b 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). the water will rise in this oipe to a height 

KL - {p. -p)l6 - \h 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. 

1 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-c*QV(atft). (4) 

where Q is the area of the external end of the mouthpiece, and cJOt 
the section of thecontracted jet beyond the mouthpiece. 

Convergent Mouthpieces {CasteTs Experiments).— Smallest diameter of 
orifice -0-05085 ft. Length of mouthpiece - 2 -6 Diameters. 

Fie. 58. 

Angle of 

Coefficient of 

Coefficient of 

Coefficient of 





o* 0' 
l # 3*' 

I 000 







4 *ic/ 

1 002 



5° a6T 
7° 52' 







10° 20' 



12* 4' 

13° 24/ 
14* 28' 
16; 36' 














ai* o* 



23° 0' 

29° 58' 







48° 50' 




The maximum coefficient of discharge is that for a mouthpiece 
with a convergence of 13° 24'. 



The values of c, and e« must here be determined by experiment. 
The above table gives values sufficient for practical purposes. Since 

.the contraction beyond 
the mouthpiece increases 
with the convergcncc.or, 
what is the same, thing, 
c, diminishes, and on the 
other hand the loss of 
energy diminishes, so 
that c, increases with 
the convergence, there 
is an angle for which the 
product c, c w , and con- 
sequently the discharge, 
is a maximum, 


}«. 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 
Fig. 59. inner end approxi- 

mately the tame 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 w, p, p be the section* velocity and pressure at CD, 
and Q, Vi, fa the same quantities at EF, p» being as usual the 
atmospheric pressure, or pressure on the free surface AB. Then, 

since there is no loss of 

energy, except the small 

frictional resistance of the 

surface of the mouthpiece, 



If the jet discharges into 

theair, p!-^; and 


., *•£<?«*>:. . 
or, if a coefficient is intro- 
duced to allow for friction, 

where c, is about 0-97 if 
the mouthpiece is smooth 
.and well formed. 

Hence the discharge de- 
pends on the area of the 
stream at EF, and not at 
all on that at CD, and the 
latter may be made as 
small as we please without 
«-.„ g^ affecting the amount of 

FIG. 60. ^ ter dtscharged. 

There is, however, a limit to this. * As the velocity at CD is greater 
than at EF the pressure is less, and therefore less than atmospheric 
pressure, if the discharge is into the air. If CD is so contracted that 
£— o, the continuity of flow is impossible. In fact the stream 
m disengages itself from the 

■ mouthpiece for some value 

of p greater than o (fig. 61). 
From the equations, 

#G«*./G-0»-* 1 «)/2g. 
LetQ/w-m. Then 

#G-*/G-r 1 »(w«- : i)/2g 

whence we find that p/G 
will become zero or nega- 
tive if 

or, puttirtg p 4 fC -34 ft., if 
In practice there will be an interruption of the full bore flow with 
a less ratio of Q/«, 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 

r Q-«VU«(*+f./G)l; 

that is, the discharge is the same as for a well-bellmouthed mouth- 
piece of area w, and without the. expanding part, discharging into 
a vacuum. 

f 5a. Jet Pump. — A divergent mouthpiece may be arranged to act 
as a pump, as shown in fig. 62. The water which supplies the energy 

Fig. 61. 


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. 

and 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 

\S3- 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 
ht 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 qf Emptying or Filling a Vertkal-sided Lock Chamber.— 
Suppose the lock chamber, which has a water surface of Q square 
ft., is emptied through a sluice in the tail gates, of area «. 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 



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 — Udh. and the outflow from the sluice in 
the same time is cwy* {2gh)dt. Hence the differential equation con- 
necting h and I is 





For the time I, during which the initial head H diminishes to any 
rther value A, 


For the whole time of emptying, during which h diminishes from 
rl too, 

romparing this with the equation for flow under a constant head, 
t will be seen that the time is double that required for the discharge 
>f an equal volume under a constant head. 

The time of filling the lock through a sluice in the head gates is 
xactly the same, ii the sluice is below the tail-water level. But if 
he sluice is above the tail-water level, then the head is constant 
ill the level of the sluice is reached, and afterwards it diminishes 
rith the time. 

PracticaiTUsb op Orifices in Gauging Watbr 

5 54. If the water to be measured is passed through a known orifice 
inder an arrangement by which the constancy of the head is ensured, 
he amount which passes in a given time can be ascertained by the 
ormulae already given. It will obviously be best to make the 
irifices of the forms for which the coefficients are most accurately 
tetermined; hence sharp-edged orifices or notches are most com- 
nonly used. 

Water Inch. — For measuring small quantities of water circular 
harp-edged orifices have been used. The discharge from a circular 
rifice one French inch in diameter, with a head of one line above the 
op edge, was termed by the older hydraulic writers a water-inch. 
i common estimate of its value was 14 pints per minute, or 677 
English cub. ft. in 24 hours. An experiment by C. Bossut gave 
34 cub. ft. in 24. hours (see Naviers edition of Belidor's Arch, 
iydr., p. 212). 

L. J. Weisbach points out tnat measurements of this kind would be 
nade more accurately with a greater bead over the orifice, and be 
proposes that the head should be equal to the diameter of the orifice, 
everal equal orifices may be used for larger discharges. 

Pin Ferrules or Measuring Cocks. — To give* 1 ite 

upply of water to houses, without the expense < lie 

rith an orifice of a definite size, or a cock, is he 

ervice-pipe. If the head in the water main i a 

efinite quantity of water would be delivered in he 

rrangement is not a very satisfactory one, an 1 a 

heck on extravagant use of water. It is interei as 

a example of regulation of discharge by 



Fig. 65. 


water. The cock 
on the right hand 
can be.used by the 
The one on the left and the 

msumer for emptying the pipes. .... 

leasuring cock are connected by a key which can be locked by a 
idlock, which is under the control of the water company. 
( 55. Measurement of the Flow in Streams. — To determine the 
jantity of water flowing off the ground in small streams, which is 
mailable for water supply or for obtaining water power, small 
mporary weirs are often used. These may be formed of planks 
1 p ported by piles and puddled to prevent leakage. The measure- 
ent of the head may be made by a thin-edged scale at a short 
stance behind the weir, where the water surface has not begun to 
soe down to the weir and where the velocity of approach is not 
gn. The measurements are conveniently made from a short pile 
iven into the bed of the river, accurately level with the crest of 
e weir (fig. 66). Then if at any moment the head is A, the dis- 
targe is, for a rectangular notch of breadth b, 

Here c— 0-62; or, better, the formula in 5 42 may be used. 
Gauging weirs are most commonly in the form of rectangular 
itches; and care should be taken that the crest is accurately 
irizontal, and that the weir is normal to the direction of flow of 
e stream. If the planks are thick, thev should be bevelled (fig. 67), 
id then the edge may be protected 6y a metal plate about j^th 
. thick to secure the requisite accuracy of form and sharpness of 
ge. In permanent gauging weirs, a cast steel plate is sometimes 
ed to form the edge of the weir crest. The weir should be large 
ough to discharge the maximum volume flowing in the stream, 
d at the same time it is desirable that the minimum head should 

not be too small (say half a foot) to decrease the effects of errors of 
measurement. The section of the jet over the weir should not exceed 
one-fifth the section of the stream behind the weir, or the velocity 
of approach will need to be taken into account. A triangular not Ji 
is very suitable for measurements of this kind. 
# If the flow is variable, the head h must be recorded at equidistant 
intervals of time, say twice daily, and then for each 12-hour period 

Fig. 66. 

ie mean of the heads at the 
his involves a good deal of 
ed to use a scale so graduated 
: per second. The lengths of 
ale are easily calculated by 
tary formulae for notches; 
taken accurately enough by 
en the principal graduations, 
charge of a stream by means 
er more difficult than might 

perly attended to. 
other difficulties of 

Fig. 67. 

~t arise. The length of the 
be very accurately deter- 
if the weir is rectangular 
is from exactness of level 
sted. Then the agitation 
, the ripple on its surface, 
esion of the water to the 

ich the bead is measured, 
ar introduce errors. Upon a 

w< long, with 1 ft. depth of 

w* { over, an error of i-ioooth 

of a foot in measuring the head, or an 
error of i-iooth of a foot in measuring 
the length of the weir, would cause an 
error in computing the discharge of 
2 cub. ft. per minute. 

Hook Gauge. — For the determination 
of the surface level of water, the most 
accurate instrument is the hook gauge 
used first by U. Boyden of Boston, in 
1840. It consists of a fixed frame with 
scale and vernier. In the instrument 
in fig. 68 the vernier is fixed to the 
frame, and the scale slides vertically. 
The scale carries at its lower end a hook 
with a fine point, and the scale can. be 
raised or lowered by a fine pitched F10.68 

screw. If the hook is depressed below 

the water surface and then raised by the screw, the moment of its 
reaching the water surface will be very distinctly marked, by the 
reflection from a small capillary elevation of the water surface over 
the point of the hook. In ordinary light, differences of level of the 
water of 001 of a foot are easily detected by the hook gauge. If such 
a gauge is used to determine the~heads at a weir, the hook should 




first be set accurately level with the weir crest, and a reading taken. 
Then the difference of the reading at the water surface and that 
for the weir crest will be the head at the weir. 

1 56. Modules used in Irritation. — In distributing water for 
irrigation, the charge for the water may be simply assessed on the 
area of the land irrigated for each consumer, a method followed in 
India; or a regulated quantity of water may be given to each 
consumer, and the charge may be made proportional to the quantity 
of water supplied, a method employed lor a long time in Italy and 
other parts of Europe. To deliver a regulated quantity of water 

Fig. 69. 

time to time. It has further the advantage that the cultivator, by 
observing the level of the water in the chamber, can always see 
whether or not he is receiving the proper quantity of water. 

On each canal the orifices are of the same height, and intended to 
work with the same normal head, the width of the orifices being 
varied to suit the demand for water. The unit of discharge varies on 
different canals, being fixed in each case by legal arrangements. 
Thus on the Canal Lodi the unit of discharge or one module of water 
is the discharge through an orifice 112 ft. high, 0-12416 ft. wide, 
with a head 01 0*32 ft. above the top edge of the orifice, or -88 ft. 
above the centre. This corresponds to a discharge of about 0*6165 
Cub. ft. per second. 

In the most elaborate Italian modules the regulating chamber is 
arched over, and its dimensions are very exactly prescribed. Thus 
in the modules of the Naviglio Grande of Milan, shown in ng. 70, 
the measuring orifice is cut in a thin stone slab, and so placed that 
the discharge is into the air with free contraction on all sides. The 


Fio. 7a 

efcj#v '.;, , ^ 

adjusted it is locked. Let «#- be the area of the 
orifice through the sluice at A, and »» that of the 
fixed orifice at B; let At be the difference of level 
between the surface of the water in the canal and 
regulating chamber; h% the head above the centre of 
the discharging orifice, when the sluice has been 
adjusted and the flow has become steady; Q the 
normal discharge in cubic feet per second. Then, 
since the flow through the orifices at A and B b the same. 

Q - Cj»i V (2g hi) - CiwtV (2gkt) , 

where d and ft are the coefficients of discharge suitable for the two 
orifices. Hence 


If the orifice at B opened directly into the canal without any 
intermediate regulating chamber, the discharge would increase for 
a given change of level in the canal in exactly the same ratio. Conse- 
quently the Italian module in no way moderates the fluctuations of 
discharge, except so far as it affords means of easy adjustment from 

opening, and conversely. Thus a per- 
fectly constant discharge with a vary- 
ing head can be obtained, provided no 
clogging or silting of the chambers pre- 
vents the free discharge of the water 
or the rise and- fall of the float. The theory of the module is very 
simple. Let R (fig. 71) be the radius of the fixed opening, r the 
radius of the plug at a distance h from the plane of flotation of the 
float, and Q the required discharge of the module. Then 

Taking c -0-63, 


Choosing a value for R, successive values of r can be found Cor 
different values of h. and from these the curve of ,the plug can be 
drawn. The module shown in fig. 72 will discharge I cubic metre per 
second. "The fixed opening is o-2 metre diameter, and the greatest 
head above the fixed orifice is 1 metre. The use of this module 
involves a great sacrifice of level between the canal and the fields. 
The module is described in Sir C. Scott- MoncricfTs Irrigation in 
Southern Europe. 

§ 59. Reservoir Gouging Basins.— In obtaining the power to store 
the water of streams in reservoirs, it is usual to concede to riparian 


owners below the reservoirs a right to a regulated supply through- 
oat the year. This compensation water requires to be measured in 
such a way that the milfowners and others interested in the matter 
can assure themselves that they are receiving a proper quantity, and 
they are generally allowed a certain amount of control as to the* 
tiroes during which the daily supply is discharged into the stream. 



Fig. 74 shows an arrangement designed for the Manchester water 
works. The water enters from the reservoir a chamber A, the object 
of which is to stilt the irregular motion of the water. The admission 
is regulated by sluices at b, b, b. The water is discharged by orifices 
or notches at a, a, over which a tolerably-constant head » maintained 
by adjusting the sluices at 6, b, b. At any time the miliowners ran 
see whether the discharge is given and whether the proper head is 
maintained over the orifices. To test at any time the discharge of 
tb* orifices, a gauging basin B is provided. The water ordinarily 

flows over this, without entering it, on a floor of cast-iron plates. 
If the discharge is to be tested, the water is turned for a definite time 
into the gauging basin, by suddenly opening and closing a sluice at c. 
The volume of flow can be ascertained from the depth in the gauging 
chamber. A mechanical arrangement (fig. 73) was designed for 
securing an absolutely constant nead over the orifices at a, a. The 
orifices were formed in a cast-iron plate capable of sliding up and 

Fie. 73- 

down, without sensible leakage, on the face of the wall of the chamber. 
The orifice plate was attached by a link to a lever, one end of which 
rested on the wall and the other on floats / in the chamber A. The 
floats rose and fell with the changes of level in the chamber, and 
raised and lowered the orifice plate at the same time. This 



Fic. 74. 

mechanical arrangement was not finally adopted, careful watching 
of the sluices at b, b, b, being sufficient to secure a regular discharge. 
The arrangement is then equivalent to an Italian module, but on a 
large scale. 

§ 60. Professor FUeming Jenkin's Constant Flow Vahe.— In the 
modules thus far described constant discharge is obtained by vary- 
ing the area of the orifice through which the water flows. Professor 
F. Jenkin has contrived a valve in which a constant pressure head 
is obtained, so that the orifice need not be varied {.Roy. Scot. Society 



of Arts, 1876). Fie. 75 show* a valve of this land suitable for a 
6-in. water main. The water arriving by the main C passes through 
an equilibrium valve D into the chamber A, and thence through a 
sluice O, which can be set for any required area of opening, into the 
discharging main B. The object of the arrangement is to secure a 
constant difference of pressure between the chambers A and B, so 
that a constant discharge flows through the stop valve O. The 
equilibrium valve D is rigidly connected with a plunger P loosely 
fitted in a diaphragm, separating A from a chamber B* connected by 
a pipe Bi with the discharging main B. Any incre&se of the differ- 
ence of pressure in A and B Will drive the plunger up and close the 

Fie. 75. 

equilibrium valve, and conversely a decrease of the difference of 
pressure will cause the descent of the plunger and open the equilibrium 
valve wider. Thus a constant difference of pressure is obtained in 
the chambers A and B. Let u be the area of the plunger in square 
feet, p the difference of pressure in the chambers A and B in pounds 
per square foot, w the weight of the plunger and valve. Then if at 
any moment p» exceeds w the plunger will rise, and if it u less than 
w the plunger will descend. Apart from friction, and assuming the 
valve D to be strictly an equilibrium valve, since « and w are 
constant, p must be constant also, and equal to w/w. By making w 
small and » large, the difference of pressure required to ensure the 
working of the apparatus may be made very small. Valves working 
with a difference of pressure of \ in. of water have beer* constructed. 


} 61. External Work during the Expansion of Air. — If air expands 
with6ut doing any external work, its temperature remains constant. 

This result was first 
experimentally demon- 
strated by J. P. Joule. 
It leads to the conclu- 
sion that, however air 
changes its state, the in- 
ternal work done is pro- 
portional to the change 
of temperature. When, 
in expanding, air does 
work against an external 
resistance, either heat 
must be supplied or the 
temperature falls. 

To fix the conditions! 
suppose 1 lb of air con- 
fined behind a piston of 
1 sq. it. area (fig. 76). 
Let the initial pressure 
be P\ and the volume of 
the air v u and suppose 
this to expand to the 
pressure pt and volume 


fi. If P and v are the corresponding pressure and volume at any 
intermediate point in the expansion, the work done on the piston 
during the expansion from v to v+dv is pdv, and the whole work 
during the expansion from si to v* represented by the area abed, is 

Amongst possible cases two may be selected. 



Case 1.— So much beat is supplied to the air during expansion 
that the temperature remains constant. Hyperbolic expansioa. 
Then pr-pM. 

Work done during expansion per pound of air 

• -Mlog«f«to-ftfilogtfc/;fr. (I) 

Since the weight per cubic foot is the reciprocal of the volume per 
pound, this may be written 

(Pi/G.) log. G»/G,. (itf) 

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 neat equivalent to the external work done 
and the temperature falls. Adiabatic expansioa. 

In this case it can be shown that 

where y is the ratio of the specific heats of air at constant |nmim 
and volume. Its value for air is 1*408, and for dry steam 1-135. 
Work done during expa n s i on per pound of air. 

- H*ft?/(Y-i)j{ito 1r -*-ifo y -M 
-lPi»»/(T-i)l|i-Ch^f-«|- (*) 

The value of pi*\ for any given temperature can be found from the 
data already given. 

As before, substituting the weights G,, G, per cubic foot for the 
volumes per pound, we get for the work of expansioa 

(pJGi)[iKy-i)\ (1 -(Gt/Gi)^l. (aa) 

-Mt./(Y-i)l |i -(*/*)<*-»/>}. (2*) 

} 62. Modification of the Theorem of Bernoulli for the Cast 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, *n, vi, Ci be the pres- 
sure, sectional area of stream, 
velocity and weight of a cubic 
foot at A, and Pi, «*, v», G» 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 B 1 

Let St, % be the heights of the sections A and B above any gives 
datum. Then the work of gravity on the mass AB in i seconds is 

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 mast AB is 

The work done by expansion of Wf lb of fluid be t wee n A and B is 
VJlJ*pdv. The change of kinetic energy as before is (W/2g) W -iflL 
Hence, equating work to change of kinetic energy, 

W(s,-s,)/+(M^i-rVG,)W/+W^pip-(W/2g) W-t&i 
.'. Bi+Px/Gx+vflig-H+f/Gt+pt/H-fZpdv. (!) 

Now the work of expansion per pound of fluid has already been 
given. If the temperature is constant, we get (eq. in, f 61) 
*+P-7G,+*W2{-*+/WG,+*iV2*-(*/G») log v (GVGO. 
But at constant temperature pJGi m Pt/Ctl 

.-. s,+nV2*-*i+*r72«-(*!/G»)*). 
or, neglecting the. difference of level, 

W-sfl/Jg-Cfc/Gi) »<*• <*/*)• 
Similarly, if the expansion is adiabatic (eq. ta, \ 61), 

|l-(rVj " 
or neglecting the difference of level 

W-^/2g-(p^G,)U+i/(T-i)(i-(^pi)< 1r - 1 >M]-/4/G». 
It will be seen hereafter that there is a limit in the ratio PxlPi bryocd 
which these expressions cease to be true.' 

{ 63. Discharge of Air from an Orifice.— The form of the «fuatios 
of work for a steady stream of compressible fluid b 
s,+^/G,+»,V^-St-r£»/G,+»» , /U-(^/Gi)ll/(ir-l)l ^_ 


Fig. 77. 





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 front 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 p%. Let v& 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%. As air is light, the work of gravity will be small 
compared with that of the pressures and expansion, so that SiSs 
may be neglected. Putting these values in the equation above— 

•* , /a«-PiA5i-pi/G,+(A/G,)|i/( ! y-i)}|i-(p l //> I )<T-«)/r l 
- (pJCtiWb - 1) - Oi/*) y - ,/ V(y- 0} -pi/G,. 
But */d>-MV •*. fc/G,«(*/G,)(*/*) (Y ~ ,Vr 

or ■iVsc-lv/fr-DI \lpiJGi)-Gfa)U 

an equation commonly ascribed to L. J. Weisbach (Civilinjenieur, 
1856), though it appears to have been given earlier by A. J. C. Barre 
de Saint Venant and L. Wantzel. 
It has already (5 9, eq. 4a) been seen that 

L , . fc/C-Cfc/CsXn/**) 

where for air £»-2ii6-8, G»- -08075 and r, -492-6. 

*W2f H*rrY/<WY-0l |i-Q>i//>i) ( »- ,)/y }; (2) 

or, inserting numerical values, 

t*Vag - i83-6nfi -(*/*)•"») : (2a) 

which gives the velocity of discharge s* in terms of the pressure and 
absolute temperature, fa, r u in the vessel from 'which the air flows, 
and the pressure p% in the vessel into which it flows. 

Proceeding now as for liquids, and putting o> 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 r% is 

Qi -«*»-o* Vlto-yM-r- OCKl -(Pifpi) iy ~ l)/r )] 

-w8-7«tVNi-(pk/piHlI. (3) 

If the volume discharged J» -measured at the pressure pi and 
absolute temperature r 4 in the vessel from which the air flows, let 
Qi be that volume; then 

piW-PM; ^ 

Qi -c» V \\2rrp1Ky-DGJ l(*/p») f7v - (fc/fc) ( ** ,)/v IJ. 

Let (tVfc)'' T -f>/fc> ( *~ *-<pi/*> l -«- WfiVW; then 


-io8-7<i-V(ri^). (4) 

The weight of air at pressure pi and temperature r, is 

Ot m Pi/$Z'2ri lb per cubic foot 
Hence the weight of air discharged is 

W-G.Q,-*- V[2rrA>G,*/(y-i)] 

-2043C«^iV(^/ri). (5) 

Weisbach found the following values of the coefficient of dis- 
charge c. — 

Conoidal mouthpieces of the form of the") 
contracted vein with effective pressures > . e » 
of *23 to i* I atmosphere .... J 097 to 0*99 

Circular sharp-edged orifices . . °'$ 6 3 •• °'7 88 

Short cylindrical mouthpieces . . . .081,, 0.84 

The same rounded at the inner end . . 0-92- „ 093 

Conical converging mouthpieces . . . 0-90 „ 099 

( 64. Limit to the Application of the above Formulae. — In the 
formulae above it is assumed that the fluid issuing from the orifice 
expands from the pressure Pi to the -pressure p%, while passing from 
the vessel to the section of the jet considered in estimating the area 
u. Hence p^is strictly the pressure in the jet at the plane of the 
external orifice in the case of mouthpieces, or at the plane of the 
contracted section in the case of simple orifices. Till recently it 
nras tacitly assumed that this pressure p% was identical with the 
general pressure external to the orifice. R. D. Napier first discovered 
that, when the ratio prfpi exceeded a value which does not greatly 
differ from 0-5, this was no longer true. In that case the expansion 
>f the fluid down to the external pressure is not completed at the 
:ime it reaches the plane of the contracted section, and the pressure 
:hcre is greater than the general external pressure ; or, what amounts 
the same thing, the section of the jet where the expansion is com- 
peted is a sect jon which is greater than the area c t u of the contracted 
lection of the jet, and may be greater than the area « of the orifice. 
Napier made experiments with steam which showed that, so long as 
H/Pi>0'$, the formulae above were trustworthy, when Pt was taken 
o be the general external pressure, but* that, if P>fPi<0'5, then the 
>rcssure at the contracted section was independent of the external 
treasure and equal to o*S£i- Hence in such cases the constant value 
>-5 should be substituted in the formulae for the ratio of the internal 
nd external pressures pt/pi. 

It is easily deduced from Weisbach 'a theory that, if the pressure 
external to an orifice b gradually diminished, the weight of air dis- 
charged per second increases to a maximum for a value of the ratio 
••0-527 for air 
-058 for dry steam. 


5 65. When a stream of fluid flows over a solid surface, or con- 
versely when a solid moves in still fluid, a resistance to the motion 
is generated, commonly termed fluid friction. It is due to the vis- 
cosity of the fluid, but generally the laws of fluid friction are very 
different from those of simple viscous resistance. It would appear 
that at all speeds, except the slowest, routing eddies are formed by 
the roughness of the solid surface, or by abrupt changes of velocity 
distributed throughout the fluid; and the energy expended in pro- 
ducing these eddying motions is gradually lost in overcoming the 
viscosity of the fluid in regions more or less distant from that where 
they are first produced. 

The laws of fluid friction are generally stated thus: — ' 

1. The factional resistance is independent of the pressure between 
the fluid and the solid against which it flows. This may be verified 
by a simple direct experiment. C. H. Coulomb, for instance, oscil- 
lated a disk under water, first with atmospheric pressure acting on 
the water surface, afterwards with the atmospheric pressure removed. 
No difference in the rate of decrease of the oscillations was observed. 
The chief proof that the friction is independent of the pressure is 
that no difference of resistance has been observed in water mains 
and in other cases, where water flows over solid surfaces under widely 
different pressures. 

2. The factional resistance of large surfaces is proportional to the 
area of the surface. 

3. At low velocities of not more than 1 in. per second for water, 
the fractional resistance increases directly as the relative velocity of 
the fluid and the surface against which it flows. At velocities of 
§ ft. per second and greater velocities, the frictional resistance is 
more nearly proportional to the square of the relative velocity. 

In -many treatises on hydraulics it is stated that the frictional 
resistance is independent of the nature of the solid surface. The 
explanation of this was supposed to be that a film of fluid remained 
attached to the solid surface, the resistance being generated between 
this fluid layer and layers more distant from the surface. At ex- 
tremely low velocities the solid surface does not seem to have much 
influence on the friction. In Coulomb's experiments a metal surface 
covered with tallow, and oscillated in water, had exactly the same 
resistance as a clean metal surface, and when sand was scattered over 
the tallow the resistance was only very slightly increased. The 
earlier calculations of the resistance of water at higher velocities in 
iron and wood pipes and earthen channels seemed to give a similar 
result These, however, were erroneous, and it is now well understood 
that differences of roughness of the solid surface very greatly influ- 
ence the friction, at such velocities as are common in engineering 
practice. H. P. G Dairy's experiments, for instance, showed that 
in old and incrusted water mains the resistance was twice or some- 
times thrice as great as in new and clean mains. 

§ 66. Ordinary Expressions for Fluid Friction at Velocities not 
Extremely Small. — Let / be the frictional resistance estimated in 
pounds per square foot of surface at a velocity of 1 ft. per second; 
01 the area of the surface in square feet; ana v its velocity in feet 
per second relatively to the water in which it is immersed. Then, 
in accordance with the laws stated above, the total resistance of the 
surface is 

R-/««* (1) 

where / is a quantity approximately constant for any given surface. 

kV&rffa, (2) 

where f 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. 




of Friction, 


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 , 



The distance through which the frictional resistance is overcome 
is 9 ft. per second. The work expended in fluid friction b therefore 
given by the equation — 

Work expended -/<** foot-pounds per second ) (3). 

-*G«P»/2f „ ., \ 

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 

in which expression the second term is 

of greatest importance at very ' ow _^_^__ 

velocities, and of comparatively little C^i^E^ 

importance at velocities over about } ft. r-^r-r^r^-i-- 
per second. Values of { expressed in this ."L_"~1T"_Z~^ 
and similar forms will be given in con- tut. 
nexion with pipes and canals. -_^_ 

All these expressions must at present 

be regarded as merely empirical ex-^rzj 

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 I '949th power of the velocity. 

§•68. Fronde'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 ia 
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 apparatuses 
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 tne 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 ot 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 tbc.expcnatttt 

prcssions 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. 

$ 6j. # 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 

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 

t A , _,tt-, , . K disk serving to measure 

~~ v : *s 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- 
> seconds, 

v « 

the velocity of the cir- 
cumference of the disk 
was less than 6 in. per 
second, the. resistance 
was sensibly propor- 
tional to the velocity. 

Fie. 78. 

BeaufoVs Experiments. — Towards the end of the 18th century 
Colonel Mark Beaufoy (1764-1827) 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 

Fie. 70; 

were A in. thick, 19 in. deep, and from 1 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 rougnne* 
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 lb per sq. fe. 

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 t Ml . 

For other surfaces the resistance varied as iM*. 
With boards 50 ft. long. 

For varnish or tinfoil the resistance varied M i 4 **. 
For sand the resistance varied as •»"•. 

3. The average resistance per square foot of surface was omen 
greater for short than for long boards; or. what is the same thing, 
the resistance per square foot at the forward part of the boarv*«as 
greater than the friction per square foot of portions more sternward. 

Mean Resistance ia 
lb per sq. ft. 
Varnished surface . 2 ft. long o 41 

50 .. 0-25 

Fine sand surface 2 „ o-8i 

50 .. 0-405 

This remarkable result is explained thus by Froude: "The 
portion of surface that goes first in the line of motion, in experienciag 
resistance from the water, must in turn communicate motion to the 
water, in the direction in which it is itself travelling. Consequent}/ 




the portion of surface which succeeds the first will be rubbing, not 
against stationary water, but against water partially moving in its 
own direction, and cannot therefore experience so much resistance 
from it." t 

( 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. 













Varnish . 













Paraffin . . 






















Calico . . 












Fine sand 












Medium sand 

2 00 









Coarse sand . 









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 tabic. 

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 fhc 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 
lb per square foot when the length is increased from 2 to 8 ft., but it 
only diminishes from 0-278 to 0250 lb per square foot for an increase 
from 20 ft. to 50 ft. 

If the decrease of friction sternwards is due to the f a 

current accompanying the moving plane, there is n jht 

any reason why the decrease should not be greater 1 wn 

by the experiments. The current accompanying the be 

assumed to gain in volume and velocity sternwards, ity 

was nearly the same as that of the moving Diane and per 

square foot nearly zero. That this does not happen a luc 

to the mixing up of the current with the still water it. 

Part of the water in contact with the board at any p iv- 

ing energy of motion from it, passes afterwards to d of 

still water, and portions of still water are fed in toi ird 

to take its place. In the forward part of the boaL tic 

energy is given to the current than is diffused into surroundine 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 
earned out by Professor W. C. Unwin (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 t* is an element of area on the disk moving with the velocity », 
the friction on this element is JusiP, where / and n are constant for 
any given kind of surface. Let o be the angular velocity of rotation, 
R the radius of the disk. Consider a ring of the surface between r and 
r+dr. Its area is 2wrdr, its velocity *r and the friction of this ring 
is Jjrrdra*^. The moment of the friction about the axis of rotation 
fe TrmTlr^dr, and the total moment of friction for the two sides of 
the disk is 

M - 4»a-f/?r»"<fr - (4xa"/(n +3)}/R ,, ♦ , . 
If N is the number of revolutions per sec., 

M »|2" + V* + >N-/(» +3))/R**\ 
mnA the work expended in rotating the disk is 

M«-U"* , * 1,4f N** , /v*+3)l/ R,, * a 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 « 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 lit tie 
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 21. 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, 

e, -0-1328(1 -0002 11). ., 

where c, is the value of c for a bright brass 

disk 0-85 ft. in diameter at a temperature /° 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 FroucVs results on planks 

50 ft. Ipng. The values given are the resistances per square loot at 

10 ft. per sec. 

Frond*' s Experiments. 
Tinfoil surface . . . 0-232 
Varnish ..... 0-226 
Fine sand . . .' . 0-337 
Medium sand . . 0-456 

Disk Experiments. 
Bright brass . 0*202 to 0229 
Varnish . . 0-220 to 0233 
Fine sand . . 0-339 

Very coarse sand 0-587 to 0-715 



I 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 alt 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 di, be- 
tween cross sections at 
z and z+dz ft. above 
any horizontal datum 
line xx, the pressures at 
the cross sections being 
p and P+dp lb per 
square foot. Further, 
let Q be the volume of 
flow or discharge of the pipe per second, the area of a normal 
cross section, and x the perimeter of the pipe. The Q cubic feet, 
which flow through the space considered per second, weigh CQ lb, 
and fall through a height -dz ft. The work done by gravity is then 

a positive quantity if cfs is negative, and vice versa. The resultant 
pressure parallel to the axis of the pipe is P- (p+dp) --dp lb per 
square foot of the cross section. The work of this pressure on the 



Fig. 80. 

volume Q is 


The only remaining force doing work on the system is the friction 
against the surface of the pipe. The area of that surface is x di. 

The work expended in overcoming the frictional resistance per 
second is (see | 66, eq. 3) 

-rG X dfrV2r. 
or. since O ° fJv. 
or. since y . -rGWmQWiWi 



the negative sign being taken because the work Is done against a 
resistance. Adding all these portions of work, and equating the 
result to ifero, since the motion is uniform, — 

Dividing by GQ, 



*+#G+r(x/Q)(t*/2«)/=constant. (i) 

( 72. Let A and B (fig. 81) be any two sections of the pipe for 
which P, t, I have the values Pi, *i, /1, and p», *>, It, respectively. 

or, if 1% -A - L, rearranging the terms, 

M*t - (i/L)|(*i+*/G) - (sj+^OWx- (2) 

Suppose pressure columns introduced at A and B. The water will 
rise in those columns to the heights prfG and Pi/G due to the 


batum £in« 

Fig. 81. 

G) is 
,-cl of 
re no 
be no 
me at 
pe of 
r the 

ins is 

introduang these values, 

JvV2g-m»/L-«». (3) 

For pipes of circular section, and diameter d t 

Then l*Vax-l<f*/L-lrfi; (4) 

or A-r(4Wrf)(^/2g); M 

which shows that the head lost in friction is proportional to the 
head due to the velocity, and is found by multiplying that head by 
the coefficient 4fL/d. It is assumed above that the atmospheric 
pressure at C and D is the same, and this is usually nearly the case. 
But if C and D are at greatly different levels the excess of baro- 
metric pressure at C. in feet of water, must be added to p*(G. 

I 73- Hydraulic Gradient or Line of Virtual Slope.— Join CD. 
Since the head lost In friction is proportional to L, any intermediate 
pressure column between A and B will have its free surface on the 
line CD, and the vertical distance between CD and the pipe at any 
point measures the pressure, exclusive of atmospheric pressure, in 
the pipe at that point. If the pipe were laid along the line CD 
instead of AB, the water would flow at the same velocity by gravity 
without any change of pressure from section to section. Hence CD 
is termed the virtual slope or hydraulic gradient of the pipe . It is 
the line of free surface level for each point of the pipe. 

If an ordinary pipe, connecting reservoirs open to the air, rises at 
any joint above the line of virtual slope, the pressure at that point 
is less than the atmospheric pressure transmitted through the pipe. 
At such a point there is a liability that air may be disengaged from 
the water, and the flow stopped or impeded by the accumulation of 
air. If the pipe rises more than 34 ft. above the line of virtual slope, 
the pressure is negative. But as this is impossible, the continuity 
of the flow will be broken. 

If the pipe is not straight, the line of virtual slope becomes a 
curved line, but since in actual pipes the vertical alterations of level 
are generally small, compared with the length of the pipe, distances 
measured along the pipe .are sensibly proportional to distances 


measured along the horizontal projection of Che pipe. Hence the 
line of hydraulic gradient may be taken to be a straight line without 
error of practical importance. 

I 74. Case of a Uniform Pipe connecting two Reservoirs, vken aU the 
Resistances are taken into account. — Let a (fig. 82) be the difference 
of level of the reservoirs, and v the velocity, in a pipe of length L 
and diameter d. The whole work done per second is virtually the 
removal of Q cub. ft. of water from the surface of the upper 
reservoir to the surface of the lower reservoir, that b GQ* foot- 
pounds. This is expended in three ways. (!) The head t*/2g, corre- 
sponding to an expenditure of GQr/2g foot-pounds of work, is 
employed in giving energy of motion to the water. This is ulti- 

.>£fe_ -v 

Fie. 82. 

mately wasted in eddying motions in the lower reservoir. (2) A 
portion of bead, which experience shows may be expressed in the 
form Stffrg, corresponding to an expenditure of GQ$*?i2g foot- 
pounds of work, is employed in overcoming the resistance at the 
entrance to the pipe. (3) As already shown the head expended ia 
overcoming the surface friction of the pipe is f (4L/4) (vVag) correspond- 
ing to GQ{(4L/d)(v'/2g) foot-pounds of work. Hence 

GQ* -GQ»*/2*+GQr*V2g+CQr4L V/*2g; 

A-<i+rt+r.4L/rf)s«/a f . 1 

»-8025VlW/Ki+Wd+4fLlJ. J 


If the pipe b bellmouthcd, ft is about * 08. If the entrance to 
the pipe is cylindrical, (•■0*505. Hence i+f»-i-o8 to 1505. 
In general this is so small compared with ULfd that, for practical 
calculations, it may be neglected ; that is, the losses of head other 
than the loss in surface friction are left out of the reckoning. It 
is only in short pipes and at high velocities that it is necessary to 
take account of the first two terms in the bracket, as weil as the 
third. For instance, in pipes for the supply of turbines, v h usually 
limited to 2 ft. per second, and the pipe is bellmouthed. Then 
i-o8tl/2f>> 0*067 ft. In pipes for towns' supply v may range from 
2 to if ft. per second, and then i*5*>/2f -o-i to 0-5 ft. In either 
case this amount of head is small compared with the whole virtual 
fall in the cases which most commonly occur. 

When d and v or d and h are given, the equations above are solved 
quite simply. When v and h are given and d is required, it b better 
to proceed by approximation. Find an approximate value of d by 
assuming a probable value for f as mentioned below. Then froo 
that value oftf find a corrected value for f and repeat the calculation. 

The equation above may be put in the form 

*- UfAOlK- +r.W4r)+Ll>V2r; (6) 

from which it is clear that the bead expended at the mouthpiece is 
equivalent to that of a length 

of the pipe.' Putting l+f "i'5°5 "id f*-o*oi, the length of pipe 
equivalent to the mouthpiece b 37-6 d nearly. This may be added 
to the actual length of the pipe to allow for mouthpiece resistance 
in approximate calculations. 

{ 75. Coefficient of Friction for Pipes discharging Water. — From the 
average of a large number of experiments, the value of f for ordinary 
iron pipes b 

r-0.007567. (7) 

But practical experience shows that no single value can be taken 
applicable to very different cases. The earlier hydraulicians occupied 
themselves chiefly with the dependence of {- on the velocity. Havmt 
regard to the difference of the law of resistance at very low and 
at ordinary velocities, they assumed that j" might be expressed in the 

f- *+$!* 
The following are the best numerical values obtained for t so «• 


R.deProny (from 51 experiments) . . . 

J . F. d'Aububson de Voisins 

J. A. Eytelwein ........ 





Webbach proposed the formula 

4f - «+£/V »- 0003598 +0004289/ v>. 



§ 76. Darcy s Experiments on Friction in Pipes.— All previous 
xperiments on the resistance of pipes were superseded by the re- 
narkable researches carried out by H. P. G. Darcy (1803-1858). the 
Inspector-General of the Paris water works. His experiments were 
arried out on a scale, under a variation of conditions, and with a 
iegree of accuracy which leaves little to be desired, and the results 
>btained are of very great practical importance. These results may 
je stated thus: — # 

1. For new and dean pipes the friction vanes considerably with 
he nature and polish of the surface of the pipe. For dean cast 
ron it is about If timesas great as for cast Iron covered with pitch. 

2. The nature of the surface has less influence when the pipes 
ire old and incrusted with deposits, due to the action of the water. 
rhus old and incrusted pipes give twice as great a frictional resist- 
toce as new and dean pipes. Darcy 's co effi ci en ts were chiefly 
letermined from experiments on new pipes. He doubles these co- 
.mcients for old and incrusted pipes, in acco r da n ce with the results 
)f a very limited number of experiments on pipes containing incrus- 
ations and deposits. 

3. The coefficient of friction may be expressed in the form 
:-a+0/»; but in pipes which have been some time in use it is 
efficiently accurate to take f — •* simply, where at depends on the 
iiametcr of the pipe alone, but a and ft on the other hand depend 
x>th on the diameter of the pipe and the nature of its surface. The 
ollowing are the values of the constants. 

For pipes which have been some time in use, neglecting the term 
jcpenaing on the vdodty ; 



r-a(i +#«*). 



For -drawn wrought'iron or smooth cast- 
iron pipes 

For pipes altered by light incrustations . . 



These coefficients may be put in the following very simple form, 
without sensibly altering their value:— 

For clean pipes . . . .,. f^ -005(1 +i/ia<f) ) ',_* 
For slightly incrusted pipes . f--oi(i+i/wi) ) vv "' 

Darcy' s Value of Ike Coefficient of Friction f for Velocities not less 
than 4 in. per second. 


of Pipe 

in Inches. 






•01 167 
•01 143 


of Pipe 

in Inches. 








•0102 r 

These values of f are, however, not exact for widely differing 
elocities. To embrace all cases Darcy proposed the expression 

r-(a+o I /aO+(0+A/*)/iF; 


•hich isa modification of Coulomb's, including terms expressing the 
lfluence of the diameter and of the velocity. For dean pipes Dai 
jund these values 

a -•004346 

oi- •0003902 


fit » '000005205. 

It has become not uncommon to calculate the discharge of pipes 
y the formula of E. Ganguillet and W. R. Kutter. which will be 
iscussed under the head of channels. For the value of c in the 
rlation p-cV(mi), Ganguillet and Kutter take 

41 '6-f I -811/11-1-0028 1 A* x > 
here n is a coefficient depending only on the roughness of the pipe, 
or pipes uncoated as ordinarily laid n -0013. The formula is very 
timorous, its form is not rationally justifiable and it is not at all 
ear that it gives more accurate values of the discharge than shnplr- 

f 77. Later Investigations on Flaw in Pipes.— The foregoing star 
icnt gives the theory of flow in pipes so far as it can be put in 
mple rational form. But the conditions of flow are really mot 
implicated than can be expressed in .any rational form. Taking 

jeven selected experiments the values of the empirical coefficient ; 
range from 0-16 to 0*0028 in different cases. . Hence means of dis 
criminating the probable value of fare necessary in using the equa 
tions for practical purposes. To a certain extent the knowledge tha 
f decreases with the site of the pipe and increases very much wit I 
the roughness of its surface is a guide, and Darcy 's method of deal 
ing with these causes of variation is very helpful. But a furthe 
difficulty arises from the discordance of the results of different ex 
perimrnts. For instance F. P. Steams and J. M. Gale both experi 
mented on clean asphalted cast-iron pipes, 4 ft. in diameter. Ac 
cording to one set of gauging* f--c©5i, and according to the othe 
f ■ •0031. It is impossible in such cases not to suspect some error ii 
the observations or some difference in the condition of the pipes no 
noticed by the observers. 

It Is not likely that any formula can be found which will givt 
exactly the discharge of any given pipe, . For one of the chief factor 
in any such formula must express the exact roughness of the pip 
surface, and there is no scientific measure of roughness. The mos 
that can be done is to limit the choice of the coefficient for a pip 
within certain comparatively narrow limits. The experiments 01 
fluid friction show that the power of the velocity to which thi 
resistance is proportional is not exactly the square. Also in deter 
mining the form of his equation for f Darcy used only eight out of hi 
seventeen series of experiments, and there is reason to think that son* 
of these were exceptional. Barre de Saint- Venant was the first ti 
propose a formula with two constants, 
<tt/4/-wV« f 

where m and n are experimental constants. If this is written in th 

log m +* log v -log (A/4J), 

we have, as Saint- Venant pointed out, the equation to a straigh 
line, of which m is the ordinate at the origin and n the ratio of tin 
slope. If a series of experimental values are plotted logarithmically 
the determination of the constants is reduced to finding the straigh* 
line which most nearly passes through the plotted points. Saint 
Venant found for n the value of 171. In a memoir on the influeno 
of temperature on the movement of water in pipes (Berlin, 1854) b' 
G. H. L. Hagen (1797-1884) another modification of the Saint-Venan 
formula was given. This is h/l-mV/d; which involves three ex 
perimental coefficients. Hagen found *■ 1*75; *— 1*25; and « 
was then nearly independent of variations of 9 and d. But the rang 
of cases examined was smalt In a remarkable paper in the Tram 
Roy. Soc., 1883, Professor Osborne Reynolds made much clearer th 
change from regular stream line motion at low velocities to th 
eddying motion, which occurs in almost all the cases with which th 
engineer has to deal. Partly by reasoning, partly by inductioi 
from the form of logarithmically plotted curves of experimenta 
results, he arrived at the general equation k/l-c(v m /d*-~)F t -' 
where n » 1 for low velodties and n — 1 -7 to 2, for ordinary velocities 
P b a function of the temperature. Neglecting variations of tempera 
ture Reynold's formula is identical with Hagcn's if *— 3-*. Fo 
practical purposes Hagen s form is the more convenient. 

Values of Index of Velocity. ' 


Surface of Pipe. 


of Pipe 
in Metres. 

Values of ». 

Tin plate . . . 

Bossut . . . 

J -036 



Wrought iron (gas I 
P»PC) J 

Hamilton Smith 

OI 59 
" -014 



Lead • . • . 

Darcy • . * 

• »027 

I 041 



. 177 

Clean brass • . 

Mair . . . 

1-795 1*795 


Hamilton Smith 

• 0266 


Asphalted . . \ 

Lampe . . . 
W. W. Bonn . 

. -4185 

1 850 
1 •582 

• 1-85 


Stearns . . . 

k I«2I9 


Riveted wrought 1 
iron | 



Hamilton Smith 

' -3*19 


• 187 

, -3749 


Wrought iron (gas 1 
P»pe) f 



Darcy . . . 

• -0266 

. ,0 3 95 

- 1-87 


New cast iron 

Darcy . . . 



' 1-95 

Cleaned cast iron . 

Darcy . . . 

2 -COO 

- 2 OO 

I -397 
f -0359 


Incrusted cast iron 

Darcy . . . 


I-OQOV 2*00 

I -2432 

I -990 J 




Fig. 83. 

In 1886, Professor W. C Unwin plotted logarithmically all the 
most trustworthy experiments on now in pipes then available. 1 
Fig. 83 gives one such plotting. The results of measuring the slopes 
of the Ones drawn through the plotted points are given in the 

It wiH be seen that the valnes of the index n range from 172 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 mjd* 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 1 to 1, so 
that the value of x must be greater than unity. The following table 
gives the results and a comparison of the value of % and Reynolds's 
value 3~#. 

Kind of Pipe. 




Tin plate . . 

I 72 



Wrought iron (Smith). 
Asphalted pipes • . . 



I -2 IO 

. 1-85 



Wrought iron (Darcy) . 




Riveted wrought iron . 




New cast iron . . . 



i- 168 

Cleaned cast iron . » 




Incrusted cast iron 

2 -CO 

1 00 


m With the exception of the anomalous values for Darcy's wrought- 
tron pipes, there is no great discrepancy between the values of x and 
3-«, but there is no appearance of relation in the two quantities. 
For the present it appears preferable to assume that x is independent 
of «. m 

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. 

Formulae for the Flow of Water in Pipes," Industries (Man- 
-. 1886). 

Here, considering the great range of diameters and velocities in 
the experiments, the constancy of m is very satisfactorily dose. 
The asphalted pipes give rather 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. 

Kind of Pipe. 


Value of 




of m. 

Tin plate 

4 [0*027 




Wrought iron 



Hamilton Smitn 




Hamilton Smith 


•02058 1 




•02107 1 

•OI83I • 




•01650 f 







•02x07 J 




' wrought iron 


* 0-375 


•01390 ► 


Hamilton ^r»?tH 


New cast iron' 



•01427 . 





Cleaned cast 




■ 0-245 

•02091 ' 



Incrusted cast 

- o-o8o 

•03530 • 




General Mean Values of Constants. 
The general formula (Hagen's) — h/l*m*fd'.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. 




Tin plate • .- 3 ? . 




Wrought iron J » * 

Asphalted iron ; ? '. 




Riveted wrought iron . 




New cast iron . . , •; 



Cleaned cast iron .* >. 




Incrusted cast iron 

1 160 


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. 
r It only remains to give the values of these coefficients when the 

{juantities arc expressed in English feet. For English measures the 
ollowing are the values of the coefficients: — 

Kind of Pipe. 




Tin plate • a ■: Y . 




Wrought iron T » j r . 
Asphalted iron .* 'J '. 




Riveted wrought iron . 

I -390 


New cast iron . . . 




Cleaned cast iron *t k . 


