Sorts Be narats a btar gis aut aS Ls i. er . rai A Sisto telgegree =: J ary it 24 7 A Lyi ge seal Ts Te peels! FY om) ee - f et Be a - Waits Bit aus gta Land a ry ey, ,% ¢ REPORT OF THE FIFTIETH MEETING OF THE BRITISH ASSOCIATION FOR THH ADVANCEMENT OF SCIENCE; HELD AT SWANSEA IN AUGUST AND SEPTEMBER 1880. LONDON: JOHN MURRAY, ALBEMARLE STREET. 1880. Office of the Association: 22 ALBEMARLE STREET, Lonvon, W. LONDON : PRINTED BY SPOTTISWOODE AND CO., NEW-STREET SQUARE AND PARLIAMENT STREET CONTENTS. Ls aigig nite Page OBIECTS and Rules of the Association .....sssscccsceceseesseesecsseescereeerensee xxi Places and Times of Meeting and Officers from commencement.............++ XXxvili Presidents and Secretaries of the Sections of the Association from com- IMENCEMENL ......seeececercscccecccsccsccaveeeveeserseesenseeese by amavaedesaces..556c0c3.ccs5sccasscccsssccccéses sossausdaled svc ope veeeenemneeee 494 » On a method of measuring Contact Electicity. By Professor Sir WILLIAM POMBO NA, SELES. . scvcvesvenapeers deer veseeoaes ecadareees Eiioshs dese nae ome 494. . On a method of determining without mechanism the limiting Steam- Liquid Temperature of a Fluid. By Professor Sir Witt1am THoMsoN, DEA) as Soa tna Pe hhc antvidesineneiseoestns sete onion eRe ree On the possibility of originating Waye-disturbances in the Ether by Electro- magnetic Forces, By G, F. FIvzGRRALD ... ..s00s00s caseas tancenesbulaatetenace On the number of Electrostatic Units in the Electro-magnetic Unit. By R. Suma, M.E., Imperial College of Engineering, Tokio, Japan » On an Electro-magnetic Gyroscope. By W. DE FonvIEttz.......... seseroves OOO . Sur les Transformations successives des Images photographiques, et les Applications 4 l’Astronomie. Par M. J. Janssmn, de l'Institut, Directeur dol Observatoire deren Oni oan... ste stecseescesecesevacoeacdenesseeewss sere 500 » On Improvements in Electro-Motors. By THropor WIESENDANGER ...... 501 On a New Mode of [luminating Microscopic Objects. By Parti Branam, BOB Gi. sak. in eee eet eet ate ee Iedast Sascdsc-ussapheadoduaenaesee 502 - On an Instrument for the Detection of Polarised Light. By Pump BRATAM; BON. aiseschaesee el esvekneierkintestaeects meni des Soe ox eeuiomnaae Paedets oad 502 Section B.—CHEMICAL SCIENCE. THURSDAY, AUGUST 26. Report of the Committee on the Best Means for the Development of Light from Coal-Gas of different qualities. Part II. ............... oé5ccecapeamanei 503 On some Relations between the Atomic Volumes of Certain Elements and the Heats of Formation of some of their Compounds. By WALTER WELDON, ERIS i. déssaess0sesaeesfessteieszets (uedeatsenaines ta eee viva. DOS CONTENTS. xk aD Page 8. On the Influence of Water on the Union of Carbonic Oxide with Oxygen at High Temperatures. By Harorp B, Drxon, M.A., F.C.S....... 0000000 502 4, On Metallic Compounds containing Divalent Organic Radicals. Part I. ESNIRU I ANCUATIOPGs tovcecte ps sovdssctasecadvorsnedsecescucctccccseseccanccousecsesse7s eee 504. _ , On the ae of Organic Acids to the Examination of Minerals. By arOloesOr td, OARRINGTON BOLTON, Ph.D) .2::.52:.2-cccccsscescsvcoseascceconcss 505 FRIDAY, AUGUST 27. Address by Joseru Henry Griisert, Ph.D., F.R.S,, F.C.S., F.L.S., President of PRCUSECIIOUIS cdsincacovasoccerectpsscuesesthleesedessersarsstadsossetsecsdesdasnddeevevens 507 1. Report of the Committee upon the present state of our Knowledge of Spectrum Analysis (Spectra of Metalloids) .........ssscescssceeceeeenenseeecenees 534. 2. Report of the Committee upon the present state of our Knowledge of Spectrum Analysis (Ultra-violet Spectra) ......sccesseeeeeeeereeneneeeeeeeens ve. 584 8. Exhibition of an Improved Volumetric Apparatus. By J. W. Star tine... 534 4, On the Coal Seams of the Eastern Portion of the South Wales Basin and their Chemical Composition. By J. W. THOMAS .......ssssesseseeeseeeeeeees 534 5. On a New Mode for the Purification of Sewage. By P. SPENCE..........+. 584 MONDAY, AUGUST 30. 1. On the Refraction-equivalent of Diamond and the Carbon Compounds. By J. H. GLaDsTONE, Ph.D., F.R.S. .......c.cscceeceeescescescescecsensenceeceecenens 535- 2. The Position of Agricultural Education and Research in this Country and on the Continent of Europe briefly compared and considered. By J. MACDONALD CAMERON, F.C.5., &C. secccececeeresereceencereenssesecesneanceseenens 537° 3. On the Specific Rotatory Power of Cane and Invert Sugar. By ALFRED EMPTIES ANOS wa odacdscnecsarcenscnesessedcncdncocacraqenassnnescdeandmeticarsesss 541 4, On the Identification of the Coal-tar Colours. By Jomn Sprurmr, F.C.S. 542 5. On the Density of Fluid Bismuth. By W. Cuanpirr Roszrts, F.R.S., and THOMAS WRIGHTSON, C.H.........csccecsecsceececserecseceecesnscneeeenenecsees 543: 6, On Crystals of Mercury. By Purrip BRAHAM, F.C\S. ......ssseeeeeeeer eee ees 544. 7, On a New Process for the Metallurgic Treatment of Complex Ores con- taining Zinc. By EpwARp A. PARNELL, F.C.S. ......sessesesseeeseeneeeeees 544. 8. On a New Process for the Production, from Aluminous Minerals contain- ing Iron, of Sulphate of Alumina free from Iron. By J. W. KYNASTON, POL iy MLC, sdesissansasiecn saunas sadvwusueosab guess oaseesieseceessnsancassndaeseossnvese 545. 9. On a New Process for separating Silver from Copper contained in Copper ‘Ores and Reguluses, By WitiIaAM HENDERSON.......:+ssscesseesseeeseneeeenes 546: TUESDAY, AUGUST 31. 1. Further Notes on Petroleum Spirit and analogous Liquids. By ALFRED i -Hy ATEN, FOS. - ssssacsscascesesss RY preee AONE CORE A TET ERO. dabgasdiseds 547 2. On the so-called ‘ Normal’ Solutions of Volumetric Analysis. By ALFRED ‘7 H. ALLEN, FE.C.S. Severe rercevessesses Oeeecececs @eorseece PTITTEe 549 8. Onthe Determination of the Loss of Heat in Steam-Boilers arising from Incrustation. By Wit1amM THOMSON, F.R.S.B. o..seeeeesseeeeseneeeeeeeeees 549: xil CONTENTS. Page 4, On the Identification of the Ink used in writing Letters and Documents in Cases of Libel, Forgery, &. By Wit11am THomson, 5. Note on Silver Sulphate. By Partie Brawam, F.O.S. ........cseseeeceeeeeees 550 6. oe ae of Magnesia on Vegetation. By Major-General Scort, C.B., 7. On the Action of Oils on Metals. By Witr1am H. Watson, F.C.S. ...... 560 8 . On Bleaching Powder Residue. By Freprrick W. Honexs, F.1.C ERUC ECE Fe Se eS et TN sh ak 7 SO A Sa MEI eee 660 Section C.—GEOLOGY. THURSDAY, AUGUST 26. Address by H. Crirron Sorsy, LL.D., F.R.S., F.G.S., President of the i. CCUION coccuscscsascscsseccnsaasonows 6eenscceleveocciscecenenocncs 6 aes soene ene netEn 565 Sixth Report on the Circulation of the Underground Waters in the Per- mian, New Red Sandstone, and Jurassic Formations of England, and the Quantity and Character of the Water supplied to towns and dis- tries Mom ChHOss FOrMatMONS. .....5....0c.ccnsoccseeses vases saacoenetsoseaneetnesyes 573 . Notes on the Submarine Geology of the English Channel off the Coast of South Devon. By ArtHur Roopr Hunt, M.A., F.GAS. .........ceceeeeceees 573 . On the Action of Carbonic Acid on Limestone. By Professor W. Boyp IVA WAGIN Ge IWA... HRS: . .cocosc oaceveop ash tigecasnenaa ecg 633 xvi CONTENTS. Page 7. Further Researches on the Prehistoric Relations of. the Babylonian, Chinese, and Egyptian Characters, Language, and Culture, and their Connection with Sign and Gesture Language. By Hype OLarkg, PY se Neder devew rick. sax ecssuceotscceessosesssseuseges on smeige angi duane ty —E—E—E——————————— Ee CONTENTS. XVii Page . Notes on a Journey from Canton to Kwei-Yang-Fu up the Canton River. BBY AW. IMIGSNY, .-.-cceocewvedastcscesdecsddedceeneveds cad@Dpocsdecctseetevscesccasescccere 660 . The Dutch Indian Government Exploring Expedition in Borneo, By PPAR SOR sno tarecn sna s gacine vss onannecceiiapiacancoace caeMeANGas thesabes duaedoadabdse 661 TUESDAY, AUGUST 31. . On the North-East Passage. By Lieutenant Guorcr T. Tempe, R.N..... 663 . On an Examination of the Balearic Islands. By Dr. Punt, F.S.A., Rca voile s vow aneuasydn suonwua4eyeo0'¥suepveSeins Husabies Vos tinesvin Mt RAS ueenay es 663 3. On a recent Examination of the Topography of the Troad. By Dr. PHEnk&, AE i CA iota, aac gaan nA deaee nat dans apbenueiints Muss urshenacs « Gndde dose $e 664 . A Visit to the Galapagos Islands in H.M.S. ‘Triumph,’ 1880. By Pisa iea THs UAT RGA ee con Soasadde ccs cacod sss dos. scvs oauy s dncstiew sande dete dus ve nccecbeacce Motecverctacecter. 56 668 FRIDAY, AUGUST 27. . Report of the Committee on the German and other Systems of Teaching the Deaf to speak ...............sccscceccsecescneas Ret Bg ectee COREE COLES 668 . On the recent Revival in Trade. By SrepHen Bovurng, F.S.S. ............ 668 ENewnCac ess eatars Bees oe ele ale eeele dats eletellsecteenicte sia eanisecicwecemessiaaececlaneesacs's 668 Report of the Anthropometric Committee ..........ccecesssceessseeeeeeseneauees 670 2 3. Sy amid Monies and Accounts. By Frank P. Fettows, F.S.S., 4. MONDAY, AUGUST 30. Address by Gzorez Woopyarr Hasrines, M.P., President of the Section ... 671 1. Protection in the United States and its Lessons. By GrorcE BapEn- MORE, DECALS H WER else) Beis thn sv dosicdesdls vangesues dus amessendbbtauanedeedets 671 2. On the Preservation of Fish and preventing the Pollution of Rivers. va Lieut.-General Sir James E, Anexanper, K.C.B., K.C.LS., F.R.S.E. ... 672 1880. a XViil CONTENTS. Page . On the required Amendment in the Marriage Laws of the United King- dom. By the Rev. Danret Ack, D.D., F.R.AS....--.c.scsescesescescenseeeee 672 . On Diminishing Annuities—a Neo-Philosophy in Lending Funds. 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Poe ee SVU “ag ‘Iol[VAoyH stduay, "Ad “bsq ‘ueqdeyg ‘9° Se te a Re eee ee” Te SIOOULB IGT, a Remtncnectat wee) SUIT JO o4NASUT UISYIION ayy JO Quapisorg “bs ‘pooA, sSvloyoIN “S98T ‘9g JSNSNY ‘ANAT -NO-ZTISVOMUN my HH} FSUBNV veces eee ee "tees osvomoN Jo Jo RECOMMENDATIONS ADOPTED BY THE GENERAL COMMITTEE AT THE Swansea Mertine in Avucust anp SepremBer, 1880. [When Committees are appointed, the Member first named is regarded as the Secretary, except there is a specific nomination. ] TInwolving Grants of Money. That the Committee, consisting of Mr. G. H. Darwin, Professor Sir ‘William Thomson, Professor Tait, Professor Grant, Dr. Siemens, Pro- fessor Purser, Professor G. Forbes, and Mr. Horace Darwin, be re- appointed for the Measurement of the Lunar Disturbance of Gravity ; that Mr. G. H. Darwin be the Secretary, and that the sum of 30. be placed at their disposal for the purpose. That the Committee, consisting of Professor Everett, Professor Sir William Thomson, Mr. G. J. Symons, Professor Ramsay, Professor -Geikie, Mr. J. Glaisher, Mr. Pengelly, Professor Edward Hull, Dr. Clement Le Neve Foster, Professor A. 8. Herschel, Mr. G. A. Lebour, Mr. A. B. Wynne, Mr. Galloway, Mr. Joseph Dickinson, and Mr. G. F. Deacon, on Underground Temperature be reappointed, with the addition of the name of Mr. A. Strahan; that Professor Everett be the Secretary, -and that the sum of 20/. be placed at their disposal. That Professor G. Carey Foster, Mr. C. Hockin, Professor Sir Wil- liam Thomson, Professor Ayrton, Mr. J. Perry, Professor W. G. Adams, Lord Rayleigh, Professor F. Jenkin, Dr. O. J. Lodge, Dr. John Hopkin- -son, Dr. Muirhead, and Mr. W. H. Preece be a Committee for the purpose of constructing and issuing practical Standards for use in Elec- trical Measurements ; that Dr. Muirhead be the Secretary, and that the sum of 1001. be placed at their disposal for the purpose. That the Committee, consisting of Mr. James Glaisher, Dr. Flight, Professor R. S. Ball, Mr. E. J. Lowe, and Professor A. 8. Herschel, on Luminous Meteors be reappointed ; that Professor A. S. Herschel be the Secretary, and that the sum of 151. be placed at their disposal. That the Committee, consisting of Dr. Joule, Professor Sir Wiliam Thomson, Professor Tait, and Professor Balfour Stewart, for effecting ‘the Determination of the Mechanical Equivalent of Heat be reappointed ; that Dr. Joule be the Secretary, and that the sum of 401. be placed at their disposal for the purpose. That a Committee, consisting of Dr. O. J. Lodge, Professor Ayrton, and Mr. Perry, be reappointed for the purpose of devising and construct- ing an improved form of High Insulation Key for Electrometer Work; that Dr. O. J. Lodge be the Secretary, and that the sum of 51. be placed at their disposal for the purpose. That the Committee, consisting of Professor Sylvester, Professor Cayley, and Professor Salmon, for the Calculation of Tables of the RECOMMENDATIONS ADOPTED BY THE GENERAL COMMITTEE. lxi Fundamental Invariants of Algebraic Forms be reappointed; that Pro- fessor Sylvester be the Secretary, and that the sum of 401. be placed at their disposal for the purpose. That Sir William Thomson, Mr. Robert Boag Watson, and Professor John Young be a Committee for the purpose of making Seismic Hxperi- ments in connexion with the great Gunpowder Blasts on Loch Fyne; that Professor Young be the Secretary, and that the sum of 30/. be placed at their disposal for the purpose. That the Committee on Tidal Observations in the English Channel and in the North Sea, consisting of Sir William Thomson, Dr. J. Merrifield, Professor Osborne Reynolds, Captain Douglas Galton, Mr. J. N. Shool- bred, Mr. J. F. Deacon, and Mr. Rogers Field, be reappointed for the purpose of making a final report ; that Mr. J. N. Shoolbred be the Secre- tary, and that the sum of 101. be placed at their disposal for the purpose. That Mr. J. M. Thomson and Mr, J. E. H. Gordon be appointed a Committee to continue Researches on the Specific Inductive Capacity of certain Crystals and Paraffines ; that Mr. J. BH. H. Gordon be the Secre- tary, and that the sum of 101. be placed at their disposal for the purpose. That Dr. J. H. Gladstone, Dr. W. R. HE. Hodgkinson, Mr. W. Carleton Williams, and Dr. P. P. Bedson be a Committee for the purpose of in-. vestigating the Method of Determining the Specific Refraction of Solids. from their Solutions; that Dr. P. P. Bedson be the Secretary, and that the sum of 101. be placed at their disposal for the purpose. That Professor Dewar, Dr. Williamson, Dr. Marshall Watts, Captain Abney, Mr. Stoney, Professor W.N. Hartley, Professor McLeod, Pro- fessor Carey Foster, Professor A. K. Huntington, Professor Emerson Reynolds, Professor Reinold, Professor Liveing, Lord Rayleigh, Dr. Arthur Schuster, and Mr. W. Chandler Roberts be reappointed a Com- mittee for the purpose of reporting upon the present state of our know- ledge of Spectrum Analysis; that Mr. W. Chandler Roberts be the Secretary, and that the sum of 101. be placed at their disposal for the purpose. That Professor P. M. Duncan and Mr. G. R. Vine be reappointed a Committee for the purpose of reporting on the British Fossil Polyzoa; that Mr. Vine be the Secretary, and that the sum of 10/. be placed at their disposal for the purpose. That Dr. J. Evans, the Rev. J. F. Blake, Professor T. G. Bonney, Mr. W. Carruthers, Mr. F. Drew, Professor G. A. Lebour, Professor L. C. Miall, Mr. F. W. Rudler, Mr. E. B. Tawney, Mr. W. Topley, and Mr. W. Whitaker be reappointed a Committee for the purpose of carrying on the Geological Record ; that Mr. Whitaker be the Secretary, and that the sum of 1001. be placed at their disposal for the purpose. That Professor E. Hull, the Rev. H. W. Crosskey, Captain Donglas. Galton, Mr. James Glaisher, Professor G. A. Lebour, Mr. W. Molyneux, Mr. G. H. Morton, Mr. W. Pengelly, Professor J. Prestwich, Mr. James. Plant, Mr. James Parker, Mr. I. Roberts, Mr. S. Stooke, Mr. G. J. Symons, Mr. W. Whitaker, and Mr. C. E. De Rance be reappointed a Committee for the purpose of investigating the Circulation of the Under- ground Waters in the Jurassic, New Red Sandstone, and Permian For-. mations of England, and the Quality and Quantity of the Water supplied +o various towns and districts from these formations; that Mr. C. E. De Rance be the Secretary, and that the sum of 10/. be placed at their dis- posal for the purpose. dxii REPORT—1880. That Professor A. C. Ramsay and Professor John Milne be a Com- mittee for the purpose of investigating the Earthquake Phenomena of Japan; that Professor Milne be the Secretary, and that the sum of 251. be placed at their disposal for the purpose. That Dr. H. C. Sorby, Professor W. J. Sollas, and Professor William Ramsay be a Committee for the purpose of investigating the Conditions under which ordinary Sedimentary Materials may be converted into Metamorphic Rocks ; that Professor Sollas be the Secretary, and that the sum of 101. be placed at their disposal for the purpose. That Professor W. C. Williamson, and Mr. W. H. Baily be reappointed a Committee for the purpose of Collecting and Reporting upon the Ter- tiary Flora, &c., of the Basalt of the North of Ireland; that Mr. Baily be the Secretary, and that the sum of 20/1. be placed at their disposal for the purpose, on the understanding that a collection of representative Fossils obtained be sent to the British Museum. That Dr. M. Foster, Professor Rolleston, Dr. Pye-Smith, Professor Huxley, Dr. Carpenter, Dr. Gwyn Jeffreys, Mr. F. M. Balfour, Sir Wyville ‘Thomson, Professor Ray Lankester, Professor Allman, and Mr. P. Sladen be a Committee for the purpose of aiding in the maintenance of the Scottish Zoological Station; that Mr. P. Sladen be the Secretary, and that the sum of 50/. be placed at their disposal for the purpose. That Dr. M. Foster, Professor Rolleston, Mr. Dew Smith, Professor Huxley, Dr. Carpenter, Dr. Gwyn Jeffreys, Mr. Sclater, Mr. F. M. Bal- four, Sir Wyville Thomson, Professor Ray Lankester, Professor Allman, and Mr. P. Sladen be reappointed a Committee for the purpose of ar- ranging for the Occupation of a Table at the Zoological Station at Naples ; that Mr. P. Sladen be the Secretary, and that the sum of 75i. be placed at their disposal for the purpose. That Lieut.-Colonel H. H. Godwin-Austen, Dr. G. Hartlaub, Sir J. Hooker, Dr. Giinther, Mr. Seebohm, and Mr. Sclater be a Committee for the purpose of investigating the Natural History of Socotra; that Mr. Sclater be the Secretary, and that the sum of 501. be placed at their dis- posal for the purpose. That Dr. Gwyn Jeffreys, Professor Sir Wyville Thomson, and Mr. Percy Sladen be a Committee for the purpose of a Zoological Exploration “of the Seabed lying north of the Hebrides; that Dr. Gwyn Jeffreys be the Secretary, and that the sum of 501. be placed at their disposal for the purpose. “That Major-General Pitt-Rivers and Mr. A. W. Franks be a Com- mittee for the purpose of issuing a revised edition of the Anthropological Notes and Queries for the .Use of Travellers; that Major-General Pitt- Rivers be the Secretary, and that the sum of 201. be placed at their dis- posal for the purpose. That Dr. Pye-Smith, Professor M. Foster, and Professor Burdon ‘Sanderson be reappointed a Committee for the purpose of investigating ‘the Influence of Bodily Exercise on the Elimination of Nitrogen (the ‘experiments to be conducted by Mr. North); that Professor Burdon ‘Sanderson be the Secretary, and that the sum of 50/1. be placed at their ‘disposal for the purpose. That Professor Rolleston, Professor Allman, General Pitt-Rivers, Mr. J. Evans, and Mr. E. Cunnington be a Committee for the Investigation of Prehistoric Remains in Dorsetshire; that Professor Rolleston be the Secretary, and that the sum of 25]. be placed at their disposal for the purpose. | : ltt tert ia — RECOMMENDATIONS ADOPTED BY THE GENERAL COMMITTEE. lxiii That Mr. Sclater, Mr. Howard Saunders, and Mr. Thiselton-Dyer be a Committee for the purpose of investigating the Natural History of Timor-lant; that Mr. Thiselton-Dyer be the Secretary, and that the sum of 501. be placed at their disposal for the purpose. That Mr. Stainton, Sir John Lubbock, and Mr. E. C. Rye be reappointed a Committee for the purpose of continuing a Record of Zoological Litera- ture; that Mr. Stainton be the Secretary, and that the sum of 100/. be placed at their disposal for the purpose. That Mr. F. Galton, Dr. Beddoe, Mr. Brabrook, Sir George Campbell, Dr. Farr, Mr. F. P. Fellows, Major-General A. Pitt-Rivers, Mr. J. Park Harrison, Mr. James Heywood, Mr. P. Hallett, Professor Leone Levi, Dr. F. A. Mahomed, Dr. Muirhead, Sir Rawson Rawson, Mr. Charles Roberts, and Professor Rolleston be a Committee for the purpose of continuing the collection of observations on the Systematic Examination of Heights, Weights, &c., of Human Beings in the British Empire, and the publi- cation of photographs of the Typical Races. of the Empire; that Mr. Brabrook be the Secretary, and that the sum of 30/. be placed at their disposal for the purpose. That Mr. Bramwell, Dr. A. W. Williamson, Professor Sir William Thomson, Mr. St. John Vincent Day, Dr. C. W. Siemens, Mr. C. W. Merrifield, Dr. Neilson Hancock, Mr. Abel, Captain Douglas Galton, Mr. Newmarch, Mr. E. H. Carbutt, Mr. Macrory, Mr. H. Trueman Wood, Mr. W. H. Barlow, and Mr. A. T. Atchison be reappointed a Committee for the purpose of watching and reporting to the Council on Patent Legislation; that Mr. Bramwell be the Secretary, and that the sum of 5/. be placed at their disposal for the purpose. That a Committee be appointed, consisting of Mr. James Glaisher, Mr. C. W. Merrifield, Mr. F. J. Bramwell, Professor O. Reynolds, Pro- fessor W. Cawthorne Unwin, Mr. Rogers Field, and Mr. A. T. Atchison, to consider and report upon the best means of ascertaining the effective Wind Pressures to which buildings and structures are exposed; that Mr. A. T. Atchison be the Secretary, and that the sum of 5/. be placed at their disposal for the purpose. That Professor Osborne Reynolds, Sir William Thomson, Mr. C. W. Merrifield, and Mr. J. T. Bottomley be a Committee for the purpose of continuing the investigation on the Effect of Propellers on the Steering of Steamships; that Professor Osborne Reynolds be the Secretary, and that the sum of 51. be placed at their disposal for the purpose. Not involving Grants of Money. That the Committee, consisting of Professor Sir William Thomson, Professor Tait, Dr. C. W. Siemens, Mr. F. J. Bramwell, and Mr. J. T. Bottomley, for continuing secular experiments upon the Elasticity of Wires be reappointed ; and that Mr. J. T. Bottomley be the Secretary. That the Committee, consisting of Mr. David Gill, Professor G. Forbes, Mr. Howard Grubb, and Mr. C. H. Gimingham, be reappointed to consider the question of improvements in Astronomical Clocks; and that Mr. David Gill be the Secretary. -That the Committee, consisting of the Rev. Dr. Haughton and Mr. B. Williamson, for the calculation of Tables of Sun-heat Coefficients be reappointed for the. purpose of completing their report; and that Dr. Haughton be the Secretary. WT ek: ‘ lxiv REPORT— 1880. That the Committee, consisting of Professor A. S. Herschel, Professor W. E. Ayrton, Professor P. M. Duncan, Professor G. A. Lebour, Mr. J, T. Dunn, and Professor J. Perry, be reappointed for the purpose of pre- paring a final report on experiments to determine the Thermal Con-. ductivities of certain Rocks, showing especially the geological aspects of the investigation ; and that Professor A. S. Herschel be the Secretary. That the Committee, consisting of Professor W. E. Ayrton, Dr. O. J. Lodge, Mr. J. E. H. Gordon, and Mr. J. Perry, be reappointed for the: purpose of accurately measuring the specific inductive capacity of a good Sprengel Vacuum, and the specific resistance of gases at different pres- sures ; and that Professor W. EH. Ayrton be the Secretary. That Sir William Thomson, Professor Roscoe, Dr. J. H. Gladstone, and Dr. Schuster be a Committee for the purpose of collecting informa- tion with regard to Meteoric Dust, and to consider the question of undertaking regular observations in various localities; and that Dr. Schuster be the Secretary. That the Committee, consisting of Professor G. Forbes, Professor W. G. Adams, and Professor W. E. Ayrton, be reappointed for the pur- pose of improving an instrument for detecting the presence of Fire-damp in Mines ; and that Professor G. Forbes be the Secretary. That the Committee, consisting of Captain Abney, Professor W. G. Adams, and Professor G. C. Foster, be reappointed to carry out an in- vestigation for the purpose of fixing a Standard of White Light; and that Captain Abney be the Secretary. That the Committee, consisting of Mr. Spottiswoode, Professor G. G. Stokes, Professor Cayley, Professor H. J. S. Smith, Professor Sir William Thomson, Professor Henrici, Lord Rayleigh, and Mr. J. W. L. Glaisher, on Mathematical Notation and Printing be reappointed; and that Mr. J. W. L. Glaisher be the Secretary. That the Committee, consisting of Professor Cayley, Professor F. Fuller, Mr. J. W. L. Glaisher, the Rev. R. Harley, Mr. R. B. Hayward, Professor Henrici, Dr. T. A. Hirst, Mr. C. W. Merrifield, Professor Bar- tholomew Price, Professor H. J. S. Smith, Mr. W. Spottiswoode, Mr.. G. Johnstone Stoney, Professor Townsend, Mr. J. M. Wilson, and Dr. Wormell, be reappointed to consider and report upon the subject of Geometrical Teaching, and particularly upon the Syllabuses prepared. under the authority of the Association for the Improvement of Geome- trical Teaching ; and that Mr. C. W. Merrifield be the Secretary. That the Committee, consisting of Professor Cayley, Professor G. G.. Stokes, Professor H. J. S. Smith, Professor Sir William Thomson, Mr. James Glaisher, and Mr. J. W. L. Glaisher, on Mathematical Tables be reappointed ; and that Mr. J. W. L. Glaisher be the Secretary. That Mr. W. M. Hicks be requested to prepare a report upon recent Progress in Hydrodynamics. That the Committee, consisting of Professor G. C. Foster, Professor W. G. Adams, Professor R. B. Clifton, Professor Cayley, Professor J. D. Everett, Lord Rayleigh, Professor G. G. Stokes, Professor Balfour Stewart, Mr. Spottiswoode, and Professor P. G. Tait, be reappointed for the purpose of endeavouring to procure Reports on the progress of the chief branches of Mathematics and Physics; and that Professor G. C. Foster be the Secretary. That Professors J. Prestwich, T. M‘K. Hughes, W. Boyd Dawkins, and T. G. Bonney, the Rev. H. W. Crosskey, Dr. Deane, and Messrs. C. H. De RECOMMENDATIONS ADOPTED BY THE GENERAL COMMITTEE. lxv Rance, G. H. Morton, D. Mackintosh, R. H. Tiddeman, J. H. Lee, James Plant, W. Pengelly, W. Molyneux, H. G. Fordham, and W. Terrill be reappointed a Committee for the purpose of recording the position, height above the sea, lithological characters, size, and origin of the Erratic Blocks of England, Wales, and Ireland, reporting other matters of in- terest connected with the same, and taking measures for their preser- vation; and that the Rev. H. W. Crosskey be the Secretary. That Mr. J. A. Harvie Brown, Mr. J. Cordeaux, and Professor New- ton be a Committee for the purpose of obtaining (with the consent of the Master and Brethren of the Trinity House and of the Commissioners of Northern Lights) observations on the Migration of Birds at Light- houses and Lightships, and of reporting upon the same at York in 1881; and that Mr. Cordeaux be the Secretary. That Mr. C. Spence Bate and Mr. J. Brooking Rowe be reappointed a Committee for the purpose of completing the Exploration of the Marine Zoology of South Devon; and that Mr. Spence Bate be the Secretary. That Professor Leone Levi, Mr. Stephen Bourne, Mr. Brittain, Dr. Hancock, Professor Jevons, and Mr. F. P. Fellows be a Committee for the purpose of inquiring into and reporting on the present appropriation of wages and other sources of income, and considering how far it is con- sonant with the economic progress of the people of the United Kingdom ; and that Professor Leone Levi be the Secretary. That Mr. James Heywood, Mr. Shaen, Mr. Stephen Bourne, Mr. Robert Wilkinson, the Rev. W. Delany, Mr. Maskelyne, M.P., Dr. Sylvanus Thompson, Miss Lydia H. Becker, Mr. E. M. Hance, and Dr. Gladstone, with power to add to their number, be a Committee for the purpose of reporting on the manner in which Rudimentary Science should be taught, and how examinations should be held therein, in EHle- mentary Schools; and that Dr. J. H. Gladstone be the Secretary. Communications ordered to be printed in extenso in the Annual Report of the Association. That Professor W. G. Adams’s paper, ‘On the Comparison of De- clination Magnetographs at various places,’ be printed i eaxtenso in the Report. That Mr. Whitaker’s ‘List of Works on the Geology, Mineralogy, and Paleontology of Wales’ be printed in extenso in the Report. That Dr. Dobson’s paper, on ‘ Additions to our Knowledge of the Chiroptera,’ be printed in extenso in the Report. That the paper by Dr. Gwyn Jeffreys, ‘On the French Deep-sea Exploration in the Bay of Biscay,’ be printed in extenso in the Report. That the paper by Mr. Stephen Bourne, on ‘ Recent Revival in Trade,’ be printed in eatenso in the Report. That the paper by Mr. C. H. Perkins, on ‘ Anthracite Coal,’ be printed in ewtenso in the Report. 1880. parmes d lxvi REPORT—1880. ~ Synopsis of Grants of Money appropriated to Scientific Purposes by the General Committee at the Swansea Meeting in August and September 1880. The Names of the Members who are en- titled to call on the General Treasurer for the respective Grants are prefixed. A.—Mathematics and Physics. £ Darwin, Mr. G. H.—Lunar Disturbance of Gravity ............ 30 Everett, Prof—Underground Temperature............:0..eseeeeee 20 Foster, Prof. G. Carey.—Electrical Standards .................. 100 Glaisher, Mr. James—Luminous Meteors ...............ceeeee eee 15 Joule, Dr.—Mechanical Equivalent of Heat .....,............... 40 Lodge, Dr. O.—High Insulation Key .............c.cececesosceeees 5 Sylvester, Prof.—Fundamental Invariants ............0.seceeeees 40 Thomson, Sir William.—Seismic Experiments ................0+ 30 Thomson, Sir William.—Tidal Observations ......... 10 Thomson, Mr. J. M.—Inductive Capacity of eypidis’ ‘afd ere 6, is... 3. ss e 10 B.—Chemistry. Dewar, Prof.—Spectrum Analysis.............s.sesseeseeseceeeceeees 10 Gladstone, Dr.—Specific Refractions ............cesseeceeceeees ees 10 C.—Geology. Paosicam, Prof P. M.——Fassil Poly zon, 0.10 ccsecbncsecneeoececes nnn 10 Evans, Mr. J.—Geological Record ...............scecesseeeneeee ees 100 Hull, Prof. E.—Underground Waters .. ...............e0008 sean es) ED Ramsay, Prof. A. C._—Harthquakes in Japan .............0...0005 25 Sorby, Dr.—Metamorphic Rocks ................sscsecsessseseeoeees 10 Williamson, Prof. W. C.—Tertiary Flora ....................000 20 D.—Biology. Foster, Dr. M.—Scottish Zoological Station .............0.ee0e0 50 Foster, Dr. M.—Naples Zoological Station ...............cecseeeee 75 Godwin-Ansten, Lieut.-Col—Natural History of Socotra...... 50 Carried forward 35: Se orerckanccdes aceeeeessastncee ice sO HO SS ey eer eS Sisk o (ie Sa eS =) OS Scoocooo eo o® Oo Co oO oooe oo Clooo SYNOPSIS OF GRANTS OF MONEY. lxvii £ 3 d. SUT is eee ee 670 0 0 Jeffreys, Mr. J. Gwyn.—Exploration of Sea-bed North of the MELE RNR nc ee daida. Asn SIBAILU BS agVi los thes AUCaiDs cea der ndeoes +05 seanee 50 0 0 Pitt-Rivers, General—Anthropological Notes ......... ange *O Pye-Smith, Dr.—Klimination of Nitrogen during Bodily ee en cere te eine os srostinns setisavedaeecesetce sss ses 50 0 0 Rolleston, Prof.—Prehistoric Remains in Dorsetshire ......... 25 0 0 Sclater, Mr.—Natural History of Timor-Lant ...............+0 50 0 0 Stainton, Mr.—Zoological Record ...........ceescesasceeeseeeeeces 100 0 0 F.— Economic Science and Statistics. Galton, Mr. F.—KHstimation of Weights and Heights of PEARL PER DITNTR oc cielo ta slgldc gna 80. w'ah > wg aides sve es'naa Galen voor 30 0 0 G.—Mechanies. Bramwell, Mr.—Patent Laws.. Mi bieissicasn mae irea pili tO Glaisher, Mr. James.—Wind eee on s Baaiiigs PER a: Oe OG Reynolds, Prof. Osborne.—Steering of Steamships ............ 5 0 0 £1010 0 0 The Annual Meeting in 1881. The Meeting at York will commence on Wednesday, August 31, 1881. Place of Meeting in 1882. The Annual Meeting of the Association in 1882 will be held at Southampton. d2 lxvili REPORT—1 880. ~ General Statement of Sums which have been paid on Account oF Grants for Scientific Purposes. £8. d. 1834. Tide Discussions ..... aiscewe 20 0 0 1835. Tide Discussions ..........-.0++ ie 0 0 British Fossil Ichthyology ... 105 0 0 ai67 0 0 1836. Tide Discussions ..... peters oo: OO British Fossil Ichthyology ....105 0 0 Thermometric Observations, Os. 3 e eo He COC ESSERE OCEERELE 50 0 0 Experiments on long-con- GUMNME VCR ee sss vescp ep etens Wid aa 0 FAA AOC i eiewte peinivaints soosentt SES a0 Refraction Experiments ...... 1b 0) 40 Munnar NgbatiOI...sccc..scseee ee 60 0 0 Thermometers .......+ teens goon +15: 66 0 ~ £435 0 0 1837 Tide Discussions ......... septs OSe eal Chemical Constants ............ 24 13 TBH ATAINTLALON cp ccecceconsscenee 70 O Observations on Waves ...... 100 12 MiGestap DTristol ete ets oveese 150 0 Meteorology and Subterra- nean Temperature............ 93 3 Vitrification Experiments ... 150 0 Heart Experiments ............ 8 4 Barometric Observations...... 30 (0 BATOMECHETS 31 vocneuscteave suseese 11 18 £922 12 1838. Tide Discussions ............... 29 0 0 British Fossil Fishes ......... 100 0 O Meteorological Observations and Anemometer Caries UGE), ap aaaenencoedeacorace ee LOO 5 Ola O Cast Iron (Strength of) . 60 0 0 Animal and Vegetable Sub- stances (Preservation of)... 19 1 10 Railway Constants ............ 41 12 10 Bristol UNidedssacwsswseescssesrece =, 100:..:0- <0 Growth of Plants ............ <0 “O- Earthquake Shocks ....... eccectplig, cae OF INCTIGVEOISONS + ..08s-ascnesdeseeees 6 0 0 Veins and Absorbents ........ 3 0 0O Mud in Rivers ...... Booeposnac 5 0 OQ GENERAL STATEMENT. Ra CE Marine Zoology ...soccersecceves - 1512 8 Skeleton Maps .......e.000. save, 20.0) 0 Mountain Barometers ......... 618 6 Stars (Histoire Céleste) ...... 18 0 0 Stars (Lacaille) .....c..s00ssse0e. 79 5, O Stars (Nomenclature of )...... 1719 6 Stars (Catalogue of).........00 40 0 0 Water on Tron wissssecsssesseeee 50 0 0 Meteorological Observations BUIMMETNESS | .,..2c00ys0eceeeds 20 0 0 Meteorological Observations (reduction Of) ........+s000 . 26 0 0 Fossil Reptiles ..........cssseeee 50 0 0 Foreign Memoirs .............06 62 0 6 Railway Sections ............... 38 1 0 Forms of Vessels. ...........0006 193 12 0 Meteorological Observations at Plymouth ..,.,.,....seses0 55 0 0 Magnetical Observations...... 6118 8 Fishes of the Old Red Sand- PRIMM Mar cncelscsscacecssscaseveess 100 0 0 Mides ab Leith | ..2653 6 c0cc.050 50 0 0 Anemometer at Edinburgh... 69 1 10 ‘Tabulating Observations...... 9 6 3 Races of Men..............5...006 5 0 0 Radiate Animals. ............... 2 0 0 £1235 10 11 1842. Dynamometric Instruments... 113 11 2 Anoplura Britannie ............ 5212 0 Tides at Bristol.............00.0 59 8 O Gases on Light .. ..........0000 30 14 7 Chronometers ......scesesseeees 2617 6 Marine Zoology......s.cecsseseees 15 0 British Fossil Mammailia...... 100 0 0 Statistics of Education ...... 20 0 0 Marine Steam-vessels’ En- ETGLGS) » seecipedneedassseeeerese dae 28 0 0 Stars (Histoire Céleste) ...... 59 0 O Stars (Brit. Assoc. Cat. of)... 110 0 0 “Railway Sections ...........s006 161 10 O British Belemnites ............ 50 0 0 Fossil Reptiles (publication of Report) ..... Beenie Sesse dhs 210 0 0 Forms of Vessels ............005 180 0 0 “Galvanic Experiments on OCS ewasavicdvasese-sarsas0es 5 8 6 Meteorological Experiments at Plymouth ................6. 68 0 0 ‘Constant Indicator and Dyna- mometric Instruments ...... 90 0 0 Force of Wind ............... . 10 0 0 Light on Growth of Seeds .. 8 0 O Vital Statistics 00.0.0... ceeee 50 0 0 Vegetative Power of Seeds... 8 1 11 Questions on Human Race... 7 9 O ; £1449 17 8 | ee 1843. Revision of the Nomenclature POMS, c osvscevvdersnecsenes - 2 0 0 ar nF Reduction of Stars, British Association Catalogue ...... 25 0 0 Anomalous Tides, Frith of Worth. » ie..svae.sietveceadiass 120 0 0 Hourly Meteorological Obser- vations at Kingussie and TRVOTIESS') nscascccwesesuswad 7712 8 Meteorological Observations at Plymouth .occsccsscssccees 55 0 0 Whewell’s Meteorological Anemometer at Plymouth. 10 0 0 Meteorological Observations, Osler’s Anemometer at Ply- mouth ....... Lge doscbcog nano 20 0 0 Reduction of Meteorological Observations .....e0.ceeeeseee 30 0 0 Meteorological Instruments and Gratuities ......606. 6 39 6 +O Construction of Anemometer at Inverness ..........ceseesee 5612 2 Magnetic Co-operation......... 10 $10 Meteorological Recorder for Kew Observatory .......60006 50 0 0 Action of Gases on Light...... 18 16 1 Establishment at Kew Obser- vatory, Wages, Repairs, Furniture, and Sundries... 133 4 7 Experiments by Captive Bal- TGONS)E 5-7 - sakhoul vs sbpeaenee 81 8 0 Oxidation of the Rails of Rail- WAY Sinnb. si5csd.cecsnetedvodd. sees 20 0 9 Publication of Report on Fos- sil’ Reptiles: ;..........c 20s 100 0 © Essential Oils............ssseeeees 30 0 0 Mathematical Tables ......... 100 0 0 Gaussian Constants .........00 10 0 0 Sub-Wealden Explorations... 25 0 0 Underground Temperature... 150 0 0 Settle Cave Exploration ...... bo», 0) (6 Fossil Flora, Ireland............ 20 0 0 Timber Denudation and Rain- LA eee cecscuesennetsetessassss 20 0 0 Luminous Meteors............++. 30 0 0 £1685 0 0 1874. Zoological Record.............. 100 0 OG Chemistry Record..........2006+ 100 0 0 Mathematical Tables ......... 100 0 O Elliptic Functions.............++ 100 0 6 Lightning Conductors ......... 10 0 0 Thermal Conductivity of ROCKS etcbeenccsceresiscievescsen's 10 0 6 Anthropological Instructions, RiCattespensacwebececeueb ori smebestcc 50 0 G6 Kent’s Cavern Exploration... 150 0 0 Luminous Meteors ............ 30 0 0 Intestinal Secretions ......... 15 0 0 British Rainfall...............4.. 100 0 0 Essential Oils...........0sseee0es LOP"O* 10 Sub-Wealden Explorations... 25 0 0 | Settle Cave Exploration ...... 50 0 0 | Mauritius Meteorological Re- Seanchineceycncapgarr assesses 100 0 0 Magnetization of Iron ......... 20 0 0 Marine Organisms............... 30° 0 0 Fossils, North-West of Scot- TERE! --Sooqneeendeuaeeeeaaceneeare 210 0 Physiological Action of Light 20 0 0 Trades Unions .........csesseees 25 0 0 Mountain Limestone-Corals 25 0 0 Hrratic Blocks ...........:.0+0+ 10 0 0 Dredging, Durham and York- shire CoastS .......cesereeseee 28: br, .O High Temperature of Bodies 30 0 0 Siemens’s Pyrometer ......... 3); 6.1.0 Labyrinthodonts of Coal- MEaSULES,....ecceeereeeeseeeeees 5) 30 £1151 16 O 1875. Eliptic Functions ............+.+ 100 0 0 Magnetization of Iron ......... 20 0 0 British Rainfall ............0sse» 120 0 0 Luminous Meteors ............ 30 0 0 | Chemistry Record.............+ 100 0 O Ixxv ixxvi £ 3. d. ‘Specific Volume of Liquids... 25 0 0 Estimation of Potash and Phosphoric ACid..........0..0+ 10 0 O Isometric Cresols ............006 20 0 O Sub-Wealden Explorations... 100 0 0 Kent’s Cavern Exploration... 100 0 0 Settle Cave Exploration ...... 50 0 O Earthquakes in Scotland...... 15 0 0 Underground Waters ......... 10 0 0 Development of Myxinoid IRKSIASS: . cerencuosebeaccessnor nero 20 0 0 Zoological Record.............+ 100 0 O Instructions for Travellers... 20 0 0 Intestinal Secretions ......... 20 0 0 Palestine Exploration ......... 100 0 O £960 0 0 1876. Printing Mathematical Tables 159 4 2 British Rainfall...............0 100 0 O Olim’seaweterce: ces accmuecscceas 915 0 Tide Calculating Machine ... 200 0 0 Specific Volume of Liquids... 25 0 0 Isomeric Cresols ..........00006 10 0 0 Action of Ethyl Bromobuty- rate or Ethyl Sodaceto- ACCLALE s wespeunanedae Seana essex 5 0 0 Estimation of Potash and Phosphoric Acid............0 13 0 0 Exploration of Victoria Cave, CULE: 5.t2sccendgeneeemaneine chs. 100 0 0 ‘Geological Record............0«: 100 0 0O Kent’s Cavern Exploration... 100 0 0 Thermal Conductivities of ROCKS). assensovecantsstorcc oxt 10 0 0 Underground Waters ......... 10 0 0 Harthquakes in Scotland...... 110-0 Loological Record...........0068 100 0 O WIOSEMBIM Ch oaasssecstescstdevarees 5 0 0 Physiological Actionof Sound 25 0 0 Zoological Station..........0.-.. cor 070 Intestinal Secretions ......... 15 0 0 Physical Characters of Inha- bitants of British Isles...... 1315 0 Measuring Speed of Ships ... 10 0 0 Effect of Propeller on turning of Steam Vessels ............ 5 0 0 £1092 4 2 1877. Liquid Carbonic Acids in Minerals aued..\. dxcss. cessor 20 0 0 Elliptic Functions ............ 250 0 0 ‘Thermal Conductivity of ROGKS ment ceses as casnesdecteree G) ia ‘Zoological Record........... se. 100 O 0 Kent’s|Caverit (n.0s)scecasesareen 100 0 0 Zoological Station at Naples 75 0 0 Luminous Meteors ,........... 30 0 0 ‘Elasticity of Wires ............ 100 0 0 -Dipterocarpz, Report on...... 20 0 0 REPORT—] 880. ‘5 aS le Mechanical Equivalent of Hatin sa. atevesrowen dseyoad eee 35 0 0 Double Compounds of Cobalt and. Nickel -s4.00--ss0ssveevates 8 0 0 Underground Temperatures 50 0 0 Settle Cave Exploration ...... 100 0 0 Underground Waters in New Red Sandstone ........ ...... 10 0 0 Action of Ethyl Bromobuty- rate.on Ethyl Sodaceto- ACETAL 2.3. 0cisssecsvencsedsns 10 0 0 British Earthworks ..........+. 25 0 0 Atmospheric Elasticity in INGid...ceasacessesedvsvecwosds 145 0 0 Development of Light from Coal-gas Avx..sit. iene sates 20 0 0 Estimation of Potash and Phosphoric Acid..............- 118 0 Geological Record........+...00 100 0 0 Anthropometric Committee 34.0 0 Physiological Action of Phos- phoric Acids &€is.s.0006seseees 15 0 0 £1128 9° 7 1878. Exploration of Settle Caves 100 0 0 Geological Record............... 100 0 0 Investigation of Pulse Pheno- mena by means of Syphon IRCCOEG OT «cece sc -- ee -ncree cman 10 0 0 Zoological Station at Naples 75 0 0O Investigation of Underground Wiah@Tes vanns-ccecc-e eee nenaees 15 0 0 Transmission of Electrical Impulses through Nerve StUruchure.- -- .cescsccncassaceda OU On O Calculation of Factor Table of Fourth Million............ 100 0 0 Anthropometric Committee... 66 0 0 Chemical Composition and Structure of less known Alkaloids............ Neen aereaee 25 0 0 Exploration of Kent’s Cavern 50 0 0 Zoological Record ........+...006 100 0 90 Fermanagh Caves Exploration 15 0 0 Thermal Conductivity of ROCKS: .scccste reaver cocme nse spare 416 6 Luminous Meteors............06+ 10 0 0 Ancient Earthworks ...........+ 25 0 0 £725 16 6 1879. Table at the Zoological Station, Naples ............... 75 0 0 Miocene Flora of the Basalt of the North of Ireland 20 0 0 Illustrations for a Monograph on the Mammoth ....... “Se 0 0 Reeord of Zoological Litera- WEY Eeteteerveds sss oc s ADDRESS. ADDRESS BY ANDREW CROMBIE RAMSAY, Esq, LL.D., F R.S., V.P.G.S., Director-General of the Geological Survey of the United Kingdom, and of the Museum of Practical Geology, PRESIDENT. On THE RECURRENCE OF CERTAIN PHENOMENA IN GEOLOGICAL Tir. Ty this address I propose to consider the recurrence of the same kind of incidents throughout all geological time, as exhibited in the various for- mations and groups of formations that now form the known parts of the external crust of the earth. This kind of investigation has for many years forced itself on my attention, and the method I adopt has not here- tofore been attempted in all its branches. Jn older times, Hutton and Playfair, in a broad and general manner, clearly pointed the way to the doctrine of uniformity of action and results, throughout all known geo- logical epochs down to the present day; but after a time, like the prophets of old, they obtained but slight attention, and were almost forgotten, and the wilder cosmical theories of Werner more generally ruled the opinions of the geologists of the time. Later still, Lyell followed in the steps of Playfair, with all the advantages that the discoveries of William Smith afforded, and aided by the labours of that band of distinguished geologists, Sedgwick, Buckland, Mantell, De la Beche, Murchison, and others, all of whom some of us knew. Notwithstanding this new light, even now there still lingers the relics of the belief (which some of these geologists also maintained), that the physical phenomena which produced the older strata were not only different in kind, but also in degree from those which now rule the external world. Oceans, the waters of which attained a high temperature, attended the formation of the primitive crystalline rocks. Volcanic eruptions, with which those of modern times are comparatively insignificant, the sudden upheaval of great mountain chains, the far more rapid decomposition and degradation of rocks, and, as a consequence, the ‘more rapid deposition of strata formed from their waste—all these were assumed as certainties, and still linger in some parts of the world among living geologists of deservedly high reputation. The chief object of this 1880. B 2 REPORT—1880. address is, therefore, to attempt to show, that whatever may have been the state of the world long before geological history began, as now written in the rocks, all known formations are comparatively so recent in geologi- cal time, that there is no reason to believe that they were produced under physical circumstances differing either in kind or degree from those with which we are now more or less familiar. It is unnecessary for my present purpose to enter into details con- nected with the recurrence of marine formations, since all geologists know that the greater part of the stratified rocks were deposited in the sea, as proved by the molluscs and other fossils which they contain, and the order of their deposition and the occasional stratigraphical breaks in succession are also familiar subjects. What I have partly to deal with now, are exceptions to true marine stratified formations, and after some other important questions have been considered, I shall proceed to discuss the origin of various non-marine deposits from nearly the earliest known time down to what by comparison may almost be termed the present day. Metamorphism. All, or nearly all, stratified formations have been in a sense meta- morphosed, since, excepting certain limestones, the fact of loose incoherent sediments having been by pressure and other agencies turned into solid rocks constitutes a kind of metamorphism. This, however, is only a first step toward the kind of metamorphism the frequent recurrence of which in geological time I have now to insist upon, and which implies that con- solidated strata have undergone subsequent changes of a kind much more remarkable. Common stratified rocks chiefly consist of marls, shales, slates, sand- stones, conglomerates, and limestones, generally distinct and definite; but not infrequently a stratum, or strata, may partake of the characters in varied proportions of two or more of the above-named species. It is from such strata that metamorphic rocks have been produced, exclusive of the. metamorphism of igneous rocks, on which I will not enter. These may be looked for in manuals of geology, and sometimes they may be found in them. As a general rule, metamorphic rocks are apt to be much contorted, not only on a large scale, but also that the individual layers of mica quartz and felspar in gneiss are bent and folded in a great number of minute convolutions, so small that they may be counted by the hundred in a foot or two of rock. Such metamorphic rocks are often associated with masses of granite both in bosses and in interstratified beds or layers, and where the metamorphism becomes extreme it is often impossible to draw a boundary line between the gneiss and the granite; while, on the other hand, it is often impossible to draw any true boundary between gneiss (or other metamorphic rocks) and the ordinary strata that have OO ADDRESS. 