11 68 


Incrusted cast iron 




§ 78. Distribution of Velocity in the Cross Section of a Pipe— Duxy 
made experiments with a Pitot tube in 1850 on the velocity at 
different points in the cross section of a pipe. . He deduced the 

where V is the velocity at the centre and » the velocity at radius r in 
a pipe of radius R with a hydraulic gradient *. Later Bazin repeated 
the experiments and extended them {Mim. de VAcadimie des Sciences, 
xxxii. No. 6). The most important result was the ratio of mean to 
central velocity. Let b - R«'/U\ where U is the mean velocity in the 
pipe; then V/U=i+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. 

f 79. Influence of Temperature on the Flaw through Pipes —Very 
careful experiments on the flow through a pipe 0*1236 ft in diameter 

Fig. 84. 

and 35 ft. lone, with water at different t e m p erat u r es, have been 
made by J. G. Mair {J* roc. 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 1} 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 a» V' w , the index being less than 2 as in 
other experiments with very smooth surfaces. Taking the ordinary 
equation of flow A— r(4L/p}(t > /2f ), 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. 



•0044 to '0052 
•0042 to -0045 
•0041 to '0045 
0040 to 0045 



•0039 tO '0043 

•0037 to -0041 
.•0037 to -0041 
•0035 to -0039 
•0035 to -0038 

Fig. 85. 

main. At Lancaster after twice scraping the discharge was increased 
56} % at Oswestry 54$ %. 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) m. 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 


organic growth. Filtration of the water appear* 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, Proc Inst. Cw. Eng., 

i ZiTTlow of Water through Fire Host.— 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. xxL, 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* Thenp-wV(ri). 




per min. 




Solid rubber ( 

hose \ 
Woven cotton, < 

rubber lined r 
Woven cotton, c 

rubber lined < 
Knit cotton, ( 

rubber lined t 
Knit cotton, ( 

rubber lined < 
Woven cotton, 5 

rubber lined < 
Woven cotton, 5 

rubber lined < 
Unlined linen 5 

hose I 











1 2*50 












III 6 
100- 1 




§ 82. Reduction of a Long Pipe of Varying Diameter to an Equivalent 
Pipe of Uniform Diameter. Dupnit'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. 


._ %.. 

— i 




Fig. 86. 

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. Jt». be the lengths, 

di, d%... the diameters, 

■k, **.~ the velocities, 

i'u «t-« the slopes, 
for the successive portions, and let /, d, *■ and * be corresponding 
quantities for the equivalent uniform main B. The total loss of 
head in A due to friction is 



and in the uniform main 


If the mains are equivalent, as defined above, 

r(s«.4//2£d)-r(»i , -4/i/2riO+r(«% , -4V2fd,)+r.. 1 

But, since the discharge is the same for all portions, 

Also suppose that f may be treated as constant lor "all the pipes. 

which gives the length of the equivalent uniform main which would 
have the same total Joss of head for any given discharge. 


§ 83. Other Lotus of Hood in Pipes— Moat of the losses of head in 
pipes, other than that due to surface friction against the pipe, are doe 

-- -1 -1 ;- «■•-- — 1 — !•-- -t «u_ _ —— J Mrfng C 4 ** 1 — 

to abrupt changes in the velocity of the stream produ _ 

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 *» to an area <* (fig. 
87) ; then 

or. if the section is circular, 

The head lost at the abrupt change 
of velocity has already been 
shown to be the head due to the 
relative velocity of the two parts 
of the stream. Hence head lost 




fc- (»»-!>i) f /2«- («l/-p- 1 W/2*- {(«V4)«-I r*i>i*g 
or h,-r*iV2*. («) 

if f. Is put for the expression in brackets. 


















X*S t.n 

ijc i-u 


141 «4l 1.M 




a-U tM 





JJ -« ^4 






9.0s itjoc 

i$jso 364 »* 

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. 88. 

Flc. 89. 

Let w be the section and • the velocity of the stream at bh. Mm 
the section will be c««#, and the velocity («*/««<•»)» "ft/ci, where c. m 
the coefficient of contraction. Then the head lost is 

and, if «. is taken 0-64, 

• $*- 0-316 s«/2g. (a) 

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 »»/2g. (3) 

If there is a diaphragm at the mouth of the pipe as in fig. 69, let •« 
be the area of this orifice. Then the area of the contracted stream 
is c**i, and the head lost is 


-t*ln (4) 

if T, is put for Kw/ccwO^i)*. Weisbach has found experimentally 
the following values of the coefficient, when the stream approadnag 
the orifice was considerably larger than the orifice : — 































1. 169 



When a diaphragm was placed in a tube of uniform section (fig. 90) 

Fig. 90. 

the following values were obtained, «« being the area of the- orifice 
and m that of the pipe:— »- * 

mi/m — 
























47 77 












S&owrv—Weisbach consider* the toss of head at elbows (fig.91) 
to be due to a contraction formed by thettream. From experiment* 
with a pipe 1 J in. diameter, he found the low of head 

b-tJlHi (5) 

£.-0-9457 ain»te+2-047 sin* fe. 

M* 40* 
0^46 1 O.IJO 





«o # 







Hence at a right-angled elbow the whole head due to th« velocity 

very nearly is lost, 
fitfndr.— Weisbach traces the loss ot head at curved bend* 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 

U-t&te; (6) 

where d is the diameter 
of the pipe and p the 
radius of curvature of 
the bend. The resistance 
at bends Is small and at present very ill determined. 

Valves, Cocks and Sluices. — These prjpduce a contraction of the 

B water-stream, similar to that for an abrupt 
diminution of section already discussed. The 
loss of head may be taken as before to be 
k-tJtei. (7) 

where v is the velocity in the pipe beyond the valve 

and f. a coefficient determinedly experiment. The 

following are VVeisbach's results. 
c Sluice in Pipe of Rectangular. Section (fig. 92). 

no. 92. Section at sluice -«i in pipe ■«. 

1 «iA*— i-o o«9 o-8 
ft- o-oo -09 -39 












Sluice in Cylindrical Pipe (fig. 93). 

feife of bdebt on 

openbg to dfauMtcr V 


to i 
t.oo I 094S 
0.00 1 0.07 





. * 







Fig. 93. Fio. 94. 

Cmck in a Cylindrical Pipe (fig. 94). Angle through which cock 
is turned — 0. 







30 # 


Ratio of] 









sections J 

















Ratio of 1 

cross > 







sections J 

r - 


31 2 






ThroilU Vain in a Cylindrical Pipe (fig. 95). 



















45 - 









■ on the Flow of Water in Pipes.— In 
will be assumed that the pipe is of so 



■ ^ Fig. 95. 

t f 76) for the solution of such problems 

as arise.— 

f-aO+i/ia*); (1) 

where a -0-005 for new and -o-oi for incrusted pipes. 

^/2g-i<K. (2) 

Q-W*. (3) 

Problem 1. Given the diameter of the pipe and Its virtus! slope, 
to find the discharge and velocity of flow. Here d and » are given, 
and Q and v are required. Find f from (1) ; then * from (2) ; lastly 
Q from (3). This case presents no difficulty. 
By combining equations (1) and (2), » is obtained directly:— 

• -VUcf*72f)-V(sV2a)VW»/ll + i/l2J]]. (4) 

For new pipes . . . V(f/2a)-> 56-72 
For incrusted pipes . .-40-13 

For pipes not less than 1, or more than 4 ft. in diameter, the 
mean values of f are 

For new pipes ...... 0-00526 

For incrusted pipes ..... 001052; 

Using these values we get the very simple expressions— 

•-55-3WW) for new pipes 1 (4a) 

- 39*11 V («•) for incrusted pipes) 
Within the limits stated, these are accurate enough for practical 

s.iiy M t j, e precis value of the coefficient f cannot 

special case. 

11 the diameter of a pipe and the velocity of flow, 
to slope and discharge. The discharge is given by 

(j ilue of f by (1); and the virtual slope by (2). 

u no special difficulty. 

n the diameter of the pipe and the discharge, to 
fin >pe and velocity. Find 9 from (3); f from (1); 

lai If we combine (1) and (2) we get 

- .(»«/2«)(4/cO-2tt|i+i/i2rfls»/«d; (5) 

and, taking the mean values of f for pipes from 1 to 4 ft. diameter, 
given above, the approximate formulae are 

i -0-0003268 s*/(f for new pipes } (5a) 

-0-0006536 +jd for incrusted pipes J 
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 (he quadratic expression 
d» - d(2os«/£i) - a**/6fi - o. 
.•.s?-atVtf+V|(s»W> («W+i/6)l. (6) 

For practical purposes, the approximate equations 

0*-2o*Vfi-H/i2 (6a) 

-0-00031 »»/<+'o83 for new pipes 
-0-00062 » , /i-i"083 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— 

rf»-^fQ»/rrH. (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 I to 4 
ft. diameter we get 

d-V(32f/«tr»)V(QV0 (8) 

-0-2216 V (QVO for new pipes 
-0-2541 V(QVO fw incrusted pipes; 
equations which are interesting as showing that when the value of 
t is doubled the diameter of ptpe for a given discharge is only in- 
creased by 13% 




(6) A second method It to obtain a rough value ofrfby assuming 
f— «. This value is 

tf-VCsaOVrrW— 06319 V(QV0Va 
Then a very approximate value of f is 

and a revised value of i, not sensibly differing from the exact value, 

<*'-V(32QV*w«0Vf -0-6319 VXQVOVf . 
(0 Equation 7 may be put in the 

' Expanding the term in brackets, 
V (1 +i/t*rf) - 1 +i/6oi-i/i8ood>... 
Neglectingthe termsafterthe second, 
d-1(vlF>)V(Q t li).U+if6od) 

-V(3Wf» , )V(Q , /^-fo-oi667;(9a) 
VteWf" 1 ) -0*219 'or new pipes 

-0-352 forincrustcd pipes. 

storage reservoir or by pumping 
: reservoir should contain three 
ises much more. Its elevation 
red at a pressure of at least about 
iistrict. The greatest pressure in 
, the pressure Tor which ordinary 
ience if the district supplied has 

if the average demand is 25 gallons per head per day, the 1 
should be calculated for 50 gallons per head per day. 

{ 86. Determination of Ike Diameters of Different Parts of a Water 
Main. — When the plan of the arrangement of mains is determined 
upon, and the supply to each locality and the pressure required is 
ascertained, it remains to determine the diameters of the pipes. Let 
fig. 97 show an elevation of a main ABCD. . ., R being the reservoir 
bom which the supply is derived. Let NN be the datum fine of rhe 
levelling operations, and H*. Hi... the heights of the main above 
the datum line, H, being the height of the water surface in the 

_. Jr.— irittjsUflaf .2xs. . 
i I 

V-Lom Le nd Zont— * j 

Fig. 96. 

great variations of level it must be divided into tones of higher and 
lower pressure. Fig. 96 shows a district of two zones each with its 
service reservoir and a range of pressure in the lower district from 
100 to 200 ft. The total supply required is in England about 25 

E lions per head per day. But in many towns, and especially in 
nerica, the supply is considerably greater, but also in many cases 

Fig. 97. 

8 good deal of the supply is lost by leakage of the mains. The supply 
through the branch mains of a distributing system is calculated from 
the population supplied. But in determining the capacity of the 
mains the fluctuation of the demand must be allowed for. It is usual 
to take the maximum demand at twice the average demand. Hence 

Fig. 98. 

reservoir from the same datum. Set up next heights AAi, BB,.... 
representing the minimum pressure height necessary for the adequate 
supply of each locality. Then A1B1C1D1... is a line which should 
form a lower limit to the line of virtual slope. Then if heights 
$«, V W. are taken representing the actual losses of head in each 
length /•• /», /«... of the main, AoBoC* will be the line of virtual 
slope, and It will be obvious at what points such as D» and E* the 
pressure is deficient, and a different choice of diameter of main it 
required. For any point s in the length of the main, we have 
Pressure height - H, - H. - (J. +fc +. . .$.). 
Where no other circumstance limits the loss of head to be a ss i gned 
to a given length of main, a consideration of the safety of the main 
f rom iracture by hydraulic shock leads to a limitation of the velocity 
of flow. Generally the velocity in water mains lies between 1 \ and 
4 1 ft. per second. Occasionally the velocity in pipes reaches 10 ft. 
per second, and in hydraulic machinery working under enormous 
pressures even 20 ft. per second. Usually the velocity diminishes 
along the main as the discharge diminishes, so as to reduce somewhat 
the total lots of head which is liable to render the pressure insufficient 
at the end of the main. 

J. T. Fanning gives the following velocities as suitable in pipes 
for towns' supply: — 

Diameter in inches ... 4 8 12 18 24 30 36 
Velocity in feet per tec . . 2*5 3*o 3*3 4-5 5«3 6«2 7-0 
§ 87. Branched Pipe connecting Reservoirs at Different Levels. — Let 
A, B, C (fig. 98) be three reservoirs connected by the arrangement of 

E'pes shown,—/,, a\, Qi, *r, /», a\, 0*^ »i; '•• *%• Q* »i being the 
ngth, diameter, discharge and velocity in the three portions of 
the main pipe. Suppose the dimensions and positions of the pipes 
known and the discharges required. 

If a pressure column is introduced at X, the water will rise to a 

height XR, measuring the pressure at X, and aR. R6, Re will be the 

lines of virtual slope. If .the free surface level at R is above ft, the 

reservoir A supplies B and C. and if 

R is below b, A and B supply C 

Consequently there are three cases:— 

I. R above ft; Qi-ft+Q». 

II. R level with b; Qi-Qa; Q1-0. 

III. R below t;Qi+Qi-Q«- 

To determine which case has to be 

dealt with in the given conditions, 

suppose the pipe from X to B dosed 

by a sluice. Then there is a simple 

main, and the height of free surface 

A' at X can be determined. For .this 


where Q/ is the common discharge 
of the two portions of the pipe. 

<*.-*')/(*'-*.) -M.VW. 
from which k' it easily obtained. If then k' 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 k' is less than h h , opening the shrice 
will allow flow from B, and the case is case III. If A' -A* the cast 
is case II., and is already completely solved. 




The true value of A mutt lie between A' and A*. Choose a new 
value of A, and recalculate Qi, Q>, Q*. Then if 

or Ql+Qi>Q<incaaelII., 

the value chosen for A is too small, and a new value must be chosen. 

If .- 

or Qi+Qi<QiincaseIII., 

the value of A is too great. 

Since the limits between which A can vary are in practical cases not 
very distant, it is easy to approximate to values sufficiently accurate. 

ft 88. Water Hammer. — If in a pipe through which water is flowing 
a sluice is suddenly closed so as to arrest the forward movement ol 
the water, there is a rise of pressure which in some cases is serious 
enough to burst the pipe. This action is termed water hammer or 
water ram. The fluctuation of pressure is an oscillating one and 
gradually dies out. Care is usually taken that sluices should only be 
closed gradually and then the effect is inappreciable. Very careful 
experiments on water hammer were made by N. J. Joukowsky at 
Moscow in 1898 (Stoss in Wasserleitungen, St Petersburg, 1900), and 
the results arc generally confirmed by experiments made by E. B. 
Weston and R. C. Carpenter in America. Joukowsky used pipes, 
a, 4 and 6 in. diameter, from 1000 to 2500 ft. in length. The sluice 
closed in 0*03 second, and the fluctuations of pressure were auto- 
matically registered. The maximum excess pressure due to water- 
hammer action was as follows :— 

Pipe 4-in. diameter. 

Pipe 6-in. diameter. 

ft. per sec. 

Excess Pressure, 
lb per sq. in. 

ft. per sec 

Excess Pressure, 
lb per sq. in. 


9 2 





In some cases, in fixing the thickness of water mains, 100 lb per sq. in. 
excess pressure is allowed to cover the effect of water hammer. 
With the velocities usual in water mains, especially as no valves can 
be quite suddenly closed, this appears to be a reasonable allowance 
(see also Carpenter, Am. Soc Meek. Eng., 1893). 

f 80. Flow of Air in Long Pipes.-— When air flows through a long 
pipe, by far the greater part of the work expended is used in over- 
coming factional resistances due to the surface of the pipe. The 
work expended in friction generates heat, which for the most part 
must be developed in. and given back to the air. Some heat may 
be transmitted through the sides of the pipe to surrounding materials, 
but in experiments hitherto made the amount so conducted away 
appears to be very small, and if no heat is transmitted the air in the 
tube must remain sensibly at the same temperature during expansion. 
In other words, the expansion may be regarded as isothermal 
expansion, the heat generated by friction exactly neutralizing the 
cooling due to the work done. Experiments on the pneumatic tubes 
used for the transmission of messages, by R. S. Culley and R. Sabine 
(Proc. Inst. Ct». Eng. xliii.), show that the change of temperature of 
the air flowing along the tube is much lest than it would be in adia* 
batic expansion. 

ioo. Differential Equation of the Steady Motion of Air Flowing in 
mg Pipe of Uniform Section. — When air expands at a constant 
absolute temperature r, the relation between the pressure p in 
pounds per square foot and the density or weight per cubic foot G 
is given by the equation 

/>/G-cr, (1) 

where c • 53* 15. Taking r - 52 1 , corresponding to a temperature of 
6o° Fahr., 

cr- 27690 foot-pounds. (2) 

The equation of continuity, which expresses the condition that in 
steady motion the same weight of fluid, W, must pass through each 
^^^^^^^^^^^^^^^^^^^ cross section of the stream in 
■■■■■■■■■■■■■■■■■t, the unit of time, 

GQu-W -constant, (3) 

where Q is the section of the 
pipe and u the velocity of 
the air. Combining (t) and 

Qȣ/W-ct = constant. (30) 

Since the work done by 

Fie. 99. gravity on the air during its 

flow through a pipe due to 

variations of its level is generally small compared with the work 

done by changes of pressure, the former may in many cases be 


Consider a short length dl of the pipe limited by sections A», A| at 
a distance dl (fig. 99). Let p, u be the pressure and velocity at Ao, 
p+dp and u+du those at Aj. Further, suppose that in a very short 

j«- — ;..<«.— 



time it the mass of air between A0A1 comes to A'#A'i so that A|A'« - 
udi and A, AS * (« +du)dt x . Let Q be the section, and m the hydraulic 
mean radius of the pipe, and W the weight of air flowing through the 
pipe per second. 

From the steadiness of the motion the weight of air between the 
sections A*A't, and A»A\ is the same. That is, • 
Wdf - GQudt - GQ(« +du)dt. ^ 
By analogy with liquids the head lost in friction is, for the length 
? ("? * ??. eo. 3), tW2g)(dl/m). Let H -*»/*£. Then the head 
lost is r(H/m)o7; and, since Ytdt lb of air flow through the 
pipe in the time considered, the work, expended in friction is 
— f (H/m) Wdf dt. The change of kinetic energy in dt seconds is the 
difference of the kinetic energy of AoA'o and AiA'i, that is, 
(W1g)dt\{*+du)'-**\l2-(W/g)ududt-WdUdL ^ 
The work of expansion when Qudt cub. ft. of air at a pressure 
p expand to Q(u+du)dt cub. ft. is QpdudL But from (30) 
u-crW/Qf, and therefore 

And the work done by expansion is— (crW/£)d>& 

The work done by gravity on the mass between Ao and Ai is zero 
if the pipe is horizontal, and may in other cases be neglected without 
great error. The work of the pressures at the sections A#A| is 
pOudt - (p+d p)Q(u -\-du)dt 
But from (3a) 

p* — constant, 
and the work of the pressures is zero. Adding together the quantities 
of work, and equating them to the change of kinetic energy, 


YldHdt --(cT\\/t>)dpdt-t(Hfm)Vtdldt 
rfH/H + (cTjnp)dp+{dl/m - 


.•.a , H/H+(2*tf/>/crW*)4>+ tdl/m -o. (4a) 

For tubes of uniform section m is constant; for steady motion W 
is constant ; and for isothermal expansion r is constant. Integrating, 

lc*H+gny/W»cr+tf/m -constant; (5) 

for /-o, let H-H«,and />-p»; 

and for /-/, let H-Hi, and p-pi. 

log (Hi/H.)+UQ»/W»cr) (Pi«-f/)+r'/*-o, (5a) 
where p* is the greater pressure and Px the less, and the flow » from 
At towards At. 
By replacing W and H, 

log(*//>,) +(rcr/itf/*»)(p 1 »-#) +ff/m -o. (6) 

Hence the initial velocity in the pipe is 

.. «o-Vlutcr(^-pi , )l/IMf/M+log(^^)}l. (7) 

When / b great, log p*lp\ is comparatively small, and then 

«.-V[(«cm/fO|(^-/h , )/A) t II, (7a) 

a very simple and easily used expression. For pipes of circular 
section «— a/4, where d is the diameter:— 

Ke-Vtterd/^ICitf-fcWI]; (7*) 

or aooroximatelv 




he obtained the following values — 



rate of 

e pipes 
and in 

1 pipes 


Diameter of Pipe 
in feet. 


f for 100 ft. 
per second. 


' 8 K 


•01 167 


It is worth while to try if these numbers can be expressed in the 
form proposed by Darcy for water. For a velocity of 100 ft. per 
second, and without much error for higher velocities, these numbers 
agree fairly with the formula 

f=ooo§(i+3/ioJ). (9) J 

whith only differs from Darcy s value for water in that the second 
term, which is always small except for very small pipes, Is larger. 



Some later experiments on a very large scale, by. E. Stockalper 
at the St Gotthard Tunnel, agree better with the value 
{- -0-0028(1 +3/iorf). 

These pipes were probably less rough than Arson's. 

When the variation of pressure is very small, it is no longer safe 
to neglect the variation of level of the pipe. For that case we may 
neglect the work done by expansion, and then 

ft-ei-fc/Gs-MW WH) CV») -o, <io) 

precisely equivalent to the equation for the flow of water, s» and t\ 
being the elevations of the two ends of the pipe above any datum, 
£0 and P\ the pressures. Go and Gi the densities, and v the mean 
velocity in the pipe. This equation may be used for the flow of 
coal gas. 

§ 92. Distribution of Pressure in a Pipe in which Air is Flowing. — 
From equation (70) it results that the pressure p, at I ft. from that 
end of the pipe where the pressure is pt, is 

p-poVli-r/^/w^rl; (») 

which is of the form 

for any given pipe with given end pressures. The curve of free sur- 
face level for the pipe is, therefore, a parabola with horizontal axis. 
Fig. 100 shows calculated curves of pressure for two of Sabine's 
experiments, in one of which the pressure was greater than atrao- 


Fig. 100. 



¥>heric pressure, and in the other less than atmospheric pressure, 
he observed pressures are given in brackets and the calculated 
pressures without brackets. The pipe was the pneumatic tube be- 
tween Fenchurch Street and the Central Station, 2818 yds. in length. 
The pressures are given in inches of mercury. 

Variation of Velocity in the Pipe. — Let p», «• be the pressure 
and velocity at a given section ot the pipe; p, u. the pressure and 
velocity at any other section. From equation (30) 
«p-crW/n- constant; * 
so that, for any given uniform pipe, 


*-*o/>o,>; (ta) 

which gives the velocity at any section in terms of the pressure, 
which has already been determined. Fig. 101 gives the velocity 

Fig. 101. 

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. 

1 93. Weight of Air Flowing per Second. — The weight of air dis- 
charged per second is (equation 3a) — 


From equation (76), for a pipe of circular section and diameter d, 

-•6nvfy&*-*.Wr}. (13) 


W-(-69l6A,-.4438/>0 WVtfr)!. (13a) 

§ 94. Application to the Case of 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 


than to telegraph by electricity. The tubes are laid underground 
with easy curves; the messages are made into a roll and placed is 
a light felt carrier, the resistance of which in the tubes in Lot 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 Tufte.— Putting { for the time of t 
from o to /, 

From (40) neglecting dH/H, and putting m-tf/4, 

From (1) and (3) 



.% I - gdcrfat-Pt^/topohif, 

"" )/60fl " 




" -Yw<p^b'fc(i*4ibt-pni 

If r-5*i*. corresponding to 6o* F., 

#— ooI4l2fl/^(^)'-^»)/<fl(^ , -^ , )^. 

which gives the time of transmission in terms of the initial and final 
pressures and the dimensions of the tube. 

Mean Velocity of Transmission. — The mean velocity is///; or, for 
r-521 , 

t^-o^oSVI^-pMrW-*')}. (16) 

The following table gives some results:— 

Pressures in 
lb per sq. in. 

Mean Velocities for Tubes of a 
length in feet. 








Vacuum ( . . 
Working { . . 

Pressure j • * 
Working ] • ' 








5 & 


43- 1 




Limiting Velocity in the Pipe when the Pressure at one End is 
diminished indefinitely. — If in the last equation there be put ^i-o, 

« / .« M -o-7o8V (<f/r/); 
where the velocity is independent of the pressure po at the other 
end, a result which apparently must be absurd. Probably for long 
pipes, as for orifices, there is a limit to the ratio of the initial and 
terminal pressures for which the formula is applicable. 


§ 05. Flow of Water in Open Canals and Rivers.— When water 
flows in a pipe the section at any point is determined by the form 
of the boundary. When it flows in an open channel with free upper 
surface, the section depends on the velocity due to the dynamical 

Suppose water admitted to an unfilled canal. The channel will 
gradually fill, the section and velocity at each point gradually 
changing. But if the inflow to the canal at its head is constant, 
the increase of cross section and diminution of velocity at each 
point attain after a time a limit. Thenceforward the section and 
velocity at each point are constant, and the motion is steady, or 
permanent regime is established. 

If when the motion is steady the sections of the stream are all 
equal, the motion is uniform. By hypothesis, the inflow Qx> is con- 
stant for all sections, and Q is constant; therefore v must be constant 
also from section to section. The case is then one of uniform steady 
motion. In most artificial channels the form of section is constant, 
and the bed has a uniform slope. I n that case the motion is uniform, 
the depth is constant, and the stream surface is parallel to the bed. 
If when steady motion is established the sections are unequal, the 
motion is steady motion with varying velocity from section to 
section. Ordinary rivers are in this condition, especially where the 
flow is modified by weirs or obstructions. Short unobstructed 
lengths of a river may be treated as of uniform section without great 
error, the mean section in the length being put for the actual sections. 

In all actual streams the different fluid filaments have different 
velocities, those near the surface and centre moving faster than 
those near the bottom and sides. The ordinary formulae for the 
flow of streams rest on a hypothesis that this variation of velocity 
may be neglected, and that all the filaments may be treated as having 
a common velocity equal to the mean velocity of the stream. On 
this hypothesis, a plane layer abab (fig. 102) between sections normal 


to the direction of motion is treated as sliding down the channel to 
a'a'b'b' without deformation. The component of the weight parallel 
to the channel bed balances the friction against the channel, and 
in estimating the friction the velocity of rubbing is taken to be the 
mean velocity of the stream. In actual streams, however, the 
velocity of rubbing on which the friction depends is not the mean 



variation of the coefficient of friction with the velocity, proposed at 
expression of the form 

*•-«(»+*/*>. ,_ . <5> 

and from 255 experiments obtained for the constants the 1 

a —0*007409 ; - o- 1920. 

This gives the following values. at different velocities:— 
















velocity of the stream, and is not in any simple relation with it, for 
channels of, different forms. The 
theory is therefore obviously based 
on an imperfect hypothesis. How- 
ever, by taking variable values for 
the coefficient of friction, the errors 
of the ordinary formulae are to a 
great extent neutralized, and they 
may be used without leading to 
practical errors. Formulae have 
been obtained based on less re- 
stricted hypotheses, but at present they are not practically so 
reliable, and are more complicated- than the formulae obtained in 
the manner described above. 

§ 96. Steady Flow of Water with Uniform Velocity in Channels of 
Constant Section. — Let aa\ bb' (fig. 103) be two cross sections normal 
to the direction of motion at a distance dl. Since the mass aa'bb' 
moves uniformly, the external forces acting on it are in equilibrium. 
Let Q be the area of the cross sections, x the wetted perimeter. 

Fie. 102. 

Fig. 103. 

bq+ qr+rs, of a section. Then the quantity tw-Q/x is termed the 
hydraulic mean depth of the section. Let v be the mean velocity 
of the stream, which is taken as the common velocity of all the 
particles, i, the slope or fall of the stream in feet, per foot, being 
the ratio befab. 

The external forces acting on aa'bb' parallel to the direction of 
motion are three: — (a). The pressures on aa' and bb\ which are 
equal and opposite since the sections are equal and similar, and tha 
mean pressures on each are the same. (&) The component of the 
weight W of the mass in the direction of motion, acting at its centre 
of gravity e. The weight of the mass aa'bb' is GQdl, and the com- 
ponent of the weight in the direction of motion is GQoVX the cosine of 
the angle between Wg and ab, that is, GQdl cos aU-GQdl bc(ab~ 
GQidl. (c) There is the friction of the* stream on the sides and 
bottom of the channeL This is proportional to the area -xdl of 
rubbing surface and to a function of the velocity which may be 
written /(r) ; /(v) being the friction per sq. ft. at a velocity v. Hence 
the friction is — xil /&). Equating the sum of the forces to zero. 

/(•,)/G-Q»7x-»u. (1) 

But it has been already shown (| 66) that/(») - fGtV2g, 

:.i*l2g-mu (2) 

This may be put in the form 

r - V (2f /f)V (mi) -*V 0*0 ; (»<*) 

where c is a coefficient depending on the roughness and form of the 

The coefficient of friction f varies greatly with the degree of 
roughness of the channel sides, and somewhat also with the velocity. 
It must also be made to depend on the absolute dimensions of the 
section, to eliminate the error of neglecting the variations of velocity 
in the cross section. A common mean value assumed for f is 0*00757. 
The range of values will be discussed presently. 

It is often convenient to estimate the fall of the stream in feet per 
mile, instead of in feet per foot. If/ is the fall in feet per mile. 


Putting this and the above value of t in (2a), we get the very simple 
and long-known approximate formula for the mean velocity of a 
stream — 

t-iW i?mf). (3) 

The flow down the stream per second, or discharge of the stream, 
is Q-Qv-fkVCmt). (4) 

i 97. Coefficient of Friction for Open Channels.— Various ex 
prcs&ions have been proposed Tor the coefficient of friction for 
channels as for pipes. Wciabach. giving attention chiefly to the 

In using this value of f when v is not known, it is best to proceed 
by approximation. 

§ 98. Darcy and Basin's Expression for the Coefficient of Friction.— 
Darcy and Bazin's researches have shown that f varies very greatly 
for different degrees of roughness of the channel bed, and that it 
also varies with the dimensions of the channeL They give for f an 
empirical expression (similar to that for pipes) of the form 

r-a(i +#*»); (6) 

where m is the hydraulic mean depth. For different kinds of 
channels they give the following values of the coefficient of friction :— - 

Kind of Channel. 


. I. Very smooth channels, sides of smooth 

cement or planed timber 



II. Smooth channels, sides of ashlar, brick- 

work, planks , . 



IIL Rough channels, sides of rubble masonry or 

pitched with stone ....... 



IV. Very rough canals in earth 



V. Torrential streams encumbered with detritus 


The last values (Class V.) are not Darcy and Bazin's, but are taken 
from experiments by Ganguillet and Kutter on Swiss streams. 

The following table very much facilitates the calculation of the 
mean velocity and discharge of channels, when Darcy and Basin's 
value of the coefficient of friction is used. Taking the general 
formula for the mean velocity already given in equation (2a) above, 

where c—iftegft), the following table gives values of c for channels 
of different degrees of roughness, and for such values of the hydraulic 
mean depths as are likely to occur in practical calculations:—- 

Values ofc in v »»cV (mi), deduced from Darcy and Basin* s Values, 














V s 























Jr 4 8 








% 99. Ganguillet and Kutter' s Modified Darcy Formate.— Starting 
from the general expression v-cV»m\ Ganguillet and Kutter 
examined the variations of t for a wider variety of cases than those 
discussed by Darcy and Basin. Darcy and Bazin's experiments 
were confined to channels of moderate section, and to .a limited 
variation of slope. Ganguillet and Kutter brought 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 tor the case of a stream of exception* 
ally large section and of very low slope. On the other hand, their 
own measurements of the flow in the regulated channels of some 

70 HYDRAULICS [flow in rivers 




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 vanes little near the 
centre of the stream, but very rapidly near the banks. In un- 
a symmetrical sections the greatest 

M *- ■* 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«tbe 
stream per second. Fig. 105 6hows 
the vertical and horizontal velocity curves and the contours of 
equal velocity in a rectangular channel, from one of Basin's 

§ ioj. 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. 

*,( \ .: |c...j : '%. 

Vertical Velocity 


'. JtotiiontpJ Velocity Curves : 

Verticil Velocity 

Contours of Equal 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 trie surface but at some distance below it. In various 
river gaugings the depth d, at the centre of the stream has been found 
to vary from o to o-xd. 

f 104. Influence of the 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 «\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, stiH 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 



Values of Coefficient tf/fr-f 35-4) in the Formu!av m ~cvJ(c+*S'4) . 

Mean Depth 



Ashlar or 


v XX2 h 















* 5 I 



•J 4 

















. , 





. , 



















, , 
















. . 

• • 






$ 107. ftarr 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 


Fig. 107 
l stream, 
lines CC 
the aides 
notion of 

( a river 
t is very 
a can be 
3 be the 
r in some 
■cnt con* 
be upper 

rf section 
nnel (ng. 
it can be 

g surface 

>ks on a 
irae form 
wis built 
but they 
» pitched 
(ng. no) 

Fig. 107. 

mucn 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 o( 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- 
InnerBanh 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 MN. 
Fie. 108. 

1, and let 
1 the area 

is always 
ninded in 
s on the 

one most 

^a^th, the 
latter the 

tort table 
s of water 
ion; then 
r and the 
have the 

Depth of water fat 
term* of cadius . . 

Hydraulic mean depth 
in terms of radius . 

Waterway in terms of 
square of radius . 























Jl 4 











| in. Big-Shaped Channels or Sewers.— In mwtn (ot w 

storm water ana bouse 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 consequent* becomes choked. 

In Bank f tn Cahinj ^ 

; ii • • » i 


flC. 112. 

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 is 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 
is shown i* fiff* US* the 
numbers marked on the 
figure being proportional 

1 112. Probltmt on 
Channels in which Ike 
Flow is Steady and at 
Uniform Velocity.—Tbe 
general equations given 
«o §§ 96. 98 «• 



Problem /.—Given the transverse section of stream and dis- 
charge, to find the slope. From the dimensions of the section 
find Q and m; from (ij find f, from (3) find v, and lastly from (2) 

Problem II. — Given the transverse section and slope, to find the 
discharge. Find v from (2). then Q from (3). 

Problem 77/.-»-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-§rf, where 
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 
leas error in the value of the velocity calculated from it, we may 
proceed thus. Assume a value for m, and calculate * from it. 
Let si be this first approximation to v. Then Q/r, is a first approxi- 
mation to 0. say Q». With this value of Q design the section of the 
channel; calculate a second value for m; calculate from it a second 

value of v, and from that a 

■ s second value for 0. Repeat 

^. I / the process till the succes- 

\j* -| / sive values of m approxi- 

mately coincide. 

S113. Problem IV. Most 
Economical Form of Channel 
r?. r ... for ghen Side Slopes.Sup- 

FlG. 114. -^ the channe i 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 

could be found satisfying the foregoing conditions. To 
the problem determinate, let it be remembered that, since for 
a given discharge Qoo -fxt other things being the same, the 
amount of excavation will ba least for that channel which has 
the least wetted perimeter. Let d be the depth and * the bottom 
width of the channel, and let the 
sides slope n horizontal to I vertical 
(fig. 114)., then 

, T-6+ady («*+i). 
Both Q and x are to be minima. 
Differentiating, and equating to 

d*/*f+2V (»'+!) -o; 
eliminating dbfdd\ 

|«-2V(n?+i)l« , +o+«a , -o; 

Inserting the value of b. 

That is, with given side slopes, 
the section is least for a given 
discharge when the hydraulic mean 
depth is half the actual depth. 

A simple construction gives the 
form of the channel which fulfils 

this condition, for it can be shown that when m~\d the aides 

of the channel are tangential to a semicircle drawn 00 the 

water line. 

Since O/x-W. 

therefore Q-ix*. (1) 

Let ABCD be the channel (fig. 115); from E the centre of AD drop 

perpendiculars EF, EG, EH on the sides. 

AB-CD-a; BC-&; EF-EH-c; and EG-i. 
Q-area AEB+BEC+CED. 

Putting these values in (1), 

ac+\bd-{o+lb)d\ and hence c»a\ 


Fig. 116. 

ire all equal, hence a semicircle struck 
fix i to the depth of the stream will pass 




sci tangents drawn at the 

The above result may be obtained thus (fig. 1 16) :— 

tl/d»b+d cot fi; 
From (1) and (2), 

X - Q/rf - d cot fi+idfmn fi. 
This will be a minimum for 

ixldd=Q/d* +cot 0-2/sin/J-o, 
or fi/<P-2 cosec. fi-cotfi. 

or d - V IQ sin 0/(2 -cos 0)1 

From (3) and (4), 

6/rf-a(i -cos 0)/sin fi—2 tan \0. 






Proportions of Chann t ts of Maximum Discharge for given Area and 
Side Slopes. Depth of channel -di Hydraulic mean deptk-kd; 
Area of section • Q. 


of Side, to 

Ratio el 

Am of 
Section 0. 


Top width - 

twica length 








6o - & 

3 5 




Semi-square . 

go* 0' 

: 1 




73° 5§' 

1 :4 

t-8124 1 



63- 26 

I :a 





$: 40; 

3 *4 
1 : 1 

I '750^ 






33* 4*' 


2-I064 1 



*9* 44 





*! 34;- 

2 : 1 




23* 58 




«• 48 





*?; 58 




3 :« 




Half the top width is the length of each side slope. The wetted 
perimeter is the sum of the top and bottom widths 

1 114. Form of Cross Section of Channel in which the Mean Velocity 
is Constant with Varying Discharge. — In designing waste channel* 
from canals, and in some other cases, it is desirable that the mean 
velocity should be restricted within narrow limits with very different 
volumes of discharge. In channels of trapezoidal form the velocity 
increases and diminishes with the discharge. Hence when the 
discharge is large there is danger of erosion, and when it b small of 
silting or obstruction by weeds. A theoretical form of section for 
which the mean velocity would be constant can be found, and, 
although this is not very suitable for practical purposes, it can be 
more or less approximated to in actual channels. 

Let fig. 1 17 r e pr es en t the cross section of the channel Prom the 
symmetry of the section, only half the channel need be considered. 

Fie. 117. 

Let oboe be any section suitable for the minimum flow, and let it 

be required to find the curve beg for the upper part of the channel 

so that the mean velocity shall be constant Take o as origin of 

coordinates, and let de,fg be two levels of the water above ob. 

Let ob-b/2; 4«-y,y^»y+4y, od—x* o/»*+4x; eg-ds. 

The condition to be satisfied is that 

p— cV (mi) 

should be constant, whether the water-level is at oh, de, or/g. Con- 

mb constant ■> A 

for all three sections, and can be found from the section oboe Hence 

Increment of section ^ydie^. 
Increment of perimeter*" df m 
/4x«-A a 4*«-«»(4jr>+4v») and 4x-tty/V (/-*•). 

*-* log* (y+ V{y*-**)}+constant; 
and, since yb/2 when x-o, 

x-tiog.ny+vcy-^i/iin-vd^-* 1 )}]. 

Assuming values for y, the values of x can be found and the curve 

The figure has been drawn for a channel the minimum section of 
which is a half hexagon of 4 ft. depth. Hence A "2; *-Q-2; the 
rapid flattening of the side slopes is remarkable. 

Steady Motion op Water in Open Channels op Varying 
Cross Section and Slope 

{115. In every stream the discharge of which is constant, or may 
be regarded as constant for the time considered, the velocity at 
different places depends on the slope of the bed. Except at certain 
exceptional points the velocity will be greater as the slope of the 
bed is greater, and, as the velocity and cross section of the stream 
vary inversely, the section of the stream will be least where the 


velocity and slope are greatest. If in a stream of tolerably un&orai 
slope an obstruction such as a weir is built, that will cause an altera- 
tion of flow similar to that of an alteration of the slope of the bed 
for a greater or less distance above the weir, and the originally uni- 
form cross section of the stream will become a varied one. In such 
cases it is often of much practical importance to determine the 
longitudinal section of the stream. 

The cases now considered will be those in which the changes of 
velocity and cross section arc gradual and not abrupt, and in which 
the only internal work which needs to be taken into account is that 
due to the friction of the stream bed, as in cases of uniform motion, 
Further, the motion will be supposed to be steady, the mean velocity 
at each given cross section remaining constant, though it varies from 
section to section along the course of the stream. 

Let fig. 118 represent a longitudinal section of the stream, AoA» 
being the water surface, B«Bi the stream bed. Let AA, AA be 

Fig. 118. 

cross sections normal to the direction of flow. Suppose the mass 
of water A*B*AiBi comes in a short time 9 to GLVTiDu and let the 
work done on the mass be equated to its change of kinetic energy 
during that period. Let I be the length A«Ai of the portion of the 
stream considered, and s the fall of surface level in that distance. 
Let Q be the discharge of the stream per second. 

Change of Kinetic Energy. — At the end of the time 9 there are as 
many particles possessing the same velocities in the space C*D»A|fii 
as at the beginning. The 
change of kinetic energy is 
therefore the difference of 
the kinetic energies of 
A«B«C«Do and A1B1C1D1. 

Let fig. 119 represent the 
cross section A*B«, and let 
ta be a small element of ks 
area at a point where the 
velocity is v. Let a be the 
whole area of the cross section and *» the mean velocity for the 
whole cross section. From the definition of mean velocity we have 

Let *-«•+«% where w is the difference between the velocity at the 
small element * and the mean velocity. For the whole cross section, 

The mass of fluid passing through the element of section v. in 9 
seconds, is (G/f M*. and its kinetic energy is (C/ifM^. For the 
whole section, the kinetic energy of the mass A*8oC»L\ passing in 9 

Fig. 119. 

energy c 
seconds is 

The factor 3tc«+w is equal to 2««+», a quantity necessarily 
positive. Consequently Tuv*> iW, and consequently the kinase 
energy of AtBgCoDt is greater than 

which would be its value if all the particles passing the section had 
the same velocity m. Let the kinetic energy be taken at 

«(G0/2sOfW - *iG9l2g)Qtto\ 
where a Is a corrective factor, the value of which was estimated by 
J. B. C. J. Belanger at 1 i. 1 Its precise value is not of great im- 

In a similar way we should obtain for the kinetic energy of 
AtBiQDi the expression 

«(G*/2£)CW -*(G9l2g)Quf, 
where ft, « t are the section and mean velocity at A|B,, and wfere 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 AtBoAtBi 
in seconds is 

o(G«/2«)Q(k»*-**). (1) 

Mothe Worh of the Weight and Pressures.— Consider a smal 
filament a«ai which comes in 9 seconds to c*u The work done by 
gravity during that movement is the same as if the portion a«co were 
carried to a\Cu Let dQ9 be the volume of a&o or aifi, and y* y\ the 
depths of a* a t from the surface of the stream. Then the volume 

1 Boossinesq has shown that this mode of determining the corrective 
factor a is not satisfactory 





fa or GdQ9 pounds Calk through a vertical height «-H*->>s, and 
the work done by gravity Is 

Putting. £• for atmospheric pressure, the whole pressure per unit of 
area at at is Gjt+A* and that at ai is -(Gyi+£.). The work of 
these pressures is 

Adding this to the worjc of gravity, the whole work is GadQt; or, 
for the whole cross section, 

G&. . (a) 

Work extended in Overcoming Ike Friction of Ike Stream Bed.— 
Let A'B', A'B r be two cross sections at <fistances s and s+ds from 
A«B». Between these sections the velocity may be treated as uni- 
form, because by hypothesis the changes of velocity from section 
to section are gradual. Hence, to this short length of stream the 
equation for uniform motion is applicable. But in that case the 
work in overcoming the friction of the stream bed between A'B' and 

where «, jr. are the mean velocity, wetted perimeter, and section 
at A'B'. Hence the whole work lost in friction from A#B» to AjB» 
wiU be 



Equating the work given in (a) and (3) to the change of kinetic 
energy given in (i), 

•(GQ»/ag) W-uJ<)-GQ*-GQlf*Wl2gKxP)dsi 

1 116. Fundamental Differential Equation of Steady Variedliotion.— 
Suppose the equation just found to be applied to an indefinitely 
short length ds of the stream, limited by the end sections ab, a t fo, 
taken for simplicity normal to the stream bed (fig, 120). For that 
abort length of stream the fall of surface level, or difference of level of 

Fio iao. 

a and Ui, maybe written ds. Also, if we write u for «*, and «+<*# for 
«t, the term (*•»-«!»)/« becomes udu/g. Hence the equation 
applicable to an indefinitely short length ofthe stream is 

d*-udutz+W)du>t2 Z )ds. (1) 

From this equation some general conclusions may be arrived at as 
to the form of the longitudinal section of the stream, but, as the 
investigation is somewhat complicated, jt is convenient to simplify 
it by restricting the conditions of the problem. 

Modification of the Formula for the Restricted Com of a Stream 
flouring in a Prismatic Stream Bed of Constant Slope. — Let i be 
the constant slope of the bed. Draw ad parallel to the bed, and ac 
horizontal. Then di Is sensibly equal to a'c. The depths of the 
stream, h and k+dk, are sensibly equal to ab and a'b', and therefore 
dh-a'tL Also cd is the fall of the bed in the distance ds, and is 
equal to ids. Hence 

dt-a'c-cd-a'd~ids-dk. (a) 

Since the motion is steady — 

Q-Q» -constant. 

Let x be the width of the stream, then dQ—xdk very nearly. In* 
setting this value, . 

du- -{uxJU)dk. x (3) 

Putting the values of du and ds found in (a) and (3) in equation (1), 
ids-dk- -(u*xlgQ)dk+(x/QH{u 2 /2g)ds. 
_ dk/ds-\i-(xin)t{u>lH))lli-(u*lt)(xfQ).} (4) 

Further Restriction to Ike Case of a Stream of Rectangular Section 
and of Indefinite Widtk. — 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. x«=Q, and if x 
is large compared with *, O/x - xkfx~k nearly Then equation (4) 

dklds-Hi -Cu*ligik)l(i -«Vf*). (5) 

5 117 General Indications as to tke Form of Water Surface fur- 
nished by Equation (5).— Let A*Ai Cfig. m) be the water surface, 

BsB| the bed ip. a longitudinal section of the stream, and ab any 
section at a distance s from Bt, the depth ab being k. Suppose 
B0B1, B«A« taken as rectangular coordinate axes, then dk/ds is the 
trigonometric tangent of the angle which the surface of the stream 
at o makes with the axis BoB,. This tangent dk/ds will be positive, 
if the stream is increasing in depth in the direction B»Br, negative. 

Fig. ui. 

if the stream is diminishing in depth from B« towards Bt. If dk/ds -o. 
the surface of the stream is parallel to the bed, as in cases of uniform 
motion. But from equation (4) 

dk/ds-o, if«-(xyO)rO«Va£)-o; 
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 b therefore a 
limiting case between two different kinds of varied motion. 
Consider the possible changes of value of the fraction 
As h tends towards the limit o, and consequently u is large, the 
numerator tends to the limit— 00. On the other hand if A -00, in 
which cast u is small, the numerator b ecomes equal to 1. For a 
value H of k given by the equation 


we fall upon the case of uniform motion. The results just stated 
may be tabulated thus:— 

For *-o.H,>H,«o. 
the numerator has the value — «o, o, > o, 1. 

Neat consider the denominator. If k becomes very small, tn which 
case « must be very large, the denominator tends to the Emit — *. 
As * becomes very large, and ss consequently very small, the de- 
nominator tends to the limit 1. For *-s//j, or «-V(fA), the 
denominator becomes aero. Hence, tabulating these results at 
before j— 

For *—o, «Vf » > *Vf . » t 
the denominator becomes — », o, > 0,1. 

§ 118. Case i%— -Suppose A>**/f, and also *>H, or the depth 
greater than that corresponding to uniform motion. In thb case 
dk/ds Is positive, and the stream increases in depth in the direction 
of now. In fig. 1 aa let B«B, be the bed, CcCi a line parallel to the 
bed and at a height above it equal to H. By hypothesis, the surface 

Fio. taa. 

A*Ai of the stream b above OCi. and it has just been shown that the 
depth of the stream increases from B# towards Bi. But going up 
stream k approaches more and more nearly the value H, and there- 
fore dk/ds approaches the limit o, or the surface of the stream b 
asymptotic to CoQ. Going down stream k increases and u diminishes, 
thenumeratorand denominator of thefraction(i — f **/agtft)/(l —n*/gh) 
both tend towards, the limit l, and dk/ds to the limit t. That is, 
the surface of the stream tends to become asymptotic to a horizontal 
line L\D t . 

The form of water surface here discussed b produced when the 
flow of a stream originally uniform b altered by the construction of 
a weir. The raising of the water surface above the level C#Ci b 
termed the backwater due to the weir. 

I 119. Case a.— Suppose h>u , ig, and also *<H. Then dk/ds h) 




will be represented by or. In a deeper stream such as that In fig. 
130, the average height to which particles are lifted, and, since the 
rate of vertical fall through the water may be assumed the same as 
before, the average distance a V of transport will be greater. Con- 
sequently, although the scouring action may be identical in the two 
streams, the velocity of transport of material down stream is greater 
as the depth »f the stream is greater. The effect is that the deep 
stream excavates its bed more rapidly than the shallow stream. 

1 126. Bottom Velocity at which Scour commences.— The following 
bottom velocities were determined by P. JL G. Dubuat to be the 
maximum velocities consistent with stability of the stream bed for 
different materials. 

Darcy and Basin give, for the relation of the mean velocity v* 
and bottom velocity «*. 

■w -n+ 10-87 V(«w)- 

, A •» -*/(i-io.87V (flag )). 
Taking a mean value for J", we get 

and from this the following values of the mean velocity are ob- 
tained: — 

1. Soft earth . . . 

2. Loam . . . . , 

3. Sand . . . . 

4. Gravel ... 

5. Pebbles . . . 

6. Broken stone, flint 

i. Chalk, soft shale 
. Rock in beds. , 
9. Hard rock . . 

Bottom Velocity Mean Velocity 

1 00 



a 62 


The. following table of velocities which should not be exceeded 
in channels b given in the Jngenieurs Taschenhnck of the Verein 

Slimy earth or brown clay . . 


Firm sand . . • 


Boulder bed 

Conglomerate of slaty fragments 

Stratified rocks 

Hard rocks 

Surface Mean Bottom 
Velocity. Velocity. Velocity. 








I 02 









f 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. But as the volume 

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 (5 107), for the slightest deflection of the 

cui * * — : * c — •'~ l ~ *— : ~ : » L: -h increases progres- 

siv If such a river is 

str its banks are pro- 


ie declivity of rivers 
her pasta rapid and 
lers, they enlarge ia 
pe diminishes, their 
they reach the sea. 
rface fall in feet per 

Fie. 132. 

Fie. 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, I 

though alteration is constantly going on. This is more likely to I 

u (1) The action of 
; the smallest debris 
table near the mouth 
the river adjusts its 
icreastng its anuoos- 
ms ; or straightening its 

coi stability of the bed 

wc e increase of volume 

an slope; for the larger 

th< given velocity. 

to a purely arbitrary 
cai d, to make the con* 

dit cd of uniform resist- 

an to maintain stability 

thi es is constant from 

soi ie river at all points 

an iver at any point, its 

hy P, where a and c are 

co let us further assume 

th juence of the supply 

fix rer from its s 


hi, where h 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 ordinatet 
are x and y, and let the river at C have the breadth b, the slope t, 
and the velocity v. 

Since velocity X area of section "discharge, vcW-hl, or 6-V (Ufcv). 
Hydraulic mean depth -oc»-aV {hllcv). 
But, by the ordinary formula for the flow of rivers, mt'-fp*; 

But i is the tangent of the angle which the curve at C makes with 
the axis of X, and is therefore ^dyfdx. Also, as the slope is smalL 
/ - AC — AD - x nearly. 

t m /.J»/fe-Ctf/a)VCc/fa); 
and, remembering that v is constant, 

y-(af*8/a)V («/*); 
or y» -constant X x; 

so that the curve is a common parabola, of which the axis is boo- 
xontal and the vertex at the source. This may be considered aa 
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. 

I 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 
elowly from changes in the river bed, and the dramv 
stances affecting the drainage into the river. 

For the purposes of 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. 

1. 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, the 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 lcveL 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, la 
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 




with the attainment of the highest level at other point*, 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 to ft. above low-water level, but in the tropics the rise of floods 
- b greater. 

3. Highest Navigable Level.— When the rivet 1 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. 

1 13a 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 wV lb, but in water only (w— 6a-A) 

Weight of a Cub. Ft. in lb. 

In Air. 

In Water. 


Brick . . . , . 
Brickwork . . . 
Granite and limestone 
Sandstone . . . 
Masonry .... 







I 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 convey-" 4 ♦" «*•*»» *~*-* «* * k * -«.*«~* 

I 13a. Delias. — The name delta wi 
shaped portion of Lower Egypt, indue 
the Nile. It is now given to the who 
river mouths formed by deposition of t 
Its velocity is checked on its entrance 1 
feature of these alluvial deltas is that 
in a single channel, but in two or man 
branch nas a tract of the delta unde 
raises the surface of that tract, and cxt 
extends itself seaward, the conditio 
different branches change- The wat 
one of the branches less obstructed i 
velocity and scouring action in that 
others they diminish. The one chann< 
of the water supply, while the other 
mouth of the new main channel extcr 
creases both from the greater length of 
of shoals at its mouth, and the river t 
AC or AD (fig. 134), and one % of these 
channel of the river. 

i 133. Field Operations preliminary to a Study of River Improve- 
ment. — There are required (1) a plan of the nver, on which the 
Editions of lines of levelling and cross sections are marked; (2) a 
ngitudinal section and numerous cross sections of the river, (3) a 
acnes of gaugings of the discharge at different points and in different 
conditions or the river. 

Longitudinal Section. — This requires to be carried out with great 
accuracy. A line of stakes is planted, following the sinuosities of the 

possible at uniform distances) in a line s 
perpendicular to the thread of the strean 
may be stretched across with equal distai 
ing tags. The depth at each of these t 
light wooden staff, with a disk-shaped si 
lithe depth is great, soundings may be ta 
To ensure the wire being perpendicular * 
it is desirable to stretch two other wire 
above and the other below, at a dista 
number of floats being then thrown in, ii 
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 la 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 
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- _ m 

ing line was dropped, and the Fio. 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 
fi and its wetted perimeter x; and from these the hydraulic mean 
depth m can be calculated. 

I 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. 

Instrumhnts for Measuring thb Velocity or Watejl 

{ 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 




them visible they may hive 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 i in. thick. For observa- 
tions near the banks, floats I in. diameter and \ in. thick were used. 
To render them visible a tuft of cotton wool was used loosely fixed 
in a hole at the centre. 

The velocity is obtained by allowing the float to be carried down, 
and noting ihe time of passage over a measured length of the stream. 
If v is the velocity of any float, t the time of passing over a length 
/, then v ■>///. 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 to 250 ft., according 
to the size ana rapidity of the river. In the Roorkee experiments 
a length of run of 50 ft. was found best for the central two-fii ths of the 
width, and 25 ft. for the remainder, except very close to the banks, 
where the run was made 12} 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 lenr' L "' — ' ? " L " ~ ' List 

be had to box sextants or th 

Let AB (fig. 136) be a r he 

thread of the stream, and \B 




Fig. 136. 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 

^^=tlz=-zl 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 some extent influences 
the motion of the submerged float. 
FlG. 137. 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. 13S 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. 

% 1 38. Twin Floats.— -Su ppose two eq ual and similar floats (fig. i£9) 
connected by a wire. Let one float be a little lighter and the other 
a little heavier than water. Then the velocity of the *- : — ■ 

Fig. 138. Fig. 139. 

floats will be the mean of the surface velocity and the velocity at die 
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 94 the velocity at the depth to which the lower float is sunk, the 
velocity of the combined floats will be 

Consequently, if v is observed, and v. determined by an experiment 
with a single float. 

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. 

I 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, 
Rcyy's meter may be selected. This is an 
ordinary screw meter of a larger size than , 
usual, more carefully made, and with its { 
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 k fixed on a common 
axis. The worm wheels are carried on a frame attached to the pin L 
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 tn can be screwed up, if necessary, to keep the counter per- 
manently in gear. The worm is two-threaded, and the worm wheel 
f 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 woridag 
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 itsef 
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 vase 




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 

Flo. 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 b put into gear for one, two or five 

minutes. Lastly,- tne 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. 

' J 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 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 s makes one rotation for 100 of the 
screw. A pin moving the lever x makes the 
electrical contact. The wires 6, 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 
<***-% dfek at an opening in the cover of the box. 
I M^frl * ,42 * Amsler Laffo* Current Meter.— A 

I t^-^l ^ vsry 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 
on« 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 tJie meter, and there is less uncertainty than when the 
XIV g + 

Pig. 143. 

counter has to be held in ( 
susptiided by a wire with a 
The wire is payed out from a small winch D, with anjndex showing 

1 gear. For deep" streams the meter A b 
susptiided by a wire with a heavy lenticular weight below (fi| 

fa. «*)• 
_ ; showing 
the depth of the meter, and passes over a pulley B. The meter b in 
gimbals and b 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 riags. 
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. 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 b a very convenient instrur 
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. I f v is the velocity of the water and 
n the observed number of rotations per second, let 

V-a+0n (l) 

where a and P 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//-P feet per second, and the number of revolutions per 
second is N/l -n. Suppose m observations have been made in thb 
way, furnishing corresponding values of v and n, the speed in each 
trial being as uniform as possible, 

Zlt = Kl-|-«*+ . . . 

Zp-vi-Hj-t- . . . 
rm»-«i»i+«iOt+ • • • 
Zrf-nJ+ni-T- . . . 




Then for the determination of the constant! « and fi in (i), by the 
method of least squares — 

n mZnv—ZvZn 

In a few cases the constants for screw current meters have been 
determined by towing them in R. E. Froude's experimental tank in 

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~h?l2i, 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 * - 1 006 ; by readings 
taken in different parts of the section of a canal in which a know* 
volume of water was flowing, he found k -0-993. He believed the 
first value to be too high in con- 
sequence oC the disturbance caused 
by the boat. The mean of the other 
two values is almost exactly unity 
(Reckerckes kydranliques. Darcy and 
Basin, 1865. p. 63). W.B.Gregory 
used somewhat differently formed 
Pitot tubes for which the * - 1 CAmu 
Soc. Meek. Ertg., 1903, 2$). T. E. 
Stanton used a Pitot tube in deter* 
mining the velocity of an air current, 
and for his instrument be found 
*- 1*030 to «- 1-032 ("On the Re- 
sistance of Plane Surfaces in a 
Current of Air," Prac Inst. Cst. 
£**., 1904, 156). 

One objection to the Pitot tube 
in its original form was the great 
difficulty and inconvenience of 

Fie. 144- 

which the resistance of ship models is ascertained, 
data are found with exceptional accuracy. 

In that case the 

I 144. Darcy Gauge or modified Piiof Tube. — A very old instru- 
t for ..... ....... 

ie FAcadhnie des Sciences, 1732, p. _ 
of a vertical glass tube with a right-angled bend, placed so that'its 

ment for measuring velocities, invented by Henri Pitot in 1730 
(Histoire de FAcadhnie des Sciences, 1732, p. 376), consisted simply 

mouth was normal to the direction of now (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 A-»V2g, 

where v is the velocity 
at the depth x. Placed 
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 
h'—t?/2g nearly, though 
the tube. in that case 
interferes with the free 
B C flow of the liquid and 

Fie. 145. 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 

But there is more disturbance of the stream. ' Darcy preferred to 
' e the mouth of the tube very small to avoid interference with the 

reading the height h in the imme- 
diate neighbourhood of the stream 
surface. This is obviated in the 
Darcy gauge, which can be remo ved 
from the stream to be read. 

Fig. 146 shows a Darcy gpuge, 
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 pne 
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 b 
as follows. If the velocity b 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 6mall, this instru- 
ment is an admirable one. It requires observation only of a single 
linear quantity, and does not require any time observation. Tee 
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 »»*V(2£*), then it 
appears from Dairy's experiments that for a well-formed instrument 
k does not sensibly differ from unity. It 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. 

f 14s. Perrodil Hydrodynamometer. — This consists of a frame 
abed (fig. 147) placed vertically in the stream, and of a height sot 
less than the stream's depth. The two vertical members of this 
frame are connected by cross bars, and united above water by a 
^:_~..i~_ u«- .:».._*-j ;_ «i__ — Kt — 1 _i 1 :__ -. borixootai 

its axis. 

. _ . . _ 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 




needfe 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 x, 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 U sliding on vm. 

Suppose the apparatus arranged so that the disk x is at that level 
In the 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 x (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 

Fie. 147. 

will be given by the distance of the needle from aero. 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 it 
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 

where E« is the modulus of elas- 
ticity for torsion, and 1 the polar 
moment of inertia of the section of 
the rod. If the rod is of circular 
section, l~\rr*. 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 
where G is the heaviness of water 
and k an experimental coefficient. 

For any given instrument, 

where c 1s 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 

1st disk . . 0-052 0-16 

2nd „ ... 0-105 °'S* 

3rd „ _ ... C-2IO O-66 

t For a thin circular plate, the coefficient «« 1*12. In the actual 

instrument the torsion rod was a brass wire 0-06 in. diameter and 

6J ft. long. Supposing a measured in degrees, we get by calculation 

v«o*335V«; o-nsVa; 0-042 V«u 

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 formula v-tVa, 

1st disk, e- 0-3126 for velocities of 3 to 16 ft. 

and „ 01177 m ,. iito3i „ 

3rd ,, 0-0349 •• .. l^ss than t\ „ 

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 fob Gauging Streams 
I 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 »* for the mean velocity of the whole 
cross section, »■»/«• has been found to have the following values.— 

De Prony, experiments on small wooden channels 08164 

Experiments on the Seine 0*62 

Destrem and De Prony, experiments on the Neva 078 

Boileau, experiments on canals 0-82 

Baumgartner, experiments on the Garonne . . 0*80 

BrQnings (mean) 0-85 

Cunningham, Solani aqueduct 0*823 

8 4 



Various formulae, either empirical or based on some theory of the 
vertical and horizontal velocity curves, have been proposed for 
determining the ratio VmJv- Bazin found from his experiments the 
empirical expression 


meter observations. 

I 147. Mean Velocity determined by observing a Series of Surface 
Velocities. — The ratio of the mean velocity to the surface velocity 
in one longitudinal section is better ascertained than the ratio of 
the central surface velocity to the mean velocity of the whole cross 
section. Suppose the river divided into a number of compartments 
by equidistant longitudinal planes, and the surface velocity observed 
in each compartment. From this the mean velocity in each com- 
partment and the discharge can be calculated. The sum of the 
partial discharges will be the total discharge of the stream. When 
wires or ropes can be stretched across the stream, the compartments 
can be marked out by tags attached to them. Suppose two such 
ropes stretched across the stream, and floats dropped in above the 
upper rope. By observing within which compartment the path of 
the float lies, and noting the time of transit between the ropes, the 
surface velocity in each compartment can be ascertained. The 
mean velocity in each compartment is 0-85 to 0*91 of the surface 
velocity in that compartment. Putting * for this ratio, and 
vi, v» . . . for the observed velocities, in compartments of area 
fi, (fc . . . then the total discharge is 

Q«*(QiivHta+ .:. )• 
If several floats are allowed to pass over each compartment, the 
mean of all those corresponding to one compartment is to be taken 
as the surface velocity of that compartment. 

This method is very applicable in the case of large streams or 
rivers too wide to stretch a rope across. The paths of the floats 
are then ascertained in this way. Let fig. 148 represent a portion 
of the river, which should be straight and free from obstructions. 
Suppose a base line AB measured 
parallel to the thread of the stream, 
and let the mean cross section 01 
the stream be ascertained either by 
; sounding the terminal cross sections 
AE, BF, or by sounding a series of 
equidistant cross sections. The 
cross sections arc taken at right 
angles to the base line. Observers 
are placed at A and B with theo- 
dolites or box sextants. The floats 
are dropped in from a boat above 
AE, and picked up by another boat 
below BF. An observer with a 
chronograph or watch notes the 
time in which each float passes 
from AE to BF. The method of 
proceeding is this. The observer 
? A sets his theodolite in the direc- 
tion AE, and gives a signal to drop 
a float. B keeps his instrument 
on the float as it comes down. At 
Fig. 148 tne moment the float arrives at 

C in the line AE, the observer at 
A calls out. B clamps his instrument and reads off the angle ABC, 
and the time observer begins to note the time of transit. B now 
points his instrument in the direction BF, and A keeps the float on 
the cross wire of his instrument. At the moment the float arrives 
at D in the line BF. the observer B calls out, A clamps his instru- 
ment and reads off the angle BAD, and the time observer notes the 
time of transit from C to D. Thus all the data are determined for 
plotting the path CD of the float and determining its velocity. By 
dropping in a series of floats, a number of surface velocities can be 
determined. When all these have been plotted, the river can be 


Suppose the depths at I., II., Ill (fig. 149)1 «t off as vertical 

ordinatcs in fig. 150, and on these vertical ordinate* suppose the 
velocities set off horizontally at their proper depths. Thus, if r 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 »* 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 1. . . . 
V. (fig. 150), thus drawn. On each of these figures draw verticals 

corresponding to vdoci- 
" r /T V ties of*, 2x, 3* . . . ft. 

Then for 
fat 111. (fig. 
jt Ml/ \u *3"/ ** the depth at 
' »• III/ 1/ which a velocity of ax 
second existed 
! vertical HI. in 
' 7 fig. 149 and if cd is set 

F* c - >50. oft at III in fig. 149 »t 

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 an 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 




\y Y : W it. per secoi 

lUo V on the vertk 

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 

I 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 pwxfp combine the functions of motor 

Riohi hank. 

4*8 4-80 6-66 rtO 0*t MO 11*21*90 1*«M40B- 

III aoll/litWIA TV0*« .\l 

lth» »SI B-60 IMS 2*30 2*00 

Fig. 151. 

sections normal to the plane of fig. 149 given by the diagrams in fig. 
ISO- 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 Qo be the area of the cross section of the river, Qi, 
Sb . . • 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 I 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 

}x(Qb+Q,), *x(Qi+00. and soon. 
Consequently the discharge is 

Q-x{i(ft+a,)+Oi-fl,+ ... +fl^J. 
The areas 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 
U.) multiplied by \ to i 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 



(see Powek 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; 1,263,34s h.p. 
in 1800; and 1,727,258 Ti.p. in 1000. The increase was 8-4% 
in the decade 1870-1880, 3*1% in 1880-1806, and no less than 
36*7% in 1890-1000. The increase is the more striking because 
in this census the large amounts of hydraulic power which are 
transmitted electrically are not included. 

I 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 

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 P« is the pressure in any direction, m the mass 
of fluid impinging per second, «• the change of velocity in the direction 
of P. due to impact, then 


If * (fig. 152) is the velocity and direction of motion before impact, 
9, that after impact, then * is the total change of motion due to 
impact. The resultant pressure of the 
fluid on the surface is in the direction of 
v, and is equal to v multiplied by the mass 
impinging per second. That is, putting 
P tor the resultant pressure, 
P«wt». .h, 
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, Ta 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 r, be the initial velocity of the fluid before striking 
the surface. Then GQpiVif is the original kinetic energy of Q cub. 
ft. of fluid, and the efficiency of the stream considered as an arrange- 
ment for moving the solid surface is 


f 154. Jet deviated entirely in one Direction.— Geometrical Solution 

(fig- >53)- — 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 ac be the velocity and direction of motion of the 


surface. Join efr; 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 —eft, tangent to the 
surface at c, then of is the relative motion of the water with respect to 
the surface at c Take 4/ equal and parallel to ae. Then fc (obtained 
by compounding the relative motion of water to surface and common 
velocity of water and surface) is the absolute velocity and direction 

Fie. 153. 

i parallel to fc 
lad direction of 
The resultant 
In the triangle 
i eg is equal and 
er and surface, 
din magnitude 
e. of which the 
ter and surface, 
re motion. 

Special Casks 

I IM. (1) A Jet impinges on a plane surface at rest, in a direction 
normal to the plane (fig. 154). — Let a jet whose section is « 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 «*. The 
pressure on the plane, which is equal to 


of momentum per second, is 


plane is moving in ike direction 

h the^velocity «*=«, the qua: 

Fig. 154. 

per second is «(»«**). The 
m of this quantity before impact 

is » u)v. After impact, the water 

st ses the velocity *a In the 

di the jet; and the momentum, 

in uwi vM.ection, of so much water as 
impinges in one second, after impact, is 
+ {Gfg)<a{vmu)u. The pressure on the 
plane, which is the change of momentum 

per second, is the difference of these quantities or P«(G/fM** ■>*• 
This differs from the expression obtained in the previous case, 
in that the relative velocity of the water and plane »*s» is sab> 
stituted for v. The expression may be written P - 2 X G X«(»* a)*/**. 
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 diss 
to the relative velocity. The pressure on the plane is twice the 
weight of that prism of water. The work done when the plane 



it moving in the tame direction as th« fet is P* = (G/f )«(»-«)* 
foot-pounds per second. There issue from the jet wv cub. ft 
per second, and the energy of this quantity before impact i 
(C/2f )•*•». The efficiency of the jet is therefore 9 -2(»- a)**/* 1 
The value of « which makesthisa maximum is found bydifferentjaun] 
and equating the differential coefficient to seroi— 
dn/du -a(t»-4»«+3M«)/»»-o; 
.*.«—* or fa. 
The former gives a minimum, the latter a m*» efficiency. 
Putting u - to in the expression above, 
n max. -A. 
(3) If, instead of one plane moving before the jet, a series of plane 
are introduced at short intervals at the same point, the quantity o 
water impinging on the series will be wo instead of <*{v-u), and the 
whole pressure -(G/gWp- «). The work done is (Gfg)ixm(p-u) 
The efficiency if-(G/*)<^(»^)+(G/2f)«**-aiK»ni)M This be- 
comes a maximum for d*fdu -a(9-?«) -o, or *-|v, and the e-f 
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 watei 
wheel. The work wasted in this case is half the whole energy of th< 
jet when the floats run at the best speed. 

| 1 56. (4) Case of a Jet impinging on a Concave Cup Vane, velocity 
of water v, velocity of vane in the same direction si (fig. 155), weigh! 
impinging per second «Gw(p- «). 

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 11 
*-(»-«) - 2* - ». Ths 
change of momentum per 
second - (G/fM»-«) f»- 

(2«-»)| - 2(G/g) W <»-*)». 

Comparing this with case a, 
it is seen that the pressure 
on a hemispherical cup is 
double that on a flat plane. 
The work done on the 
cup-2(G/g)w (» -*)** foot- 
pounds per second. The efficiency of the jet is greatest when v -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 uv instead of <*(v~u), then the whole 
pressure on the chain of cups is (G/g)w&|t>-(2i»-v)|«2(G/f)u»r(r-*j). 
In this case the efficiency is greatest when v-2«, and the maximum 
efficiency is unity, or all the energy of the water is expended on the 

I 1 57- (5) Case of a Flat Vane oblique to the Jet (fig. 1 56).— This case 
presents some difficulty. The water spreading on the plane in all 



Fig. 155- 

f 10. 156. 

directions from the point of impact, different particles leave the plane 
with different absolute velocities. Let AB-r- velocity of water, 
AC— «- 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 j>lane. 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 -*, and let AD -*,. Then AE -a, cos •; DE -tv sin $. 
If Q is the volume of water impinging on the plane per second, 
the change of momentum is (G/f)Q*> cos 9. Let AC -a "velocity 
of the plane, and let AC make the angle CAE-a with the normal 
to the plane. The velocity of the plane in the direction AE- 

9 cos a. The work of the jet on the plane - (G/g)Qs> cos • at cos ». 
The same problem may be thus treated algebraically (fig. 157). 
Let BAF - a. and CAF - 1. The velocity v of the water may be de- 

composed into AF -v cos • normal to the plane, and FB -v sin a 
parallel to the plane. Similarly the velocity of the plane - u - AC - 
DD can be decomposed into BG - FE - u cos 1 normal to the plane, 
and DC -a bin a 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 a normal to the plane becomes after 

plane, that is, « cos I. Hence the 
pact-AE-tF cos a-u cos a. The 
and, and consequently the normal 

G. 157. 

g) Q (p cos a-ttcos a). The pressure 
ne is moving is P-N cos a-(G/g)Q 
e work done on the plane is P«- 
a, which is the same expression as 

(*-« cos a. 

1 so that the point A (fig. 158) cornea 

Fig. 158. 
1 a. Inserting this* in the formulae 

dos *-» cos a)*; (1) 

> cose -mods a)*; (2) 

j(vcosa-*«cosa)s. (3) 


1 *-o, N - (G/g)«s» cos «; and the 

efficiency of the jet are sero. 

to the jet. Then a -a, and Ph-: 

maximum when a — to. 

,G/g)<j0 t cos *e, and the efficiency 

cnlarly to the jet. Then a -oo e -a; 
-(9 cos c-k sin a)*. This is a nuud- 

urn work and the efficiency are the 

ttwt Water. — When water impinges 
te, it is scattered in all directions 
id away by the water is then gener- 
f dealing afterwards with streams of 
on*. By suitably forming the vane, 


j. 159. 

rly deviated in one direction, and 
of the water is entirely avoided, 
n which a jet of water impinges at 
n AC. Take AC -»- velocity of 




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. 

$ ico. Floats ofPoncelet Water Wheels.— Let AC (fig. 160) repre- 
sent the direction of a thin horizontal stream of water having the 


i a 

iiic waici iiiiu auu vui vi n»t wntvi, »«, is iiicm iicvomi y niai mc Up 

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 
i\*%^ at B. Since the surface is at rest, 
{ \a** % /v v « both the absolute velocity of 
p-*\ *» % / the water and the velocity relatively 
( \ % * x Q / to the surface, and this remains un- 

1 x *-/ changed during contact with the 

! \ 

hanged during contact 
surface, because the deviating force 
is at each point perpendicular to 
.jhe direction of motion. The water 
is deviated through an angle 
BCD-AOB-+. Each particle, of 
water of weight p exerts radially 
a centrifugal force pt£Jrg. Let the 
thickness of the stream - / ft. Then 
the weight of water resting on 
unit of surface ■ G* lb; and the normal pressure per unit of 
surface «-n-Gto»/$r. The resultant of the radial pressures uni- 
formly distributed 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 « 
2t sin to; let b 'breadth of the surface perpendicular to the plane 
of the figure. The resultant pressure "on surface 

* g r g 2 

which is independent of the radius pf 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 

Case a. Cylindrical Surface moving in the Direction AC with Veto- 

city u.— The relative velodty-»-tt. The final velocity BF (fig. 16a) 
is found by combining the relative velocity BD=»— 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)l(v-u) l /r. The resultant 

^FiG. 162. 

normal pressure R - 2 {Gfg) bt(v — u)* sin * 4. This resultant pressure 
may be resolved into two components P and parallel and he 
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-Rsin fe-(Gfe)*K*-ii)'Ci-cM+); 
L - R cos U - (G/g)bt(v - k)« sin +. 
rhe work done by the jet on the vane is Pu-(GJg)bt*(v- sli- 
ces 4), which is a maximum when u ■ Js*. 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 *--i, 1 -cos ♦-a; then P-a(G/g)fe(v-«)>, 
the same result as for a concave cup. 

•I 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 alb (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 
resultant of the pressures on 
the plane is determined for 
different angular positions. Experiments of this" kind have beat 
made by Hagen. Some of his results are given in the f 

Fig. 163. 

Larger plane. 

Smaller Plane. 

a/* -10 

♦ »r.. 

♦ -90* 








43 s 












I 162. Direct Action distinguished from Reaction (Rankin*. . 
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. 
153. § 154. °* 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 impute 
is then 

Pi -GQ(o* cos bae-ae)fg. 
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 eke 
water and the vane. In Case 2, 1 160, the direct pressure is 

That due to reaction is 

If + <oo°, the direct component of the water's motion is not 
wholly converted into the velocity of the vane, and the whJt 


pressure due to direct impute it not obtained. If f>90 s , cos ^ is 

Ttive and an additional pressure due to reaction is obtained. 
163. Jet Propeller.— In the case of vessels propelled by a jet of 
water Tug. 164), driven sternwards 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 » relatively to the ship, or 
*-V relatively to the earth, IfQ is 
the total sectional area of the jets, Q» is 
the quantity of water discharged per 
Fig 16a. second. The momentum generated per 

' ^" second in a sternward direction is 

(G/j)Q»(*-V), and this is equal to the forward acting reaction P 
which propels the ship. 
The energy carried away by the water 

-i(G/j)ttr<*-V)>: (1) 

The useful work done on the ship 

PV-(G/*)lto(*-V)V. (a) 

Adding (t) and (2), we get the whole work expended on the water, 
neglecting friction : — 


Hence the efficiency of the jet propeller is 

PV/W-aV/Cr+V). 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 ]. 

§ 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 





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 A1A1, and converge again, 
leaving a mass of eddying water behind the plane. Suppose the 
section A«A« taken at a point where the parallel motion has not 
begun to be disturbed, and AtAs where the parallel motion is re- 
established. Then since the same quantity of water with the same 
velocity passes A«A* AjAi in any given time, the external forces 
produce no change of momentum on the mass A«A«AjAi, and must 
therefore be in equilibrium. If Q is the section of the stream at 
A»A« or AjA», and « the area of the plate CD, the area of the con- 
tracted section of the stream at AiAi will be c e (Q— «), where e, is the 
coefficient of contraction. Hence, if v is the velocity at A*A« or AiA,. 
and vi the velocity at A1A1. 

•Q-c t ri(0— w); . 

.\*,-»0/c.(0-«). (1) 

Let P*, pi, Pi be the pressures at the three sections. Applying 
Bernoulli's theorem to the sections A0A0 and AiA», 



Also, for the sections A1A1 and A,A,. allowing that the head due 
to the relative velocity vi-v is lost in shock: — 

.••A>-*»-G(*i-«0 , /2r, (?) 

or, introducing the value in (1), ■ f 

Now the external forces in the direction of motion acting on the 

mass AoA»AtAt are the pressures foO, — Pft 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, 


••• R - G0 C-*£=r')£ w 

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 diminibhes as increases, 
If Q/« a Pi the equation (4) becomes 

which is of the form 

where K depends only on the rat\o of die sections of the stream and 

For example, let c-085, a value which is probable, if we allow 
that the sides of the pipe act as internal borders to an orifice. Then 

K -'(' ^-'); 

P« K-J 

1 00 

a 366 

3 «75 

4 1*29 

5 110 
xo 1-04 
50 a ! oo 

100 3*50 

The assumption that the coefficient of contraction 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 ti at the section A1A1 and 
a common velocity v at the section AtA> is not true when the stream 
is very much larger than the plane. Hence, in the expression 

K must be' determined by experiment tn each special case. For a 
cylindrical body putting u for the section, c, for the coefficient of 
contraction, c«(Q— ») for the area of the stream at A1A4, 

vi -»Q/c e (Q-«)i Pi -»Q/(Q-«) ; ' 
or, putting p.=Q/«, 

v ri-pp/c,(p-i), p»=»p/(p-i).J 
Then / 

\ R-KiGws*^: 

where N 



"For simplicity suppose the jet is a vertical one. Let * t (fig. 167) be 
the depth of the orifice from the free surface, and pi the velocity of 
discharge. Then, if u is the area of the orifice, the quantity of water 
impinging on the plane is obviously 

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 
r«V(2*fc); • V 
where * 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 




can in no caae exceed the pressure s«/2g or k 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 creature 

Fie. 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. 

GV = (G/*)«cip; 
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. Bercsford 
(Prof. Papers on Indian Engineering, No. ccexxii.), 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 
h 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 

Fig. 168 shows the pressure curves obtained in three e xp e rim ents 
with three jets of the sizes shown, and with the free surface level ta 
the reservoir at the heights marked. 


EipertmciK t. 

let io 5 is- itiiiMMr 














I s 












39-40 h „ 


41 9 o 






37-5-39-5J .. 







35 1 .> 







335-37 I » 





26 4-26 < 



31 1 .. 




263-26 -( 






























2 i 







i 5 
































42 15 




































As the general form of the pressure curve has been already indi- 
cated, it may be assumed that its equation is of the form 

v-a*"'. (O 

But it has already been shown that for x-o, y m h, hence a -a. 
To determine the remaining constant, the other condition may be 
used, that the solid formed by rotating the pressure curve rep 
the total pressure on the plane. The volume of the solid w 

-2rrkflb~ mt xdx 

-(t*/1o & 6)[-6^]" 

DtaUftcc b«m ub of |ct ta lacHc*. 

Fic. 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 t//2f . 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 tiroes the area of section of the jet. 

Using the condition already stated, 


log. 6 = (»/2«)V (A/A.). 
Putting the value of b in (2) in eq. (t), and also r for the radios of 
the jet at the orifice, so that «*ff*, the equation to the pressure 
curve is - 

f 166. Resistance of a Plane moving through a Fluid, or Pressure 
of a Current on a Plant. — When a thin plate moves through the 
air, or through an indefinitely large mass of still water, in a direction 
normal to its surface, there is an excess of pressure on the anterior 
face and a diminution of pressure on the posterior face. Let * be 
the relative velocity of the plate and fluid, Q the area of the plate, G 
the density of the fluid, h the height due to the velocity, then the 
total resistance is expressed by the equation 

R -/GO v*l2g pounds «=/GQ* ; 
where / is a coefficient having about the value 1*3 for a plate moving 
in still fluid, and 1 -8 for a current impinging ona fixed plane, whether 
the fluid is air or water. The difference in the value of the coefficient 
in the two cases is perhaps due to errors of experiment. There is a 
similar resistance to motion in the case of all bodies of " unfair ** 
form, that is, in which the surfaces over which the water slides are 
not of gradual and continuous curvature. 

The stress between the fluid and plate arises chiefly in this way* 


The «treami 
definitencsa I 
laterally at t 
ing fluid, in 
plate. Othei 
motion to fil 
pressure less 
whole resista 
pressure in fi 
is independe 
simply to iti 
edge of the plate. 

Experiments made by a whirling: machine, in which the plate is 
fixed on a long arm and moved circularly, gave the following values 
of the coefficient /. The method is not free from objection, as the 
centrifugal force causes a flow outwards across the plate. 




Area of Plate 

in sq. ft. 

Values of/. 






1 24 


There is a steady increase of resistance with the size of the plate, 
in part or wholly due to centrifugal action. 

P. L. G. Dubuat (1734-1809) made experiments on a plane 1 ft. 
square, moved in a straight line in water at 3 to 6) ft. per second. 
Calling m the coefficient of excess of pressure in front, and n the 
coefficient of deficiency of pressure behind, so that /-m+», he 
found the following values: — 

m«i ;«-o-433:/» 1-433- 
The pressures were measured by pressure columns. Experiments 
by A. J. Morin (1795-1880), G. Piobert (1793-1871) and 1. Didion 
(1798-1878) on plates of 0-3 to 2-7 sq. ft. area, drawn vertically 
through water, gave jf»2«i8; but the experiments were made in a 
reservoir of comparatively small depth. For similar plates moved 
through air they found /«i«36, a result more in accordance with 
those which precede. 

For a fixed plane in a moving current of water E. Mariotte found 
/— 1-25. Dubuat, in experiments in a current of water like those 
mentioned above, obtained the values m = i-i86; n =0-670; /- 
1-856. Thibault exposed to wind pressure planes of 1-17 and 2-5 
sq. ft. area, and found /to vary from 1-568 to 2-125, the mean value 
being/" 1-834, a result agreeing well with Dubuat. 

1 167. Stanton's Experiments on the Pressure of Air on Surfacer.~* 
At the National Physical Laboratory, London. T. E. Stanton carried 
out a series of experiments on the distribution of pressure on surfaces 
in a current of air passing through an air trunk. These were on a 
•mall scale but with exceptionally accurate means of measurement. 
These experiments differ from those already given in that the plane 
is small relatively to the cross section of the current (Proc. Inst. 
C». Eng. clvi., 1904). Fig. 169 shows the distribution of pressure 
on a square plate, ab is the plate in 
vertical section, acb the distribution 
of pressure on the windward and adb 
that on the leeward side of the central 
section. Similarly aeb is the distribu- 
tion of pressure on the windward and 
a/b on the leeward side of a diagonal 
' section. -The intensity of pressure at 
the centre of the plate on the windward 
side was in all cases p*G«*/2g lb per 
aq. ft., where G is the weight of a cubic 
foot of air and v the velocity of the 
current in ft. per sec. On the leeward 
side the negative pressure is uniform 
except near the edges, and its value 
depends on the form of the plate. For 
a circular plate the pressure on the 
leeward side was 048 Gt*l2g and for 
a rectangular plate 066 Gtffrg. For 
circular or square plates the resultant 
pressure on the plate was P- 0-00126 
v 1 tb per sq. ft. where v is the velocity 
of the current in ft. per sec. On a lonj 

Fie. 169. 

r MIg 

narrow rectangular plate the resultant pressure was nearly 60% 
greater than on a circular plate. In later tests on larger planes in 
free air. Stanton found resistances 18% greater than those observed 
with small planes in the air trunk. 

1 168. Case when the Direction oj Motion is oblique to the Plane. — 
The determination of the pressure between a fluid and surface in this 
case is of importance in many practical questions, for instance, in 
assigning the load due to wind pressure on sloping and curved roofs, 
and experiments have been made by Hutton, Vince, and Thibault on 
planes moved circularly through air and water on a whirling machine. 

Flo. 170. 

Let AB (fig. 170) be a plane moving in the direction R making 
an angle * 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*. 
In the case of wind pressure on 
a sloping roof surface, R is the 
horizontal and L the vertical 
component of the normal pres- 

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 * to its direction of motion, the resistance was 
found by Hutton to be 


A simpler and more convenient expression' given by Colonel 
Duchemin is 

R-2P sin» *\/(i-Hin» *\). 
Consequently, tne total pressure between the fluid and plane is 

N -2P sin */(i +sin» *) -2P/(cosec + + sin +), ' 
and the lateral force b 

L - 2P sin 4 cos */(i -fsin" «\). 

In 1872 some experiments were made for the Aeronautical Society 
on the pressure of air on oblique planes. These plates, of 1 to 2 ft. 
square, were balanced by ingenious mechanism designed by F. H. 
VVcnham and Spencer Browning, in such a manner that both the 
pressure in the direction of the air current and the lateral force were 
separately measured. These planes were placed opposite a blast 
from a fan issuing from a wooden pipe 18 in. square. The pressure of 
the blast varied from 1% to l in. 01 water pressure. The following are 
the results given in pounds per square foot of the plane, and a com- 
parison of the experimental results with the pressures given by 
Duchemin's rule. These last values are obtained by taking P "33X, 
the observed pressure on a normal surface: — A 

Ancle between Plane and Direction ) 
of Blast S 


20 m 



Horizontal pressure R . . . . 
Lateral pressure L . . . . . 
Normal pressure V L'-r- R" . . . 
Normal pressure by Duchemin's rule 








Water Motors 

In every system ot machinery deriving energy from a natural 
water-fall there exist the following parts: — 

1. A supply channel or head race, leading the water from the 
highest accessible level to the site of the machine. This may be 
an open channel of earth, masonry or wood, laid at as small a 
slope as is consistent with the delivery of the necessary supply of 
water, or it may be a closed cast or wrought-iron pipe, laid at 
the natural slope of the ground, and about 3 ft. below the surface. 
In some cases part of the head race is an open channel, part 
a closed pipe. The channel often starts from a small storage 
reservoir, constructed near the stream supplying the water motor, 
in which the water accumulates when the motor is not working. 
There are sluices or penstocks by which the supply can be cut 
off when necessary. 

2. Leading from the motor there is a tail race, culvert, or 
discharge pipe delivering the water after it has done its work 
at the lowest convenient level. 

3. A waste channel, weir, or bye-wash is placed at the origin 
of the head race, by which surplus water, in floods, escapes. 

4. The motor itself, of one of the kinds to be described presently, 
which either overcomes a useful resistance directly, as in the case 
of a ram acting on a lift or crane chain, or indirectly by actuating 
transmissive machinery, as when a turbine drives the shafting, 
belting and gearing of a mill. With the motor is usually com- 
bined regulating machinery for adjusting the power and speed 
to the work done. This may be controlled in some cases by 
automatic governing machinery. 



§ 169. Water Motors with Artificial Sources of Energy.—Thc 
great convenience and simplicity of water motors has led to their 
adoption in certain cases, where no natural source of water 
power is available. In these cases, an artificial source of water 
power is created by using a steam-engine to pump water to a 
reservoir at a great elevation, or to. pump water into a closed 
reservoir in which there is great pressure. The water flowing 
from the reservoir through hydraulic engines gives hack the 
* energy expended, less so much as has been wasted by friction. 
Such arrangements are most useful where a continuously acting 
steam engine stores up energy by pumping the water, while the 
work done by the hydraulic engines is done intermittently. 

f 1 70. Energy of a Water-fall.— Let H, be the total fall of level from 
the point where the water is taken from a natural stream to the 
point where it is discharged into it again. Of this total fall a portion, 
which can be estimated independently, is expended in overcoming 
the resistances of the head and tail races or the supply and discharge 
pipes. Let this portion of head wasted be k. Then the available 
ncad to work the motor is H « H»— k. It is this available head which 
should be used in all calculations of the proportions of the motor. 
Let Q be the supply of water per second. Then GQH foot-pounds 
per second is the gross available work of the fall The power of the 
fall may be utilized in three ways, (a) The CQ pounds of water may 
be placed on a machine at the highest level, and descending in con- 
tact with it a distance of H ft., the work done will be (neglecting 
losses from friction or leakage) GQH foot-pounds per second, (b) 
Or the water may descend in a closed pipe from the higher to the 
lower level, in which case, with the same reservation as before, the 
pressure at the foot of the pipe will be p «GH pounds per square foot. 
If the water with this pressure acts on a movable piston like that 
of a 6team engine, it will drive the piston so that the volume described 
is Q cubic feet per second. Then the work done will be pQ-GHQ 
foot-pounds per second as before, (e) Or lastly, the water may be 

allowed to acquire the velocity v «» V H H by its descent. The kinetic 
energy of Q cubic feet will then be jGOWie«GQH, and if the water 
is allowed' to impinge on surfaces suitably curved which bring it 

finally to rest, it will impart to these the same energy as in the 
previous cases. Motors which receive energy mainly in the three 
ways described in (a), (M, (c) may be termed gravity, pressure and 
inertia motors respectively. Generally, if Q ft. per second of water 
act by weight through a distance h t , at a pressure p due to ht ft. of 
fall, and with a velocity v due to A, ft. of fall, so that Ai+At+A»«H, 
then, apart from energy wasted by friction or leakage or imperfection 
of the machine, the work done will be 

GQ*i+pQ+(G/*)Q(**/a«) -GQH foot pounds, 
the same as if the water acted simply by its weight while descending 
H ft. 

§ 171. Site for Water Motor. — Wherever a stream flows from 
*m higher to a lower level it is possible to erect a water motor. 
The amount of power obtainable depends on the available head 
and the supply of water. In choosing a site the engineer will 
select a portion of the stream where there is an abrupt natural 
fall, or at least a considerable slope of the bed. He will have 
regard to the facility of constructing the channels which are to 
convey the water, and will take advantage of any bend in the river 
which enables him to shorten them. He will have accurate 
measurements made of the quantity of water flowing in the 
stream, and he will endeavour to ascertain the average quantity 
available throughout the year, the minimum quantity in dry 
seasons, and the maximum for which bye- wash channels must 
be provided. In many cases the natural fall can be increased 
by a dam or weir thrown across the stream. The engineer will 
also examine to what extent the head will vary in different 
seasons, and whether it is necessary to sacrifice part of the fall 
and give a steep slope to the tail race to prevent the motor being 
drowned by backwater in floods. Streams fed from lakes which 
form natural reservoirs or fed from glaciers are less variable than 
streams depending directly on rainfall, and are therefore advan- 
tageous for water-power purposes. 

f 172. Water Power at Holyoke, U.SA.— About 83 m. from the 
mouth of the Connecticut river there was a fall of about 60 ft. in 
a short distance, forming what were called the Grand Rapids, below 
which the river turned sharply, forming a kind of peninsula on which 
the city of Holyoke is built. In 1845 the magnitude of the water- 
power available attracted attention, and it was decided to build a 
dam across the river. The ordinary flow of the river is 6000 cub. ft. 
per sec., giving a gross power of 30.000 h.p. In dry seasons the 
power is 20,000 h.p., or occasionally less. From above the dam a 
system of canals takes the water to mills on three levels. The first 
canal starts with a width of 140 ft. and depth of 22 ft., and supplies 


the highest range of mills. A second canal takes the water which 
has driven turbines in the highest mills and supplies it to a second 
series of mills. There is a third canal on a still lower level supplying 
the lowest mills. The water then finds its way back to the nver. 
With the grant of a mill site is also leased the right to use the water- 
power. A mill-power is defined as 38 cub. ft. of water per sec 
during 16 hours per day on a fall of 20 ft. This gives about 60 h-p, 
effective. The charge for the power water is at the rate of 20c per 
h.p. per annum. 

§ 173. Action of Water in a Water Motor. — Water motors may 
be divided into water-pressure engines, water-wheels and 

Water-pressure engines are machines with a cylinder and piston 
or ram, in principle identical with the corresponding part of a 
steam-engine. The water is alternately admitted to and dis- 
charged from the cylinder, causing a reciprocating action of the 
piston or plunger. It is admitted at a high pressure and dis- 
charged at a low one, and consequently work is done on the piston. 
The water in these machines never acquires a high velocity, and 
for the most part the kinetic energy of the water is wasted. 
The useful work is due to the difference of the pressure of 
admission and discharge, whether that pressure is due to the 
weight of a column of water of more or less considerable height, 
or is artificially produced in ways to be described presently. 

Water-wheels are large vertical wheels driven by water falling 
from a higher to a lower level In most water-wheels, the water 
acts directly by its weight loading one side of the wheel and so 
causing rotation. But in all water-wheels a portion, and in some 
a considerable portion, of the work due to gravity is first em- 
ployed to generate kinetic energy in the water; during its 
action on the water-wheel the velocity of the water diminishes, 
and the wheel is therefore in part driven by the impulse doe to 
the change of the water's momentum. Water-wheels are there- 
fore motors on which the water acts, partly by weight, partly by 

Turbines are wheels, generally of small size compared with 
water wheels, driven chiefly by the impulse of the water. Before 
entering the jnoving part of the turbine, the water is allowed 
to acquire a considerable velocity; during its action 00 the 
turbine this velocity is diminished, and the impulse due to the 
change of momentum drives the turbine. 

In designing or selecting a water motor it is not sufficient to 
consider only its efficiency in normal conditions of working. 
It is generally quite as important to know how it will act with 
a scanty water supply or a diminished head. The greatest 
difference in water motors is in their adaptability to varying 
conditions of working. 

Water-pressure Engines. 

$174. In these the water acts by pressure either due to the 
height of the column in a supply pipe descending from a high- 
level reservoir, or created by pumping. Pressure engines were 
first used in mine-pumping on waterfalls of greater height than 
could at that time be utilised by water wheels. Usually they 
were single acting, the water-pressure lifting the heavy pump 
rods which then made the return or pumping stroke by their 
own weight. To avoid losses by fluid friction and shock the 
velocity of the water in the pipes and passages was restricted 
to from 3 to 10 ft. per second, and the mean speed of plunger to 
1 ft. per second. The stroke was long and the number of strokes 
3 to 6 per minute. The pumping lift being constant, such engines 
worked practically always at full load, and the efficiency was 
high, about 84%. But they were cumbrous machines. They 
are described in Weisbach's Mechanics of Engineering. 

The convenience of distributing energy from a central station 
to scattered working-points by pressure water conveyed in pipes 
—a system invented by Lord Armstrong— has already been 
mentioned. This system has led to the development of a great 
variety of hydraulic pressure engines of very various types, 
The cost of pumping the pressure water to some extent restricts 
its use to intermittent operations, such as working lifts and 
cranes, punching, shearing and riveting machines, forging **A 
flanging presses. To keep down the cost of the distributing 




mains very high pressures are adopted, generally 700 lb per 
sq. in. or 1600 ft. of head or more. 