3 partly undergone metamorphism. Under these circumstances, it is not surprising that when chemically analysed, there is often little difference in the constituents of the unmetamorphosed and the metamorphosed rock. This is a point of some importance in relation to the origin and non- primitive character of gneiss and other varieties of foliated strata, and also of some quartzites and crystalline limestones. I am aware that in North America formations consisting of meta- morphic rocks have been stated to exist of older date than the Laurentian gneiss, and under any circumstances it is obvious that vast tracts of pre- Laurentian land must have existed in all regions, by the degradation of which, sediments were derived wherewith to provide materials for the de- position of the originally unaltered Laurentian strata. In England, Wales, and Scotland attempts have also been made to prove the presence of more ancient formations, but I do not consider the data provided sufficient to warrant any such conclusion. In the Highlands of Scotland, and in some of the Western Isles, there are gneissic rocks of pre-Cambrian age, which, since they were first described by Sir Roderick Murchison in the North-west Highlands, have been, I think justly, considered to belong to the Laurentian series, unconformably underlying Cambrian and Lower Silurian rocks, and as yet there are no sufficient grounds for dissenting from his conclusion that they form the oldest known rocks in the British Islands. It is unnecessary here to discuss the theory of the causes that produced the metamorphism of stratified rocks, and it may be sufficient to say, that under the influence of deep underground heat, aided by moisture, sand- stones have been converted into quartzites, limestones have become crystalline, and in shaley, slaty, and schistose rocks, under like circum- stances, there is little or no development of new material, but rather, in the main, a re-arrangement of constituents according to their chemical affinities in rudely crystalline layers, which have very often been more or less developed in pre-existing planes of bedding. The materials of the whole are approximately the same as those of the unaltered rock, but have been re-arranged in layers, for example, of quartz, felspar, and mica, or of hornblende, &c., while other minerals, such as schorl and garnets, are of not infrequent occurrence. It has for years been an established fact that nearly the whole of the mountain masses of the Highlands of Scotland (exclusive of the Laurentian, Cambrian, and Old Red Sandstone formations), mostly consist of gneissic rocks of many varieties, and of quartzites and a few bands of crystalline limestone, which, from the north shore to the edge of the Old Red Sand- stone, are repeated again and again in stratigraphical convolutions great _and small. Many: large bosses, veins, and dykes of granite are asso- ciated with these rocks, and, as already stated, it sometimes happens that it is hard to draw a geological line between granite and gneiss and vice wersd. ‘These rocks, once called Primary or Primitive, were first proved by Sir Roderick: Murchison to be of Lower Silurian age, thus revolu- B2 4 REPORT—1880. tionising the geology of nearly one-half of Scotland. To the same age belongs by far the greater part of the broad hilly region of the south of Scotland that lies between St. Abb’s Head on the east and the coast of Ayrshire and Wigtonshire on the west. In the south-west part of this district, several great masses of granite rise amid the Lower Silurian rocks, which in their neighbourhood pass into mica-schist and even into fine-grained gneiss. In Cornwall the occurrence of Silurian rocks is now well known. They are of metamorphic character, and partly associated with granite ;, and at Start Point, in South Devonshire, the Silurian strata have been metamorphosed into quartzites. In parts of the Cambrian areas, Silurian rocks in contact with granite have been changed into crystalline hornblendic gneiss, and in Anglesey there are large tracts of presumed Cambrian strata, great part of which have been metamorphosed into chlorite and mica-schist and gneiss, and the same is partly the case with the Lower Silurian rocks of the centre of the island, where it is almost impossible to disentangle them from the associated granite. In Ireland similar metamorphic rocks are common, and, on the authority of Prof. Hull, who knows them well, the following statements are founded :—‘ Metamorphism in Ireland has been geographical and not stratigraphical, and seems to have ceased before the Upper Silurian period. ‘The epoch of greatest metamorphism appears to have been that which intervened between the close of the Lower Silurian period and the commencement of the Upper Silurian, taking the formations in ascending order. ‘It is as yet undecided whether Laurentian rocks occur in Ireland. There are rocks in north-west Mayo very like those in Sutherlandshire, but if they are of Laurentian age they come directly under the meta- morphosed Lower Silurian rocks, and it may be very difficult to separate them. ‘Cambrian purple and green grits are not metamorphosed in the coun- ties of Wicklow and Dublin, but the same beds at the southern extremity of County Wexford, near Carnsore Point, have been metamorphosed into mica-schist and gneiss. ‘In the east of Ireland the Lower Silurian grits and slates have not been metamorphosed, except where in proximity to granite, into which they insensibly pass in the counties of Wicklow, Dublin, Westmeath, Cavan, Longford, and Down; but in the west and north-west of Ireland they have been metamorphosed into several varieties of schists, horn- blende-rock, and gniess, or foliated granite.’ It would be easy to multiply cases of the metamorphism of Silurian rocks on the continent of Europe, as, for example, in Scandinavia, and in the Ural Mountains, where, according to Murchison, ‘by following its masses upon their strike, we are assured that the same zone which in one ADDRESS. 5 tract has a mechanical aspect and is fossiliferous, graduates in another parallel of latitude into a metamorphic crystalline condition, whereby not only the organic remains, but even the original impress of sedimentary origin are to a great degree obliterated.’ The same kind of phenomena are common in Canada and the United States; and Medlicott and Blan- ford, in ‘The Geology of India,’ have described the thorough metamor- phism of Lower Silurian strata into gneiss and syenitic and hornblende schists. In Britain, none of the Upper Silurian rocks have undergone any serious change beyond that of ordinary consolidation, but in the Eastern Alps at Gratz, Sir Roderick Murchison has described both Upper Silurian and Devonian strata interstratified with separate courses of metamorphic chloritic schist. Enough has now been said to prove the frequent occurrence of metamorphic action among Cambrian and Lower and Upper Silurian ‘strata. If we now turn to the Devonian and Old Red Sandstone strata of England and Scotland, we find that metamorphic action has also been at work, but in a much smaller degree. In Cornwall and Devon, five great bosses of granite stand out amid the stratified Silurian, Devonian, and Carboniferous formations. Adjoining or near these bosses the late Sir Henry De la Beche remarks, that ‘in numerous localities we find the coarser slates converted into rocks resembling mica-slate and gneiss, a fact particularly well exhibited in the neighbourhood of Meavy, on the south-east of Tavistock,’ and ‘near Camelford we observed a fine arena- ceous and micaceous grauwacke turned into a rock resembling mica-slate near the granite.’ Other cases are given by the same author, of slaty strata turned into mica-schist and gneiss in rocks now generally con- sidered to be of Devonian age. The Devonian rocks and Old Red Sandstone are of the same geological age, though they were deposited under different conditions, the first being of marine, and the latter of fresh-water, origin. The Old Red Sandstone of Wales, England, and Scotland has not, as far as I know, suffered any metamorphism, excepting in one case in the north-east of Ayrshire, near the sources of the Avon Water, where a large boss of granite rises through the sandstone, which all round has been rendered crystalline with well-developed crystals of felspar. On the continent of Europe, a broad area of Devonian strata lies on both banks of the Rhine and the Moselle. Forty years ago, Sedgwick and Murchison described the crystalline quartzites, chlorite, and micaceous slates of the Hundsruck and the Taunus, and from personal observation I know that the rocks in the country on either side of the Moselle are, in places, of a foliated or semi-foliated metamorphic character. In the Alps also, as already noticed, metamorphic Devonian strata occur interstratified with beds of metamorphic schists, and, Sir Roderick adds, ‘we have ample data to affirm, that large portions of the Hastern Alps . . . are 6 REPORT—-1880. occupied by rocks of true paleozoic age, which in many parts have passed into a crystalline state.’ I know of no case in Britain where the Carboniferous strata have been thoroughly metamorphosed, excepting that in South Wales, beds of coal, in the west of Caermarthenshire and in South Pembrokeshire, gradually pass from so-called bituminous coal into anthracite. The same is the case in the United States, in both instances the Carboniferous strata being exceedingly disturbed and contorted. In the Alps, however, Sir Roderick Murchison seems to have believed that Carboniferous rocks may have been metamorphosed : a circumstance since undoubtedly proved by the occurrence of a coal-measure calamite, well preserved, but otherwise partaking of the thoroughly crystalline character of the gneiss in which it is imbedded, and which was shown to me by the late Prof. Gastaldi, at. Turin. I am well acquainted with all the Permian strata of the British Islands and of various parts of continental Europe, and nowhere, that I have seen, have they suffered from metamorphic action, and strata of this age are, I believe, as yet unknown in the Alps. This closes the list of metamorphism of paleozoic strata. I will not attempt (they are so numerous) to mention all the regions of the world in which Mesozoic or Secondary formations have undergone metamorphic action. In Britain and the non-mountainous parts of France, they are generally quite unaltered, but in the Alps it is different. There, as everyone knows who is familiar with that region, the crystalline rocks in the middle of the chain have the same general strike as the various flanking stratified formations. As expressed by Murchison, ‘as we follow the chain from N.H. to 8.W. we pass from the clearest types of sedimentary rocks, and, at length, in the Savoy Alps, are immersed in the highly altered mountains of Secondary limestone,’ while ‘the meta- morphism of the rocks is greatest as we approach the centre of the chain,’ and, indeed, any one familiar with the Alps of Switzerland and Savoy knows that a process of metamorphism has been undergone by all the Jurassic rocks (Lias and Oolites) of the great mountain chain. "Whether or not any strata of Neocomian and Cretaceous age have been well meta- morphosed in this region I am unable to say ; but it seems to be certain that the Eocene or Lower Tertiary Alpine formation, known as the Flysch, contains beds of black schists which pass into Lydian stone, and also that in the Grisons it has been converted into gneiss and mica-schist, a) fact mentioned by Studer and Murchison. I also have seen in the country north of the Oldenhorn, nummulitic rocks so far foliated that they formed an imperfect gneiss. In Tierra del Fuego, as described by Dareitn; clay slates of early cre- taceous date pass into gneiss and mica-slate with garnets, and in Chonos Islands, and all along the great Cordillera of the Andes of Chili, rocks of Cretaceous or Cretaceo-oolitic age have been metamorphosed into foliated mica-slate and gneiss, accompanied by the presence of granite, syenite, and greenstone. ADDRESS. 7 This ends my list, for I have never seen, or heard, of metamorphic rocks of later date than those that belong to the Hocene series. Hnough, however, has been said to prove, that from the Laurentian epoch onward, the phenomenon of extreme metamorphism of strata has been of frequent recurrence all through Paleozoic and Mesozoic times, and extends even to a part of the Hocene series equivalent to the soft unaltered strata of the formations of the London and Paris basins, which excepting for their fossil contents, and sometimes highly inclined positions, look as if they had only been recently deposited. Volcanoes. The oldest volcanic products of which I have personal knowledge are of Lower Silurian age. These in North Wales consist of two distinct series, the oldest of which, chiefly formed of felspathic lavas and volcanic ashes, lie in and near the base of the Llandeilo beds, and the second, after a long interval of repose, were ejected and intermingled with the strata forming the middle part of the Bala beds. The Lower Silurian rocks of Mont- gomeryshire, Shropshire, Radnorshire, Pembrokeshire, Cumberland and: Westmoreland are to a great extent also the result of volcanic eruptions, and the same kinds of volcanic rocks occur in the Lower Silurian strata of Ireland. I know of no true volcanic rocks in the Upper Silurian series. In the old Red Sandstone of Scotland lavas and volcanic ashes are of frequent occurrence, interstratified with the ordinary lacustrine sedimen- tary strata. Volcanic rocks are also intercalated among the Devonian strata of Devonshire. I know of none in America or on the Continent of Europe. In Scotland voleanic products are common throughout nearly the whole of the Carboniferous sub-formations, and they are found also asso- ciated with Permian strata. Inow come to the Mesozoic or Secondary epochs. Of Jurassic age (lias and Oolites), it is stated by Lyell with some doubt, that true voleanic products occur in the Morea and also in the Apennines, and it seems probable, as stated by Medlicott and Blanford, that the Rajmahal traps may also be of Jurassic age. In the Cordillera of South America, Darwin has described a great series of volcanic rocks intercalated among the Cretaceo-oolitic strata that forms so much of the chain ; and the same author in his ‘ Geological Observations in South America,’ states that the Cordillera has been, probably with some quiescent periods, a source of volcanic matter from an epoch anterior to his Cretaceo-oolitic formation to the present day. In the Deccan volcanic traps rest on Cretaceous beds, and are overlaid by Nummulitic strata, and according to Medlicott and Blanford, these were poured out in the interval between Middle Cretaceous and Lower Eocene times. In Europe the only instance I know of a volcano of Hocene age is 8 REPORT—1880. that of Monte Bolca near Verona, where the volcanic products are asso- ciated with the fissile limestone of that area. The well-preserved relics of Miocene volcanoes are prevalent over many parts of Hurope, such as Auvergne and The Velay, where the volcanic action began in Lower Miocene times, and was continued into the Pliocene epoch. The volcanoes of the Hifel are aiso of the same general age, together with the ancient Miocene volcanoes of Hungary. The volcanic rocks of the Azores, Canaries, and Madeira are of Miocene age, while in Tuscany there are extinct volcanoes that began in late Miocene, and lasted into times contemporaneous with the English Coralline Crag. In the north of Spain also, at Olot in Catalonia, there are perfect craters and cones remaining of volcanoes that began to act in newer Pliocene times and continued in action to a later geological date. To these I must add the great cowlées of Miocene lava, so well known in the Inner Hebrides, on the mainland near Oban, &c., in Antrim in the north of Ireland, in the Faroe Islands, Greenland, and Franz-Joseph Land. It is needless, and would be tiresome, further to multiply instances, for enough has been said to show that in nearly all geological ages volcanoes have played an important part, now in one region, now in another, from very early Paleozoic times down to the present day ; and, as far as my knowledge extends, at no period of geological history is there any sign of their having played a more important part than they do in the epoch in which we live. Mountain Chains. The mountain-chains of the world are of different geological ages, some of them of great antiquity, and some of them comparatively modern. It is well known that in North America the Lower Silurian rocks lie uncomformably on the Laurentian strata, and also that the latter had undergone a thorough metamorphism and been thrown into great anti- clinal and synclinal folds, accompanied by intense minor convolutions, before the deposition of the oldest Silurian formation, that of the Potsdam Sandstone. Disturbances of the nature alluded to imply beyond a doubt that the Laurentian rocks formed a mountain chain of pre-Silurian date, which has since constantly been worn away and degraded by sub-aerial denudation. In Shropshire, and in parts of North Wales, and in Cumberland and Westmoreland, the Lower Silurian rocks by upheaval formed hilly land before the beginning of the Upper Silurian epoch; and it is probable that the Lower Silurian gneiss of Scotiand formed mountains at the same time, probably very much higher than now. However that may be, it is certain, that these mountains formed high land before and during the deposition of the Old Red Sandstone, and the upheaval of the great Scandinavian chain (of which the Highlands may be said to form an out- ADDRESS. 9 lying portion) also preceded the deposition of the Old Red Strata. In both of these mountain regions the rocks have since undergone consider- able movements, which in the main seem to have been movements of elevation, accompanied undoubtedly by that constant atmospheric degra- dation to which all high land is especially subject. The next great European chain in point of age is that of the Ural, which according to Murchison is of pre-Permian age, a fact proved by the Permian conglomerates which were formed from the waste of the older strata. On these they lie quite unconformably and nearly undis- turbed on the western flank of the mountains. In North America the great chain of the Alleghany Mountains under- went several disturbances, the last (a great one) having taken place after the deposition of the Carboniferous rocks, and before that of the New Red Sandstone. The vast mountainous region included under the name of the Rocky Mountains, after several successive disturbances of upheaval, did not attain its present development till after the Miocene or Middle Tertiary epoch. In South America, notwithstanding many oscillations of level recorded by Darwin, the main great disturbance of the strata that form the chain of the Andes took place apparently in post-cretaceous times. The Alps, the rudiments of which began in more ancient times, received their greatest disturbance and upheaval in post-Hocene days, and were again raised at least 5,000 feet (I believe much more) at the close of the Miocene epoch. The Apennines, the Pyrenees, the Carpa- thians, and the great mountain region on the east of the Adriatic and southward into Greece, are of the same general age, and this is also the case in regard to the Atlas in North Africa, and the Caucasus on the borders of Europe and Asia. In the north of India the history of the Great Himalayan range closely coincides with that of the Alps, for while the most powerful known disturbance and elevation of the range took place after the close of the Eocene epoch, a subsequent elevation occurred in post-Miocene times closely resembling and at least equal to that sustained by the Alps at the same period. It would probably not be difficult by help of extra research to add other cases to this notice of recurrences of the upheaval and origin of special mountain chains, some of which I have spoken of from personal knowledge; but enough has been given to show the bearing of this question on the argument I have in view, namely, that of repetition of the same kind of events throughout all known geological time. Salt and Salt Lakes. I now come to the discussion of the circumstances that produced numerous recurrences of the development of beds of various salts (chiefly common rock-salt) in many formations, which it will be seen are to a great extent connected with continental or inland conditions. In com- 10 REPORT——1880. paratively rainless countries salts are often deposited on the surface of the ground by the effect of solar evaporation of moisture from the soil. Water dissolves certain salts in combination with the ingredients of the under- lying rocks and soils, and brings it to the surface, and when solar evaporation ensues the salt or salts are deposited on the ground. This is well known to be the case in and near the region of the Great Salt Lake in North America, and in South America in some of the nearly rainless districts of the Cordillera, extensive surface-deposits of salts of various kinds are common. The surface of the ground around the Dead Sea is also in extra dry seasons covered with salt, the result of evaporation, and in the upper provinces of India (mentioned by Medlicott and Blanford) ‘many tracts of land in the Indo-Gangetic alluvial plain are rendered worthless for cul- tivation by an efflorescence of salt known in the North-West Provinces as Reh,’ while every geographer knows that in Central Asia, from the western shore of the Caspian Sea to the Kinshan Mountains of Mongolia, with rare exceptions nearly every lake is salt in an area at least 3,500 miles in length. This circumstance is due to the fact that all so-called fresh-water springs, and therefore all rivers, contain small quantities of salts in solu- tion only appreciable to the chemist, and by the constant evaporation of pure water from the lakes, in the course of time, it necessarily happens that these salts get concentrated in the water by the effect of solar heat, and, if not already begun, precipitation of solid salts must ensue. The earliest deposits of rock-salt that I know about have been described by Mr. A. B. Wynne of the Geological Survey of India, in his Memoir ‘ On the Geology of the Salt Range in the Punjab.’! The beds of salt are of great thickness, and along with gypsum and dolomitic layers occur in marl of a red colour like our Keuper Marl. This colour I have for many years con- sidered to be, in certain cases, apt to indicate deposition of sediments in inland lakes, salt or fresh, as the case may be, and with respect to these strata in the Punjab Salt Range, authors seem to be in doubt whether they were formed in inland lakes or in lagoons near the seaboard, which at intervals were liable to be flooded by the sea, and in which in the hot seasons salts were deposited by evaporation caused by solar heat. For my argument, it matters but little which of these was the true physical con- dition of the land of the time, though I incline to think the inland lake theory most probable. The age of the strata associated with this salt is not yet certainly ascertained. In ‘The Geology of India’ Medlicott and Blanford incline to consider them of Lower Silurian age, and Mr, Wynne, in his ‘ Geology of the Salt Range,’ places the salt and gypsum beds doubtfally on the same geological horizon. The next salt-bearing formation that I shall notice is the Salina or Onondaga Salt Group of North America, which forms part of the Upper Silurian rocks, and lies immediately above the Niagara Limestone. It is rich in) gypsum and in salt-brine, often of a very concentrated character, ? Many earlier notices and descriptions of the Salt Range might be quoted, but Mr. Wynne’s is enough for my purpose. ADDRESS. 11 ‘which can only be derived from original depositions of salt,’ and it is also supposed by Dr. T. Sterry Hunt to contain solid rock-salt 115 feet in thickness at the depth of 2,085 feet, near Saginaw Bay in Michigan. In the Lower Devonian strata of Russia near Lake Ilmen, Sir R. Murchison describes salt springs at Starai Russa. Sinkings ‘made in the hope of penetrating to the source of these salt springs,’ reached a depth of 600 feet without the discovery of rock salt, ‘and we are left in doubt whether the real source of the salt is in the lowest beds of the Devonian rocks or even in the Silurian system.’ In the United States brine springs also occur in Ohio, Pennsylvania, and Virginia, in Devonian rocks. In Michigan salts are found from the Carboniferous down to the Devonian series; and in other parts of the United States, Western Pennsylvania, Virginia, Ohio, Illinois, and Kentucky, from the lower Coal-measures salts are derived which must have been deposited in inland areas, since even in the depths of inland seas that communicate with the great ocean, such as the Mediterranean and the Red Sea, no great beds of salt can be deposited. Before such strata of salt can be formed, super- saturation must have taken place. In the North of England at and near Middlesbrough two deep bore- holes were made some years ago in the hope of reaching the Coal-measures of the Durham coal-field. One of them at Salthome was sunk to a depth of 1,355 feet. First they passed through 74 feet of superficial clay and gravel, next through about 1,175 feet of red sandstones and marls, with beds of rock-salt and gypsum. The whole of these strata (excepting the clay and gravel) evidently belong to the Keuper marls and sandstones of the upper part of our New Red series. Beneath these they passed through 67 feet of dolomitic limestone, which in this neighbourhood forms the upper part of the Permian series, and beneath the limestone the strata consist of 27 feet of gypsum and rock-salt and marls, one of the beds of rock-salt having a thickness of 14 feet. This bed of Permian salt is of some importance, since I have been convinced for long that the British Permian strata were deposited, not in the sea, but in salt lakes comparable in some respects to the great salt lake of Utah, and in its restricted fauna to the far greater salt lake of the Caspian Sea. The gypsum, the dolomite or magnesian limestone, the red marls covered with rain-pittings, the sun-cracks, and the impressions of footprints of reptiles made in the soft sandy marls when the water was temporarily lowered by the solar evaporation of successive summers, all point to the fact that our Permian strata were not deposited in the sea, but in a salt lake or lakes once for a time connected with the sea. The same may be said of other Permian areas in the central parts of the Continent of Europe, such as Stassfurt and Anhalt, Halle and Altern in Thuringia, and Sperenberg, near Berlin, and also in India.! ' 1 See «Physical Geology and Geography of Great Britain,’ 5th edition, where the question is treated in more detail. ; 12 REPORT—1880. Neither do I think that the Permian strata of Russia, as de- scribed by Sir Roderick Murchison, were necessarily, as he implies, deposited in a wide ocean. According to his view all marine life universally declined to a minimum after the close of the Carboniferous period, that decline beginning with the Permian and ending with the Triassic epoch. Those who believe in the doctrine of evolution will find it hard to accept the idea which this implies, namely, that all the prolific forms of the Jurassic series sprang from the scanty faunas of the Permian and Triassic epochs. On the contrary, it seems to me more rational to attribute the poverty of the faunas of these epochs to accidental abnormal conditions in certain areas, that for a time partially disappeared during the deposition of the continental Muschelkalk which is absent in the British Triassic series. In the whole of the Russian Permian strata only fifty-three species were known at the time of the publication of ‘ Russia and the Ural, Mountains,’ and I have not heard that this scanty list has been subse- quently increased. I am therefore inclined to believe that these red marls, grits, sandstones, conglomerates, and great masses of gypsum and rock- salt were all formed in a flat inland area which was occasionally liable to be invaded by the sea during intermittent intervals of minor depression, sometimes in one area, sometimes in another, and the fauna small in size and poor in numbers is one of the results, while the deposition of beds of salt and gypsum is another. If so, then in the area now called Russia, in sheets of inland Permian water, deposits were formed strictly analogous to those of Central Europe and of Britain, but on a larger scale. Other deposits of salt deep beneath overlying younger strata are stated to occur at Bromberg in Prussia, and many more might be named as lying in the same formation in northern Germany. If we now turn to the Triassic series it is known that it consists of only two chief members in Britain, the Bunter Sandstones and the Keuper or New Red Marls, the Muschelkalk of the Continent being absent in our islands. No salt is found in the Bunter sandstones of England, but it occurs in these strata at Schéningen in Brunswick and also near Hanover. In the lower part of the Keuper series deposits of rock-salt are common in England and Ireland. At Almersleben, near Calbe, rock-salt is found in the Muschelkalk, and also at Erfurt and Slottenheim in Thuringia and at Wilhelmsgliick in Wurtemburg. In other Triassic areas it is known at Honigsen, in Hanover, in middle Keuper beds. In the red shales at Sperenberg and Lieth on the Lower Elbe, salt was found at the depth of 3,000 feet, and at Stassfurth the salt is said to be ‘ several hundred yards thick.’ In Central Spain rock-salt is known, and at Tarragona, Taen, and also at Santander in the north of Spain, all in Triassic strata. Other locali- ties may be named in the Upper Trias, such as the Salzkammergut, Aussee, Hallstatt, Ischl, Hallein in Salzburg, Halle in the Tyrol, and Berchesgaden in Bavaria. ADDRESS. 163 In the Salt Range of mountains in Northern India saliferous strata are referred with some doubt by Medlicott and Blanford to the Triassic strata. In the Jurassic series (Lias and Oolites) salt and gypsum are not uncommon. One well-known instance occurs at Berg in the valley of the Rhone in Switzerland, where salt is derived from the Lias. Salt and gypsum are also found in Jurassic rocks at Burgos in Spain. At Gap in France there is gypsum, and salt is found in the Austrian Alps in Oolitic limestone. In the Cretaceous rocks salt occurs, according to Lartet, at Jebel Usdom by the Dead Sea, and other authorities state that it occurs in the Pyrenees and at Biskra in Africa, where ‘mountains of salt’ are mentioned as of Cretaceous age. The two last-named localities are possibly uncertain : but whether or not this is the case, it is not the less certain that salt has been deposited in Cretaceous rocks, and, judging by analogy, probably in inland areas of that epoch. In the Hocene or Older Tertiary formations, rock-salt is found at Cardona in Spain, and at Kohat in the Punjab it occurs at the base of Nummulitic beds. It is also known at Mandi in India in strata supposed to be of Nummulitic Hocene age. The record does not end here, for a zone of rock-salt lies in Sicily aé the top of the Salina clays in Lower Miocene beds, and in Miocene strata gypsum is found at several places in Spain, while salt also occurs in beds that are doubtfully of Miocene age (but may be later) at Wie- litzka in Poland, Kalusz in Galicia, Bukowina, and also in Transylvania. In Pliocene or Later Tertiary formations, thick beds of gypsum are known in Zante, and strata of salt occur in Roumania and Galicia, while in Pliocene rocks, according to Dana, or in Post-Tertiary beds, according to others, a thick bed of pure salt was penetrated to a depth of 38 feet at Petit Anse in Louisiana. This ends my list, though I have no doubt that, by further research, many more localities might be given. Enough, ‘however, has been done to show that rock-salt (and other salts) are of frequent recurrence throughout all geological time, and as in my opinion it is impossible that common salt can be deposited in the open ocean, it follows that this and other salts must have been precipitated from solu- tions, which, by the effect of solar evaporation became at length super- saturated, like those of the Dead Sea, the great salt lake of Utah, and in other places which it is superfluous to name. Fresh-water. Lakes and Estuaries. I now come to the subject of recurrences of fresh-water conditions both in lakes and estuaries. In the introduction to the ‘ Geology of India’ by Messrs. Medlicott and Blanford, mention is made of the Blaini and Krol rocks as probably occupying ‘hollows formed by denudation in the old gneissic rocks,’ and the inference is drawn that ‘ if this be a correct view, 14 REPORT—1880. it is probable that the cis-Himalayan palzozoic rocks are in great part of fresh-water origin, and that the present crystalline axis of the Western Himalayas approximately coincides with the shore of the ancient paleeozoic continent, of which the Indian peninsula formed a portion.? The Krol rocks are classed broadly with ‘Permian and Carboniferous’ deposits, but the Blaini beds are doubtfully considered to belong to Upper Silurian strata. If this point be by-and-by established, this is the earliest known occurrence of fresh-water strata in any of the more ancient palsozoic formations. It is a fact worthy of notice that the colour of the strata formed in old lakes (whether fresh or salt) of palzozoic and mesozoic age is apt to be red: a circumstance due to the fact that each little grain of sand or mud is usually coated with a very thin pellicle of peroxide of iron. Whether or not the red and purple Cambrian rocks! may not be partly of fresh- water origin, is a question that I think no one but myself has raised.” There is, however, in my opinion, no doubt with regard to the fresh- water origin of the Old Red Sandstone, as distinct from the contem- poraneous marine deposits of the Devonian strata. This idea was first started by that distinguished geologist, Doctor Fleming, of Edinburgh, followed by Mr. Godwin-Austen, who, from the absence of marine shells and the nature of the fossil fishes in these strata, inferred that they were deposited, not in the sea, as had always been asserted, but in a great fresh-water lake or in a series of lakes. In this opinion I have for many years agreed, for the nearest analogies of the fish are, according to Huxley, the Polypterus of African rivers, the Ceratodus of Australia, and in less degree the Lepidosteus of North America. The truth of the supposition that the Old Red Sandstone was deposited in fresh water, is further borne out by the occurrence of a fresh-water shell, Anodonta Jukesii, and. of ferns in the Upper Old Red Sandstone in Ireland; and the same shell is found at Dura Den in Scotland, while in Caithness, along with numerous fishes, there occurs the small bivalve crustacean Histheriép Murchisoniz. I think it more than probablethat the red series of rocks that form the Catskill Mountains of North America, (and with which Iam personally acquainted) were formed in the same manner as the Old Red Sandstones of Britain; for excepting in one or two minor interstratifications, they contain no relics of marine life, while ‘the fossil fishes of the Catskill beds, according to Dr. Newberry, appear to represent closely those of the British Old Red Sandstone.’ (Dana.) The Devonian rocks of Russia, according to the late Sir Roderick Murchison, consist of two distinct types, viz. Devonian strata identical in general character with those in Devonshire and in various parts of the 1 By Cambrian, I mean only the ved and purple rocks of Wales, England, Scot- land, and Ireland, older than the Menevian beds, or any later division of the Silurian strata, that may chance to rest upon them. 7*On the Red Rocks of England of older date than the Trias.’ Jow. Geol. Soc. 1871, vol, 28. ADDRESS. 15 continent of Hurope. These are exclusively of a marine character, while the remainder corresponds to the Old Red Sandstone of Wales, England, and Scotland. At Tchudora, about 105 miles 8.E. of St. Petersburg, the lowest members of the series consist of flag-like compact limestones accumulated in a tranquil sea and containing fucoids and encrinites, together with shells of Devonian age, such as Spirifers, Terebratule, Orthis, Leptenas, Avicula, Modiola, Natica, Bellerophon, &c., while the upper division graduates into the Carboniferous series as it often does in Britain, and, like the Old Red Sandstone of Scotland, contains only fish-remains, and in both countries they are of the same species. ‘Proceeding from the Valdai Hills on the north,’ the geologist ‘quits a Devonian Zone with a true “ Old Red” type dipping under the Carboniferous rocks of Moscow, and having passed through the latter, he finds himself suddenly in a yellow-coloured region, entirely dissimilar in structure to what he had seen in any of the northern governments, which, of a different type as regards fossils, is the true stratigraphical equivalent of the Old Red system.’ This seems to me, as regards the Russian strata, to mean, that just as the Devonian strata of Devonshire are the true equivalents of the Old Red Sandstone of Wales and Scotland, they were deposited under very different conditions, the first in the sea and the others in inland fresh-water lakes. At the time Sir Roderick Murchison’s work was completed, ‘the’ almost universal opinion was that the Old Red Sandstone was a marine forma- tion. In the year 1830, the Rev. Dr. Fleming, of Edinburgh; read a paper before the Wernerian Society in which he boldly stated that the ‘Old Red Sandstone is a fresh-water formation’ of older date than the Carboniferous Limestone. This statement, however, seems to have made no impression on geologists till it was revived by Godwin-Austen in a memoir ‘On the Extension of the Coal-measures,’ &c., in the Journal of the Geological Society, 1856. Even this made no converts to what was then considered a heretical opinion. I have long held Dr. Fleming’s view, and unfortunately published it in the third edition of ‘The Physical Geology and Geography of Great Britain,’ without at the time being aware that I had been forestalled by Dr. Fleming and Mr. Godwin- Austen. 2) To give anything like a detailed account of all the fresh-water forma- tions deposited in estuaries and lakes from the close of the Old Red Sandstone times down to late Tertiary epochs, is only fitted for a manual of geology, and would too much expand this address ; and I will therefore give little more than a catalogue of these deposits in ascending order. In the Coal-measure parts of the Carboniferous series, a great propor- tion of the shales and sandstones are of fresh-water origin. This is proved all over the British Islands by the shells they contain, while here and there marine interstratifications occur, generally of no great thickness. There is no doubt among geologists that these Coal-measure strata were chiefly 16 REPORT—1880. deposited under estuarine conditions, and sometimes in lagoons or in lakes ; while numerous beds of coal formed by the life and death of land plants, each underlaid by the soil on which the plants grew, evince the constant recurrence of terrestrial conditions. The same kind of phenomena are characteristic of the Coal-measures all through North America, and in every country on the continent of Europe, from France and Spain on the west, to Russia in the east, and the same is the case in China and in other areas. In Scotland, according to Prof. Judd, fresh-water conditions occur more or less all through the Jurassic series, from the Lias to the Upper Oolites. In England, fresh-water strata, with thin beds of coal, are found in the Inferior Oolite of Yorkshire, and in the middle of England and elsewhere in the Great Oolite. The Purbeck and Wealden strata, which, in a sense, fill the interval between the Jurassic and Cretaceous series, are almost entirely formed of fresh-water strata, with occasional thin marine interstratifications. By some the Wealden beds are considered to have been formed in and near the estuary of a great river, while others, with as good a show of reason, believe them to have been deposited in a large lake subject to the occasional influx of the sea. In the eastern part of South Russia the Lias consists chiefly of fresh- water strata, as stated by Neumayr. The Godwana rocks of Central India range from Upper Paleozoic times well into the Jurassic strata, and there all these formations are of fresh-water origin. Fresh-water beds with shells are also interstratified with the Deccan traps of Cretaceous and Tertiary (Hocene) age, while 2,000 feet of fresh-water sands overlie them. In South-western Sweden, as stated by Mr. Bauerman, ‘the three coal-fields of Hoganas, Stabbarp, and Rodingé, lie in the uppermost Triassic or Rheetic series.’ In Africa, the Karoo beds, which it is surmised may be of the age of the New Red Sandstone, contain beds of coal. In North America, certain fresh-water strata, with beds of lignite, apparently belong to the Cretaceous and Eocene epochs, and in the north of Spain and south of France, there are fresh-water lacustrine formations in the highest Cretaceous strata. In England the lower and upper Eocene strata are chiefly of fresh- water origin, and the same is the case in France and other parts of the Continent. Certain fresh-water formations in Central Spain extend from the Hocene to the upper Miocene strata. There is only one small patch of Miocene beds in England, at Bovey Tracey, near Dartmoor, formed of fresh-water deposits with interstratified beds of lignite or Miocene coal. On the continent of Europe, Miocene strata occupy immense independent areas, extending from France and Spain to the Black Sea. In places too numerous to name, they contain beds of ‘brown coal,’ as lignite is sometimes called. These coal-beds are often of great thickness and solidity. In one of the pits which I descended near Teplitz, in Bohemia, the coal, which lies in a true basin, <<“ <= - ADDRESS. ig is 40 feet thick, and underneath it there is a bed of clay, with rootlets, quite comparable to the underclay which is found beneath almost every bed of coal in the British and other coal-fields of the Carboniferous epoch. The Miocene rocks of Switzerland are familiar to all geologists, who have traversed the country between the Jura and the Alps. Sometimes they are soft and incoherent, sometimes formed of sandstones, and some- times of conglomerates, as on the Righi. They chiefly consist of fresh- water lacustrine strata, with some minor marine interstratifications which mark the influx of the sea during occasional partial submergences of portions of the area. These fresh-water strata, of great extent and thick- ness, contain beds of lignite, and are remarkable for the relics of numerous trees and other plants which have been described by Prof. Heer of Zurich, with his accustomed skill. The Miocene fresh-water strata, of the Sewalik Hills in India are well known to most students of geology, and I have already stated that they bear the same relation to the more ancient Himalayan mountains that the Miocene strata of Switzerland and the North of Italy do to the pre-existing range of the Alps. In fact, it may be safely inferred that something far more than the rudiments of our present continents existed long before Miocene times, and this accounts for the large areas on those continents which are frequently occupied by Miocene fresh-water strata. With the marine formations of Miocene age this address is in no way concerned, nor is it essential to my argument to deal with those later tertiary phenomena, which in their upper stages so easily merge into the existing state of the world. Glacial Phenomena. I now come to the last special subject for discussion in this address, viz., the Recurrence of Glacial Epochs, a subject still considered by some to be heretical, and which was generally looked upon as an absurd crotchet when, in 1855, I first described to the Geological Society, boulder-beds, containing ice-scratched stones, and erratic blocks in the Permian strata of England. The same idea I afterwards applied to some of the Old Red Sandstone conglomerates, and of late years it has become so familiar, that the effects of glaciers have at length been noted by geologists from older Palzzoic epochs down to the present day. In the middle of last July I received a letter from Prof. Geikie, in which he informed me that he had discovered mammilated moutonnée surfaces of Laurentian rocks, passing underneath the Cambrian sand- stones of the north-west of Scotland at intervals, all the way from Cape Wrath to Loch Torridon, for a distance of about 90 miles. The mammi- lated rocks are, says Prof. Geikie, ‘as well rounded off as any recent roche moutonnée,’ and, ‘in one place these bosses are covered bya huge angular breccia of this old gneiss (Laurentian) with blocks sometimes five or six feet long.’ This breccia, where it occurs, forms the base of the Cambrian strata of Sutherland, Ross, and Cromarty, and while the higher strata are 1880. C 18 REPORT—1880. always well stratified, where they approach the underlying Laurentian gneiss ‘they become pebbly, passing into coarse unstratified agglomerates or boulder-beds.’ In the Gairloch district ‘it is utterly unstratified, the angular fragments standing on end and at all angles,’ just as they do in many modern moraine mounds wherever large glaciers are found. The general subject of Paleozoic glaciers has long been familiar to me, and this account of more ancient glaciers of Cambrian age is peculiarly acceptable. The next sign of ice in Britain is found in the lower Silurian rocks of Wigtonshire and Ayrshire. In the year 1865 Mr. John Carrick Moore took me to see the Lower Silurian graptolitic rocks at Corswall Point in Wigtonshire, in which great blocks of gneiss, granite, &c., are imbedded, and in the same year many similar erratic blocks were pointed out to me by Mr. James Geikie in the Silurian strata of Carrick in Ayrshire. One of the blocks at Corswall, as measured by myself, is nine feet in length, and the rest are of all sizes, from an inch or two up to several feet in diameter. There is no gneiss or granite in this region nearer than those of Kirkeud- brightshire and Arran, and these are of later geological date than the strata amid which the erratic blocks are imbedded. It is therefore not improbable that they may have been derived from some high land formed of Lauren- tian rocks of which the outer Hebrides and parts of the mainland of Scotland form surviving portions. If so, then I can conceive of no agent capable of transporting large boulders and dropping them into the Lower Silurian mud of the seas of the time save that of icebergs or other float- ing ice, and the same view with regard to the neighbouring boulder-beds of Ayrshire is held by Mr. James Geikie. If, however, any one will point out any other natural cause still in action by which such results are at present brought about, I should be very glad to hear of it. I must now turn to India for further evidence of the action of palzo- zoic ice. In the Himalayas of Pangi, 8.H. of Kashmir, according to Medlicott and Blanford, ‘old slates, supposed to be Silurian, contain boulders in great numbers,’ which they believe to be of glacial origin. Another case is mentioned as occurring in ‘transition beds of unknown relations,’ but in another passage they are stated to be ‘very ancient, but no idea can be formed of their geological position.’ The wnderlying rocks are marked by distinct glacial striations. The next case of glacial boulder-beds with which I am acquainted is found in Old Red Sandstone in Scotland, and in some places in the north of England, where they contain what seem to be indistinctly ice-scratched stones. I first observed these rocks on the Lammermuir Hills, south of Dunbar, lying unconformably on Lower Silurian strata, and soon inferred them to be of glacial origin, a circumstance that was subsequently con- firmed by my colleagues, Prof. and Mr. James Geikie, and is now familiar to other officers of the Geological Survey of Scotland. I know of no boulder formations in the Carboniferous series, but they are well known as occurring on a large scale in the Permian brecciated conglomerates, where they consist ‘of pebbles and large blocks of stone, ADDRESS. 19 _ generally angular, imbedded in a marly paste. ... the fragments _. have mostly travelled from a distance, apparently from the borders of __ Wales, and sorhe of them are three feet in diameter.’ Some of the stones are as well scratched as those found in modern moraines or in the ordinary boulder-clay of what is commonly called the Glacial Epoch. In 1855 the old idea was still not unprevalent that during the Permian Epoch, and for long after, the globe had not yet cooled sufficiently to allow of the climates of the external world being universally affected by the constant. radiation of heat from its interior. For a long time, however, this idea, has almost entirely vanished, and now, in Britain at all events, it is. little if at all attended to, and other glacial episodes in the history of: the world have continued to be brought forward and are no longer looked upon as mere ill-judged conjectures. The same kind of brecciated boulder-beds that are found in our Per- mian strata occur in the Rotheliegende of Germany, which I have visited. in several places, and I believe them to have had a like glacial origin. Mr. G. W. Stow, of the Orange Free State, has of late years given most elaborate accounts of similar Permian boulder-beds in South Africa. There, great masses of moraine matter not only contain ice-scratched stones, but on the banks of rivers where the Permian rock has been re- moved by aqueous denudation, the underlying rocks, well rounded and mammillated, are covered by deeply incised glacier grooves pointing in a. direction which at length leads the observer to the pre-Permian mountains. from whence the stones were derived that formed these ancient moraines! Messrs. Blanford and Medlicott have also given in ‘ The Geology of Tndia’ an account of boulder-beds in what they believe to be Permian strata, and which they compare with those described by me in England many years before. There the Godwana group of the Talchir strata con- tains numerous boulders, many of them six feet in diameter, and ‘in one instance some of the blocks were found to be polished and striated, and the underlying Vindhyan rocks were similarly marked. The authors also cor- relate these glacial phenomena with those found in similar deposits in South Africa, discovered and described by Mr. Stow. Iu the Olive group of the Salt range, described by the same authors, there is a curious resemblance between a certain conglomerate ‘and that of the Talchir group of the Godwana system.’ This ‘ Olive conglomerate ’ belongs to the Cretaceous series, and contains ice-transported erratic boulders derived from unknown rocks, one of which of red granite ‘is polished and striated on three faces in so characteristic a manner that very little doubt can exist of its having been transported by ice.’ One block of red granite at the Mayo Salt Mines of Khewra ‘is 7 feet high and 19 feet in circumference.’ In the ‘Transition beds’ of the same * Mr. Stow’s last memoir on this subject is still in manuscript. It is so exceed- ingly long, and the sections that accompany it are of such unusual size, that the Geological Society could not afford their publication. It was thought that the Govern- ment of the Orange Free State might undertake this duty, but the late troubles in South Africa have probably hindered this work—it is to be hoped only for a time. c2 3 20 REPORT—1880. authors, which are supposed to be of Upper Cretaceous age, there also are boulder beds with erratic blocks of great size. I know of no evidence of glacial phenomena in Eocené strata except- ing the occurrence of huge masses of included gneiss in the strata known as Flysch in Switzerland. On this question, however, Swiss geologists are by no means agreed, and I attach little or no importance to it as affording evidence of glacier ice. Neither do I know of any Miocene glacier-deposits excepting those in the north of Italy near Turin, described by the late eminent geologist, Gastaldi, and which I saw under his guidance. These contain many large erratic boulders derived from the distant Alps, which, in my opinion, were then at least as lofty or even higher than they are now, especially if we consider the immense amount of denudation which they underwent during Miocene, later Tertiary, and post-tertiary times. At a still later date there took place in the north of Hurope and America what is usually misnamed ‘ The Glacial Epoch,’ when a vast glacial mass covered all Scandinavia, and distributed its boulders across the north of Germany, as far south as the country around Leipzig, when Ireland also was shrouded in glacier ice, and when a great glacier covered the larger part of Britain, and stretched southward, perhaps nearly as far as the Thames on the one side, and certainly covered the whole of Anglesey, and probably the whole, or nearly the whole, of South Wales. This was after the advent of man. Lastly, there is still a minor Glacial Epoch in progress on the large and almost unknown Antarctic continent, from the high land of which in latitudes which partly lie as far north as 60° and 62°, a vast sheet of -glacier-ice of great thickness extends far out to sea and sends fleets of icebergs to the north, there to melt in warmer latitudes. If in accordance with the theory of Mr. Croll, founded on astronomical data, a similar climate were transferred to the northern hemisphere, the whole of Scan- dinavia and the Baltic would apparently be covered with glacier-ice, and the same would probably be the case with the Faroe Islands and great part of Siberia, while even the mountain tracts of Britain might again maintain their minor systems of glaciers. Conclusions. In opening this address, I began with the subject of the oldest meta- morphic rocks that I have seen—the Laurentian strata. It is evident to every person who thinks on the subject that their deposition took place far from the beginning of recognised geological time. For there must have been older rocks by the degradation of which they were formed. And if, as some American geologists affirm, there are on that continent meta- morphic rocks of more ancient dates than the Laurentian strata, there must have been rocks more ancient still to afford materials for the de- position of these pre-Laurentian strata. i eee ADDRESS. 21 Starting with the Laurentian rocks, I have shown that the phe- nomena of metamorphism of strata have been continued from that date all through the later formations, or groups of formations, down to and including part of the Eocene strata in some parts of the world. In like manner I have shown that ordinary volcanic rocks have been ejected in Silurian, Devonian, Carboniferous, Jurassic, Cretaceo-oolitic, Cretaceous, Eocene, Miocene, and Pliocene times, and from all that I have seen or read of these ancient volcanoes, I have no reason to believe that voleanic forces played a more important part in any period of geo- logical time than they do in this our modern epoch. So, also, mountain chains existed before the deposition of the Silurian rocks, others of later date before the Old Red Sandstone strata were formed, and the chain of the Ural before the deposition of the Permian beds. The last great upheaval of the Alleghany Mountains took place between the close of the formation of the Carboniferous strata of that region and the deposition of the New Red Sandstone. According to Darwin, after various oscillations of level, the Cordillera underwent its chief upheaval after the Cretaceous epoch, and all geologists know that the Alps, the Pyrenees, the Carpathians, the Himalayas, and other mountain-chains (which I have named) underwent what seems to have been their chief great upheaval after the deposition of the Eocene strata, while some of them were again lifted up several thousands of feet after the close of the Miocene epoch. The deposition of salts from aqueous solutions in inland lakes and lagoons appears to have taken place through all time—through Silurian, Devonian, Carboniferous, Permian, Triassic, Jurassic, Cretaceous, Eocene, Miocene, and Pliocene epochs—and it is going on now. Tn like manner fresh-water and estuarine conditions are found now in one region, now in another, throughout all the formations or groups of formations possibly from Silurian times onward ; and glacial phenomena, so far from being confined to what was and is generally still termed the Glacial Epoch, are now boldly declared, by independent witnesses of known high reputation, to begin with the Cambrian epoch, and to have occurred somewhere, at intervals, in various formations, from almost the earliest Paleozoic times down to our last post-Pliocene ‘ Glacial Epoch.’ If the nebular hypothesis of astronomers be true (and I know of no reason why it should be doubted), the earth was at one time in a purely gaseous state, and afterwards in a fluid condition, attended by intense heat. By-and-by consolidation, due to partial cooling, took place on the surface, and as radiation of heat went on, the outer shell thickened. Radiation still going on, the interior fluid matter decreased in bulk, and, by force of gravitation, the outer shell being drawn towards the interior, gave way, and, in parts, got crinkled up, and this, according to cos- mogonists, was the origin of the earliest mountain-chains. I make no objection to the hypothesis, which, to say the least, seems to be the best that can be offered and looks highly probable. But, assuming that 22 REPORT—1880. it is true, these hypothetical events took place so long before authentic geological history began, as written in the rocks, that the earliest of the physical events to which I have drawn your attention in this address was, to all human apprehension of time, so enormously removed from these early assumed cosmical phenomena, that they appear to me to have been of comparatively quite modern occurrence, and to indicate that from the Laurentian epoch down to the present day, all the physical events in the history of the earth have varied neither in kind nor in intensity from those of which we now have experience. Perhaps many of our British geologists hold similar opinions, but, if it be so, it may not be altogether useless to have considered the various subjects separately on which I depend to prove the point I had in view. REPORTS: ON THE STATE OF SCIENCE. im 9 _ REPORTS ON THE STATE OF SCIENCE. Report of the Committee, consisting of Professor Sir WILLIAM THomson, Professor Tair, Professor GRANT, Dr. SIEMENS, Pro- fessor PuRSER, Professor G. Forses, Mr. Horace Darwin, and Mr. G. H. Darwin (Secretary), appommted for the Measwrement of the Lunar Disturbance of Gravity. Tue Committee beg leave to report as follows :— The sum of £30 granted in 1879 for the purposes of the Committee has been paid to Mr. G. H. Darwin. Before the meeting of 1879 Mr. G. H. Darwin and Mr. Horace Darwin were making preparations for carrying out experiments with a view of detecting small variations in the directions of the force of gravity. With the aid of the above grant some preliminary experiments have been made during the past year by Mr. G. H. and Mr. H. Darwin in the Cavendish Laboratory of the University of Cambridge by means of an instrument of which the principle was suggested to the experimenters by Sir William Thomson. The experiments have not as yet been carried sufficiently far to make it desirable to present a detailed report to the British Association. It may nevertheless be mentioned that results of some interest have been attained with regard to the warping of stone columns under the influence of minute changes of temperature or of small stresses. The chief conclusion, however, to which the experimenters have been led is that it is now necessary to entirely re-design the apparatus. It seems probable that the experiments will occupy a considerable time, and may possibly prove expensive. Under these circumstances the Committee think it expedient to defer the presentation of their Report and of the accounts until the meeting of the Association in 1881. Supplementary Report. The Secretary of this Committee having got inand paid an outstanding account since the Report was sent in, finds that nearly the whole sum granted for the purposes of the Committee in 1879 has been expended. 26 REPORT—1 880. As, however, the experiments are still only in an incipient stage, it is necessary to defer the report of the results attained. Under these circumstances the Secretary suggests the advisability of the continuation of the Committee on the Lunar Disturbance of Gravity for another year. As the plan which the experimenters intend to pursue will involve some masonry work and the use of a good deal of copper for apparatus—an expensive material and difficult to work—it seems likely that future operations may prove expensive. The Secretary, therefore, ventures to suggest that the Association should grant a further sum of 301. for the purposes of this Committee. Thirteenth Report of the Committee, consisting of Professor EVERETT, Professor Sir WiLuiAM THomson, Mr. G. J. Symons, Professor Ramsay, Professor GEIKIE, Mr. J. GLAISHER, Mr. PENGELLY, Professor Epwarp Hutu, Dr. CLEMENT LE NEVE Foster, Professor A. S. HERSCHEL, Professor G. A. LEBourR, Mr. A. B. Wynne, Mr. GatLtoway, Mr. JoserpH Dickinson, Mr. G. F. DEacon, and Mr. E. WETHERED, appointed for the purpose of investigating the Rate of Increase of Underground Temperature downwards im various Localities of Dry Land and under Water. Drawn up by Professor EVERETT (Secretary). OxssERVATIONS have been taken in the Talargoch Lead Mine, Flintshire (between Rhyl and Prestatyn), under the direction of Mr. A. Strahan, of the Geological Survey, and Mr. Walker, Chairman of the Board of Direc- tors of the mine. The top of the shaft is 190 feet above the level of the sea, and is at the foot of a hill 500 feet above the sea. The lowest workings are 900 feet below sea-level. The veins run across an angle of Carboniferous Lime- stone, bounded on both sides by faults which throw down coal-measure shale; and as the faults have a considerable inclination, the lowest work- ings run beneath the shale for a considerable distance. The limestone dips at angles varying from 45° to 55°, and is of two kinds, one white and massive, the other thin bedded black with thin shale partings. There are levels at intervals of about 20 yards vertically, in the vein, most of which have been driven for some years; but all the observations have been taken in newly opened ground. They have been taken by boring a hole 24 inches deep at a distance of from 14 to'5 yards from the fore breast, and either on the same day or the next day inserting one of the Committee’s slow-action thermometers, with a foot of plugging consisting of dry rag and clay behind it. After an interval generally of four days the thermometer was taken out and read, then reinserted, and read again about a week later, the difference between the two readings never amounting to so much as half a degree, The observations were taken at six different places in the mine, which are designated by the observers Stations I. to VI.; but in one instance, that of Station II., owing to the swelling of newly exposed shale, the hole ON THE RATE OF INCREASE OF UNDERGROUND TEMPERATURE. 27 became distorted, so that after extracting the dry rag and clay, an hour was expended in working out the thermometer, the reading of which has therefore been rejected. The following is a list of the five remaining stations, arranged in order of depth :-— Depth Distance and ees from Surface Teptperature Direction from i in feet 4 Mostyn Shaft TVs ne ; 465 . : 534° . 190 yds. S.W. Mist ale é 555, r, 529°. . 170 yds. §.E. Vikeroesic A 636. ‘ 588°. . 840 yds. S.W. DS < c 660 . ‘ BAe. . 120 yds. 8. Taya LOL Ti 7 60°8° . 190 yds. N.E. It will be observed that the order of the temperatures is not the same as the order of the depths; it therefore becomes important to describe the positions with some particularity. Stations IV., V., and III. are near together in ground plan, IV. and V. being about 250 yards apart, and III. nearly midway between them, and they have all the same rock overhead between them and the surface, namely, black and white limestone. At Station I. the rock overhead consists almost entirely of sandstones and shales, with thin coal-seams. At Station VI. it consists of white limestone and shale. ; It may be mentioned that the temperature at VI. was observed on three several occasions, namely, January 14, January 21, and February 19, and was in each case found to be thesame. Mr. Strahan further states that this station is near a large fault, which contains iron pyrites and gives off water charged with sulphuretted hydrogen ; the temperature of the water as pumped up Walker’s shaft from a depth of 770 feet, being 63° at the top of the lift. It seems probable that the decomposition of this pyrites may be the cause of the exceptionally high temperature at this station. The comparison of the temperatures will be most clearly brought out by tabulating the rate of increase from the surface down to each station, as calculated from an assumed surface temperature, which may be fairly taken as 48°. As all the depths are considerable, an error of a degree in the surface temperature will not have much influence on the comparison, which stands thus :— : Depth Excess above Feet per Station in feet Surface Depiee LV. . 5 465 e ‘ 5-4° 86 Vv. A s 555 49° s | TS VI. 5 4 636 a : 10°8° : “ 59 Ii. ° a 660 ri a 6:0° 110 Ne ' » 1041 3 12°8° 81 Stations V. and III., which give the slowest rate of increase, are both of them ina vein called the ‘South Joint;’ and Stations IV. and I., which agree well with each other, though differing from the rest, are both of them in another vein called the ‘Talargoch vein;’ while Station VI. is in the rock. The horizontal distance between IV. and III. is oaly 120 yards: but if we attempt to deduce the rate of increase from com- paring these two, we have an increase of only 0°6° in 195 feet. It thus appears that, notwithstanding the proximity of the two veins, their con- ditions as to temperature are very different. Widely as the results differ among themselves, they agree upon the whole in showing that the average rate of increase is slow; and this e 28 REPORT—1880. general result is in harmony with what has been found at the nearest localities mentioned in our previous reports, namely, Dukinfield and Liver- pool. Here, as at Dukinfield, all the strata are highly inclined. Some additional observations at Dukinfield have recently been made for the Committee, by Mr. Edward Garside, student of engineering in Queen’s College, Belfast. The Astley Pit, in which they were taken, has now been carried to a much greater depth than it had extended at the time of Sir Wm. Fairbairn’s observations, to which allusion was made in our Report for 1870. The two deepest seams of ccal in if are called the ‘Cannel Mine’ and the ‘Black Mine,’ the former heing the deeper of the two; they both slope downwards at.about 15°, the deepest point being the far end of the Cannel Mine. The following is Mr. Garside’s summary of the observations; the ‘surface-depth’ being distinguished from the ‘shaft-depth ’ because the surface is not level, but slopes slightly in the same general direction as the seams. The shaft-depth gives the difference of levels, but the surface-depth, which is practically the same as the distance of the nearest point of the surface, is what we must use in com- puting the rate of increase of temperature. jl ele : Distance urface Shaft Temperature Temperature from main A Se ae ue Depth. Depth. of Strata, in ir Road, Air Column. in 188 oe Feet Feet Fahr. Fahr. Yards June 17 Cannel 2,700 2,754 863 754 160 Peg) ) black 2,4073 2,631 80 782 630 » 21 #£Cannel 2,4164 2,4823 81 79 600 July 2 Black 1,9874 2,0474 74 714 460 — The pit is described as being entirely free from water. All the observations were taken with one of the Committee’s slow- acting thermometers, in holes drilled in the floors at the far ends of newly opened horse-road levels; the holes being 4 feet deep and 2 inches in diameter. All the holes were free from cracks, and were in thesame kind of rock—an argillaceous earth called ‘warren earth.’ They were allowed to stand for a short time, to allow the heat caused by drilling to escape. The thermometer was then inserted, and the portion of the hole between it and the mouth plugged with cotton waste and the dust which came out of the hole in drilling. After being left for forty-eight hours, it was taken out and read. Arranging the observations in the order of the surface-depths, we have the following data :— Surface Feet per Degree Seam Depth Temperature Som Surkiee Black . c . - 1,987% Die : : 79°5 3 4 . : - 2,408, + - 980 ° : Cbs bed Cannel . : . » Ale, Ae OL s ; 75°5 » : ° : . 2,700 ; - 86t 72 The numbers in the last column are calculated from an assumed surface-temperature of 49°, and show that the increase of temperature becomes more rapid as the depth increases. If, without making any assumption as to surface-temperature, we compare the observations among themselves, the two shallower give an increase of 6° in 420 feet, which is at the rate of 1° in 70 feet, and the two deeper give an increase of 55° in 2834 feet, which is at the rate of 1° in 51} feet, a result which confirms the increase of rapidity with depth. The greatest depth in Sir Wm. Fairbairn’s observations was 685 yards ON AN IMPROVED FORM OF HIGH INSULATION KEY. 29 or 2055 feet, and the temperature which he found at this depth (754°) is within less than a degree of the temperature which would be calculated from the observations now reported. The Committee have to express their regret at the loss of two of their colleagues—Prof. Clerk Maxwell, and Prof. Ansted—by death, during the past year. Report of the Comittee, consisting of Dr. O. J. Lopax (Secretary), Professor W. E. AyRTON, and Professor J. PERRY, appointed for the purpose of devising and constructing an improved form of High Insulation Key for Electrometer Work. In the construction of the key it was considered desirable to secure as far as possible the following conditions :— 1. That the insulation should be nearly perfect. 2. That the conductors should have a very small electrostatic capacity. 3. That they should be entirely protected from all external induction by a metal case. 4. That the hand of the operator should work the moving parts from the outside of the case, so as neither to act inductively on the conductors, nor to electrify insulators by friction. 5. That there should be no friction whatever between insulators and conductors in the moving parts. 6. That all the insulating parts should be easily removable occasionally for cleaning purposes. 7. That the commercial price of the key should not be unreasonably high. In the original form of the key the conductors were platinum wires suspended inside a metal case by silk threads, the leading wires being brought to them through large holes in the case. It was found, however, that this arrangement was rather too delicate and troublesome for general use, and it was impossible to artificially dry the air in the case because of the large holes in it. It was determined, therefore, to abandon silk strings and to use rigid supports for the conductors, and to allow the conductors to protrude through small holes in the case, so that the leading wires might not have to enter the case to reach them. For the supports it was ultimately decided to use, not ebonite, but glass, as the latter is more easily cleaned, and in a dry atmosphere has probably the better insulating power ; moreover it is not liable to contract a coat of acid, which acting on the metal conductors gives rise to a feeble E.M.F. causing some keys to act as extremely weak batteries. The insulators are four thin pillars of carefully selected glass, mounted in the case in such a way that they can be easily taken out and cleaned occasionally. Brass caps are cemented to the top of each of the pillars, which are so arranged that each cap is near a small hole in the side of the case, and a short thin rod ending in a binding screw is passed through this hole and screwed into each brass cap after they are in position. Small ebonite plugs slide on these rods and ordinarily close the holes through which the rods pass, except when pulled out. When very good 30 REPORT—1 880. insulation. is required they are pulled out so as to leave the conductors free of the holes, touching nothing. To each of one pair of brass caps a short brass pin is attached, the two projecting horizontally one above the other. To the other pair two brass or bronze flat springs are screwed, which project between the two pins attached to the other pair of caps. Except when depressed the springs both press upon the upper of the two pins and make contact with it. All the contact surfaces are gilt. Hither spring can be depressed separately without bringing the hand near it, by means of a thin glass rod, which works through a hole in the top of the case, and which is shod with metal above and below, so that it may not be subject to any friction which might electrify it. The piece of metal at the top is a brass cap sliding over a tube fixed in the top of the case in such a way as to exclude dust; it can be pressed down with the fingers, and is sent up again by a spiral spring. A pin and double bayonet-slot is also arranged so as to fix the piece perma- nently in either of three positions, viz., completely up and in contact with the top pin, completely down and in contact with the bottom pin, half-way or insulated. Tn its present form the key is in principle simply an ordinary double reversing key turned upside down and shut up in a box. The glass pillars are fixed to the lid instead of to the floor of the case for several reasons, one of which is that it economises space and reduces the height of the key. The lid can be unscrewed and taken out of the case with all the working parts im situ, which is very convenient. The floor of the case is quite free and can be removed at pleasure. A dish stands on it to contain pumice soaked with sulphuric acid whenever extra insulation is required. Without any artificial drying, however, the insulation is very good. ‘The dish is made either of lead, or of glass pro- tected from the working parts by a covering of wire gauze. The key has been made by Elliott Bros. in two forms—one square, the other round. The round form of case is distinctly the cheaper; it necessitates a slight modification in the arrangement of the working parts, but it appears to be nearly as convenient as the other. Report of the Committee, consisting of Professor CayLEy, F.R.S., Professor G. G. SToKES, F.R.S., Professor H. J. S. Smrru, F.R.S., Professor Sir WitL1aM THomson, F.A.S., Mr. JAMES GLAISHER, F.RS., and Mr. J. W. L. GuaIsHER, F.R.S. (Secretary), on Ma- thematical Tables. Drawn wp by Mr. J. W. L. GuaIsHER. Tue present Report relates to the factor tables for the fourth, fifth, and sixth millions, and to some results of the enumeration of the primes in the fifth million and the first five millions. In Section I. an account is given of the state of the work, two volumes of which have been published, while a portion of the third and concluding volume is already in type. Section IT. contains in a condensed form results relating to the distribu- tion of primes in the fifth million, obtained by enumerating the primes in ce) ON MATHEMATICAL TABLES. 31 each hundred, or century, in that million: it is similar to Part I. of last year’s Report, which related to the fourth million. As the factor tables for the first five millions are now published, so that it is for the first time possible to extend the enumerations continuously from 0 to 5,000,000, it was thought desirable to give here in a tabular form the main facts relating to the distribution of primes over this range : these tables form Section III. The results are given very briefly, because it is hoped that by next year the series of tables will be complete as far as 9,000,000, and a more detailed examination is deferred till it can be rendered as complete as possible. One of the objects to which enumerations of primes are most directly applicable is the examination of the degree of accuracy with which the numbers of primes in any given intervals are represented by certain formule: which have been proposed for the purpose. A formula of this kind was proposed by Legendre, and another was independently obtained by Gauss, Tchebycheff, and Hargreave. Certain comparisons between the numbers of primes counted and the numbers given by these two formulz for intervals between 0 and 5,000,000 are contained in Sec- tion IV. I. State of the Factor Tables for the Fourth, Fifth, and Siath Millions. During the year the calculation for the three millions has been com- pleted, and the printing of the tables has been steadily continued under the direction of Mr. James Glaisher. The volumes containing the factor tables for the fourth and fifth millions have been published, and twenty pages of the volume containing the sixth million are now printed and stereotyped. The fowrth million was published in December, 1879, by Messrs. Taylor and Francis. The table itself occupies 112 pages, and is uniform with those of Burckhardt and Dase. There is an introduction of fifty- two pages, consisting of eight sections and an appendix. The titles of the sections are (1) Mamner of using the Table; (2) The Tables of Burckhardt, Dase, and Chernac; (3) Mode of Construction of the Table ; (4) On Factor Tables; (5) On the Distribution of Prime Numbers; (6) List of Writings on the Distribution of Prime Num- bers; (7) Results of the Enumeration of the Prime Numbers in the Fourth Million; (8) Application of the Table to the Calculation of Logarithms. The appendix contains a list of prime numbers from 1 to 30,541 with differences: this list was used in the determination of least factors by the multiple method. There is also a specimen of one of the lithographed sheets used in the calculation of the table, and from which the sieves were formed by stamping out certain of the squares. An abstract of the third section, which relates to the mode of construction of the table, appeared in the Report for 1878, and an abstract of the seventh section, which contains the tables derived from the enumeration of the primes in the fourth million, formed Part I. of last year’s Report. The introduction to this million is intended to apply to the whole three millions. The fifth million was published in July of this year. The introduction, which contains eleven pages, consists of only two sections, the first of which relates to the manner of using the table, and the second to the results of the enumeration of the primes in the fifth million. An abstract of the latter forms Section II. of this Report. 32 REPORT—1880. The sith million is stillin the press, and the printing and stereotyping of the table will be completed early next year. It is intended to prefix to this volume an introduction containing the results of the enumerations for the whole nine millions over which the printed tables will then extend, with comparisons of the numbers found by counting with those given by Legendre’s formula and. the liw formula. S |S So |S 2S |S S| ai) o|> i=) ==) o/> =i) So n S ojo ae SS Sls so Salo SiogioisS SiSe oom ce =) So | So |Oo =i) So |S o|> ei) S| ==) ° | —s a) o Ssologolosoloesclo Solosoclosoliosoleolo Sol ols, > o|Oo o|/> SS |\> o|o — ai) o|> ai) So |\> a) o|co So Se ar ee SH So SEN a Fate SEN ae NSE, OSD Saal See oie STN er ISS Po I i I OI OI OWI od Pad (0) 0 0 0 0 0 0 2 0 0 0 2 1 3 3 3 0 By 2 3 3 2 4 26 2 15 17 Wi, 16 13 18 14 20 10 21 161 3 29 39 31 35 37 55 48 49 4] 39 403 4 92 90 | 110 | 100 75 96 83 | 105 | 109 83 943 5 142 | 156 | 151 | 143 | 153 | 132 | 162 | 140] 149 | 160] 1488 6 201 | 195 |' 206 | 212 | 207 | 193 | 198 | 188 | 199 | 200 | 1994 7 215 | 200 |} 161 | 205 | 190 | 192 | 187 | 191 | 194 | 194 | 1929 8 133 | 137 | 166 | 133 | 163 | 155 | 141 | 138 | 130 | 137 | 1438 9 93 89 93 94 96 97 97 97 80 86 922 10 45 48 37 44 37 35 42 47 45 46 426 11 21 16 17 15 18 19 20 12 29 22 189 12 7 Uf 5 2 5 6 6 9 9 7 63 13 3 3 2 1 2 0 2 1 3 1 18 14 1 0) 1 0 1 0 0) 0 0 0 3 No. of © ‘ 2 ‘ 17 ‘ : 6628 | 6540 |6510 | 6511 | 6613 | 6493 | 6523 | 6475 | 6554 | 6522 |65,369 primes This table shows the number of centuries in each group of 100,000, each of which contains no prime, each of which contains one prime, two primes, &c. For example, between 4,000,000 and 100,000 there is no century containing no prime (%.e. consisting wholly of composite numbers), there are three centuries which contain each one prime, fifteen which contain two primes, and so on, there being only one which contains fourteen primes. The number at the foot of each column is the total number of primes in the group of numbers to which the column relates ; thus, for example, there are 6,628 primes between 4,000,000 and 4,100,000. The next table shows the numbers of primes in each successive group of 10,000 between 4,000,000 and 5,000,000. Thus, for example, between ON MATHEMATICAL TABLES. 33 : 4,000,000 and 4,010,000 there are 660 primes, between 4,010,000 and 4,020,000 there are 658 primes, and so on. 4,000,000 to 5,000,000. s s/s sis sis sis sig gis sig slg sig.g SS SES NS | OE Sh SRS ON OL SOR SOO Se SOcS S#s\s8s|SFs\s"s |S¥sis“s|\sFsl\s¥s\sesisks ee, SUS Cen a SEAS a Sea ES BS oro aca: toi Wit Sit Vit Tit Hit Hit Hit Hid 6 I. 660 | 663 | 670| 662] 641} 653) 662) 652} 658 | 651 II. 658 | 628 | 644] 666 | 679 | 638} 656} 653 | 655 | 634 Ii. 668 | 652) 663 | 641 | 683) 646} 645 | 643 | 631 | 653 IV. 677 | 632) 628 | 656 | 656} 631 | 651 | 663) 678 | 655 Wie 681 | 661 | 664} 635 | 672 | 648 | 651 | 644] 634] 650 VI. 643 | 662) 660 | 640] 655] 659] 616] 642 | 645] 640 VII. 653 | 671 | 644] 653 | 660) 673 | 665 | 655) 669) 683 VIII. 670 | 651 | 656] 661 | 646} 650] 666] 628] 636]| 661 Ix. 653 | 673 | 632) 662 | 683 | 640 | 667 | 657 | 669 | 654 X. 665 | 647 | 649 | 635 | 638 | 655 | 644] 638 | 679 | 641 mea \ 6628 | 6540 | 6510 | 6511 | 6613 | 6493 | 6523 | 6475 | 6554 | 6522 primes The following is a list of successions of composite numbers of ninety- nine and upwards occurring in the fifth million. SEQUENCES OF 99 AND UPWARDS. Lower Limit 4,044,077 4,047,157 4,131,109 4,166,893 4,234,537 4,297,093 4,315,607 4,359,403 4,447,321 4,478,423 4,535,717 4,536,179 4,571,107 4,596,731 4,640,599 4,652,353 4,665,553 4,686,709 . 4,738,651 4,783,873 4,958,021 Upper Limit 4,044,179 4,047,257 4,131,223 4,166,999 4,234,651 4,297,199 > 4,315,709 * 4,359,503 4,447,423 4,478,527 4,535,819 4,536,283 4,571,207 4,596,833 4,640,717 4,652,507 4,665,653 4,686,811 4,738,777 4,783,973 4,958,131 Sequence | This table shows that the 101 numbers between 4,044,077 and 4,044,179 are composite, and so on; the numbers in the first two columns being the primes which bound the sequences of composite numbers. ; The introductions to the Fourth Million and Fifth Million contain similar tables giving the sequences of 79 and upwards. 1880. D 34 REPORT— 1880. III. Results of the Enumeration of the Primes in the first Five Millions. The following table is similar in form to the first table of Section II. ; each column relates to a million numbers, and the last column to the whole five millions. The last column but one, which refers to the fifth million, is of course identical with the last column in the table in Section II. 0 to 5,000,000. Number of centuries each of which contains x primes n 0 1,000,000 | 2,000,000 | 3,000,000 | 4,000,000 0 to to to to - Seto to 1,000,000 | 2,000,000 | 3,000,000 | 4,000,000 | 5,000,000 | 5,000,000 0 0 1 1 2 2 6 1 3 16 25 30 26 100 2 29 72 97 136 161 495 3 140 257 | 338 400 403 1538 4 372 667 | 775 862 943 3619 5 801 1253 1408 1480 1488 6430 6 1362 1743 | 1878 1929 1994 8906 7 1765 2032 1997 1849 1929 9572 8 1821 1612 1526 1561 1433 7953 9 1554 1182 1036 950 922 5644 10 1058 691 | 558 497 426 3230 11 592 Si06 w|i 297 221 189 1540 12 316 113 98 60 63 650 13 122 39 28 19 18 226 14 32 7 6 4 3 52 15 20 3 1 0 0 24 16 8 1 0 0 0 9 17 3 0 1 0 0 4 21 1 0 0 0 0 1 26 1 0 0 0 0 1 pelea 78,499 70,433 67,885 66,329 65,369 348,515 It will be seen from this table that the centuries with eight primes are the most numerous in the first million, the centuries with seven primes in the second and third millions, and the centuries with six primes in the fourth and fifth millions. It may be mentioned that the centuries with six primes are also the most numerous in the seventh, eighth, and ninth millions. ‘The 26-prime century is of course the first, namely, from 0 to 99, and ‘the 21-prime century the second. In the first century 1 is counted as a rime. ‘ The next table shows the number of primes in each. group of 10,000 from 0 to 5,000,000, with differences. For example, the number of primes between 0 and 10,000 is 9,593, between 10,000 and 20,000 is 8,392; between 1,000,000 and 1,010,000 is 7,216 ; and so on. ——=. St ON MATHEMATICAL TABLES. 35 0 to 5,000,000. NUMBER OF PRIMES IN EACH GROUP OF 10,000. 0 1,000,060 2,000,000 3,000,000 4,000,000 to to to to to 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 No. of | Differ-| No. of | Differ-| No. of | Differ- | No. of | Differ-| No. of | Differ- primes} ence | primes} ence | primes| ence |primes| ence | primes} ence I. 9593 7216 8 | 6874 | 29 | 6676 | 32 | 6628 7 II. 8392 | 1201 | 7225 | —9 | 6857) 17 | 6717 | 59 | 6540 | —12 III. 8013 | 279 | 7081 | 164 | 6849 8 | 6691 | 26 | 6510 30 EV 7863 | 150} 7103 |—22 | 6791} 58 | 6639 | 52 | 6511 —1 We 7678 | 185 | 7028 |} 75 | 6770} 21 | 6611 | 28 | 6613 |—102 VI. 7560 | 118 | 6973 | 55 | 6809 |—39 | 6575 | 36 | 6493 | 120 VII. 7445 | 115 | 7015 |~42 | 6765 | 44 | 6671 |—96 | 6523 | —30 VALET 7408 37 | 6932 | 83 | 6716] 49 | 6590} 81. | 6475 48 IX, 7323 85 | 6957 |—25 | 6746 |—30 | 6624 |—34 | 6554 | —79 Xx. 7224 99 | 6903 | 54 | 6708 |} 38 | 6535 | 89 | 6522 32 No. of ) primes f 78,499 70,433 67,885 66,329 65,369 The numbers of primes in each quarter million in the first five millions, with differences, are: Number of Primes Difference 0— 250,000 22,045 250,000 — 500,000 19,494 2,551 500,000 — 750,000 18,700 794 750,000. — 1,000,000 18,260 440 1,000,000 — 1,250,000 17,971 289 1,250,000 — 1,500,000 17,682 289 1,500,000 — 1,750,000 17,455 227 1,750,000 — 2,000,000 17,325 130 2,000,000 — 2,250,000 17,150 175 2 250,000 — 2,500,000 16,991 159 2,500,000 — 2,750,000 16,922 69 2,750,000 — 3,000,000 16,822 100 3,000,000 — 3,250,000 16,761 61 3,250,000 — 3,500,000 16,573 188 3,500,000 — 3,750,000 16,566 us 3,750,000 — 4,000,000 16,429 37 4,000,000 — 4,250,000 16,437 —8 4,250,000 — 4,500,000 16,365 72 4,500,000 — 4,750,000 16,271 94 4,750,000 — 5,000,000 16,296 — 25 and the numbers for the complete millions are : Number of Primes Difference First million . “ : ‘ 78,499 BISGCOna (5, GHI9 Tiel Geil a: 70,433 8,066 BEBATA ye say spaely ebay aethacr « 67,885 2,548 Fourth ,, ° * ‘ : 66,329 1,556 Fifth 5 3 - 2 r 65,369 960 D2 36 REPORT—1880. The following table contains the two longest successions of composite numbers met with in each of the five millions: Lower Limit | Upper Limit | Sequence First Million. 370,261 | 370,373 111 492,113 492,227 | 113 Second Million. 1,357,201 1,357,333 131 1,561,919 1,562,051 | 131 Third Million. 2.010,733 | 2,010,881 147 2,898,239 2,898,359 —. 119 Fourth Million. 3,826,019 __ 8,826,157 ave 3,933,599 3,933,731 131 Fifth Million. 4,652,353 4,652,507 153 4,738,651 . 4,738,777 | 125 In the ‘Philosophical Magazine’ for August, 1854, the late Mr. C. J. Hargreave determined the number of primes inferior to 5,000,000 at 348,527. His method, which is there described, consisted in calculating the number of numbers which are the products of two prime factors, of three prime factors, &c., and thus determining the total number of com- posite numbers between the limits in question. The number of primes in the five millions obtained by enumeration from the tables is 348,515. This includes unity as a prime, and it appears that Hargreave excluded unity, so that if it be included, his number would become 348,528, which differs by 13 from the number obtained from the tables. IV. Comparison of the wumbers of Primes counted with the Values given by Legendre’s and Gauss’s Formule. Legendre’s formula for the number of primes inferior to a given number z is . log «—1:08366 ; This expression Legendre published in the second edition of his ‘ Théorie des Nombres’ (Part iv. 1808), and he there gave a table containing com- parisons between the numbers obtained from it and the numbers obtained by counting up to 400,000. This table Legendre subsequently extended in 1816, after the publication of Chernac’s ‘Cribrum Arithmeticum,’ to 1,000,000. It does not appear why Legendre assigned the value 1:08366 to the constant which occurs in his formula, but it is probable that this value was originally determined so as to render very close the agreement with the numbers counted in the earlier enumerations, and as the formula still continued to yield good results as far as the later enumerations ex- tended, no attempt was made to improve the value at first assigned to it. The logarithm-integral li x, where li z denotes the integral, ” aa Lees we eo loge ON MATHEMATICAL TABLES. 37 a was employed by Gauss early in the century to represent approximately _ the number of primes inferior to x; but his researches were not published till 1863.!, This integral was also used for the same purpose by _ Tchebycheff ? in 1848 and Hargreave * in 1849, The following table exhibits the amount of deviation between the numbers of primes counted and the values given by Legendre’s formula. Number of primes z : z count a _ jog 2—1-08366 Difference . 250,000 22,045 22,035 — 10 500,000 41,539 41,533 — 6 750,000 60,239 60,269 + 30 1,000,000 78,499 78,543 + 44 1,250,000 96,470 96,488 + 18 1,500,000 114,152 114,179 + 27 1,750,000 131,607 . 131,663 + 56 2,000,000 148,932 148,976 + 44 | 2,250,000 166,082 x 166,140 + 58 2,500,000 183,073 4 183,175 +102 : 2,750,000 199 99 bN 200,095 +100 : 3,000,000 216,817 - 216,913 + 96 3,250,000 233,578 ; ; 233,636 © + 58 3,500,000 250,151 250,275 +124 3,750,000 266,717 ~ 266,835 +118 4,000,000 283,146 283,323 +177 4,250,000 299,583 299,744 +161 4,500,000 315,948 316,102 +154 4,750,000 332,219 332,400 +181 5,000,000 348,515 348,644 +129 The next table exhibits the deviations between the numbers of primes counted and the values of li z. x N add we liz | Difference 250,000 ~ 22,045 4 22,094 + 49 , 500,000 . 41,539 41,606 + 67 750,000 60,239 . 60,350 +111 1,000,000 ~° 78499 © "718,628 +129 1,250,000 kK 96,470 _ 96,573 +103 rt 1,500,000 ~ 114,152 Fr 114,263°! +111 . i 1,750,000 : 131,607 > 131,746 +139 _ 2,000,000 Cis oe ATA OSD 149,055 +123 2,250,000 166,082 sn '| Meese, LOUD 1 133 2,500,000 183,073 183,245 4172 2,750,000 - 199,995 200,160 ~ _ 4165 3,000,000 216,817 216,971 +154 3,250,000 233,578 233,688 -- +110 3,500,000 250,151 250,319 +168 3,750,000 266,717 266,872 +155 4,000,000 283,146 283,352 +206 4,250,000 299,583 299,765 +182 4,500,000 315,948 316,114 +166 4,750,000 - 382,219 332,404 +185 5,000,000 348,515 348,638 +123 1 Gauss, Werke, t. ii. _ ? Mém de V'Acad. de St. Pétersbourg (Sav. Etr.) t. vi. or Liouville, t. xvii. * Phil. Mag. July 1849. More detailed references to those papers will be found in Section V. of the Introduction to the Fourth Million, pp. 36, 37, — 38 REPORT—1880. From these tables it appears that although the deviations are less for’ Legendre’s formula than for the liz formula, the former increase in a more rapid ratio than the latter. As Legendre’s formula contains a disposable constant, chosen so that the values given by the formula might represent well the results of the enumerations for comparatively small values of z, it is to be expected the deviations would for some time be less than in the case of the logarithm integral formula, in obtaining which z is is supposed to be very large. The portion of the former of these two tables up to 4,000,000 has appeared in a paper ‘On the value of the constant in Legendre’s formula for the number of primes inferior to a given number,’ ! but the extension to 5,000,000 is new. This paper also contains comparisons between the numbers of primes counted and those given by the formule: az log «—1 and x log oT log up to 4,000,000. These have also been extended to 5,000,000; but it seems scarcely worth while to give the tables here, as the extension amounts to only one million. Report of the Committee, consisting of Professor SYLVESTER (Chair- man), Professor CAYLEY, and Professor SaLMon, appointed for the purpose of calculating Tables of the Fundamental Invariants of Algebraic Forms. In consequence of the academical engagements of Mr. (now Dr.) F. Franklin, the trained and skilled assistant in the computation of the tables, only a small portion (87. 5s.) of the 501. granted by the Associa- tion has been expended. With this sum the tables for the generating functions and ground- forms of all single quantics, up to the 10th order inclusive, have been corrected and completed, and the tables relating to binary systems of quantics for all combinations of orders up to the 4th inclusive, re- calculated. The results have been published in extenso in the ‘ American Journal of Mathematics.’ This revision has led to the discovery that two of the forms included in the table of ground-forms for a pair of cubics previously accepted as correct. are composite forms, and should be omitted from the catalogue. The table affected with this error had been calculated by the German mathematicians after Gordan’s, and by Mr. Sylvester after an entirely different method, and the results were in perfect but fallacious accord. The German method, it may be stated, never offers a complete guarantee against the occurrence of an error of this nature; its per- 1 Proceedings of the Cambridge Philosophical Society, vol. iii. pt. vil, pp. 295-308 December 8, 1879). ; OBSERVATIONS OF LUMINOUS METEORS. 39 petuation in the table as calculated by Mr. Sylvester was due to an arithmetical oversight on his part. The detection of this grave error is due to the fortunate circum- stance of the co-operation of Dr. Franklin, whose skill, fidelity, and accuracy as a computer it is impossible to praise too highly. gojas:_ His time being now again available for undertaking this kind of work, for which he possesses unrivalled aptitude, the Committee request a renewal of the grant of 501. for carrying it on. Report of Observations of Luminous Meteors during the year 1879-80, by a Committee consisting of JAMES GLAISHER, F.R.S., &e., E. J. Lowe, F.R.S., &c., Professor R. S. Bau, F.RS., &c., Professor G. Forbes, F.R.S.E., WaLTeR Fuicut, D.Se., F.GS., and Professor A. S. HerscHEL, M.A., F.R.A.S. Twenty annual reports having been already presented by this Committee since its first appointment in the yéar 1859, it is proposed in this, its. twenty-first report, to review the result of the records and researches upon which (independently of the twelve preceding annual reports presented by Professor Baden-Powell) the Committee has during that long period been engaged. In a treatise on ‘ Atmospheric Phenomena,’ published by Mr. E. J. Lowe (one of the present, as well as an original member of this Com- mittee,) in the year 1846, a copious collection of accounts of halos, auroras, and other unusual meteorological appearances, omitting, however, notes of fireballs and shooting stars, served, for the first time probably to many English readers, an important purpose in separating entirely the’ latter class of phenomena from those equally conspicuous and notable appearances which are of a purely meteorological origin and signification. The example of orderly arrangement of such descriptions which this work supplied was followed up and soon afterwards supplemented by the records of ordinary and extraordinary observations of luminous meteors begun by Professor Baden-Powell in the year 1855, and continued in subsequent annual reports of the British Association until the present time. ' Immensely as the theory of meteor-systems has progressed during the - long season of attention which has thus been directly bestowed upon them, the apparitions of fireballs and falling stars are still as striking and remark- able phenomena as they used formerly to be, and in some important respects also they remain just as truly problematical ‘ exhalations of the skies’ as. they were in former days. For although they are now known to be as- tronomical bodies, instead of objects depending on the winds and other uncertain meteorological conditions for their various aspects and produc- tion, yet no astronomical theory has yet been discovered or constructed sufficiently far-reaching and adapted to account at the same time satis- factorily both for the well-known occurrences of meteor-showers, and also for sporadic meteors, including the rarer phenomena of fireballs and aérolites. References and allusions are abundantly made in the later years of these Reports both to the well-known discovery of tle clustering together 40 REPORT—1880. a») of meteoric showers and certain periodic comets in the same circum- solar orbits, and also to the general theory of gatherings of star-dust in nebular bodies, applied to explain the origin of all classes of meteoric phenomena by Schiaparelli. : In recent years’ appendices to the Reports the additions to our know- ledge of the mineralogical structure and probable past history of aérolites is also amply reviewed; and the real paths of aérolitic and detonating meteors have in several instances been found from observations. A recapitulation of these leading views, and of the observations chronicled in aérolitic and meteoric parts of the Reports during the latter and larger part of the long period of their continuation, leads to the conclu- sion that little (if any) similarity of character can yet be confidently recognised to exist between aérolites, or detonating fireballs and the equally rare and magnificent meteoric phenomena of cometary star- showers. The intermediate class of sporadic fireballs and shooting stars has been largely and closely examined and discussed, with consequences of the greatest importance to their scientific discrimination and description. The number of meteor-showers or radiant-points proved to be productive of ordinary displays of shooting stars has been greatly multiplied by observations and reductions; some few of them, in particular, being shown to be limited and confined to one or two days only of duration, in the annual dates of their appearance. Fireballs of various magnitudes, of whose real paths simultaneous observations furnished good determinations, have not unfrequently been shown to be conformable to well-established radiant-points of shooting stars; and among the many hundreds of meteor radiant-points that have now been recorded, there is also sufficient evidence to show that many of the ordinary meteor-systems which they denote may very probably be following in the trains or orbits of certain formerly recorded comets. Although presumptive views of a naturally wide distinction between aérolites and cometary shower-meteors are far from being yet refuted and explained away by recent theories and observations; yet the real paths of more than one detonating meteor have now been retraced to recognised ordinary radiant-points of shooting stars. The course of the large detonating fireball of Nov. 23, 1878, moreover, while it was strictly con- formable to the well-marked radiant-point of the a-Taurids of November, presented also a very close accordance with the somewhat uncertainly determined orbit (because founded on rather scanty observations) of the periodic comet of 1702. Much aid, it will be seen from this short outline of the Committee’s labours during twenty years, has been afforded by its annual compilations to advance the present astronomical theory of shooting stars with materials of observation and by reviews of contemporary speculations. The opportunities of which the Committee has hitherto been able to avail itself for correspondence and reductions of the observations annually received have not been adequate during the last two years for producing a complete category of their yearly undertaking. A detention like that required last year of some of the meteor contributions, and a deferment for a season of some reviews of printed memoirs on meteoric subjects, must accordingly be granted for the present, until the occasion may occur ween % more convenient opportunity may offer itself for their presenta-_ 10n. ; OBSERVATIONS OF LUMINOUS METEORS. 