In a large number of hydraulic machines worked by water at 
high pressure, especially lifting machines, the motor consists of a 
direct, single acting ram and cylinder. In a few cases double- 
acting pistons and cylinders are used; but they involve a 
water-tight packing of the piston not easily accessible. In some 
cases pressure engines are used to obtain rotative movement, 
and then two double-acting cylinders or three single-acting 
cylinders are used, driving a crank shaft. Some double-acting 
cylinders have a piston rod half the area of the piston. The 
pressure water acts continuously on the annular area in front 
of the piston. During the forward stroke the pressure on the 
front of the piston balances half the pressure on the back. During 
the return stroke the pressure on the front is unopposed. The 
water in front, of the piston is not exhausted, but returns to the 
supply pipe. As the frictional losses in a fluid are independent 
of the pressure, and the work done increases directly as the 
pressure, the percentage loss decreases for given velocities of 
flow as the pressure increases. Hence for high-pressure machines 
somewhat greater velocities are permitted in the passages than 
for low-pressure machines. In supply mains the velocity is 
from 3 to 6 ft. per second, in valve passages 5 to 10 ft. per second, 
or in extreme cases 20 ft. per second, where there is less object 
in economizing energy. As the water is incompressible, slide 
valves must have neither lap nor lead, and piston valves are 
preferable to ordinary slide valves. To prevent injurious com- 
pression from exhaust valves closing too soon in rotative engines 
with a fixed stroke, small self-acting relief valves are fitted to the 
cylinder ends, opening outwards against the pressure into the 
valve chest. Imprisoned water can then escape without over- 
straining the machines. 

In direct single-acting lift machines, in which the stroke is 
fixed, and in rotative machines at constant speed it is obvious 
that the cylinder must be filled at each stroke irrespective of the 
amount of work to be done. The same amount of water is used 
whether much or little work is done, or whether great or small 
weights are lifted, Hence while pressure engines are very 
efficient at full load, their efficiency decreases as the load de- 
creases. Various arrangements have been adopted to diminish 
this defect in engines working with a variable load. In lifting 
machinery there is sometimes a double ram, a hollow ram 
enclosing a solid ram. By simple arrangements the solid ram 
only is used for small loads, but for large loads the hollow ram is 
locked to the solid ram, and the two act as a ram of larger area. 
In rotative engines the case is more difficult. In Hastie's and 
Rigg's engines the stroke is automatically varied with the load, 
increasing when the load is large and decreasing when it is small. 
But such engines are complicated and have not achieved much 
success. Where pressure engines are used simplicity is generally 
a first consideration, and economy is of less importance. 

§ 1 75. Efficiency of Pressure Engines. — It is hardly possible to form 
a theoretical expression for the efficiency of pressure engines, but 
some general considerations are useful. Consider the case of a long 
stroke hydraulic ram, which has a fairly constant velocity * during 

the stroke, and valves which are fairlv wide open du~ * -' *he 

stroke. Let r be the ratio of area 01 ram to area o ge, 

a ratio which may vary in ordinary cases from 4 * lie 

loss in shock of the water entering the cylinder will I in 

ft. of head. The friction in the supply pipe is also to 

**. The energy carried away in exhaust will be pr s*. 

Hence the total hydraulic losses may be taken to b ely 

t&i2g ft., where f is a coefficient depending on the p he 

machine. Let / be the friction of the ram packing sm 

reckoned in lb per sq. ft. of ram area. Then if ipe 

pressure driving the machine is p lb per sq. ft., the c ing 

pressure will be 

p-G&/2g-f lb per sq. ft. 
Let A be the area of the ram in sq. ft., v its velocity in ft. per sec. 
The useful work done will be 

{p-GMu-f)A* ft. lb per sec, 
and the efficiency of the machine will be 

This shows that the efficiency increases with the pressure p, and 
diminishes with the speed v, other things being the same. If in 



Lwtltf Sa 

regulating the engine for varying load the pressure is throttled, 
part of the available head is destroyed at the throttle valve, and 
P.»n " above is reduced. Direct-acting hydraulic lifts, 

wtthc liate gearing, may 

have - of 95 % during the 

world f a hydraulic jigger is 

used 1 id sheaves to change 

the s| ram to the speed of 

the L iency may be only 

50% lgton has given the 

efficic ts with hydraulic 

balan during the working 

strokt _ m essure engines have 

an efficiency of 85 %, but small rota- 
tive engines probably not more than 
50 % and that only when fully loaded. 

§ 176. Direct- Acting Hydraulic 
Lift (fig. 171).— This is the 
simplest of all kinds of hydraulic 
motor. A cage W is lifted directly 
by water pressure acting in a 
cylinder C, the length of which is 
a little greater than the lift. A 
ram or plunger R of the same 
length is attached to the cage. 
The water-pressure admitted by a 
cock to the cylinder forces up the 
ram, and when the supply valve is 
closed and the discharge valve 
opened, the ram descends. In 
this case the ram is 9 in. diameter, 
with a stroke of 49 ft. It consists 
of lengths of wrought-iron pipe 
screwed together perfectly water- 
tight, the lower end being closed 
by a cast-iron plug. The ram 
works in a cylinder iz in. dia- 
meter of 9 ft. lengths of flanged 
cast-iron pipe. The ram passes 
water-tight through the cylinder 
cover, which is provided with 
double hat leathers to prevent 
leakage outwards or inwards. As 
the weight of the ram and cage is 
much more than sufficient to cause - 
a descent of the cage, part of the 
weight is balanced. A chain at- 
tached to the cage passes over a 
pulley at the top of 
the lift, and carries 
at its free end a 
balance weight B, 
working in T iron 
guides. Water is ad- 
mitted to the cylinder 
from a 4-in. supply 
pipe through a two- 
way slide, worked by 
a rack, spindle and 
endless rope. The 
lift works under 73 
ft. of head, and lifts 
1350 lb at 2 ft. per 
second. The effi- 
ciency is from 75 to 

The principal pre- 
judicial resistance to 
the motion of a ram 
of this kind is the fric- 
tion of the cup leathers, 
which make the joint 
between the cylinder 
and ram. Some ex- 
periments by John Hick give for the friction of these leathers 
the following formula. Let F- the total friction in pounds; 




** -diameter of ram in ft.; p>> water-pressure in pounds per aq. ft.; 
k a coefficient. 

k — 0*00393 if the leathers are new or badly lubricated; 
>b 0-00262 if the leathers are in good condition and well lubricated, 
e- u- *^-i *u j 8 p.,1,^ the fraction f t h c 

ig the friction of the leathers is 


ire column measured from the 

the bottom of the ram in its 
the discharge reservoir to the 

1 above its lowest point at any 
area of the ram, W the weight 
might of balance weight, «r the 
F the friction of the cup leather* 
riction, if the ram is rising the 

and if the ram is descending 

P,- -G(H»-A)Q+W+R-B+w(S-A) -tdk-F. 
If v»} GO, Pi and P» are constant throughout the stroke; and 
the moving force in ascending and descending is the same, if 

Using the values just found for w and B, 

Let W+R+tuS+B-U, and let P be the constant accelerating 
force acting on the system, then the acceleration is (P/lty*. Thc 
velocity at the end of the stroke is (assuming the friction to be 


and the mean velocity of ascent is \v. 

fi 177. Armstrong's Hydraulic Jigger. — This is simply a single- 
acting hydraulic cylinder and ram, provided with sheaves so 
as to give motion to a wire rope or chain. It is used in various 
forms of lift and crane. Fig. 172 shows the arrangement. A 
hydraulic ram or plunger B works in a 
stationary cylinder A. Ram and cylinder 
carry sets of sheaves over which passes a 
chain or rope, fixed at one end to the 
cylinder, and at the other connected over 
guide pulleys to a lift or crane. For each 
pair of pulleys, one on the cylinder and one 
on the ram, the movement of thc free end 
of the rope is doubled compared with that 
of the ram. With three pairs of pulleys the 
free end of the rope has a movement equal 
\ to six times the stroke of the ram, the force 
« exerted being in the inverse proportion. 
1 1 178. Rotative Hydraulic Engines. — Valve- 
gear mechanism similar in principle to that 
of steam engines can be applied to actuate 
the admission and discharge valves, and the 
pressure engine is then converted into a con- 
tinuously-acting motor. 

Let H be the available fall to work the 
engine after deducting the loss of head in- the 
supply and discharge pipes, Q the supply of 
water in cubic feet per second, and n . thc 
efficiency of the engine. Then the horse-power 
of the engine is 

H.P.-,CQH/55a . 
The efficiency of large slow-moving pressure engines is q« *66 to -8. 
In small motors of this kind probably q is not greater than -5. 
Let v be the mean velocity of the piston, then its diameter d is given 
by the relation 

Q-rrftyA in double-acting engines, 
«*dh>/8 in single-acting engines. 
If there are n cylinders put Q/i* for Q in these equations. 
Small rotative pressure engines form extremely convenient 
motors for hoists, capstans or winches, and for driving small 
machinery. The single-acting engine has the advantage that 
the pressure of the piston on the crank pin is always in one 
direction; there is then no knocking as the dead centres are 
passed. Generally three single-acting cylinders are used, so 
that the engine will readily start in all positions, and the driving 
effort on the crank pin is very uniform. 

Brotherhood Hydraulic Engine. — Three cylinders at angles of 120° 
with each other are formed in one casting with the frame. The 

Fig. 17a. 

Fio. 173. 


plungers are hollow trunks, and the connecting rods abut in 
cylindrical recesses in them and are connected to a common crank 
pin. A circular valve disk with concentric segmental ports revolves 
at the same rate as the crank over ports in the valve face com moo to 
the three cylinders. Each cylinder is always in communication with 
cither an admission or exhaust port. The blank parts of the circular 
valve close the admission and exhaust ports alternately.. The fixed 
valve face is of lignum vitae in a metal recess, and the revolving 
valve of gun-metal.. In the case of a small capstan engine thc 
cylinders arc 3! in. diameter and 3 in. stroke. At 40 rcys. per minute, 
the piston speed is 31 ft. 
per minute. The ports 
are 1 in. diameter orA 
of the piston area, ana 
the mean velocity in 
the ports 6-4 ft. per 
sec With 700 lb per 
sq. in. water pressure 
and an efficiency of 
50% the engine is 
about 3 h.p. A com- 
mon arrangement is to 
have three parallel 
cylinders acting on a 
three-throw crank shaft, 
the cylinders oscillating I 
on trunnions. 

Hastie* s Engine. — Fig. ' 
173 shows a similar «. 
engine made by Messrs a 
Hastie of Greenock. G, * 
G, G are the three 
plungers which pass out 
of the cylinders through cup leathers, and act on the same crank pin. 
A is the inlet pipe which communicates with the cock B. This cock 
controls the action of thc engine, being so constructed that it acts as 
a reversing valve when the handle C is in its extreme positions and 
as a brake when in its middle position. With the handle in its 
middle position, the ports of the cylinders are in communicatioa 
with the exhaust. Two passages are formed in the framing leading 
from the cock B to the ends of the Cylinders, one being in com- 
munication -with the supply pipe A, the other with the discharge 
pipe Q. These passages end as shown at E. The oscillation of the 
cylinders puts them 
alternately in com- 
munication with each of 
these passages, and thus 
the water is alternately 
admitted and exhausted. J 

In any ordinary rota- 
tive engine the length of 
stroke is invariable. 
Consequently the con- 
sumption of water de- 
pends simply on the 
speed of the engine, 
irrespective of the effort overcome. 

must be varied without altering the number of rotations, 
the stroke must be made variable. Messrs Hastie have con- 
trived an exceedingly ingenious method of varying the stroke 
automatically, in proportion to the amount of work to be done (fig. 
174). The crank pin I 
is carried in a slide H 
moving in a disk M. 
In this is a double 
cam K acting on two 
small steel rollers J, 
L attached to the 
slide H. If the cam 
rotates it moves the 
slide and increases or 
decreases the radius of 1 
the circle in which the I 
crank pin I rotates. 
The disk M is keyed 
on a hollow shaft sur- 
rounding the driving 
shaft P, to which the 
cams are attached. 
The hollow shaft N 
has two snugs to 
which the chains RR 
are attached (fig. 175). 

The shaft P carries the Fl . 

spring case SS to which '^* 

also are attached the 

other ends of the chains. When the engine is at rest the springs 
extend themselves, rotating the hollow shaft N and the frame M, 
so as to place the crank pin I at its nearest position to the axis of 
I rotation. When a resistance has to be overcome, the shaft N rotates 

Fig. 174. 

If the power of the engine 
ts, tbess 




relatively to P, compressing the springs, tin their resistance balances 
the pressure due to the resistance to the rotation of P. The engine 
then commences to work, the crank pin being in the position in 
which the turning effort just overcomes the resistance. If the 
resistance diminishes, the springs force out the chains and shorten the 
stroke of the plungers, and vice versa. The following experiments, 
on an engine of this kind working a hoist, show how the automatic 
arrangement adjusted the water used to the work done. The lift 
was 22 ft. and the water pressure in the cylinders 80 lb per sq. in. 
Weight lift«M Chjjn J m 6JJ 74J 8J7 ^ I0gl „ M 

W g Sr l ' !n { 7» «► »4 l« 17 SO « » 


\ 179. Accumulator Machinery.— -It has already been pointed 
out that it is in some cases convenient to use a steam engine 
to create an artificial head 0/ water, which is afterwards employed 
in driving water-pressure machinery. Where power is required 
intermittently, for short periods, at a number of different points, 
as, for instance, in moving the cranes, lock gates, &c, of a 
dockyard, a separate steam engine and boiler at each point is 
very inconvenient; nor can engines worked from a common 
boiler be used, because of the great loss of heat and the difficulties 
which arise out of condensation in the pipes. If a tank, into 
which water is continuously pumped, can be placed at a great 
elevation, the water can then be used in hydraulic machinery 
in a very convenient way. Each hydraulic machine is put 
in communication with the tank by a pipe, and on opening a 
valve it commences work, using a quantity of water directly 
proportional to the work done. No attendance is required when 
the machine is not working. 

A site for such an elevated tank is, however, seldom available, 
and in place of it a beautiful arrangement termed an accumulator, 
invented by Lord Armstrong, is used. This consists of a tall 
vertical cylinder; into this works a solid ram through cup 
leathers or hemp packing, and the ram is loaded by fixed weights, 
so that the pressure in the cylinder is 700 lb or 800 lb per 
In some cases the ram is fixed and the cylinder moves on it. 

The pumping en- 
gines which supply 
the energy that 
is stored in the ac- 
cumulator should 
be a pair coupled 
at right angles, so. 
as to start in any 
position. The en- 
gines pump into 
the accumulator 
cylinder till the 
ram is at the top 
of its stroke, when 
by a catch ar- 
rangement acting 
on the engine 
throttle valve 
the engines are 
stopped. If the 
accumulator ram 
descends, in con- 
sequence of water 
being taken to 
work machinery, 
the engines im- 
mediately recom- 
mence working. 
Pipes lead from 
the accumulator 
to each of the 
machines requir- 
ing to be driven, 
and do not require to be of large size, as the pressure is so 

Fig. 176 shows a diagrammatic way the scheme of a system o 1 
Accumulator machinery. A is the accumulator, with its ram carry 

Fie. 176. 

ing a cylindrical wrought-iron tank W, in which weights are placed 
to load the accumulator. At R is one of the pressure engines or 
jiggers, worked from the accumulator, discharging the water after use 
into the tank T. In this case the pressure engine b shown working a 
set of blocks, the fixed block being on the ram cylinder, the running 
block on the ram. The chain running over these blocks works a 
lift cage C, the speed of which is as many times greater than that of 
the ram as there are plies of chain on 
the block tackle. B is the balance 
weight of the cage. 

In the use of accumulators on ship- 
board for working gun gear or steering 
gear, the accumulator ram is loaded by 
springs, or by steam pressure acting on a 
piston much larger than the ram. 

R. H. Tweddell has used accumula- 
tors with a pressure of 2000 lb per 
sq. in. to work hydraulic riveting ma- 

The amount of energy stored in the 
accumulator, having a ram d in. in 
diameter, a stroke of S f t , and deliver- 
ing at p lb pressure per sq. in., is 

~pd*S foot-pounds. 

Thus, if the ram is 9 in., the stroke 20 ft., 
and the pressure 800 lb per sq. in., the 
work stored in the accumulator when the 
ram is at the top of the stroke is 1 ,01 7 ,600 
foot-pounds, that is, enough to drive a 
machine requiring one horse power for 
about half an hour. As, however, the 
pumping engine replaces water as soon 
as it is drawn off, the working capacity 
of the accumulator is very much greater 
than this. Tweddell found that an ac- 
cumulator charged at 1250 lb discharged 
at 1225 lb per sq. in. Hence the friction 
was equivalent jo 12) lb per sq. in. and 
the efficiency 98 %. 

When a very great pressure is required FlC. 177. 

a differential accumulator (fig. 177) is 

e ..... i>t. .-- *— a -_j pagge, through both ends of 

tl diameters at the two ends, 

A meters of the ram in inches and 

p sq. in., the load required is 

\ Jus kind used with riveting 

n be pressure is 2000 lb per sq. in. 


ed by water or steam pressure 
i, 78 shows tl 

o i of much 

J by 

8 shows the arrangement. A 

of much 
8 rom town 

n the high 

fj ]ischargcd 

, cs. If r is 

t! n, neglect- 

ii ir cylinder 

is . With a 

v from the 

u Kt ~. -,.... - r and falls, 

maintaining always a constant pressure in the 
upper cylinder. 

Water Wheels. 

§ 180. Overshot and High Breast Wheels. 
—When a water fall ranges between 10 
and 70 ft. and the water supply is from 3 
to 25 cub. ft. per second, it is possible to 
construct a bucket wheel on which the water 
acts chiefly by its weight. If the variation 
of the head-water level does not exceed 2 ft., 
an overshot wheel may be used (fig. 179). 
The water is then projected over the summit 
of the wheel, and falls in a parabolic path 
into the buckets. With greater variation of head-water level, a 
pitch-back or high breast wheel is better. The water falls over 
the top of a sliding sluice into the wheel, on the same side as the 
head race channel. By adjusting the height of the sluice, the 
requisite supply is given to the wheel in all positions of the 
head-water level. 

The wheel consists of a cast-iron or wrought-iron axle C 
supporting the weight of the wheel. To this are attached two 


Fig. 178. 

9 6 


sets of arms A of wood or iron, which support circular segmental 
plates, B, termed shrouds. A cylindrical sole plate dd extends 
between the shrouds on the inner side. The buckets are formed 

Fig. 179. 

by wood planks or curved wrought-iron plates extending from 
shroud to shroud, the back of the buckets being formed by the 
sole plate. 

The efficiency may be taken at 0*75. Hence, if h.6. is the effective 
horse power, H the available fall, and Q the available water supply 
per second, 

K p.-075(GQH/55o)-o.o85 QH. 

If the peripheral velocity of the water wheel is too great, water is 
thrown out of the buckets before reaching the bottom of the fall. 
In practice, the circumferential velocity of water wheels of the kind 
now described is from 4} to 10 ft. per second, about 6 ft. being the 
usual velocity of good iron wheels not of very small size. In order 
that the water may enter the buckets easily, it must have a greater 
velocity than the wheel. Usually the velocity of the water at the 
point where it enters the wheel is from 9 to 12 ft. per second, and 
to produce this it must enter the wheel at a point 16 to 27 in. below 
the head-water level. Hence the diameter of an overshot wheel 
may be 

Overshot and high breast wheels work badly in back-water, and hence 
if the tail- water level varies, it is better to reduce the diameter of 
the wheel so that its greatest immersion in flood is not more than 

1 ft. The depth d of the shrouds is about 10 to 16 in, The number 
of buckets may be about 

Let 9 be the peripheral velocity of the wheel. Then the capacity 
of that portion of the wheel which passes the sluice in one second is 

"V b d nearly, 
b 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 » mQi «* mbdv. 
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 a*- distance between two 
buckets on periphery of wheel. Make ed~\ cb, and bc = \ to } ik. 
Join cd. For an iron bucket (fig. 180, B), take e&~\ eb; oc- f«*. 
Draw eO making an A D 

angle of io°toi5*with ,_ <« . — B 

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 dt. 

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 Fic * ,8 °* 

the power to the shafting. It is obvious that the 
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 inn 
suspension arms incapable of resisting the bending action doc 
to the transmission of the turning effort to the aide. In that 
case spur segments are bolted to one of the shrouds, and the 
pinion to which the power U 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 12 s h.p., erected 
by Sir W. Fairbairn in 1825 at Catrine in Ayrshire. These wheels 
are still working. 

f x8i. Poncdd Water Wheel.— When the fall does not exceed 
6 ft n the best water motor to adopt in many cases is the Poncdet 
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, and 
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 whok 
of its original kinetic energy. 

Taking the efficiency at 0-60, and putting H for the available faB. 
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 cot 
be less than twice the Tall 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 


depth of bucket should tx 
of buckets about half t 
usually of cast iron with 
may be of iron i in. thic 

Let H' be the fall mi 
water to the point T" whe 
velocity at which the 1 
circumferential velocity 
number of rotations of 
thickness of the sheet 
portant. The best thic 
in. The maximum thicl 
there is a surplus "water i 
of water entering the wh 

bcv-Q; or b-Qfev. 
Crashof takes 4 - |H, and then 

AUowing for the contraction of the stream, the area of 
through the slake may be 1*25 be to 1*3 be. The inside width 
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, i8a. 

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 




Fig. 182. 

the dose 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-0-5 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 b 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 o-68. It is better to take it at 0*6 in estimating the power 
of the wheel, so as to allow some margin. 

In fig. 182 «< is the initial and «• the final velocity of the water, 
* parallel to the vane the relative velocity of the water and wheel, 
and V the velocity of the wheel. 


% 1S1. 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 Socie'te' 
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 Benolt Fourneyron • (1802-1867), 
whose turbine, but little modified, is still constructed. 

Classification of Turbines.— lu 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 the 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 t' 
same; they receive water equal!; 
In the latter case, they receive v 
only. The former may be 1 
admission, the latter turbines wi 
turbine should always have cc 
turbine may have complete or 1 

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 

( ) Complete admission. (Rare.) 
'&) Partial admission. (Usual.) 


II. Reaction Turbines. 

(Wheel passages filled, discharge 
ing above or below the tail 
water or into a suction-pipe.) 

Always with complete admis- 

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 C 
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- Fig. 183. 

tical pipe to the centres of the orifices, 

r the radius from the axis of rotation to the centres of the orifices, 
v the velocity of discharge through the jets, • the angular velocity of 




the machine. When the machine is at rest the water issues from 
the orifices with the velocity V (zgH) (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/ag ft. of water, and the velocity of discharge 
through the orifices is vj (2gH+ah*). If the total area of the 
orifices is u, the quantity discharged from the wheel per second is 

While the water passes through the orifices with the velocity v, the 
orifices are moving in the opposite direction with the velocity •/. 
The absolute velocity of the water is therefore 

The momentum generated per second is (GQ/*)(»-*r), 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 

(OQ/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-*r)*r W2£H+a i r*-*r]ar 

* gH gH ■* 

Let v^^...' 

then i-i-gH/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 
huh velocities of rotation, the friction would considerably reduce the 
efficiency. Experiment seems to show that the best efficiency is reached 
when or — V (2gH). Then the efficiency apart from friction is 
l-{V(2aV)-«V/fH * 
t »o-4i4««r , /f H -0828, 
about 17 % 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 ai % of the energy of the fall is lost in friction, in 
addition to. the energy cirried away by the water. 

1 184. General SkfUment of Bydrodynamkal Principles necessary for 
the Theory of Turbines, 
(4) 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. «i the velocity, and si the 
elevation above any horizontal datum plane, and that at a section 
B the same quantities are denoted by hu t% a> Then r 

^-(•s^/ai-Hk-* CO 

If the flow is horizontal, s» — *i ; and » »: 

Ai-fc-dt*-**)/**. (to) 

(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 (8 36). Let vi, vt be the velocities before and 
after the abrupt change, then a stream of velocity 9i impinges on a 
stream at a velocity «a, and the relative velocity is sft*. The 
head lost is (vr+tPfag. Then equation (10) becomes 

iWi-(ftMtf)/2H^)V2f-*frr^/* (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. 

Jc) Equality of Angular Impulse 
I Chants of Angular Momen- 
tum. — Suppose that a couple, the 
moment 01 which is M, acts on a 
body of weight W f or I seconds, 
during which it moves from Ai 
to As (fig. 184). Let p, be the 
velocity of the body at Ai, t* its 
velocity at A,, and let Puptbc 
the perpendiculars from C on si 
and t»|. Then Ml is termed the 
angular impulse of the couple, and 
the quantity 

is the change of angular momen- 
tum relatively to C. Then, from 
the equality of angular impulse 

Fie. 184. 

and change of angular momentum 

M/-(W/s)fo/>r*fr) t 
or, if the change of momentum is estimated for one second, 

Let ft, ft be the radii drawn from C to A,, A*, and let Vi, u\ be the 
components of v t , vi, perpendicular to these radii, making angles 
fi and a with vu •*. Then 

t»i -Wi sec 0; t* -Wt sec a; 

Pi - fi cos 0; pi -r t cos a. 
.\\l-(W/*)(ttVrWi). (J) 

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 

Now the water flowing through a turbine enters at the l 

surface and leaves at the discharge surface of the wheel, with its 
angular momentum relatively to the axis of the wheel ftungrd 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 w>, a* be 
the tangential components of the velocity of the water at the re 
ing and discharging surfaces of the wheel, r it r% the radii of 1 
surfaces By the principle above, 

., . -M-(GQ//)(«vrWi). (4) 

If « is the angular velocity of the wheel, the work done by the 
water on the wheel is 

T - Ma ■■ (GQ/g) (wkrrHPtrt)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 b p be that toss of head, which varies with the local conditions in 
which the turbine is placed. Then 

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 b 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-fc, bat the 
efficiency of the turbine for the head H. 

f 186. Cross Efficiency and Hydraulic Efficiency of a Turbine.— Let 
Te be the useful wodc done by the turbine, in foot-pounds per 
second, Ti the work expended in friction of the turbine shaft, 
gearing, Sec, a quantity which varies with the local conditions kx 
which the turbine is placed. Then the effective work done by tat 
water in the turbine is 

The gross efficiency of the whole arrangement of turbine, races, 
and transnriasive machinery is 

m-TVGQrU (6) 

And the hydraulic efficiency of the turbine alone is 

i-T/GQH. (7) 

It is this last efficiency only with which the theory of turbines is 
From equations (5) and (7) we get 

*GQH - (GQ/g)(w,r,-ivt)a; 

n - <wuv-uy»)a/gH. (8) 

This is the fundamental equation in the theory of turbine*. la 
general, 1 u\ and Wt, the tangential components of the water*! 
motion on entering and leaving the wheel, are completely ode- 
pendent. That the efficiency may be as great as possible, it a 
obviously necessary that u& -o. In that case 

A-Wifia/gH. (9) 

art b the circumferential velocity of the wheel at the inlet surface. 
Calling this Vi, the equation becomes 

f-w»V,/gH. (9*) 

This remarkably simple equation is the fundamental equation ia 
the theory of turbines. It was first given by Retche {Turbine*- 
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 uV 
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 ate 
added to a turbine at the discharging side, then ft may in part dfpre* 
on fi, and the statement above is no longer true. 




on entering the cue 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. 

Fie. 186. 

Fio. 187. 

Fig. 188. 

acquires ft velocity about equal to that due to half the fall, and is 1 the centre plate are the curved wheel vanes, on which the pressure 
directed into the wheel at ao 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 




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. 189. 

Fig. 19a 

J, /, / 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 

•f * 

Fig. 193. 



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 
Bow turbines have the wheel as in C* The vanes are limited by two 
concentric cylinders. ^ 

Theory of Reaction Turbinen \ 

% 190. Velocity of Whirl and Velocity of Flow.—Lti~dcQ (fig. ,103) 
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 t>. in 
the direction of a 
tangent to the path. 
That velocity may be 
resolved into two 
components, a whirl- 
Fig. 193. «* velocity w in the 

direction 0/ the 
wheel's rotation at the point c, and a component « 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 v., *>.,** be the velocity of the water, the whirling velocity and 
velocity of flow at the outlet surface of the wheel, and Vu w«, v< 
the same quantities at the inlet surface of the wheel. Let a and fi 
be the angles which the waters direction of motion makes with the 
direction of motion of the wheel at those surfaces. Then - 


«•»«• cosl; *.«tr.sin fi 

Vi«v<cosa: Ui—vt sin 
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 
Q* Qi 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), 

Q.-2rr d < ,>,Q i -2TTidi. (120) 

Similarly, for an outward flow turbine, 

C-awr^ai-asTrf; («&) 

and, for an axial flow turbine, 

n.-Qj-»(r^-ri«).- (wO 

• 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 may be resolved 
into a component V, 
which the water has 
in common with the 
wheel, and a component 
a., 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 
p T/ , fA . smaller the wheel is 

™' x 94« made. But if the wheel 

works under water, the 
skin friction of the wheel cover in crease s 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 Urge 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 to 02 V fa H) ; 
In outward flow turbines, m -o^sV 2g(H - p). 

tu-o-21 too-l 7V2g( H-fr);' 
In inward flow turbines, «, -** -o- 125 V fa H). 
I 191. Speed of Ike Wheel.— The best speed of the wheel depends 
partly on the frictional losses, which the ordinary theory of turbines 


disregards. It is beat, therefore, to assume for V. and V< values 
which experiment has shown to be most advantageous. 

In axial flow turbines, the circumferential velocities at the mean 
radius of the wheel may be taken 

V.-V*-o-6V"5rT to 0-66V2iTn 
In a radial outward flow turbine, 

V # -V^r,, 
where r«, r< are the radii of the outlet and Inlet surfaces. 

In a radial inward flow turbine, 

If the wheel were stationary and the water flowed through it, the 
water would follow paths parallel to the wheel vane curves, at least 
when the vanes were so close that irregular motion was prevented. 
Similarly, when the wheel is in motion, the water follows paths rela- 
tively to the wheel, which are curves parallel to the wheel vanes. 
Hence the relative component, *, of the water's motion at c is tan- 
gential to a wheel vane curve drawn through the point c. Let »* 
V* »,. be the velocity of the water and its common and relative 
eompocents at the outlet surface of the wheel, and v it V«, *w be the 
same quantities at the inlet surface; and let 6 and 4 be the angles 
the wheel vanes make with the inlet and outlet surfaces; then 

*«?- V W+V.'-aV** cos +) ) 

K -V0*>+V|»-2V < t* cos *) 1» 


equations which may be need to determine + and #. 

§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.<-o. Hence, 
from (10), cos /J-o, 
0-90 » «•-»#, 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 

Drawing t> # or «• 
radial or axial as the \ Fl0m IQ5> 

case may be, and V» > '" 

tangential to the direction of motion, *• can be found by the 
parallelogram of velocities. From fig. 195, 

tan *-*/V.-«W.; (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 flown, and velocity of the wheel V, are known. When + is thus 
dete rT n ?nffl, 

ty f -«.coefie*-VW(i+«.W).^ (140) 

Correction of the Angle * to allow for Thickness of Vanes.— In 
determining 4* it is most convenient to calculate its value approxi- 
mately at first, from a value of *• 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 > 

♦'- tanr«(«W.) - tan->(QAi.V.) v . 
be the first or approximate value of +. and let I be the thickness, 
and n the number of wheel vanes which reach the outlet surface of 
the wheel As the vaneexut the outlet surface approximately at 
the angle +', their width measured on that surface is / cosec ♦'. 
Hence the space occupied by the vanes on the outlet surface is 
For A, fig. 192, ntd cosec * "1 J 

B. fig. 192, ntd cosec + V (15) 

C, fig. 192, nHft-ry) cosec +J 1 

Call this area occupied by the vanes u. Then the true value of the 
dear discharging outlet of the wheel is 0,-w, and the true value 
of «. is QI(P,-v). The. corrected value of the angle of the vanes will 
be ~ 

+-tan [Q/V\(0.-»)]. 


1 103. Head producing Velocity with which the Water enters the 
When. — 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 work done by gravity on the water passing 
through the wheel In the case of an axial flow turbine, in whicn 
the flow is vertical, the fall d between the inlet and outlet surfaces 
should be taken into account. 


Let Vi, V* be the velocities of tbe wheel at the inlet and 
outlet surfaces, 
•u, K the velocities of the water, 
Hi, Um the velocities of flow, 
»X,«Vv the relative velocities, 
hi, K the pressures, measured in feet of water, 
U, r» the radii of the wheel, 

a 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— «/ 
equal to the velocity at that point of the wheel, and a relative com- 
ponent tv. 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; (b) a flow along curves 
parallel to the wheel vane curves. Taking the latter first, and using 
Bernoulli's theorem, the change of pressure due to flow through the 
wheel passages is given by the equation 




Tbe variation of pressure due to rotation in a forced vortex la 
Consequently the whole difference of pressure at the inlet and outlet 
surfaces of the wheel is 

k t -k.»h'i+h't-h'.-h': 

-W-V.»)/2f+(iv.*-*w«)/a*. (17) 

Case i. Axial Flow Turbines.'- V<-V.; and the first term on the 
right, in equation 17, disappears. Adding, however, the work of 
gravity due to a fall of d ft. in passing through the wheel, 

ft* -ft. - (t^-tn 1 )/** -d. (17a) 

Case a. Outward Flow Turbines.— The inlet radius is less than 
the outlet radius, and ( W— W)/2g is negative. The centrifugal head 
diminishes the pressure at the inlet surface, and Increases the velocity 
with which the water enters the wheel. This somewhat increases 
the frictional loss of head. Further, if the wheel varies in velocity 
from variations in the useful work done, the quantity (W— V.')/2* 
increases when the turbine speed increases, and vice versa. Conse- 
quently the flow into the turbine increases when the speed increases, 
and diminishes when the speed diminishes, and this again augments 
the variation of speed. The action of the centrifugal head in an out- 
ward flow turbine is therefore prejudicial to steadiness of motion. 
For this reason r,:n is made small, generally about 5 14. Even 
then a governor is sometimes required to regulate the speed of the 





From (14a), 

It will be shown immediately that 

or, as this Is only a small term, and is on the average 90*, we 
may take, for the present purpose, tx -n« nearly. 

Inserting these values, and remembering that for an axial flow 
turbine V< - V«, b -o, and the fall d in the wheel is to be added, 

For an outward flow turbine, 

For an inward flow turbine, 

*-*>IM "-£(■+$«*}]•■ 

( 19a. Angle which ihe Guide-Blades make with the Circumference 
ef Ihe Wheel. — At the moment the water enters the wheel, the 
radial component of the velocity is «♦, and the velocity is »<. Hence, 
if y is the angle between the guide-blades and a tangent to the 

-?- tin' 1 («•/»!)• 


This angle can, if necessary, be corre cte d to allow for the th 
of tbe guide-blades. 

S 195. Couddum determining Ihe And* ef Ike Vanes at the Inlet 
Surface ef the Wheel.— Tbe 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 

Let A (fig. 196) be a 
point on the inlet sur- 
face of the wheel, and 

let s - 


tie iter entering* the wheel, and V* the velocity 

of g the parallelogram, tv< is the direction of 

rel the angle between sv< and V, is the angle § 

wl lake with the inlet surface of the wheel. 

Method ef designing a Turbine. Professor 
Jo Flew Turbine. — 

t>le 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 
' » -the efficiency of the turbine. 
The work done per second is ifGQH, and the horse-power of the 
turbine is h.p. -^GQH/550. If i? is taken at 0*75, an allowance will 
be made for the frictional losses in the turbine, the leakage and tat 
friction of the turbine shaft. Then h.p. -0065QH. 

The velocity of flow through the turbine (uncorrected tor the 
space occupied by the vanes and guide-blades) may be taken 

«<-«• -o-i25V**H, 
in which case about Ath <* the "»* r 8y of the fall is carried away by 
the water discharged. 

The areas of the outlet and inlet surface of the wheel are then 
a*r,d.-*rr<d, -Q/0125V (2gH). 
If we take r„ so that the axial velocity of discharge from the central 
orifices of the wheel is equal to u„ we get 
*" "" r.-o-39«4V(Q/VH). 

If, to obtain considerable steadying action of the centrifugal bead. 

n - 2r«, then di = $d«. 

Speed of the Wheel.— Let V< -o-66VlirT, or the speed due to half 
the fall nearly. . Then the number of rotations of tbe turbine per 

N-Vi/asr* -I-0579VCHVH/Q);, 
also V. - VirJn - 033 i/lgH. 

A ngle of Vanes with Outlet Surface. 

Tan 4> - «,/V. - o- 1 25/6-33 - 37*8 ; 
$-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 - (V,V2*)0 +«.W.«) +u % >l*g 
-H{i — 4336(1 +00358) +0156I 

Then the velocity is ___ ___ 

V< - o6V2«(-5646H) -6721 v^iH. 
Angle of Guide-Blades. 

Sin y -*./», - 0-125/0-72 1 -0-173; 
*-io° nearly. * 
Tangential Velocity of Water entering BW. 
Wi —Vicony -0-7101 JlgH. 
Angle ef Vanes at Inlet Surface. 

Cot • - (** - V,)/m - (-7IOI — 66)/- 125 - -4008; 
• -68° nearly. 
Hydraulic Efficiency of Wheel. 

*-tCiVi/*H = -7ioiX-66X2 
This, however, neglects the friction of wheel covers and leakage. 
The efficiency from experiment has been found to be 075 to o-So. 

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 tbe efficiency is considerably reduced when the rGfulatng 




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 lull 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. AIL 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 W8tcr 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 
•res of the wheel, and the forces driving the turbine were sym- 
metrically placed. As soon as this arrangement was adopted, 

Fie. 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 
r> %ssagc 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. 

i 108. General Description of an Impulse Turbine or Turbine with 
Free Deriotion.—Fis. 197 shows a general sectional elevation of a 



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 jgear. a,a,a 
are the shiice 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, 

Flo. 199. 

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 



sluice successively, any number of sluices can be opened or closed as 
desired. The turbine is of 48 horse power on via ft. fall, and the 
Supply of water varies from 35 to 112 cub. ft. per second. The 

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 4} ft., and 


a am* 

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* 

Swith the direc- 
tion of motion, 
and the final 
angle of the wheel 
vanesis20°. The 
efficiency on trial 
was from 75 to 

I VW 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 
Fig. 202. the- wheel oppos- 

ing the discharge 

from the guide-blades. Hence the velocity with which the water 

enters the wheel is simply 


where b is the height of the top of the wheel above the tail water. 

If the hydro pneumatic system is used, then fc-o. Let Q m be the 

maximum supply of water, r u r% the internal and external radii of 

the wheel at the inlet surface; then 

The value of *k may be about o-45V2£(H-b), whence r u r% can be 
The guide-blade angle is then given by the equation 
sin y m *ihn -o*45/o-04 - -48 ; 
T-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 
vn -», cosy -082 V 2g(H -ft). 
The circumferential velocity of t he wheel m ay be (at mean radius) 


Hence the vane angle at inlet surface is given by the equation 
cotf- (tPi - V»)/«, - (o-82-os)A>*45 « 71 ; 

The relative velocity of the water striking the vane at the inks 
edge is tw-«< cosec0-i-22a l . 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 sw « i-22»,. 
Also in an axial flow turbine V # - V». 

If the final velocity of the water is axial, then 

cos* - V.M. - Vtfoi -0-5/(1 -22 Xo-45) -cos 24° 23'. 
This should be corrected for the vane thickness. Neglecting this, 
M«-fW«n+-ftisin4-tt<co5ec0sin4-O'5B«. 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 sbowa 
in the section (fig. 199). 

ft 200. PeUon Wheel.— la 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 oa a hori- 
zontal axis. Round the circumference were fixed flat vane* 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. 20t shows a Pelton vane. 
Some small modifications have been made 

Fig. 203. 

n other makers, but they are not of any great importance. 
ig. 204 shows a complete Pelton wheel with frame and < 

Fi& . . ^ 

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 tangcntially 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 


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 1 80 ft. per sec. With a i-fc. 
nozzle the wheel uses 32 cub. ft. of water per minute and develops 
too h.p. At the Chollarshaft, Nevada, there are six Pelton wbeeh 
on a fall of 1680 ft. driving electrical generators. With f -in. nozzle 

each develops 125 h.p. 

f 201. Theory of the PeUon Wheel.— Suppose a jet with a velocity 
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 *— u and at B will have the tangential 


relative velocity •— « making an angle < 
vane's motion. Combining this wit L * L - 
absolute velocity of the water leaving 
ponent of v in the direction of mo 



i the direction of the 

Fie. 205. 

ing on the vanes per second is t\ ie, 

and the energy expended at the he 

efficiency of the arrangement is, wb 

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 a caanot be quite zero or the water leaving one 
vane would strike the back of the next advancing vane. Fig. 203 
show* a Pelton vane. The water divides each way, and leaves the 
vane on each side in a dii *~~ ' ••«--■ ^ 

motion of the vane. The xi> 

mately half the velocity ol 

$202. Reiulalion of the ;re 

adjusted to varying loads his 

method involves a total I or 

throttle valve. In additi he 

relation between wheel vel of 

greatest, efficiency. Next jet 

so that only part of the ws ras 

reduced, the rest going to lal 

quantity of water for Urge me 

cases is an advantage, the in 

the supply pipe due to th ses 

now regulation is effectet A 

conical needle in the nozal to 

occupy more or less of the , an 

be controlled by an ordinary governor. 

$ 203. General Considerations on the Choke of a Type of 
Turbine.— -The circumferential speed of any turbine is necessarily 
* fraction of the initial velocity of the water, and therefore is 
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 
i* 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 10J ft. to 4I 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 807% with all the rings working. 

§ 204. Speed Governing. — When 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. 

.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 



used, and the tendency oC relay governors to hunt mutt 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 fig. 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 w 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 A forces 
a portion of the water to rise to a height At, greater than A. 
It consists of a supply reservoir (A, fig. 207), into which the water 
enters from some natural stream. A pipe s 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 s may be fitted with a flap valve for stopping the 
ram, and this is attached in some cases to a float, so that the ram 
starts and stops itself automatically, according as the supply 
cistern fills or empties. The lower float is just sufficient 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 

Flo. 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 c, 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 | in. in diameter, made in a brass screw 
plug b. The hole is reduced to tV «. in diameter at the outer 
end of the plug and is dosed by a small valve opening inwards. 
Through this, during the rebound after each stroke of the. ran, 
a small quantity of air is sucked in which keeps the air vessel 
supplied with Us 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 the column 
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 0, 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 p IO# 20 g 

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 and expanding the pipe itself. This causes a recofl 
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 sumaendy 
great to enable a pump to be attached to the ram body instead 
of the direct rising pipe. With this arrangement a ram workiag 
with muddy water may be employed to raise dear 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. 

§ 206. The different classes of pumps cone* 
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. Cbaia 
and bucket pumps are in principle simiUr 
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 bj 
the water instead of by automatic machinery. They may be 
classed thus: — 

x. Lift Pumps. — The water drawn through a foot valve oa 
the ascent of the pump bucket is forced through the bucket 
valve when it descends, and lifted by the bucket when it reasceads. 
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 



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 airpumps 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 00 to 95% 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 00 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 Marin to have an efficiency of 16 to 40%, or on 
the average 25% When used to pump water at considerable 
pressure, through bose pipes, the efficiency rose to from 18 to 
57 %t 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 '. 14) 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 

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 (an 

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 h 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 hat 6 to 12 vanes. For a double-inlet fan of diameter 

D, the diameter of the inlets is D/2. If Q is the discharge in 

rut>. It. per second D» about 06 VQ in average cases. The 


peripheral speed is a little greater than the velocity due to the lift. 

Fig. 900. 

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 onty. 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 
velocity 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 the 
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 of a Centrifugal Pump. — The design 
of the pump disk is very simple. Let r„ r. be the radii of the inlet 
and outlet surfaces of the pump disk, d>, d. the clear axial width at 
those radii. The velocity of flow through the pump may be. taken 




the si 

t a* for a turbine. If Q is the quantity pumped, and H the 

Alto in practice 


•25 V arH. 




if „ «-'*57iV(Q/VH).J 

Usually r,-2fi, 

and rf.-iiorJi< 

according aa the dt«1c Ii parallel-sided or coned. The water enters 

the wheel radially with the velocity m, and 

t».-Q/2»rA. (x) 

Fig. ail shows the notation adopted for the velocities. 
Suppose the water enters the wheel with the velocity w, while 
„ the velocity of the 

.»# wheel is V*. Com- 

1 ** — pleting the parallelo- 
gram, sw is the rela- 
tive velocity of the 
water and wheel, and 
is the proper direction 
of the wheel vanes. 
Also, by resolving, m 
and w are the com- 
ponent velocities of 
flow and velocities of 
whir of the velocity *t 
of the water. At the 
1 outlet surface, v, is the 
FlG. ait. final velocity of dis- 

charge, and the test 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 r» is radial. Then, in normal conditions of work- 
ing, at the inlet surface, 

Un"i-!./V« f vi) 

If the pump is raising less or more than its proper quantity, • will 
not satisfy the last condition, and there is then some loss of head in 
At the outer circumference of the wheel or outlet surface, 
fw-tucoscc* "J 

W.-V.-K.COt+ V (5) 

».-Vl«u»+(V.-«. «*♦)«}] 
Variation of Prtssurt in far Pump Di**.— Precisely aa in the case 
of turbines, it can be shown that the variation of pressure between 
the inlet and outlet surfaces of the pump is 

k.-ki - (V.«- Vfl/at-W-tvfl/af. 
Inserting the values of *», s* in (4) and (3), we get for normal 
conditions of working 

A.-A<-(V.«-Vi«)/2c-i..»cosec«4/jf+(i.»«+V < s )/*f 

-V.V*f-i^cceec*/2g+iVAf. (6) 

# Hydraulic Efficiency of the Pump.— Neglecting disk frictioa. 
journal friction, and leakage, the efficiency of the pump can be fatso 1 
in the same way as that ot turbines (I 186). Let M be the momeat 
of the couple rotating the pump, and « its angular velocity; «* p. 
the tangential velocity of the water and radius at the outlet 
surface; uh, r< the same quantities at the inlet surface. Q bang 
the discharge per second, the change of angular momentum per 
second is 

{GQft)(v t r.-Wir i ). 


In normal working, t* - o. Also, multiplying by the angular velocity 

the work done per second is 

But the useful work done in pumping is GQH. Therefore the 
efficiency is 

t -GQH/Mo -f H/w^^i -f H/w.V- (7) 

| 209. Case 1. Centrifugal Pump with no Whirlpool Chamber — 
When no special provision ts 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 «w 
and impinges on a mass flowing to the discharge pipe at the mack 
slower velocity *». The radial component of ». is almost necessarily 
wasted. From the tangential component there is a gain of prrwwir 

(».«-P.*)/2*-( W .-t>.)V2« 
-P.(w # -».)/g, 

which will be small, if *• is small compared with nv. Its greatest 
value, if r, - )w«, is iw«*/2f , 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 heart 
ii.V2f necessary to give the initial velocity of flow in the eye of the 

! «r7*f+H - V.V** -«.* cosec V2g +«<»/»*. 

H-V.V2f-n."cosec^/2gi (I) 

or V. -VtoH+a. 1 cosec V .{ 

and the efficiency of the pump is, from (7), 

f -fH(V^.-gU/lV(V.-«.cot4)l. 
- W-a.« cosec ^)/l2V.(V.-». cot ♦!. (9) 

For ♦-oo*. *-(V.«-*.«)/2V.«. 

which is necessarily less than f. That is, half the work e x pen d ed in 
driving the pump is wasted. By recurving the vanes, a plan intov 
duced by Appold. the efficiency is increased, because the velocity 
Sj of discharge from the pump is diminished. If + b very small, 

cosec 4- cot 4; 
and then *j - (V.+s. cosec #)/aV^ 

which may approach the value 1 , as 4 tends towards o, Equatiai 
(8) shows that «• cosec + cannot be greater than V*. Pwtisf 
u, -o 25V (2(H) we get the following numerical values ol tat 
efficiency and the circumferential velocity of the pump : — 









v. _„ 

1-75 .. 

cannot practically be made Jem than ao°; and. allowing for the 
ictional losses neglected; the efficiency of a pump in which 4-20* U 
>und to be about -6o, 

| a 10. Case a. Pump with a Whirlpool Chamber, at in fig. 210. — 
rofessor James Thomson first suggested that the energy of the water 
Iter leaving the pump disk might be utilised., if a space were left 
1 which a free vortex could be, formed. In such a free vortex the 
elocity varies inversely as the radius. The gain of pressure in the 
ortex chantber is, putting r„ r tf for the radii to the outlet surface 
f wheel and to outside of free vortex* 



lie lift is then, adding this to the lift In the last case, 

H -|V.»-*V cosecV+«J(i -h*)\l2g. 
lut «•• - V.t-aV*, cot ++«** cosecV ; 

.\H -l(3-**)V.«-aAV.«. cot +-«W cosecWag. (10) 
Putting this in the expression for the efficiency, we find a con* 
idcrable increase of efficiency. Thus with' 

4-90* and A -I, *- J nearly, 

+ a small angle and s - J, t- 1 nearly. 

Vith this arrangement of pump, therefore, the angle at the outer 
nds of the vanes b of comparatively little importance. A moderate 
ngle of 30* or 40* may very well be adopted. The following 
umerical values of the velocity of the circumference of the pump 
ave been obtained by taking k - J, and au-o-asV (2fH). 

♦. V - r-r, 

30* -9U II 

ao° 1-023 „ 

The quantity of water to be pumped by a centrifugal pump neces- 
arily varies, and an adjustment for different quantities of water can- 
tot easily be introduced. Hence it is that the average efficiency of 
>umps of this kind is in practice less than the efficiencies given above. 
The advantage of a vortex chamber is also generally neglected. The 
xlocity in the supply and discharge pipes is also often made greater 
han is consistent with a high degree of efficiency. Velocities of 6 
>r 7 ft. per second in the discharge and suction pipes, when the lift 
& small, cause a very sensible waste of energy; 3 to 6 ft. would 
*c much better. Centrifugal pumps of very large sire have been 
onstructed. Easton and Anderson made pumps for the North Sea 
anal in Holland to deliver each 670 tons of water per minute on a 
if t of 5 ft. The pump disks are 8 ft. diameter. J. and H. Gwynne 
onstructed some pumps for draining the Ferrarese Marshes, which 
ogcther deliver aooo tons per minute. A pump made under Pro- 
essor J. Thomson's direction for drainage works in Barbados had 

pump disk 16 ft. in diameter and a whirlpool chamber 3a ft. in 
liamcter. The efficiency of centrifugal pumps when delivering less 
•r more than the normal quantity of water is discussed in a paper in 
he Proc. Inst. Cio. Eng. vol. 53. 

§ 211. High Lift Centrifugal Pumps. — It has long been known 
hat centrifugal pumps could be worked in series, each pump 
•vercoming a part of the lift. This method has been perfected, 
nd centrifugal pumps for very high lifts with great efficiency 
lave been used by Sulxer and others. C. W. Darley {Proc. Inst. 
Tif. Eng., supplement to vol. 154, p. 156) has described some 
•umps of this new type driven by Parsons steam turbines for 
he water supply of Sydney, N.S.W. Each pump was designed to 
Iclivcr 1 \ million gallons per twenty-four hours against a head 
f 240 ft. at 3300 revs, per minute. Three pumps in series give 
hcrefore a lift of 720 ft. The pump consists of a central double- 
ided impeller 12 in. diameter. The water entering at the 
ottom divides and enters the runner at each side through a 
•clj- mouthed passage. The shaft is provided with ring and 
roove glands which on the suction side keep the air out and on 
he pressure side prevent leakage. Some water from the pressure 
idc leaks through the glands, but beyond the first grooves it 
asses into a pocket and is returned to the suction side of the pump, 
or the glands on the suction side water is supplied from a low- 
ressure service. No packing is used in the glands. During 
he trials no water was seen at the glands. The following are 
he results of tests made at Newcastle:— 

Duration of test . . hours 
Steam pressure lb per sq. in. 
Weight of steam per water 

h.p. hour lb 

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. 





















In trial IV. the steam was superheated 9s 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. 

\ aia. 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 bore 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 
dimin ishes 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 1 
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. MaxweU at 

the Tunbridge ffrfT" 

Wells water- W 

works. There is a Lj 

two-stage steam 
air compressor, 
compressing air to Fie. 212. 

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 13) in. diameter for 
the lower 150 ft. The rest level of the water is 06 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 bole and to 
20 ft. above the ground-level. The air pipe is i\ in. diameter 
In a trial run 31,402 gallons per hour were raised 133 ft. ajwve 
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 {Joum. Amur. Assoc Eng. Soc. vol. 25, 



1 900). Maxwell found the best results when the ratio of immersion 
to lift was j to 1 at the start and 2-2 to 1 at the end of the trial. 
In these conditions the efficiency was 37% calculated on 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 
bole 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 graver which cannot be kept out of the bore hole. 
The initial cost is small. 

§ j 13 Centrifugal Fans.— Centrifugal fans are constructed 
similarly to 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 

It it 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 -644 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 e*/a; ft. of air, or 
000024 s* in. of water, where v is the velocity of the tips of the fan 
blades in feet per second. If d is the diameter of the fan and f the width 
at the external circumference, then wdl is the discharge area of the fan 
disk. If Q Is the discharge in cub. ft. per sec., u -Q/vdt is the radial 
velocity of discharge which is numerically equal to the discharge per 
square foot of outlet in cubic foet per second. As both the losses in the fan 
and the work done arc roughly proportional to «* in fans of the same 
type, and are also proportional to the gauge pressure p, then if the 
Iomcs are to be a constant percentage of the work done u may be 
taken proportional to V p. In ordinary cases u - about 22 V P- The 
width I of the fan is generally from 035 to 0-454. Hence if Q is 
given, the diameter of the fan should be:— 

For/-o-35d. <f -020V (Q/V P) 

For t - 0-45^. d - o- 1 8 V (Q/V p) 

If p is the pressure difference in the fan in inches of water, and N the 
revolutions of fan, 

• -wfN/oo ft. per sec. 

N - 1 330V P/d revs, per min. 
As the pressure difference is small, the work done in compressing the 
air is almost exactly 5-2^Q 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 t^/ar foot-pounds per lb 01 air as kinetic energy. In Q cubic feet 
or oo8o7Qlb the kinetic energy is 0-00125 0** foot-pounds per 

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 01 compression is 

On the other hand, if the kinetic energy in the delivery pipe is taken 
as part of the useful work the efficiency is 

* - (5-*/>Q+o oou5Qw*)/55oB.H.P. 
Although the theory above is a rough one it agrees sufficiently with 
experiment, with some merely numencal modifications. 

An extremely interesting experimental investigation of the action 
of centrifugal tans has been made by H. Heenan and W Gilbert 
(Pr«w. Inst. Ctv £«£. 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 sixes. 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 
curve marked total gauge is the compression pressure -f 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 in the air trunk is diminished. The brake horse-power increases 
as the resistance is diminished because the volume of discharge in- 
creases very much. The curve marked efficiency U the efficiency 

calculated on the work of com pre s sion only. It is sero for ao dkv 
charge. and aero also when there b no resistance and all the energy 
given to the air is carried away as kinetic energy. There is a <h* 
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 cur re so u n d- 
ing to the greatest efficiency of compression are those ordinarily 
taken as the best normal conditions of working. The curve marked 



— ■• 







— * 












Discharge • Cflp€r min. * 
Tip S/m*d m 100 ft per m. 

Fig. 213. 

total efficiency gives the efficiency calculated on the work of cob* 

Eression and kinetic energy of discharge. Messrs Gilbert and 
Icenan found the efficiencies of ordinary fans calculated on the 
compression to be 40 to 60% when working at about normal 

Taking some of Messrs Heenan and Gilbert's results for ordinary 
fans in normal conditions, they have been found to agree fairly vita 
the following approximate rules. Let p t be the compression pressure 
and q the volume discharged per second per square foot of outlet area of 
fan. Then the total gauge pressure due to pressure of compressk» 

and velocity of discharge is approximately: p—p t +0-0004$* in. °* 
water, so that if p t is given, p can be found approximately. The 
pressure p depends on the circumferential speed v of the fan disk— 

£-o-ooo25»* in. of water 
»"63VP it. per sec. 
The discharge per square foot of outlet of fan is— 

j -15 to i8Vpcub. ft. per sec. 
The total discharge is 

Q-vdtq-47 to 56 dt<jp 
For * - 35*. d -022 to 025V (Q/V p) ft. 

/ - -45d, d-o-JO to o-22V (Q/V P) ft. 
N -1203V />/<*• 
These approximate equations, which are derived purely fro* 
experiment, do not differ greatly from those obtained by the rough 
theory given above. The theory helps to explain the reason foroe 
form of the empirical results. (W. C V.) 

HYDRAZINE (Diamidocen), N1H4 or HjNNHi, a compound 
of hydrogen and nitrogen, first prepared by Th. Curtius in 1887 
from diaxo-acetic ester, NiCH-COjCtH*. This ester, which is 
obtained by the action of potassium nitrate on the hydrochloride 
of amidoacetic ester, yields on hydrolysis with hot concentrated 
potassium hydroxide an acid, which Curtius regarded is 
C»H*N*(COjH)j, but which A. Hantxsch and O. Silberrad 
(Bcr., 1000, 33, p. 58) showed to be CtHjN/COxH),, bisdaao- 
acetic acid. On digestion of its warm aqueous solution with 
warm dilute sulphuric acid, hydrazine sulphate and oxalic sod 
axe obtained. C. A. Lobry de Bruyn (Ber. t 1S95, 28, p. 30S5) 
prepared free hydrazine by dissolving its hydrochloride is 
methyl alcohol and adding sodium melhylate; sodium chloride 
was precipitated and the residual liquid afterwards fractiocoied 
under reduced pressure. It can also be prepared by reduces 
potassium dinitroso6ulphonate in ice cold water by means <& 
sodium amalgam: — 

K |S)>N-NO-> KS ^>N.N»j-»KsS0 4 +N»Ha. 


P. J. Schestakov (/. Russ. Pkys. Chan. Soc., 1905, 37, p. 1) 
obtained hydrazine by oxidizing urea with sodium hypochlorite 
in the presence of benzaldebyde, 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. 
Shet terry, /. Amer. C£., 1008, p. 53). By fractional distilla- 
tion of its aqueous solution hydrazine hydrate N3H4H1O 
(or perhaps HjNNHjOH), 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, 
J. Chem. Soc. t 1904, 85, p. 913). The sulphate NtHrHsSOi, 
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 Emit 
Fischer in 1877. It can be best prepared by V. Meyer and Lecco's 
method (Bcr., 1883, 16, p. 2976), which consists in reducing phenyl- 
diazoniura chloride in concentrated hydrochloric acid solution with 
stannous chloride also dissolved m 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 E. Bam- 
berger. The diazonrum 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— 

CH*N,CI + K,SOi - KC1 + C«H»N, SO,K, , 
C*H.N t SO,K + 2H - C.H.-NH NHSO.K, v 

Phenylhydrazine is a colourless oily liquid which turns brown on 
exposure. It boils at 241 s C, and melts at 17-5° C. It is slightly 
soluble in water, and is strongly basic, forming well-denned 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 kydrautnts 
(see Aldehydes, Ketones and Sugars). It is a strong reducing 
agent; it precipitates cuprous oxide when heated with Fehling's 
solution, nitrogen and benzene being formed at the same time — 
QH,NHNH,+ 2CuO « Cu,0+Nj-f HaO+C«H* By energetic re- 
duction of phenylhydrazine (e.g. by use of zinc dust and hydrochloric 
acid), ammonia and aniline are produced — C»H»NH-NHi + 2H ■* 
C«H»NHj + 1NH1. It is also a most important synthetic reagent, 
It combines with aceto-acetk ester to form phenylmcthylpyrazoTone, 
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 

HYDRAZINE, in chemistry, a compound formed by the con- 
densation of a hydrazine with a carbonyl 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 provided 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 hydrocarbons, 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, Ac. 

HYDROCELE (Gr. Gfop, water, and rtfa, tumour), the 
medical term for any 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 
without apparent cause, but it is usually associated with chronic 
orchitis or with tertiary syphilitic enlargements. The hydrocele 
appears as a rounded, fluctuating translucent swelling in the 
scrotum, and when greatly distended causes a dragging pain. 
Palliative treatment consists in tapping aseptically and remov- 
ing the fluid, the patient afterwards wearing a suspender. 
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 

HYDROCEPHALUS (Gr. «wp, water, and «*aXi), 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 

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 is apt to be a source 
of difficulty in parturition. It is however more commonly 
developed in the first six months of life; but it occasionally 
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 bones of the skull have not become 
welded together, the enlargement may go on to an enormous 
extent, the spaces between the bones becoming more and more 
expanded. In a well-marked case the deformity is very striking; 
the upper part of the forehead projects abnormally, and the 
orbital plates of the frontal bone being inclined forwards give 
a downward 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 
ill-nourished, 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., 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 
20 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. 
Occasionally 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 mental condition is impaired. The child is dull, 
listless and irritable, and sometimes imbecile. The special senses 
become 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. 



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-dural space, and 
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 (Stratioies alettes). The order contains 
about fifty species in fifteen genera, twelve of which occur in 
fresh water while three arc marine: and includes both floating 

and submerged forms. 
Hydrocharis floats on 
the surface of still 
water, and has 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. 
Stratioies aloides 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 warmer 
parts of both hemi- 
spheres and reaching 
as far north as south 
Morsus-ranae— 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 ate formed at 
the end of horizontal 
runners. Another type 
is represented by 
Elodca 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 tropical 
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 

FiQ. I. — Hydrocharis 
Frog-bit — male plant. 

1, Female flower. 

2, Stamens, enlarged. 

3, Barren pistil of male flower, enlarged. 

4, Pistil ot female flower. 

?, Fruit. 
, Fruit cut transversely. 
7, Seed. 
8, 9, Floral diagrams of male and female ' 

flowers respectively. 
s. Rudimentary stamens. 

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. StratioUs 
has similar flowers 
which come above 
the surface only 
for pollination, 
becoming sub- 
merged again 
during ripening of 
the fruit InVaU 
lisneria (fig. a), 
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- Fta. a.— Vallisneria *f*rgis—F*A grass— 

tile; the flowers SfeSS'iaSf "*" 
become detached ^ 

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 stalk; the ovary bears three broad styles, en 
which some of the 
large, sticky 
pollen-grains from 
the floating male 
flowers get de- 
posited (fig. 3). 1 
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. 

Elodca has poly- Fig. 3. 

gamous flowers 

(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 a 
the temperate zones. 



HYDROCHLORIC ACID, also known in commerce as " spirits 
of salts " and " muriatic add/' a compound of hydrogen and 
chlorine. Its chemistry is discussed under Chlokjnx, and its 
manufacture under Alxali Manufacture. 

HYDRODYNAMICS (Gr. fiflwp, water, d'foo/iis, 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. (fop, 
water, and yew&HP, 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 

Hydrogen is found in the free state in some volcanic gases, in 
fumaroles, in the carnallitc 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-CLairc Deville (Comptes rendus, 1870, 70, p. 1105) 
and by H. Dcbray (ibid., 1879, 8B, p. 1341), who found that at 
about 1 500 C. a condition of equilibrium is reached. H. Moissan 
(Bull. soc. ckim., 1902, 27, p. 1141) has shown that potassium 
hydride decomposes cold water, with evolution of hydrogen, 
KH+HjO= KOH+ Hi. Calcium hydride or hydrolite, prepared 
by passing hydrogen over heated calcium, decomposes water 
similarly, z gram giving 1 litre of gas; it has been proposed 
ms a commercial source (Prats Aymerich, Abst. J.C.S., 1907, ii. 
P« 543)* *s 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-Besupre', 
Compies 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 sine or iron. So obtained, it contains 
many impurities, such as carbon dioxide, nitrogen, oxides of 
nitrogen, phosphoretted hydrogen, arseniuretted hydrogen, &c, 
t be removal of which is a matter of great difficulty (see E. W. 
Morley, After. Chem. Journ., 1800, 12, p. 460)* When prepared 
fay the action of metals on bases, zinc or aluminium and caustic 
soda or caustic potash are used. Hydrogen may also be obtained 
h>y the action of zinc on ammonium salts (the nitrate excepted) 
<Lorin, Compies rendus, 1865, 60, p. 745) and by heating 
ttae alkali formates or oxalates with caustic potash or soda, 
lsfa«C^)4-|-2NaOH-H J +2Na 1 CCV Technically it is prepared 
i>y the action of superheated steam on incandescent coke (see 
Jr*~ Hembert and Henry, Compies 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, 
XIV 3 

Chem. ZeU., 1698, 22, p. 609; " Die Elektrizitats-AktiengeseU- 
acbaft," ZeU. J* EUktrockem., xooi, 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 0-06047 (air- 1) (Lord Rayieigh, 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, Complex rendus, 1809, 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*- x), 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, X48, 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 Defille and L. Troost, Compies 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. ckim. pkys., 1874, (5) 2, p. 279) 
considered that a palladium hydride of composition Pd«H was 
formed, but the investigations of C. Hoitsema (ZeU. pkys, Chem., 
1895. '7. p. i)> 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 
wanned in a current of hydrogen, at about 360° C, form hydrides 
of composition RH(R«Na, K, Rb, Cs), (H. Moissan, Bull, soc 
ckim., 1902, 27, p. 1 141); calcium and strontium similarly 
form hydrides CaH* SrHs at a dull red heat (A. Guntz, Compies 
rendus, xooi, 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. ckim. phys., 1843 (3), 8, 
p. 189; O. Erdmann and R. F. Marchand, ibtd. p. 212; E. H. 
Reiser, Ber., 1887, 20, p. 2323; J. P. Cooke and T. W. Richards, 
Amer. Chem. Journ., 1888, 10, p. iqi; Lord Rayieigh, Chem. News, 
1889, 59. P. 147; E. W. Morlcy, ZeU. pkys. Chem., 1890, 20, p. 417; 
and S. A. Leduc, Compies rendus, 1899, 128 » P> ' *5& 

Hydrogen combines with oxygen to form two definite com- 
pounds, namely, water (q.v.), HjO, and hydrogen peroxide, 
Hid, whilst the existence of a third oxide, ozonfc acid, has been 

Hydrogen peroxide, HjOi, was discovered by L. J. Thenard in 
1818 (Ann. ckim. pkys., 8*, p. 306). It occurs in small quantities 
in the atmosphere. It may be prepared by passing a current of 
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), 
BaO«+CQi+HjO«H«0,+BaCO*. E. Merck (Abst. J.C.S., 
1007, ii., p. 859) showed that barium percarbonate, BaCO«, is 
formed when the gas is in excess; this substance readily yields 
the peroxide with an add. Or barium peroxide may be decom- 
posed by hydrochloric, hydrofluoric, sulphuric or s'licofluoric 
acids (L. Crismer, Bull, soc. ckim., 1891 (3), 6, p. 24; Hanriot, 
Comptes rendus, 1885, 100, pp. 56, 1 72), theperoxide being added 



in small quantities t6 a cold dilute solution of the add. 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 with 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 nitrate, 
when a crystalline precipitate of hydrated barium peroxide, 
BaO&'HtO, 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, 
*7. p. 2307) prepared practically anhydrous hydrogen peroxide 
(containing oo-i% HjO») 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% HjO». 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 

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 xinc amalgam with 
alcoholic sulphuric acid and air (M. Traube, Ber., 1882, 15, 
p. 659); in the oxidation of zinc, lead and copper in presence of 
water, and in the electrolysis of sulphuric add of such strength 
that it contains two molecules of water to one molecule of 
sulphuric add (M. Berthclot, Complex rendu* , 1878, 86, 
p. 71). 

The anhydrous hydrogen peroxide obtained by Wolffenstein 
boils at 84-85°C. (68 nun.); its specific gravity is 1-4996 (1-5° C). 
It is very explosive (W. Spring, Zeit. anorg. Chem., 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 {Bar., 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 ioo° C. An aqueous solution containing 
more than 1*5% hydrogen peroxide reacts sliglrUy add. To- 
wards lupetidin [ao' dimethyl piperidine, C»U 9 N(CU a )e] hydrogen 
peroxide acts as a dibasic add (A. Marcuse and R. Wolffenstein, 
Ber., 1 90 1, 34, p. 2430; see also G. Bredig, Zeit. Electrochem., 
1001, 7, p. 622). Cryoscopic determinations of its molecular 
weight show that it is HjO». [G. Carrara, Rend, delta Accad. 
dei Lincei, 1892 (5), 1, ii. p. 19; W. R. Orndorff and J. White, 
Amer. Chem. J own., 1893, 15, p. 347.J 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 
MO18H1O, titanium dioxide is converted into the trioxide, 
iodine is liberated from potassium iodide, and nltrilcs (in alkaline 
solution) are converted into acid-amides (B. Radziszewski.Ber., 
1884, 17, 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, glygolKc, lactic, tartaric, malic, 
benzoic and other organic adds are readily oxidized in the 
presence of ferrous sulphate (H. J. H. Fenton, Jour . Chem. Sk., 
1000, 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. Rastle and A. S. Locvcnhart, 
Amer. Chem. J own., 1903, 29, pp. 397, 517). Hydrogen peroxide 
can also react as a redudng agent, thus silver oxide is reduced 
with a rapid evolution of oxygen. The course of this react ion can 
scarcely be considered as definitely settled; M. Berthefot 
considers that a higher oxide of silver is formed, whilst A 
Baeyer and V. Villiger are of opinion that reduced silver is 
obtained [see Comples rendus, 1901, 133, p. 555; Ann. GKs». 
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,+ 
3HiSO«+5HjCfe«KtSO«+2MnS04+8H«0+50». Lead peroxide 
is reduced to the monoxide.. Hypochlorous add and its sahi, 
together with the corresponding bromine and iodine compounds, 
liberate oxygen violently from hydrogen peroxide, giving hydro- 
chloric, hydrobromic and hydriodic adds (S. Tanatar, Ber., 1899, 
32, p. 1013). 

On the constitution of hydrogenperoxide see C. F. Schonbcia, 
Jour. prak. Chem., 1858-1868; M. Traube, Ber., 1882-1889; J. W. 
Bruht, Ber., 1895, 38, p. 2847; 1900, 33, p. 1709; S. Tanatar, Ber., 
19<>3> 36. P- 1893- 

Hydrogen peroxide finds application as a bleaching agent, as to 
antiseptic, for the removal of the last traces of chlorine and 6ulphor 
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 ia 
add solution; with potassium fcrricyanide in alkaline solution, 
ing arsenious acid in alkaline solution with the peroxide aod 
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 add; by the orange-red colour it gives with a solution of 
titanium dioxide in concentrated sulphuric add; and by the pre- 
cipitate of Prussian blue formed when it is added to a sohrBot 
containing ferric chloride and potassium ferricyanide. 

Ozonic Acid, H|0«. By the action of ozone on a 40% solutioe 
of potassium hydroxide, placed in a freezing mixture, an orange- 
brown substance is obtained, probably KtO«, which A. Baeyer sad 
V. Villiger (Ber., 1902, 35, p. 3038) think is derived from ocoax 
acid, produced according to the reaction 0»+HiO — HgO* 

HYDROGRAPHY (Gr. (top, water, and yp&fat*, to write), 
the science dealing with all the waters of the earth's surface, 
including the description of thdr physical features and con- 
ditions; the preparation of charts and maps showing the poatioa 
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 sdentific description of the position, 
volume, configuration, motion and condition of all the waters 
of the earth. See also Surveying (Nautical) and Occam am* 
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. Cfep, water, Xfaj% to loosen), in chemistry, 
a decomposition brought about by water after the manner shown 
in the equation RX+HOH-RH+XOH. Modern research 
has proved that such reactions are not occasioned by water 
acting as H 2 0, but really by its ions (hydrions and hydroxidkms). 
for the vdodty 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 tens 
" saponification " (Lat. sapo, soap) has the same meaning, bat 
it is more properly restricted to the hydrolysis of the fats, it 
glyceryl esters of organic adds, into glycerin and a soap (set 
Cmbmicai. Actio*). 



HYDROMECHANICS (Gr. uSpojarxayuta), 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 (?.*.). 

Historical. — The fundamental principle* of hydrostatics were first 
given by Archimedes in his work Utpl r£* ix<»wb*», or De us quae 
vehuntur in kumido, about 250 B.C., and were afterwards applied 
to experiments by Marino Gbetaldi (1566- 1627) in his PronuHus 
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 

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 12a b.c. the fountain 
of compression, the siphon, and the forcing-pump were invented by 
Ctcsibiusand 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 1 its 

attention does not seem to have been of 

fluids; and the first attempt to investig de 

by Sextus Julius Front inus, inspector < at 

Rome in the reigns of Nerva and Traja te- 

ductibus urbis Komae commentarius, h ds 

which were at that time employed for ai of 

water discharged from ajutages, and tk he 

waters of an aqueduct or a fountain. He of 

water from an orifice depends not only on ice 

itself, but also on the height of the watei at 

a pipe employed to carry off a portion < ict 

should, as circumstances required, haw » 

inclined to the original direction of the as 

unacquainted with the law of the vcloi as 

depending upon the depth of the orifice, t ch 

appears in his results is not surprising. 

Benedetto Castelli {1577-1644), and Evangelista Torricefii (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 deW acque corrcnti, in which he satis- 
factorily explained several phenomena in the motion of fluids in 
rivers and canals; but he committed a great paralogism in sun- 
posing the velocity of the water proportional to the depth of the 
orifice below the surface of the vessel TorricclU, 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 arc 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 projeclorum, and it was con- 
firmed by the experiments of RaffaeHo Magiotti on the quantities 
of water discharged from different ajutages under different pressures 

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'iquilibre 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 Edm6 Manotte (1620-1684), whose 
Traiti du moueemenl 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 bjottom. But as Mariottc observed similar obstructions even 
in glass pipes 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 01 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- 




remains always horizontal; and, if the fluUTmass is conceived to be 
divided into an infinite number of horizontal strata of the same 

k^i, .•__ ... . main contiguous to. each other, and that 

all vertically, with velocities inversely pro- 

po h, or to the horizontal sections of the 

res Pennine the motion of each stratum* he 

en rf the conservotio virium vttvrum, and 

ob itions. But in the absence of a general 

de nciple, his results did not command the 

co rould otherwise have deserved, and it 

be theory more certain, and depending solely 

on of mechanics. Colin Maclaurin (1698- 

17 (1667-1748), who were of this opinion, 

res >re direct methods, the one in his Fluxions, 

pu ie other in his Hydraulica nunc primum 

dei . Je 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 
lean 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 

motions of bodies to that of their equilibrium. 

He applied this 




principle to the motion of fluids, and gave a specimen of its applica- 
tion at the end of hb Dynamics in 1 743. it was more fully developed 
in his Traitt desfiuides, published tn 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 1753, in his Essai sur la rlsistanu des fluider, was brought to per- 
fection in his Opuscules malhtmatigues t ind was adopted by Leonhard 

The resolution of the questions concerning the motion of fluids 
was effected by means of Eulcr's partial differential coefficients. 
Th»s calculus was first applied to the motion of water by d'Alembert, 
and 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- 

e desfiuides, ,,, _ r . . , 

a revised edition of his Principes d'hydraulique, which contains a 

•4»iafa«4An> »h«nj nl »lu msttiskn est (K.%\Am tn\tw%AmA anlalu nnMi 


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. Bazm. 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 kydrauliques, Paris, i860). German 

engineers have also devoted special attention to the* measurement 
of the flow in rivers; the Beitrdge but Hydrographie des Kdmifr 
retches BOhmen (Prague, 1 872-1 875) of A. R. Harlacher (1842-1890) 
cc ' --»--■-- • ' this kind, together whn a con> 

CLh the formulae of flow that had 
mblication, and important data 
wi Mississippi made for the United 

St sysandH. L. Abbot, by Robert 

G nd by Allen J. C. Cunninghams 

es te friction of water, investigated 

fo neasured for higher speeds by 

W work is of great value in the 

tfa Report., 1869), and stream lis* 

m ante Reynolds and by Pr o f taa m 

H CX.) 


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 Stales of a Substance or Matter.— AH 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, at 
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 summarised 
thus in 0. Lodge's Mechanics: — 

A solid has both size and 'shape. 

A liquid has size but not shape. 
A 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 whkh 
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, (ti.) a vapotor, 
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 certaia 
length of time for the effect to be appreciable. ' 




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 sobd, however soft and plastic 
it may be. Put 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 of 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 a 
reservoir, the pressure at any point of the plane is P/A lb 
or P/144A lb per sq. in. (lb/ft.* and lb/in. 1 , in the Hospitalie 
to be employed in the sequel). If the distribution of th 
not uniform, as, for instance, on a vertical or inclined face < 
reservoir, then P/A represents the average pressure over thi 
the actual pressure at arty point is the average pressure 01 
area enclosing the point. Thus, if a thrust AP lb acts on a a 
area AA ft.* enclosing a point B, the pressure p at B is tl 

in the notation of the differential calculus. 

or any 



6. The Equality of Fluid Pressure in alt Directions.— This funda- 
mental principle of hydrostatics follows at once from the principle of 
the normality of fluid pressure implied in the definition of a fluid in 
f 4. Take any two arbitrary directions in the plane of the paper, and 
draw a small isosceles triangle abc, whose sides are perpendicular 
to the two directions, and consider the equilibrium of a small triangular 
prism of fluid, of which the triangle is the cross section. Let P, Q 
denote the normal thrust across the sides be, ca % and R the normal 
thrust across the base ab. Then, since these three forces main- 
tain equilibrium, and R makes equal angles with P and Q, therefore 
P and Q must be equal. But the faces be, ea, over which P and Q 
act, are also equal, so that the pressure on each face is equal. A 
scalene triangle abc might also be employed, or a 

It follows that the pressure of a fluid requires 
to be calculated in one direction only, chosen as 
the simplest direction for convenience. 

7. The Transmissibilify of Fluid Pressure. — Any 
additional pressure applied to the fluid will be 
transmitted equally to every point in the case of 
a liquid; this principle of the transmissibility of 
pressure was enunciated by Pascal, 1653, and 
applied by him to the invention of the hydraulic 

This machine consists essentially of two communicating cylinders 
fig. ia), filled with liquid and closed by pistons. If a thrust P lb is, 
pplied to one piston of area A ft.*, it will be balanced by a thrust 
v tt> applied to the other piston of area B ft.*, where 

*-P/A-W/B, (1) 

ie pressure p of the liquid being supposed uniform; and, by 
taking the ratio B/A sufficiently large, the mechanical advantage 
in be increased to any desired amount, and in the simplest manner 
ossible, without the intervention of levers and machinery. 

Fig. id shows also a modern form of the hydraulic press, applied 
> the operation of covering an electric cable with a lead coating. 

8. Theorem. — In a fluid at rest under gravity the pressure is the 
ime at any two points in the same horizontal plane; in other 
ords, a\ surface of equal pressure is a horizontal plane. 

This is proved by taking any two points A and B at the same 

Fig. io. 

pa-p*a=v*. AB, 


Thus in water, where w- ©^•alb/ft.*, the pressure increases 
62-4 lb/ft. 1 , or 62-4+144 -0-433 lb/in.* for every additional foot of 

10. Theorem.— U 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 o rises to the height h and of density p 
to the height h, and £» denotes the atmospheric pressure, the pressure 
in the liquid at the level of the surface of separation will be *A+p» 
And ph+f*, and these being equal we have 



The principle is illustrated in the article Barometer, where a 
column of mercury of density o 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 h, 
called the height of the homogeneous atmosphere. Thus water being 
about 800 times denser than air and mercury 13*6 times denser 



and with an average barometer height of 30 in. this makes £27,200 
ft., about 8300 metres. 

11. The Head of Water or a Liquid.— The pressure oh at a depth 
h ft. in liquid of density # 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 + 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*; and one ton/inch*, 
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 acts 
vertically upward through the centre of gravity of the fluid displaced, 
and b equal to the weight. 

When the body b floating freely like a ship, the equilibrium of 
thb liquid thrust with the weight ot the ship requires that the weight 
of water displaced b 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 b greater than tht 
weight of the balloon, and it is in equilibrium when the weights are 
equal. Thb theorem b 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' b the weight required to balance when the 
body b suspended in water, then the upward thrust of the liquid 



or weight of liquid displaced is W-W\ to that the specific gravity 
(S.G.). defined as the ratio-of the weight of a body to the weight 
of an equal volume of water, is W/(W-W'). 

As stated first by Archimedes, the principle asserts the obvious 
fact that a body displaces its own volume of water; and he utilized it 
in the problem of the determination of the adulteration of the crown 
«r u:~~r> Um .»;<r*ww4 «..» • i.. m « «f a rAA an d of silver of the same 

e three in succession in 
a of water in the ratio 
chat the gold: silver alloy 

rust on any portion of a 
)f a fluid at rest under 
ertical lines drawn round 

rust in any direction is 
nes round the boundary, 
their direction in a plane 
>n this plane area, which 

is before, employing the 
r instance, in the deter- 
n of the bottom of a ship. 
II, it will be seen that the 
y be many times greater 
is experiment has been 
classed as a hydrostatic 

casting a hemispherical 
in, the upward thrust on 
the outside mould, when 
the level has reached 
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 \wy*, 
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. Afterwards, 
when the metal has risen 

— K 

: . 


■ 1 


/Y , 

Sj n. 



7 J 


Fig. 2. 

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. 

Analytical 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-jjfpXdxdydz. (1) 

where /, m, n denote the direction cosines of the normal drawn 
outward of the surface S. 

But by Green's transformation 

SPt*-ffjfr**. w 

thus leading to the differential relation at every point 

3S-* 8-' Y - a?-' z - w 

The three equations of equilibrium obtained by taking moments 
round the axes arc 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 ; 

&&&«*•*>* «> 

are the partial differential coefficients of some function P, -fdpfp, 
of *, y, s; so that X, Y, Z must be the partial differential coefficients 
of a potential -V, such that the force in any direction is the down- 
ward gradient of V ; and then 

37+ 2C "°' <* P+V " constont » w> 


in which P may be called the hydrostatic head and V the head of 

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 Os directed vertically down- 
ward ; employing the gravitation unit of force, 

1 dp ^ 1 dp ^ 1 dp m 


P -Jrfp/p «*+a constant. (2) 
When the density p is uniform, this becomes, as before in (2) f 9 

p~p*+p* (3) 

Suppose the density p varies as some nth power of the depth 
below O, then 

dp\dx-p~p* U) 
A *»♦' p% 

M »+i n + i 

» + iW 


supposing p and p to vanish together. 

These equations can be made to represent the state of convective 
equilibrium of the atmosphere, depending on the gas-equatior 

where f denotes the absolute temperature; and then 

-de d /p\ 1 
r 3S-2.1p7 "»T? 



so that the temperature-gradient do/dz is constant, as in convective 
equilibrium in (11). 
From the gas-equation in general, in the atmosphere 

idpidpxddpidoiido /a v 

p-£ m p£-$a?-p *£-*-*£• (8) 

which is positive, and the density p diminishes with the ascent, 
provided the temperature-gradient dd/ds does not exceed 0/k. 
With uniform temperature, taking * constant in the gas-equation, 
dpjd»-p-p/k, p-p*" k , (9) 

so that in ascending in the atmosphere of thermal equilibrium the 
pressure and density diminish at compound discount, and for 
pressures p% and p» at heights *i and h 

(*-**)/* -log.tfc/pj -a-3 1og,,(pi/p.). (10) 

In the convective equilibrium of the atmosphere, the air A sup- 
posed to change in density and pressure without exchange of heat by 
conduction; and then 

$-Hf- ( " +,) S- ( " +f)R - *- ,+ * 

where y is the ratio of the specific heat at constant pressure and 
constant volume. 

1 n the more general case of the convective equilibrium of a spherical 
atmosphere surrounding the earth, of radius o, 

?-<"+»££--£*• <»> 

gravity varying inversely as the square of the distance r from the 
centre; so that, ft-p»/p», denoting the height of the homogeneous 
atmosphere at the surface, is given by 

(«+!)*(!-#/*) -o(i -o/r), (13) 

or if c denotes the distance where 0-0, 


• a e—r 
$\ m r ' c— o* 

When the compressibility of water is taken into account in a 
deep ocean, an experimental law must be employed, such as 

p-p»«*(p-Ao), or pl»- 1 +(p-po)/X. X-ftp., (15) 
so that X is the pressure due to a head ft of the liquid at density m 
under atmospheric pressure p«: and it is the gauge pressure required 
on this law to double the density. Then 

dpldt-kdpfdt-p, p-p*'\ p-*«ft*(«"*-i): (16) 
and if the liquid was incompressible, the depth at pressure p would 
be (p—fr)fp* so that the lowering of the surface due to compression is 
fe»/i_*_, . |*/*, when ft is large. (17) 

For sea water, X is about 25,000 atmospheres, and ft it then 25^00 
times the height of the water barometer, about 250,000 metres, so 
that in an ocean 10 kilometres deep the level is lowered about joo 
metres by the compressibility of the water; and the density at the 
bottom is increased 4 %. 

On another physical assumption of constant cubical elasticity X, 
dp-\dpfp, (p-p.)/X-log(p/p.), (18) 

2f-}2-* >(s-;) "• -?4 >-»- <"> 





*-/#>< - - 

xR^Ufixik —x cofco — y sin a)t 

yR - f)py(h — x cos a — y sin •)< 

ew origin at the C.G. of the area 

and the lowering of the surface is 

.«=fc-,-»h,i.,— *!„(,.§..** („> 
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 O*. the resultant thrust 

. . R-ffpdxdy, (1) 

and the co-ordinates x t y of the C.P. are given by 

xR-ffxpdxdy, yR-ffypdxdy. (a) 

The C.P. is thus the C.G. of a plane lamina bounded by the area, 
in whiqh 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 

xco««+y$in«-»-o, (3) 

"fp(k—x cos a — y sin o)dxdy, (4) 

*)dxdy, <5) 

Placing the new origin at the C.G. of the area A, 

f(xdxdy-o, jfydxdy-o, (6) 

R=pJ«. (7) 

xkA - -cos •Jf x*<*A - sin affxydA, (8) 

y«A *» - cos ajfxydA - sin aff y*dA. (9) 

Turning the axes to make them coincide with the principal axes 

of the area A, thus making ffxydA-o, 

xk - — a* cos a, yh - —J* sin a, (10) 


//*VA-Afl», J/vVA-AP, (11) 

a and 6 denoting the semi-axes of the momental ellipse of the area. 

This shows that the C.P. is the antipole of the line of intersection of 
its plane with the free surface with respect to the momental elHpse 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 lower side; of a triangle with a 
vertex in the surface and base horizontal b $ 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 

The core of an area is the name given to the limited area round 
its C.G. within which the C.P. must lie 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 b a concentric circle or ellipse of one quarter the size. 

The C.P. of water lines passing through a fixed point lies on a 
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 b 
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.—Tht principle of Archimedes in % 12 leads 

immediately to the 
conditions of equili- 
brium of a body sup- 
ported freely in fluid, 
Kke 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 tn 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; 


r ** 


H c 









Fie. 3. 

for equilibrium these two forces must be equal and opposite in 
the Bame 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., 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 dbtance 
G»Ga— c(P/W); and if B, called the centre of buoyancy, moves 
to Bi, along the curve of buoyancy BBi, the normal of this curve at 
Bi will be the new vertical BiG,, meeting the old vertical in a point 
M, the centre of curvature of BBi, called the meiacentre. 

If the ship heels through an angle 6 or a slope of x in m, 

GM-GG,cot*«m<(P/W), ' (1) 

and GM is called the metacentric height; and the ship must be 
ballasted, 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 dbtance of 42 ft., caused the bob 
of a pendulum 20 ft. long to move through 10 in. ( so that 


CM-agX4iX-&- M4 fc.; 


COt* -24, »-2 # 24*. (3) 

In a diagram it is conducive to clearness to draw the ship in one 
position, and to incline the water-line; and the page can be turned 
if it b 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 d\ if the water-line area from the axb of 
rotation, the change of displacement is ZydA tan 9, so that there is 
no change of displacement if XydA**o, that », if the axb 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 

ZwydA tan 9.y - w tan 9XyHA =* w tan 0.AA* ft- tons, (4) 

w denoting the density of water in tons/ft.', and W-wV, for a 
displacement of V ft,' 

This couple, combined with the original buoyancy W through B, 
b equivalent to the new buoyancy through B, so that 

W.BBi-wAJPtan*. (5) 

BM-BB,cot*-A*VV, (6) 

giving the radius of curvature BM of the curve of buoyancy B, in 
terms of the displacement V, and A** 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 FP, then £|, bt, the C.G. of the wedge of immersion 
and emersion, will be the C.P. with respect to FF' of the two parts of 
the water-line area, so that bibt 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 VV.BM, and the stability of ballast- 
««*« represented by W.BG. Ballasted with G at B, the righting 
couple when the ship is heeled through 8 is given by W.BM. tan*; but 
if weights inside the ship are raised to bring G above B, the righting 
couple b diminished by W.BG. tan $, so that the resultant righting 
couple b W.GM. tan 9. Provided the ship b 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 f 16 for the determination of the C.P. of an 
area, the same argument will show that an inclining couple due to 

^ 20 

,-jovcmcnt of a weight P through a distance c will cause the ship 
-rt^J^el through an angle about an axis FF* through F, which h 
CO Sueate to the direction of the movement of P with respect to an 
<zO?Uc t not the momental ellipse of the water-line area A, but a 
^***Tacal to it, of squared semi-axes 
c*>** ««-AV/A, P-AV/A, (,) 


-noting the vertical height BG between C.G. and centre of 
jancy. The varying direction of the inclining couple Pc may be 
^j by swinging the weight P from a crane onthc ship, in a circle of 

Vif P 

«>■» "_J#£d over r i i/ui. ucjAiaiicu iu/wikii: «w, say uvcT Q Of. -. 

^lep^iiiie area, the ship would turn about a line the antipolar ofQ 

denoting "* VCTI 

w~-m- .« c «- weight P was lowered on the ship from a c 

rs»<** ttore. the vessel would sink bodily a distance P/wA if P 
«»*» JSed over F; but deposited anywhere e' 
«XcP°z;Kne area, the ship would turn about a 

from a crane 

_ was 

say over Q on the 

«|<?P*?iine area, the ship would turn about a line the antipolar of 
'^9 t S\ e spect to the confoca! ellipse, parallel to FF', at a distance F 

Xro<* F FK> (*»-#V/A)/FQ sin QFF' (a) 

_wrh an angle • or a slope of one in m, given by 
•hro** , p P V 

1 denotes the radius of gyration about FF' of the water-line 
«**** Burning the coal on a voyage has the reverse effect on a 


Ib considering the motion of a fluid we shall suppose it 
a^taa, so lhat whatever the state of motion the stress 
^^AaVsertiou is normal, and the principle of the normality 
*?!i«nc* U the equality of fluid pressure can be employed, as 
*»» ^^ja. The practical problems of fluid motion, which 
** *^!«HBiMtto ssathematkal analysis when viscosity is taken 
*** ^zUr** rrrtr 1 " 1 from treatment here, as constituting 
"^^SS^eawrf-hydrauhcs"^.). Two methods are 
• af * - ^Jwjh«UrBiBatSs called the Eulerian and Lagrangian, 
•^5? SS*T Anr *i*nally to Leonhard Eulcr. In the 
■^^--Aiil ^ar **»*»»• * &Md on a P* rticul «* Point of 
t *" B "i5"Sc&smir fc****** 1 thcre of Praure, density 
***• jSafc* "*■** **""* lhc moti °n; but in the 

^ -ri^JT~~ trfu* *p a particle of fluid and observe 
1 *^^ icst aaay be called the statistical method, 
j^agial, according to J. C. Maxwell. The 
^^j benf employed rarely, we shall confine 
3B & Ejfaaft treatment. 

i Fsrsi •/ Ac Equations of Motion. 

i to be established is the equation of 
asoeessa the fact that the increase of. matter 

-• <- ^j,^K^*» e t0 ^ fl ° W ° f flU * d aCr ° 58 thC * urfaCe 

t of fluid of density p, flowing with 

k *\ tor pw«... ~- — — 
.^*««t iWocity normal to the plane. 
"^1 ^ dosed surface, fixed in the fluid, M the 
- "* * »my time /. and • the angle which the 

ZZ ^#»™ h lhc vc,0C1t y 8 at that point, 
* uot rfft""* inside the surface, (i) 

dw ^srface into the interior 

" ;: *" ,S U, 

..-.•AimnfY* . 

.%* % t. w denote the components of the 
"L\ ^i»*»te axes at any Doint (x, y, t) at the 
. «* A ». y. «. '• thc »ndependent variables; 
.^.c. »*ttal differentiation with respect to 
.» k «*fe«t variables, all capable of varying 

r4tt 4tion into the differential equation of 
"* ^«ui«iw« » required again, namely, 

^ . ^)4**»WJ('*+*f+*«dS i (2) 
. $!■**-//*«•... 0) 

, . .,». throughout the volume and over the 

; *> ■ denoting the direction cosines 

li m ta* surface element dS, and f , «, f 

p (i ) may now. be written 



which becomes by Green's transformation 

leading to the differential equation of continuity when the integration 
is removed. 

«. The equations of motion can be established in a similar 
way by considering the rate of increase of momentum in a fixed 
direction of the fluid inside the surface, and equating it to the 
momentum generated by the force acting throughout the space 
S, and by the pressure acting over the surface S. 

Taking the fixed direction parallel to the axis of *, the time-rate 
of increase of momentum, due to the fluid which crosses the surface, b 

-//^cosWS.-JJ^t+w^+^p^)^ (I y 

which by Green's transformation is 

The rate of generation of momentum in the interior of S bv the 
component of force, X per unit mass, is ^ w 

^ . . fSI-Xdxdyd*. 0) 

and by the pressure at the surface Sis 

-///#c--/jf/gw,*. ( 4) 

by Green's transformation. 
The time rate of increase of momentum of the fluid in ^ A " S is 

and (5) is the sum of (i), (2), (3), (4), so that 

leading to the differential equation of motion 

ipu * m • 






j, . l^+*V»+*>»)dS-o # 

with two similar equations. 

I h !f ab "i lutc Ul ^ it offorcc b wnpJoyed here, and not the gravitation 
unit of hydrosuues; in a numerical aoplicaUon it is assumed that 
C.G.S. units are intended. 

These equations may be simplified slightly, using the eauation of 
continuity (5) % 21; for ^ «^«*wm w 

+«(^+^+f+^). <«) 

reducing to the first line, the second line vanishing in conseauence of 
the equation of continuity; and so the equation of motion may be 
written in the more usual form y 

^u.du,du, du 

with the two others 




33. As a rule these equations are established immediately 
by determining the component acceleration of the fluid particle 
which is passing through (* f y, s) at the instant / of time 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'Alemberfs principle 
form a system in equilibrium. 

To determine the component acceleration of a particle, suppose F 

To determine the component acceleration of a part! 
denote any function of x,j, s, 1, and investigate the 
r a moving particle; denoting the change by DF/«fc, 

CD . 

and D/A Is called particle differentiation, because it follows the rate 
of change of a particle as it leaves the point x. y, s; but 

JF/A, dF/dx, dF/dy, dF/rfs (2) 

represent the rate of change of F at the time i, at the point, x. y, * 


The components of acceleration of a particle of fluid are conse- 

D« du . du, du, dii ,_* 

D» do , do , do , dv , A y 

*•%+%*&%• <«> 

hiding to the equations of motion above. 

If F (*, y, s, -o represents the equation of a surface containing 
always the same particles of fluid, 

*DF dF , dF . dF. dF ,~ 

TT -°« or H+ u JZ +9 Ty+ w &-°' « 

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 sec 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 

X- -dV/dx, Y- -dV/dy, Z- -dV/ds; (1) 

and putting 

the equations of motion may be written 

^-^r+Wfs+^f-c (4) 

f—wi+art+gi-o. (6) 


H-/aW,+V+|*. ( 7 ) 

tf-tf+^+t* (8) 

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 kq* is replaced by fflt . 
Eliminating H between (5) and (6) 

Df ' Au do jtw . „ (du , do , dw\ - % 

and combining this with the equation of continuity 



we have 

with two similar equations. 

•J-f+s'+J*. (») 

a vortex lino is defined to be such that the tangent is in the direction 
of «, the resultant of (, i», f, called the components of molecular 
rotation. A small sphere of the fluid, if frozen suddenly, would 
retain this angular velocity. 

If M vanishes throughout the fluid at any instant, equation (ix) 
shows that it will always be aero, and the fluid motion is then called 
irrokUional', and a function 4 exists, called the velocity function, 
such that 

udx+vdy+wds— d*, (13) 

and then the velocity in any direction is the space-decrease or 
downward gradient ot 4. 