41 In the following appendix of this interim Report some errors are cor- rected of which the occurrence in the last two years’ Reports passed undetected until after the publication of the volumes in which they were accidentally recorded. The earliest opportunity within its reach is now taken by the Committee to rectify these errors and to point out some errors in earlier Reports, to the appearance of which the brief survey of those Reports required for preparing the above short outline of the whole series of them has been the immediate occasion of drawing the Committee’s attention. - In another appendix, by Dr. Walter Flight, the occurrences of stonefalls, and abstracts of the analyses and discussions relating to them, which have taken place during the past year, are recorded. AppenpDIx I. Revisions and Corrections of real paths of Meteors, and of other results of observations contained in the Reports of the last two and of some pre- ceding years. During the first years following the appointment of the Committee in the year 1860 for the collection of meteor observations, the importance of noting the radiant-points of observed meteors’ tracks was not yet recog- nised, and was far from being generally practised and regarded. The real directions of flight of many shooting-stars and fireballs, the positions of whose real courses were found from simultaneous observations during several years previous to 1866, were accordingly only indicated, if at all, by the altitude and azimuth of the point from which the meteor proceeded or was directed in its line of flight towards the earth. Many ofthe meteors of which the real paths were investigated from more or less plentiful accounts of their appearance, in the appendices of these reports for the years 1860-65, were brilliant and sometimes detonating fireballs, besides some smaller shooting-stars. Among the adjustments needed to accommodate the rough observations to each other the choice and deduc- tion of the radiant-point had at that period of the Committee’s first proceedings not yet acquired the significancy with which on astronomical grounds it has more recently been invested, the principal objects of those earlier determinations having simply been to obtain the real heights and the lengths of path and velocities of the meteors’ flights. Fair weight for determining the radiant-point was accordingly not always allowed to the best recorded observations for this purpose ; and some obvious radiant- points like those of the ‘ Leonids,’ &c., not being then established; con- siderable errors from this cause, and occasionally also from mistaken calculations, have been detected in a review of the many real paths de- scribed in the above-named part of these reports as regards the directions, or as concerning the astronomical positions in right-ascension and declina- tion of the radiant-points from which those fine meteors were directed. The radiant-point positions given in the subjoined list sometimes differ slightly, from fresh projections and comparisons of the best observations, from those of the real paths adopted in the earlier reports. In cases where the errors discovered are, from various causes, of much larger magnitude, however, than these small emendations of the original ‘re- ductions, the nature of the hitherto unnoticed misconstructions is stated and explained in notes which are appended to the list. — “ “ 1880. REPORT AI ~ 08 ‘d ‘ZosT 61 ‘go ‘dd ‘Z9sT 6L ‘ez “dd ‘Zost (paurol -qus ‘ajou oat} ag) “gL ‘F'dd ‘Zggt gL ‘F dd ‘Zogt 11% ‘dd ‘z9st 61g ‘d ‘g98T pues ‘9 “d ‘98ST 1g¢ ‘d ‘gost éL ‘d “0981 Sig “d ‘g98t pure ‘gz ‘dd ‘Tost *sqa0daa dsoyy JO SOUIN[OA IaTp1va Jo ased @ sivok ! souerosoy (S,119X9T) I OLLI P sjurod JuBIper UAOUy (steH) o10g YON oy srVoN _ SLIvlOg IeaNt (suory -BAlasqo = 4seaq oy} Jo uwopool (OT ¥ “Z) 01g) “I prey, J IMe], 4 ION g + og jnoqy ‘T primey, | ney, (4 sea) > (o8 F) 26 + §9 jusoordey p iwaN | (og *) Ss — OTE — #pouoipuy g Ivan TG-086 ‘9 “ony 03 8 Ayn £8 03.2 (of F) ES + 16 THB]ILSVg (08 #) 0% — 982 ‘] pene, Lmey, & 1woN 006 + (01 *) ¢9 =s (‘do}MON “V “H) SF —- GOg OQy — styuediag d tw GE + LEZ ynoqy o0l_*F (ST + #9 ‘T puny, (rmey, “) §10) LL + ol F SIB]S poxy JSoelveu Ag g n WGI suostredu0s9 qurod-juvripet poydopy Aue ‘nes -saq. ‘surywuoyo(y ALOHON 09 seg ‘“surjzeuojod ‘ony ‘JoIsSIIg * C= IaysayouUry, puv uopuoyT & < JeuuvyO yssug =f C F vog YON + < ox ‘A10}BAIOS -qQ woysvoq ¢ = I09}9UL o51e'T “BOLIOULY on "V'S'a “Ox “yO X MON ! OT [LASTU -uaq ‘Sutyeuoye(y purjeriy pue peayAjoH °C = ‘urd eT OF ‘urd 0¢ 8 ‘urd g¢ 2 ‘Ue OF 6 Curd eT 2) Ss. Ww UE souvivedde jo sov{d puv ozIs [e10ues) (awry [vo0]) 10 SLID 20H g ‘eq 61 “AON GI “AON 9 ‘suy 9T Aine 9t Aue ‘T98T I ‘AON ‘09ST 9 ‘ony ‘098T GT “AON GB ‘990 ‘6S8I 0y8q pie) 0G go} Om peutofqns ay} 04 sroquinu gola1AjJoyY “G9-698T SUVHA WHHL DNIVOG GHAUHSHO ATANOG SUVIS*DNILOOHS GNV STIVAHNIA JO SNOLLISOd LNIOd-LNVIGVa 43 1a¢ ‘F¥ ‘dd ‘gost Tag ‘so “dd ‘g98T “Pra ‘Pla 0zg ‘og ‘dd ‘ggg 068 “Zaz “dd ‘g9gT pue ‘9, ‘d ‘Z9gt 0zg “d ‘g98T pue ‘9, ‘d ‘Z98T 0zE ‘0zz “dd ‘go8T 61g ‘61g ‘dd ‘g9gt 0s ‘F¢ “dd ‘Zogt 08 ‘9F ‘dd ‘Z98T (ajou poutol -qnus 94} 999) ‘0s ‘9F “dd ‘z9sr OBSERVATIONS OF LUMINOUS METEORS. 6L “ze ‘dd ‘Z98T 08 ‘oF ‘dd ‘ggg (j) praraey (sqjed guoredde oy3 jo uorjool -oid yoarrp Aq) ‘TIL PlmMey, ST[NOIO_] 9 IVON 1]90 ¢ IwoN UINIOUIMIE > Tey stoudry 4b van STLOUTT suzy) g Jjvon TWMIOSTY a + IwaN Isudoq (9 ») f emby d ran 1909 '? Ivon stjoog > Ivan Tney, & Le93N STUISITA 5 IVAN (1% + 8 HMey, 5) WeIVqePLY IVON (.01 +) ge + 012 (oT *) 81 — &1 (09 +) 93 + ZOE (o8 #) €¢¢ + SOT (68 +) 8 + OLT (oS *) 86 + ST (of F) 0G + GFE Gs *) GI + (.9 *) 008 (08 F )F + Cok FOE (0ST *) 0g + 086 (01 #) 21 + $9 (og ¥)9 + 02 (.0L #) 8 + 16 CH'S'V) sninvy, ur ‘ondypos a4} UO eirqyUe) FO TMA 0} sopliqoy pystpay ur! ¢ = aILysyyleg puv suIpeyg = “FYSTT “Tap ur $y C f= Apueur410o 0} IPLPYOS OGL ‘Suryeuojog ‘C € = Aqriayoory 0} YALA “Surly -euojog °C $= T1esuroy Joymog *§ XG Tleausoy 07 orlysyIM °C $= Ammqst[eg 04 YOM IO ‘qustIMg ur’ € 7 = xossng puv uopuotT fi = PLOFXO OF Amqioyueg € = STEM YON 0F 7 O1TYS -Aqiaq *€ $= artysAqiaq 04 aiTysyesiog °C = detTysoy) 07 { PITYS1A4sa010'T :1eq4s suryooyg I04svo “UBT ‘SUT}eUOZOg moy rod Q¢g roMoys -1e4S qystaq, ‘quoy ‘syBoueaeg ‘md og 9 umd Og g ‘urd pF ‘umd OF 9 ‘ud cf OL ‘md 0g 9 ‘umd et 9 ‘urd ZZ OL ‘urd gt OT ‘urd of 6 ‘urd 0% 8 ‘ud F TT ‘urd of g ‘urd [1 036 LO 1G “uel “E98T LG ‘AON 96 “AON 9T “AON 93 “qdag ee “dag ao dag 61 “ydeg &6 “QOL 6 A9 83 “URL ‘ZO8T 8 99d FG *997 LI 9T OT REPORT—1880. sH (Ayo = Ay,-1) an V3 (A?y7o + A? Yn—2) Tee St = View 1 ArYo a (—)* AY \ StS eee which is the usual formula of quadratures.* Section 2.—Inverse Interpolation. Using the common formula of direct interpolation, the problem is to find the value of n from the formula BS Naecety iget ys we: oral a2 where everything but » is known. Stopping at any given order (say the +") of differences, neglecting all beyond it, which is evidently permissible provided the differences be con- vergent, and sufficiently so (and only on that hypothesis) this really involves the solution of an equation of the 7? degree in n. It is usual to effect the solution by successive approximation, that is to say, by stopping successively at the first, second, third, &c., differences in succes- sion, and determining at each step a new and more accurate value of n. _ Thus, neglecting all beyond the first difference, a first approximation gives A? by + . e e ee ° UT (on 7 0) 2A Po- This merely amounts to the use of proportionate parts. The second step is to calculate &(m — 1) 4° 6). = 4, * See De Morgan, Diff. and Int. Cale. p. 313. The proof there given is sub- stantially the same as this, only differing in arrangement. The above arrangement perhaps shows a little more obviously the reason why the constant part used is the same in both formule. Stated more exactly, what is done is to introduce an inter- mediate (but indefinite) limit, and to reverse one of the definite integrations, Doe , REPORT—1880. then, neglecting all further terms, as a second approximation No = ($n — $0): (A bo + 1). For a third approximation ¥Gis-D) { A% +3 - 2) Ago b= cy may be calculated: this gives 2. 23 = (bn — $0) = (A 0 + 62). The process is very cumbrous when carried beyond the first correction of the proportional part. But it has one very marked advantage, namely, that, being a tentative process, any error in one step is more or less com- pletely corrected at the next step, and the practical effect of accidental error is thus to make the approximation less rapid, instead of absolutely vitiating the result. It might even happen that an error of calculation, by being nearer the required answer, might give a more rapid approxi- mation. The rapidity of approximation depends, firstly, upon the degree of convergence ; and, secondly, upon the first approximation being sufficiently near the required result. This is exactly parallel to what takes place in the numerical solution of equations, and there is, here as there, the same difficnlty, presenting itself where any given approximation is nearly half- way between two solutions, and the successive results oscillate between the two, instead of converging to either.* When convergence is assured, this tentative method is probably the best, and is at any rate the safest. An extension of Hutton’s rule for extracting roots t might possibly be found of use. But the criterion of convergence in this process has not been satisfactorily determined. There is, however, reason for believing that the convergence is not so good as in the direct tentative process given above. This process is applicable, not only to the common formula of inter- polation by descending differences, but to all formule which can be arranged by ascending powers or factorials of n, the index of interpolation For in any such form it still remains as the approximate solution with respect to of an equation of the form ; 4 Gye ag 2? Fe ag te where a™ is either a power or a factorial of z. Section 3.—Lquidistant Ordinates, not differenced. In general, writing U, = CoUp FOU F..... Cy Uy where UU, «. ~. « are certain given values of w corresponding to given values of x, namely, a, 2, .... 2, and then assuming a form of w in terms of « which will allow the coefficient ¢ to be so determined that a = #,,shall make c, = 1 (when 2, is one of the given values) and all the other c’s vanish, a formula of interpolation is obtained which can be con- verted into a formula of quadrature by integrating with regard to x from * See Horner, in Leybowrn’s Repository, No. 19, p. 63, and J. R. Young, Theory and Solution of the Higher Equations, second edition (1843) note, pp. 474-6. { For which see the London, Edin.and Dublin Philos. Mag. vol. xx. (1860) p. 446, and the Philos, Trans. for 1862, vol. clii. pp. 429-431. ON QUADRATURES AND INTERPOLATION. 333 0 ton. When the values are equidistant, 7 h or + A « must be used instead of 2,,. There is usually an advantage, both in the symmetry of the formule and in the probability of an accurate result, in taking ordinates on both sides of the origin of interpolation. .On any reasonable hypothesis, a mean result is generally better than one near an extreme, and this remark is verified by the greater tendency to convergence of the formule when the interpolated value lies near the origin of interpolation than when it lies away from it. As a general rule, where extreme accuracy is required, it should not lie farther off than half the equidistant interval. There are then two kinds of symmetry to consider: symmetry to a central ordinate, involving an odd number of ordinates and an even number of intervals ; and symmetry to an interval, involving an even number of ordinates and an odd number of intervals. Taking the former case, of symmetry to an ordinate, we may write for the ordinates Uun + 2 «oe Ung 5 WU} » Un, Uy, U2 abet te cet U ny and the general formula of interpolation will be given by Je ee PE Se Cy Uy + Coy + 2 we ee HF CQUny where the coefficients c are functions of z, determined by the condition that z=rh shall make c,—1, and all the others vanish. The simplest way in which thig cay be done rationally and integrally is by writing w (h? — a?) (4h?—2?) . 2... (n? h? — 2”) 4, = — SX | 2a... h™ {2 Uo _ Un=1 U1 _ Un-1 U=1 x ew—-h “«e+h 4 Un Un * 2 — nh = e+nh where v, is the coefficient of «” in the binomial expansion (1 + )?". This gives for n= 0, u,, = Uo (as it ought) a (h? — 27) f2u wm wy EO. 2h? Ay e—-h wth Be = (Ra Oe ae ie _ 4m, 40, ieee 2414 ri. a a TG is Uo U_9 e—2h we+2h In the second case, of symmetry to an interval, let any even number of ordinates be ee Ma assis ty As Any Diy. cents aif M,, N, and let the variable « = 4 z, or a be the independent variable measured from the middle point of the middle interval AA; =h=2k. Then if v" * Boole writes this in 4 slightly different form; see his Finite Differences 2nd edition, p. 50. The formule themselves are due to Newton; see his Methodus Differentialis (London, 1711, published by W. Jones as part of the Analysis per quantitatum series, fluwiones, &c.) pp. 93-101. They are also te be found in vol. i. of Horsley’s edition of Newton’s works. 334 REPORT—1880. be the coefficient of 2 in the binomial expansion of (1 + 2)?"-1, the corresponding formula is geet 3 A ee eee (2n-1)7 kh? — 2? 2 ° a, 6 cele isl erlanen(Ane'= 2) han Vv A Vv A, wn Un—1 B ae, Un—1 B, k+z k—2z 8k—2z 38k +2 N N, \ # ro LT Rite Shxgey ach) RL ass (Bad ly fee Thus if n=1 Uz = =e — Se a (as it ought). This formula gives a very important theorem for the bisection of an interval. Making z = 0, k& divides out, and there remains eer tiene Ce a — ’ MT siagTgD, wh wees ee ae 5B + B,) + ; Un-2 (CO + O)- ceeeee \ When n=1,2u,=A+A, n=2,16%=9(A+A,) —(B+B,) n= 8, 256 u) = 150 (A + A,)— 25(B + B,) + 3(C4+0C)). The general case of » =1 is simply equivalent to the use of pro- portional parts. ye{ Although, as has been already remarked, the rules for quadrature by ordinates can be obtained by integrating the corresponding expressions for interpolation by ordinates, that is not the easiest way of obtaining them. One way is to integrate ’ (1 + A)* dz after expanding it, and 0 then, rejecting all the terms after A’, make n = r and substitute E — 1 for A. This process is given in most of the text books. But a simpler and more symmetrical method, and one which can easily be extended to higher integrals, is by the use of indeterminate multipliers, as follows: Write vu = a) + a.27 +a,24 +a,a°+..... whence - : ude=nday + lepap ews Datwet Paris - 2 -—n 3 5) é Again substituting 0, 1;=2,+3..... in succession for 2, Up = A 5 (tar Hh) = do + ay + ay + a5 + @ ss: ode aAt * See De Morgan, Diff. and Int. Cale. p. 549. t See Boole, Finite Differences, art. 10; also Murray’s Shipbuilding, p. 32. ON QUADRATURES AND INTERPOLATION. 335 1 5 (Uug + Uy) = My + 22a, + 2tay + Bag + wee vcee 5 (tas + Uy) =a + Say + Bay + Bag + eoeeeee . . . . ———- e ° . e e e Now, introducing indeterminate multipliers, 1 gnu timer ta ait reece ee AN Ay + 27Ay + 37Ag +. 2... WA, = Lis 3) AyH BAH BAG + eee MA SEH Ay + 25r, + BA, +1... . nr, = ae from which the value of any 2 is easily formed, by means of determinants if necessary. For any given value of x the coefficients are those of the corresponding rule for 2” ordinates or 2n + 1 intervals, Thus, stopping at n=1 i! devs 4 gto PALA N Sig No 7 1 a ude = : (w_, + 49 + 41) Sl Again, stopping at n =2 Nh bi Nia Nya, BIS Ny ichahen i BF 2 3 5 14 64 24 whence A, = re ie 4g) ®° = AE JS. uda =— (7u_» -+ 82u_,; + 12a) — 32u, + Zu2). -2 The rules for an odd number of intervals or an even number of ordinates may be got by giving «# the successive values +1,+3,+4 5 -..-.. Then w,+4, takes the same value as before. Writing n= 2m + 1, and using as indeterminate multipliers pry, 3, ws . . . . the equations become Pet a Pp +e eee ee Pome, = 2mM+1 Py + 8? 34+ SO? pst ee eee (2m + 1)"Hone1 = 5 2m +18 Py + 84 pg + Of ps5 + wae ee (2m + 1)"pone1 = 5 2m + iy Stopping at m = 0, hp, =1 Sf: ude = : (wa1 + %) -1 2 336 REPORT—1880. Stopping atm=1,2m+1=8 Oo” Bree eae ce Py + ps = 3, oy + 93 = 9 i YS as dp Oe and eo (uz Ae 3 uy +3, + U3) -3 It is to be observed that the interval in the » formula is 2, and not unity. ans bati i The actual coefficients for quadrature by means of equidistant ordinates, when the interval’is taken as unity, are * 2 Mecca : (1 +.1).. The trapezoidal rule 3 ordinates or i The parabolic rule, or 2 intervals \ 3 ie a Simpson’s first rule 4. ordinates or 3 intervals a - . . : . , . . . : (1+3+4+3+41) Simpson’s second rule 5 ordinates or 2 4 intervals \ 4B (7 + 82 + 12 + 32 + 7) - ntonale } ggg (9+ 75 +50 +504 75 + 19) 5 intervals 288 7 ordinates or il 6 intervals \ jap (Al + 216 + 27 + 272 + 27 + 216 + 41) 8 ordinates or 7 (751 + 3577 + 1323 + 2989 + 2989 4+ 1323 7 intervals 17280 +3577 + 751) 9 ordinates or 4 (989 + 5888 — 928 + 10496 — 4540 + 10496 8 intervals 14175 — 928+ 5888 + 989) 10 ordinates or 9 (2857 + 15741 4+ 1080 + 19344 + 5778 + 5778 9 intervals 89600 + 19344 + 1080 + 15741 + 2857) 11 ordinates or 10 (16067 + 106300 — 48525 + 272400 — 260550 10 intervals § 598752 + 427568 — 260550 + 272400 — 48525 + 106300 + 16067) In the, foregoing the numerical coefficients only are given, and the ordinates have to be inserted. Thus, the ordinates being a, b, c, d, e, the rule for five ordinates or four intervals is S (7a +82b4+ 12c +°32d + 7e) x interval. To the above should be added Weddle’s approximate rule for 7 ordinates, or 6 intervals, namely : f AQ +541464145+)). * These are all taken from Cotes, Harmonia Mensurarum, by Robert Smith, Cambridge, 1722, De Method Differential, p. 33. The principle of these rules seems to have been known to Newton; see his Methodus Differentialis already quoted. ON QUADRATURES AND INTERPOLATION. aor This is a modification of the rule of seven ordinates already given, aE ; 1 differing from it only by 140 ‘AB.* It will be observed that these formule are symmetrical end for end, and since the integration is between definite limits, the origin of the abscisse is indeterminate, and may be taken so as to fall in the middle, or so that the equivalent integration is from — rhto + rh. It follows that, for the purposes of comparison, instead of taking y= bo tbeatbw+t.. es. Neetu a we may take, since +1 af a?™-! da = 0 always =1 Y= bo + by x? + ale ey le) eB lel eure: ‘. (i Adil omitting the terms containing odd powers of #; and that we therefore obtain no greater generality by using 2m ordinates instead of 2m — 1. The error in either way is of the same order.f The formule of quadrature for an odd number of ordinates or an even number of intervals appear to have been also given by James Stirling,t who adds a set of what he calls corrections. The number of ordinates being 2 m — 1, the correction is of the form — AE-"(E— 1) x base the coefficient A being apparently determined so as to make the corrected value exactly agree with the result obtained from integration, when both are applied to #7". But they do not lead to the next rule, for 2m +1 ordinates. As a particular example, the correction for the rule of three ordinates, namely, pase (w_, + 49 + 4) x base, is — base (wy — 4u_, + 6uy — 4u,; + uy) X base. The values of the coefficients A are inexactly given by Stirling as ot eels (i bop 180’ 470 ’ 930’ 1600 i 2 3 296 180’ 945 ’ 2800 ° 467775 The inaccuracy is not a mistake, because Stirling only uses them as a test of approximation, and not as a means of obtaining accuracy. Bertrand (Calcul Intégral) gives the corrections in a slightly different form, from which the coefficients just given are obtainable by multiplying Bertrand’s corresponding coefficient by 27": A?”0?". In the following table we give Bertrand’s first coefficient only. It is the excess of the com- instead of * The first eight formule are given by Thomas Simpson and verified by Atwood. All the rules are given (but with some misprints) by Bertrand (Calcul Intégral). Atwood makes a curious mistake in the rule of 8 ordinates. He is endeavouring to correct Simpson, with whom, however, his result is really identical, only that Atwood has introduced the factor 49 into both numerator and determinator, without seeing that it divides out: see A Disquisition on the Stability of Ships, by George Atwood, F.R.S., read before the Royal Society, March 8, 1798, and reprinted separately (p. 62 of reprint). : + See Todhunter, On the Functions of Laplace, Se. pp. 98 and 104. t See his Methodus Differentialis; London, 1730, p. 146, Prop. xxxi. He stops at nine ordinates. 1880. Z 338 ; REPORT—1880. putation by the rule for 2m — 1, or 2 m ordinates, over the actual value of 1 . the integral f” ada. 0 Number of | Number of J Number of | Number of ordinates intervals Excess ordinates intervals Excess 1 1 2 = v4 woke 6 é 38880 1 167 3 2 — 8 . eo 120 10588410 1 37 4 3 — 9 8 —— 270 17301504 if 865 5 4 wee 10 9 poeta | 2688 631351908 6 5 11 ll 10 260927 52500 136500000000 This is a fair indication of the error to be expected in treating a con- vergent form by these rules. It is no criterion where the curve approaches parallelism to the ordinate. It must be remembered also that the higher rules use more ordinates, and therefore ought to give more accuracy. As regards relative accuracy, the proper test is so to use the rules as to cut up the function or curved area into the same number of intervals, for which purpose it is necessary to use the least common multiple of the order of (or number of intervals in) the rules. Thus, what has hitherto been considered, in the case of two and three intervals, is the comparison of r {1900) + 49(F5) +190) } with £ {1 9(0) + 39(5) + 39(5) “ 19(1) } 8 3 3 the proposed comparison is between gits+2+4+ 244 4 1) md 3(1+8+3424+ 343841) with corresponding ordinates, namely 1 2 (0), o(G) (=) eoee3nvee (1) In this way, using 21 ordinates, or 20 intervals, +10 ; f afde gives -~ 10 Accurate value by integration ° : 2,857,1428 Errors By rule of 5 ordinates F - js 2,857,17324 + 3032 By rule of 6 ordinates ‘ » . 2,857,2084 + 6532 Ratio of errors 128: 275 eS a ON QUADRATURES AND INTERPOLATION. 339 20 Again, f° (wide gives Accurate value by integration . 3 182,857,142§ Errors By rule of 5 ordinates : é : 182,857,1734 + 30}9 By rule of 6 ordinates é : ; 182,857,20382 + 653° which accords with the former result. In the same way, using 7 ordinates or 6 intervals; we find that +3 ‘ f wdz gives -3 Accurate value by integration . : , , 97°2 Errors By rule of 3 ordinates. : ; ; , 98 + 08 By rule of 4 ordinates. : : , . 99 + 18 Ratio of error 4 : 9 6 Again, f” a'dx gives 0 Accurate value by integration - . : 15552 Errors By rule of 3 ordinates . . “ : 1556 + 08 By rule of 4 ordinates ; : A : 1557 + 18 which accords with the former result. These coincidences arise from the change of origin not affecting the definite integration. In this particular case the errors may be shown symbolically by operating at once upon ¢ + 4)" from « = 0 tox = 6 by (1) Simpson’s first rule (three ordinates) (2) Simpson’s second rule (four ordinates) (3) The rule of 7 ordinates The results are, in ascending powers of A i) Gagged 6418 +274 2441254 Ba+5 ope Sa 6418+ 27 4244123 4 343 3 Son Bevel € cy 2 ‘ aL (3) ..... 6418427 +242 4 384 7) and the errors are for (1) + 55 4 +35 AS +75 As Sate ADA Sila "AG en Oy 4g 8 ea + 980, Neglecting the last term, it appears that the ratio of error is as 4:9 in favour of Simpson’s first rule as against the second. It is worth while to continue this comparison backwards. For thus it is not necessary to have recourse to arithmetic. Taking a parabola with axis parallel to the ordinates, it is easily seen that the rectangle between the middle ordinate and the base is a better approximation than the trapezium consisting of the chord, the base, and the extreme ordinates, and that the ratio of the errors is + 1: — 2, the errors being of opposite si So far as the first six cases go, therefore, it appears that a rule with Z2 340 REPORT—1880. an even number of ordinates has an error numerically about double that of the corresponding rule for one ordinate less. The number of cases tried is not sufficient to warrant any general inference as to the compara- tive amount of error, especially when we consider their signs; but it is highly probable that the rule with an odd number of ordinates is always better arithmetically than, and not only of the same order of error as, the rule with one more ordinate. As has already been stated, no general investigation of these comparative values appears to have been made. The point is, however, one rather of analytical curiosity than of real importance. The rules requiring high orders of differences are better replaced by lower rules with more ordinates, unless in the very rare cases where the ordinates themselves are difficult to calculate. It is claimed that such an exception is found in calculating the curve of stability of a ship when the mainwale, or armour shelf, and the deck are successively immersed ; but there is at least a doubt in these cases whether the dis- continuity, which makes the calculation of more ordinates difficult, does not vitiate the accuracy of the higher orders of differences. If that be so, the advantage sought by their use—namely, to be sure of not adding an error of calculation to the errors of measurement, or to the errors due. to wide intervals—would of course be lost.’ Nevertheless the higher rules are analytically nearer the truth, and must be actually so in certain cases. Only it must not be taken for granted that these are usual cases. It is the practice of French naval architects to use the polygonal rule through- out their calculations, in deliberate preference to the rule of three ordinates. The arithmetical work is thereby much simplified, and so the liability to accidental error is diminished. Moreover by taking ordinates sufficiently close, the error of the rule can be reduced without limit, and where the ordinates are inexact, it is not clear that the parabolic rule has any advantage.* In dealing with actual data, the use of a large number of ordinates has evidently the advantage of taking a more complete account of the facts than the use of a smaller number. Any want of continuity between the ordinates is necessarily ignored by all the rules, and that to the greater extent, the greater the interval. The rule of nine ordinates, and many of the higher rules, involve nega- tive as well as positive coefficients, and are inconvenient on that account. The amount of the difference between the use of the polygonai rule and the parabolic (or Simpson’s first) rule is best shown geometrically as follows: il B Cc * Dr. Farr has used the same rule, or an arithmetical process equivalent to it, for the integrations used in the Life Tables calculated under his superintendence by the Registrar-General’s Department. See the Sixth, Hleventh, and Tivelfth Reports of the Registrar- General for Births, Deaths, and Marriages in England (1847, 1852, 1853), and the English Life Table published by the Registrar-General. —- ON QUADRATURES AND INTERPOLATION. 341 Let Aa, Bb, Cc be three consecutive equidistant ordinates. Then, by the polygonal rule, the area is represented by the trapeziums AabB and BbcC. Let at, tc be tangents at the extremities of the curve, and draw at’ parallel to tc. Then the actual area of the curve regarded . 2 : as a common parabola is the trapezium AacC plus 3 of the triangle ate (=ta?’) while the polygonal area AabecC is AacC See te 2 =AacC + =f at’, and the difference between these is( — 3) tat’ — - Tichstes When more ordinates are used, it is easy, by repeating the construction, to form a triangle which shall give a superior limit to the error made by substituting the trapezoidal rule for the parabolic. For the geometrical addition of the curvilinear segments, taking each as two-thirds of its circumscribing triangle corresponds very nearly (although not exactly) ‘to an algebraical addition which can be effected graphically on the second ordinate from each end, by drawing parallels to the chords and tangents from the head of the first ordinates.* It also follows that if the tangents at the extremities of the curve are parallel, the difference between the two rules disappears, and they lead toa result practically identical— that is to say, only differing by an error of a high order. Section 4.—Multiple integrals, ordinates not differenced. a b A multiple integral of the form oe. s-. & de dy, in which —a,/—b the limits are all constant, and the variables (except w) all independent, can be computed by treating each variable separately, by a repeated appli- cation of any process of arithmetical integration. In the case of a double integral applied to the calculation of volume this is equivalent to cutting the volume by parallel plane sections, obtaining the areas of these by any method of ordinates, and then summing the areas of these sections, each taken as an ordinate, to obtainthe volume. Thus, taking nine equidistant ordinates with the interval 4 in one direction, and & in another at right angles to it, and calling them a, b; cy Qo by Co a3 bg cg an application of Simpson’s rule gives us for the plane areas Fh (a + 4d, + 6), 5 h (aa + Aba + 00), 4h (as + Ads + 09) or, using the vertical sets, Ak (aly 4a + as), 51 Real eae a ee ee * See Woolhouse ‘On Interpolation, &c.’ Assurance Magazine, vol. xi. p. 308—sepa- rately published by C. and E. Layton in 1865. See also Leclert, ‘Note sur le Calcul numérique des aires curvilignes planes,’ Annales du Génie civil, tome viii. p. 630. M. Leclert states that his note isin great part a reproduction of M. Réech’s lessons. 342 REPORT—1880. A second application of the rules to either set gives 1 a, + 46,4 ¢ —hk< + 4a, +166, +4c, > = V 9 +a3;+ 4b3+ cz It might be supposed that this represented the volume-integral of a paraboloid with its axis parallel to the ordinates; but this is not so, for in the paraboloid, since all parallel sections are equal and similar, a, — 2b, + ¢, = a, — 2b, + ag = a, — 263 +.€5 or a, — 2b, + c, —2a, + Ab, —2c, = 0) + a3 — 2b, + cy Combining this with V (above) gives ; fe Jape O1*. ae aia al aaa V==hk << +a, 4+2b, +e, > == hk SO 4+ 803,40 3 np peak 0 as Ol stes So that the volume of the paraboloid for nine ordinates is given by either set of five symmetrical ordinates only : that is to say, by either the central one and those at the four corners, or by the central one and the four at the middle points of the sides of the square. Dr. Woolley, to whom this simplification is due, showed that this rule applied not only to one paraboloid through the heads of the nine ordi- nates, but to the sum of the volumes of two paraboloids in two ways, either ay a, by cy hy by + bs Co 3 b3 C3 C3 a, b; cy Cy Ay by + by Cy a3 a3 bs C3 In fact, let 6, be taken for origin, a, b, c, for the axis of #, and b, b, b for the axis of y, z being normal to the plane of the paper, then writing the equation to a paraboloid as 2=at+ be + cy + dx? + ey? + fay + av* + Ba?y + y ay? +3 and integrating first with regard to y between the limits +4 #, and then with regard to « between the limits 0 and h, the volume whose base is the triangle c, b, cz is expressed by 2 Sagal iin : dik +3 oh? + 2 alk + A ile, 3 The other three components may be obtained by interchanging h and k, and other corresponding letters, and then by changing the signs of h and k. The altitudes of the nine points are obtained by writing 0 and + h for * See the Mechanic's Magazine for 5th April, 1851, vol. 54, p. 265; also Dhuaray’s Shipbuilding, pp. 35-6. See also Inst. Nav. Arch. vol. vi. (1865), p. 44, and vol, viii. (1867) p, 210. ON QUADRATURES AND INTERPOLATION. 343 zand 0,and + & fory. Making these substitutions, the volume of the whole solid is found to be V == hk (6a + 2dh? + ek?) Qo! bo bo = 5 hk (ay + b + 2b, + 03 +02) co = 5 Uh (a + a3 + 8b, + ¢3 + ¢,). If, moreover, the paraboloid be reduced to one of the second degree by making a/3yé vanish, the following equations also hold:— vol. on a, ¢; ¢3 = : hk(b, + by + ¢2) = . hk (2b, + ¢,) — Ala 3 vol. on a, a; as hk (ay + 05 + b3) = : hk: (2by + a3) -; fH? 9 elie, aes 2 i (ayia) aot he Chr tateydt 5 fle? vol. one, ¢3 3 = 4 hie (bs + ba + 6s) = 2 ik (35. ey ¥ 5 hohe a The rule for the corner ordinates is not very convenient, The other rule, when we have nine ordinates only, may be written, having regard to the coefficients alone, as 010 121 010 For a considerable number, say 5 x11, it becomes 01010101010 12222222221 02020202020 12222292221 01010101010 The rule for the coefficients is that all the ordinates which are odd in both planes of section have the coefficient zero: all the others have the co- efficient 2, except the border rows and columns, where the coefficient is 1 instead of 2. The summation, governed by these coefficients, has then to be multiplied by 3 hike A geometrical proof is easily given, as follows. Let abed be a portion of the paraboloid corresponding to the rectangular base ABCD, and let the planes of section be supposed (in the first instance) parallel to principal planes. It is a well-known property of the paraboloid that its sections by any series of planes parallel to one another and to the axis, are similar and equal parabolas. Project the are cd orthogonally on the plane ABba by a cylinder passing through cdéy. It is plain that the solid ABCDdéyc is this parabolic cylinder plus a solid rec- tangle. Allthe sections of the outlying solid abeddy, parallel to BCcd, are equal and similar portions of equal parabolas, and therefore its volume is the same as that of a cylinder, having the parabolic segment cby for 344 REPORT—1880. its base, and AB for its altitude. Hence the volume of the paraboloid between the extremities of nine ordinates,a,..... ¢3, resolves itself into 2kw, the parabolic area whose ordinates are ay by cy, added to 2h x the parabolic area whose ordinates are by — by, by — by (= 0), bs — dy or, by the rule for parabolic areas, V = 2k (a, + Abs A ¢y).-+ 2n { (ive Be) teh (OR (Bs — by | = 3 hk (ay BP 2by4 Be hee) The restriction as to the direction of the principal planes is equivalent to writing F = 0 in the general equation of the paraboloid Z=A + Bu + Cy + Da? + Ey? + Fay but 5 (@@ + p) (@ + q) = 4ay identically, and (« + p) (e +q) — zy is the variation of any ordinate (p,q) from the middle one, as regards this term alone; it is therefore evident that, for the symmetrical integral, the effect of this term vanishes. Two applications of the polygonal rule are easily seen to be equivalent to drawing a hyperbolic paraboloid through the heads of every four ordi- nates, the four right lines joining the ordinates two and two being the generators (of both systems). The last paragraph shows that its volume- integral can be expressed by interpolating a middle ordinate, and using that only, instead of the four others. This appears to be equivalent to the reduction obtained by Woolley’s rule in the degree above; but it is of no practical use, seeing that it only substitutes the sum of (m—1) (n— 1) ordinates for that of mn ordinates, an advantage which, in general, is no compensation for the interpolation. : Two applications of the polygonal rule lead to the scheme of multi- pliers :— | oO | — (Pa a Dole pw He Dole bo j= I — a (= Jousd = Hel Dol DO] bo] BY GC —-——__, --—____ J 1 bord, = - O- 0 ore ae 9 3 ret Dat a TOO LAO 1 multipliers 1 —\—-——_—Y Hy 4 NiRF On| — _ i me — — DIR ON] — oO | fo) | f=) \— (=) _ lan —) bo] bo bo bo — ON QUADRATURES AND INTERPOLATION. 345 it is to be observed that, while the first is less accurate on the supposition thatthe surface is of strictly parabolic character, and convergent, yet it has the advantage of taking account of the surface (using the above example) at 45 points instead of 30. It thus secures that the surface to which the arithmetical summation refers shall coincide with the surface to be measured in 45 points as against 30, on the assumption of accurate measurements. The advantage of the higher rule, therefore, depends upon there being no possibility of a periodic term, and upon there being no such want of convergence as would render terms of higher degree than 2? y? noticeable. If the ordinates are inexact, this advantage of the polygonal rule holds a forttort. The author has shown* that there exists a similar reduction in the number of ordinates necessary for the summation of a triple integral. Writing the 27 ordinates of U= dy) + ae + Puy + 12 + aya? + Boy? + yo2? + Aye + paw + vay + a3z? + B3y? + 7323 + ie + Aoy) ye + (pe + poz) zw We or tn a) oy as ay Oy C4 a,’ by" ¢," ay! byt! e,! ar as’ By Gy ay" Bel! cgt! ag bg C3 tix! Ba! 3! ay! bs" cg! the treble integral = af _1 1 du dy dz is expressed by = id Coa er a onl oak gh) bras My in which the absolute middle ordinate does not appear. In fact, arrang- ing the 27 letters which represent the ordinates in a cube, the only ones which appear are the middle ordinates of faces. The late Professor Rankine expressed this rule in the following form: ‘The mean density of a parallelopiped is the mean of the densities at the middle points of its six faces.’ This supposes the density to be a parabolic function of the three co-ordinates, not higher than the third degree, and thus, of course, excludes the case (which usually presents itself physically) of the density varying from the middle to the bounding surface. This rule, like Woolley’s, may be modified by using. corner ordinates, or the ordinates corresponding to the middle points of the edges: only then the formule are Jess simple, and the middle ordinate of all does not disappear. All the remarks about Woolley’s rule inadequately representing the surface, as compared with the polygonal rule, apply a fortiori to this. Whatever may be the convergence, except upon a certain limited hypo- thesis, namely, that the function is of definite parabolic form, coincidence between the actual subject of integration, and the subject of summation, is secured at too few points for the results to be reliable. It had been observed by the author that there was a peculiar relation of the ordinates in these rules, namely, * See Scott Russell’s Modern Naval Architecture, vol. i. p. 127, and Trans. I. NLA. vol, vi. (1865) p. 47. : 346 REPORT—1880. 1. Simple measurement x =+ (6a) 2. Simpson’s rule fi dx =+ h(a + 4b + c) 3. Woolley’s rule Sf: dx dy =< Ht (ig +, + 2g + By to,) 4, Meritela’s (ff de dy dz =< HL (ag! + by + By! + by! 4 ba" + 65’) or, as the multipliers may be graphically arranged, i Lee fe 1 Dia i oa lg a) i there being a curious tendency of the middle ordinate to ‘move out.’ The late H. J. Purkiss, by operating upon the equivalent form Uy = Uy + Ax? + By? + Cz? +.... (n variables) * showed that the n” integral h k l i : Vg nf -3 eT ae udx dy dz... was represented by voor oe {2- 2 (n'a 3) u, | when 2, =f (0,0,0....) and Z=f(h,0,0....) +f(—h,0,0....) +f (0,4,0....)+/(0,4 —h&0....) +7 (0,00 ....) +/(0,0,-J,....) + &e. Multiple integrals of the form SN: A tt, (dare Wi, may be treated by rules nearly similar to those already given for simple integrals. It is worth while to observe that in this form of integral only one integration (the last) is between definite limits, the others being rather algebraical forms expressed by the notation of the integral calculus, than actual integrations. Thus f fu da* between the limits +m is not the analogue of af : af 5 i u dx dy, where h and k& are each made = n, —hJ —k but is an abbreviated expression for fi "dee fs “udu. This becomes evi- —n 0 m dent, when it is remembered that U,, is simply the solution of dan =U Moreover, after one integral has been taken between limits, all following integrals are mere multiples, with a parabolic series added, on account of * See Zrans. I, N. A., vol. vi. for 1865, p. 48. ON QUADRATURES AND INTERPOLATION. 347 the constants of integration. These constants must not be forgotten, but as they disappear when the origin of integration is suitably taken, they need not be further discussed here. The same treatment which was applied to the investigation of Cotes’s formule may also be applied to a double integral, only then it is necessary to use a series with odd powers only, because the even powers disappear for + limits. Writing U = Ay% + Age? + ase® 4+ oc ecccenes and taking the integral between limits + n 1 1 1 ar U, = on + 53 ayn? + Zp aan + 5 gaa + arin a ave Assuming the first integral to vanish with z, ¢ vanishes, and the first significant term ise a,n8, Now writing in succession +1,+3,+5......forz. 1 @ (ay +) Ha Hag tas te. eeeeee 1 9 (— Wz + U3) = 8a, + 88a3 + Das +e econ 5 (— ts + tis) = Bay + 58a + 58a, =f stars whe (Ce or, using indeterminate multipliers E 1 Ay + 3Ay + DAZ H+... ee Th, = 5-3 1 A, + 379A, + 5°AZ +..... \,, = 4.5” A, + BA, + S*AZH+..... A, = apn &e. : a stopping at n = 1, dA, = e , DOr s. OL stopping at n = 3, A, = 160" A, = 160 that is to say, Sf: dz? between limits + h is is (— wy + 4) Sf: dz? between limits + 3h is 3 30 h? (— 17%u_3 — 189u_, + 189u, + 173) Similar formule, symmetrical to an ordinate instead of to an interval, would be obtained by writing 0, +1,4+2..... for z. But the integral vanishes for « = 0, and these formule would evidently be less advan- tageous than those of the odd series, for the same reason that in a simple integral the even series is the better. 348 REPORT—1880. These formule are, however, rather curious than useful. For the treatment of multiple integrals, symmetrical differences are more con- venient. Section 5— Quadrature by differential coefficients. The reciprocal of the formula d iN = Ta De —1 enables the difference between a definite integral and the term of a series of ordinates to be expressed by means of the successive differential coefficients for values corresponding to the extreme values of the function. Calling these u, and w,, hs = A“ thy, — Ant ig = 4 & da — i} {m4}, There is nothing indeterminate about this equation, the left-hand side of which is the sum Ug + Uy +Ug+..... + Un] while the right-hand side has for its first term ae Mh a de, for its second be/o term — > (uv, — Up) and for its general term thereafter, (— yr i q2"+1 q?rtl (RRORSE Wig ae Srp Barty BO) ape Mo — gape where B,,,, represents Bernoulli’s numbers taken without regard to sign. The complete formula in its usual form is h { a + Uy + Uo 4. fe arletiers 4- Un—} + + uy } nh 1 # 1 hi — ude + = ——(2', oss wy) ie aie er all's) ae , 6. | 2. “ae ah ia r hert2 q2r+l qzti Fees + (—) Bares [ar 42 Ci Un — aru”) aF dood The meaning to be attached to oo an a “is that they are the values x" xv I” of aa when « is made severally equal to nh and to zero.* The use of this formula presents no difficulty except in one remark- able case, pointed out by Legendre,+ in which all the odd differential co- efficients after some particular value of 7 take the same value at both limits. Among these may be instanced u= /(1 — i? sin 2x), the ‘limits being 0 and ->- ~ or ~. All the odd differential coefficients are affected with the factor sin a cos z, which vanishes at both limits, so that each term of the expansion contains zero as a factor. Nevertheless, * See Woolhouse On Interpolation, Summation, §c., part ii. p. 45 (note), for a very singular extension of this formula. { See his Ponctions Hlliptiques, vol. ii. p. 57 ON QUADRATURES AND INTERPOLATION. 349 the summation is not identical with the complete elliptic integral, as may easily be ascertained upon trial—and there are many other functions which present the same peculiarity. The paradox seems the greater, in- asmuch as the numerical coefficients of the differential forms are highly convergent, seeing that when r is large Bot A Bo,-1 [2r+2 °°] Q,r =1:47? = 1:40 nearly. The explanation, however, is, that the numerical coefficients introduced by the differentiation performed upon w increase without limit, so that q?2rt1 ’ jf ; 2 qari (uv, — Uo) becomes really co — oo, which is necessarily indeter- minate, and may (and usually will) exceed the corresponding factor in the previous term in some ratio which is a multiple of +2, and which increases without limit as + increases. Then the series finally becomes divergent, and the paradox is solved. In many such cases, and notably so in the rectification of the quarter-ellipse, the subdivision of the base, that is to say, an increase in the number of ordinates, gives extremely rapid convergence towards the true value. Thus for / = sin 45°, if we take three ordinates only, viz., “=> 0) Uy, =i! @ = 45° Uy = sin 60° = 0°8660254 x= 90° Uz = sin 45° = 0:7071068 ul orn oes 0:5 uy = 0°8660254 54s = 0°3535534. 1-7195788 This, multiplied by 47 gives for the length of the quarier ellipse 1350284. The value taken from Legendre’s table is 1:3506438820. If we were to use the parabolic rule we should have heh 4u, = 3°4641016 uz = 0°7071068 3 | 51712084 1:7237361 This, multiplied by i m, gives 1:35382, which is not so good a result as we got before. The anomaly here is the counterpart to the one already mentioned. Its explanation is, that if the ordinates are differenced, the differences diverge at once, and, therefore, the series of which Cotes’ rules are a mere transformation is divergent from the beginning, so that the more terms of it are taken, the farther from the truth is the result. In other words, the higher rules are worse, instead of better, than the poly- gonal rule. This is an instructive example of the advantage of a sub- divided interval over a rule of a higher order. 350 REPORT—1880. Section 6.