25. But in the most general case it is possible to have three 
functions 4, 4, ** of x, y, s, such that 

udx+vdy+wdz--d+-md+ t 0) 

as A. Clebsch has shown, from purely analytical considerations 
(CreUe, Ivi.) ; and then 


«-<3B# -«*# *-&& » 

$+$+$-». £+»§+«£-* (J) 

so that, at any instant, the surfaces over which 4 and m are constant 
intersect in the vortex lines. 






the equations of motion (4), (5), (6) 1 24 written 

&-"H-»,-3k#-o. ; 

and therefore 

Equation (5) becomes, by a rearrangement, 

+fc(*+«MHEH » 

dK d*T>m .dmD* f ~ 

sens St + zr7f ""° (8 > 

and as we prove subsequently ({37) that the vortex lines are composed 
of the same fluid particles throughout the motion, the surface m and 
4 satisfies the condition of (6) { 23; so that K is uniform throughout 
the fluid at any instant, and changes with the time only, and so 
may be replaced by F(/). 

26. When the motion is steady, that is, when the velocity at any 
point of space does not change with the time, 

^-»f+2Wf-0, (I) 


»dK, dK.JK dK, dK^ dlC , . 

K-/SW.+V+W-H (3) 


is constant along a vortex line, and a stream line, the path of a fluid 
particle, so that the fluid is traversed by a scries of H surfaces, each 
covered by r. network of stream lines and vortex lines; and if the 
morion is irrotational H is a constant throughout the fluid. 

Taking the axis of * for an instant in the normal through a point 
on the surface H« constant, this makes n-o, {«p ; and in steady 
motion the equations reduce to 

dH/do~2o[—2ttm-2qwnn$ t (4) 

where is the angle between the stream line and vortex line; and 
this holds for their projection on any plane to which d» is drawn 

In plane motion (4) reduces to 

if r denotes the radius of curvature of the stream line, to that 

the normal acceleration. 

The osculating plane of a stream line in steady motion contains 
the resultant acceleration, the direction ratios of which are 

&&*-%-«+-*&■%.•.. » 

and when q is stationary, the acceleration is normal to the surface H 
• ■ - - ---«-■-- rtream line is a geodesic. 

f the pressure and potential head the statical 
he instant statical and dynamical head 'intersect 

in the three surfaces touch where the velocity is 


led Bernoulli's equation, and may be interpreted 
as of the energy which enters and leaves a given 


luid is drawn off from a vessel so large that the 
m surface at a distance may be neglected, then 

B< may be written 

H-p/p+s+sVag-P/p+#, (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 Os is 
taken vertically upward. 
In particular, for a jet issuing into the atmosphere, where p-P, 

tVaf-ft-s. (9) 

or the velocity of the Jet is due to the head *-* 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 

so that we can put 

35 + 3y" ' 
«- -d+/dy, v-d+Jdx, 



where * is a function of x, y, called the stream- or current-function ; 
interpreted physically, f-tft. the difference of the value of f at a 
fixed point A and a variable point P is the flow, in ft.'/ second, across 
any curved line AP from A to P, this being the same for all lines in 
accordance with the continuity. 

Thus if d+ is the increase of 4> due to a displacement from P to P*. 
and k is the component of velocity normal to PP\ the flow across 
PP* is oV-A-PP 7 ; and taking PP* parallel to Ox, d+-vdx\ and 
similarly d+--udy with PP' parallel to 0>; and generally ety/d* 
is the velocity across ds, in a direction turned through a right angle 
forward, against the clock. 

In the equations of uniplanar motion 

*-£-g-3+g --**-»•» "CD 
so that in steady motion 

4gf+Wj!;-o. 35?+i*#-<». 35+W-o. (4) 

and VV must be a function of *. 
If the motion is irrotational, 

— &~& •— £-& » 

to that ^ and + are conjugate functions of x and y, 

♦+*»-/(*+*), vV-o. v^-o; (6) 

or putting 

♦+*»-», s+yj-t, w«/(s). 
The curves ♦-constant and * -constant form an orthogonal 


system; and the interchange of ♦ and ^ will give a new state of 
uniplanar motion, in which the velocity at every poii * 
through a right angle without alteration of magnitude. 

For instance, in a uniplanar flow, radially inward towards O, the 
flow across any circle of radius r being the same and denoted by 
2rm, the velocity must be mjr, and 

+-mlogr, +=m8, ++ft-jn log re», w-mlogfc (7) 

Interchanging these values 

f-mlogr. +-**, * +**-m log ref (8) 

gives a state of vortex motion, circulating round Or, 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 ; analogous to the magnetic field of a straight electric current. 

If other vortices are present, any one may be supposed to move 
with the velocity due to the others, the resultant stream function 

tl e value of f at the 

v< [itself. 

surface, the motion 
of a series of vortex- 

in ross the boundary. 

al reflection of the 
v< ortices, moving on 

a corresponding pair 

of be path of a vortex 


... . <to) 

this is therefore the path of a single vortex in a right-angled corner; 
and generally, if the angle of the corner is tin, the path u the Cotes' 

rsinafl-na. (11) 

• A single vortex in a circular cylinder of radius a at a distance e 
from the centre will move with the velocity due to an equal opposite 
image at a distance a'/c, and so describe a circle with velocity 

mc/(a*-<f)ln the periodic time 2»-(a*-e f )/m. (12) 

Conjugate functions can be employed also for the motion of liquid 
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 

*-abftdb*~* ™ 

and then 

«+f»-.F(tanJ#.«*). (14) 

28. Uniplanar Motion of a Liquid duo to Ik* Passat* of a Cylinder 
through ♦/.— A stream-function + must be determined to satisfy the 

vV -o. throughout the liquid ; (1) 

* - 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, 
d+lds- -Udylds, or tf+U? -constant over the moving cylinder; 


and *+Uy-*' is the stream function of the relative motion of the 
liquid past the cylinder, and similarly *- Vx for the component 
velocity V along Oy; and generally 

*'«*+Uy-Vx (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, 

oV/tfr- norma! velocity reversed 



*+iR0t»+y*>«f\ (6) 

a constant over the boundary; and *' is the current-function «f 
the relative motion past the cylinder, but now 

VV+2R-0. (J) 

throughout the liquid. 
Inside an equilateral triangle, for instance, of height ft, 

*'--aRa/fv/*, (8) 

where *, 0, y are the perpendiculars on the sides of the triangle. 

In the general case *' -*+Uy- Vx+lR(x*+/) is the relative 
stream function for velocity components, U, V, R. 
29. Example /.—Liquid motion past a circular cylinder. 
Consider the motion given by 

»-U(s+oV«), (I) 

so that 

♦ -u(r-rf)cos«-u(i+£)x, 
f .u(r-£)sin«-u(i-£)j. 


Then 4> -o over the cylinder r-a, which may be considered a fixed 
post; and a stream line past it along which yV-Uc, a constant, is 
the curve 

(r-^)sin«-c, (x»+/)(y-*)-a«7-o. (j) 


trie cylinder, external or internal, c 

^-f+U i y-[U(i-j') + UJy. 

a cubic curve (Ci). 
Over a concentric cylinder, external or internal, of radius r -*, 


and *' is sero if 

U,/U«(a«-&»)/6»; (5) 

so that the cylinder may swim for an instant in the liquid without 
distortion, with this velocity Ui; and w in (1) will give the liquid 
motion in the interspace between the fixed cylinder r— a and the 
concentric cylinder r- b, moving with velocity U|. 

When 6—0, U1-00; and when 6-00, Ui-— U, so that at 
infinity the liquid is streaming in the direction xO with velocity U. 

If the liquid is reduced to rest at infinity by the superposition of 
an opposite stream given by v— —Us, we are left with 

w-UaVs. (6) 

*-U(<r»/r)cos*- Ua»x/(jr«+/), (7) 

*« -U(a«/r) sin «- -Ua«y/(x»+/). (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 B* with Ox, 

™ 9 '-% l di m x&? mVUi *> •-** 

and the velocity is Ua*/r*. 
Along the path of a particle, defined by the Ci of (3), 





on the radius of curvature is iaV(y — \c), which shows that the curve 
is an Elastica or Lintearia. (J- C. Maxwell, Collected Works, u. 208.) 
If «H denotes the velocity function of the liquid filling the cylinder 
r-6, and moving bodily with it with velocity Ui, 

*--U,x, (12) 

and over the separating surface r-fr 


"Ui( f +t) -?T& 


and this, by 1 36, is also the ratio of the kinetic energy in the annular 
interspace between the two cylinders to the kinetic energy of the 
liquid moving bodily inside r-6. 

Consequently the inertia to overcome in moving the cylinder 
r = b, solid or liquid, is its own inertia, increased by the inertia of 
liquid (a*+&>)/{a , _W times the volume of the cylinder r-*; 
this total inertia is called the effective inertia of the cylinder r-a, 
at the instant the two cylinders are concentric. 




With liquid of density p, this gives rise to a kinetic reaction to 
acceleration dV/dt, given by 




if M' denotes the mass of liquid displaced by unit length of the 
cylinder r=b. In particular, when a - 00 , the extra, inertia is M '. 

When the cylinder r-a is moved with velocity U and r-6'wi^h 
velocity Ui along Ox, 

♦- "»^(7+')«»»-«W??('+7) e "* (,s> 

*'-V^(y-r)<in>-V,^(r-f)ati«;' (.6) 
and similarly, with velocity components V and V» along Oy 

*- V^ s ,(^-r)co.«+V,j ! ? 5 ,(r-^co.»i (.8) 
and then for the resultant motion 

The resultant impulse of the liquid on the cylinder is given by the 
component, over r-a (| 36), 

X-/rfcos e.odO—pa* (U £±£-U,r/^i) ; (jo) 

and over r-6 

X,-/^cos^.6«»-»py(UT|^rU,^), (ai) 

and the difference X-X t is the component momentum of the liquid 
in the interspace; with similar expressions for Y and Y». 
Then, if the outside cylinder is free to move 

X1-0, Tj-p+tfi' X m ***Uvn£&- 


But if the outside cylinder is moved with velocity Ui, and the 
inside cylinder is solid or filled with liquid of density <r, 

v fit U « 3P» 

and the inside' cylinder starts forward or backward with respect to 
the outside cylinder, according as p> or <<r. 

30. The expression for w in (1) J 29 may be increased by the 
addition of the term 

im log t — md + im log r, (1) 

representing vortex motion circulating round the annulus of 

Considered by itself, with the cylinders held fixed, the vortex 
sets up a circumferential velocity mfr on a radius r, so that the 
angular momentum of a circular filament of annular cross section dh 
is pmd\, and of the whole vortex is p*»r(6 , -a"). % 

Any circular filament can be started from rest by the application 
of a circumferential impulse spmdr at each end of a diameter; so 
that a mechanism attached to the cylinders, which can set up a 
uniform distributed impulse -rpm across the two parts of a diameter 
in the liquid, will generate the vortex motion, and react on the 
cylinder with an impulse couple -pm*a' and pmvP, having re- 
sultant pmrft-a*), and this couple is infinite when 6-00, as the 
angular momentum of the vortex is infinite. Round the cylinder 
r-a held fixed in the U current the liquid streams past with velocity 

$'-aUain0+«/c; (2) 

and the lost of head due to this increase of velocity from U to f is 
y*-U» (aUsing+m/q)'-U» () 

2g 2g W 

00 that cavitation will take plate, 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 
amU sin 0/ga, and its thrust is as-pniU absolute units in the direction 
Cy, to be counteracted by a support at the centre C; the hquid 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 2*pmV in the direction xC. 

Now if the cylinder is released, and the components U andv are 
reversed so as to become the velocity of the cylinder with respect 

to space filled with liquid, and at rest at infinity, the cylinder will 
experience components of force per unit length 
(i.) -2TpmV, as-pmU, due to the vortex motion; 

(ii.) -Tptt 1 ^, -Tpo^r, due to the kinetic reaction of the liquid; 

(Ui.) o, — *(*— p)o«gy due to gravity, 
taking Oy vertically upward, and denoting the density of the cylinder 
by 9; so that the equations of motion are 



or, putting m-a*<* % so that the vortex velocity is due to an angular 
velocity « »* a radius a. 

•W^f- -*pc^+2*pmV-*(*-p)aU. 

Thus wit! 
velocity 2, 
is v. With 
way the 1 
and waves 

so the sw 
ball, or gou. 

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- *&, 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 F at opposite ends of the diameter PF, la 
pdy (U - UaV^cosa»+mr- | sin«)(Ua«r- , sXna«+»ir*cos«) 

+ pdy (-U+UoV^cosaM-wr^smfKUa^ainal-sj** cos*) 

-apdymUr«(cos«-oV<cos3«). (8) 

and with y-b tan 9, r-fr sec 9, this is 

apmU*(i -o*&-*cos 3* cos*), (9) 

and integrating between the limits 0- *}«-, the resultant, at before, 
is as-pmU. 

31. Example 2.—Confocal Elliptic Cylinders.-' Employ the elliptic 
coordinates «, {, and f -*+#, such that 

a-echf, *-cch*cos{,y»csh*Binf; (1) 

then the curves for which « and I are constant are confocal ellipses 
and hyperbolas, and 

J-3tiir« t < ch '«- co *> 

- Jc» (chan -cosal) - r,r, -OD», (a) 

if OD is the semi-diameter conjugate to OP, and n, r» the focal 

*,rt-£(cliv*cos{); (3) 

rs-xs+yi -ft(ch«»-«n«e) 

-}c*(chan;+cos a{). (4) 

Consider the streaming motion given by 

»-mch(f-7). Y-«+/fc\ (5) 

♦ -»chGt-e)cos(|-0), *«msh(,-a)sin(*-0). (6) 

Then *-o over the ellipse f -a, and the hyperbola f-tf, so that 
these may be taken as fixed boundaries; and + is a constant on a C* 
Over any ellipse 4, moving with components U and V of velocity, 

-[msh(»-e)sinpN-Vccln]cosf; (7) 
so that*' -o, if , 

U. Jjph^co, fi, V- -SSMj^sin A (8) 

having a resultant in the direction PO. where P is the intersection of 
an ellipse q with the hyperbola fi; and with this velocity the ellipse 
t; can be swimming in the liquid, without distortion for an instant. 
At infinity 

U- -"*-cx»fi - - ^rflcos A 

V--7rHm0--5fysuift (9> 

a and b denoting the semi-axes of the ellipse •; so that the liquid is 
streaming at infinity with velocity Q -«/(<»+©) in the direction of 
the asymptote of the hyperbola A. .... 

An ellipse interior to u-e will move in a direction opposite to 
the exterior current ; and when *-o,U-«o.butV- (m/c) sh a sin A 

Negative value* of * must be interpreted by a streaming motion 
on a parallel plane at a level slightly different, as on a double Riemann 
sheetT the stream .passing from one sheet to the other across a cut 
SS' joining the fociSTS'. A diagram has been drawn by Col. R. A- 




The components of the liquid velocity q, in the direction of the 
normal of the ellipse ij and hyperbola |, are 

-wJ-*ih(^-ft)cos^/5) f mJ-«ch(rni)dn(€-«. (10) 

The .velocity q is zero in a corner where the hyperbola fi cuts the 
ellipse a; and round the ellipse a the velocity q reaches a maximum 
when the tangent has turned through a right angle, and then 

i-Q ^ffT"^ <»> 

and the condition can be inferred when cavitation begins. 
With 0»o, the stream is parallel to xo, and 

- - Ik ch(»-a)shicos £/sh(«-a) (12) 

over the cylinder *, and as in (12) 5 29, 

^—TJx— Ucchacosf, (13) 

for liquid filling the cylinder; and 

*-£&> <M> 

over the surface of •; so that parallel to Ox, the effective inertia 
of the cylinder *, displacing M' liquid, is increased by M'thf/thfa-a), 
reducing when a -00 to M'tb*=»M'(6/a). 

Similarly, parallel to Qy, the increase of effective inertia is 
M'/th.i tb(jj-a), reducing to M'/th e*M'(a/6), when*— «o, and 
the liquid extends to infinity. 

32. Next consider the motion given by 

4->«ifch2(i)-a)sin2(, f --mshafo-e)cos2{; (1) 

in which f »o over the ellipse a, and 

-[-* sh 2(f-o)+JR««lcos 2{+JR«» ch 2* (2) 
which is constant over the ellipse 9 if 

lR*««msh20i-«); (3) 

so that this ellipse can be rotating with this angular velocity R for 
an instant without distortion, the ellipse a being fixed. 
For the liquid filling the interior of a rotating elliptic cylinder of 

so that 

cross section 

*!*+?/» »U 




with vVi'— 3R— smtO/tf-f-i/P), 



wi -*+** - - *i'R(*+yiW- JW+6»). 

The velocity of a liquid particle is thus (a*— b*)((a*+b*) 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 i-.&>)*/(a'+6 > ) a of the solid; and the effective radius of gyration, 

solid and liquid, is given by 

* J -J(a'+6 , ),andJ(a«-W(fl , +6«). (7) 

For the liquid in the interspace between a and 9, 

4 2(tf-«) sin 2{ 

-i/th2(r-a)th2i; (8) 

and the effective A* of the liquid is reduced to 

fc»Ah2(,-*)thn. (9) 

which becomes }c*/sh2ir~i(a*-6*)/a6, when •-ao.and the liquid 
surrounds the ellipse 9 to infinity. 

An angular velocity R, which gives components — Ry, R* of 
velocity to a body, can be resolved into two shearing velocities, — R 
parallel to Ox, and R parallel to Oy; and then f is resolved into 
fi-W*. such that fc+jRx 1 and iM-JRy 1 »» constant over the 
Inside a cylinder 

*+*V - - *«R(*+yi)V/(o'+*). (10) 

*+*V- Ji*R(*+yiW(a«+6»). (11) 

and for the interspace, the ellipse a being fixed, and at revolving 
with angular velocity R 

*+*V- ~ tfto'sh 2fo-a+#)(ch 2«+l)/sh 2(oi-e), (12) 
*+*>»- t»Rt*sh2fa-n+#)(ch2n-i)/sh2(a,-a), (13) 
satisfying the condition that ft and +t are zero over 17-0, and over 

#i+|Rx«=iRc«(ch2a,+i) f (14) 

sM-|R/-tR*(clias»-i). (is) 

constant values. 

1 n a similar way the more general state of motion may be analysed, 
given by 

w«mch2(r— y), y»*+fii $ (16) 

as giving a homogeneous strain velocity to the confocal system; 
to which mav be added a circulation, represented by an additional 
term mf in m 

Similarly, with 
the function 



*-QcshJ(,-a)sinl({-*) (18) 

will give motion streaming past the fixed cylinder if = «u and dividing 
Along l m Pi and then 

«•—?*»<• suit ch 4, 2xy-<*co8fshv. (19) 

In particular, with sh-a«" i f the cross-section of n •• a is 

« 4 +6xV+v«-ac« f or« < +y«-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 ft is to be made to satisfy the conditions 


(ii.) to+iRx > -JRo«, or^i-owhcnx- *«, 
CiiL) ^i+iRx«-iRa», *»-JR(a«-*«), when y- +b 
Expanded in a Fourier series. 

"-^S 2 ^^ 


an elliptic-function Fourier series; with a similar ex p re s sion for ft 
with x and y, a and b interchanged ; and thence f -fi +ft« 

Example 4.— Parabofic cylinder, axial advance, and liquid stream- 
ing past. 
The polar equation of the cross-section being 

rlcos j0-ai,orr +x-2a, (3) 

the conditions are satisfied by 

f'-Ursin0-2Ualrt sin p«2Ur) sin P(rl cos H-aft), (4) 
f -aUoM sin |*« -UV{2o(r-x)J, (5) 

w— 2UttW, (6) 

and the resistance of the liquid is 2rpaV , /2g. 
A relative stream line, along which f'-lfc, is the quartic curve 

y -,-Vl»<r-,)]. «-«ffl>- ^ . (7) 
and in the absolute space curve given by f , 

34. Motion symmetrical about an Axis. — When the motion of a 
liquid is the same for any plane passing through Ox, and lies in the 
plane, a function f can be found analogous to that employed ia 
plane motion, such that the flux across the surface generated by the 
revolution of any curve AP from A to P is the same, and represented 
by 2»(f — fo); and, as before, if d+ is the increase in f due to a 
displacement of P to P, then k the component of velocity normal 
to the surface swept out by PP* is such that 2«<f ■■a*yfc.PP'; and 
taking PP / parallel to Oy and Ox, 

»«-rff/yrfy, vo+fydx, (1) 

and f is called after the inventor, " Stokes's stream or current 
function," as it is constant alonga stream line (7Va*u. Camk. PhsL 
Soc., 1842; "Stokes's Current Function," R. A. Sampson, Phi. 
Trans., 1892) ; and d+fyds is the component velocity across ds ia a 
direction turned through a right angle forward. 
In this symmetrical motion 

suppose; and in steady motion, 

so that 

2r/y«-y-W-<flW (4 ) 

is a function of f% say /(f), and constant along a stream line; 

dH(d»-2qt, H -/(f) -constant, (5) 

throughout the liquid. 
When the motion is irrotational. 

f»o, «' 

" 3x y ay* 

d4 tsV 
•— 3y°y2? 




Changing to polar coordinate*, x«r cos 0,y**rsin 0, the equation 
(2) become*, with cos 8 «*, 

+%+{i-*$r*V*H (8) 

of which a solution, when f-o, is 

*- (i^£)<« V^-(Ar-^)y^ (9) 
♦-|(*+i)Af-*Br— MP„. (10) 

where P. denotes the 2onal harmonic of the nth order; also, in the 
exceptional case of 

*-A«cos*, *-A*/r; 
*-B*, *--B t logtan4* 

--»«*/y. (II) 

Thus cos • is the Stokes* function of a point source at O, and 
PA- PB of a line source AB. 

The stream function ^ of the liquid motion set up by the passage 
of a solid of revolution, moving with axial velocity U, is such that 

T& m - U & * +lW - const » nt ' < I2 > 

over the surface of the solid; and ^ must be replaced byy-' ■»* -Htyv" 
in the general equations of steady motion above to obtain the steady 
relative motion of the liquid past the solid 

For instance, with «-»i in equation (9), the relative stream 
function is obtained for a sphere of radius «, by making it 

* , »*+|Uy'-sU(r«-aVr)Bin , 0, *«-iUc» sin'tf/r; (13) 
and then 

+'-Ux(i+ia'/r*) t ♦-JUa'coif/r*. (14) 

-£-u£cos*\ -^-JU^sin*. (15) 

so that, if the direction of motion makes an angle f with Orf, 

tan (*-*)-itanfl, tan* =3 tan 0/(2 -tan* 6). (16) 

Along the path of a liquid particle 4>' is constant, and putting it 
eaual to ll/A 

^ ' (r»-o»/r) sin*««e*, sin*«-*W-o>). (17) 

the polar equation; or 

■""" •* y»-cV/(r»-o«), H-aV/(y«-c^ (18) 

a curve of the 10th degree (Cm). 

In the absolute path in space 
cos * - (2 -3 m*9)N (4 -sin««), and ain» $ - (y*-*y)la*, (19) 
which leads to no simple relation. 

The velocity past the surface of the sphere is 

so that the loss of head is 

(\ sin'fl-OUVa*. having a maximum |UV2& (21) 
which must be less than the head at infinite distance to avoid 
cavitation at the surface of the sphere. 
With « -2, a state of motion is given by 

*--JU/oV/H. *'-jUy»(l-flWH), (22) 

♦'-Ux+* ♦«-iU(aVH)P.. Pa-fM 1 -!. (*3) 

representing a stream past the surface r* »aV 

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 Erst, 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. Trrotational Motion in General.— Liquid originally at rest in 
2 singly-connected space cannot be set in motion by a field of force 
Jue to a single-valued potential function; any motion set up in 
he liquid must be due to a movement of the boundary, and the 
notion will be irrotational; for any small spherical element of the 
iquid may be considered a smooth solid sphere for a moment, and 
he normal pressure of the surrounding liquid cannot impart to it 
iny rotation. 



The kinetic energy of the liquid inside a surface S due to the 
velocity function 4 is given by 

t -«'JJ/[© , +0 , +®1*** 

by Green's transformation, dr denoting an elementary step along 
the normal to the exterior of the surface; sothatd+/dr«o over 
the surface makes T «o, and then 

»'+»•+»•-* *-* *-**-* « 

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 

o-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 4, the liquid can circulate in the circuits inde- 
pendently of any motion of the surface ; thus, for example, 

*«m*-mtan-V* ($) 

will give motion to the liquid, circulating in any ring-shaped figure 
of revolution round Ox. 

To find the kinetic energy of such motion in a multiply connected 
space, the channels must tie 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 4 in any circuit, or the 
value by which 4> 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 

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 («), the cyclic constant * « 2vm. 
In plane motion the kinetic energy per unit length parallel to Os 

For example, in the equilateral triangle of (8) } 28, referred to co- 
ordinate axes made by the base and height. 

*'- -2R«*7/A- - JRyKa-y)'-^/* 


L --iRlltf+i** +A)* , -y') -3*^+^/* (9) 

and over the base y™o, 

dxld,- -dx/dy- +JR(J*"-3x«)/a^- - *R(*tf +*«). (10) 
Integrating over the base, to obtain one-third of the kinetic 
energy T, 

JT " ,P /-A/V3 iR,C3 * V/r * 4W * 

-PRW/I35V3 (") 

so that the effective k* of the liquid filling the triangle is given by 
' A>-TApR*A-.2*V45 

- 1 (radius of the inscribed circle) 1 , (12) 

or two-fifths of the «* for the solid triangle. 
Again, since 

d+ld*-d+/ds, d4>jds--d+ld,, (13) 

T-|p/*d*--W*fc. (14) 

With the Stokes' function 4> for motion symmetrical about an 



37. Flow, Circulation, and Vortex Motion. — The line integral of 
the tangential velocity along a curve from one point to another, 
defined by 

/( u Ts+ v a£+ »'£) * -/<«**+•&+**>. <»> 

is called the " flux " along the curve from the firllt 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 

-/*-*-*. (a) 



so that the flow is independent of the curve for all curvet 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 4 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 

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 Ox with angular velocity f , 
the circulation round a curve in the plane xy is 

ff ( x j£ -y%)ds»t times twice the area. 13) 

In a fluid, the circulation round* an elementary area dxdy is 
equal to 

^ + (H-^)^-(.+gi>)&-f^-g-g)*^ (4) 

so that the component spin is 



in the previous notation of { 24; so also for the other two com- 
ponents I and 9. 

Since the circulation round any triangular area of given aspect 
b the sum of the circulation round the projections of the area on 
the coordinate planes, the composition of the components of spin, 
{, «, 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 «« is 
constant where a is the crosfrsection of the filament and <* the 

resultant spin (W. K. Clifford, Kinematic, book iii.). 

So far these theorems on vortex motion are Irinemaucai; out 
introducing the equations of motion of 1 22, 

SMB-* SMJ-* M-* «> 

Q-fdp/p+V, (7) 

and taking dx, dy, ds in the direction of «, v, to, and 
dx: dy. ds—u: v: w, 

— 42+W. («) 

and integrating round a closed curve 

%J{udx+vdy+wdz)-o. (9) 

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 cut 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 

Denoting the cross-section a of a filament by dS and its mass by 
dm, the quantity udS/dm is called the vortieity; this is the same at 
all points of a filament; and it does not change during the motion; 
and the vortieity is given by w cos tdSfdm. if dS is the oblique 
section of which the normal makes an angle • with the filament, 
while the aggregate vortieity of a mass M inside a surface S is 
M-*/tt cos sdS. 

Employing the equation of continuity when the liquid is homo- 

•$-$)-'- *-&-&-&• <•<» 

which is expressed by 

*«(«, », w) - 2 curt ({. n. f). («, * f) - 1 curl («, v, v>). (11) 

38. Moving Axes in Hydrodynamics.— In many problems, such as 

the motion of a solid in liquid, it is convenient to take coordinate 

axes fixed to the solid and moving with it as the movable trihedron 

frame of reference. The components of velocity of the moving 


origin are denoted by O, V. W. and the components of angular 
velocity of the frame of reference by P, Q, R; and then if u, v. w 
denote the components of fluid velocity in space, and *', v*, W the 
components relative to the axes at a point (x, y, s) fixed to the 
frame of reference, we have 

-U -rV-yR +tO. 


p-V -fV-.sP +xR 
w-W +w'-*Q +>P. 
Now if k denotes the component of absolute velocity in a c 1 
fixed in space whose direction cosines are /, m, n, 

k-lu+mv+nvo; (2) 

and in the infinitesimal element of time dt, the coordinates of the 
fluid particle at (x, y, s) will have changed by (*', r\ w')dti so that 
^^ u4 .dm,dm 


r + ** +r ^ 


H+ u Tx* v Ty^1i)- (3) 

But as/, m, n are the direction cosines of a line fixed in apace, 

£ - mR-nQ.%- «P-iR.$-JQ-«P; U) 

so that 

D* m , (£-,R +wQ+ «£ x +/£ + *%) +»(. . .)+.(• . .) 

for all values of /, m, *, leading to the equations of motion wkh 
moving axes. 
When the motion is such that 

w d+ dtff d+ d+ U J± ta 

as in } 25 (l), a first integral of the equations in (5) may be written 

+("-0 (fi+ m 1y) +<*-»') (S +m $s) - p W' & 
in which 

-^-(U->R+«Q)3i-(v-«P+xR)^-(W-xQ+>P)^ (t> 

is the time-rate of change of * at a point fixed in space, which is 
left behind with velocity components u— »', »— v* t w—nf. 

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 

f/p+V+lfWGO -constant (9) 

becomes transformed into 

^ + V + i5»-^+JU«-/(*+iU/) -constant. (10) 
f-t+Wy*, (II ) 

subject to the condition, from (4) § 34, 

Thus, for example, with 

f-!U/(Ar«-i), r»-x*+>«, (13) 

for the space inside the sphere r-a, compared with the vamc of 
+' in 5 34 (13) for the space outside, there is .no discontinuity of the 
velocity in crossing the surface. 

Inside the sphere 

so that $ 34 (4) is satisfied, with 
and (10) reduces to 

£+ v -f u l (sr')'-(l?- , ) , | " con,Unt: (,6 > 

this gives the state of motion in M. J. M. Hill's sph eri ca l vortex, 
advancing through the surrounding liquid with uniform velocity. 

30. As an application of moving axes, consider the modem of 
liquid filling the ellipsoidal case 

$+$+$-« <•> 

and first suppose the liquid to be frozen, and the ellipsoid to he 




rotating about the cento* wkh component* of angular velocity f , 
t». r; then 

*- ->f +*». *- -*l+*f. »« -*i+Jt- (a) 

Now suppose the liquid to be melted, and additional components of 
angular velocity Qi. Sk. U» communicated to the ellipsoidal case; 
the additional velocity commu n ica t ed to the liquid will be due to 
a velocity-function 

«_,• c*-a* <*•-** 

as may be verified by considering one term at a time. 

If *', v', u»' denote the components of the velocity of the liquid 
relative to the axes, 

i»'^+,R-«Q- 5 ^Q l y-- ? ^|Osi. (4) 








so that a liquid particle remains always on a similar ellipsoid. 

The hydrodynamical equations with moving axes, taking into 
account the mutual gravitation of the liquid, become 

ig+4» / ^x+^-i>R+«Q+«'g+»'^+«^5-o. (9) 


A n /"• abcik 

A.B.C.-j^ ( fl i.j. Xf 4»+x,c*+x)r l 

P»-4(a , +X)(*+X)(<»+X). (10) 

With the values above of «, *, w. «', •. 1/. the equations become 
of the form 

^+4*AA*+a*+Aj+|t-o. (11) 

£3£+4*pBy+**+0y+/s-o. (is) 

j^+4»pC»+g*+/»+Ti-o. (13) 

and integrating 


+l(«x»+^+^+^>»+2<«x+a»«y) -const., (14) 
so that the surfaces of equal pressure are similar quadric surfaces, 
which, symmetry and dynamical considerations show, must be 
coaxial surfaces; and /, g, h vanish, as follows also by algebraical 
reduction ; and 

-%£ms#w): (,s) 

with similar equations for fi and y. 

If we can make 

( 4 »AA+a)x>« UrpB+flP-UrpC+Y)* (16) 
the surfaces of equal pressure are similar to the external case, which 
can then be removed without affecting the motion, provided a, 0, y 
remain constant. ... .... ^ 

This is so when the axis of revolution is a principal axis, say Os; 
when , % 

Oj-o. (b-o, {«o, i»-o. (17) 

If d"0 or 9r m t in addition, we obtain the solution of Jacobi's 
ellipsoid of liquid of three unequal axes, rotating bodily about the 
least axis; and putting 0-6, Maclaurin's solution is obtained of 
the rotating spheroid. 

In the general motion again of the liquid filling a case, when a »&. 
Q, may be replaced by zero, and the equations, hydrodynamical 
and dynamical, reduce to 

of which three integrals are 



-7^[^-N. + {l,^^-M^N^}^ 

where Z is a quadratic in {•, so that f is an elliptic function of A 
except when c -a, or 30. 

Put Qi-Qcos*,C%--Qsin *, 

^■1*-^"^-^+^, («4) 

1 sSfsT.y. 



which, as Z is a quadratic function of f 1 , arc non-elliptic integrals; 
so also for ^. where { ■»«* cos <+,*- ~w sin ^. 
In a state of steady motion 

2-o.a-& <„> 

♦ »*-n/. suppose, (28) 

0,1+0* -0«. (*>) 

S-^fr <*» 

. o»+«« * aa» O ,„. 

1 o^?Q , "7+"^ W 

and a state of steady motion is impossible when £a>c>0. 

An experiment was devised by Lord 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 be 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 JH. — 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 4 and stream function f are given as conjugate 
functions of the coordinates x, y by 

and then 

w-/(s). where s-x+yi, w-^+^t. 



so that, with %~q cos 0, »-ff sin #, the function 

r—flfe-«?S -§(«+»') -§(cos 9+i*n9). CO 

S'ves f as a vector representing the reciprocal of the velocity f In 
rcction 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 


direction 8 along a plane boundary, and to give a c 
velocity over the surface of a jet, where the pressure h) 
It is convenient to introduce the function 

Q«logr-log(Q/«)+W (4) 

to that the polygon representing Q conformatry hat a boundary 
given by straight lines parallel to the coordinate axes; and then to 
determine Oand w as functions of a variable u (not to be confused 
with the velocity component of q) t 
, such that in the confonnal repse- 
'* sentation the boundary of the Q 
and w polygon is made to coincide 
with the real axis of a. 

It will be sufficient to give a 
few illustrations. 

Consider the motion where the 

liquid is coming from an infinite 

p.,, A 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 0-\wfn. 

The theory of confonnal representation shows that the motion is 
given by 

where «•«, c' at the edge A, A 1 ; «-»at a corner B: «-o across 
xx* where ♦ -oo;and ■-«, $-• across the end J y of the iet, 
bounded by the carved lines APJ. A'PI*. over which the skin 
velocity is 0. The stream lines xBAJ, xA 1 )' are given by *-o, ss; 
so that if c denotes the ultimate breadth JJ' of me jet, where the 
velocity may be supposed uniform and equal to the skin velocity Q> 

ss-Qc c-ss/Q. 

If there are more B corners than one, either on xA or x*A', the 
expression for f is the product of corre sp onding factors, such as in (5). 
Restricting the attention to a single comer B, 

shaQ-sklog(^) coss#+«chlog(Q)*sias# 

HYDROMECHANICS ihydrodynamks 

ch «Q«-cos S3a- 'YjEJ. «k «0-lsin «a»t^^t, 




and the* 

d& l V(K-a,»~aO dm %» 
isT ^»-iK(»-«.«-« J >' g*~is? 

tWftrawbtt by whkh the conformities^ 
For the O poryfoasasarif>casw>atB-a,«\andaseroaatleat 

* -a, where • chingri from o to J»> and Q larrt a ws by J*r>; so 


And the w polygon has a aero angle at n»o,m. where ft hingf i 
from o to si and back again, so that w changes by sss, aad 

whareB-- ", (11) 


dm B 

Aba* the stream EaexBAPJ. 

and over the jet sarface J PA, where the skin velocity is Q, 

&*-l — Q> »««•***-•••**; (14) 

denoting the arc AP by a, starting at «•«: 

chno-c— -\^\fe^ («5) 

ahafi.tsmsw-.\^\^. (16) 

• >»-ar~*>n, (r7) 

aM this gma the mtriniia. eqwatsaa of the jet. aad then the sasfai 

ds id* tdv idmfi 





+m- ^-»zyj5"-*i (») 

-ain ^(«;t^ ; 

. a-o'+fr+a') cos g*« -to +«'+(«-«') cos a—lcos atsf 
(a— o'jain'xaa 

w cos 2— —'Cos ynf 
* .anas* ' 
Along the wall AB, cos tti-o, sin ■#■>!, 



* dso> jw_ c£ 


-/ [ vf ^w%^g3T K ^ ^ » 

Along the wall Bx, cos af- 1, sin af-o, 


chrt-chlog©--^^ <*) 

ah—ahlo,©-.^^. M 

At s where ♦-«• . a »©. and f-fk 

la crossing to the fine of flow x'ATT. * changes from o to •*,» 
that with g-Q across JJ', while across xaT the velocity is f>sothtt 
s*-».rr'-Q.JJ' (31) 

giving the contraction of the jet compared with the in i ti al hreadtk 

of the stream. 

Along the fine of flow x'AT'J'. f-st, »-«V**/-. and from x* to 
A*, cos af - 1. am af -o. 

Along the jet 








gi iia f the iai i i a w, eq matkm . 

41. The arst aeohsem of this saad, worked oat 
hostx, of the eaasx of a jet between two edges A aad 
■el ■ nlmiaiil lij thr irrmrninl ihsfTritinn rrf Thr ifrniT ~irt 
a - u •««w«'--«.as as fia> S 

chO-\fe^.shO-^^: (1) 

dt^."*"*-^«i. (J) 

aad akmg the jet APJ. • > a -at*^>«. 


so that PT-c/h". »ad the curve AP b the tractrix; and the co- 
efficient of contraction, or 



breadth of the jet 



'breadth o( the < 

wince *•+** 


9* m 

olution for 
1 angle **/*• 
by making 
un line of 
iy duplica- 
an be ob- 
wed «, a, 
fflux from 
xm verging 

-« a'7 



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, «/ will give the 
results of special problems considered by J. M. MicheU, Phil. 
Trans. 1800. 

Thus with a'-o, a stream is split symmetrically by a wedge of 
angle r/n as in Bobyleff's problem; and, by w*Mng a— «o, the 
wedge extends to infinity; then 


* **- yjtt * *°~ V*=* 

Over the jet surface f -m, j-Q, 

ch Q-cos «t- ^7rpi/«h Q-sdn *-s%^££- ( 2 ) 

^/■■tansl,^^* .**|„a. (.1) 

"""•<• smart* w# 

For a jet impinging normally on an infinite plane, as in fig. 6, n » 1, 

«!■•/• - tan 0, ch (r«/«) sin a# - 1 , (4) 

sh \wx\c -cot 9, sh fr>/c -tan 0, 

ah \n\c sh Jry/c-i, «»•<•♦»>/— ri»«/-+s»«^+i. (5) 

With H"}, the jet is reversed in direction, and the profile is the 
catenary of equal strength. 
In Bobyteff's problem of the wedge of finite breadth, 

ch -°-^>^S' 8h - -\pi £ V^ (6) 

and along the free surface APJ, j-Q, f •<>, «-#•*•>/* ««■•/•, 

cositf-cosna ^.^^ , 

«••/• cos*wa sin*afl 
""sin 1 !**— sin*na' 


the intrinsic equation, the other free surface AT' J' being given by 
_. fc cosft—sin'wg , » 

^^"sinW-sinW (9) 

Putting A - f gives the case of a stream of finite breadth disturbed 
by a transverse plane, a particular case of Fig. 7. 

When a—b, 0-0, and the stream is very broad compared with 
the wedge or lamina; so, putting w-w' (a—b)fa in the penultimate 
case, and 

«-ar»««-(o-fr)s/, (10) 

&**-yj^***Q-yljp> (11) 

in which we may write 

*'«♦+*». (12) 

Along the stream line xABPJ, + «o; and along the jet surface 
APJ, —!>♦>— 00; and putting $-— rs/c— i, the intrinsic 
equation is 

ws/c-cothti, (13) 

which for «- 1 is the evolute of a catenary. 

43. When the barrier AA' is held oblique to the current, the 
stream line xB is curved to the branch point B on AA' (fig. 7), and 
so must be excluded from the 
boundary of u; the conformal re- f \ 
presentation is made now with 

35 («-*)V (u-0.1t -o') <*> 


m-fm' n— ft 

taking «-• at the source where 


£"^.*_" 6 ** A he _ b f anch P "" B » f ";'• i' at the en* 1 ©* the two 
~" ; while ^-o along the stream 

diverging streams where 4» . . 

line which divides at B and passes throui 
along the outside boundaries, so that m, 
of the jets, and 0»+w')/Q is the initial 
stream. Then 

one 1 
1 A, A'; and *-m, -m' 
m'/Q is the final breadth 
eadth, c, of the impinging 



2b -a -a' 







Along a jet surface, $-Q, and 

chQ«cos«-cose-Jsin«a(«-tf')/(*-»). (5) 

if 0-a at the source x of the jet xB, where *-• ; and supposing 
• ~0, ft at the end of the streams where u - j, j' 
.Si— b jsin'a si— j . . . cos 6 ' — cos fi 

a -a' "cos a-cosf'o-a' 8 '* • mH (posa-cos/?) (cose- cos #)» 

5=5-1*1^ cos^ce^ 


a -a' ~ ■ "" (cos a-cos/S'; (cos a— cos?}' 
and f being constant along a stream line 
d+ dw rds ds dw du 

wQ ds wds (cos a— cos 0) (cos a-cosflQ sin » 

'*•+»' S"?;d5" (cos a-cos 0)(cos*-cos ^) (cos -cos /PJ* 
M sin» .cosa— cosjy sing 
cos e— cos^cos/J— cos^*cos«— cos£ 

cos a— cos $ sing / . 

cos^-cos^ /, cos«-cos^ , W 

giving the Intrinsic equation of the surface of a jet, with proper 
attention to the sign. 
From A to B, a>u>b, 0-0, 

ch O-ch log J-cos tt-J sin *a~=J. 

shQ-shlog 1 

J5 (u-6) cos a-j(a-oQ sin'a-f-V (a-a.a-aQsin a 

^2u m ^d4au m '~qa r u 
m+m' (u—b)co*a—\(a- 

•oQ sin *a-f V (a — u . a -aQ sin a 



with a similar expression for BA'. 

The motion of a jet impinging on an infinite barrier is obtained 
by putting j-o, 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-0-0\ and G. KirchhofTs solution is 
obtained of a barrier placed obliquely in an infinite stream. 

Two corners B, and B, in the wall xA, with o'- — <» , and «» 1, 
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. Michetl, A. E. H. Love and M. Rethy. 




When the polygon is dosed by the walls joining, instead of reach- 
ing back to infinity at xx\ the liquid motion must be due to a 
source, and this modification has been worked out by B. Hopkinson 
in the Proc. Lend. Math. Soc., 1898. 

Michcll has discussed also the hollo W vortex stationary inside a 
polygon {Phil. Trans., 1890) ; the solution is given by 

ch nQ=snw, shn(2»scnw (ti) 

so that, round the boundary of the polygon, *=K', sinitf-o; 
and on the surface of the vortex ^ -o, q «= Q, and 

cos n9 m sn $,«? "•J«— am s/c, (12) 

the intrinsic equation of th< 

This is a closed Sumner arysconsists 

of two parallel walls; and 1 

44. The Motion of a . important 

problem in the motion of i of the state 

of velocity set up by the | and thence 

of the pressure and reactio of the solid, 

by which its motion is influ 

Beginning with a single nfinity, and 

denoting by U, V, W, P. £ and angular 

velocity with respect to ax ity function 

takes the form 

♦ -U*+Vfc+W*,+P»+Q*+Rxi, (0 

where the +'s and x's are functions of x, y, s 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 ♦ may be determined one at a time, and this problem 
is purely kinematicaf ; thus to determine <h, 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.) y'^i-o, throughout the liquid; 

("-) ^p «■ — /. the gradient of + down the normal at the surface 

of the moving solid ; 
Cm.) ?$■ -o, over a fixed boundary, or at infinity; 

similarly for fe and ♦*. 
To determine x> the angular velocity P alone is introduced, and 
the conditions to be satisfied are 
(L) V a xi - o, throughout the liquid ; 

(u.) 777 ■ w * ~ n V> at *n* surface of the moving body, but zero over 
a fixed surface, and at infinity; the same for » and xi- 
For a cavity filled with liquid in the interior of the body, since the 
liquid inside moves bodily for a motion of translation only, 

* - -x, * - -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 Medium (1833) ; 
the extension to any other surface will form an important step in 
this subject. 

A system of confocal ellipsoids is taken 

and a velocity function of the form 

*=**. - (4) 

where ^ is a function of X only, so that I is constant over an ellipsoid ; 
and we seek to determine the motion set up, and the form of + 
which will satisfy the equation of continuity. 

Over the ellipsoid, p denoting the length of the perpendicular from 
the centre on a tangent plane, 


l "aff\* w "^\' *"?+X 


? - (a»+X)/»+ (6»+X)»i«+(e*+X)ii». (7) 




to that the velocity of the liquid may be resolved into a component 
—4> parallel to Ox, and —2{a*+\)ld4rfd\ along the normal of the 

ellipsoid; and the liquid flows over an ellipsoid along a line of slope 
with respect to Ox, treated as the vertical. 
Along the normal itself 

g- 1 *+*<«•+*$ I 



U— s>-i(«t+X)g, 

so that over the surface of an ellipsoid where X and f are constant, 
the normal velocity is the same as that of the ellipsoid itself, moving 
as a solid with velocity parallel to Ox 


and so the boundary condition is satisfied ; moreover, any ellipsoidal 
surface X may be supposed moving as if rigid with the velocity ia 
(1 1), without disturbing the liquid motion for the moment. 

The continuity is secured if the liquid between two ellipsoids X 
and X|, moving with the velocity U and U» of equation (11), is 
squeezed out or sucked in across the plane x -o at a rate equal to the 
integral flow of the velocity ^ across the annular area oi— a of the 
two ellipsoids made by x«=o; or if 

•U-iU.-J^cfX, <„) 

•-••VCP+x.^+x) (13) 

Expressed as a differential relation, with the value of U from (11). 

ax["* +a (..+x).f*]-*£-o. <■«> 

*g+»«*+»>£(.3)-* <■*> 

and integrating 

so that we may put 

(tf+M 1 ^"! constant, 

,_r Mdx 



P»-4(a»+X)(6HW+X), (18) 

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 

a(o»+X)2*+*-o, (19) 

and this is the Infinite boundary ellipsoid if we make the upper limit 
Xj ™oo. 
The velocity of the ellipsoid defined by X -o is then 

with the notation 

M F Mix 

aTc"). T^+XlP 





so that in (4) 

♦"oB^-i^AV *-7=a? {22) 

in (1) for an ellipsoid. 

The impulse required to set up the motion in liquid of density » is 
the resultant of an impulsive pressure p* over the surface S of the 
ellipsoid, and is therefore 

//p^-P* //xUS 

-p^o (volume of the ellipsoid) - AW, (23) 
where W denotes the weight of liquid displaced. 

Denoting the effective inertia of the liquid parallel to Ox by «W. 
the momentum 

«W'U-*W (24) 

in this way the air drag was calculated by Green for an ellipsoidal 
Similarly, the inertia parallel to Oy and Oe is 

For a sphere 

n r - f* abcd\ 
Ba ' C * J*(M+X,«J+X)P j 

A+B+C-oAc/iP, Ao+B,+Co-i. 






to that the effective inertia of a sphere is increased by half the weight 
of liquid displaced; and in frictionless air or liquid the sphere, of 
weight W, will describe a parabola with vertical acceleration 

WTTW* (30) 

Thus a spherical air bubble, in which W/W" is insensible, will begin 
to rise in water with acceleration 2%. 

45. When the liquid is bounded externally by the fixed ellipsoid 

:al posit . . , 

1 will satisfy the conditions in the shape 


■ Ux- 

abc , Cm abc&k 

abc ~r*\ ~abcd\ 




and any confocal ellipsoid defined by X, internal or external to 
X — Xi, may be supposed to swim with the liquid for an instant, 
without distortion or rotation, with velocity along Ox 


J B.+ C.-B,-(V 
Since - Ux 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 

If the ellipsoid is of revolution, with 6-c, 

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, 

*-i0»(i+£).?-w(i-£). <6) 

Changing the origin from the centre to the focus of a prolate 
spheroid, then putting 6* -pa, X-X'o, and proceeding to the limit 
where a ■• 00 , we find for a paraboloid of revolution 





7&x->+ v -**» 


with V-0 over the surface of the paraboloid; and then 
*— iUp{V(x»+y«)-*]; 

♦— iup log tv(»«+y)+xi. 

The relative path of a liquid particle is along a stream line 

f ' • JUc«, a constant, (12) 

a C«; whik the absolute path of a particle in space wDl be given by 
dy = r-x a y-c* 
3x y ~~ 2py* 

46. Between two concentric spheres, with 

c*+X-r», a*+Xa -<!!», 


and the effective inertia of the liquid in the interspace is 

When the spheres are not concentric, an expression for the effective 
inertia can be found by the method of images (W. M.' Hicks, Phil. 
Trams., 1880). 

The image of a source of strength m at S outside a sphere of 
radius aba source of strength naff at H, where OS*/, OH -0*//, 
and a line sink reaching from the image H to the centre O of 
line strength - p/a; this combination will be found to produce no 
flow across the surface of the sphere. 

Taking 0* along OS, the Stokes' function at P for the source S 




is » cos PS*, and of the source Hand line sink OH is #»(«//) cos PHx 
and -0»/tt)(PO-PH); so that 

f -^ (cos PSx+ JcosPH*-£°_zPH) f (4) 

and *« -*, 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 on the same radius, taken along Ox, 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 



and for its image at H the Stokes* function is 
ss^cosPHx-s.^ v * 
so that for the combination 





where <h, <h, a-aidi/V (af+af) is the radius of the spheres and 
their circle of intersection, and n, n, r the distances of a point 
from their centres. 
The corresponding expression for two orthogonal cylinders will be 

*'-«>('-*-*+#• «> 

With flj-oe , these reduce to 

for a sphere or cylinder, and a diametral plane. 
Two equal spheres, intersecting at 120 , will require 

jj i¥T~«r* a* ,o«(g-3x) , a* c«(»+3x) 1 , . 

J'-iU/kr;,? ! V 'l^i - \ r% i ' J. (11) 

with a similar expression for cylinders; so that the plane x-o 
may be introduced as a boundary, cutting the surface at to*. The 
motion of these cylinders across the line of centres is the equivalent 
of a line doublet along each axis. 

47. The extension of Green's solution to a rotation of the ellipsoid 
was made by A. Clebsch, by taking a velocity function 

♦ -*7X (1) 

for a rotation R about Os; and a similar procedure shows that an 
ellipsoidal surface X may be in rotation about Os without disturbing 
the motion if 

( gTX-rPTx)^^ 
" i/(*+X)- i/(a»+A) • 
and that the continuity of the liquid is secured if 


r NdA N Ba-Aa , . 

(oHx)(*4-X)P"S5? "o 7 ^"' U ' 

and at the surface X-o, 

/i ,i\ N Br-A. N 1 

R " i/y-i/a' ' 





N - 



1 /I , i\B«- 






The velocity function of the liquid inside the elliptoid X«o due 
to the same angular velocity will be 

♦,-R*y(a*-4W+6»). (7) 

and on the surface outside 

so that the ratio of the exterior and interior value of <t> at the surface 



and this is the ratio of the effective angular inertia of the liquid, 
outside and inside the ellipsoid X—o. 

The extension to the case where the liquid is bounded externally 
by a fixed ellipsoid X*>Xi is made in a similar manner, by putting 
*«*y(x+M), (xo) 

and the ratio of the effective angular inertia in (9) is changed to 

( B,.A.)-(B,-A,)+lk£ a -gf r 

a -~^ g «'-ft'^ 


Make c-» for confocal elliptic cylinders; and then 

and then as above in $ 31, with 

a-ccho, 6-cah o, ai-VCa'+XJ-cchoj, ^-cshoi (13) 
the ratio in (11) agrees with 1 31 (6). 

As before in § 31, the rotation may be resolved into a shear-pair, 
in planes perpendicular to Ox and Oy. 

A torsion of the ellipsoidal surface will give rise to a velocity 
function of the form 4>-xyzp, where Q can be expressed by the 
elliptic integrals A A , B A , C x , in a similar manner, since 



48. The determination of the *'s and x'» is a kinematical 
problem, solved as yet only for a few cases, such as those discussed 

But supposing them determined for the motion 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 x u *t, xt, Jx, Jt, ?i, 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 as considered 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 

<rr <rr <rr ... 

»»-3U' **"2V' ** m ZW w 

<n* dT <rr 
*-JP » m %? *-JK ; 

but when it is expressed as a quadratic function of X), xt, x t , yi, 


oT ,, dT „. dT 

"-&• v -§5- w -ar.- 

D dT ~ <rr „ dT 

?m iy7 Q "33? R "37. 


The second system of expression was chosen by Clebsch and 
adopted by Halphen in his Functions eiiiptiquts; aivd thence the 
dynamical equations follow 

L -^->»g+^-*^+'^ * — •■ M-....W 

where X, Y, Z, L, M, N denote components of external applied force 
on the body. 

These equations are proved by taking a line fixed in space, whose 
direction cosines are /, m, n, then 

^-mR-»Q, ^-»P-/R, 3j«JQ-«P. (5) 

If P denotes the resultant linear impulse or momentum in this 

P -/*»+«**+«*!, (6) 

dP dt t< dm .dn 

■3T-di* + '-d7*+**» 

for all values of /, m, *. 


+ m (1s ! -* p+ * R ) 




Next, taking a fixed origin and axes parallel to Ox, Oy, Os 
through O, and denoting by x, y, s the coordinates of O, and by G 
the component angular momentum about Q in the direction (/, m, m) 

+»(yr-«ky+xkx}. (8) 

Differentiating with respect to /, and afterwards moving the fixed 
origin up to the moving origin O, so that 

*.,.,.o, but^-U. $-V, £-W. 

1!h(£-» r +*q-*vv+*.v) 

+» (^jf-y»P-r^R-*sU+x 4 w) 

-/L+mM+isN, ft) 

for all values of /, m, n. 

When no external force acts, the case whidi we shall consider, there 
are three integrals of the equations of motion 
(L) T- constant, 

(li.) x^+atf+x^ -P, a constant, 

(lii.) *iyi +xo*+x,y« ■»» - GF, a constant ; 
and the dynamical equations in (3) express the fact that x%, it, x» 
are the components of a constant vector having a fixed directioo; 
while (4) shows that the vector resultant of yi, 3%, y% moves at if 
subject to a couple of components 

X.W-X.V, *,U-*,W, XiV-xtU, (10) 

and the resultant couple is therefore perpendicular to F, the re- 
sultant of x t , xt, xi, 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 casts, 
investigated by H. Weber, F. Kdtter, R. Liouville. Caspary, 
Jukovsky, Liapounoff, Kolosoff and others, chiefly Russian mathe- 
maticians; and the general solution requires the double-thro 
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 

+fWl +-»ifl*>+ fxiyt 

u , c .ffrjW+jfl+arW (1) 

so that a fourth integral is given by 

dytjdt »oji« constant ; (1) 


•tf-xitoxt+ryd-xtigxi+ryj-rixiyt-xiyi), (3) 

£ (^ ? ) t -(*' , +*» , )(^ , +y* , )-(«.y,+x^)« 

-(xi»+x^)(yi*+y/)-(FG-x J y,)» 

- U , +x^&»- r o* a +y.M3*)-(Gxr-Fy,)». (4) 

in which 

-, . . r*-x?,xiyi ___ 
rW+tf) -2T-p(x i '+xf)-p'x t * 

-29(*iyi +x*y,)-2f 'x»y«Vy^ 


&F<£y )x »'+ mi - s 

AH - *T-*F*-* qFG-riyt 
so that 

where Xj is a quartic function of xi, and thus I is given by an efliptr 


integral of the first kind; and by inversion s» h in elliptic function 
of the tine U Now 



(*i -**)(*+*») -*i2^+*i*+»(*i*i-*iy») 


aj(*i+**0 - -tW-8)*i+r'*]+t>* l (y l +*i), 

jg log(*i+*«0 - - (tf -fl)*»-r>»+rxr 








requiring the elliptic integral of the third kind; thence the ex* 
preMion of xi+x* and yi+y»f. 
Introducing Euler's angles #, +, £, 

•d «F tin * sin +, x* ■■ F sin 8 cos +, 

avf*t* ■•Fain #•"•', *i-Fcos0; (14) 

sin^f-PsinsM-Qcos* (15) 

dT . dT 

■2yI* + 3** 

- («*i+ryO*i+ (8^+o*)«t 

- g(xi , +«* f ) +K*iyi +*»j*) 

-jF» sin" «+r(FG -*#«), (16) 

elliptic integrals of the third kind. 

Employing G. Kirchhoff's expressions for X, Y, Z, the coordinates 
of the centre of the body, 

FX - * cos iY-fy, cos >7+* cos 17, (18) 

FY - -yi cos *X+y» cos yJT+yi cos s3C, (19) 

G -yi cos «Z+yi cos yZ+y« cos sZ, (ao) 

P(X«+Y»)-y,»+>k , +yr , -G», (ai) 

F(X+V») - ^(pTlffi X ' «*- (») 

Suppose xi-F is a repeated factor of Xt, then yi-G, and 

X.-(x,-F)«[^(x,+F)»+a^G(x,+F)-G«], (*3) 

and fMi tt' n g x#— F«y, 

so that the stability of this axial movement is secured if 

A-4*T*F«+4£=*FG-C» (a 5 ) 

is negative, and then the axis makes rV (-A)/f nutations per second. 
Otherwise, if A is positive 

"- fyJUi+X+C/) 

1 sh^ VAV(A+aBy+Cy) 1 dr* A+By , - 

-TTCch-* >v(^x5 ^ -Tash-t yvaE-Acv (a6) 

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 stereographk projection by putting tan \fi -*, 

(N***) ,/, -(*+i)VX,+«(*-i)yX* (27) 

*«« *a**+2ax»*3(a+&)x»+2a*** f (a8) 

N« 8(0+*), (39) 

will give a possible state of motion of the axis of the body; and the 
motion of the centre may then be inferred from (2a). 

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 

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 

y «i«W+W'«.*-W-fW'iJ, d) 

where a, ft are numerical factors depending on the externa! shape; 
and if the C.G is moving with velocity V at an angle 4> with the axis, 
so that the axial and broadside component of velocity is u - V cos *, 
f-V sin +, the total momentum F of the medium, represented by 
the vector OF at an angle $ with the axis, will have components, 
expressed in sec lb, 

Fcost-ftj-0rV+W'a)jcoss\Fsin«-^-(W+W'^sin4\ (a) 

Suppose the body is kept from turning as it advances; after 1 
seconds the CG. will have moved from O to O', where OC-VJ; 
and at C the momentum is the same in magnitude as before, but 
its vector is displaced from OF to 0*F'. 
. For the body alone the resultant of the components of 1 

Wjcos+andWjsta*bWjsec. lb, 

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 OT' requires an impulse 
couple, tending to increase the angle FOC, of magnitude, in sec. 

F.OCsin FOC-FV/ sin <*-♦). 
equivalent to an incessant couple 


cos «\-F cos $ sin +)V 



-(F sin a „ _ 


of the 

This NIs the couple in foot-pounds changing the 

medium, the momentum of the body alone remaining the n 

medium reacts on the body with the same couple N in tbe . . 

direction, tending when c%-ci is positive to set the body broadside 
to the advance. 

An oblate flattened body, like a disk or plate, has trc\ 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 el on ga t ed body like a ship has 4-4 positive, and the couple N 
to disturb tbe axial movement and makes it unstable, so that 

tion at the I 

a steamer requires to be steered by constant attention 1 

i helm. 

Consider a submarine boat or airship moving freely with the 
of the resultant momentum honsontaU and the axis at a 

direction __ __ 

slight inclination *. 

_-._ - of buoyancy W" 

couple N, tending to increase #, has the effect of diminishing the 

With no 1 
_--...--.-- „ » increase . 
metacentric height by h ft. vertical, where 

- W\ and the 

WAtanf-tf-fo-eO—tan*. (6) 

Si. 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 b sufficient; and the investigation proceeds in 
the same way for tbe two problems (see Gyioscope). 

The effective angular inertia of the body in the medium is now 
required ; denote it by Ci about the axis of the figure, and by Cf 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 C% is 
the moment of inertia of the body about the axis, denoted by W*J. 
But if Wtf is the moment of inertia of the body about a mean 
diameter, and » the angular velocity about it generated by animptuse 
couple M, and M' is the couple required to set the surrounding medium 
in motion, supposed of effective radius of gyration #', 
W*I--M-M', W'a^-M', 


in which we have put A* »•«*, where 
ing on the shape. 


t is a numerical factor depend- 



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 group* 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 (Hydrotoa Craspedota). 
Order 1. Efeutheroblastea. 

II. Hydroidca {Jbetiolinae). 
Sub-order I. Gymnoblastea (Antkomedusae). 
,, 2. Calyptoblastea {Leptomedusae). 
Order 111. Hydrocoraliinae. 
„ IV. Graptolitoidea. 
„ V. Trackylinae. 
Sub-order i. Trackomedusae. 
2. Narcomedusae. 
Order VI. Siphonophora. 

Sub-order i. Qiondrophorida. 
„ 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 
of more or fewer individuals com- 
bined and connected together. 
The morphology of the group 

I hi 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 

Fig. i.-Diagram of a typical here in a general way, and the 
Hvdropolyp. morphology of the Siphonophora 

?• H yc ! ran .' W >N °e considered under the head- 

i s&ss?' ing °u he ^ up ^ 5clf ;« ^ 

f, Tentacle; «• The Hydropolyp (fa. i)-The 

ps, Pcrisare, forming in the general characters of this organism 

region of the hydranth are. described above and in the 

acuporhydrothecatf,/), articles HYDaoaox and Poly f. It 

— which, however,is only » rarely free, buf -««*—• —^ 

found in polyps of the incapable of toco 
order Calyptoblastea. by which it is at > 

out root-like pn 
rkita (c). The column (b) b generally long, 
like {hydrocaulus). Just below the crown of 1 
the body widens out to form a " head," term© 
containing a stomach-like dilatation of the digest 

upper face of the hydranth the crown of ten tack. ,., j 

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 
stares (planula), and may be naked, or clothed in a cuticle or exo- 
skeleton, the perisarc {ps), which in its simplest condition is a 
chitinoos me mbrane secreted by the ec t oderm. The perisarc when 
present invests the hydrorhiza and hydrocaulus; it may stop short 

a < 



below the hydranth, or it may extend farther. In general there are 
two types of exoslceleton, characteristic of the two principal divisions 
of the Hydroidca. 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 («.{. Bimerta, see G. J. Allman ft], 1 pi. xit. figs. 1 and 3). 
In the Calyptoblastea the pensarc is always continued above the 

Fie. 2. — Stauridium produetum, portion of the colony magnified; 
P, polyp; rk, hydrorhiza. 

hydrocaulus, and forms a cup, the hydrangium or hydrotheca (A. /), 
standing off from the body, into which the hydranth can be retracted 
for shelter and protection. 

find in the aberrant forms Protokydra and Microkydra tentacles 

entirely absent. In the curious hydroid Monobrackium a single 

tentacle is present, and the same is the 

case in Clotkrozoon; in Amp'.ibrockium 

and in Lor (fig. n, A) the polyp bears 

two tentacles only. The reduction of 

the tentacles in ail these forms may be 

correlated with their mode of life, and 

especially with living in a constant 

* _* — — — c ich brings food- 

>ne direction and 

tiorl or circle of 

Thus Microkydra 

, and appears to 

oduced by these 

Kxurs in oyster- 

\m also grows on 
and both these 
in the currents 

llibranchs. Am- 

the tissues of a 

id protrudes its 

al-system of the 

1 on the tubes of 
ma wurm tjvu***v. 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. p IC - Digram erf 

It is rare to find in the polyp a regular, rZOLw *L* A VYvtM. 
symmetrical disposition of tie tentacles S2T22n rivin^S 
as in the medusaVThe primitive number J^-BSSrff SS 
of four in a whorl is seen, however, in ft budffiS^roS^S 
Stauridium (fig. 2) and Cladonema 21„;„ 2^ h e dSt- R 

however, the number in a whorl is ^S«Sffil !LS3S 
irregular^ The tentacles may form a ^SS&SA ScTonlv 
single whorl, or more than one; thus £?ZXzE IJSS, Alf 
in Corymorpka (fig. 3) and Tubular* 2Sf nttde - (AflCT AU * 
{fig. 4) there are two circlets; in Staur* mmu ' m 
idtum (fig. 2) several; in Coryne and Cordylopkora 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 

* The numbers in square brackets ( ] refer to the bibliography at 
the end of this article; but when the number is preceded by the 
word Hydrosoa, it refers to the bibliography at the end of the article 



This impute 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. Mat., April 1893, by 
G. H. Bryan, in which the analytical equations of motion are 
deduced of a perforated solid in liquid, from considerations purely 

The effect of an external circulation of vortex motion on the 
motion of a cylinder has been investigated in l 39; 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 C in time /. with velocity Q, and 
angular velocity R, the components of liquid momentum change 

oM'U -H and /WV along Or and Oy 
to «M'U'+| and fiM'V along OV and 0'/. (1) 

the axis of the ring changing from Ox to OV; and 
U-Qcos*. V-Qsin*. 
U'-Qcos(*-Ri). V'-Qsin(*-R/), (a) 

so that the increase of the components of momentum, Xi, Yi, and N ( , 
linear and angular, are 

Xj-CaMTJ'+l) cos Ri-aM'U-{-0M'V' sin Rl 

■ (•-0)M'Q*to(«-R/)sinR/-{verR/ (3) 

Y> (aMTJ'+O sin Ri+^MV cos Rl-flM'V 

- (a-0)M'Q cos (0-Ri) sin R/-K sin RT, (4) 

N.-l-CaMTJ'+l) sin (*-R/)+0M'V'cos (*-Ri)100' 

- 1 - (a -l)M'Q cos (0 - R/) sin (0 - Ri) - 1 sin(0 - R/)]Qf. (5) 

The components of force, X, Y, and N, acting on the liquid at 0, 
and reacting on the body, are then 

X-lt. XJ<-(a-0)M'QRsin*-(e-*)M'VR, (6) 

Y-!t. Y,//-(a-0M'QRcos*-KR-(«-0)M'UR+{R, (7) 
Z-lt. Zi//«-(a-0)M'Q I su»«cos«-{Q»in# 

-(-(a-flMTJ+flV. <8) 

Now suppose the cylinder is free; the additional forces acting on 
the body are the components of kinetic reaction of the liquid 

-.M'($-VR). -*l'(g+OR). -«C& (,) 
to that its equations of motion are 

M (tjt-Vr) --aM'(^-VR) -(.-flNrVR. (10) 

M (1sf +UR ) --*M'(3f+UR) -(«-0M'UR-*R.(n) 
C^-.-«C^+(a-5)M'UV+$V; (12) 

and putting as before 

M+aM'-c„ M+0M'-*, C+«C'-C, 



showing the modification of the equations of plane motion, due to 
the component ( of the circulation. 
The integral of (14) and (15) may be written 

CiU+{-Fcos*. e»V--Fsin«. 
£_yt - u-^ Fcos»g , Fsjn«* 



J.Udn# + Vco...g-D. 



r*<* p.. a /T F'cos'g Psin'0 , F{ A , „1 , K 

so that cos* and y is an elliptic function of the time. 

When { is absent, dxfdt ib always positive, and the centre of the 
body cannot describe loops; but with (, the influence may be great 
enough to make dx/dt change sign, and so loops occur, as shown in 
A. B. Basset's Hydrodynamics, i. 192, resembling the trochoids! 
curves, which can be looped, investigated in J 29 for the motion of 
a cylinder under gravity, when surrounded by a vortex. 

The branch of hydrodynamics which discusses wave motion in a 
liquid or gas is given now in the articles Sound and Wave; while 
the influence of viscosity is considered under Hydraulics. 

References. — For the history and references to the original 
memoirs see Report to the British Association, by G. G. Stokes (1846), 
and W. M. Hicks (1882). See also the PorlsckriiU dtr Maiktmttik, 
and A. E. H. Love, " Hydrodynamik " in the Encykhpddia dot 
mathemaHschen Wtssonschafttn (1901). (A, G. G.) 

HYDROMBDUSAR, a group of marine animals, recognized 
as belonging to the Hydrozoa (q.v.) by the following characters. 

(1) The polyp (hydropolyp) is of simple structure, typically much 
longer than broad, without ectodermal oesophagus or mesenteries, 
such as are seen in the anthopolyp (see article Anthozoa); the 
mouth is usually raised above the peristome on a short conical 
elevation or hypostome; the ectoderm is without cilia. 

(2) With very few exceptions, the polyp is not the only type of 
individual that occurs, but alternates in the life-cycle of a given 
species, with a distinct type, the medusa (q.v.), while in other 
cases the polyp-stage may be absent altogether, so that only 
medusa-individuals occur in the life-cycle. 

The Hydromedusae represent, therefore, a sub-class of the 
Hydrozoa. The only other sub-class is the Scyphomedusae 
(q.v.). The Hydromedusae contrast with the Scyphomedusae 
in the following points. (1) The polyp, when present, is without 
the strongly developed longitudinal retractor muscles, forming 
ridges (taeniolae) projecting into the digestive cavity, seen in the 
scyphistoma or scyphopolyp. (2) The medusa, when present, 
has a velum and is hence said to be crasptdotc; the nervous 
system forms two continuous rings running above and below 
the velum; the margin of the umbrella is not lobed (except 
in Narcomedusae) but entire; there are characteristic differences 
in the sense-organs (see below, and Scyphomedusae); and 
gastral filaments (phacellae), subgenital pits, &c, are absent, 

(3) The gonads, whether formed in the polyp or the medusa, 
are developed in the ectoderm. 

The Hydromedusae form a widespread, dominant and highly 
differentiated group of animals, typically marine, and found in 
all seas and in all zones of marine life. Fresh-water forms, 
however, are also known, very few as regards species or genera, 
but often extremely abundant as individuals. In the British 
fresh-water fauna only two genera, Hydra and Cordylophora, are 
found; in America occurs an additional genus, Microhydra. 
The paucity of fresh-water forms contrasts sharply with the great 
abundance of marine genera common in all seas 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 is usually second- 
arily simplified, but in marine forms the life-cycle may be 
extremely complicated, and a given species often passes in the 
course of its history through widely different forms adapted to 
different habitats and modes of life. Apart from larval or 
embryonic forms there are found typically two types of person, 
as already stated, the polyp and the medusa, each of which may 
vary independently of the other, since their environment and 
life-conditions are usually quite different. Hence both polyp 
and medusa present characters for classification, and a given 
species, germs 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, which cannot always be done in 

1 1n some cases hydroids have been reared in aquaria from ova 
of medusae, but these hydroids have not yet been found in the sea 
(Browne lio a]). 




access of water to the contents; when the cnidoci! is stimulated it 
sets in action a mechanism or perhaps a series of chemical changes 

by which the plug is dissolved or remove J - '" -— " ^e- 

trates into the capsule and causes its o he 




m ^. ... „, „ ~..ier 

the cnidoblasts migrate 
with them to the region 
where they are most 
needed; the fact that in 
Hydra, for example, there 
are no interstitial celts 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 Trom 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 
Fie. 7.— Diagrams to show the struc- further stage in evolution 
ture of Nematocysts and their mode of » that the muscle-cells 
working. (After Iwanzov.) k«* ttetr connexion with 

a. Undischarged nematocyst. the epithelium and come 

Commencing discharge. Jo lie entirely beneath it. 

Discharge complete. . forming a sub-epithelial 

Cnidocil contractile layer, de- 

Nucleus of cnidoblaat. veloped chiefly in the ten- 

Outer capsule. toe 1 " of the polyp. The 

Plug closing the opening of the evolution of the ganglion- 
outer capsule. <*"* w probably similar; 
Inner capsule, continuous with the *« epithelial cell develops 
wall of the filament, /. processesof nervous nature 
b Barbs. • rom tne ^ a9C * wnicn 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 cells to the contractile elements. 
The ganglion-cells of Hydromcdusae 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 
From GcecnUur'ft Ekmtats ej Cam- processes lying in the plane of 
puatmAmtkmy. the transverse section of the body. 
Fig. 8.— Vacuolated Endo- In different parts of the coelen- 
derm Cells of cartilaginous teron the endoderm may be of 
consistence from the axis of the three principal types — (i) 
tentacle of a Medusa (Cunina). digestive endoderm, 'tne primi- 
tive type, with cells of large 
size and considerably vacuolated, found in the hydranth; some 
of these cells may become special glandular cells, without 
flagclla 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 
of the tentacle, greatly resembling notochordal tissue, particularly 
that of Amphicxus at a certain stage of development; as a fourth 
variety of endodermal cells excretory cells should perhaps be reckoned, 
as seen in the pores in the foot of Hydra and elsewhere (cf. C. Chun, 
Hydrozoa |i], pp. 314. 315). 
The mesogloea in the hydropolyp is a thin elastic layer, in which 

may be lodged the muscular fibres and ganglion cells mentioned above* 
but which never contains any connective tissue or sk cl e to ge nuua 
cells or any other kind of special mesogloeal corpuscles. 

2. The Polyp-colony.— b\\ known hydropotyps possess the | 
of reproduction by budding, and the buds produced may f~ 
cither 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 onlv 
are produced and 

sexual elements From Maui's GfmmtUtSc Byinfds. by penrini <4 
are developed the Council ©I the Ray Soccty. 

upon the polyps Fig. 9. — Colony of Hydraciinia echinata.gmw- 
themselves; or, ing 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 arc 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, Pelatohydra, &c. The founder-polyp usually produces by 
budding polyp-individuals, and these in their turn produce other 
buds. Tne 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 founder- 
polyp remains solitary, that b 
to say, does not produce polyp- 
buds, but only medusa-buds, 
from the first (Corymorpha, fig. 3, 
Myriothda, &c.). In primitive 
forms the medusa-individuals 
are set free before reaching 
sexual maturity and do not con- 
tribute anything to the colony. 
In other cases, however, the 
medusa-individuals become 
sexually 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 yom 
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 oh 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 From AOmmt CymmUattk ffjtofe. 
always clearly marked out. |y j P« riniasi00 °* "* Co** 6 * °* *** **» 
Hence it is necessary to distin- ***** 

guishbetween,first,the"zooids," Fig. 10. — Polyps from a Colony 
indicated in the case of the polyps of Hydraciinia, magnified, di, 
by the hydranths, each with dactylozoid; fs, gastrozoid: b, 
mouth and tentacles; and, blastostyle; ton, gonophores; 
secondly, the "coenosarc," or rk, 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- 
individual. The coenosarc constitutes a system by which tat 
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 




function of circulating and distributing nutriment through the 

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 
and covered over by 
a common perisarc. 
Encrusting colonies of 
this kind are seen in 
Clava squamata {fig. 
s, A) and Hydracitnta 
(figs. 9, 10), the latter 
having the perisarc 
calcified. A further 
very important modifi- 
cation is seen when the 
tubes of the basal 
perisarc do not remain 
Pic. i I . — Lar sabellorum and two stages spread out in one plane, 
of its Medusa, WUlia stellata. A, colony of but grow in all planes 
Lar;B and C, young and adult medusae, forming a felt-work; 

the result is a massive 
colony, such as is seen in the so-called Hydrocorallines (fig. 60) , 
where the interspaces between the coenosarcal tubes are filled up 

After Hbdks, Forbes, and Browne. A and B 

from Hindu; C modioed from Forbes'* BriL Afofc* 

with calcareous ' matter, or cocnosteum, 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 coenosarc; it 

7 is practically all hydrorhiza. 
j Massive colonies may assume 
various forms and are often 
branching or tree-like. A fur- 
ther peculiarity of this type of 
colony is that tneentire coeno- 
sarcal complex is covered ex- 
ternally by a common layer 
of ectoderm; it is not clear 
how this covering layer is 

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 
Flo. 12.— Colony of Bougainvilleo distinct types of budding are 
fndicosa, natural size, attached to the found, which are best de- 
underside of a piece of floating tira- •cnbed in botanical termino- 
be*. (After Allmaa.) logy as the monopodia! or 

m 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- 

In the monopodial method (figs. 12, 14) the founder-polyp is. 

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, the second bud is above 
the first, the third above this again, and so on. Each bud produced 

Fie. it. — Portion of colony of BomgoinvilUa fruticoso (Antko- 
medusae-Gymnoblasteo) more magnified. (From Lubbock, after 

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 trie 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 founder-polyp; o\ b , r, the succession 
of polyps budded from 1 ; a", 6*. polyps budded from 2; a*, 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 side, 
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- 



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- 
sonal type (fig. 1 6), 
the buds are 
formed always on 
the same side, 
forming a " hcli- 
Fic. 15. — Diagram of sympodial budding, coid cyme," as in 
biserial type, shown in five stages (1-5). F, Hydrallmania, 
founder-polyp; 1, 2, 3, 4, 5, 6, succession of according to H. 
polyps budded from the founder; o, b, c, Driesch, in which, 
second series of polyps budded from the founder; however, the 
a*, b*, 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 
polyp may then form a second 
bud, which becomes the starting 
point of a new system, the 
beginning, that is, of a new 
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 Plumulandae (figs. 17, 

r, rt< n:«- M « ^ . umn ~iui 18) there is formed a main stem 

FiG.16.— Dia gram ot sympodial b biserial budding . each poi yp 

budding, uniserial type, shown J the mail| 8t * m form y£ 

in four stages (1-4).. F, founder- 8CCOnd bud which u$ually 

Eftft A^SESC ' poyp8 forrn * a 8ide branch or #""-*' 

budded from the founder. by uni ,erial 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 Anten- 
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 
a 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 
Fig. 17. — Diagram of sympodial budding, system, from which 
simple unbranched Plumularia-type. r . uniserial pinnules arise 
founder; 1-8, main axis formed by biserial as from the main stem 
budding from founder; a-e, pinnule formed — type of Aglaophenia 
by uniserial budding from founder: a'-d 1 , (fig. 19). The laws of 
branch formed by similar budding from 1 ; budding in hydroids 
aKP from 2, and so forth. 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 arc formed by organic union of separate individuals, 
there is ever a tendency for the polyp-colony aa a whole to act as a 


to become subordinated to 
ipecialization for particular 
tulate organs and their io- 
x less degree. Perhaps the 
ted with the reproductive 
p in a colony may produce 
ledusae are budded only by 
>, b). At first not differing 


Diagram showing method 
in the Plumularia-typt; 
fig. 1 7. Polyps 3 and 6, 
oducing uniserial pinnules, 
sed biserial branches (3', 3*. 
'). which give off uniserial 
their turn, 
riuced or absent, but have 

dactylozoids capture food 
iwallow and digest it. 
tbove mentioned, there are 

which the individuality is 
' (machopolypa) of Plumm- 
iduals of the nature of dac- 
of budding in this hydroid 
ard-polyps were not true 
osed in a small protecting 
>phorc Again, the spinet 

mowing method of branch- 
ta-type. Polyp 7 has pro- 
i, 8; as its second bud. a*. 
ial pinnule; and as a third 
a biserial branch (1P-VF) 
lure of the main stem and 
The main stem is indicated 
m by 

norphology of the medusa 

Organism.— rThe general 
isa are described elsewhere 
I it is only necessary here to 

. edusa. 

As regards habit of life the vast majority of Hydromedusae are 

f and morphology, HYDROMEDUSAE 141 

Trwchoroedusae tney are given on in iuiw »w wmuw \m S . •*/* 




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. *6. 



Nerve ring. 

Radial nerve. 


Circular caaaL 

Radiating canal. 


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 

external epithelium is flat 
on the sub-umbral surface, 
sub-umbrella and the vcl 
may be grouped to form ba 
ana oral lappets. In pla< 
thickly as to form a tough, i 
cartilage, chiefly developed 

kastata, one of the Trachomedusae. 

solid larval tentacles, re- 
' sembling those of Cunina. 
k, Dilatation (stomach) of the 

/, Telly of the disk. 
P, Manubrium. 
A 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, 
' *y Velum. 

i he 

i he 

I lis 

1 ial 

i es 

i be 

i its 

l , ,.„ ,_ ial 

muscular layer becomes separated com- 
pletely from a more superficial body- 

iA.^A21^» fa j?£2£L^ In it8 an™g*nwrt the muscular tissue 
Muirum of CooSntiwi form * two «y*tems: the one composed 
Zoology. Cambridge Man., of striated fibres arranged circularly, that 
U-SA. ; s to say, concentrically round the central 

Fig. 2i.—Slomotota ax j 8 f tne umbrella; the other of non- 
dmtsa, oneof the Ttartdae striated fibres running longitudinally, 
(Anthomedusae). tna t 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 surface, 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 

he animal progresses. The longitudinal system i 

and is subdivided into proximal, medial and distal 

«g«p#fe|.l,Jij.j ■ 

by which the animal i 

continuous, and is au .__ ,_ 

portions. The proximal portion forms the retractor muscles of the 
manubrium, or proboscis, well developed, for example, in GeryenuL 
The medial portion forms radiating tracts of fibres, the so-called 
" bell-muscles " running underneath, and parallel to, Che radial 
canals; when greatly developed, as in Tiartdat, 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 cndodermal muscles in craspedote 

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 M 
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- (Liazia). The uppermost is a purely muscular 
n P£ 4t if* .n™* 10 cell from the sub-umbrella; the two lower are 
?l E? t u u '. near epidermo-muscular cells from the base of a 
theoaseof the velum, tentacle; the upstanding nucleated portion 
' u i Upper forms P*" ^ tn * epidermal mosaic on the 
ri^derSed 1 ^ ta ,urfaCC ° f thc **»" (Ate "«** > 
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 thc velum (see diagram in article Medusae). 
The two nerve-rings are connected by fibres passing from one to the 

The sensory cells are slender epithelial cells, often with a cflium 
or stiff protoplasmic process, and should perhaps be regarded as the 
only ectoderm-cells which retain thc primitive ciliation of the larval 
ectoderm, otherwise lost in all Hydrozoa. The sense-cells form. 
>n 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 epitbetium 
covering the nerve-centres; in thc second place, the seme-ceils 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 

The sense-organs of 
medusae are of two 
kinds — first, organs 
sensitive to light, 
usually termed ocdli 
(fig. 39); secondly, 
organs . commonly 
termed oUcysls, on 
account of their re- 
semblance to the audi- 
tory vesicles of higher After M Cwp***n Mtimsm 4m Sibm 
animals, but serving ExptdUtm. by pormMoo of E. a Brill * Co. ^^ 
hLLJil T»«H e «£nta F,G - 99-— Tmprit rosea (Ag. and Mayer) 
ST «„H 1 »££££ * howin g the eight adradial Statocysts. each 
given th«pecial^ c,osetoan0cA - Cf ' fi * *>• 
of statocysts (fig. 30). The sense-organs may be Untactdocvsts, it. 
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 ia 
Leptolinae. In Hydromedusae the sense-organs are always exposed 
at the umbrellar margin (hence Gymnopklhalmala), while in Scypbo- 
medusae they are covered over by flaps of the umbrellar margia 
(hence Steganophlhalmaia). 

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 



bearing at its free upper end a stiff bristle and nmnfof oatatlts base 
into a nerve-fibre; (3) coocrement-cells, which produce intercellular 

concretions, so-called oto- 
liths. By means of 
vibrations or shocks 
transmitted through the 
Y-Sul 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 
Modified after Linko, Tntua See. Imp. NoL, St. an be recognized, the 
IWnbou, * xlU - first that of an open pit 

Fie. 30. — Section of a Statocyst and on a freely - projecting 
Ocellusol Tiaropsis diademata; cf.fig.29. knob, in which the oto- 
ex, Ex-umbral ectoderm, liths are exposed, the 

sub, Sub-umbral ectoderm. «c? n 1 < 1 that of a closed 

ex, Circular canal. v»*le. in whichthe oto- 

v Velum ,lth$ * re covered over. 

six. Cavity ol statocyst. Further, two distinct 

con, Concrement-cell with otolith. types of otocyst can be 

recognized in the Hydro- 
medusae; that of the Leptolinae. in which the entire organ is 
ectodermal, concrement-cells and all. and the organ is not a tenta- 
culocyst; and that of the Trachylinae. in which the organ b 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- 

In the Leptolinae the oto- 
cysts are seen in their first 
stage in Mifrocoma anna* 
(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 
m. the ex-umbral side of the 
by velum. At the fundus are 
placed the concrement-cells 
Fie. 31.— Section of a Statocyst of with their conspicuous oto- 



Modified after O. aad R. Hert»ig, Nm 
*r Mdlim. 

tyUtm «W Siwtesorta** 
penxuauoo of F. C W. VogsL 

liths (con) and the incansptcu* 
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 
(fig*. 32. 33). The otocyst* arc placed on the outer wall of the 


Milrocoma attnac. 
sub, Sub-umbral ectoderm 
ex. Circular canal. 
v. Velum. 

six. Cavity of statocyst. 
con, Concrement-cell with otolith. 

— con 



Modified after O. and R. Hertwk. Strttn- 
IjnJm wmi 5i«*ewrfan* itr Mtiium 

Nermuytfem ttmd Sinnaorcniu 
Medntem, by penniadaej of #. C W. 

» of F. C W. Vogei. 

Fig. 32. — Section of a Statocyst 

of Pkialidium. 
ex, Ex-umbral ectoderm. 
sub, Sub-umbral ectoderm. 
», Velum. 

stx. Cavity of statocyst. 
con. Concrcment-ccll with otolith. 

vesicle (the fundus of the original pit) or on its sides; their arrange- 
ment and number vary greatly and furnish useful characters for 
The sense-cells arc innervated, as before, 

Modified after 0. and R. Hertwig. 
t dtr 

. tu. bv rtrrmhrinn of F. C 


Fig. 33. — Optical Section of 
a Statocyst of Octorckis. 

con, Concrement • cell with 

stx, Cavity of statocyst. 

distinguishing genera. 

from die sub-umbral nerve-ring. 

The inner wall of the vesicle 


;ntly thickened to form a so-called " sense- 
;anglionic offshoot from the sub-umbral 


After a and R. Hertwig. NtntmyUtm vm Siwm- 
ertam* 4m Mtiuum, by penusatoo of F. C \* 

Fig. 34.— Tentaculocyst (statorhabd) 
of Cunina solmaris. nx, Nerve-cushion; 
end, endodermal concrement-cells; con, 

— ..jed (con.). Other sensory cells with long 



lai-~ — «.«._... _.« — ...ed (con.). Other sensory cells with long 
cilia cover a sort of cushion (nx.) 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 Rhopah- 
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 MtaOaod^Hatrnt, NenmuyHmmd Sbmo- 
the surface, as in Ceryojtta •£«• *» MmUum, by penntton of F. C W. 
(fig. 37). VotfL 

The ouIU are seen in Fig. 35. — Tentaculocyst of Cunina lots' 
their simplest form as a renins. 

pigmented patch of ecto- ect. Ectoderm, 
derm, which consists of nx. Nerve-cushion, 
two kinds of cells— (1) end, Endodermal concrement-cells. 
pigment-cells, which are con, Otolith, 
ordinary indifferent cells 

of the epithelium containing pigment-granules, and (2) visual cells, 
slender sensory epithelial cells of the usual type, which may develop 
visual cones or 
rods at their free 
extremity. The 
bcelli occur 
usually either on 
the inner or outer 
sides of the ten- 
tacles; if on the 
inner side, the 
tentacle is turned 
upwards and 
carried over the 
ex • umbrella, so 
as to expose the 
ocellus to the 
light; if the Fig. 36.— Simple tentaculocyst of Rkopalo* 
ocellus be on the noma veiaium. The process carrying the otolith 
outer side of a or concretion hk, formed by endoderm cells, is 
tentacle, two enclosed by an upgrowth forming the " vesicle," 
nerves run round which is not yet quite closed in at the top. 
the base of the (After Hertwig.) 
tentacle to it. In 
other cases ocelli may occur between tentacles, as in Tiaropsis (fig. 29). 

The simple form of ocellus described in the foregoing paragraph 
may become folded into a pit or cup, the interior of whicn becomes 
filled with a clear gelatinous secretion forming a sort of vitreous 



body. The distal portion of the vitreous body may project from the 
cavity of the cup, forming a non-cellular lens as in Litsid (fig. 28). 
Beyond this simple condition the visual organs of the Hydromedusae 
do not advance, and are far from reaching the wonderful develop- 
ment of the eyes of Scyphomedusae (Ckorybdaea). 

Besides the ordinary type of ocellus just described, there is found 

in one gtnu*(Tioropns) a type of ocellus in which the visual elements 

. are inverted, and 

SLC have their cones 

turned away from 

the light, as in the 

human retina (fig. 

30). In this case 

the pigment-cells 

r are endodermal. 

' & forming a cup of 

pigment in which 
the visual cones 
arc embedded. A 
similar ocellus is 
formed in Aurelia 
among the Scypho- 
medusae (q.v.). 

After ttnjK. Hertwfc. N uv emi i U m vmd S iwHt m pM Other sense 
*r Midmm. by peraitaoo of F. C W. Vopi organs of Hydro- 

Fic. 37. — Section of statocyst of Geryouia medusae are the 
(Carmarina hastata). so-called sense- 

six, Statocyst containing the minute tentaculo- **«*», <* cordyli 
cyst. found in a few 

nr u Ex-umbral nerve-ring. L* P t o » e d u s a e, 

nr„ Sub-umbral nervc-ring. especially in those 

ex, Ex-umbral ectoderm. genera in which 

sub, Sub-umbral ectoderm. otocysts are incon- 

cx. Circular canal. taicuous or absent 

», Velum. (»«• ,39)-. Each 

cordylus is a ten- 
tacle-like structure with an endodermal axis containing an 
axial cavity which may be continuous with the ring-canal, or may 
be partially occluded. Externally the cordylus is covered by very 
flattened ectoderm, and bears no otoliths or sense-cells, but the base 
of the club rests upon the ex-umbral nerve-ring. Brooks regards these 
organs as sensory, serving for the sense of balance, and representing 
a primitive stage of the tentaculocysts of Trachylinae; Linko.on 
the other hand, finding no nerve-elements connected with them, 
regards them as digestive (?) in function. 

The sense-organs of the two fresh-water medusae Limnocodium 
and Limnocnida are peculiar and of rather doubtful nature (see E. T. 
Browne (10]). 

The endoderm of th< of 

structure as in the poly; [1) 




called " marginal tubercles," opening, on 

the one hand, into the ring-canal and, on 

the other hand, to the exterior by " marginal 

funnels," which debouch into the sub-umbral 

cavity above the velum. As has been de- 

Ff G. 38. — Ocellus of scribed above, the endoderm may also con- 

Liszia koellikeri. oc, tribute to the sense-organs, but such 

Pigmented ectodermal contributions are always of an accessory 

cells; /, lens. (After nature, for instance, concrement-cells in 

Hertwig.) the otocysts, pigment in the ocelli, and 

never of sensory nature, sense-cells being 

in all cases ectodermal. 

The reproductive cells may be regarded as belonging primarily 
to neither ectoderm nor endoderm, though lodged in the ectoderm 
in all Hydromedusae. As described for the polyp, they are wandering 
cells capable of extensive migrations before reaching the particular 
spot at which they ripen. In the Hydromedusae they usually, if 
not invariably, ripen in the ectoderm, but in the neighbourhood of the 
main sources of nutriment, that is to say, not far from the stomach. 
Hence the gonads are found on the manubrium in Anthomedusae 
generally; on the base of the manubrium, or under the gastral 
pouches, or in both these situations (Oetorckidae), or under the radial 
canals, in Trachomedusae; under the gastral pouches or radial 
canals, in Narcomediisae. When ripe, the germ-cells are dehisced 
directly to the exterior. 

Brook*. Jm 


Hydromedusae are of separate sexes, the only known exceptioa 
being Amphotona apsteini, one of the Trachomedusae (Browne (91). 
Moreover, all the medusae budded from a given hydroid colony are 
either male or female, so that even the non-sexual polyp must be 
considered to have a latent sex. (In Hydra, on the other hand, the 
individual is usually hermaphrodite.) The medusa always reproduce* 
itself sexually, and in some cases non-sexually also. The non-sexual 
reproduction takes the 
form of fission, budding 
or sporogony, the details 
of which are described 
below. Buds may be pro- 
duced from the manu- 
brium, radial canals, J 
ring-canal, or tentacle- 
bases, or from an aboral 
stolon (Narcomedusae). 
In all cases only medusa- , 
buds are produced, never 

The mesogloea of the 
medusa is largely de- 
veloped and of great 
thickness in the umbrella. 
The sub-epithelial tissues, 
\a. the nervous and mus- 
cular cells, are lodged 
in the mesogloea, but in 
Hydromedusae it never 
contains tissue-cells or AfUf w lK . Bn) 
mesogloeal corpuscles. bypcraikiiaQofGiaai 

o < ^LP e » M t e V^fV^ F*°- 39- Section of a Cordytus of 

Subordinate Individuality. *" Laodiu. 

—It has been shown ex Circular canal. 

above that polyps are v Velum. 

budded only from polyps j Tentacle 

and tiiat the medusae ^ CordyUA, composed of flattened 

f^y _., "r* 18 ^ e J^ e 5 ectoderm ee covering a laxse-cefled 






ture state; they swim 
away, feed, grow and 
become adult mature 
individuals. From the 
bionomical point of 
view, the medusa is to 
be considered as a 
means of spreading the 
species, supplementing 
the deficiencies of the 
sessile polyp. It may 
be, however, that in* 
creased reproductive- 
ness becomes of greater 
importance to the 
species than wide diffu- 
sion; such a condition Fie. 40. — Portions of Sections through 
will be brought about if the Disk of Medusae— the upper ooe of 
the medusae mature Lizxia, the lower of Aurdia. (After 
quickly and are either Hertwig.) 
set free in a mature d Endoderm lamella. 
^K»i>> Mu^p^oftheecUxkn^A, 
colony protected rf< ?£££"**"■ 
JESiJ lirtk\£!«". Endoderm linin£ the enteric aviw. 
SE^Si. AA?lE2 «• Wandering entoderm cells of tie 

sonality to an organ of the polyp-colony, becoming a so-called 
medusoid gonopkore, or bearer of the reproductive organs, and losing 
gradually all organs necessary for an independent existence, nasnely 
those of sense, locomotion and nutrition. 

In some cases both free medusae and gonophores may be produced 
from the same hydroid colony. This is the case in Synci 

(Allman (1). p. 978) and in Campanularia volubilis; in the latter, 
free medusae are produced in summer, gonophores. in winter 
(Duplessis (14)). Again in Pennaria, the male medusae arc set foe 


in a sta 
The i 
from or 
the simi 
41. A), 
and mc 
with the 
of the gi 
(fig. 41. 
and the 
closed a 
which t 
female j 

A. Weisi 
A. "Mi 
S' J yp 

£• J yp 
S' I yp 

I:g t h; 

F. Wit! 

G, Wit! 


have bo 
entire en 
and disa 
such a o 
Carveia < 
the form 
the gone 
for the d 
It isevk 
cavity 1 

The nex r _ 

xiv 3* 




(histocytes) and germinal cells, actual or potential (archaeo- 
cytes), amongst the constituent cells of the animal body. " In 
this way we may distinguish, first, vegetative reproduction, the 
result of discontinuous growth of the tissues and cell-layers 
of the body as a whole, leading to (1) fission, (2) autotomy, or 
(3) vegetative budding', secondly, germit*al reproduction, the 
result of the reproductive activity of the arcbaeocy tcs or germinal 
tissue. In germinal reproduction the proliferating cells may be 
undifferentiated, so-called primitive germ-cells, or they may be 
differentiated as sexual cells, male or female, i.e. spermatozoa 
and ova. If the germ-cells are undifferentiated, the offspring 
may arise from many cells or from a single cell; the first type 
is (4) germinal budding, the second is (5) sporogony. If the germ- 
cells are differentiated, the offspring arises by syngamy or sexual 
union of the ordinary type between an ovum and spermatozoon, 
so-called fertilization of the ovum, or by parthenogenesis, i.e. 
development of an ovum without fertilization. The only one of 
these possible modes of reproduction not known to occur in 
Hydromedusae is parthenogenesis. 