—Interpolation of direction : maxima and minima, It frequently happens that it is required to find, by means of given ordinates, whether differenced or not, the value of some particular differential co-efficient, or else the value of the variable corresponding to some given value of the differential coefficient. These ultimately depend upon the symbolic equation d — = log. = og. (1 + A) suitably transformed and duly interpreted, or solved. In certain cases, the desired result may be obtained by mere algebraical transformation, by indeterminate coefficients or otherwise. As an example, let it be required to obtain a formula for the tangent at the head of the middle ordinate of the set the common interval being h. The analytical problem is to determine ae = h (1 +A)? log. (1 + A) uo in such a form as to stop the ce series at Atuy. The work is pe = ul “ 2 2 = ANG ce Ne = (1 +A) (a- = At + = At) 19 3 : 1 = (a+ pat Ale = A3 — 54!) uw 2 1 — 3 (v3 — m4) — oi (U4 — Uo). The process is perfectly general, and needs no further remark, except that the work might have been made a little more symmetrical by taking the middle ordinates as origin. This will give considerable simplification in the algebraical solution. To obtain this, write w= aw + cx omitting the even powers, which evidently disappear in the result, Then a =a + 3ca? (=a when « = 0) ai — w= — Uy =z (| — U1) = ah + ch8 Ug = — U2 = (us a U9) = 2ah + Sch? and \, and A, are to be so determined that Ay (Uy — U1) + Ay (Ua — Ung) = ah This gives 2A, + 4A, = 1, 2A; + 161. =0 2 i whence A; = 3° A= — o This, allowing for the change of origin, is the same result as that already obtained. ON QUADRATURES AND INTERPOLATION. 351 The general problem of maxima and minima is, in interpolation as in d ordinary analysis, to determine w and 2 so as to make SS =0. Itisa 5 PRK: Fa particular case of the more general problem in which ea = a, but it is practically much simplified by the consideration that Aw is generally very d z = : small when vanishes, so that the approximate position of the maximum or minimum is visible at sight ; but there is no such help in the general case. . The process for determining a maximum or minimum is to expand (1 + A)* uw as a rational integral function of x, and also such that the functions of A appearing in it shall be capable of interpretation ; then to differentiate with regard to x, and equate the result to zero, The appro- priate root of the resulting equation thus gives the value of a, and that of w, is then found by interpolation. As already stated, there is practi- cally an approximate value, obtained at sight, to start the more exact approximation, The most obvious course is to take the ordinary bi- nomial expansion, namely, pe es 32 — 372 ‘ w= Uy + Amy += Bpse eg Bammutt ty 20 veo, sigs 1 2 6 whence m =0 = Au + ge a : Deu) + se bet 8 A3uy + &e. and this equation has to be solved with respect to 2, preferably by succes- Sive approximation, after which w is determined. But any other expan- sion, such as that by symmetrical differences, in which the expansion variable is A: /(1 + A) may also be taken. When the solution is obtained otherwise than by successive approximation, as, for instance, by solving as a quadratic, care must be taken to select the proper root. Values corresponding to inflexional points in a curve, are, of course, 2, determined by operating in like manner upon “ In the use of equidistant ordinates, no difficulty can arise from w and 2 reaching a maximum together. But when the ordinates are not equi- distant, this point requires attention. It presents no other difficulty than is met with in the ordinary theory of implicit maxima, The case of “ = a, only differs from that of ae 0, as far as work dx is concerned, by its being less easy to see what the first approximation is to be. Graphical processes, however, or trial and error, soon remove any difficulty. It must be remembered that the determination of a tangent is of a higher order of precision than the determination of the point of contact. It follows that the determination of the argument corresponding to the maximum or minimum value of a tabulated function is less precise than that of the corresponding value of the function, and also less precise than its determination generally, 302 REPORT—1880. Section 7.—Symmetrical Differences. If the successive values of a function are written down in a column and differenced, the successive differences belonging to a given value run across the scheme in a diagonal line, down or up accordingly as the process is begun from top or bottom. Thus, beginning from the top, the series Uy... .U, gives the following scheme :— Uo Arty Bays. SAG Adie sc seA°tg Ug ss PNoia east ft Nay tack e LNs Uz +... Aw3z ... Agry ae a Au, Us This process is essentially unsymmetrical, as is evidenced by its diagonal character. But any horizontal line has symmetry as regards the general scheme, and accordingly the line w., A?u,, Atug is said to be a set of symmetrical differences, that is to say, symmetrical to a value or ordinate. So again the set Aw, Au,, A°wo is said to be symmetrical to an interval. It will be observed that this process is an alternate one—that it is not possible to pass from one column to the next, but always to the next but one. The operative symbol at each actual step, as, for instance, from A3u, to Au, is always A? : (1 + 4) and the direct problems of interpo- lation and quadrature by symmetrical differences are to express (1 + A)* and Fudx in a series of ascending powers of A?:1+A=Z2. It so happens that (1 + 4)” can be expanded by ascending powers of Z, but not by powers of Z?. This introduces terms of the form A: /(1 + 4) which cannot be interpreted so long as terms used are confined to one horizontal line, thus implying that the expansion must be a double series. The series itself was given by Newton,* but without proof. The connec- tion between the two parts of the series is a differential one. This is perhaps best shown as follows, using the notation Z=4?:(1+A)=(E-1)?: E=E4+ 4H - 2, = Sse oy DOR Jatt Ay _A(2:4+ 4) ee a (83 Ft) = 5 ea aE Solving the first equation with respect to EH, gives B=1+4=14+324 a/ (e+ i 2) E-! =14 52%, /(4+42) The form of these values shows that E and its powers involve, in their * See his Mcethodus Differentialis, already quoted, Prop. III.; also Stirling, Methodus Differentialis, Prop. XX. pp. 104-8; De Morgan, Caleulus, pp. 544-7, Lacroix, 2nd ed. of his Caleulus, vol. iii. pp. 26-31 and 327-330, ON QUADRATURES AND INTERPOLATION. 353 expansion, both odd and even powers of /Z; but that H* + E-* may be expanded in integral powers of Z, and KH” — E-* in odd. powers of / Z. Then the differential coefficient of E” + E-” with regard to Z is (Br! = Bo") 22 in which 22 =1 -E2 = M 2 (E*-! = E-*-!) az? 2 which TE 1-—E oR” whence ae r : =—x as ie ao Wl=-« ag ee Meta ge t E) and also : : . * bd (et E-*) + 5 (E'S EM) =(o 40 a) OSE If the upper sign be taken, writing + (i 4 Eo) a $ BZ + yBP 4808 +... suitably determining the coefficientsaPy..... and giving the proper interpretation to M, furnishes the formula for interpolation symmetrical to an ordinate ; while, if the lower sign be taken, writing 3 5 5 (BP — E+) =a V2 +0523 PE Lae | furnishes the formula for interpolation symmetrical to an interval. The coefficients may be determined either by the ordinary methods of in- determinate coefficients, by the calculus of generating functions, or by writing Uy, S Cun Uin Fie vnee + Colo + CU, +...» Cyn and determining the coefficient c in the simplest form, so that « =rh shall make c.,= 1 and all the rest vanish.* _ The actual formule are best expressed in a notation similar to that originally given by Newton and Stirling, namely, for the case symmetrical to an ordinate, in which the differences run, - Aw_; A3y_» Abu_s Uy Aty_, A4u_o ASiye Sheba laa Au, A3u_) A®u_» write B = 5 (Au_, + Au) 1 . C aa, (A8u_, + Alu_r) oi $ (A®u_s Ee A5u_.) &e. and @ = u,b = A2u_;, c= At. uy &e. so that C= BZ, D= CZ = BZ? and b= aZ,c=bZ=aZ? &. Then * See a paper by the author in the Messenger of Mathematics, vol. iv. p. 110. Another proof is given by Professor Emory McClintock, of Milwaukee, in the American Journal of Mathematics, pure and applied, vol. ii. 1880. AA 354 ‘ REPORT—1880. te = a + ( Be + 5 be’) 2 + (20x + 5 ex®) x 3.4 | 1 2 eg? —1 gy? — 4 + (3Dz + 3 de") x Sta ab | A w—1 a—4 oo? —9 + (5Ee + 5 en) x S-. S ‘7B + &e. the common interval being supposed unity. If the interval is other than unity, say h, the formula must be rendered homogeneous by the substitu- tion of « : h for a. : For the formula symmetrical to an interval, the differences run Uy eeee A?u_» ceee Atu_s oeee Bis, . phwe AB g Caw en MPa dues TAL os ae SS pala «Pa 1 Then writing A’ = 9 (uy + Uo) 13 a (A?u_. + A*u_;) es $ (A‘u_s + Atlus) &e. and a! = Au_,, -b’ = A®u,», c’ = Aus; &e. there is the same relation as before between the successive letters, and the formula is U, = (A! + a/v) (ahh, oe + (3B’ + b'z) ii , pes 4a? — 1 4g? — 9 +(0'4ee) Sot Be 1 apart — 1 4a2®— 9 Aak—25') og 1 ED aa hey aes ee Making w = 0 in this gives the well-known formula of bisection by sym- metrical differences, yiz., —— babe ea 1459 1 ae 1:9. 25 "D—! & ly aN — 76? ag EB GID Tale) 8, 10 = ale ye Tee 5 / =A 3B + jog 1094) f+ ecccee Formule for quadratures by these symmetrical differences may be at once obtained by integrating Newton’s formule between + limits, in which case the terms involving odd powers of « disappear on integration, leaving only the even differences in the formula symmetrical to an ordinate, and the even mean-differences in the formula symmetrical to an interval. The interval between the ordinates is assumed to be unity. if Hence if there are » + 1 ordinates the limits will be = 3 (n+1), and ON QUADRATURES AND INTERPOLATION. 355 not simply 0 to 1 or + e unless the formula be first duly transformed, Proceeding in this way the following formule are obtained.* Number of Ordinates Expression for the Area + 3 6 fat sbt ie + gah 8 86 92 989 a {oats Be ¢ + i892 + 99370 ° 175 3445 , . 4045. 16067 1 oa ees {a a+ 2b + yee + d + oo79 ° + sara t 1512 ie 158 1833 4813 12 {a ot 4 18, ES Fr pal SST + 37550 1364651 + 6306300 9 A similar set of formule may be obtained, symmetrical to an interval, and in terms of A’, B’ &c.; but the coefficients, as well as the form of the series, are more complicated, and the accuracy somewhat less, on the parabolic hypothesis, than the corresponding rule of the other series. The first rule in this set is the common polygonal rule ; the next is got by 5, and is area = 3 (“ + t B’) integrating from — 3 to + which is equivalent to Cotes’s rule of four ordinates. These rules may also be cbtained by the direct substitution of sym- metrical differences for the ordinates in Cotes’s rules, with which they are of course identical, except in form. The application of symmetrical differences to quadratures may also be made to depend upon the formula : c ® dan — { tog a + A) be * See Stirling, Meth. Diff. p. 148. In the formule for 9, 11, and 13 ordinates, Stirling simplifies the numerical coefficient of the final term, just as he has done in the table of corrections for Cotes’s rules, apparently for easier use. The practice is not a satisfactory one, as it prevents verification, and saves but little work. + In the above formulz the interval between the ordinates is taken as unity. If the whole base is taken as unity, the area is given hy omitting the numerical factor outside the S \ The table has been independently computed, and compared with Stirling’s table. AAR 356 : REPORT—1880. It is not, however, commonly used in this form for mere quadrature; but the method is used in the calculation of tables in the form Am he Feet = An { tog @! + Aye and in most cases in practice, mis taken equal to . The algebraical process consists in the development of the right-hand side of the last equation in terms of Z= =o A= Slt y/(Z44 2) « 1+A log (1 + A) = log {l+5 Zt forint & nN 1 1 a bh Sf ava & ) a Z Mas 2 oo eee Se ae tee 14 5B 9. HB VOT be } Repfesenting the mth power of the series in{ py ; 14+ M,Z + M,Z? + M,Z? + M,Z + ai ecat elena ts ; and restoring 4-(1 + A)-4in place of Z! m Am+2 m+4 ATU +M, Nera Of M, Nise Sf (+4)2° 2 (pay (U+.ay?™ which has to be interpreted. Denote the successive values of u by....U,.. uP U,,U or wu, m4, Uy, Ugy) wre are Uy, 1D Which w= ¢ (#) 4, == F (@ + nh), U rn=o (@— mh). Then the aaale of relation is U7 ~ aye te + Ayu TE ty pore(e+s ie 1) be also denoted by V or v, it gives rise to a parallel scale, WioritoM ry ; OF V, Vj) Vo 20» Uns with the same relation between its successive terms, and for its connect- ing relation with the other scale, V, = (1 +A 2 We If m be even (= 2m), direct substitution gives { tog (ick, a) ny = AMT, + M, A”+2U,,, + MA”HUp) fees eee If m be odd (= 2n + 1), { log (1+ 4) ba = AHY, + MAmV, 5 + MA" V5 +. The values of the coefficients are as follows :— Mh Sea MS amps” + 22): My = = 5 = yay (85m? + 462m + 1528), My = gig gp Tgp (1753 + 4520u? 4+ 40724 + 119856); ON QUADRAJURES AND INTERPOLATION. 357 and by giving m any positive or negative value, the series for any diffe- rential*coefficient or integral may be at once found. In practice, however, there is frequently a difficulty in using the series, where m-is odd, from the values of V, V,, V., &c., not being obtainable without a distinct interpolation, where the values of U, Uj, U,, Uz, &c., only are given. When m is even, the converse may be the case.» -«This-may be obviated by using mean differences, as follows: 2 Making Z = i + a3 before, i 2 1 hit jee.” Pete 5 Ze | ——_ = A)7-z4 L— = aint iene ahey a. eh gear + yf ma ee a 6 oe I Combining this with the previous expressions, we get 2 { 10 el + ay} Qny A2 U +N A2nt2 U — o SS SSS n et n 24al ° V1+A i Een A2nt4 N, STs im, Uaea + Leds ae — AV iy + Bs paar eras + NjAv HVS SBN ie San ey A Now, since (2 + A)V, = V, + V,-1, log (1 + A) Van = $ (PV = A*V,) +4 N, (A2"2V 45 $A? PV ns) ote > N,(A*"*4V 43 ae Am+4V7 5) + eae 43 STs sl a He 3 and similarly, when m is odd, { log e! a4 ay pone = FO ues + A22+ 1G.) — a4 (m + 3), N, => oT. 32.5 (5m? + 52m + 135), 1 N;=—- g034. 8.7 Wan + 777m? + 5749m + 14175), N, E By (175m4 + 5720m3 + 96794? + 619776m 7 BS 788.5. a + 1488375). Remember that the sum of two successive differences is the difference of alternate numbers in the preceding column. The formule most frequently occurring in practice are, for integrals,* I ni ny Dy OLE ae. afute=s (u +m) rn) GD; + Au) + 790 (A‘U, + A‘U)) e. - * The higher coefficients cannot be relied upon for accuracy. They were calcu- lated, with some care, many years ago; but they are not of much practical use, and have not been satisfactorily verified, 358 REPORT—1880, 191 119981 ~ B10. a8 AUS + ACU») + srg799 gn APUs + APUs) =e 1 1 17 367 27859 SN lime APY Lt Gone SO Din oy a eeesOps ix. h sf V toa YY 5769 V5 * 190m “°V5 > S6700 28 1295803 Alo 15183675231 ASV, + ALY @ she siete auth 1871100 . 216 > 7662154500 . 220 LOY Gee a pa ean Vey obsess ner = jet fda =" ig op Ut dean ovens 289 L291. ti poping sting 56700 .o8 Us + Most of Legendre’s tables of definite integrals were computed by the second or third of these formule, His great table of elliptic functions was calculated by the second. For differential coefficients du...1 1 1 erie 5 (AU, + Au) — a (A8U, + A3U)) +65 (AU; + A*U)) ss Acta 280 uf => AY, + 3, 23 A8V, =F CAD VALU a) Aciagis ois « sesh se uheve otnid bia 3 4 5.g7 Vs — 2a 35 +9. 915 AQV = SEL If #» =0 in the N formula, it becomes i =4 Wet a's ee a (A°V, + A°V,) +2. (A‘V, + A‘V2) 98 a 7 gil (A°V, + A°V,) +53 (PV, + AV) meee a well-known formula of bisection, Some obvious transformations will enable corresponding formule to be obtained for A" "dz" where m and x are different.* It is to be observed that the formula for integration above given is not _fruse, but G A fds which is a different thing. rtf udz itself be required, it must be obtained by summation. A very compendious method of interpolating tables by means of bisection is derivable from the ordinary formula of bisection, by affecting it with A. Thus, stopping at the first term, namely, vw = 5M + V) Aw= 5 (AN, + AV) = AV, +54°Vi SAV —5atV. * See Woolhouse on ‘ Interpolation, Summation, &c.’ in the Asswrance Magazine, vol, Xi, p. 301 et seg. for some interesting transformations of these theorems, ON QUADRATURES AND INTERPOLATION. 359 Tf the second difference is small, the correction for the alternate difference is very easy. A particular case of this formula was suggested by Sir John Leslie * for continuing either Briggs’ or Vlacq’s logarithm tables. For the difference between the logarithms of (say 11000 and 11002 is the same as between those of 5500 and 5501, and the formula given above enables us to find from it the difference between the logarithms of 10099 and 11001, and so on, so that the odd series can thus be quickly calculated, and the extension of the table to double its former range effected with very little more than mere copying. ‘Mere copying,’ however, when applied to an extensive table of logarithms, is so laborious, and such a fruitful source of error, that this application of the method has never been made. Nevertheless, it is a very convenient process for interpolating tables of physical or other observations, where the second difference is not very considerable. Section 8.— Definite or Tabula Interpolation. The problem of definite or tabular interpolation is this: given a table, or a set of differences, corresponding to a given equal interval; to con- struct from it a table corresponding to some other equal interval, usually a sub-multiple of the former. For example, suppose a function to be tabulated (or given by differences) for every ten minutes, and that it is required to find the means of tabulating it to every minute ; it would be possible to interpolate separately to every intermediate value; but this would be unreasonably laborious, and what is usually needed is to find a set of differences corresponding to the reduced interval, from which the table may be set up, either by arithmetical summation, or by a difference engine. Let A be the symbol of differencing for the wider interval, and 6 for the smaller interval, and let BK=1+A,e=1+d then the fundamental relation between the two scales is EH = e”, and the analytical problem is simply to express a selected function of e in terms either of H, or of a selected system of functions of it. The equation E = e” arises simply from a comparison of the original and interpolated series, namely, Oripmial heriba "Uy ss te + Opie’ ened e wee Une bh a sf interpolated series, vg Uy, Uy 6 Um—y Um Unt) Unto + + © Uom—1 Vam 2 eee Where Uy = Uo) E Uo = U, = Loe 7 ey, EU, = EU, =U, = Us, = ep, =? Uo, &e. All the remainder of the work consists, firstly, of algebraical trans- formation; and, secondly, of the actual arithmetic. The kind of transformation needed turns, firstly, upon how the E’s are expressed ; secondly, upon how it is desired to express the e’s. Thus the H’s may be expressed either by a mere tabulated series Up, U,,U,, Uz .... -, that is, by powers of E; or by Up and its ordinary differences, that is, by: ascending powers of A or H—1; or again by symmetrical differences, that is, by powers of Z = A?: (1 + A); or even by ascending differences, that is to say, by powers of A: (1 + A). So it may be desired to express the interpolation by powers of e, of d or e— I, of z= d®: (1+ d) or of * See the article ‘ Logarithms,’ in the recent editions of the Hncycl. Britannica. The article originally appeared in the supplement to the fourth edition. 360 P REPORT—1 880. d:(1 + d), and in any case the problem is simply the analytical expression of any such function of e in terms of the selected function of HK. The assumption, that U, and wu should coincide, is not a necessary one. The only effect of their not coinciding is to substitute the equation kK” = et” for the simpler form E” = e””, An exposition of the application of this method to symmetrical differences appears to have been first given by Henry Briggs in his Arith- metica Logarithmica, published in 1824. But it appears from his preface that the tables of sines, afterwards published by Gellibrand in the Tri- gonometria Britannica, had been calculated by Briggs, by a more or less complete application of these rules, twenty years earlier.* His exposition is, however, not very well suited to modern use, being rather too much specialised, with a view of suiting his own work. A more general exposition of the method is given by Roger Cotes in his Canonotechnia, sive constructio tabularum per differentias.t This, besides general rules, contains the tabulated coefficients for the bisection, trisection, and quin- quisection of the interval. It does not appear that the subject was resumed until recently, when Mr. Woolhouse gave both tables and formule for the division of the interval by 5 and by 10.t According to Lacroix, the method of tabular interpolation for ordinary differences was first published by Mouton, to whom it was given by his friend Regnaud, in 1670, and afterwards reduced to a general formula by Lagrange and Prony. The method is as follows. Let ugu,wy....-. be a series of numbers, of which the fourth difference may be neglected, and snppose that it is desired to obtain the differences for interpolating two numbers between each. Let the required differences be b, c, d, the original differences being represented in the usual way by Au, Ayu, &e. . Then, if the interpolated series 2%, %) + b, uy + 2b +c, &c. be formed, and the terms representing 2) u, &c. be picked out, they give Uy = Ug U; =U +96 +3c+d Us = Uy + 6b + ldc + 20d Uz = Up + 9b + 36c + 84d and differencing these, Au, = 3b + 38¢+d A?u,) = 9c + 18d er aN oly Ayan Dd eee es solving these as a set of simultaneous equations, = 5 Au — : Aru) + a Au i ; Aug — - A3ug ihe a Adu, § * Brigts’s words are ‘Nam Differentic, que ante annos viginti mihi maximo usui fuerunt in novo canone sinuum condendo, in horum Logarithmorum caleculo sunt mihi multo melius perspecte et cognite.’ An explanation and proof of Briggs’s method of quinquisection are given by Legendre in the Connaissance des Temps for 1817, p. 219. ; ¢ Published in the same volume with the Harmonia Mensurarwm, by R. Smith, Cambridge, 1722. t Vide op. cit. part ii. Also Assurance Magazine, vol. xi, p. 61 et seq. § For the general formula see Lacroix, Traité de Calcul. vol. iii. p. 43. ON QUADRATURES AND INTERPOLATION. 361 The tables given by Cotes and Woolhouse for symmetrical differences appear to have been formed upon the same principle. A question of some interest in the interpolation of tables, in which the number tabulated is only approxiniately’cdrrect, is whether it is preferable to apply proportional parts to the true calculated difference of the function, or to the actual tabular difference. Thus in the seven-figure logarithms log 66310 = 48215790 log 66311 = 4°8215856 the tabular difference is 66, while the correct difference as obtained from Vega’s ten-figure table is 65494, which, to seven figures, is only 65, The question is, whether it is better to use 65 or 66 for finding the proportional parts. By a comparison of the extreme cases, M. Lefort * has shown that so long as the tabular difference (that is to say, the difference actually found between the numbers as given in the table) is used, the last figure in the interpolated result cannot be in error by more than unity ; while if the true calculated difference, cut down to the nearest figure, be used, the last figure may be in error by more than unity. It follows that the actual difference of the table, and not the mean difference given in some tables (such as Hutton and Callet), should be used for the interpolation. Section 9.—Interpolation of Double Entry Tables, or Functions of two or more cians Variables, The problem of the interpolation of functions of two variables presents but few difficulties beyond those of interpolation of functions of a single variable, excepting what is due,to the increased complexity of the process. This renders many of the special artifices practically unmanageable, although the very fact of the complexity increases the importance of simplifying the actual work. Nevertheless, it is better on the whole, in processes which are not of frequent use, to encounter deliberately a little excess of arithmetical labour, rather than to risk the chances of error from want of analytical simplicity and perspicuity. If any one process should be often wanted, those who need it may be left to invent the special machinery. The general theorem of interpolation for double entry is expressed in the two formal identities. Uy, =f (zy) tay = (1+ A)*(L +8)" to 0 in which A refers to variation with regard to a, on the supposition that 7 is constant, and 6 refers to variation with regard to y, on the supposition that x is constant. In general it is usual to give equal weight to the two variations, that is to say, that if it is proposed to neglect terms of the order p, then all terms of the form A” 6", where m + » =p, are to be discarded, whatever may be the separate values (always supposed positive) of mandn. The terms of the expansion would thus be grouped as Uxy = U9 0 + (tA +y8) uo0 * See the Proceedings of the Royal Soc. of Edinburgh, vol. viii. (1875), p. 610. 362 : REPORT—1880. + 5 (a2 A? + Say Ad + 9" 67) uo 0 +. je So, 94.48, orje it But this supposition is entirely arbitrary, and not even justifiable if it happens to be known that. the second and higher differences are con- siderably greater in one direction than in the other. This, and the remedy for it, are only to be ascertained by a special study of the function. Tn accordance with common practice, the direct expansion by ordinary differences has been used; but there is no motive for this except con- venience and simplicity. Subject to the difficulties of interpretation and handling which they introduce, any form of the expansion Uy = (1 + A)” (1 + A)" ut 9 = E* EF’ uy 9 will answer the purpose. There are even cases in which it would be desirable to form an interpolated table for the given value of one variable on the supposition that the other is constant, and then to interpolate that as a single entry table. Thus, supposing that going along a line in the table represents the variation of y, and going down a column represents the variation of 2, then the whole column corresponding to a particular value of y might be interpolated, value by value, so as to give the series arranged in colunun Udy Uy Uo, Ugy 2 ee ee ee and then interpolation to w,,, might be effected by single entry; or the process might be reversed, and the line Uno Ux} U;9 Un3 @ 0:0! 0. 0, 0 formed first, and then w,,, by single entry interpolation. It is worth while to remark that the interpolation may occasionally be reduced to single entry interpolation along a diagonal line. This is always the case in bisection; but it is by no means confined to that case. The inverse problem of interpolation is in general of a higher order of indeterminateness, unless some other data are given than the mere value of the ordinate. _ For if the two variables be regarded as horizontal, and the function as representing a vertical ordinate, then the ordinate being given in value, merely furnishes a locus, namely, a level line. So if one of the variables be given, a special table may be formed for that value of the variable, and then the inverse interpolation is an operation of single entry. . But if, instead of this, some equation be given between # and y, the problem falls out of the province of direct synthesis, unless the relation between « and y be that they are in a constant ratio. The analogy is of course that of the representation of a surface in geometry of three dimensions, and that analogy is really the key to the question. An example of the interpolation of a double entry table as far as third differences is given by Legendre.* Quadrature in two dimensions is really equivalent to the evaluation of solid volume. The two quadratures may be effected either separately, or by the methods indicated in Section IV, 4, of this report. Another problem arising out of a double entry table is that of inter- * Traité des Fonetions Elliptiques, vol. ii. p. 201 (cap. xv-) ON QUADRATURES AND INTERPOLATION. 363 polation to the direction of a normal line or tangent plane. This, in the ordinary language of partial differential coefficients, is the evaluation of Vere) The first thing is to find p and qg by the methods for interpolation, of ordinates (IV, 6) and then to form the. radical. _Graphical methods are, however, generally the most convenient for this. The integration of this radical in two dimensions gives the surface. For an example of this particular form of interpolation combined with quadrature, see Scott Russell’s ‘ Modern Naval Architecture,’ and the ‘Transactions of the Institution of Naval Architects,’ vol. vi. for 1865, p. 64. Tables of treble (or higher multiples) entry are of course confined within very narrow limits. Their interpolation calls for no special re- mark, unless it be that the indeterminateness, as well as the complexity, increases with every additional dimension. This remark is true, as a separate consideration, ‘firstly with regard to the general indeterminate- ness of all interpolation, and secondly with regard to the indeterminateness of the inverse processes, with reference to the possibility of more roots than one, and to the requirement of more data than the ordinate.* ‘V.— INTERPOLATION AND QUADRATURE WITH ORDINATES NOT EQUIDISTANT. Section 1.—Nenton’s method. The principal theorem of interpolation when the distances between the ordinates are arbitrary instead of equidistant, is given by Newton, in his ‘*Principia,’} under this title, ‘Invenire lineam curvam generis parabolici que per data quotcumque puncta transibit.’ It consists of a method of divided differences, and Newton uses it in a form which is, as exactly as may be, the counterpart of that which he uses when the ordinates are equidistant. It is not thought necessary to reproduce it here, as the reference to it is very easy.f Professor Emory McClintock, of Milwaukee, has given § a modifica- tion of Newton’s formula, which lends itself better to logarithmic com- putation. The terms being $a, or $%,, $%2 Or $p%g, and. so forth, the general term of his divided differences is m &n — Pm tp Dm41 cL, = $ 4 $ a ®, — Unt) which gives, on multiplying up, On vy, = Dm Gmn+1 a (#,, ey nit) Pm-+1- Bye Giving m the values 0, 1, 2, &c. in succession, and substituting suc- cessively, we get Po Un = bo % + (@, — 1) $1 2 + (a, — 2) (@, — 22) bo 3 + (%, — 2) (a, — @o) (2%, — #3) o3 %4 + ceoee ee * See on this G. Darwin, on ‘Fallible measures of variable quantities,’ Zondon, Edin. and Dublin Philos. Mag. for July, 1877. See also Lacroix, Jraité de Calcul, vol. iii. p. 44 e¢ seg. (arts. 913 et seq). Tt Book iii. Prop. xl. Lemma V. case 2; see also his Methodus Differentialis, Prop. iv. t See also De Morgan, Caleulus, p. 550; Lacroix, Traité de Calcul, vol. iii. p. 31, et seqg.—or page 552 of the Cambridge translation. See also Stirling, ZInterpolatio Serierwm, Prop. xxix., and Hall, ‘ Finite Differences,’ Zncycl. Metrop. p. 249. § See the American Jowrnal of Mathematics, pure and applied, vol. ii. pp. 307-314, 364 t REPORT—1880. which, if a' fractional value be given to n, becomes a formula of inter- polation. Section 2.—Lagirange’s method. Lagrange’s theorem of interpolation, although identical in its results with Newton’s, is in a form analogous rather to the case of ordinates not differenced, than to the use of differences, which is the analogy followed by Newton. As is well known, it depends upon cia 2#G1) (BissBa) a saeteesinn (w— a) (apo — 4) (9 — Ga) «wee, (a — a,) becoming unity for « = a, and vanishing when @ is equated to any other of the quantities a, a,a3....4,. Then interchanging ay with a, a, &e. in succession, so as to obtain a series of quantities Ky X, X, . . . X,, the formula of interpolation is Ug == Koy Up. Ky Uy + Ko tg ia.e «yee + Xiu, The proof consists in the observation that since X, = 1, and all the other Xs vanish when a = a, it leaves uv, = u, as it ought todo. Although this formula usually bears Lagrange’s name, it is said to be really due to Euler. The chief advantage of it over Newton’s method is, that the co- efficients are in a form adapted to logarithmic computation. The differential coefficients of w, with regard to x may be obtained by actually differentiating the resulting formula, either in Newton’s or in Lagrange’s method. But they may also be obtained, as in the common theory of equations, by an obvious application of Maclaurin’s theorem.* The quadrature can also be effected, as was pointed out by Newton, by the application of the ordinary methods for the measurement of an area of parabolic form. It does not appear that the details have as yet received much attention, but it is evident that the final formula of either Newton or Lagrange may be integrated between limits, by direct integ- ration, and that the result of the integration may be expressed in terms of the intervals and ordinates, either by direct substitution, or by the help of indeterminate coefficients. Judging from the form in which Laplace has placed the differential coefficients, it is probable that some interesting results would be obtained by such an investigation ; but these results would be likely to be more interesting as a matter of form, than useful as a matter of arithmetic. Section 3.—Gauss’s Method of Quadrature. This method is of high analytical interest, as connecting the theory of interpolation with what are known indifferently as Spherical Harmonics, or as Lagrange’s or Laplace’s functions. It is also useful and in- teresting from the point of view of their inventor, in making the best possible use of a small number of ordinates, when the function subjected to this mode’ of ‘quadrature is capable of exact expression in a parabolic form. If this last condition be not assured, its arithmetical value also becomes in a like degree uncertain. It has assuredly never been proved that. there is any general advantage in adapting the rules, indicated by the parabolic theory as the most exact, to cases which are not known to fall strictly within that theory. * See Boole’s Finite Differences, 2nd edit. p. 41. ON QUADRATURES AND INTERPOLATION. 365 Gauss’s proposal is to select the abscissw in such a manner that the error of a quadrature, obtained by means of 1 selected ordinates, shall disappear in the application of this quadrature to any rational function not exceeding the degree of 2n—1. For this purpose, supposing the limits of integration to be + ; the abscissee are the 7 roots of the equation del cade 7 Ga laa which are the halves of the roots obtained by equating to zero the co- efficients of Legendre.* Thus the multipliers for quadrature are easily obtained by substitution or by indeterminate coefficients. The roots of the sets up to » = 5 can be obtained as quadratic surds, and, with the co- efficients, are as follows: n=l, #2#=—0,¢,=1 arsatt | 1 nm=2, oe = —,¢, = Cy =5 12 7, =o, fous ora = 0 20 oy = em oy ¥ 80 ey ey= E+ cy 30 pean 2 = 55 (8) £2 / 70) or 2 = : wg ot 822. = 13 V 70 Snes 1800 18 we BIDAR TB ES 70. far ae 1800 co = 2 + Sere LADO) tee Section 4.—Other Methods and Suppositions, For some extensions of Gauss’s method, and for some particular forms * See Legendre, Fonctions Elliptiques, vol. ii. p. 531; Todhunter on the Functions of Laplace, Sc., chapter x.; Boole, Finite Differences, 2nd edit. p. 51, (ch, iii, art 12); Bertrand, Caleul Intégral, p. 339. Gauss’s own memoir is Methodus nova integralium valores per approximationem inveniendi. Géttingen—Comm, III. [1814] Wow. Ann. Math. xv. (1856). + The numerical values of these and of some of their logarithms are given by Gauss, Bertrand, and Todhunter in the works already quoted. The limits of error are also fully discussed by the two latter. But an attentive perusal of Bertrand’s reasoning will show that the limit of error depends upon the convergency of the parabolic expression of the function, and cannot be relied upon where this is not secured, 366 REPORT—1880, of the other theorems of interpolation, the reader is referred to Mr. Moulton’s notes to ch. iii. of Boole’s ‘Finite Differences,’ second edition, and to the examples of the same chapter. The extensions of Gauss’s method are of too special application to need exposition here, especially con- sidering their very doubtful utility in dealing with actual, as distinguished from analytical, data. It is important to observe that both Newton’s and Cotes’s methods admit of a far wider generalisation of form. The parabolic character of the assumption usually made, that the function subjected to interpolation or quadrature is either a rational integral function of the variable, or a convergent series, is not by any means necessary. On the contrary, the very form of Lagrange’s expression shows that it is permissible to sub- stitute for the simple factors, functions of those factors arbitrarily chosen, with only such restriction as to form as is needed to prevent the formula becoming confused or nugatory.* This is merely another way of stating the essentially indeterminate character of interpolation. If has to be shown, as a prior condition of the use of any such specialised formula, that there is good reason for applying it, aud that its results are reliable. The reason for generally selecting the ordinary methods turns upon the two principles, that a, function can be approximately represented by a convergent rational series, and that the approximation can be made as great as we please by taking the intervals sufficiently small. It has already been pointed out that these principles are not universally true, and, as particular cases, that they are not so when there is either physical dis- continuity, or discontinuity within the meaning given to it in the proofs of Taylor’s theorem, Anexamination into the questions corresponding to these is needed in using any such functional substitute for the simple factors of the parabolic assumption, in order to render the method safe and complete. There are doubtless many cases in which this may be practically neglected. In those cases there may bea doubt as to the necessity for any such refinement at all, except as a mere matter of selecting the proper function for interpolation,} and indeed the complete investigation frequently amounts, in the end, to nothing more than doing this. It even sometimes brings back the question to the determination of an analytical expression which shall adequately represent the table or series of observations. A very remarkable instance of this is the repre- sentation, due to the late Benjamin Gompertz,t of the decrements of life by means of a double exponential function. The equivalent physical assumption is that the stock of vital force undergoes a weakening proportional to the time, and this assumption, not improbable in itself, is found, with a suitable determination of the parameters in each case, to represent, with a high degree of accuracy, all the best life-tables, through * This may very well happen if very general forms are incautiously subjected to special interpretation, or if special forms are incautiously generalised, g- ox is a well-known example of this trap for the unwary. } Cf. Stirling, Methodus Diff. p. 88, ‘Nam interpolatio non est temere suscipienda, sed ante exordium operis inquirendum est quenam sit Series simplicissima, ex cujus intercalatione pendet ea seriei proposite. Atque hec preparatio est magna ex parte omnino necessaria, ut deveniamus ad conclusiones concinnas et elegantes.’ { The formula is dy =— abv y dx, where y is the number living at the end of # years. See Gompertz ‘On the nature of the Function expressive of the law of Human Mortality,’ Philos. Trans, 1825, p. 613. See also another paper by the same author, Phil. Trans. 1862, p. 571. See also the article < Mortality ’ in the Penny Cyclopedia and in the English Cyclopedia (Arts and Sciences). : ON QUADRATURES AND INTERPOLATION. . 367 a very considerable portion of their range. Nevertheless its insufficiency is shown by its being impossible to apply the rule to the whole range of the observed life-table (including infant and senile life), without either losing accuracy, or introducing a discontinuous change into the para- meters. Investigations of this description, however, belong rather to analysis’ than to mere interpolation. Their importance can hardly be overrated, especially when functions involving more than one parameter have to be considered ; for tables of double entry are very cumbrous, and to go beyond that is practically impossible. Hence the importance of Gompertz’s formula, and the corresponding importance of those of Jacobi’s investigations* which have rendered it possible to reduce the evaluation of elliptic functions, primarily depending upon three variable quantities, to a combination of results obtained from interpolating double- entry tables. It seemed advisable to point out the bearing of these considerations upon the subject of interpolation, although their detailed exposition lies outside the scope of this report. VI.—INTERPOLATION AND QUADRATURE FOR UNCERTAIN VALUES. When a number of observations of a phenomenon, which can yield but a single numerical value, have to be compared, the ordinary theory of the errors of observation furnishes the most probable numerical amount of that value, or of any given function of that value ; and this whether the observations be all equally good, or have definite numerical weights attached to each. A further refinement has been introduced by attaching weights themselves derived from the departure of the individual observa- tions from the first mean. This is a perfectly definite process, and the only remark which needs to be made upon it here is, that the most probable value of a given function of the result is not the same thing as the given function of the most probable value of the result. When an unknown curve is only known by a number of points, each determined subject to some unknown but appreciable error, the problem of finding the curve is absolutely indeterminate, unless some assumption be made as to the nature of the curve. This will be best seen by taking an easy problem, in which the indeterminateness is removed by a simple supposition, Let us assume that a right line has been observed, and is to be plotted by means of a set of equidistant ordinates, but that upon setting them off, the heads are not in a right line. It is then a perfectly definite problem to find a right line such that the squares of the distances of the points from it shall be a minimum, and in accordance with the fundamental principle of the ordinary theory, we shall find the same right line in whatever uniform direction we measure the distances. But the assumption that the line through the observed points is a right line, is exactly what we want to avoid in the general problem. On the other hand, when points of a curve are definitely given, we may make the curve determinate by assuming that its continuity is of the highest order possible. In its simplest form this is effected by assuming the curve to have a parabolic equation ; but this is not essential, and we may settle it by circular curvature instead of by parabolic order. But whatever law * See Legendre, Traité des Fonctions Elliptiques, vol. iii. pp. 141-2 (2nd supp. art 171); also Jacobi, Fundamenta nova Theorie Lunctionum Ellipticarum, pp. 139, 140, 368 ‘ REPORT—1880. of facility we take for the nature of the curve connecting the points, that is evidently independent of the law by which the points are assumed, aud there is no law connecting the two systems of probability. Any attempt to attain determinateness is therefore of necessity futile. This indeterminateness is experienced in practice as well as indicated by theory. One of the commonest. modes of ‘fairing’ a curve through given points is by using a flexible batten, or spline, which is pinned down by lead weights to the points through which the curve is to be drawn, and the pen is then drawn along the batten. Now, in practice, it is found impossible to use similar battens for all curves. The batten has to be weakest where the curvature is the greatest, and it is a matter of taste and discrimination to select a batten with the proper taper, and to use it discreetly, so as to get a reasonable and presentable result. The use of moulds or curved patterns is still more a matter of eye. : In the case of a curved surface such as that of a ship, the problem is rendered somewhat more determinate by the consideration that all the sections, and all their projections, must be fair curves. The two sets of vertical sections, and the water sections, thus correct one another, and it is not an uncommon thing to complete the ‘fairing’ by means of diagonal lines. Another mode, nearly equivalent, is to make a model, and to work it until it is not only quite smooth, but until, when it is held up in every possible light, the shadows fall evenly and fairly upon it. This is quite as severe a test as the drawing. Nevertheless, in either case the adjustment is not a matter of rule, but of taste and judgment. Apart from the mechanical skill necessary to produce such work, there are many people whose perceptions are not sufficiently delicate to appreciate or test it. While the problem is thus really and intrinsically indeterminate, all the solutions being strictly secundum quid, instead of being general, the difficulty is by no means beyond the reach of practical skill in the most useful cases. A comparatively small number of sections in two dimensions will enable two experienced draughtsmen to produce a couple of ships which shall differ very little in size or shape when they come to be built. It may be worth while to repeat that the indeterminateness really turns upon the want of any arithmetical comparison between two inde- pendent systems of variation of error, or of any analytical means of com- bining them so as to give a single determinate result.* * On this subject see Mr. G. H. Darwin on ‘Graphical Interpolation and Integration,’ Messenger of Mathematics, January 1877, p. 134, and the same author on ‘Fallible Measures of Variable Quantities,’ Philos. Mag. for July 1877. In the former paper Mr. Darwin gives a simple proof that the use of the trapezoidal rule gives a less probable error for the area of a curve, when the ordinates are taken as having each the same possible numerical error, than is given by the higher parabolic rules. The arbitrariness of this assumption as to the law of error should not pass unnoticed. See also a paper by Mr. Eckart in the Transactions of the Institution of Naval Architects, vol. xiii. (1872) p. 318 and plate xv., for an example of a fair curve drawn through a series of points whose positions require correction. See, further, a paper by Dr. McAlister in the Quarterly Journal of Mathematics for this year (1880), on the use of the Geometrical Mean for giving the most probable result. This is equivalent to using the logarithms of the terms, instead of the actual terms, in the equation of probability. ON QUADRATURES AND INTERPOLATION. 369 VII.—PERIOpICITY. The ordinary assumption of interpolation is that there shall be no periodicity in the function, and this assumption is involved in the approximate equation virtually assigned to the curve being of parabolic form. Any periodicity vitiates the accuracy of the result, and the detection of this periodicity is necessary before any correction can be applied, or any special methods adapted to the periodic character. In observed results, rather long series are required before periodicity can be detected, unless it can be independently inferred from analytical or physical considerations. It is best detected by plotting a curve of the function, and the process may be facilitated by first transforming the function so as to deprive it of any very abrupt curvature. The oscillation will then generally become visible, or may be made so by an elliptic exaggeration of ordinates, taken nearly normal to the general direction of the curve. The arithmetical methods of detecting periodicity are mere trans- formations of this geometrical principle. They are very difficult and intricate pieces of work, especially when the periodicity is of high order and small amplitude. Examples may be seen in the discussions of the inequalities of the planetary systems in astronomical works, and, in a less elaborate way, in the discussion of the various periodicities which have been associated with the sun-spot period.* They also present themselves in the discussion of tides ; but in these cases the probability of a period is sufficiently evident to cause it to be looked for in the proper way. When the period is once found, there is seldom much difficulty in dealing with it, either for interpolation or for quadrature. VIII.