(1) True fission or longitudinal division of an individual into 
two equal and similar daughter-individuals is not common but 
occurs in Gastroblasta, where it has been described in detail by 
Arnold Lang [80]. 

(2) Autotomy, sometimes termed transverse fission, is the name 
given to a process of unequal fission in which a portion of the 
body separates off with subsequent regeneration. In Tubularia 
by a process of decapitation the hydranths may separate off 
and give rise to a separate individual, while the remainder of 
the body grows a new hydranth. Similarly in Sckizocladium 
portions of the hydrocaulus are cut off to form so-called " spores," 

which grow into new 
individuals (see 
Allman [1]). 

(3) Vegetative bud- 
ding is almost uni 
versal in the Hydro- 
medusae. By budding 
is understood the 
formation of a new in 
dividual from a fresh 
growth of undiffer- 
entiated material. It 
is convenient to dis- 
tinguish buds that 
give rise to polyps 
from those that form 

(a) The Polyp.— The 
buds that form polyps 
are very simple in 
mode of formation. 
Four stages may be 
distinguished; the first 
is a simple outgrowth 
of both layers, ecto- 
derm and endoderm, 
containing a prolonga- 
tion of the coelcnteric 
cavity; in the second 
stage the tentacle* 

Much moifified (ram C Cbua, 
Bioon'» TitmidL 

Fig. 43.— Direct Budding of Cunina. 

A.B.C, E.F.Inver- t. Tentacle, 

tical section. s.o, Sense organ. 

D, Sketch of exter- v. Velum. 

nal view. s.c, Sub-umbral 
st, Stomach. cavity, 

m, Manubrium. 

b grow out as secondary 
diverticula from the 
side of the first out- 
growth; in the third 
stage the mouth is 
formed as a perfora- 
tion of the two layers: 
and, lastly, if the bud 

from the parent polyp and begins a free existence. 

(6) The Medusae. — Two types of budding must be distinguished 
— the direct, so-called palingcnetic type, and the indirect, so-called 
cocnogenctic type. 

The direct type of budding is rare, but is seen in Cunina and 
MUUpora. In Cunina there arises, first, a simple outgrowth of both 
layers, as in a polyp-bud (fig. 43. A); in this the mouth is formed 
distally as a perforation (B) , next the sides of the tube so formed 

bulge out laterally near the attachment to form the umbrella, wade 
the distal undilatcd portion of the tube represents the manubrium 
(C); the umbrella 

now grow* out /s^CPs,^^- 

into a number of 
lobes or lappets, 
and the tentacles 
and tentaculocysts 
grow out, the 
former in a notch 
between two 
lappets, the latter 
on the apex of each 
lappet (D. E); 
finally, the velum 
arises as a growth 
of the ectoderm 
alone, the whole 
bud shapes itself, 
so to speak, and 
the little medusa is 
separated off by 
rupture of the thin 
stalk connecting it 
with the parent (F). 
The direct method 
of medusa-budding 
only differs from 
the polyp-bud by 
its greater com- 
plexity of parts and 

The indirect 
mode of budding 
(figs. 44. 45) is the 
commonest method 
by which medusa- 
buds are formed. 
It is marked by the 
formation in the 
bud of a character- 
istic structure 
termed the ento- 
codon (Knospen- 
kern, Clockenkern). 

The first stage is 
a simple hollow 
outgrowth of both 
body-layers (fig. 44, 
A); at the tip of 
this is formed a 
thickening of the 
ectoderm, arising 

Eritnitivcly as a 
ollow ingrowth 
(fig. 44, B), but 
more usually as a 
solid mass of ecto- 

Fig. 44. — Diagrams of Medusa budding with 
the formation of an cntocodom The endoderm 
is shaded, the ectoderm left dear. 
A, B, C, D, F, Sucees- sub-umbral 

souu n«» o. ccw- sive stages in ver- cavity. 

^.rt»,^u «L ii tical section. st. Stomach. 

similar to D. eJ, Endoderm lamella. 

in, Manubrium. 

ingrowth is the -.«..„ „ 

entocodoa «*.); it - £££££ 

bullies into, and Gc ' Entocodoi 

™sf£s doWn. die ** Cv ? tv °f en ^ 

codon, forming 
the future 


endoderm at the 

apex of the bud, 

and if solid it soon 

acquires a cavity (fig. 44, C, s.c). Hie cavity of the entocodoa 

increases continually in sue, while the endoderm pushes up at the 

sides of it to form a cup with hollow walls, enclosing but not quite 

surrounding the r 

cntocodon, which ^\* *rt 

remains in contact ^ra^ y i^S^SjS&^^V 

at its outer side /£&?& jh2r&&QBs& \ 

with the ectoderm 

covering the bud 

(fig.44.D,»). The 

next changes that 

take place are 

chiefly m the endo- 

derm-cup (fig. 44, 

D, E); the cavity a r — ~ 

between the two .. - . . ... 

walls of the cup Fig. 45. — Modifications of the method 0! 

becomes reduced budding shown in fig. 44, with solid Ento- 

by concrescence to codon (Gc.) and formation of an e ct othera jocL). 

form the radial 

canals (r.c), ring-canal (ex.), and eadoderm-lameua (eJ., fig. 44. E). 

and at the same time the base of the cup is thrust upwards to forta 

the manubrium (at), converting the cavity of the entocodoa iato a 




•pace which is erescentic or horse-shoe-like in section. Next ten- 
tades ft fig. 44, F) grow out from- the ring-canal, and the double 
plate of ectoderm on the distal side of the entocodon becomes 
perforated, leaving a circular rim composed of two layers of ectoderm, 
the velum (v) of the medusa. Finally, a mouth is formed by breaking 
through at the apex of the manubrium, and the now fully-formed 

medusa becomes 
separated by rup- 
ture of the stalk 
of the bud and 
swims away. 

If the bud, how- 
ever, is destined to 
S've rise not to a 
ce medusa, but 
to a gonophore, 
the development 
is similar but be- 
comes arrested at 
various points, ac- 
cording to the 
degree to which 
_ m _ M .^ the gonophore is 

A fc^^ ^fl WjL 1 I M degenerate. The 

■ H ^^ ^^ yg$&r t^ J & entocodon is 

1 V II |T ^^S. *&^ usually formed, 

fl ff >. ^\ jr proving the medu- 

■^--%* ■* "l" soid nature of the 

bud, but in sporo- 
sacs the entocodon 
may be rudiment- 
ary or absent 
altogether. The 
process of budding 
as above described 
may be varied or 
complicated in 
various ways; 
thus a secondary, 
amnion-like, ecto- 
dermal covering 
or ectotheca (fig. 
45. C, eel.) may be 
formed over all, as 
in Garveia, &c. ; 
or the entocodon 
may remain solid 
and without cavity 
until after the 
formation of the 
manubrium, or 
may never acquire 
a cavity at all, as 
described above 
for the gono- 
Phylogenetic Sig- 

_.,•«.. «_ »t_ . .* nificance of the 

Fig. 46.— Diagrams to show the significance Entocodon.— it is 

of the Entocodon in Medusa-buds. (Modified tcen f rom t h e 

from a diagram given by A. Weismaim.) foregoing account 

I, Ideally primitive method of budding, in of medusa • bud- 

which the mouth is formed first (Tic), ding that the ento- 
next the tentacles (16), and lastly the codon is a very 
umbrella. important constt- 

II, Method of Cunina; (a) the mouth arises, tuent of the bud. 

next the umbrella (6), and lastly the ten- furnishing some of 
tacles (c). a the most essential 

III, Hypothetical transition from II to the in- portions of the 

direct method with an entocodon; the medusa; its cavity 
formation of the manubrium is retarded, becomes the sub- 
that of the umbrella hastened (I I la, b). umbral cavity, 

IV, a. b, e, budding with an entocodon (cf. and its lining fur- 

fig. 44). nishes the ecto- 

V, Budding with a solid entocodon (cf. fig. 45). dermal epithelium 

of the manubrium 
and of the sub- umbral cavity as far as the edge of the velum. 
Hence the entocodon represents a precocious formation of the 
sub- umbral surface, equivalent to the peristome of the polyp, 
differentiated in the bud prior to other portions of the organism 
which must be regarded as antecedent to it in phylogeny. 

If the three principal organ-systems of the medusa, namely mouth, 
tentacles and umbrella, be considered in the light of phylogeny, 
it is evident that the manubrium bearing the mouth must be the 
oldest, as representing a common property of all the Coelentera, 
even of the gastrula embryo of all Enterozoa. Next in order come 
the tentacles, common to all Cnidaria. The special property of the 
medusa is the umbrella, distinguishing the medusa at once from 
other morphological types among the Coelentera. If, therefore, the 
formation of these three systems of organs took place according to 

a strictly phylogenetic sequence, we should expect them to appear 
in the order set forth above (fig. 46, la, b, c). The nearest approach 
to the phylogenetic sequence is seen in the budding of Cunina, where 
the manubrium and mouth appear first, but the umbrella is formed 
before the tentacles (fig. 46, lid. b, c). In the indirect or coeno- 
genetic method of budding, the first two members of the sequence 
exhibited by Cunina change places, and the umbrella is formed first, 
the manubrium next, and then the tentacles; the actual mouth- 
perforation being delayed to the very last (fig. 46. IVo, b, c). Hence 
the budding of medusae exemplifies very clearly a common pheno- 
menon in development, a phylogenetic series of events completely 
dislocated in the ontogenetic time-sequence. 

The entocodon is to be regarded, therefore, not as primarily an 
ingrowth of ectoderm, but rather as an upgrowth of both body- 
layers, in the form of a circular rim (I Vo), representing the umbrellar 
margin; it is comparable to the bulging that forms the umbrella in 
the direct method of budding, but takes place before a manubrium 
is formed, and is greatly reduced in size, so as to become a little pit. 
By a simple modification, the open pit becomes a solid ectodermal 
ingrowth, just as in Teleostean fishes the hollow medullary tube, or 
the auditory pit of other vertebrate embryos, is formed at first as a 
solid cord of cells, which acquires a cavity secondarily. Moreover, 
the entocodon, however developed, gives rise at first to a closed 
cavity, representing a closing over of the umbrella, temporary in 
the bud destined to be a free medusa, but usually permanent in the 
sessile gonophore. As has been shown above, the closing up of the 
sub-umbral cavity is one of the earliest degenerative changes in the 
evolution of the gonophore, and we may regard it as the umbrellar 
fold taking on a protective function, either temporarily for the bud 
or permanently for the gonophore. _, 

To sum up, the entocodon is a precocious formation of the umbrella, 
closing over to protect the organs in the umbrellar cavity. The 
possession of an entocodon proves the medusa-nature of the bud, 
and can only be explained on the theory that gonophores are de- 
generate medusae, and is inexplicable on the opposed view that 
medusae are derived from gonophores secondarily set free. In the 
sporosac, however, the medusa-individual has become so degenerate 
that even the documentary proof, so to speak, of its medusoid 
nature may have been destroyed, and only circumstantial evidence 
of its nature can be produced. 

4. Germinal Budding. — This method of budding is commonly 
described as budding from a single body-layer, instead of from 
both layers. The layer that produces the bud is invariably the 
ectoderm, i.e. the layer in which, in Hydromedusae, the generative 
cells are lodged; and in some cases the buds are produced in the 
exact spot in which later the gonads appear. From these facts, 
and from those of the sporogony, to be described below, we may 
regard budding to this type as taking place from the germinal 
epithelium rather than from ordinary ectoderm. 

(a) The Polyp. — Budding from the ectoderm alone has been 
described by A. Lang [29] in Hydra and other polyps. The tissues 
of the bud become differentiated into ectoderm and endoderm, and 
the endoderm of the bud becomes secondarily continuous with that 
of the parent, but no part of the parental endoderm contributes 
to the building up of the daughter-polyp. Lang regarded this 
method of budding as universal in polyps, a notion disproved by 
O. Seeliger 152) who went to the opposite extreme and regarded the 
type of budding described by Lang as non-existent. In view, 
however, both ofthe statements and figures of Lang and of the facts 
to be described presently for medusae (MargeUium), it is at least 
theoretically possible that both germinal and vegetative budding may 
occur in polyps as well as in medusae. 

(W The Medusa. — The clearest instance of germinal budding is 
furnished by MargeUium (Rathkea) octopunetatum, one of the 
Margelidae. The budding of this medusa has been worked out in 
detail by Chun (H ydrotoa, [1]), to whom the reader must be referred 
for the interesting laws of budding regulating the sequence and 
order of formation of the buds. 

The buds of MargeUium are produced on the manubrium in each of 
the four interradii, and they arise from the ectoderm, that is to say, 
the germinal epithelium, which later gives. rise to the gonads. The 
buds do not appear simultaneously but successively on each of the 

four sides of the manubrium, thus: 3 4 and secondary buds 

may be produced on the medusa-buds before the latter are set free 
as medusae. Each bud arises as a thickening of the epithelium, which 
first forms two or three layers (fig. 47. A), and becomes separated into 
a superficial layer, future ectoderm, surrounding a central mass, future 
endoderm (fig. 47, B). The ectodermal epithelium on the distal side 
of the bud becomes thickened, grows inwards, and forms a typical 
entocodon (fig. 37. D, E, F). The remaining development of the bud 
is just as described above for the indirect method of medusa-budding 
(fig. 47, G. H). When the bud is nearly complete, the body-wall of 
the parent immediately below it becomes perforated, placing the 
coelenteric cavity of the parent in secondary communication with 
that of the bud (H), doubtless for the better nutrition of the latter. 



Especially noteworthy in the germinal budding of liargeBtum 
is the formation of the entocodon, as in the vegetative budding of 
the indirect type. 

5. Sporogony.— This method of reproduction has been described 
by E. Metchnikoff in Cunina and allied genera. In individuals 
either of the male or female sex,. germ-cells which are quite un- 
differentiated and neutral in character, become amoeboid, and 
wander into t]ie endoderm. They divide each into two sister- 
cells, one of which— the spore— becomes enveloped by the other. 
The spore-cell multiplies by division, while the enveloping cell 
is nutrient and protective. The spore cell gives rise to a " spore- 
larva," which is set free in the coelenteron and grows into a 
medusa. Whether sporogony occurs also in the polyp or not 
remains to be proved. 

6. Sexual Reproduction and Embryology.— -The ovum of Hydro- 
medusae is usually one of a large number of oOgonia, and grows 
at the expense of its sister-cells. No regular follicle is formed, 
but the oocyte absorbs nutriment from the remaining oogonia. 
In Hydra the oocyte is a large amoeboid cell, which sends out 
pseudopodia amongst the odgonia and absorbs nutriment from 
them. When the oocyte is full grown, the residual odgonia 
die off and disintegrate. 

The spermatogenesis and maturation and fertilization of the 
germ-cells present nothing out of the common and need not be 

Fig. 47. — Budding from the Ectoderm (germinal epithelium) in 
Morgellium. (After C. Chun.) 

A, The epithelium becomes two- 


B, The lower layer forms a solid 

mass of cells, which (C) 
becomes a vesicle, the future 
endoderm, containing the 
coelenteric cavity (cod), 
while the outer layer 
furnishes the future ecto- 
D, E, F, a thickening of the ecto- 
derm on the distal side of 

the bud forms an entocodon 

G,H, Formation of the medusae. 

xx, Sub-umbral cavity. 

rx, Radial canal. 

st, Stomach, which in M ac- 
quires a secondary com- 
munication with the diges- 
tive cavity of the mother. 

ex, Circular canal. 

v. Velum. 

I, Tentacle. 

described here. These processes have been studied in detail 
by A. Brauer (2] for Hydrai 

The general course of the development is described in the article 
Hydrozoa. We may distinguish the following series of stages: 
(1) ovum; (2) cleavage, leading to formation of a blastula; (3) 
formation of an inner mass or parenchyma, the future endoderm, 
by immigration or delamination, leading to the so-called parenchy- 
mula-stage; (4) formation of an archenteric cavity, the future 
coelenteron, by a splitting of the internal parenchyma, and of a 
blastopore, the future mouth, by perforation at one pole, leading to 
the gastrula-stage; (5) the outgrowth of tentacles round the mouth 
(blastopore), leading to the actinula-stage; and (6) the actinula 
becomes the polyp or medusa in the manner described elsewhere 
(see articles Hydrozoa. Polyp and Medusa). This is the full, ideal 
development, which is always contracted or shortened to a greater or 
less extent. If the embryo is set free as a free-swimming, so-called 
planula-larva, in the blastula, parenchymula, or gastrula stage, then 
a free actinula stage is not found; if, on the other hand, a free 
actinula occurs, then there is no free planula stage. 




The cleavage of the ovum follows two types, both seen in Tubularia 
(Brauer (3]). In the first, a cleavage follows each nuclear division; 
in the second, the nuclei multiply by division a number of times. 
and then the ovum divides into as many blastomeres as there are 
nuclei present. The result of cleavage in all cases is a typical 
blastula, which when set free becomes oval and develops a flagellum 
to each cell, but when not set free, it remains spherical in form and 
has no fla g»lla_ 

The germ-layer formation is always by immigration or delamina- 
tion, never by invagination. When the blastula is oval and free- 
swimming the inner mass is formed by unipolar immigration from 
the hinder pole. When the blastula is spherical and not set free, the 
germ-layer formation is always multipolar, either by immigration 
or by delamination, i.e. by tangential division of the cells of the 
blastoderm, as in Geryonia, or by a mixture of immigration and 
delamination, as in Hydra, Tubularia, &c. The blastopore is formed 
as a secondary perforation at one spot, in free-swimming forma 
at the hinder pole. Formation of archenteron and blastopore may, 
however, be deferred till a later stage (actinula or after). 

The actinula stage is usually suppressed or not set free, but it is 
seen in Tubularia (fig. 48). where it is ambulatory, io Gonionemus 
(Trachomcdusae), and in Cunina (Narco- 
medusae), where it is parasitic. 

In Leptolinae the embryonic develop- 
ment culminates in a polyp, which is 
usually formed by fixation of a planula 
(parenchymula), rarely by fixation of an 
actinula. The planula may fix itself (1) 
by one end, and then becomes the hydro- 
caulus and hydranth, while the hydro- * 
rhiza grows out from the base; or (2) 
partly by one side and then gives rise to .... 
the hydrorhua as well as to the other Jjgfgv hT* 
parts of the polyp; or (3) entirely by its*"* u ->' n ' 
side, and then forms a recumbent hydro- pi C . 48.— Free Actinula 
rhiza from which a polyp appears to be of Tubularia. 

budded as an upgrowth. 

In Trachylinae the development produces always a medusa, and 
there is no polyp-stage. The medusa arises direct from the actinula- 
stage and there is no entocodon formed, as in the budding described 

Li/e-cycUs of the Hydromedusae.— The life-cycle of the Leptolinae 
consists of an alternation of generations in which non-sexual indi- 
viduals, polyps, produce by budding sexual individuals, medusae, 
which give rise by the sexual process to the non-sexual polyps again, 
so completing the cycle. Hence the alternation is of the type termed 
metagenesis. The Leptolinae are chiefly forms belonging to the in- 
shore fauna. The Trachylinae, on the other hand, arc above all 
oceanic forms, and have no polyp-stage, and hence there is typically 
no alternation in their life-cycle. It is commonly assumed that the 
Trachylinae are forms which have lost the alternation of generations 
possessed by them ancestrally, through secondary simplification of 
the life-cycle. Hence the Trachylinae are termed -" hypogenetic " 
medusae to contrast them with the metagenetic Leptolinae. The 
whole question has, however, been argued at length by W. K. Brooks 

J 4], who adduces strong evidence for a contrary view, that is to say, 
or regarding the direct type of development seen in Trachylinae as 
more primitive, and the metagenesis seen in Leptolinae as a secondary 
complication introduced into the life-cycle by the acquisition of 
larval budding. The polyp is regarded, oh* this view, as a form 
phylogenetically older than the medusa, in short, as nothing more 
than a sessile actinula. In Trachylinae the polyp-stage is passed 
over, and is represented only by the actinula as a transitory embry- 
onic stage. In Leptolinae the actinula becomes the sessile polyp 
which has acquired the power of budding and producing individuals 
cither of its own or of a higher rank; it represents a persistent larval 
stage and remains in a sexually immature condition as a neutral 
individual, sex being an attribute only of the final stage in the de- 
velopment, namely the medusa. The polyp of the Leptolinae has 
reached the. limit of its individual development and is incapable of 
becoming itself a medusa, but only produces medusa-buds; hence a 
true alternation of generations is produced, Jn Trachylinae also the 
beginnings of a similar metagenesis can be found. Thus in Cunina 
octonaria, the ovum develops into an actinula which buds daughter- 
actinulae; all of them, both parent and offspring, develop into 
medusae, so that there is no alternation of generations, but only 
larval multiplication. In Cunina parasitica, however, the ovum 
develops into an actinula, which buds actinulae as before, but only 
the daughter-actinulae develop into medusae, while the original 
parent-actinula dies off; here, therefore, larval budding has led to a 
true alternation of generations. In Gonionemus the actinula becomes 
fixed and polyp-like, and reproduces by budding, so that here also an 
alternation of generations may occur. In the Leptolinae we must 
first substitute polyp for actinula, and then a condition is found which 
can be compared to the case of Cunina parasitica or Gonionemus, if 
we suppose that neither the parent-actinula («\e. founder-polyp) nor 
its offspring by budding (polyps of the colony) have the power of 
becoming medusae, but only of producing medusae by budding. 
For further arguments and illustrations the reader must be referred 
to Brooks's most interesting memoir. The whole theory is one most 

eleutheroblasteaj HYDROMEDUSAE 1 49 

intimately connected with the question of 
and medusa, to be discussed presently, 
however, that whatever view may be heli 
genesis in Hydromedusae, in the case ol 
other view is possible than that the alterr 
direct result of larval proliferation. 

To complete our survey of life-cycles i 
necessary to add a few words about th< 
allies. If we accept the view that Hydra 
that its gonads are not gonophorcs (i.*. m< 
of degeneration, then it follows from Bi 
must oe descended from an archaic form i 
of organisation had not vet been evolved, 
a living representative of the ancestor of 
a transient reminiscence in the devclopi 
may be pointed out in this connexion tk 
only temporary, and that the animal is 
itself, to move to a new situation, and to t 
difficulty whatever in regarding Hydra as 
to the actinula-stage of other Hydromedu 
a trochophore-larva or a fish to a tadpole 

The Relation of Polyp and Medusa. — 1 
forward as to the morphological relati 
types of person in the Hydromedusa 
polyp and medusa have been regard 
common type, a view supported by the i 
medusae (?.».), of sessile polyp-like m< 
R. Lcuckart in 1848 compared medu 
flattened polyps. G. J. Allman [1] put 
view, which was as follows. In some 
webbed at the base, and it was suppos 
polyp of this kind set free, the umbrella 
web or membrane extending between 
different theory was enunciated by E, 
hydroids the founder-polyp, developed : 
tion, throws out numerous outgrowths f 
hydrorfaiza; these outgrowths may be r 
form by contact or coalescence a flat plat* 
the plate thus formed at the base of 
to the umbrella, and the body of the p 
manubrium, of the medusa; on this vie 
almost invariably present in medusae 
the tentacles' of the polyp are represem 
oral arms which may occur round the 
times, e.g. in Margclidae, have the app 
tentacles. Apart from the weighty argu 
ment furnishes against the theories of 
it may be pointed out that neither hypo 
explanation of a structure universally 
whatever class, namely the endodern 
the brothers O. and R. Hertwig. It woi 
this structure as a secondary extension 
tentacle-web, on Allman's theory, or 
of the hydrorhiza, on Mechnikov's h) 
ment, on the contrary, shows unequivo 
lamella arises as a local coalescence of th 
primitively extensive gastral space. 

The question is one intimately conne 
as to the nature and individuality of ; 
phore respectively. On this point the 
been put forward. 

1. The theory that the medusa is sim 
become detached and has acquired a certa 
like the well-known instance of the hect 
On this view, put forward by E. van Bene 
snorosac is the starting-point of an evoluti 
various types of gonophorcs to the free r 
point of a phyletic series. The evidence 
classed under two heads: first, compai 
very different in their structural charact< 
the systematic classification of these organ: 
very similar, at least so far as the cssei 
organization are concerned; on the oth« 
perhaps almost indistinguishable, may pro 
case, medusae in the other; for example, 
and Podocorvne (medusae), Tubvlaria (g< 
(medusae), Coryne (gonophorcs) and Syncc 
If it is assumed that all these genera bo 
then medusa of similar type must have 



Protokydra is a marine genus characterized by the absence of 
tentacles, by a great similarity to Hydra in histological structure, and 
by reproduction by transverse fission. It was found originally in an 
oyster-farm at Ostcnd. The sexual reproduction is unknown. For 
further information see C. Chun (Hydrozoa [1}.P1. I.). 

Polypodium hydriforme Ussow is a fresh-water form parasitic on 
the eggs of the sterlet. A " stolon " of unknown origin produces 
thirty- two buds, which become as many Polypodia; each has 
twenty-four tentacles and divides by fission repeated twice into four 
individuals, each with six tentacles. The daughter-individuals grow, 

form the full number 
oftwenty-four tentacles 
and divide again. The 
polyps aref ree and walk 
on their tentacles. See 
Ussow [54]. 

Tctraplalia voiitans 
Viguier is a remarkable 
floating marine form. 
See C. Viguier (56) and 
Delage and Herouard 
(Hydrozoa [2]). 

Haieremita Schau- 
dinn. SeeF.Schaudinn 
[50] and Delage and 
Herouard (Hydrozoa 

In all the above- 
mentioned genera, with 
the exception of Hydra, 
the life-cycle is so im- 
perfectly known that 
their true position can- 
not be determined in 
the present state of 
our knowledge. They 
may prove eventually 
to belong to other 
orders. Hence only the 
genus Hydra can be 
considered as truly re- 
presenting the order 
Eleuthcroblastea. The 
«. —.. . . ... phylogcnctic position 

F I£ *9«— D »gram showing possible & th £ p.^ hasbeen 
modifications of persons of a gymnoblastic discussed above. 
Hydromtdusa. (After Altaian. j 

0, Hydrocaulus (stem). ORDER II. Hy- 
6, Hydrorhiza (root). . droidea seu Lep- 
"l iSSE"* ton„.«_Hyd,o. 
«, Ectoderm. medusae with alter- 
/, Perisarc, (horny case). nation of generations 

1, Hydranth (hvdriform person)expanded. ( me tagcnesk)in which 
* traced ^ y<Sniorm t*™* con - a non-sexual polyp- 
», Hypostome, bearing mouth at its generation (tropho- 

extrcmity. some) produces by 

*, Sporosac springing from the hydro* budding a sexual 

r, sSIJdsa'c springing from m, a modified medusa-generation 
hydriform person (blastostylc) : the (gonosome). The 
genitalia arc seen surrounding the polyp may be solitary, 
spadix or manubrium. m fc ut morc usually pro- 

duces polyps by 
budding and forms 
a polyp-colony. The polyp usually has the body distinctly 
divisible into hydranth, hydrocaulus and hydrorhiza, and is 
usually clothed in a perisarc. The medusae may be set free or 
may remain attached to the polyp-colony and degenerate into 
a gonophore. When fully developed the medusa is characterized 
by the sense organs being composed entirely of ectoderm, 
developed independently of the tentacles, and innervated from 
the sub-umbral nerve-ring. 

The two kinds of persons present in the typical Hydroidea make 
the classification of the group extremely difficult, for reasons ex- 
plained above. Hence the systematic arrangement that follows 
must be considered purely provisional. A natural classification 
of the Hydroidea has yet to be put forward. Many genera and 
families are separated by purely artificial characters, mere shelf- 
and-bottlc groupings devised for the convenience of the museum 
curator and the collector. Thus many subdivisions are diagnosed by 
setting free medusae in one case, or producing gonophorcs in another, 
although it is very obvious, as pointed out above, that a genus pro- 
ducing medusae may be far morc closely allied to one producing 
gonophorcs than to another producing medusae, or vice versa, and 

/, Mcdusiform person or medusa. 
m, Blastostyle. 


that in some cases the production of medusae or gonophorcs varies 
with the season or the sex. Moreover, P. Hallez [22] has recently 
shown that hydroids hitherto regarded as distinct species are only 
forms of the same species grown under different conditions. 

Sub-Order i. Hydroidea Gyunoblastea (Anthouedusal). 
— Trophosome without hydrotbecae or gonolhecae, with monc- 
podial type of budding. Gonosome with free medusae or 
gonophorcs; medusae usually with ocelli, never with otocysls. 
The gymnoblastic polyp usually has a distinct perisarc investing 
the hydrorhiza and the hydrocaulus, sometimes also the hydranth 
as far as the bases of the tentacles (Bimeria); but in such cases 
the perisarc forms a closely-fitting investment or cuticulc on 
the hydranth. never a hydroiheca standing off from it, as in the 
next sub-order. The polyps may be solitary, or form colonies, 
which may be of the spreading or encrusting type, or arborescent, 
and then always of monopodia! growth and budding. In some 
cases, any polyp of the colony may bud medusae; in other 
cases, only certain polyps, the blastostylcs, have this power. 
When blastostyles are present, however, they are never enclosed 

Fie. 50. — Sarsia 
(Dipurena) gemnifera, 
0, The long manu- 
brium, bearing medusi- 
form buds; a, mouth. 

Fie. 51.— Sarsia prolifera. 
Ocelli are seen at the base of the 
tentacles, and also (as an ex- 
ception) groups of medusiform 

in special gonothecae as in the next sub-order. In this sub-order 
the characters of the hydranth are very variable, probably owing 
to the fact that it is exposed and not protected by a hydrotbeca, 
as in Calyptoblastea. 

Speaking generally, three principal types of hydranth can be 
distinguished, each with subordinate varieties of form. 

1. Club-shaped hydranths with numerous tentacles, generally 
scattered irregularly, sometimes with a spiral arrangement, or in 
whorls (" vert ic ilia tc "). 

la) Tentacles filiform; type of Clava (fig. 5), Cordytepktna, Ac. 
(©) Tentacles capitate, simple; type of Coryme and Syncoryne; 
Myriolhela is an aberrant form with some of the tentacles 
modified as " claspers " to hold the ova. 

(c) Tentacles capitate, branched, wholly or in part; type of 


(d) Tentacles filiform or capitate, tending to be arranged in 
definite whorls; type of Stauridium (fig. 2), Ciadonema 
and Pennaria. 

a. Hydranth more shortened, daisy-like in form, with two whorls 
of tentacles, oral and aboral. 

(a) Tentacles filiform, simple, radially arranged or scattered 

irregularly; type of Tubularia (fig. 4), Corymorpha (fig. 3). 
Nemopsis, Pdagohydra. &c 

(b) Tentacles with a bilateral arrangement, branched tentacles 

in addition to simple filiform ones; type of Bronchi* 

3. Hydranth with a single circlet of tentacles. 

(a) With filiform tentacles; the commonest type, seen in 

BougaimilUa (fig. 13), Eudendrium, &c. 

(b) With capitate tentacles; type of Oavatella. 

4. Hydranth with tentacles reduced below four; type of Lar 
(fig. 11), Monobrachium, &c 


The Anihomedusa in form is generally deep, bell-shaped. 
The sense organs are typically ocelli, never otocysts. The gonads 
are borne on the manubrium, either forming a continuous ring 
(Codonid type), or lour masses or pairs of masses (Occanid type). 
The tentacles may be scattered singly round the margin of the 
umbrella (" monerenematous ") or arranged in tufts (•' lophone- 
malous") ; in form they may be simple or branched (Cladonemid 
type); in structure they may be hollow (" coelomerinthous "); 
or solid (" pyenomerinthous "). When sessile gonophores are 
produced, they may show all stages of degeneration. 

Classification. — Until quite recently the hydroids (Gymnobtastea) 
and the medusae (Anthomedusae) have been classified separately, 
since the connexion between them was insufficiently known. Delage 
and Herouard (Hydrozoa (2]) were the first to make an heroic 
attempt to unite the two classifications into one, to which Hickson 
(Hydrozoa [4]) has made some additions and slight modifications. 
The classification given here is for the most part that of Delage and 
Herouard. It is certain, however, that no such classification can be 
considered final at present, but must undergo continual revision in 
the future. With this reservation we may recognize fifteen well- 
characterized families and others of more doubtful nature. Certain 
discrepancies must also be noted. 

1. Margdtdae (- medusa-family Margtlidae+bydxoid families 
BougattmUtdae, Dicorynidae, Btmeridae and Eudendridae). Tropho- 
some arborescent, with hydrant hs of BougainviUea-typc ; gonosome 
free medusae or gonophores, the medusae with solid tentacles in 
tufts (lophonematous). Common genera are the hydroid Bougain- 
villea (figs. 12, 13), and the medusae Hippocrene (budded from 
BougainvilUa), Margelis, Ratkkea (fig. 24). and Margellium. Other 
hydroids are Carveia, Bimeria, Eudendrium and HelerocordyU, with 
gonophores, and Dicoryne with peculiar sporosacs. 

2. Podocorynidaei - medusa -families Tkamnostomidae ind Cytaridae 
-fhydroid families Podocorynidae and Hydracliniidae). Trophosome 
encrusting with hydranths of Bougainvillea-ty?*, polyps differenti- 
ated into blastostyles, gastrosoids and dactytozoids; gonosome free 
medusae or gonophores. The typical genus is the well-known 

hydroid Podo- 
coryne, budding 
the medusa known 
as Dysmorphow ; 
CyUuts, Ac, are 
other medusae 
with unknown 
hydroids. Hydrac- 
tittia (figs. 9, 10) 
is a familiar 
hydroid genus, 
bearing gono- 

3. Cladonemidae. 
I — Trophosome, 
1 polyps with two 

whorls of ten- 
tacles, the lower 
filiform, the upper 
capitate; gono- 
some, free med- 
usae, with ten- 
tacles solid and 
branched. The 
type-genus Clado- 
nema (fig. 20) is a 
common British 

4. ClavateUidae. 
polyps with a 
single whorl of 
capitate tentacles; 
gonosome, free 
medusae, with ten- 
tacles branched, 
solid. ClavakUa 
(fig. 21), with a 
peculiar ambula- 

Aiter Hxckd, Sytkm 4* U*duttn, by pmnimlon tt Carts* tory medusa is a 
Factor. British form. 

Fig. 52.— Ttara pUeata, L. Agassis. 5; P********** 

r ^ — Trophosome, 

polyps with an 
upper circlet of numerous capitate tentacles, and a lower circlet of fili- 
form tentacles. Pennaria, with a free medusa known as Globictps, is a 
common Mediterranean form. Staurtdium (fig. 2) is a British hydroid. 
6. Tubular iidae. — Trophosome, polyps with two whorls of ten- 
tacles, both filiform. Tubular ta (fig. 4), a well-known British hydroid, 
bears gonophores. 




with a form Mich at Corymorpka, which alto b not fixed but only 
rooted in the mud. The medusae, on the other hand, have the 
tentacles in four tufts of (in the buds) five each, and thus resemble 

the medusae of the 
family Margelidae. 
See A. Dendy 1121. 

Perigonimus. — This 
common British hy- 
droid belongs by its 
characters to the 
family Bougainvil- 
lidae; it produces, 
however, a medusa 
of the genus7Yara (fig. 
I 52), referable to the 

family Clovidae; a 
fact sufficient to indi- 
cate the tentative 
character of even the 
most modern classifi- 
cations of this order. 
Sub-order II. 
Hydroidea Calyp- 


medusae).— Tropho- 

some with polyps 

always differentiated 

into nutritive and 

reproductive indi- 


enclosed in hydro- 

thecae and gono- 

thecae respectively; 

with sympodial type 

Fie. 54. — Diagram showing possible modi- of budding. Gono- 

fications of the persons of a Calyptoblastic some with free med- 

Hydromedusa. Letters a to h same as in „^ ft annnnhnn»«- 

fig. 49. •'. The horny cup or hydrotheca of ^ 0r B ™?™ ***.* 

the hydriform persons; /, medusiform person tnc medusae typi- 

springing from m, a modified hydriform cally with otocysts, 

person (blastostyle); «, the horny case or sometimes with cor- 

gonangium enclosing the blastostyle and d y or oceUi / fi 

its buds. This and the hydrotheca i give uyu 'f vcm v **' 

origin to the name Calyptobtastea. (Alter 54»55J« . ... 

Allman.) The calyptoblastic 

polyp of the nutritive 
type is very uniform in character, its tendency to variation 
being limited, as it were, by the enclosing hydrotheca. The 
hydranth almost always has a single circlet of tentacles, like 
the BougaimilUa-typc in the preceding sub-order; an excep- 
tion is the curious genus ClcUkrozoon, in which the hydranth has 

a single tentacle. The 
characteristic hydrotheca 
is formed by the bud at 
xj \ ^WHS' 1 fHU^faiit^' r an early stage (fig. 56); 
^>&JHr ~ »Ht T^vsk J when complete it is an 
open cup, in which the 
hydranth develops and 
can be protruded from the 
opening for the capture 
of food, or is withdrawn 
into it for* protection. 
Solitary polyps are un- 
known in this sub-order; 
the colony may be creep- 
ing or arborescent in form; 
Fig. 55.— View of the Oral Surface of «f the latter, the budding 
one of the Ltbtomcdnsac {Irene pellu- of the polyps, as already 
cida, Hacckcl), to show the numerous stated, is of the sym- 

tentacles and the otocysts. 

podial type, and either 

ge, Genital glands, re. The four radi- k;^-:-! *«««,•„» e t* m . 
if. Manubrium. ating canals. blscn t a /» /?"?."« . SlCmS 

oi, Otocysts. Ve, The velum. capable of further branch- 

ing, or uni serial, forming 
pinnules not capable of further branching. In the biscrial type 
the polyps on the two sides of the stem have primitively an 
alternating, zigzag arrangement; but, by a process of differential 
growth, quickened in the 1st, 3rd, 5th, &c, members of the 
stem, and retarded in the 2nd, 4th, 6th, &c, members, the polyps 

may assume secondarily positions opposite to one another on 
the two sides of the stem. Other variations in the mode of 
growth or budding bring about further differences in the building 
up of the colony, which are not in all cases properly understood 
and cannot be described in detail here. The stem may contain 
a single coenosarcal tube (" monosiphonk ") or several united 
in a common perisarc (" polysiphonic "). An important variation 
is seen, in the form of the hydrotheca itself, which may come 
off from the main stem by a stalk, as in Obdia, or may be 
sessile, without a stalk, as in Serlularia. 

In many Calyptoblastea there occur also reduced defensive 
polyps or dactylozoids, which in this sub-order have received 
the special name of sarcostyks. Such are the " snake-like xoids " 
of Ophioda and other genera, and as such are generally inter- 
preted the" macho- 
polyps" of the 
These organs are 
supported by cup- 
like structures of the 
perisarc, termed 
nematophores, re- 
garded as modified 
hydrothecae sup- 
porting the special- 
ized polyp-indi- 
viduals. They are 
specially character- 
istic of the family 

The medusa-buds, 
as already stated, 
are always produced 
from blastoslyles, 
reduced non-nutri- 
tive polyps without 
mouth or tentacles. 
An apparent, but 
not real, exception 
is Halecium halcei- 
num, in which the 
blastostyle is pro- 
duced from the side 
of a nutritive polyp, 
and both are en- 
closed in a common 
theca without a 
partition between 
them (Allman [1] 
p. 50, fig. 24). The 

gonotheca is formed in its early stage in the same way as the 
hydrotheca, but the remains of the hydranth persists as an 
operculum closing the capsule, to be withdrawn when the 
medusae or genital products are set free (fig. 56). 

Theblastostyles, gonophoresand gonothecae furnish aseries of varia- 
tions which can best be considered as so many stages of evolution. 

Stage 1 , seen in Obdia. Numerous medusae are budded successively 
within the gonotheca and set free; they swim off and mature in the 
open sea (Allman [11, p. 48, figs. 18, 10). 

Stage 2, teen in Gonothyraea. Medusae, so-called " meconidu," 
are budded but not liberated; each in turn, when it reaches aexual 
maturity, is protruded from the gonotheca by elongation of the 
stalk, and sets free the embryos, after which it withers and is re- 

After ABnun. GymwtUUic Bydmds. by 
the council of the Ray Society . 

Fig. 56. 
formation of the 

Diagrams to show the 1 

the Hydrotheca and Gc 

in Calyptoblastic Hydroids. A-Dare stages 

common to both; from D arises the hydro- 
theca (E) or the gonotheca (F) ; tk, theca; 
st, stomach; J, tentacles; m, mouth; ssfc, 

Stage 3, seen in Scrtulario. 
the "" 

lores arc reduced in varying 

nee, it may be to tporosacs; they are budded successively from 
blastostyle, and each in turn, when ripe, protrudes the spadix 
►ugh the gonotheca (fig. 57, A, B). The spadix forms a gelatinous 

placed by another (Allman [1] ,p. 57, fig. 28) 
" . — The gonophorc 

it may dc to tporo 

tostvle. and each i 

through „ . „ ., r „ 

cyst, the so-called acrocyst (ac), external to the gonotheca (gtk), 
enclosing and protecting the embryos. Then the spadix withers, 
leaving the embryos in the acrocyst, which may be further protected 
by a so-called marsupium, a structure formed by tentacle-like 
processes growing out from the blastostyle to enclose the acrocyst. 
each such process being covered by perisarc like a glove-finger 
secreted by it (fig. 57, C). (Allman [1], pp. 50, 51, figs.. 21-24: 
Wcismann [58], p. 170, pi. ix., figs. 7, 8.) 




Stage 4t Ken in Plumtdaridae.— The generative elements are 
produced in structures termed corbulac, formed by reduction 
and modification of branches of the colony. Each corbuia 
contains a central row of blastostylcs enclosed and protected 
by lateral rows of branches representing stunted buds (Allman [1], 
p, 60, fig. 30). 

The Lepiomcdusa in form is generally shallow, more or less 
saucer-like, with velum less developed than in Anthomedusac 
(fig- 55)* The characteristic sense-organs are ectodermal oto- 
cysts, absent, however, in some genera, in which case cordyli 
may replace them. When otocysts are present, they are at least 
eight in number, situated adradially, but are often very numerous. 
The cordyli are scattered on the ring-canal. Ocelli, if present, 
are borne on the tentacle-bulbs. The tentacles are usually 
hollow, rarely solid (Obelia). In number they are rarely less than 
four, but in Dissonema there are only two. Primitively there 
are four perradial tentacles, to which may be added four inter- 
radial, or they may become very numerous and are then scattered 
evenly round the margin, never arranged in tufts or clusters. 

In addition to 
tentacles, there 
may be marginal 
cirri (Laodice) 
with a solid 
endodermal axis, 
spirally coiled, 
very contractile, 
and bearing a 
terminal battery 
of nematocysts. 
The gonads are de- 
veloped typically 
beneath the radial 
canals or below 
the stomach or 
its pouches, often 
stretching as long 
...--. bands on to the 

After /Jkoaa,GymmatUaU ByiroUs. by pcrmasioo of tbt base of the man- 
endi of tbt R^fedecy. ubrium. InOctor. 
Fie. 57.— Diagrams to show the mode of chidac (fig. s8) 
formation of an Acrocyst and a Marsupium. M . _„_tr u~~a 
InAtwomedusa-budsai* «ccnwithinthcgono- eac . h such o™ 
theca (ztk), the upper more advanced than the > s interrupted, 
lower one. InBthespadixof the upper bud has forming one mass 
protruded itself through the top of the gono- a t the base of the 
theca and the acrocyst (ac) is secreted round it. -», „„!„-•,,_. «-j 
In C the marsupium (m) is formed as finger-like man « br ""n *"<» 
process from the summit of the blastostylc, en- another below the 
closing the acrocyst; b, medusa-buds on the radial canal in 
blastostylc. each radius, in all 
eight separate gonad-masses, as the name implies. In some 
Leptomedusae excretory "marginal tubercles" are developed 
on the ring-canal. 

Classification. — As in the Gymnoblastea, the difficulty of uniting 
the hydroid and medusan systems into one scheme of classification 
is very great in the present state of our knowledge. In a great many 
Leptomedusae the hydroid stage is as yet unknown, and it is by no 
means certain even that they possess one. It is quite possible that 
some of these medusae will be found to be truly hypogenctic, that is 
to say, with a life-cycle secondarily simplified by suppression of 
metagenesis. At present, ten recent and one extinct family of 
Calyptoblastea (Leptomedusae) may be recognized provisionally: 

1. Eucopidae (figs. 55, «o). — Trophosomc with stalked hydro- 
thecae; gonosome, free medusae with otocysts and four, rarefy six 
or eight, unbranched radial canals. Two of the commonest British 
hydroids belong to this family, Obelia and Clytia. Obelia forms 
numerous polyserial stems of the characteristic zigzag pattern grow- 
ing up from a creeping basal stolon, and buds the medusa of the same 
name. In Clytia the polyps arise singly from the stolon, and the 
medusa is known as Phialidium (fig. 50). 

2. Aequoridae. — Trophosomc only known in one genus (Poly- 
canna), and similar to the preceding; gonosome, free medusae with 
otocysts and with at least eight radial canals, often a hundred or 
more, simple or branched. Aequorea is a common medusa. 

3. Thaumantidae. — Trophosomc only known in one genus (Thau- 
mantias), similar to that of the Eucopidae; gonosome, free medusae 
with otocysts inconspicuous or absent, with usually four, sometimes 
eight, rarely more than eight, radial canals, simple and unbranched, 
along which the gonads are developed, with numerous tentacles 

bearing ocelli and with marginal sense-clubs. foodie* and Thau- 
mantias are representative genera. 

4. £ero«tViaa*.-— Trophosome unknown; gonosome, free medusae, 
with four or six radial canals, bearing the gonads, with numerous 
tentacles, between which occur sense-clubs, without otocysts. 
Berenice, Staurodiscus, &c. 

5. Polvorckidae. — Trophosomc unknown; gonosome, free medusae 
of deep form, with radial canals branched in a feathery manner, and 

After BaKkd, Symm ia Mtdmsa, by pemHoatf Gmttr Ffatsr. 
Fic. 58. — Ocierchandra canadensis, from life. 

hearing gonads on the main canal, but not on the branches, with' 
numerous hollow tentacles bearing ocelli, and without otocysts. 
Pdyorchis, Spirocodon. 

6. Campanularidae. — Trophosomc as in Eucopidae; gonosome, 
sessile gonophores. Many common or well-known genera belong 
here, such as Halecium, Campanularia, Gonotkyraeo, &c. 

7. Lafottdoe.— Trophosome as in the preceding; gonosome, free 
medusae or gonophores, the medusae with large open otocysts. 
The hydroid genus Lafoea is remarkable for producing gonothecae on 
the hydrorhiza, each containing a blastostylc which Dears a single 
gonophore; this portion of the colony was formerly regarded as an 
independent parasitic hydroid, and was named Coppinia, Medusan 
genera are Juitrocoma. Halopsis, Tiaropsis (fig. 29, ac). 

(So far as the characters of the trophosomc arc concerned, the 
seven preceding families are scarcely distinguishable, and they form 

After E.T. Browne. Aw. zW. St.tfLmidm. 1806. 

Fig. 59. — Three stages in the development of Phialidium tern- 
porarium. a. The youngest stage, is magnified about 22 diam.; b, 
older, is magnified about 8 diam. ; c, the adult medusa, is magnified. 

a section apart, contrasting sharply with the families next to be 
mentioned, in none of which are free medusae liberated from the 
colony, so that only the characters of the trophosome need be con- 

8. Sertularidae.—Hyoxothtcac sessile, bi serial, alternating or 
opposite on the stem. Sertularia and Sertularella are two very 
common genera of this family. 

o. Plumularidae.—Hydrotbccac sessile, biserial on the main stem, 
umserial on the lateral branches or pinnules, which give the colony 
its characteristic feathery form; with nematophores. A very 
abundant and prolific family; well-known British genera are 
Ptumularia. Antennularia At\6 AeUxophenia. 

10. Hyiroceraiinidae. — This family contains the single Australian 
species Clalhrotoon vnlsoni Spencer, in which a massive hydrorhiza 




bears sessile hydrothecae. containing hydranths each with a single 
tentacle, and numerous nematophores. See W.