—Systrematic CoMPUTATION OF QUADRATURES AND INTERPOLATIONS. In all work connected with either interpolation or quadrature it is necessary, both for convenience and correctness, to do the work in a neat and well-arranged tabular form. The expression given in many books for the parabolic quadrature, namely, ‘to the sum of the first and last ordinates add four times the sum of all the even ordinates, and twice the sum of all the other ordinates, and multiply the total by one-third of the interval’ is not the form in which any practised computer would think of working. The slight repetition of labour involved in the tabular form is as nothing compared with the trouble and chance of error involved in disturbing the regular order of the ordinates. Moreover, when moments are required, as well as mere area, the tabular arrangement is a clear gain of work. An example of the arrangement for obtaining the centre of gravity of a curvilinear area is given below. The curve selected for integration is y= 2 ./(« + 1) — 2, for the values 0, 1, 2, 3, 4, 5, 6 of a. The result is that the area is 11:3568, and that the codrdinates of the centre of gravity are 435586 a, 13-2840 4 42, T13e78 = 28377, and Fs = 11096. is See also Messrs. C. & F. Chambers ‘On the Mathematical Expression of Obser- vations of Complex Periodical Phenomena,’ Phil. Trans. vol. 165 (for 1875) p. 361. . BB 370 REPORT—1 880. | y ty dx a pry dx yr Jyde | 5 B H ; Te eal d@iovhe & | ucla neck Stan chee | ae aera S rt =: = BA ba | == a 3 P Boar s a Bralia| seal Tey gO hiettg 1 hoo 1 Loli 0 | 0 0: 1. LO 1 2 | 08984 | 4 33136 | 1 |. 3:3136 || 06862 | 4 | 27448 | 2 3 | 14641 | 2 | 2:99892 | 2 | 5:8564 || 21433 | 2 | 49866 | .3 ae a eae: 3 | 24m 4: 4 | 16 4 5 | 24721 | 2 | 49442 | 4 | 19-7768 || 61110 | 2 | 19-9290 | 5 6 | 28990 | 4 | 115960 | 5 | 57-9800 || 84042 | 4 | 33-6168 | 6 7 | 32915 | 1 | 32915 | 6. | 19-7490 || 10-8338 | 1 | 10-8338 | 7 Zh — "| "34-0735 | — [130-6758 = — | 7970407a=S re — | % | 113578 | 4 | 435586 gh 2 | 13-2840 | — Tf the interval is other than unity, account must be taken of it, multi- plying the sum for fi dx by the interval, and the sums for fay dx and fv dz by the square of the interval.* When the integration has to take place in two dimensions, as in eal- culating the displacement and mechanical centres of ships, a much greater saving can be effected by systematic arrangement. It is sometimes more convenient to compute the area of a curve from the polar expression J — i 7?d6 ; but this needs no special remark. or The rectification of a curve is but a particular species of quadrature, being either J / (du? + dy?) or f (sec .dv,) where ¢ is the angle between the tangent and the axis of abscisse. Its arithmetical treatment presents no special feature, unless it be that the secant of @ has to be obtained from ordinates. This is fully treated of in Cap. IV. Sec. 6 of this report. The quadrature of a curved surface by means of ordinates rests on a similar principle, namely, on the quadrature of the double integral sec @ dudy where # is the angle between the tangent plane, and the “plane of the base (ay). The greater part of the work turns upon the 2 y\2 determination of sec ¢ = «f i 1+ e) _ (FZ) \. This done, the dx dy. * See some examples of integrations differently arranged for other purposes, in various papers in the Zvansactions of the Institution of Naval Architects—especially vol. ii. p. 163, vol. v. p. 9, vol. vi. p. 51. ae RY, : + For examples of a ‘displacement sheet’ see Shipbuilding, Theoretical and Practical, by Napier, Rankine, Barnes, and Watts (Mackenzie) p. 46 ; and Theoretical Naval Architecture, by Thearle (Collins) pp. 50-58 and Table I. Fora similar sheet suited to the application of Woolley’s rule see Trans. I.N.A., vol. vill. p. 213. Many other interesting examples of carefully arranged integration will be found scattered throuvh the Trans. I.N.A. and treatises on naval architecture, such as Scott Russell’s, and the works already quoted. ON QUADRATURES AND INTERPOLATION. 371 double integration is easily effected between the required limits, cither by Woolley’s rule, or by any other method which may suit the case.* It is of some consequence to conduct the work so that the degree of accuracy may be as nearly as possible the same throughout. It is best to follow the rule of using as nearly as possible the same number of signifi- cant figures right through. Thus it is idle to use five or six figures for a moment, and only two or three for the coordinate of the centre of gravity, because either there are more than we want for the moment, or else there are not enough if we require any further step to be taken from the value so found for the centre of gravity. It is a common thing to see much good work disfigured by want of attention to this. The rule above sug- gested is not absolute ; but it is onghe whole the best to work from, except in some special cases, which a little thought will easily discriminate. It is scarcely necessary to enter into any detailed disquisition con- cerning the application of arithmetic to interpolations. Probably too much has already been written on the subject. With regard to inter- polation in two dimensions, the reader may usefully consult Legendre, Fonctions Elliptiques, vol. ii. cap. xv. pp. 201-207. TX.—GrapuicaLt Mrrmops. Of mere interpolation, there is no need to say anything here. Whew once a function is represented by the ordinate of a curve, the interpolation is effected at sight, whether the direct interpolation from the intermediate -yalue of the variable, or the inverse operation of obtaining the value of the variable corresponding to a given value of the ordinate. “In the same way a parallel ruler will give us the means of interpolating direction, and. of finding maxima and minima. In the case of quadrature there is something to be said, although that is very little more than the translation of the arithmetic into geometry. The geometry is practically restricted to the simple parabolic rule, or to the trapezoidal rule—the parabolas of higher order are of course unsuited to graphical work. That they are so has already been shown to be a matter of no great consequence. The fundamental operation of quadrature is that of finding the ares of a plane curve. It is convenient to reduce the construction to that of finding the area included between a base line, two parallel ordinates at right angles to the base, and a curved line forming a fourth side to the figure. As has been already remarked, this curve must never be parallel to an ordinate, nor should it have any abrupt curvatures. If we work by the trapezoidal rule, we may divide the base into any number of intervals; if by the parabolic (or Simpson’s) rule we must take an even number of intervals ;—and in either case we draw ordinates through the points of division. Taking the simpler rule first—which is equivalent to assuming that the line joining the heads of two successive ordinates is straight—the sum of the first and second ordinates is set off on the second ordinate. This represents twice the area of the curve between those ordinates, which doubled area is a strip equal to the length so set off, and of the width of the interval between the ordinates. Twice the area between the second and third ordinates is similarly represented. * An example of one arrangement for this purpose was given by the author im vol. vi. of the Trans. I._N.A. pp. 64-72, and also in Scott Russell's Naval Architecture, pp. 135-138, It is a cumbrous process at best. ° BeBe 372 REPORT—1 880. by their sum. This, added to the length previously laid off on the first ordinate, gives the area up to the third ordinate, and is set off upon that, and soon. ‘This gives the ordinates of a new curve,* which repre- sents double the area of the first curve up to any given ordinate, original or interpolated. The curve passes through the foot of the first ordinate, because there is no area until that has been passed. If the curve is inconveniently tall, it must be reduced by dividing all the ordinates in the same ratio. If the parabolic method is preferred, we divide the base into an even number of intervals, and draw ordinates. Join the heads of all the odd ordinates by right lines cutting the even ordinates (produced if necessary ) and divide the portion of the even ordinates included between the curve and the chord into three equal parts. Then the distance from the base to the point of division nearest the curve gives the area comprised between the adjacent odd ordinates. That is to say, it is the length of a strip, whose base is the double interval, and whose area is equal to that of the corresponding curved area. The length thus obtained on the second ordinate, is set off on the third: the length similarly obtained on the fourth ordinate is added to that on the second, and the joint length laid off on the fifth. We thus obtain ordinates for a curve of areas; only the scale is one-fourth of what would be obtained by the previous process applied to the same curve. It is very important to keep an accurate account of the scale. This is best written along each curve: thus curve of lengths, one inch representing (say) 2 feet curve of areas, one inch representing » 8 square feet curve of volumes, one inch representing ,, 8 cubic feet reduced curve of volumes, one inch = », 128 cubic feet. The additions are best performed by setting off the lengths in suc- cession on a straight-edged strip of paper. If only the total area is required, the whole operation can be performed upon the strip. If moments are required, the first thing is to construct a curve repre- senting the moments of the ordinates. Start from the foot of the first ordinate (whose moment about itself is zero), take the head of the second ordinate, double the third, treble the fourth, and so on. Integrate the curve thus obtained, and we get a curve of moments, any ordinates of which represent the moment of the area of the original curve up to that ,ordinate—the moment being taken about the first ordinate.t The mo- ment may, of course, be taken about any other ordinate; but the new ordinates on one side of the selected ordinate must be set off below in- stead of above the base. The scale may be reduced at the first operation by taking the multipliers 0, n, 2n, 3n, 4n, &c., where n is a fraction, instead of using 0, 1, 2, 3, 4, &e. If the curve of areas be again integrated from the foremost end, the complete integral represents the moment of the original curve about the final ordinate. This is a consequence of the formula (easily obtained by integrating by parts) fy de= WE dx dx + fay dx ** See chapter vi. for some observations on the mode of drawing these curves. + The moments must be taken about an ordinate, not about the base. If moments ‘about the base are wanted, a fresh set of ordinates must be taken parallel to the base. ea. ON QUADRATURES AND INTERPOLATION. 373 The interval used in the graphical process is quite immaterial provided careful account be kept of scale. It is impossible to pay too much atten- tion to this point. It is, of course, not necessary that the original ordinates should re- present lengths. They may represent areas, in which case their curve of areas will represent volumes; or they may represent pressures, in which case, with a suitable interpretation of the interval, the areas will repre- sent work; or, again, the integral of a curve of temperatures may represent heat. Whether it actually does so, or not, depends upon what is taken for the interval. What all these processes effect is mere summation with suitable coefficients. The processes of multiplication or division, except by a small integer, are not conveniently performed in this way. So, although we get out the moments graphically, we must have recourse to arith- metical division, to find the position of the centres of gravity, or of gyration, Similarly, if we want to set off the squares, or the cubes, of the ordinates, we must use a table of squares or cubes, and set off from that. It is best to use printed or lithographed sheets divided into squares, the interval being chosen with reference to the work to be done, In English shipbuilding work, which is usually drawn on a scale of z-inch to the foot, quarter-inch squares are the mest conyenient. There should be a thicker rule at every fifth or tenth line, to prevent mistakes in counting. Any sized square will do, only if the right size be chosen, it saves, at least, one set of reductions. For mere quadratures, it is not necessary that the lines should be exactly at right angles, but in cross- measurements it is inconvenient to have the two diagonals measuring different lengths. The intersections of curves drawn to the same scale solve graphically a number of equations, differential and other, which it would be difficult to treat otherwise. There is no difficulty in changing the independent variable. One of the simplest ways of doing this is by the interchange of wand y, by taking a fresh set of ordinates at right angles to the old ones. But as there is no restriction to rectangularity, and as we may measure to an inclined or even a curvilinear base, it is obvious that the range of transformation is very wide indeed, An example of the appli- cation of this to the problem of rectilinear motion in a resisting medium will be found in the ‘ Phil. Mag.’ for June, 1868, Neither of these points, however, falls strictly within the scope of this report, and therefore it is unnecessary to enlarge upon them, As regards the accuracy of these graphical methods, the work in the Royal School of Naval Architecture was generally done from drawings on a scale of 3-inch to the foot. The displacement got out correctly in two ways used generally to agree within about } percent. If it exceeded 2 per cent., it used to be regarded as evidence of a blunder, As regards blunders, graphical processes have the advantage of making these appa- rent by a corner in the curves, Polar quadrature of an area.—It was pointed out to the author by the late M. Normand of Havre, that the polar quadrature could be very rapidly applied to finding the area of transverse section of a ship’s hold. For this purpose the angles could be marked on a wooden quadrant held vertically athwartships at the corner underneath a deck, and divided into equal angular intervals, while a tape would pass from the centre of the Sys nePoRT—1880. quadrant to the opposite side or bottom of the ship and would be made to cover one of the divisions. The observed length of this tape being 7, the integral On 7d) would give the area. The work might be still further shortened by graduating the tape according to 3 7? instead of by equal divisions. There would then remain nothing but the quadrature. This method might be conveniently applied geometrically in the case of curves having two axes of symmetry, like the ellipse, to which parabolic quadrature is not applicable. This is, however, only one of a very great number of the possible transformations of the independent variable. Length of « curve-—Draw a chord between its extreme points, divide the chord into equal parts and draw ordinates at the points of division, at right angles to the chord. Draw tangents to the curve where these ordinates cut it, and let these tangents be produced both ways to meet the ordinates at the extremities. Use the lengths of these tangents as ordinates, and integrate them by any method of quadrature, dividing by the number of ordinates. The result will be the length of the curve.* Curved Surface.—The only general method of dealing with this is first to construct, and then to integrate between the requisite limits, sec @ da dy, where ¢ is the angle between the tangent plane and the base, or plane of (x,y). The construction of the term sec ¢ for any given point is easy enough, since this is simply the through diagonal of a parallelopiped, of which the base is given, and the directions of the diagonals of faces are also given. The number of ordinates, however, for which this calculation has to be made is large, being in two dimensions, and there is then a double integration to be performed. Moreover the limits are not neces- sarily or usually constant, and then again the methods fail where the surface is parallel to au ordinate, and in either of these cases the surface has to be specially cut up, presenting in reality several different pieces of work. All this renders it a very laborious task, and unfortunately the integral for the surface does not present any such reductions, when treated by ordinates, as the volume-integral. In iron shipbuilding, when the work is complete, and a separate account is taken of every plate, the weight of skin and area of the surface are of course mere matters of addition. But while the design is in draft, it sometimes becomes necessary to estimate the surface in a more summary manner. ‘The usual mode is to obtain the lengths of all the level lines and transverse sections of the surface, and then to expand the surface on the flat by means of two sets of strips of paper, which secure equal lengths for the sides of the quadrilaterals, the angles being allowed to take up their own adjustment. This is a very coarse representation, even sup- * posing the expansion to be split where the distortion is great, as it usually is where the skin of a ship meets the sternpost. This process is occa- sionally modified by using an orthogonal network on the surface, instead of orthogonally dividing the plan, and that is probably a little better. Another more accurate plan has been given by Mr. Crossland + of th Admiralty. A model of the ship is usually more convenient to work from * This method is given by Rankine in his Rules and Tables, p. 75, It is nothing more than the graphical quadrature fs sec >. da. t See the Annual of the Royal School of Naval Architecture (for 1873) pp. 12-14. ON QUADRATURES AND INTERPOLATION. 375 than drawings, although it is quite possible to get the constructions without much difficulty from these. Nevertheless, it is a laborious and unsatisfactory process, and quite inapplicable to complex or highly curved surfaces. It does, however, give a rough approximation, and, as such, is found both useful and necessary by shipbuilders, X.—MECHANICAL QUADRATURES. Rectification.—The only satisfactory mechanical means of doing this is by running a wheel along the curve, and observing its travel. In the opisometer it is done by starting the wheel from a stop, running it along the path to be measured, and then applying it to the scale of the map or diagram, and running it backwards until the stop is felt. This saves the trouble of any readings, except the final one upon the scalé, and it also avoids all conversion of scale. It may be objected to it that it is a little wanting in minute accuracy, from a small yielding at the stop giving a considerable error at the edge of the wheel. This, however, can easily be tested on a plain scale, and careful use of the instrument with a delicate hand gives very good results. There is a more elaborate but very convenient form of the machine sold under the curious name of ‘ Wealemefna.’ Direct mechanical quadrature.—If a disk revolve at uniform velocity, and a friction wheel roll upon it, having its axis parallel to the plane, aud meeting the axis of the disk, then it is clear that the travel of the friction wheel will be directly proportional to its distance from the centre of the disk. If, therefore, the friction-wheel be made to slide upon the disk, so that its point of contact shall be separated from the centre by a distance equal to the varying ordinate of a curve, while the disk rolls along a straight line base, the travel of the friction-wheel will integrate the area of the curve. ‘This is the simplest mechanical integrator there is, It is used in one form as the ‘ continuons indicator’ in steam-engines, and in another form it is used for integrating the curves of the German tide-gauges. It is also used in the recording part of Morin’s dynamometer, and in Sang’s planimeter. > James Thomson’s integrator—This ingenious instrument was devised inorder to get rid of the sliding which takes place in ‘the continuous integrator, and in Amsler’s planimeter. It consists of a plane circular disk inclined at an angle of 45° to the horizon, and turning freely on an axis normal to its plane. A cylinder with its axis horizontal and parallel to the plane of the disk is mounted on journals in front of the disk, so that they just clear one another. A smooth sphere is dropped into the trough between the disk and the cylinder, and the machine is so adjusted that the sphere can just roll over the centre of the disk. The amount of rotation of the cylinder as the disk turns through a given angle, will vary as the distance of the point of contact of the sphere and disk from the centre of the latter. The travel of the sphere laterally is obtained by means of a fork, which is made to slide in the direction of the axis of the cylinder, and which nips the sphere between two pads or cushions, on which it slips easily. If now a flat templet with a straight base and a curved edge opposite the base, is moved in the plane of the disk and at right angles to the axis of the cylinder, so that the disk, or a pinion in gear with it, rolls along the base, while a pin in the fork-handle 376 REPORT—1880. follows the curve on the other side of the templet, the travel of the cylinder will effect the quadrature of the curve on the templet. * The use of the machine is by no means limited to this simple quad- rature. By putting the fork in gear with the disk through the intervention of suitable wheel or link-work, or belting; or by gearing two such machines suitably together, it is possible to obtain the mechanical solution of differential equations. Sliding motion is not altogether escaped in this machine, In the first place, there is sliding motion of the sphere in the fork. Further, the rolling of the sphere along a small circle is not pure rolling, but, although not having any actual sliding, is intermediate between sliding and rolling. For if we separate the pure rolling along a great circle from the twist necessary to make it describe a small circle, the aggregate of this twisting is the same as we should get by turning the sphere through a definite angle about an axis perpendicular to the disk; but instead of being finite sliding, as it would be on this last supposition, it is in fact distributed over a line instead of concentrated at a point. It is thus infinitesimal at every point of the line, along which, however, there ceases to be pure rolling.t There is also a source of error in the necessity of giving some clearance to the fork, which would otherwise not slide on the sphere. This clear- ance introduces a slight error every time the fork reverses its motion. It is, however, a constant error; but it is always in the same direction, and is not compensated on a double reciprocation. This is the chief drawback to the machine, which is nevertheless a most valuable instrument. Amsler’s planimeter.—In this wonderful little instrament a pointer is made to run round the closed curve, which has to be measured, and a little wheel, which partly rolls and partly slides, gives the area by the mere reading of its rolling motion. The main principle on which it de- pends is this: that if a finite right line moves in its own plane, the whole area swept out by it is measured by the product of the length of the line, and by the sum of the components of the motion of the middle point (resolved at every instant) at right angles to the line. A wheel turning on an axis parallel to the line, and free either to roll or to slide on the paper or plane, will effect this instantaneous resolution, and its reading will integrate the required component, When one end of the bar makes a complete circuit of a closed curve, coming back to the point from which it started, while the other end reciprocates along an are of any fixed curve, wholly external to the closed curve, the area of the latter is given by the difference between the initial and final readings of the wheel. In this case, moreover, the principle of the separation of the motions of rotation and translation shows that the total reading of the friction wheel will be the same, if it be moved from the middle to any other point of the line, or even of the line produced. The only adjustment required, there- fore, is that the axis of the rolling wheel should be parallel to the bar which carries the pointer. This freedom from adjustment is one of the most valuable properties of the instrument. As a practical matter, the accuracy of the results which it gives is quite equal to that of the very best drawings which can be made. * See Roy. Soc. Proceedings, vol. xxiv. p. 262, On an Integrating Machine having anew Kinematic Principle,’ by Professor James Thomson. ft See two papers by Sir Wm. Thomson at pp. 266 and 269 of the same volume. { The motion is intermediate, in much the same sense that #¢ (log w)’ is inter- mediate in dimension to a and a¢+%, See De Morgan’s Diff. and Int. Cale. p. 323. ON QUADRATURES AND INTERPOLATION, ort In the usual form of the instrument, the reciprocating curve, traced by the other end of the bar, is an arc of acircle. This is for facility of use and construction, and is by no means essential. Amsler’s Mechanical Integrator—By an ingenious extension of the principle of his planimeter, Professor J. Amsler-Laffon, of Schaffhausen, has constructed a machine which, while a pointer describes a closed curye, records simultaneously its area, its statical moment, and its moment of inertia about a given axis. In this case the butt end of the bar which carries the pointer is made to move along aright line. The area is read off from a wheel mounted on the bar itself, and this part of the operation is thus the same as in the common planimeter. The moments are read off from wheels mounted on arms whose centres also describe right lines, but which are so geared with a wheel rigidly connected with the bar carrying the pointer, as to turn relatively to it with the fixed velocity ratios of 2:1land3:1. Supposing the angular motion of the pointer-bar to be 0, and the velocity ratio 7:1, the quantity of rotation of the second circle will be n@ + a, a being an arbitrary constant depending upon the initial position. When the pointer goes round any closed curve which does not contain the centre of the first circle, this measurement of this rotary motion comes to nothing, for the angular movement is the same forward as backward, and it may therefore be left out of account. But its angle (n 6+ a) settles the direction of the resolution of which the component is measured by the instrument, when there is linear motion of the centre. The rolling wheel records a constant multiple of — dz cos (n9+ a), where dz represents the movement parallel to the axis, and its complete record is — faa e058 (n 040) =~" taken over the whole area of the curve. This has to be multiplied by a numerical factor, which is one of the constants of the instrument. Where n = 2, if we make a = 0, we have 2 w= fi docos29= fie {1-2 Gino? } = fd (1-2 4) y being an ordinate perpendicular to the axis of a. In this case therefore the difference between two readings of the rolling wheel counter is always proportionate to fy dx, which thus gives the statical moment. When n = 3, if we make a = — om we have cos (3 0-57 )=sin3 6=3 (ain 6)? — 4-sin 0 3 ES a ig k3 i and therefore the reading given by the wheel is few dx = fory dae 378 REPORT—1880. that is to say, it gives the difference between a fixed multiple of the moment of inertia and a fixed multiple of the area. In this way the moment of inertia is known. The subtraction is not performed by the machine, but is left to the calculator.* Sang’s planimeter is described and figured in a paper by Mr. Sang in the ‘ Transactions of the Royal Scottish Society of Arts’ for 1852, vol. iv. There is also a paper by Mr. Clerk Maxwell in the same ‘ Transactions’ (for 1855, vol. iv.) describing a planimeter invented by himself, and the action of which depends on the mutual rolling of two equal spheres. These are the principal mechanical integrators known to the author. So far as a draughtsman’s purpose is concerned, Amsler’s instruments appear to be the most convenient practically. The French Deep-sea Exploration in the Bay of Biscay. By J. Gwyn Jerrreys, LL.D., PRS. [A communication ordered by the General Committee to be printed in extenso among the Reports. ] I reen that I am indebted for the opportunity of giving an account of the French expedition, which forms the subject of this paper, to my esteemed friend and colleague, the Marquis de Folin, of Bayonne, He was until lately the commandant of that port, and is a most zealous and excellent naturalist. J may, indeed, say that the expedition originated with him. For more than ten years he had, at his own expense, assi- duously and carefully explored the sea-bed lying off Cape Breton, in the Department of the Landes, as well as could be done in a fishing-boat ; and the result of his researches among the marine Invertebrata has been described, with illustrations by his pencil, in a useful work called ‘ Les onds de la Mer,’ published at Bayonne under his direction. M. de Folin has from time to time sent me the Mollusca procured in his dredg- ings for my opinion; and our correspondence, with a visit which I paid him in December 1878, led to his making an application to the French Government for the grant of a vessel to explore the depths which were known to exist at a comparatively short distance from the northern coasts of Spain in the Bay of Biscay. This evidently could not be done ina fishing-boat ; and naturalists have much less money than science. It was, in fact, a project for a nation, and not for an individual. The application was, ; believe: referred to the Dean of the Academy of Sciences, M. Milne. Edw ards, whose reputation as an eminent zoologist has been universally / recognised for more than half a century. His report was favourable ; and a Government vessel was ordered to be placed at the disposal of a Com- mission of which M. Milne-Edwards was appointed President. The other members of the Commission were the Marquis de Folin, Prof. Alphonse Milne-Edwards, Prof. Vaillant, Prof. Marion of Marseilles, Dr. Paul Fischer, and M. Périer of Bordeaux. The selection of these savants * A detailed description and drawings of the machine is given in the volume of the Zransactions of the Institution of 1 Naval Architects for 1880. It will not escape the reader that this machine requires several rather nice adjustments which are not needed in the common planimeter. The machine, as actually made for sale by Mr. Amsler, is very beautifully contrived, with recard to allits mechanical details, and it works very smoothly and satisfactorily. The cost is between £16 and £20. ON THE FRENCH DEEP-SEA EXPLORATION IN THE BAY OF BISCAY. 379 augured well for the success of the expedition, and it has been fully jus- tified. At the suggestion of M. de Folin, the Minister of Public Instruc- tion graciously invited me and the Rey. A. M. Norman (a well-known naturalist) to take part in the expedition. Mr. Norman had been my valued companion for many years past in similar but less important excursions to Shetland and Norway. It was to mea great pleasure to be again associated with him. I regarded the invitation as far more than a compliment; it was a great honour. I may here mention that, immediately before the commencement of the expedition, M. de Folin, Mr. Norman, and myself had some prepara- tory boat-dredging in the Fosse de Cap Breton. This was done at the expense of the French Government. When has our own Government shown such generosity in the cause of science to French naturalists ? The vessel assigned for the purposes of the expedition was the | Travailleur, a paddle-wheel steamer of over 900 tons, of 150 horse-power, . and carrying four guns. She is an aviso, or despatch-boat, and is stationed ‘ at Rochefort for occasional service. She was supplied with a capital donkey-engine, and immense stores of cordage, sounding-wire, and other apparatus. She had a very happy name, being an indefatigable worker. Capt. E. M. F. Richard was the commander, or lieutenant de vaisseau, and the other officers were Lieuts. Mahieux, Jecquet, Villegente, and Bourget, Aide-Commissaire Gousselin, and Dr. Duplouy. Let me now express my sincere thanks to the officers for their great kindness and urbanity. They took a great interest in the work, and materially promoted the welfare of the expedition. The crew consisted of 128 men; the usual number was between 80 and 90, but extra hands were taken in consequence of the heavy work entailed by sounding during the night, All these men seemed to be well-conducted, as weil as good sailors ; and, although they had only two meals a day, their physique was quite equal to that of our best British seamen. Mr, Norman and I took with us, as dredger, a steady and intelligent man, John Wilson ; and Prof. Marion had his dredger named Armand. These men were of great use in sifting the material brought up by the dredges. For the captain, J can only echo the opinion expressed by Prof. A. Milne-Edwards in his preliminary Report, that his arrangements were first-rate, and his skill admirable, especially con- sidering that the kind of work was new to him, and that he had not previously made or even seen any deep-sea dredging. The members of the Commission assembled at Bayonne; and the Travailleur arrived there on the 16th of July. The next morning she went to sea, with all the party on board except the President, who was obliged to return to Paris, and might also have justly claimed exemption from active service, being in his eightieth year. Until the 1st of August (with the exception of two days, the 18th and 25th, which we spent at San Sebastian and Santander,) we were hard at work sounding, dredging, and trawling. The weather was very fine, and the dreaded Bay of Biscay lost its stormy character on this occasion. The principal object of the expedition was to ascertain the nature of the fauna which inhabits at considerable depths this part of the Bay of Biscay ; and this object was thoroughly and successfully accomplished. Twenty-three dredgings were made for that purpose at depths ranging from 337 to 2600 métres, each métre being about 39 inches, or rather more than half a fathom. The dredgings between 600 and 1000 fathoms were the most important. Every department of the Invertebrata was } 380 REFORT—1880, well represented, and novelties were discovered in the Mollusca, Crus- tacea, Nchinoderms, Annelids, Actinozoa, and Sponges. As regards myself, this expedition had a peculiar charm. Having had the scientific charge of similar expeditions for the Royal Society in H.M.S8. Porcupine in 1869 and 1870, and in H.M.S. Valorous in 1875, and having examined the collections made during the voyages of H.M.SS. Shearwater and CUhallenger, as well as those made in nearly all the Swedish, Norwegian, Dutch, and American deep-sea and exploring ex- peditions in the North Atlantic, I was naturally glad to participate in the French expedition, and particularly as it embraced that part of the sea which was at no great distance from the scene of my former labours in the cruise of the Porcupine along the western coasts of Spain and Portugal, and which cruise was so unusually productive. Impelled by this recollection, I made last year a verbai and informal application to the late First Lord of our Admiralty, for the use of one of her Majesty’s ships to explore the Bay of Biscay this summer. The answer I received was very favour- able; but the pecuniary resources of our Government were then at a low ebb, and I was encouraged to renew the application when commerce revived and times became more prosperous. I hope our new Govern- ment will avail itself of the now improved finances, and not neglect this genuine and beneficial method of instructing the nation, and maintaining its credit for maritime discovery. The fauna observed during the Travailleur cruise closely resembled that which I ascertained during the Porcwpine cruise of 1870 at corre- sponding depths. This will be shown, so far as the Mollusca are concerned, in the list of species appended to the present paper; and I have no doubt that the other branches, when they have been worked out by the experi- enced naturalists to whom they have been entrusted, will confirm my opinion. In a physical and geological point of view this French expedition has borne good fruit. No less than 103 soundings were made. They have proved the existence, within a few miles of the coast, of a submarine valley opening from the Fosse de Cap Breton and extending to a point opposite Cap Pefias. The large diagram and chart which I now exhibit will give a better explanation than I can do by any words. The diagram was pre- pared for me when I presented to the Royal Society my reports of the Porcupine expeditions of 1869 and 1870; and the chart has been filled up and given to me by my kind friend the Hydrographer.! The striking in- equalities of depth within a narrow area which thus appear were noticed in a Bayonne newspaper of August 4 as ‘des grands fonds sous-marins, qui continuent sous les eaux de |’Atlantique les vallées pyrénéennes.’ As a general rule, it may be said that where mountains or high land approach the sea the depth of water is greater off that coast than where the land lies low. But this must depend in a great measure on the geological nature of the land adjacent to the sea. If the formation be granitic or gneissie, the wear and tear or denudation must be slower than if the formation be sandstone, cretaceous, or tertiary; and the action of rivers and streams on the surface of the land must be proportionably increased or diminished, and cause the sea-bed to be more or less filled up in the course of time. Every- where during the dredgings of the Travailleur in deep water the sea-bed was found to be covered by a thick layer of mud, of a different colour from * See Proceedings of the Royal Society for 1870, and the Admiralty Chart of the Bay of Biscay. ON THE FRENCH DEEP-SEA EXPLORATION IN THE BAY OF BISCAY. 38] that of the Atlantic ooze; and this mud has probably accumulated from untold ages by the incessant efflux of the Gironde, the Adour, and nume- rous other rivers and streams into the Bay of Biscay. As may be supposed, the fauna which inhabits such mnd is very scanty ; and it required a con- siderable amount of patience and perseverance to extract even a few organisms from the unpromising material. No wonder that Dr. Carpenter was discouraged, as a zoologist, by what he termed ‘ the singular barren- ness of this deposit in regard to animal life,’ when he described the Mediterranean cruise of the Porcupine in 1870. Within a few days after the return of the expedition, Prof. A. Milne- Edwards presented to the Academy of Sciences at Paris a preliminary report of the zoological results of the expedition, which was published in the Journal Officiel de la Republique Francaise as well as in the Comptes | Rendus. As most of the departments of the marine Invertebrata have been so fully and carefully treated by him in this Report, I will content myself with a few supplementary remarks as to the Mollusca, which especially engaged my attention during the cruise. At the request of Dr. Fischer, who will undertake this department, and with the sanction of the President, I was entrusted with all the more critical specimens of Mollusca; and these specimens I have now cleaned, assorted, and com- pared with my own collection from the Porcupine Expedition of 1870 on the western coasts of Spain and Portugal. I subjoin a complete list of the Travailleur Mollusca, distinguishing in separate columns those species which are Porcupine, those which were previously known to me from Norway or the Mediterranean only, and those which I consider new to science. The total number of the species in this list is 198, out of which 169 are Porcupine, nine only appear to be exclusively northern, one exclusively southern or Mediterranean, and seventeen new to science, ‘T'wo of the Porcupine species are northern also. The results, especially in the last-mentioned category, are most noteworthy. They serve to show how little we know of the deep-water Mollusca, when we reflect that the area of the sea-bed lately explored, in a short period of time and in a necessarily cursory manner, is but a very small corner of the Atlantic, and that it would take many years to complete the exploration so auspiciously commenced. The space traversed by the dredge during this cruise represents probably much less than a ten- thousandth part of the sea-bed lying between Cap Breton and Cap Peiias ; and our means of exploration by the dredge are by no means satis- factory, particularly on muddy ground, of which the deep water zone is mainly composed. Instead of our being able to scrape a few inches of the surface of the sea-bed at considerable depths, so as to collect in the dredge all the animals which inhabit the superficial layer, we find too often, to our disappointment, that the dredge when it reaches the bottom sinks into the mud from its own weight and from the momentum given to it by the motion of the ship, and that it then acts as a subsoil plough and not as a scraper. I must ask one of my engineering friends to devise some instru- ment more efficient than the modern dredge. Although it cannot be positively stated that the abyssal zone, or even the benthal zone, is inhabited by species of Mollusca peculiar to it, some species observed by me during the preparatory excursion to Cap Breton and the Travailleur cruise bear out the statement to some extent. For instance, Nucula nitida, Dischides bifissus, Rissoa abyssicola (a now inap- propriate specific name), and Defrancia decussata occurred only in the 382 RnErPorT—1880. shallow-water excursion, while Nucula corbuloides, Siphodentalium Olivi, Rissow deliciosa, and Defrancia hispidula occurred only in the deep-water cruise. The list of Mollusca will show that several species are supposed to have been drifted from shallow water. This may have been owing to the proximity of the coast and to the consequent action of rivers and tides. Several deep-water species of Mollusca occurred in this expedition which had been until lately supposed to be extinct; they are fossils of the Upper Tertiaries of Europe.! A curious provision of Nature—if we may in these philosophical days use such a phrase—was observable in the case of a deep-water mussel of considerable size, which I propose to name Mytilus luteus. It inhabits the layer of mud which i have above described, and moors or fixes itself by means of a large and densely matted byssus which is spun by the foot. This byssus is capable of being spread over a considerable extent of sur- face; and it not only prevents the mollusc sinking into the soft mud and being smothered or buried alive, but enables it to feed comfortably on the innumerable animalculz which swarm on the surface of the sea-bed. It is to some extent of the same use to the mollusc as a snow-shoe is to the Arctic traveller. This species of Mytilus I at first took to be the Modiola incurvata of Philippi= MW. Martorelli of Hidalgo—which lives on the south coast of Spain in rather shallow water; but on comparison I am satisfied that they differ essentially in shape, sculpture, colour, and epidermis. I cannot conclude this account without tendering my most grateful acknowledgments to the French Government for their extremely generous conduct, and for the excellent hospitality which I enjoyed on board the Travailleur, as well as to the President and members of the Scientific Commission for their obliging and friendly companionship. The zoological results of this French expedition are fully equal to those obtained by Capitaine Baudon in 1801, M. d’Urville in 1829, the Re- cherche in 1835, the Bonite in 1836 and 1837, the Astrolabe in 1841, and other expeditions; and I sincerely hope that a further expedition of the present kind may take place next year in the Mediterranean, where our good and gallant neighbours have such an important stake. A List of the Mollusca procured during the cruise of the Travailleur in the Bay of Biscay, 1880. a= Bo4o4 ‘an| § | & |#8| No. | Name of Species sg| 5 eto) ES Remasks | ech Pat sie tes | Relea | we |7@ S} | BRACHIOPODA. | See as to this and other Mollusca in the 1 Terebratula caput - serpentis, | — | | | | list the ‘ Proceed- | Linné | 2 T. subquadrata, Jeffreys . ° | 3 | T. cranium, Miiller; afragment | — ingsofthe Zoological 4 | Platydia anomioides, Scacchi | — Society of London’ | and Philippi | / for 1878 and 1879. 5 | Megerlia truncata, L. : 5 — | 6 | Crania anomala, Mill. . el i 1 For the geological definition of this term see British Conchology, vol, i. pp. 315 and 316, j ON THE FRENCH DEEP-SEA EXPLORATION IN THE BAY OF BISCAY. -List oF MoLiusca—continued. Name of Species Porcupine | eruise, 187! Northern Southern New to Science Remarks CONCHIFERA. Anomia ephippium, L. . Spondylus Gussoni, O. G. Costa, Pecten pes-lutre, Ee . P. groenlandicus, G. B. Sowerby P. fragilis, J. . ‘ 3 P. obliquatus, J. (MS.) . P. vitreus, Chemnitz ° Pecten similis, Laskey . 4 Amussium fenestratum, Forbes. A. lucidum, J. . . Lima elliptica, J. L. subauriculata, Montacu L. Jeffreysi, Fischer (MS.) Mytilus luteus, J.(MS.) . Mytilus edulis, L. . . . Modiolaria marmorata, Forbes . M. Aiceallgrg Libassi , M. cuneata, J. (MS.) . Dacrydium vitreum (Holbill) Miiller. Arca pectunculoides, Sc.; var. septentrionalis. Arca lactea, L. . 7 ° Leda messanensis, Seguenza L. pustulosa, J. z : L. striolata, Brugnone L. tenuis, Ph. . : L. lucida, Lovyén 5 - L. pusio, Ph. . : L. sericea, J. . 3 L. Jeffreysi, Hid. . L. expansa, J. Nucula egeensis, Forb. N. corbuloides, Seg. . 3 } N. striatissima, Seg. s N. tumidula, Malin , N. sulcata, Bronn , F Limopsis cristata, J. ° i | | | | P. septemradiatus, Mill. And variety abyssorwm. A single valve ; pro- bably drifted. curvata, Philippi = M. Martorelli, Hi- dalgo ; but it differs in shape, sculpture, epidermis, and co- lour. Dr. Hidalgo agrees with me as to this. A valve of a young specimen; probably drifted. Same remark. A single valve; pro- bably, drifted. L. acuminata, J. (not Von Buch). v. Miinster. | And a variety. And variety lation. L. lata, J. (aot Hinds). Anda monstrous variety, Allied to Modiola in- | DL. pygme@a, auct., not | 383 384 , REPORT—1880. List oF MoLLUScA—continued. 2& =| S| SO] 5 =x | So gn g oO co No. Name of Species sg| 5 = ES Remarks Sela | a [40 43 | L. minuta, Ph. : ~|— 44 | Malletia obtusa, M. Sars ‘ .|— 45 | M. cuneata, J. —_ 46 | Montacuta ferruginosa, Mont. — 47 | M. tumidula, J. A : 48 | M. ovata, J.(MS.) . ‘ = 49 | Decipula ovata, J. . F of — | 50 | Kellia symmetros, J. ‘ : =) Valorous Expedition, 1750 fathoms; Nor- wegian Arctic Expe- dition, 656 and 1200 fathoms. 51 | Laswa rubra, Mont. . a <|— A single valve; pro- | bably drifted. 52 | L. pumila, $8. V. Wood . A ie A Coralline Crag fossil. 53 | Loripes Jacteus,L. . . .| — Probably drifted. 54 | Axinus flexuosus, Mont. . | — 55 | A. croulinensis, J. . ; .|-— | 56 | A. eumyarius, M. Sars. . || = | 57 | A. ferruginosus, Forb. . 2 | 58 | A. subovatus, J. F . yk | 59 | A. granulosus, J. F A = 60 | A. tortuosus, J.(MS.) . — 61 | Mytilimeria? Fischeri, J. (MS. ) _ 62 | Cardita corbis, Ph. . . = 63 | Cardium minimum, Ph. . ‘l= 64 | Isocardia cor, L. . ‘ | — And the fry, which has | many synonyms. 65 | Woodia digitaria, L. . ei A single valve; pro- | bably drifted. 66 | Tellina gladiolus, J. (MS.) 2 — 67 | Scrobicularia alba, W. Wood . | — 68 | S. longicallus, Sc. . . | 69 | §. nitida, Mull 5 ~f— 70 | Lyonsia formosa, J. (MS.) -[— 71 | Verticordia insculpta, J.(MS.). | — 72 | Thracia convexa, W. Wood .| — Young. 73 | T. tenera, J.(MS.) . . . i 74 | Newra abbreviata, Forb. . -|— 75 | N. rostrata, Spengler 5 | — 76 | N. cuspidata, Olivi; var. . A 77 | N. bicarinata, J. (MS.) . -|— A fragment. 78 | N. sulcifera, J. (MS.) : | 79 | N. truncata, J. (MS.) < | 80 | N. lamellosa, M. Sars : -{|— 81 | N.striata,J. . . {| 82 | N. imbricata, J. (MS.) . ne 82* Panopea plicata, Mont. . ~|— 83 | Saxicava rugosa, L. . ‘ oo SOLENOCONCHIA. 84 | Dentalium striolatum, Stimp- | — D. abyssorum, M. Sars; son. and variety agilis. 85 | D. capillosum, J. : . | = Fragments. 86 | D. gracile, J. . ° ° i Not D. filum, G. B. Sowerby, jun. ON THE FRENCH DEEP-SEA EXPLORATION IN THE BAY OF BISCAY. List oF MoLtLusca—continued. 385 2& 8S| BE) E lose . g al eae be i No. Name of Species 5 ee =| es Remar = z oS An 87 | Siphodentalium lofotense, M. | — Sars. 88 2 Olivi, Se. ‘ = ; 89 8. tetragonum, Brocchi . — Dentalium quinguan- gulare, Forb. = S. pentagonum, M. Sars. 90 | Cadulus semistriatus, J. ig Yr = 91 | C.tumidosus, J... 5 == 92 | C. artatus,J.(MS.) . . == Ts 93 | C. ovulum, Ph. . ‘ . A Calabrian and Sici- lian fossil. 94 | C. gibbus, J. (MS.). . : si 95 | C. propinquus, G. O. Sars. == 96 | C. subfusiformis, M. Sars . = 97 | C. gracilis, J. . % ° a 98 | C. cylindratus, J. . . = GASTROPODA. 99 | Chiton alveolus,G.O. Sars . = ; 100 | Rimula asturiana, J. (MS.) — |Probably R. radiata, Libassi, a Sicilian fossil. 101 | Cyclostrema spheroideum, 8.V. | — A Coralline Crag fossil. Wood. 102 | C. trochoides, J. Pn 103 | Molleria costulata, Méller F = 104 | Trochus gemmulatus, Ph.. — A Sicilian fossil. 105 | Turbo filosus, Ph, , : a A Calabrian and Sici- lian fossil = Zrochus glabratus, Ph. 106 | Hela tenella, J. é . — 107 | Rissoa cimicoides, Forb. . _ 108 | R. abyssicola, Forb . — 109 | R. deliciosa, J. (MS.) : — 110 | R. subsoluta, Aradas. . S| . ge) RK. parva, Da Costa .- . . | — A dead specimen ; pro- bably drifted. 112 | R. semistriata, Mont. — Same remark. 113 | R. tenuisculpta, J. (MS.) . — 114 | Hydrobia ulve, Pennant; var. | — Barkei 115 | Scalaria Trevelyana, Leach == 116 | 8. clathratula, Adams = 117 | 8. Cantrainei, Weinkauff . — 118 | Aclis Walleri, J. ‘ = 119 | Odostomia conoidea, Bre. — 120 | O. Lukisi, J. . : -|— 121 | O. prelonga, J. (MS. ) : i) = 122 | O. acicula, Ph.; var. obeliscus. | —- 123 | O. blandula, J. (MS.) R 7a 124 | O. nana, J.(MS.) . ‘ -{|— iapO. insculpta, Mont. . .° 94) — Probably drifted. 126 | O. nitidissima, Mont. . Same remark, 127 | O. sceptrum, J. (MS.) = 128 | O. lineata, J. (MS.) . : : == 129 | O. paucistriata, J. (MS.) . ol— 1880. ce REPORT —1880. List oF MoLuuscA—continued. | P. modiolus, De Cr. and Jan 386 ] | —] 25 | No. Name of Species a | 130 | O. fasciata, Forbes . S 5 = 131 | O. scille, Se. a eee ti { 132 | O. plicatula, Bre. . 4 == ; 133 | Ianthina exigua, Bruguitres = | 134 | Eulima stenostoma, J. “ 4 135 | E. pyriformis, Brugn. . a 136 | E. subangulata, J.(MS.) ; = | 187 | E. solidula, J. (MS.) : — 138 | E. intermedia, Cantraine . = 139 | E. obtusa, J. (MS.) = 140 | E. distorta, Dishayes = 141 | E. curva, J.(MS.) . = 142 | Natica sordida, Ph. . aa 143 | N. subplicata, J. (MS.). a | 144 | Solarium pseudoperspectivum, | — : Bre. 145 | Adeorbis umbilicatus, J. Saige 146 | Sequenzia, elegans, J. t = 147 | Lamellaria perspicua, L? . — 148 | Aporrhais serresianus, Michaud | — 149 | Cerithium metula, Lov. a 150 | Buccinum Humphreysianum, | — Bennett. 151 | Ranella gigantea, Lamarck . | — 152 | Trophon muricatus, Mont. = 153 | T. rugosus, J. (MS.) . qh 154 | Fusus gracilis, Da Costa . {ie 155 | F. turgidulus, J.(MS.) . “= 156 | F. berniciensis, King = 157 | Cassidaria tyrrhena, Ch. —— 158 | Nassa semistriata, Bre. = 159 | N. incrassata, Strdém = 160 | N. limata, Ch.; var. — ; 161 | Columbella halizeti, J. _- | 2&2 | C. seripta, L. . - . = | | | 163 | Taranis cirratus, Brugn. = | 164 | Defrancia crispata, De Cristofori | — | and Jan. 165 | D. parvula, J. (MS.) . — 166 | D. formosa, J. (MS.). = 167 | Pleurotoma nivalis, Loy. — | 168 | P. pinguis, J. (MS.) . = | 269 — Northern Southern Remarks | | | | i | ‘Trophon Morehi, Malm. Turbonilla speciosa, H. Adams. Brought by Gulf Stream And a fragment of per- haps a new species. JV. fusea, de Blainville, may be either this species or a variety | of NV. millepunctata. S. discus, Ph. Or perhaps a distinct species. Adriatic (Stossich). And a fragment of per- haps another species. Fragments. ' Perhaps a variety of C. echinophora, L. A fragment of a young | specimen; probably | drifted. | P. carinata, Ph. ON THE FRENCH DEEP-SEA EXPLORATION IN THE BAY OF BISCAY. 387 List oF Moutuusca—continued. dredgings. No. 172 | C. ovata, J..(MS.) | 175 | U. excavatus, J. (MS.) | 176 | U. pusillus, J. (MS.) 177 | U. globosus, Lov. | 178 | Actzeon exilis, J. | 182 | B. semilevis, J. (MS.) | 187 | P. catena, Mont. i Southern | Remarks 25| ¢ an| Name of Species 3 cs) 3 gee 170 | Ringicula leptochila, Brugn. = 171 | Cylichna umbilicata, Mont. sy 173 | Utriculus expansus, J. = 174 | U. obesus, J. (MS.) . 179 | A. ovatus, J.(MS.) . = 180 | Bullina elongata, J. (MS.) 181 | Bulla pinguicula, J. (MS.) = / 183 | Scaphanderpunctostriatus, Mig- | — hels and Adams 184 | Philine scabra, Miill . = 185 | P. striatula, J. (MS.) : | -— 186 | P. quadrata, 8. V. Wood . = | 188 | Melampus myosotis, Drapar- | — naud. ‘189 | Carinaria mediterranea, Péron | — and Lesueur. PITEROPODA. 190 | Limacina helicoides, J, ee 191 | L. carinata, J. (MS.) .|— 192 | Spirialis retroversus, Fleming . | — 3 | Cavolinatrispinosa, Pér.and Les. | — 194 | C. labiata, D’Orbigny = 195 | Clio pyramidata, Browne . — 196 | C. lanceolata, De Bl. ‘4 = 197 | C. cuspidata, Lam. . = CEPHALOPODA. 198 | A sucker of a small Octopod 169, 9 17 A young specimen. S. librarius, Lov. Young. A single specimen; probably drifted. Brought from the shore. | Pelagic. All these are Pelagic. 4 ' Hyalea inflexa, Pér. and Les. | Pelagic. Supplementary Paper by the Rev. A. M. Norman, F.L.S. As might have been expected, many of the Crustacea obtained off the Portuguese coast by the Porcupine occurred in the North Spanish Among these were Dorhynchus Thomsoni, Norman, Amathia Carpenteri, Norman, Hbalia nux, Norman, Ethusw granulata, Norman, Pagurus tricavinatus, Norman, Munida tenwimana, G. O. Sars, and Apsewdes spinosa, Sars, and grossimana, Norman. Brachyuran (feryon tridens, Kroyer, which was traced southwards by the cc2 The large Norwegian 388 REPORT—1880. Porcupine to the entrance of the Bay of Biscay, was found to be the most abundant species within the bay, though in size greatly dwarfed as com- pared with Norwegian specimens. A Thysanopoda, probably norvegica, was taken several times abundantly, and was probably caught as the dredge approached the surface. The large, most remarkable, and blood- red Schizopod Gnathophausia Zoéa, Willemoes-Sahm, which was dis- covered in the Challenger Expedition near the Azores and off the coast of Brazil, delighted us with its beauty. Many undescribed species were met with. Pre-eminent among these were a new genus allied to Dromia;' a very curious new genus of Galatheide, which is blind, and has the eye- stalks converted into spine-tipped processes; a new Palemonid, remark- able for having its carapace girt with a ring of spines; and a Scalpellwm, apparently new. Among the Gephyrea were two species recently described by Danielssen and Koren, from the Norwegian coast, and not hitherto found further south; the grand Sipunculus priapuloides, which is the largest and most interesting species of the genus known to me; and the curious little Ochnesoma Steenstrupii. This latter species I dredged last year in great abundance at the mouth of the Hardanger Fiord, Norway. A third Gephyrean obtained is also perhaps the Phascolosoma squamatum of the same authors. In the Fosse de Cap Breton the curious Annelid, Sternaspis thalasse- moides, Otto, which was formerly referred to the Gephyrea, was found abundantly. Several examples of the much-disputed Chetoderma nitidulum were obtained. This is one of those animals which, exhibiting relationship to more than one class in almost equal ratio, becomes, by its somewhat inter- mediate characters, of special interest. Only a single Polyzoon occurred. This was Triticella Boeckiw, or an allied species. It was infesting the crab Geryon tridens, on which same host the species just named was discovered by Professor G. O. Sars. There was a remarkable absence of Hydrozoa. In no class is the collection finer than among the Actinozoa. Of Actinians not secreting a corallum there were a new Palythoa parisitic on the spines of Cidaris papillata; an Actinia (Adamsia ?), parasitic on an Isis; and two or three other things which were not recognised by us. Of corals there were Caryophyllia clavus; a Flabellum belonging to the Flaubellum apertum group, in which the corallum is little or not at all com- pressed; a Deltocyathus, and Lophohelia prolifera. Of Gorgonian allies there were Gorgonia verrucosa, and at least two species of Isis, one of which was of considerable size, and when dredged at night was gorgeously phosphorescent, exhibiting a blaze of light. Of Virgularians there were many fine species, including two large forms of Virgularia (or closely allied genus) ; what appeared to be a Scytaliwm of very elegant form and bright red, widely separated fins; a genus which, from the curved, flaccid state of the polyparium, appeared to be devoid of all calcareous axis; Kopho- belemnon stelliferum, and an example of the genus Umbelluria.? This genus, first discovered in the Arctic seas in 1753, and admirably figured by old Ellis, was lost sight of for 120 years, when it was rediscovered by Lindahl in the Swedish expedition between Greenland and Newfoundland. 1M. Alphonse’ Milne-Edwards had previously seen this among the Crustacea dredged by A. Agassiz in the Blake, and proposes to name it Dioranodromia ovata, * Probably U. Thomsoni, Kolliker. ON THE FRENCH DEEP-SEA EXPLORATION IN THE BAY OF BISCAY. 389 Subsequently the Challenger dredged it in several spots, and as far south as midway between Cape St. Vincent and Madeira. But the finding of this most interesting animal within a few miles of the European coast by Le Travailleur (July 30, in 1,160 métres) leads us to hope that hereafter it may even be added to the British Fauna. Echinodermata, as is usual in deep-sea dredgings, were numerous. Of Holothuroidea there was a form entirely unknown to me furnished with only two rows of suckers remarkable for their great size, and ten tenta- cula; a Molpadia, which has generally been regarded as an Arctic genus; and Echinocucumis typica, an abundant Norwegian type, of which the pre- sence in the Bay of Biscay was evidenced bya single specimen. A curious instance occurred of the meeting in the Bay of Biscay of species hitherto supposed to be confined to Scandinavia with others regarded as eminently Mediterranean. The trawl had been down in 306 métres, and when taken up out of it rolled one or two hundred huge Holothurians, each about a foot long. It was at once evident that they belonged to two species, and further examination proved about two-thirds of them to be the rosy-coloured Hoiothuria tremula of Norway, and the remainder, known at a glance by their light brown colour and flattened side, were Stichopus regalis of the Mediterranean. They had apparently met on this neutral ground, and were living together on the most amicable terms. Sea Urchins were represented by Echinus microstoma, Wyville Thom- son; Calveria hystrix (or an allied species), of which several fine specimens occurred; Pourtalesia Jeffreysi; and a new Spatangoid, remarkable on account of its globular form, and referable perhaps to the genus Agassizia, Starfishes were not numerous in species, and gave us nothing new. Archaster tenuispina and bifrons, Astropecter Andromeda, and Brisinga coronata were the rarer forms. The Brittle Stars were of much importance, for though the number of examples was not great the number of species, and perhaps of new forms, was considerable. The Ophiuridans require attentive study, and cannot be determined at a glance. It will suffice, therefore, to say that there were many which were not familiar to me, belonging apparently to the genera Asteronyx (parasitic on Isis, rather small, and possibly distinct from Loveni), Ophiomusium, Ophiacantha, Ophioscolex, together with a remark- ably large and fine form which I was unable to refer to any genus known tome. An Ophiurid was also met with which I had discovered !ast year in Norway, and which I propose to name Amphiura Danieisseni. Sponges, both with respect to the number of species and of specimens obtained, were scarce. Thenea muricata, Bowerbank (= Wyvillethom- sonia Wallichit, P. Wright) and Holtenia Carpentert, W. Thomson, only occurred in a young state; and a little bunch of the strong coarse spicula of the great Askonema Setubalense, Kent, came up wrapped round the dredging line; a single Hyalonema Lusitanicwm, Bocage, was dredged in about 600 fathoms; and a fine, though dead, specimen of Farrea or Lefroy- ella was procured, though unfortunately in fragments. The Foraminifera of course could not, from their minute size, be examined as they were dredged, but among the larger forms noticed in the sieves were many very interesting and recently described types. Foremost among these were the largest and most perfect examplee of the beautiful Orbitolites tenuissimus, Carpenter, I had ever seen ; they equalled a@ sixpence in size, and were dredged in about 1200 fathoms (July 20) ; and the very remarkable thread-like Bathysiphon filiformis, G. O. Sars, 390 REPORT—1880. which had, as far as I am aware, only before been met with in the Nor- wegian fiords. Arenaceous forms were abundant and fine, and included the following recently described species :-— Rhabdammina abyssorum, M. Sars. Hyperammina ramosa, H. B, Brady. Saccammina spheerica, M. Sars. Psammosphera fusca, Schultze. Storthosphera albida, Schultze. Astrorhiza arenaria, Norman. Tituola subglobosa, M. Sars. Cyclamnvina cancellata, H. B. Brady. In concluding these rough notes, I must express the deep sense I en- tertain of the kindness, courtesy, and attention which we received from the French naturalists who were members of the Commission, and also from Captain Richard and all the officers of Le Travailleur. Third Report of the Committee, consisting of Professor Sir WILLIAM TuHomson, Dr. J. MERRIFIELD, Professor OSBORNE REYNOLDS, . Captain DouGLas GaLton, Mr. J. N. SHOoLBRED (Secretary), Mr. J. F, Deacon, and Mr. Rocers FIELp, appointed for the purpose of obtaining information respecting the Phenomena of the Stationary Tides in the English Channel and in the North Sea ; and of representing to the Government of Portugal and the Governor of Madeira that, in the opinion of the British Associa- tion, Tidal Observations at Madeira or other islands in the North Atlantic Ocean would be very valuable, with the view to the ad- vancement of our knowledge of the Tides in the Atlantic Ocean. . ty their last report the Committee requested, that the thanks of the Association be conveyed, to the First Lord of the Admiralty, the President of the Board of Trade, the French Minister of Public Works, the Belgian Minister of Public Works, to the several authorities and private individuals, both in this country and on the Continent, who have, gratuitously aided in obtaining tidal observations for the Committee ; and especially to the French Association for the Advancement of Science for, the cordial support and assistance it has always afforded to the Committee in carrying out its task. As this recommendation came too late to be given effect to at the Sheffield Meeting, the Council during the past year, in its own name, performed this pleasing duty. At the Sheffield Meeting, the further consideration of two points in particular was urged upon the Committee: Ist, the great utility of a re- cognised datum suitable for international observations, similar to the one made use of by the Committee ; and 2ndly, the benefit likely to accrue to science, if the various maritime Governments, of Europe especially, were to arrange among themselves to carry out a lengthened series of tidal observations, and extending over a considerable area of coast. ON THE PHENOMENA OF STATIONARY TIDES IN THE ENGLISH CHANNEL. 391 The Committee, having carefully considered these points, and as they cordially agreed in them, urged the Council to press them upon the several Governments with whom they were communicating, respecting the labours of this Committee. It having also been pointed out, that, although the form in which the tidal observations as presented in last year’s report (referred all'to the English Ordnance Datum, and to Greenwich time) was most suitable for all observers on this side of the Channel, yet that it was hardly so for those on the Continent who had taken part in those observations, the Committee therefore decided upon reducing all the observations to the French official Datum of levelling and to Paris time. A pamphlet containing these tables, and prefaced by a special report in the French language, has been prepared for presentation to each of the foreign Governments, and observers on the Continent; and copies of it were transmitted through the Council with the thanks of the Association as above referred to. A copy of this document is appended hereto. It is with much pleasure that the Committee have to report that the self- registering tide-gauge, which, at the instance of this Committee, the Board of Trade established on the Admiralty Pier at Dover, has been working, apparently with satisfaction, for nearly twelve months. A valuable series of tidal records may, therefore, now be commenced at this important station. This is highly desirable; and it is a measure which the Com- mittee would strongly urge upon the Board of Trade. Seeing that similar self-registering records have been most carefully collected for some time back at Ostend, at Dunkerque, at Boulogne, and at Havre, on the opposite coasts ; while on our own side, already, self-registering gauges exist at Sheerness, at Ramsgate, and at Portland. The self-registering tide-gauge at Madeira, which the Portuguese Government, at the instance of H.M. Secretary of Foreign Affairs, acting on the request of this Committee, sent out to the Bay of Funchal, has been recently erected, and, it is understood, will soon be working: satisfactorily. The Committee beg to report that the sum of £10 has been expended in the preparation, printing, and distribution of the pamphlets to foreign observers. They request that the Committee be reappointed, with a grant of £10 to cover these expenses. APPENDIX. RAPPORT DE LA COMMISSION CHARGSE D’OBTENIR DES OBSERVATIONS. SIMUL- TANKES SUR LES Maries pe LA Manche ET DE LA Mer pu Nor», er DES RENSEIGNEMENTS SUR LE PH&NOMENE DES Marfes STATIONNAIRES QUI ONT LIEU DANS CES MERS. Les Membres de la Commission sont—Sir WitutaAm THomson (Président), Je Dr. Merrirtenp, le Professeur Osporne Reyrnoups, le Capitaine Doveras Gatton, et M. James N. Suoonpred (Secrétaire et Lap- porteur). Av Congrés de Plymouth, en 1877, une Commission a été nommée par YAssociation Britannique dans le but indiqué ci-dessus; et aussi pour prier le Gouvernement Portugais, par l’intermédiaire du Gouvernement de sa Majesté Britannique, d’entreprendre un strie d’observations sur les marées au Nord de l’Ocean Atlantique. Cette derniére demande a été 392 REPORT—1880. gracieusement accordée par le Gouvernement Portugais ; et afin d’obtenir les observations d’une maniere reguliere, un marégraphe enregistreur (systeme de Sir W. Thomson) a été installé dans la Baie de Funchal des Iles de Madere. Avant d’entreprendre des observations simultanées dans la Manche et la Mer du Nord, la Commission s’est adressée, par les soins de son secré- taire, aux membres de 1|’Association Frangaise pour l’avancement des Sciences, qui a l’époque du Congrés de Plymouth étaient réunis au Havre. Un mémoire y fut présenté de sa part, exprimant ‘le désir de voir sa pro- position acceptée, et demandant, dans l’intérét commun de la Science, un bon accueil de l’Association Frangaise, et son appui auprés du Ministre des Travaux Publics 4 Paris. Grace aux démarches qui furent faites plus tard par M. le Secrétaire du Conseil de l’Association Francaise, M. C. M. Gariel, auprés de M. A. Rousseau, Directeur du Département des Routes et de la Navigation au Ministére, son Excellence le Ministre des Travaux Publics a bien voulu donner l’autorisation nécessaire, en ce qui concernait les observations 4 faire sur les cétes de la France: et elles furent confiées par M. Rousseau a MM. les Ingénieurs des Ponts et Chaussées, attachés aux ports de Mer de la Manche. Une semblable permission fut gracieusement accordée par son Excel- lence le Ministre des Travaux Publics de Belgique, grace 4 l’intervention bienveillante de M. le Chevalier Maus, Inspecteur Général des Ponts et Chaussées, 4 Bruxelles, pour les observations du maréographe enregistreur (van Rysselberghe) 4 Ostende. Le Gouvernement de sa Majesté Britannique accorda aussi la méme permission, et se chargea de faire les observations nécessaires 4 certains endroits sur les cétes septentrionales de l’Angleterre. Plusieurs par- ticuliers voulurent bien aussi se charger de faire des observations aux endroits indiqués, aussi bien en Hollande qu’en Angleterre. Le programme suivant fut ensuite dressé pour régler une série d’ob- servations simultanées en 1878, dans les mois de Février, Mars, Avril, Juin, et Aott. Pendant le premier trimestre, ce furent les marées d’équinoxe qu’on voulait étudier; et dans les deux derniers mois-les marées ordinaires. L’étendue des cdtes du Continent comprises dans le programme s’étend depuis le Havre jusqu’a l’entrée du Canal de la Mer du Nord, qui conduit a Amsterdam; et en Angleterre, depuis Portland, en face du Havre, jusqu’a Yarmouth, situé 4 peu pres en face d’Amsterdam. Dans le tableau comparatif qui suit, aussi bien que dans les courbes qui l’accompagnent, on n’a représenté que les marées d’équinoxe, qui ont été observées sur tous les points 4 la fois, dans le courant du mois de Mars. II] peut servir de type a celles des mois de Février et d’Avril, ot les marées observées ont présenté une grande concordance avec celles qui sont dans le tableau. Les observations des mois de Juin et d’Aotit de la méme année, ainsi que d’autres résultats qu’on espére retirer de cette étude préliminaire sur les marées de la Manche et de la Mer du Nord, ne sont pas encore en état d’étre présentées avec ce rapport. La nécessité s’est bientét fait sentir 4 la Commission de chercher un plan de comparaison commun, auquel toutes les observations pourraient étre rapportées. Le seul moyen rationnel de comparer deux séries de nivellements opérés des deux cdtes de la Manche paraissait de se servir ON THE PHENOMENA OF STATIONARY TIDES IN THE ENGLISH CHANNEL. 393 du niveau moyen de Ja mer; et cette comparaison ne pouvait étre qu’ap- proximative. En supposant, en effet, que ‘le niveaw moyen de lV Océan Atlantique,’ donné par Bourdaloue dans son nivellement général de la France, représente le méme plan que le ‘ mean sea level of the Ordnance Survey’ donne pour les cdtes d’Angleterre, on trouve qu’un plan passant 4 5°50 métres en-dessous du zéro de Bourdaloue coincide, 4 0°01 métre prés, avec celui qui est & 20 pieds au-dessous de 1’*Ordnance Datum’ de la Grande-Bretagne. En vue de l’approximation de laquelle on est forcé de se contenter, cette erreur peut étre negligée. Ce plan de comparaison, outre l’avantage des chiffres ronds qu'il présente, a encore celui-ci qu'il n’y a que peu de basses mers d’équinoxe (méme dans la Baie de St. Malo) qui descendent plus bas: et dans les observations qui sont 4 comparer aucun de ces cas exceptionnels ne se produit. Dans le tablean comparatif des observations qui suit on a donc adopté ce plan de comparaison pour les nivellements des deux cdtes de la Manche. Oeux de la Belgique et de la Hollande sont facilement rattachés au niveau de Bourdaloue au moyen des nivellements de précision faits dans chaque pays. C’est sur cette hypothése de la coincidence du niveau moyen de la mer qu’a été établie l’échelle comparative qui suit (voir Rapport, 1879, Pl. XIII.). De l’examen attentif de ce tableau comparatif, on peut facilement con- clure, que si sur une étendue considérable de cétes et pendant une durée de temps plus longue, il se faisait d’une maniére reguliére une série d’observations simultanées sur les marées, soit de quart d’heure en quart d’heure, ou méme seulement aux moments de Ja haute et de la basse mer, on en retirerait probablement des résultats trés-importants pour la science : tant au point de vue d’une connaissance plus exacte de ce qu’on appelle ‘le niveaw moyen’ de la mer, qu’d celui des moments exacts des hautes et des basses mers. On arriverait ainsi 4se rendre meilleur compte des lois de la propagation de l’ondemarée dans les mers et détroits qui entourent nos cotes. Mais une telle série d’observations ne peut étre enterprise par une commission scientifique composée seulement de simples particuliers. lle doit étre la conséquence d’un accord entre les divers gouvernements des pays interéssés: chacun d’eux devrait se charger des observations a faire le long de ses propres cétes. On a vu, qu’il a été nécessaire, dans la redaction des observations qui font lobjet de cette communication, d’essayer de résoudre le probléme d’un plan de comparaison commun aux divers nivellements. L’importance de ce sujet a été déji reconnu plusieurs fois par diverses commissions internationales. Si, 4 la suite des observations de marée ici rapportées, chaque gouvernement avait la complaisance de présenter 4 la commission sa manicre de voir, soit sur le plan de comparaison choisi, soit sur tout autre qui lui paraitrait préférable, ce serait un pas de gagné ; qui, lui seul, serait une récompense pour la commission en raison des travaux qu'elle a enterpris. Il ne reste plus aux membres de la Commission de 1’Association Britannique qu’d remercier, en leur nom personnel, les Gouvernements Frangais et Belge, par l’intermédiaire de leurs Excellences MM. le Minis- tres des Travaux Publics de chaque pays, aussi bien yue le Gouvernement Anglais, pour l’appui bienveillant qu’ils ont donné chacun 4 ces obser- vations des marées. Ils remercieront aussi |’ Association Francaise pour Vavancement des Sciences, pour le bon accueil qu’elle a fait 4 la propo- 394 REPORT—1880. sition, et pour les encouragements qu’elle luia donnés. IIs remercieront encore les observateurs particuliers (trop nombreux pour étre nommés ici) qui ont si généreusement participé dans l’exécution du projet d’observa- tions simultanées des marées de la Manche et de la Mer du Nord. MAREES DE LA MANCHE ET DE LA MER DU NORD. OBSERVATIONS EN 1878. 1. Observations chaque quart d’heure, de Basse Mer en Basse Mer. Marée Moment de la haute mer. ‘) Les observations doivent commencer une terminer qu'une heure apres la derniére | heure avant la premiére Basse Mer, et ne de chaque marée. + Le moment exact des Hautes et des Basses (a Douvres). du 12 Février 5.46 soir. ao eae | 0.3L, 26 6.37 ;, 13 Mars 5.23 45 20” #3 Oras 27 6.16 ,, 11 Avyrill 5.12) 155 Sa) wis 11.35 matin ZA A 5.39 soir. ) Mers sera noté ; les autres observations & chaque quart d’heure exact (de Vhorloge). Temps moyen de Paris sera observé par- tout. 2. Observations sur les moments des Hautes et des Basses Mers seulement. Au mois de Juin Au mois d’Aott { i les m, ” ” ” arées du matin, le 10 au 16 inclusives. SOU etapa! (imag oe a matin, , ‘8 ,, 14 a sont, Tb se23 Be N.B.—II faudra 4 chaque endroit rattacher le zéro des observations avec le plan de comparaison des cartes du nivellement de la France. L’état du barométre, et la direction et force du vent seront notés de temps en temps. ENDROITS DES Yarmouth, Douvyres. Lowestoft. Newhaven. Harwich. Shoreham. Sheerness. Portland. Ramsgate. OBSERVATIONS, Mer du Nord, Boulogne. Entrée du Canal ‘Tréport. d’Amsterdam. Dieppe. Flessingue. St. Valéry en Caux. Ostende. Fécamp. Dunkerque. Le Havre. Calais. 1 1 > o 395 o ae os) | 3 peg 1D oom AG Le od oD 10 bk 19 Drm Oem HY 19 t cooo MO. 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By WiLL1aM WuitakeR, B.A., F.G.S., of the Geological Survey of England. [A communication ordered by the General Committee to be printed in ewtenso among the Reports. ] 1. Preratory Norice. Tats List, in which Monmouthshire is included with Wales, forms one of a set, the parts published or in the press being as follows :— CamprincesHire. Pp. 15. Privately printed, University Press, Cam- bridge (1873). Reprinting, with additions, in the Geological Survey Memoir on the Neighbourhood of Cambridge. Cursuire. Proc. Liverpool Geol. Soc. pp. 127-147 (1876). Cornwatt. Journ. R. Inst. Cornwall, No. xvi. pp. 61-110 (1875). DevonsHireE. Trans. Devon. Assoc. (1870), pp. 330-352, and vol. v. pp. 404-415 (1872). Fentanp. By 8. B. J. Sxerrcuty, pp. 306-313 of the Geological Survey Memoir on that district (1877). GLOUCESTERSHIRE and SomerRseTsHirE. By W. Wairaker and H. B. Woopwarp, pp. 216-255 of the Geological Survey Memoir on the EH. Somerset and the Bristol Coal-fields (1876). Hamesuire Basin. Journ. Winchester and Hants Set. and Lit. Soc. (1873), pp. 108-127. HertrorpsHire. Trans. Watford Nat. Hist. Soc. vol. i, pt. 3, pp. 78-82 (1876). Lake District (N. part). By J. C. Warp [and W. Wuiraxer], pp. 113= 125 of the Geological Survey Memoir on the district (1876). LANCASHIRE (part). Pp. 191-218 of the Geological Survey Memoir on the Burnley Coal-field (1875). Lonpon Basin (part). Pp. 393-421 of Geological Survey Memoirs, vol. iv. (1872). NorrivcHamsHire. Pp. 47-50 of the Geological Swrvey Memoir on sheet 71, N.E., ed. 2 (in the press). RorLanp (and parts of adjoining counties). Pp. 294-801 of the Geological Survey Memoir on the district, sheet 64 (1875). peace Rep. Rugby School Nat. Hist. Soc. for 1873, pp. 66-76 (1874). Weatp. By W. Toptey, pp. 446-483 of the Geological Survey Memoir on the Weald (1875). Witrsutre. Mag. Wilts. Archeol. Nat. Hist. Soc., vol. xiv. pp. 107-121 (1873). Yorksuire. Pp. 281-320 of Prof. J. Pumurrs’ Illustrations of the Geology of Yorkshire, part 1, ‘The Yorkshire Coast,’ ed. 3 (1875). Partly re- printed, with additions, in the Geological Survey Memoir on the York- shire Coalfield, pp. 786-806 (1878). 398 REPORT—1880. 2. Inpex or AUTHORS, WITH THE NOS. PREFIXED TO THEIR WORKS. Accum, — 141 Adams, W. 511, 550, 551, 596, 597, 618 Aikin, A. 131, 16s, 186 Aitken, J. 598, 599 Anon. 110, 113, 151, 165, 179, 190, 196, 222, 263, 354, 391, 404, 419, 446, 552, 632, 652 Ansted, Prof. D. T. 355 Anstie, J. 83 Aubry, — 109 Aveline, W. T. 2, 4, 6, 7, 10, 11, 13-16, 24, 26, 27, 29-32, 34, 36, 42-46, 55, 57, 58, 67-79, 81, 94, 293 Babbage, C. 228 Banks, R, W. 341 Barrande, J. 307, 619 Barrat, J. 378 Bate, 8. 295 Bauerman, H. 80, 81 Beaumont, E’de. 181, 187 Beckett, H. 434, 653 Beddoes, Dr. T. 129 Bedlington, R. 481 Belt, T. 512, 513 Benson, 8. 296, 297 Bevan, Dr. P. G. 356-358, 367, 368, 379- 381, 392, 447, 553 Bigsby, Dr. J. J. 3869 Bingley. Rev. W. 152 Binney, E. W. 308, 382, 405, 448, 514, 620 Bishop, W. 171 Blake, C. C. 406 Bonney, Rev. Prof. T. G. 515, 516, 575 Booker, ‘T. W. 212, 290° ; Bostock, R. 554 RBowinanhy J. EH. 229, 248-250, 254 Boyd, C. 140. Brady, H. B. 614, 654 Bretherton, EH. 342 Bristow, H. W. 1, 2, 15, 16, 25, 66-71, 98, ° 517 Brown, T. F. 449 Buckland, Rev. Prof. W. 172, 251, 255, 256, 264, 269, 298 Burr, ¥. 230, 231, 236, 243 Byres, R. W. 270 LG, ETC Calvert, J. 323 Carruthers, W. 621, 655 Clark, G. T. 631 Clarke, Dr. E. D. 160 Clement, J. H. 420 Conybeare, Rev: J. J. 169 Conybeare, Rev. W. D. 177, 202, 213 Crutwell, A. 633 Curley, T. 555 Da Costa, E. M. 124 Daniel, E. 99-102 Darbishire, R. Darlington, G. Darwin, C. 257 Daubeny, Prof. C. 191, 197 Davidson, T. 329, 393, 422, 482, 518, 557, 576, 622 Davies, D. C. 370, 435, 436, 450-456, 519, 520, ‘600, 656, 657 Davies, W. 147 Davis, J. E. 280, 304 Dawkins, Prof. W. B. 521, Dean, A.,274, 275 De la Beche, Sir H. T. 2-4, 6-10, 20, 41, 55-57, 64, 65, 88-90, 94-96, 103, 104, 184, 192, 207, 276, 309 Delesse, — 317 Dickinson, J. 281, 631 Donovan, — 138 Duckworth, H. 394, 423 Dufrénoy, P. A. 180, 181, 187 Duncan, Prof. P. M. 507, 522 ci 22; 577 D. 421, 556, 574 407 558, 601 523, 559, Egerton, Sir P. De M. G. 305 Eskrigge, R. A. 457, 483, 560 Etheridge, R. 98, 106e, 634 Evans, F. G. 602, 635 Evans, Rev. J. 143 Eyton, Miss, 484, 561 Fairbairn, W. 258, 348 Falconer, Dr. H. 383, 437, 562 Farey, J. 148, 149, 154 Flight, Dr. W. 640 Forbes, D. 349, 524, 525, 563, 603 Forbes, Prof. E. 104, 106a, 271, 293 Forster, F. 1.93 Fosbroke, J. 166 Fothergill, W. 604 Fox, R. W. 203 Freeman, E. A. 345 Gages, A. 371 Gilby, Dr. W. H. 161, 167 Glass, N. 395 Glassbrook, — 438 Green, Prof. A. H. 526 Greenwood, Col. G. 485 Gregory, J. R. 354 (?), 396 Griffith, N. R. 605 Griffiths, Rev. H. 527 _ Gruner, — 424 Haime, J. 320, 339 Hall, C. R. 458 Hall, H. F. 486, 564, 606 Ham, J, 237 Harkness, Prof. R. 528, 623 Hassall, C. 144 Hatchett, C. 136 WORKS ON GEOLOGY, MINERALOGY, AND PALHONTOLOGY OF WALES. Haughton, Rev. Prof. 8. 330-332, 343 Henry, Dr. W. 194 Henslow, Rev. Prof. J. 8. 173 Henwood, W. J. 208, 318, 350, 624 399 Meade, R. 106b Mello, Rev. J. M. 533, 534 Menteath, J. 8. 204 Meunier, C,. 645 Hicks, H. 439, 473, 487, 529, 530, 541, | Meyrick, 8. R. 142 578-580, 593, 607, 623, 636, 658, 659 Higgins, W. M. 565 Holl, Dr. H. B. 460 Hooker; Dr. W. 104 Hopkins, W. 324 Hopkinson, J. 581, 608, 637, 660 Howell, — 141 Hull, Prof. E. 27, 31, 32, 45, 47, 81, 82, 384, 408-410, 582 Hunt, R. 104, 106b, 459, 566 Huxley, T. H. 106e James, T. E. 2, 10-12, 15, 59, 60, 66 Jenkins, T. L. 638 Johnson, C. 283 Johnson, W. R. 252 Johnston, Prof. J. F. W. 238 Jones, Prof. T. R. 338, 344, 460, 609, 636 Jones, W. B. 345 Joseph, T. 610, 625 Jukes, J. B. 26, 29, 30-32, 36, 42, 43, 72- 74; 76, 78, 79, 291, 359, 461, 626 Kelly, J. 385 Kidd, Dr. J. 153, 155 Kingsley, W. 661 Kirwan, R. 132 Klaproth, M. H. 135 Lankester, Prof. E. R. 662 Lau, — 424 Lee, J. E. 611, 663 Lentin, A. G. L, 133 Lévy, — 182 Lewis, W. T. 612 Lihwyd, Lloyd or Llwyd, E. 108, 111, 112, 1154119 Linden, Dr. D. W. 121 Logan, Sir W. E. 2, 3, 8, 61-63, 84-87, 90, 239, 259 Lucy, W. C. 664 McConnochie, — 567, 568 M‘Coy, Prof. I’. 299, 306, 310-313, 319, 340 MacCulloch, Dr. J. 189 M‘Cullough, Dr. D. M. 583 Macintosh, A FF. 277 Mackintosh, D. 489-492, 569, 665 Maclauchlan, H. 260 Mallet, R. 411, 425 Manisty, G. E. 585 Marecou, J. 488 Martin, E. 137 - Maskelyne, Prof. N. 8. 640 Matthews, E. 122 Maw, G. 440, 462-464, 493-495, 5: * 570, 571, 613 584, 639, co rear or oo bo Miller, Prof. W. H. 261 Milne- Edwards, Prof. H. 320, 339 Moggridge, M. 346 Moore, C. 535, 614 Moore, IT’. J. 536 Morris, Prof. J. 360 Morris, Dr. M, 126 Morton, G. H. 426, 496, 497, 586, 627 Mostyn, R. 107 Murchison, Dr. C. 562 Murchison, Sir R. I. 209, 214-219, 223, 225, 244, 284, 285, 322, 333, 482 Murlon, H. 232 Mushet, D. 139, 145 Muspratt, Dr. 5. 465 Ness, W. 466 Newton, E. T. 106e Nicholson, Dr. H. A. 615, 641 Nixon, EH. 498 Noad, Dr. — 397 Owen, G. 130 Owen, Prof. R. 265, 467, 587 Paris, Dr. J. A. 163 Pattison, 8. R. 372, 388 Pennant, T. 123, 127 Perceval, 8. G. 499 Perey, Dr. J. 397, 441 Phillips, Prof. J. 1, 4, 6, 7, 56, 57, 95, 96, 104a, 198, 273, 351 Phillips, J. A. 412 Phillips, R. 178 Phillips, W. 174 Phipson, Dr. T. L. 468 Plant, John, 500, 501 Playfair, Dr. L. 104 Prestwich, Prof. J. 383 Prichard, Dr. J. C. 156 Prosser, W. 469 Purton, W. 502, 666 Ramsay, Prof. A. C. 1, 4, 6, 7, 13-20, 23- 27, 29-32, 34-36, 39-43, 46, 55, 57-60, 67-74, 77, 80, 103, 105, 106c, 292, 293, 300, 314, 821, 325, 334, 361, 386, 398, 413, 427, 642 Rawlinson, R. 503 Read, C. 8. 301 Readwin, T. A. 362, 387, 399, 400, 414, 415, 428, 442, 470, 628 Reed, L. E. 199 Reeks, T. 106d Rees, J. 4, 6, 10, 11, 55, 94 Rees, T. 157 Reynolds, M. 612 | Richards7n, J. 286, 302 400 REPORT—1880. Ricketts, Dr. C. 537, 572, 629, 643 Thomas, D, 648 Riley, E. 397, 416, 441, 644 Thomas, J. E. 546, 667 Roberts, D. W. 589, 616 Thomson, E. P. 183 Roberts, G. E. 363, 401, 471 Thomson, W. 200 Rogers, H. 373 Tooke, A. W. 234 Rowlands, H. 120 Townshend, Rey. J. 150 Rowlandson, T. 287 Traill, Dr. T. S. 170 Rudler, F. W. 106d Trevelyan, Sir W. C. 279, 328 Rutty, Dr. J. 125 Trimmer, J. 201, 242, 245, 246, 316: Tylor, A. 595 Salter, J. W. 58, 104a-106a, 293, 315, 325, 326, 335, 347, 352, 374, 388, 396, 429- | Vaux, F. 303 431, 443, 444, 472-475, 487, 504, 505, | Verneuil, — de, 226 530, 538-541, 573, 590-593 Victor-Frére-Jean, F. 185 Samuel, W. 574 Vivian, H. H. 99-102, 631 Sandford, W. A. 558 Vivian, Capt. W. 375, 376 ? ; Scheurer-Kestner, A. 645 Vivian, W. 649, 650 ht same] Sedgwick, Rev. Prof. A. 210, 211, 220, | Voelcker, Dr. A. 366, 508 224, 225, 240, 253, 266, 272, 278, 288, 322, 336, 340 Wallace, A. R. 547 Selwyn, A. R. 22, 23, 26, 28, 29, 33-43, | Waller, W. 115 67-74, 77, 291 Watson, Dr. J. J. W. 377 Sharpe, D. 267, 282, 289 Watson, — 337 Sloane, Dr. H. 112 Weston, — 397 Smith, Rev. G. N. 391 (?), 402, 432, 506 Whitley, N. 268 Smith, J. D. 477 Williams, Rev. D. 227 Smith, W. 156, 162, 273 Williams, D. H. 1, 2, 4, 6, 8, 9, 12, 31, 82, Smyth, W. W. 20, 40, 41, 44-47, 103, 104, 45, 55, 64-66, 82, 91-93, 97 106d, 417 Williams, J. 128 Sopwith, T. 262 389 Sorby, H. C. 327, 364, 365 Williams, W. 134 Sowerby, G. B. 241 Williams, W. M. 479 Sowerby, J. 145, 159, 168, 175 Williamson, E. 501 Stanley, Rev. E. 205 ‘ Winwood, Rev. H. H. 480 Steel, T. D. 542 Wood, 8. V. jun. 617 Stoddart, W. W. 476 Woods, 8. 174, 247 Stokes, C. 233 Woodward, H. 651 Struvé, W. P. 62, 294 Woodward, H. B. 2, 3, 83 Symonds, Rev. W. 8. 353, 403, 445, 478, | Wright, Dr. T. 390, 433 543, 594, 630, 646, 647 Wright, T. 418 Wyatt, J. 235 Tate, R. 544, 545 Wyatt-Edgell, H. 509, 510, 548, 549 Tawney, E. B. 507 Taylor, R. C. 221 Yates, Rev. J. 188, 206 Thomas, A. 195 3. GroLocicaL Survey PUBLICATIONS. I have to thank my colleague, Mr. W. Topley, for aid in this part of the List, which includes a few works issued after 1873. Sheets of the Map (scale, an inch to a mile). (1) 35. N.W. part (Chepstow). By H. D. Witt1ums, J. Paris, and A. C. Ramsay. 1845. Additions, by H. W. Bristow, 1865. (2) 36 (Merthyr, Bridgend, Cowbridge, Cardiff, Newport, Pontypool). By Sir H. T. De ta Becue, Sir W. E. Logan, D. H. Witu1ams, W. T. AveELINe, and T. E. James. No date. Revisions, by H. W. Bristow and H. B. Woopwarp, 1873. (3) 37 (Gower, Swansea, Neath, Llanelly). By Sir W. E. Logan and Sir H. T. De 1a Brcuz. No date. Revisions (S.E. margin), by H. B. Woopwarp, 1872. WORKS ON GEOLOGY, MINERALOGY, AND PALHZONTOLOGY OF WALES. 401 (4) 38 (Milford, Pembroke, Tenby). By Sir H. T. Dr 1a Becue, A. C. Ramsay, J. Poituirs, D. H. Witiiams, W. T. Avetine, and J. Rens. No date. (5) 39 (Bishop and Clerks, islands). No date. (6) 40 (St. David’s, Haverfordwest, Narberth, Newport). By Sir H, T. De ta Becuz, J. Paitiips, A. C. Ramsay, H. D. Witurams, W. T. Aveting, and J. Rezs. 1845. Additional lines, by W. T. AvEtine, 1857. (7) 41 (Caermarthen, Llandeilo, Llandovery, Neweastle-Emlyn). By Sir H. T. Dr 1a Becue, J. Puiiurrs, and A. C. Ramsay. 1845. Additional lines, by W. T. Avetiny, 1857. (8) 42, S.W. (S.W. Brecknockshire). By Sir H. T. Dr 1a Becnz, [Sir] W. E. Locan, and D. H. Witurams. No date. (9) 42, S.E. (Abergavenny, Crickhowel). By Sir H. T. Dr 1a Brcwe and D. H. Wittiams. No date. (10) 42, N.W. (Brecknock). By Sir H. T. De 1a Bucun, W. T. Avz- LINE, J. Reus, and T. EH. Jamus, 1845. Additional lines, by W. T. AveLie. 1857. (11) 42, N.E., greater part (Talgarth, Hay). By W.T. Aveting, T. E. James, and J. Rens. No date. (12) 43, S.W., W. part (Monmouth). By D. H. Wituams and T. E. JAMES. (13, 14) 56, S.W. (Builth) and N.W. (Rhayader). By A. C. Ramsay and W. T. Avetine. 1850. (15) 56, S.E., greater part (New Radnor). By A. C. Ramsay, W. T. AvELINE, H. W. Bristow, and T. KE. Jamus. 1850. (16) 56, N.E., greater part (Knighton). By A. C. Ramsay, W. T. AYELINE, and H. W. Bristow. 1850. (17-19) 57, S.W. (Aberafron), N.W., and 8.E. (Tregaron). By A. C. Ramsay. 1848. (20) 57, N.E. (Aberystwyth). By A. C. Ramsay. The Lodes by Sir H. De 1a Becuz and W. W. Smyru. 1848. (21) 58 (Cardigan). No date. (22) 59, S.H. (Coast S.W. of Machynlleth). By A. R. Sxtwyy. 1848 (23) 59, N.E. (Coast N.W. of Machynlleth). By A. C. Ramsay and A. R. Serwyy. 1850. Corrections, 1855. (24) 60, S.W. (Llanidloes). By A. C. Ramsay and W. T. Avenine. 1850. (25) 60, S.E., W. part (Montgomery, Newtown). By A. C. Ramsay and H. W. Bristow. 1850. (26) 60, N.W. (Dinas, Llanfair). By A. C. Ramsay, A. R. SELwyy, W. T. Avetine, and J. B. Juxes. 1851. Additions, 1855. (27) 60, N.E., greater part (Welshpool). By A. C. Ramsay, W. T. AVELINE, and EH. Hunt. 1850. Additions, 1855. (28) 73, N.E., small part at N.W. By A. R. Senwyy. 1857. (29) 74, S.W. (Bala). By A.C. Ramsay, J. B. Juxes, W. T. AVELINE, and A. R. Senwyy. 1850. Corrections, 1855. (30) 74, N.W. (Corwen). By A. C. Ramsay, J. B. Juxzs, and W. T. Avetine. 1850. Corrections, 1855. (31, 32) 74, S.E., W. half (Llanrhaiadr), and N.E., nearly all (Llan- gollen, Wrexham). By A. C. Ramsay, J. B. Juxus, W. T. AVELINE, D. Witiiams, and EK. Hunn. 1850. Corrections, 1855. (33) 75, S.W. (Pwllheli). By A. R. Sznwyn. 1851. 1880. DD 402 REPORT— 1880. (34) 75, S.E. (Harlech). By A. C. Ramsay, A. R. Senwyn, and W. T, Avetinge. 1851. Corrections, 1855. (35) 75, N.W. (Nevin). By A. C. Ramsay and A. R. Sezwyn. 1850. (36) 75, N.E. (Tremadoc). By A. C. Ramsay, A. R. Srtwry, W. T. Avene, and J. B. Juxes. 1851. “Additions, 1854. - (37, 38) 76, S. and N. (E. end of Carnarvonshire). By A. R. Senwyy. 1850. (39) 77, N. (Holyhead). By A. C. Ramsay and A. R. Sunwyy. 1852. (40) 78, S.W. (Carnarvon, S. Anglesea). By A. C. Ramsay, W. W. Suytg, and A. R. Senwyy. 1852. (41) 78, N.W. (N. Anglesea). By Sir H. Dr 1a Becun, A. C. Ramsay, W. W. Smyru, and A. R. Setwyn. 1852. (42, 43) 78, S.E. (Bangor, Beaumaris, Llanrwst), and N.E. (Conway). By A. C. Ramsay, W. T. Avetine, A. R. Setwyn, and J. B. Juxes. 1852. (44) 79, S.W. (Denbigh, St. Asaph). By W.T. Avenine. The Lodes W. W. Suyre. 1850. (45) 79, S.E., nearly all (Flint, Mold). By W. W. Smyrna, D. H. Wituams, W. T. Averine, and E. Hurr. 1850. (46) 79, N.W. (Abergele). By A. C. Ramsay, W. T. Avetine, and W. W. Smuyrx. 1850. (47) 79, N.E., S.W. corner (N. of Holywell). By W. W. Smyru and EK. Hutn. 1850. (48) 80, S.W., small piece at S.W. corner. By E. Hunt. 1855. Sheets of Index Map (scale, 4 miles to an inch). (49) 9. (St. David’s, Pembroke, Swansea, Llandovery.) 1858. (50) 10. (Brecon, Monmouth, Newport, Cardiff, Chepstow.) 1858. New. ed. 1874. (51) 14. (Aberystwyth, Cardigan.) 1858. (52) 15. (Montgomery, Builth.) 1858. (53) 19. (Anglesey, Carnarvon, Bangor.) 1858. (54) 20. (Flint, Llangollen, Wrexham.) 1858. Sheets of ‘ Horizontal Sections’ (scale, 6 inches to a mile). (55) 1. Section 1—From St. Bride’s Bay, near Solva, to the North Chiff of Ynys-y-Barry. By A. C. Ramsay and W.T. Avetiyn. Section 2 —Across Pembroke from St. Govan’s Head to Dinas Head, near Fish- guard. ‘By Sir H. De 1a Buca, A. C. Ramsay, W. T. Avetine, J. Rens, and D. H. Wintiams. 1845. (56) 2. Section 1—From the sea, near Tenby . . . . to Landewi Velfrey, Pembroke. Section 2—From near Cil-rhew . .\. . to near Hendre, Pembroke. Section 3—Through Pant Yiar and Clog-y-Fran, Caermarthen. Section 4—From Laugharne to the river Dewi-Fawr, Caer- marthen. Section 5—From Maes Gwrda to Mydrim, Caermarthen. Section 6—Across the Traps and Conglomerates of Pen-y-Moelfre, S.W. of Caermarthen. By Sir H. Dr ta Bucur and J. Puups. 1844. (57) 3. Section 1—Near Llandeilo, from Cerrig-dwfn to Mynydd- banc-y-ffair. Section 2—From near Llandibie to Llangathen. Section 3 —From the Black. Mountain, near Llangadoc, to Cefn-llwyn-hir, near Cynfil-Cays. By Sir H. Dm 1a Becue, J. Purnuies, A. C. Ramsay, and W.T. ‘Avetinge. 1844. (58) 4. Section from the Old Red Sandstone, Mynydd-Bwlch-y-groes, WORKS ON GEOLOGY, MINERALOGY, AND PALEONTOLOGY OF WALES. 403 Brecknock, to Craig-ddu, Cardigan Bay. ... . By A.C. Ramsay. 1845. Correction, by W. T. Avetine, 1856, Notes on the Fossils by J. W. Satrer, 1857. (59) 5. Section across the Old Red Sandstone and underlying Rocks, from the Black Mountain range S.H. of Glasbury, to Allt-wen, Cardigan Bay, near Aberystwyth. By A. C. Ramsay and T. H, James. 1845. Additions in 1858. (60) 6. Section 1—Continuation of Sheet 5. Section 2—Across the Silurian Rocks, from Gwaun Ceste to Rhiw Gwraidd, Radnor. By A. C. Ramsay (? and T. E. James). No date (? 1845). (61) 7. Section 1—Across the Coalfield of South Wales, from the Mountain Limestone near Mynydd Garreg to the Mountain Limestone near Spiritsail Tor, Gower. Section 2—On the North Crop of the South Welsh Coalfield, from Brondyne Hill to the Mountain Limestone near Yr Hen Coed, Caermarthen. Section 3—From Penclawdd,... . to Oxwich Point, Gower. By [Sir] W. E. Locay. No date. (62) 8. Section across the Coal Measures of Caermarthenshire and Glamorganshire from the Carboniferous Limestone on the north of Cot- tage Hall, to the Sea, in Caswell Bay. By [Sir] W. HE. Locan and W. P. Srruve. No date. (63) 9. Section 1—Across the South Wales Coalfield, from Craig and Cefn Drim to the Mountain Limestone at Caswell Bay, Gower, Glamor- ‘gan. Section2—From Cilfay Hill, Swansea, to Castell Craig Cennen . . . By [Sir] W. E. Locay. No date. (64) 10. Section 1—Across part of the Coalfield of Glamorgan, from near Bryn Cethin Uchaf to Blaen Afon. Section 2—Across part of the Coalfield of Glamorgan, from Mynydd Moel Genlam to Mynydd Llandy- fodwg. Section 3— (542) Sruut,T.D. The Tillery Coal Seam and Workings, Abertillery. Trans. S. Wales Inst. Eng. vol. v. p. 230. Discussion, p. 282. (543) Symonps, Rev. W. S. The Geology of the District (Builth). Trans. Woolhope Field Club for 1866, p. 234. (544) Tare, R. On the Fossiliferous Development of the Zone of Ammonites angulatus, Schloth., in Great Britain. Quart. Journ. Geol. Soc. vol. xxiii. p. 305. (545) On the oldest known Species of Exogyra, with a Descrip- tion of the Species [from Leckwith, Glamorganshire]. Geol. Nat. Hist. Repertory, vol. i. p. 380. (546) Tuomas, J. HK. Prize Essay upon the Encroachment of the Sea between the River Mersey and the Bristol Channel. 8vo. Lond. (547) Watxacr, A. R. Ice Marks in North Wales (with a Sketch of Glacial Theories and Controversies). Quart. Journ. Sci. vol. iv. p. 33. (548) Wyarr-Epcrnt, H. On the Genera of Trilobites Asaphus and Ogygia and the Sub-genus Ptychopyge. Geol. Mag. vol. iv. p. 14. (549) —— On the Arenig and Llandeilo Groups. Ibid. p. 118. 1868. (550) Apams, W. Address on the Objects of the Society. Ann. Rep. Cardiff Nat. Soc. p. 26. [Geology and section at docks referred to, . 32. : ( eae) Collection of Fossils [S. Wales Coal-field]. Ibid, p. 53. (552) Anon. Penlyan Field Meeting. Ibid. p. 38. (553) Bevan, G. P. Address on the South Wales Coalfield. Ibid. p. 43; and Trans. Woolhope Nat. Field Club for 1868, p. 35 (1869). (554) Bostock, R. The probable Source of Holywell Spring. Proc. Liverpool Geol. Soc. session 9, p. 62. (555) Curuey, T. On the Geology of Llandrindod; its Mineral Springs, and Conglomerate Boulders. Truns. Woolhope Nat. Field Club for 1867, p. 28. (556) Darsisnirn, R. D. Notes on some Superficial Deposits at Great Orme’s Head, and as to the Period of its Elevation. Mem. Lit. Phil. Soc. Manchester, vol. iv. p. 1, and Proc. vol. vii. No. 2, p. 12 (1867). (557) Davinson, T. On the Earliest Forms of Brachiopoda hitherto discovered in the British Paleozoic Rocks. Geol. Mag. vol. v. p. 303. (558) Dawxins, W. B.,and W. A. Sanprorp. The British Pleistocene Mammalia. Part II. British Pleistocene Felide. Felis spelea. (Wales, plate ii.) Palcontograph. Soc. 4to. Lond. (559) Duncan [Prof.] P. M. A Monograph of the British Fossil Corals. Second Series. Part IV. No. 2 [Liassic]. Appendix, ‘ Note on the Age of the Sutton Stone and Brocastle, &c., Deposits,’ p. 69. Palcon- tograph. Soc. 4to. Lond. (560) Esxriace, R.A. Geological Observations on the Country round Maentwrog, North Wales. Proc. Inverpool Geol. Soc. session 9, p. 51. (561) Hyron, Miss. The Drift-Beds of Llandrillo Bay, Denbighshire. Geol. Mag. vol. v. p. 349. (562) Fatconnr, Dr. H. Paleontological Memoirs and Notes of the late, by Dr. C. Murcutson, vol.ii. 8vo. Lond. On the European Pliocene and Post Pliocene Species of the Genus Rhinoceros, p. 309 (R. hemi- toechus, Gower Caves, 8. Wales, pp. 311, 348, 351; plates 15-21, 23-25.) WORKS ON GEOLOGY, MINERALOGY, AND PALZONTOLOGY OF WALES. 431 —Note on the Occurrence of Felis speleea in the Mendip Caverns and else- where, and on a Species of Felis found in one of the Gower Caves, pp. 4.55, 458.—Note on the Remains of a Hyenoid Wolf from Spritsail-Tor Cave [Gower], pp: 462, 463—Notes on Fossil Species of Ursus. iv. from De- borah’s Den [Gower], p. 466, &c.—Observations on the Ossiferous Caves in the Peninsula of Gower, South Wales, pp. 498-540.—On the Fossil Remains found in Cefn Cave, near Bryn Elwy, N. Wales, pp. 541, 542. (563) Forses, D. Researches on British Mineralogy. Il. Phil. Mag. ser. 4, vol. xxxv. p. 171. (Polytelite, N. Wales, p. 171.) (564) Hatt, H. F. On the Geology of the District of Creuddyn. Proc. Iiverpool Geol. Soc. session 9, p. 34. (565) Hicatns, W.M. The Geological Distribution of the Ores of Iron. (Reprinted from the Colliery Guardian.) Ato. Lond. (566) Hunt, R. The Iron Ores of Great Britain. Quart. Jowrn. Sci. vol. v. p. 3l. (567) [McConnocuin, —] Section of Bore Hole at the Hast Bute Docks. 1 Ann. Rep. Cardiff Nat. Soc. p. 34, plate. (568) Artesian Well, Bute Docks, Cardiff. Ibid. p. 35 [same thing as the above]. (569) Macxintosu, D. On the Origin of Smoothed, Rounded, and Hollowed Surfaces of Limestone and Granite. (Minera.) Quart. Jowrn. Geol. Soc. vol. xxiv. p. 277 (Abstract). (570) Maw, G. On the Disposition of Iron in Variegated Strata. Quart. Journ. Geol. Soc. vol. xxiv. p. 351. (Wales, pp. 360, 379, 380-2.) 571) On a New Section of the Cambrian Rocks in a Cutting of the Llanberis and Carnarvon Railway, and the Banded Slates of Llan- beris. Geol. Mag. vol. v. p. 121. (572) Ricxerrs, Dr. C. Remarks on the Upper Silurian Formation. Proc. Liverpool Geol. Soc. session 9, p. 62. (573) Satter, J. W. On Sacocaris: a New Genus of Phyilopoda from the Lingula Flags. Proc. Geol. Polytech. Soc. W. Riding, York. vol. iy. p. 588. (574) Samust, W. Llandilo, Present and Past. .... (Geology, pp. 153-164.) 8vo. Carmarthen. 1869. (575) Bonnny, Rev. T. G. On the Supposed Occurrence of Pholas Burrows in the Upper Parts of the Great and Little Ormesheads. (Geol. Mag. vol. vi. p. 483. Letter on the above, vol. vii. p. 98, and by R. D. DarsisHire, p. 92. And Proc. Camb. Phil. Soc. part xi. pp. 150-152 (1870). (576) Davinsoy, T. A Monograph of the British Fossil Brachiopoda. Part VII. No. iii. (Pp. 169-248), The Silurian Brachiopoda. Palconto- graph. Soc. 4to. Lond. (577) Duncan, Prof. P. M. First Report on the British Fossil rome (Sutton and Brocastle, pp. 108, &c.) Rep. Brit. Assoc. for 1868, p: 75. (578) Hicks, H. On some recent Discoveries of Fossils in the Cam- brian Rocks [St. Davids]. Rep. Brit. Assoc. for 1868, Sections, p. 68. (579) Notes on a Species of Eophyton (?) from the Lower Are- nig Rocks of St. David’s: Geol. Mag. vol. vi. p. 534. (580) Notes on the Arenig Rocks in the Neighbourhood of St. Davids. Proc. Liverpool Geol. Soc. session 10, p. 72. 432 ‘REPORT—1880. (581) Hopkinson, J. On British Graptolites. Journ. Quekett Micros. Club, vol. i. (part 8), p. 151. (582) Hui, E. On the Evidences of a Ridge of Lower Carboniferous Rocks crossing the Plain of Cheshire beneath the Trias, and forming the boundary between the Permian Rocks of the Lancashire Type on the North, and those of the Salopian Type on the South. Quart. Journ. Geol. Soc. vol. xxv. p. 171. (583) M‘Cuttoucu, Dr. D. M. The Cornstones of Herefordshire and Monmouthshire. Trans. Woolhope Nat. Field Club for 1868, p. 8. (584) Macxintosn, D. The Scenery of England and Wales; its Character and Origin. 8vo. Lond. (585) Manisty, G. E. Visit to Esgair [refers to Glaciation]. Rep. Marlborough Coll. Nat. Hist. 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On some Silicious Stones found in the Coal WORKS ON GEOLOGY, MINERALOGY, AND PALZONTOLOGY OF WALES. 433 Measures, and on a White Substance found on the Cardiff Moors during a recent excavation. Trans. Cardiff Nat. Soc. vol. ii. p. 55. (603) Forzes, D. The Structure of Rock Masses (Stratification, Joints, Cleavage). Pop. Sci. Rev. vol. ix. p. 113. (604) Fornuraitt, W. The Farming of Monmouthshire [Account of the Soils, &c.]. Journ. Roy. Agric. Soc. ser. 2, vol. vi. p. 275. (605) Grirrirs, N. R. On the Flintshire Cannel Seam. Trans. N. Inst. Mining Eng. vol. xix. p. 75. (606) Hatt, H. F, On the Glacial and Post-Glacial Deposits in the Neighbourhood of Llandudno. (Geol. Mag. vol. vii. p. 509, and Rep. Brit. Assoc. for 1870, Sections, p. 72 (1871). (607) Hicks, Dr. H. Notes on the Discovery of some Fossil Plants in the Cambrian (Upper Longmynd) Rocks, near St. David’s. Rep. Brit. Assoc. for 1869, Sections, p. 90. (608) Hopkinson, J. On the Structure and Affinities of the Genus Dicranograptus. Geol. Mag. vol. vii. p. 353. (609) Jones, Prof. T. R. On some Bivalved Entomostraca from the Coal-measures of South Wales. Geol. Mag. vol. vii. p. 214. Reprinted in Trans. Cardiff Nat. Soc. vol. ii. p. 112, pl. iu. (610) Joseru, T. On the Changing Character of the Coal from Bitu- minous to Anthracite between Tredegar Iron Works and the Venallt in Glyn-Neath. Proc. S. Wales Inst. Eng. vol. vii. No. 2, p. 137. Discus- sion in Nos. 4 and 5, pp. 193, 271 (1871), and vol. viii. No. 1, p. 19 (1872). (611) Len, J. E. Notice of remarkable Glacial Strie lately exposed at Portmadoc. ep. Brit. Assoc. for 1869, Sections, p. 95. (612) Lewis, W. T., and’ M. Reynorps. Neath Mineral District. Proc. 8S. Wales Inst. Eng. vol. vii. No. 2, p. 84. Discussion in No. 5, p. 264 (1871). (613) Maw, G. On the Trappean Conglomerates of Middletown Hill, Montgomeryshire. Rep. Brit. Assoc. for 1869, Sections, p. 96. ~ (614) Moorn, C. Report on Mineral Veins in Carboniferous Lime- stone and their Organic Contents. With Notes on the Foraminifera by H. B. Brapy. Rep. Brit. Assoc. for 1869, p. 360. (615) Nicnotson, Dr. H. A. On the British Species of Didymograp- sus. Ann. Nat. Hist. ser. 4, vol. v. p. 337. (616) Rozerts, D. W. Notice of the occurrence of ‘ Actinocrinus pulcher’ in the Upper Silurian Flag of Denbighshire, North Wales, being 4 new locality for this Encrinite. Trans. Edin. Geol. Soc. vol. i. p. 329. (617) Woop, 8. V. jun. Observations on the Sequence of the Glacial Beds. Geol. Mag. vol. vii. p. 61. f 1871. (618) Apams, W. On the Geological Features of the South Wales Coalfield. Jowrn. Tron Steel Inst. No. 1, p. 13. (619) Barranvs, J. Trilobites. 8vo. Prague and’ Paris. Systéme Cambrien en Angleterre, pp. 246-254. (620) Binney, E. W. Observations on the Structure of Fossil Plants found in the Carboniferous Strata. Part 2 (p. 59), Lepidostrobus and some allied Cones. Palcontograph. Soc. 4to. Lond. (621) CarrurHers, W. On some supposed Vegetable Fossils. Quart. Journ. Gieol. Soc. vol. xxvii. p. 448. a?) Davipson, T. A Monograph of the British Fossil Brachiopoda. : FF 434 REPORT—1880. Part VII. No. iv. (pp. 249-397), The Silurian Brachiopoda, Palconto- graph. Soc. 4to. Lond. (623) Harkness, Prof. R., and H. Hicks. On the Ancient Rocks of the St. David’s Promontory, South Wales, and their Fossil Contents, With Descriptions of the New Species by H. Hicks. Quart. Journ. Geol. Soc. vol. xxvii. p. 384. (624) Henwoop, W. J. Observations on Metalliferous Deposits. (N. Wales, pp. 635-42.) Trans. Roy. Geol. Soc. Cornwall, vol. viii. part 1. (625) Joseru, T. On Colliery Explosions. South Wales Coal Field (with Sections). Proc. S. Wales Inst, Eng. vol. vii. No. 4, p. 208. Dis- cussion, vol. viii. No. 1, p. 32 (1872). (626) Jukes, J. B. Letters and Extracts from the Addresses and Occasional Writings of. Hdited by his sister. 8vo. Lond. (627) Morton, G. H. On the Mountain Limestone of Flintshire and part of Denbighshire. Rep. Brit. Assoc. for 1870, Sections, p. 82. (628) Reapwin, T. A. Notes ona Merionethshire Gold Quartz Crystal, and some Stream Gold recently found in the River Mawddach. Ibid. p. 84. (629) Ricxerrs, Dr.C. Remarks on the Lower Silurian Rocks in the Neighbourhood of Llanfyllin, and on the Contortions of the Strata. Proc. Liverpool Geol, Soc. session 12, p. 30. (630) Symonps, Rey, W. 8S. On the Physical Geology of the Bone- caves of the Wye. ep. Brit. Assoc. for 1870, Sections, p. 88. (631) Report of the Commissioners appointed to inquire into the several matters relating to Coal in the United Kingdom. Vol. i. General Report, &c.—H. H. Vivian. Report on South Wales Mineral Basin, p. 1. —G. T. Crarx. South Wales Coalfield. Eastern Division, p, 9.—J. Dickinson. North Wales, p. 16. Vol. ii. General Minutes and Pro- ceedings of Committees. Fol. Lond. 1872. (632) Anon, Observations on certain Districts in North Wales with reference to the final wasting and disappearance of the Glaciers, (Cam- bridge Phil. Soc.) Nature, vol. vii. p. 76. [See 661.] (633) Crutwett, A. The Coal-field of South Wales. Trans. Clifton Coll, Sci. Soc. part ii. p. 58. (634) Erueripcr,R. On the Physical Structure and Organic Remains of the Penarth (Rhetic) Beds of Penarth and Layernock, &e. Trans, Cardiff Nat. Soc. vol. iii. pt. ii. p. 39, pls. (635) Evans, F.G. The Carboniferous Limestone. Ibid. pt. i. p, 39. (636) Hicks, H. On some Undescribed Fossils from the Menevian Group. With a Note on the Entomostraca by Prof. T, R, Jones. Quart. Journ, Geol. Soc. vol. xxviii. p. 173. (637) Hopkinson, J. On Callograptus radicans, a New Dendroid Graptolite. Ann. Nat, Hist, ser. 4, vol. x. p, 233. (638) Jenxins, T. L. The Natural History of Tenby. (Geology, p. 21.) Trans, Clifton Coll. Sei. Soc. part ii. p. 19. (639) Macxintosu, D. The Age of Floating Ice in North Wales, Geol. Mag. vol, ix. p. 15, (640) Maskenyne, Prof. N.S.,and Dr. Fricut. Mineralogical Notices. 12 Analyses of some Pisolitic Iron Ores from North Wales. Jowrn. Chem. Soc. ser. 2, vol. x. p, 1055. (641) NicHonson, Prof. H. A. Migrations of the Graptolites. Quart. Journ. Geol, Soc. vol. xxviii. p. 217. WORKS ON GEOLOGY, MINERALOGY, AND PALHONTOLOGY OF WALES. 435 (642) Ramsay, Prof. A. C. On the River-courses of England and Wales. Ibid. p. 148. (643) Ricxerrs, Dr. C. Valleys, Deltas, Bays, and Estuaries, (Pre- sident’s Address.) Proc. Liverpool Geol. Soc. session 1871-2. (644) Ritry, E. The Manufacture of Iron and Steel. (Analysis of Welsh Ironstone, p. 534.) Quart. Journ. Chem. Soc. ser. 2, vol. x. p. 533. (645) Scururer-Kustner, A., and C. Meuntmr. On the Calorific Value and Composition of two Welsh Coals (from Comptes Rendus, \xxiii. 1061), Ibid. p. 91. (646) Symonps, Rev. W.S. On a New Fish-spine from the Lower Old Red Sandstone of Hay, Breconshire. ep. Brit. Assoc. for 1871, Sections, p. 110. (647) Records of the Rocks; or Notes on the Geology ,... of North and South Wales, Devon, and Cornwall. 8vo. Lond. (648) Tuomas, D. On ‘The Avon Valley Mineral District.’ Proc. 8. Wales Inst. Eng. vol. vii. (No. 6) p. 317. (649) Vivian, W. The Mwyndy Mines. Trans. Cardiff Nat. Soc, vol. iii. [pt. 1] p. 79. (650) Rocks—Do they Grow? Ibid. p. 75, pl. 3 [N. Wales]. (651) Woopwarp, H. A Monograph of the British Fossil Crustacea, belonging to the Order Merostomata. Part 4. (Wales, pp. 124-126.) Paleeontograph. Soc. 4to. Lond. 1873. (652) Anon. The Slate Quarries of North Wales, Reprinted from the Carnarvon and Denbigh Herald. (653) Bucxerr, H. The Geology of the Minera District. Trans. Severn Valley Nat. Field Club, 1865-1870, p. 85. (654) Brapy, H. B. On Archediscus Karreri,a New Type of Car- boniferous Foraminifera. Ann. Nat. Hist. ser. 4, vol. xii. p. 286. (655) CarrutHers, W. On Halonia of Lindley and Hutton, and Cyclocladia of Goldenberg. (S. Wales, fig.3.) Geol. Mag. vol. x. p. 145. (656) Davirs, D.C. On the Overlapping of Several Geological For- mations on the North Wales Border. Proc. Geol. Assoc. vol. ii. No. 8,p. 299. (657) On Coal Seams in the Permian, at Ifton, Shropshire (refers to Wales). Ibid. vol. iii. No. 3, p. 138. (658) Hicks, H. On the Tremadoc Rocks in the Neighbourhood of St. David’s, South Wales, and their Fossil Contents. Quart. Journ. Geol. Soc. vol. xxix. p. 39. [See Rep. Brit. Assoc. for 1872, Sections, p. 107 (1873). ? Abstract of part of above. | (659) On the Classification of the Cambrian and Silurian Rocks. Proc. Geol. Assoc. vol. iii. No. 8, p. 99, table. (660) Hopxinsoy, J. On the Graptolites of the Arenig Rocks of St. David’s. Proc. Liverpool Geol. Soc. session 14, p. 36; Rep. Brit. Assoc. for 1872, Sections, p. 107; and Geol. Mag. vol. ix. p. 467 (1872). (661) Kinastey, W. On certain facts connected with the wasting and final disappearance of the Glaciers of North Wales. Proc. Camb. Phil. Soc. part xiv. pp. 283-285. (662) Lanxesrer, E.R. On Holaspis sericeus, and on the Relation- ships of the Fish-genera Pteraspis, Cyathaspis, and Scaphaspis [Mon- mouthshire]. (feol. Mag. vol. x. p. 241. (663) Luz, J. E. Notice of Veins or Fissures in the Keuper, filled with Rhetic Bone-bed, at Goldcliffe, in Monmouthshire. Rep. Brit. Assoc. for 1872, Sections, p. 116. FRF2 436 REPORT—1880. » (664) Lucy, W. C. Notes on the Extension of the Boulder-clay over the Great and Little Orme, and the Cementing together by Lime of some large Boulders in the Clay near the Little Orme. Geol. Mag. vol. x. p. 041. (665) MackinrosH, D. Observations on the more remarkable Boulders of the North-west of Hngland and the Welsh Borders. Quart. Journ. Geol. Soc. vol. xxix. p. 351. (666) Purron, Rev. W. The Geology of Cader Idris and the Arrans. (Severn Valley Wield Club, July 3, 1873.) Local Newspaper. (667) Tuomas, J. E. Prize Essay npon the Mineral Resources of the Counties of Flint and Denbigh, with Suggestions for their Development. Pp. iv. 41. 8vo0. Oswestry. On the recent Revival in Trade. By StePHEN Bourne, F.S.S. [A communication ordered by the General Committee to be printed in extenso.] Tue latest issued official accounts of the foreign and colonial trade of the United Kingdom, together with those of the several preceding months, bear testimony to a very considerable increase in the quantity and value of both imports and exports. The figures in which these are set forth have been received as evidence that a real revival of trade has set in, and is about to extend beyond the bounds which have been reached in former years. Such an analysis of these figures as may serve to indicate their real bearing on the welfare of the country—both present and future—will not, therefore, be uninteresting, either to those engaged in trade or manu- facture; nor to those who are any way concerned to understand the position in which we stand, or that to which we may look forward. It was during the sitting of the British Association in the manufactur- ing town of Sheffield last year, that the first gleams of returning prosperity were distinctly seen. There had been for some months previously more fre- quent appearances of ‘ paper’ in the London Money Market, of American origin, which were taken as indications that there was a stir in American trade ; and many proofs that the depression into which trade on the other side of the Atlantic had fallen was passing away. Not a few hopes were expressed that this country would in like manner emerge from the depth into which its trade had fallen, so soon as prosperity was again brightening the pros- pects of the United States. The receipt, therefore, of orders for various de- scriptions of our iron products—and especially for rails—was immediately viewed as a precursor to manufacturing activity. Nor was the expectation unwarranted by the results. A spirit of confidence at once sprung up, and prices rose so high as to show that in addition to that which had a sound basis, much speculative business was going on. Thus a stimulus was given to production. Higher prices were asked and given, and for a time there seemed to be no lack of buoyancy in almost every market. Prices again gave way, but are now being partially recovered, and the opinion is almost universally entertained that a new era of prosperity is being entered upon. Such being the case it may be worth while to com- pare a year’s transactions with those of the preceding one. The early date at which the monthly accounts are now issued from the Custom House gives us the means of taking for such comparison the twelvemonth ON THE RECENT REVIVAL IN TRADE. 437 ended Jaly 31 last with those which came to a conclusion on the last day of July in 1879. We can thus place side by side the figures for the worst year of depression and the first year of recovery. Before entering into an examination of the details of the last two years, it may be well to state the totals for each year since 1871— that is, so far back as they were collected on the same system as now exists; and to show the difference in value between the goods imported and those ex- ported, as follows :— [In millions of £’s to two decimals. ] Excess Year ending Imports | Exports| of ) Imports | £ £ £ July 31,1880 . : : ; j ‘ . | 40431 | 271°24 | 133-07 A) 1879. - : ; : : : . | 345°78 | 239°86 | 105-92 fe LSS: ; , - 3 : ‘ . | 387:35 | 250°59 | 136-76 = STi) eas : ; : ; ; ; . | 389°76 | 254°31 | 135-45 a 1876. ; ; 3 . : : . | 372°37 | 266°81 | 105-56 or 1875. : 4 é : : : . | 369°48 | 288-87 80°61 3, Vi4<. : 2 : ; : é -| 375°12 | 301-23 73°89 _ L873) : : a : : ‘ . | 36643 | 32072 45°71 5 HET: -. : : < ‘ ; .-| 349°85 | 30473 45°12 | It will thus be seen that of the imports the twelve months just ended were the highest, and those of the preceding twelve the lowest of the whole series. Of the exports, the period ending in 1879 was likewise the lowest, but that just ended was by no means the highest ; whilst as regards the preponderance of imports, the most recent is very nearly the greatest, there having been, until 1880, a progressive decline in the value of the exports. Comparing the years ending in 1880 and 1879 together, they differ in all these particulars more widely from each other than any of the preceding years, the growth in imports having been 58°53/., in exports 31381, and in the excess of the former 27°15]. These figures include the whole of the imports—those again sent away, as well as those retained for home consumption ; and of the exports both the re-exports and the articles of British produce and manufacture. Separating one class of exports from the other, it appears that in the latter year they have amounted in value to 214,000,000/. British, and about 57,000,0001. foreign and colonial, as against 187,000,0007. of the one and 53,000,000/. of the other. These figures are not exact, for the accounts of the foreign goods are only shown in total at the proper end of each year, but they are accurate enough for the present purpose, and tell the increase of British to have been twenty-seven, and in foreign between four and five millions of pounds. These foreign and colonial goods show the activity of trade, and add to the national receipts by the commissions and profits on their sale, but, as regards the employment of labour and capital, are of inferior importance to the British. In estimating the worth of this increase, very much depends upon whether it has taken place in the quantities of the goods that have been sold, or in the prices they have realised. From so many of the articles being shown in the accounts in value only it is not possible to say how this may have been as regards the whole, but by abstracting the principal articles that are stated, both quantity and value, the relation of the one to 438 REPORT—1880. the other may be ascertained for such portion of the exports, and it is not likely that the proportions of the remainder will vary greatly. Classifying the articles so abstracted, and calculating how far the difference in value is due to greater quantities or altered values, the following results appear. As before, in million pounds to two decimals :— ites | Increase or Decrease | Value of | More or due to | Exports | lessthan} | 1879-80 | 1878-79 Quantity | Price ) eee | ese | £5 | £ £ £ Coals . ‘ . : 5 : ; : 8:01 | 96 | 113 — 17 Copper . : 3 3 4 - 2 ail 3:16 | 24 10 14 15 em enarimiames Sauamit oe car ne ian abana Ts Mee de eS, ‘81 Mineral , ; 4 37°29 9°64 8°86 78 Cotton Piece Goods 53-42 730 | 759 |. —-29 Jute ie as 2:12 | 310) 26 04 Linen ,, a 5:03 “49 “44 05 Woollen ,, + 15°95 1219 1:83 — 64 Textile , * ‘ ’ f . ;: 76°52 9°28 10°12 —'$4 | Cotton and other yams . . . .| 19:02 ‘1 | —58} ~ -59 Alkali . é 3 ; d : : alt 2°32 *38 “24 14 Beer . A : i 3 : é 5 Liss 109 | e==-09 saa TeArer AL eee OV RA orgie frre 292) —09 | —-23 | 14 Seed-oil x ; : A ; - r 161 ‘OL —°03 “O4 | TUE re Mate at Oe ee | ORD 22: | —-69 ‘91 | Total specified . . . . . .| 141-41] 1914] 18:29] -85 Since the full value of all the British manufactures exported for the year is 214 millions, and that of these specified articles is nearly 142, the evidence thus afforded relates to two-thirds of the whole. In like manner with the increase, twenty-seven millions for the whole and nineteen for the enumerated. Examining these particulars more closely, it will be seen that the increase of 19°14, is between 15 and 16 per cent. on the exports of the previous twelve months, and that of this amount 18:291., or 951 per cent., as owing to the quantities having been greater, and only ‘85/., or 44 per cent., has arisen from better prices having been obtained. But whilst these are the proportions of the whole, the rates on the different classes of goods differ very much. Thus in coals and metals the increase has been 35 per cent., on textile manufactures 14 per cent., and in the miscellaneous less than 1 per cent. So in respect to the gain in quantities, the minerals are greater by 92 per cent., and the prices are better by 8 per cent. In textile fabrics the increased quantities should have given 9 per cent. more money than was actually credited, but failed to do so because the prices were less to this extent. On the contrary, in the few miscellaneous articles shown above there was a real diminution of quantity, but an increase in price, whereby what would have been a loss of 24 per cent. became converted into a gain of something less than 1 per cent. Descending more into detail, ON THE RECENT REVIVAL IN TRADE. 439 . iron figures for very nearly one-third of the whole year’s gain, viz., 844d. out of 271., and cotton piece goods for 7°301., or one-fourth. Of the gain _ in iron, one-tenth only is due to price, whilst cotton goods have sold for a - trifle less than the previous price. On the other hand, cotton yarn has decreased in quantity but somewhat gained in price, and woollen piece goods, though increasing 13 per cent. in quantity have fallen 4 per cent. in price. ‘Taking the whole of the exports together, these figures establish the fact that the very low prices of manufactured goods which prevailed in the latter part of 1878 and the earlier part of 1879, have continued to rule since that time; and that for very nearly all the addition to the values of that which left our shores before the revival, we have had to give extra quantities, the advantage in point of prices obtained having been incon- siderable. If, therefore, the business of selling has yielded any better return, it must have been because the manufacturer received less; and if the manufacturer gained at all, it must have been either from the lesser value of money or a reduction in the wages of his labourers. Further, as will be shown in dealing with the imports, in the cost of the raw materials from abroad from which most of our textile fabrics are woven there has been, especially in cotton, a decided increase. Turning now to the imports, and separating those retained at home from those re-exported, we find a total value of about 347,000,000/., as against 293,000,000. in 1879. Abstracting, as with the exports, the chief articles, and classifying them according to their uses, the following figures present themselves :— Increase or Decrease Value of | More or due to | Imports, | lesa than |e. ee | Lets 80) | Tape Quantity | Price £ £ £ £ Meat, live anddead . ; : ° Poll ewe at 406 3°70 36 Butter and cheese 3 : i 3 2] 16°34 118 1:15 “03 Corn and flour ‘ - i ‘ 4 64:35 13:96 6°32 7:64 Potatoes 4 F . 2 . : 3 3°68 1:93 1:95 —*02 Coffee, tea, and sugar , : C - - 32°66 "26 — 68 94 Spirits and wine . : : 2 = Q 8:24 1°69 1:18 BL Tobacco r : 6 “4 7 “ 1:95 —'58 — 18 — 40 Food 7 : 4 . c 4 . | 149-94 22°50 13°44 9°06 Cotton, raw : ; ; F 3 .| 37°63 10°50 7-21 3:29 Flax, hemp, and jute . : : : sain 2°66 2:03 63 Ee Ny 2-64 ‘76 92 | *—-16 Wool, sheep's - A ; - : ; 11:77 1:79 2:02 —°23 Textile , . ‘ 4 . : c 61°35 1571 12°18 3°53 Tron, ore and manufactured . is : : 5°80 1:86 178 “08 Copper . : ° ; ; ( é ; 4:13 B34 _— “B34 Wood . < ; : 4 ; ; : 12°38 2:03 2:28 —'25 Hides and leather : . - - - 5°02 1:36 1:03 33 Metals, &e, . . . . . . 27°33 5°59 5:09 “50 Total specified , ° ’ . A - | 238°62 43°80 30°71 13°09 440 REPORT—1880, As with the exports, these selected articles form about two-thirds of the whole of the importations retained for home consumption or manu- facture—namely, 238 millions out of 347; but they absorb more than that proportion of the increase over the previous year—namely 44 out of 54, which is equal to four-fifths. Coming to details, it will be seen that this increase of 43-80 is 224 per cent. on the value of the previous year, whereas on the exports it was not much more than 15 per cent., from which it is clear that the value of the additional goods received for home use has exceeded that of the deliveries for sale abroad in the proportion of very nearly 3 to 2. Of this amount. 30°711., or 70 per cent., is owing to the quantities having been greater, and 13°091., or 30 per cent., from better prices having been obtained. The first division in the foregoing table, consisting of food, with which are included beverages and tobacco, is by far the largest, taking more than one-half of the articles—150 millions out of 239; and its share of the increase for the year is nearly in the same proportion (224 out of 44), the increase itself being 17} per cent. beyond last year’s supplies. In the raw material for textile manufactures—61°35/., which is rather more than a fourth of the whole, shows an increase over last year of 15°711., equal to 34 per cent. In the remaining glass, including the principal metals, wood and leather, 27°33/., comprising one-sixth of the whole, the increase in the year is 5'59/., or 26 per cent. Dividing then the surplus between volume and value, it appears that the increase of food has been 60 per cent., in textile materials 77 per cent., and in the others 91 per cent. on the quantities. So, in respect to the prices paid, which have been 40 per cent. on food, 23 on textile materials, and 9 per cent. on metals, &c, It needs no very close observation of these figures to discover the marked contrast they present to those for the exports—in that, whilst those showed the rise of prices to have been comparatively little, these manifest a decided advance, particularly in almost every article of food proper. We have not only consumed more, but that consumption has been more costly, as well as more abundant. In proof that this is really the case, two articles may be singled: out, sharing between them in nearly equal portions rather more than half the whole increase in outlay. These are wheat—the food for the body, that on which more than on anything else we depend for the power to manufacture; and cotton, the food for our mills, on which vastly more than on any other article we depend for the maintenance of our power to produce that which we can exchange for food. Of wheat we have consumed within the year, or are storing up for consumption, that which has cost us 12,000,000/. more than in the previous year; and of this amount 7,000,000/. has been spent because our growth at home was deficient in quantity, and 5,000,000J. because that deficiency enhanced the price the consumers have had to pay. Of cotton wool we have imported and kept that which has cost us 10,500,000. ; and of this 7,250,000/. has gone to provide the additional weight, and 3,250,000/. the extra price at which it has been procured. Of this addi- tional cotton as nearly as possible one-half has gone away again in the shape of manufactured goods, the other half being added to the stocks on hand, or consumed for home purposes. Thus far we have been considering the articles in which the country has traded, and the money value they represent; but an important branch of the inquiry relates to the countries with which that trade has been | | | ON THE RECENT REVIVAL IN TRADE. 441 carried on, and the altered conditions in which it stands. The figures that may serve to illustrate these points are not so complete as those with which we have been dealing, for it is only at the close of each year that the necessary accounts are published, and these do not show the trans- actions of the respective months which must form a portion of any period ending otherwise than on December 31. The quarterly accounts farnish materials for compiling the value of the whole imports for the twelve- month ending in June, but not for those re-exported; and those for the exports contain only the values of British produce and mannfacture. From these data, however, it is possible to obtain a pretty clear idea of the directions which the trade has been taking, and the differences between its progress during each of the twelvemonths completed on June 30, 1879 and 1880. The following is a condensed account of the value of the United Kingdom manufactures which have been exported to the British posses- sions and foreign countries. Excess 1879-80 | 1878-79 of former £ £ £ To British India . y : F : 2 5 4 28°68 23°39 5:29 a Africa ; : F : F $ : 8:46 8-05 | “41 33 Australia . ‘ sy : g t F 15°48 18:46 | —2:98 43 North America . d : ‘ ‘ 3 6°50 5-70 “80 753 1:14 Other Possessions ‘ a R : : 8°67 To Foreign Countries in Europe . - : - : 79°88 80°72 — 84 a A Asia. - : : F 11:20 8-78 2°42 os an Africa . aN “ : 4°26 3:97 29 -,, United States of America. . i ; f 30-49 15-14 15°35 Other Countries in ditto 4 - ; : F 17:05 16°43 62 Total to British Possessions and Foreign Countries . | 210-67 | 188°17 22°50 | If we except Australia, to which there has been so marked a decline— the effect, doubtless, of her protective tariff —the only countries that show a great difference in the two years—and these hoth in the way of increase —are British India and the United States of America. India has taken from us in cotton yarn and piece goods to the value of 18:99/. against 14°72/., thus nearly accounting for the above excess, and going far towards repaying us for the raw cotton purchascd from her. The United States have drawn upon us for iron and other metals to the value of 11-031. against 3:14/., and for cotton and other textiles 9'56/. against 5°34/., thus more than returning the increased sums paid by us for her wheat and flour. Following the same arrangement, the imports for the same period show thus :— 449 REPORT—1880. | Excess 1879-80 | 1878-79 of former £ £ £ From British India . fs ‘ ° c . 7 35°51 31°64 3°87 pag tine kerio : “ ° ‘ 5 - 6°67 6:01 “66 ,» Australia : 2 - : : : 23°26 22-80 “46 ;, North America J ; ‘ F 3 10°69 971 98 Other Possessions . ‘ ; P ‘ 7 10°30 8-42 1:88 86°45 78:58 7:85 161°88 | 14650 15°38 17°35 16°23 1:12 14°19 8°67 5°52 . . | 100°92 81:63 19:29 . : 20°62 19-74 “88 From Foreign Countries of Europe = rs Asia + Atrica United States of America Other Countries in ,, ” ” 314:°96 | 272-77 42-19 Total from British Possessions and Foreign Countries | 401°39 | 351-35 50°04 These figures indicate that the expansion of our import trade has been a benefit to almost every country, though here India and the United States, with Egypt, have been the most prominent. In all these the two great articles of corn and cotton have had the principal part. That with the various countries of Europe is so large that a slight addition to each, arising in great measure from our demands for corn, makes up a con- siderable total. The chief interest, however, centres in the supplies we have drawn from the United States. Wheat and flour together amounted in 1878-9 to 17°46/., and in 1879-80 to 26°58/.; cotton to 22°682. in the former, to 28°371. in the latter. The analysis to which these figures have been submitted serves to bring out many points of especial interest connected with the present revival, and should afford much food for thought as regards its probable course and duration. In the first place, it shows that, great as has been the increase in our exportations, that in our import trade is far greater. If we have sold in the last twelve months to the value of 82,000,0007. more than we did in the previous twelve, we have also received more goods to the value of 59,000,0001., thus leaving a greater balance to be provided for. No doubt a considerable portion of that 27,000,000. will remain with us in payment for freights, commissions earned, or profits realised; but an ample allow- ance for these must still leave a large amount to be met either by payments in bullion, the transfer of securities, or as deferred obligations. Nor must it be forgotten that there is a continual stream of capital flowing from this country for investment in our colonies and in foreign lands, which going out mostly in goods, or in bills which serve as payment for goods, the actual receipts for our exports are lessened thereby. There is, on the other hand, capital returning for investment here, which in like manner is represented by imports; but all our experience justifies the supposition that the influx from this cause is less than the efflux. Much of the former is held here on foreign account, liable at any moment to be withdrawn ; ON THE RECENT REVIVAL IN TRADE. 443 hence the doubts so freely expressed at the present moment whether a drain of gold may not soon set in. Secondly, it is evident that on the whole the prices obtained for our exports are only to a trifling extent better than they were, whilst the prices paid for our imports are considerably enhanced. Thus the revival has been much more to the advantage of the sellers of the goods we have consumed than to that of those who sold our own produce or manufacture. In the complicated state of trade transactions it is impossible to say whether any or how much of this advantage belongs to our merchants, since this ‘depends upon the ownership at the time when the sales are effected. As between the actual producers and consumers it is clear that a higher rate of payments for imports, with nearly stationary receipts for exports, cannot increase the prosperity of either one or the other. It would seem to be the case that sales are effected because prices are low, and that purchases are made because we need them although prices are high. Take, for instance, the fact that the cotton used up in the manufacture of our piece-goods has failed to bring in the higher price which the advanced cost of the raw material would justify or require. Thirdly, the whole excess in the value of the exports is scarcely equi- -yalent to the extra cost of the food we have imported. Unless we can suppose that large stocks of produce and manufacture, or the means of producing them, are prepared for future sale, in readiness to obtain a profit when parted with, it follows that, asa whole, all the gain of extended foreign outward trade has but gone in the sustenance of those by whom the goods have been produced, leaving nothing wherewith to recompense capital or for the accumulation of wealth. This brings us to the really important consideration whether the food question is not truly at the bottom of the recent fluctuations in trade. For a series of years our own supplies have been scanty, and the bad harvest of last year rendered us more than ever dependent upon the pro- duce of foreign countries, particularly of America. Purchasing largely from the Western growers, and giving them remunerative prices, they have large profits to expend upon our manufactures. Encouraged by the successive annually increasing quantities they were able to sell, they have been laying themselves out to meet our wants, and, anticipating an ever-growing call for their produce, they have determined by means of new railways to bring larger quantities, and at lesser cost, from the distant fields in the West to the seaboard in the East. Hence the sudden demand for rails and for the iron to make them which the pits and the mills of their own country could not supply, but which the diminution of prices here enabled them to obtain sufficiently low to counteract the otherwise prohibitory duties of their own tariff. Trade thus started in one direction speedily spread in others, and thus extended far beyond the boundaries in which it emanated. The repeated adversities of former years have caused the depression of 1878-9 to be greater than the causes warranted, and with the changes of last autumn confidence became restored, and this of itself creates trade. The supposition that this revival is greatly owing to the failure of our _ home crops derives much confirmation from the fact, that whilst the best authorities estimate the diminished growth of wheat last year at from five _ to six million quarters, worth some eleven or twelve millions of money, our purchases of corn from the United States alone were fully that amount » im excess; to compensate for which they took from us iron and other 444 REPORT—1 880. metals and textile manufactures together to the value of twelve millions more than in 1878-9. We have here a beautiful illustration of the way in which Nature—rather let us say the Author of Nature’s laws, the Divine Ruler, who orders the course of Nature for the welfare of His creatures— counteracts one disturbing element by the restorative power of another. When the fertilising influence of the sun’s heat failed us last year, vege- tation languished and our fields failed to yield their accustomed supplies. From whence did relief come but from the latent heat, which ages back became imprisoned in the depths of our coal-pits, being brought forth and utilised for the production of those manufactures wherewith we purchased corn elsewhere ? Where can we look for a more convincing argument in favour of free trade than is to be found in the blessings it procured for us in permitting this unrestricted exchange of the commodities absolutely necessary to our existence, and of special importance to our brethren in America? Whilst we sympathise with our agriculturists in the loss of their substance and the severe trials which they are enduring, let.us rejoice that the evil was stayed from spreading to our manufacturers and traders, and thereby involving them in the like suffering. Let us not, however, be led away by undue expectations for the future. A good harvest at home—still more a succession of them, if combined with greater produc- tiveness abroad—would so far depress prices as to lessen the purchasing power of the food-growers at home, whilst we shall not need to buy so largely from abroad. Thus those who have latterly supported our markets will fail to purchase as they have done, and if our manufacturing industries are to be sustained we must not rely on a repetition of the demands that have latterly been made upon them. There is too much danger at present that we shall drawn into wild speculations and expectations, such as led up to the fictitious prosperity of seven years back, and culminated in the depression of more recent years. Let us not delude ourselves with the belief that the inflation of 1871-3 is about to return—that fortunes are going to be made as rapidly as then, or wages to rise to the same level. Let us not, however, give way to gloomy fears. Cheap food will foster cheap production, and, though our old customers may under its influence be enabled to supply their own wants, there are new races of purchasers to be found or called into being, and new homes to be founded by those who are cumbering the ground here rather than tilling it in the distant parts of the Empire. The judicious transferal of much of our capital and labour to places abroad, where there is ample room for its profitable employment, together with greater thrift—individual, family, and national—at home, are the true sources on which to rely for the maintenance or restoration of our manu- facturing and commercial supremacy. . TRANSACTIONS OF THE SECTIONS. anti. auure’ ‘fo AON Piss ial TRANSACTIONS OF THE SECTIONS. Sectron AAW—MATHEMATICAL AND PHYSICAL SCIENCE, PRESIDENT OF THE SECTION—Professor W. GRYLLS ADAMS, M.A.,, F.R.S., F.G.S., F.C.P.S. THURSDAY, AUGUST 26. The Prusrpent delivered the following Address :— Ir has been said by a former President of this Section of the British Association that the President of a Section ought to occupy your time, not by speaking of himself or his own feelings, but by a review ‘more or less extensive of those branches of science which form the proper business of this section.’ He may give a rapid sketch of the progress of mathematical science during the year, or he may select some one special subject, or he may take a middle course, neither so extensive as the first nor so limited as the second. There are many branches of science which have always been regarded as pro- perly belonging to our Section, and the range is already wide ; but it is becoming more and more true every day that the sciences which are dealt with in other sections of the Association are becoming branches of Physics, z.e. are yielding results of vast importance when the methods and established principles of Physics are applied to them. I wish to direct your attention to investigations which are being made in that fertile region for discovery, the ‘ border land’ between chemistry and physics, where we have to deal with the constitution of bodies, and where we are tempted to speculate on the existence of matter and on the nature of the forces by which the different parts of it are bound together or become so transformed that all resemblance to their former state is lost. It is not long since the theory of exchanges became thoroughly recognised in the domain of Radiant Heat, and yet so rapid is the progress of science that it is already recognised and accepted in the theory of Chemical combination. Just as the molecules of a body which remains at a constant temperature are continuously giving up their heat-motion to surrounding molecules, and getting back from them as much motion of the same kind in return, so in a chemical compound which does not appear to be undergoing change, the combining molecules are continuously giving up their chemical or com- bining motions to surrounding molecules, and receiving again from them as much combining motion in return, We may say that each molecule is, as far as we can see, constantly dancing in perfect time with a partner, and yet is continuously changing partners, When such an idea of chemical motion is accepted, we can the more easily understand that chemical combination means the alteration of chemical motion, which arises from the introduction of a new element into the space already occupied, and the consequent change in the motion of the new compound as revealed to us in the spectroscope. We can also the more readily understand that in changing from the old to the new form or rate of motion, there may be a deve- lopment of energy in the shape of heat-motion which may escape or become dis- sipated wherever a means of escape presents itself. We know from the experiments of Dr. Joule and of M. Favre that as much heat is absorbed during the decomposi- tion of an electrolyte as is given out again by the combination of the substances composing it, 448 REPORT—1880. We are making rapid strides towards the exact determination of those relations between the various modes of motion or forms of energy which were so ably shadowed forth, and their existence established long ago, by Sir William Grove in his ‘Correlation of the Physical Forces,’ where, in stating the conclusion of his com- parison of the mutual interchange of physical forces, he distinctly lays down the principles of energy in this statement: ‘Each force is definitely and equivalently convertible into any other; and where experiment does not give the full equivalent, it is because the initial force has been dissipated, not lost, by conversion into other unrecognised forces. The equivalent is the limit never practically reached.’ The laws of Faraday, that (1) when a compound is electrolysed the mass of the substance decomposed is proportional to the quantity of electricity which has produced the change, and that (2) the same current decomposes equivalent quanti- ties of different substances, 7.e. quantities of their elements in the ratio of their combining numbers, have given rise to several determinations of the relation between chemical affinity and electromotive force. Ina paper lately communicated to the Physical Society, Dr. Wright has discussed these several determinations, and has given an account of a new determination by himself. The data at present extant show that when ] gramme of hydrogen unites with 7-98 grammes of oxygen there are about 34,100 units of heat given out, making the latent heat of dissociation of 1 gramme of water equal to 8797 units. The results obtained are compared with the heat given out by the combustion of hydrogen and oxygen, and the value of the mechanical equivalent of heat is deduced from these determinations. The value of this mechanical equivalent obtained by Dr. Wright, which depends on the value of Clark’s standard cell, and therefore depends on the value of the ohm, agrees fairly well with Joule’s determination from the heat produced by an electric current in a wire, but is greater than Joule’s value as obtained from his water-friction experiments. This may be accounted for by supposing an error in the value of the ohm or B.A. unit, making it too large by 1°5 or 2 per cent. Kohlrausch has also made comparisons of copies of the B.A, unit with standard coils, and comes to the conclusion that the B.A. unit is 1:96 per cent. too large. On the other hand, Pro- fessor Rowland, in America, has made a new determination, and finds that accord- ing to his calculations the B.A. unit is nearly 1 per cent. too small. These differences in the values obtained by different methods clearly point to the necessity for one or more new determinations of the unit, and I would venture to suggest that a determination should be made under the authority of this Association, by a Committee appointed to carry out the work. And it is not sufficient that this determination should be made once for all, for there is reason to think that the yesistance of standard coils alters with time, even when the material has been care- fully selected, It has been found that coils of platinum silver which were correct copies of the standard ohm haye become so altered, and have their temperature coefficients so changed, that there are doubts as to the constancy of the standards themselves. Pieces of platinum-silver alloy cut from the same rod have been found to have different temperature-coeflicients. The value ‘031 for 1° C. is given by Matthiessen for this alloy, yet two pieces of wire drawn from the same rod have given, one ‘021 per cent. and the other -04 per cent. for 1° C. Possibly this irregularity in the platinum-silver alloys may he due to something analogous to the segregation which Mr. Roberts has found to take place in copper-silver alloys in their molten state, and which Matthiessen in 1860 regarded as mechanical mixtures of allotropic modifications of the alloy. A recommendation has been made that apparatus for determining the ohm should be set up in London, and that periodically determinations be made to test the electrical constancy of the metals and alloys used in making coils. A com- mittee should be authorised to test coils and issue certificates of their accuracy, just as is done by the Kew Committee with regard to meteorological instruments. The direct relation between Heat and Chemical work has been established, and the principles of Conservation of Energy been shown to be true in Chemistry by the experiments of Berthelot and of Thomsen, so that we may say that when a system of bodies passes through any succession of chemical changes, the heat evolved or absorbed when no external mechanical effect is produced depends solely upon the TRANSACTIONS OF SECTION A. 449 - initial and final states of the system of bodies, whatever be the nature or the order of the transformations. The extension of this principle to the interaction of the molecules and atoms of bodies on one another is of vast importance in relation to our knowledge of the constitution of matter, for it enables us to state that each chemical compound has a distinct level or potential which may be called its own, and that when a compound gives up one of its elements to another body, the heat eyolyed in the reaction is the difference between the heat of formation of the first compound, and that of the resulting product. We have become accustomed to regard matter as made up of molecules, and those molecules to be made up of atoms separated from one another by distances which are great in comparison with the size cf the atom, which we may regard as the smallest piece of matter that we can have any conception of. Each atom has been supposed to be surrounded by an envelope of ether which accompanies it in all its movements. The density of the ether increases rapidly as an atom is approached, and it would seem that there must be some force of attraction between the atom and its ether envelope. All the atoms have motions of translation in all possible directions, and according to the theories of Maxwell and Boltzmann, and the experiments of Kundt, Warburg, and others on the specific heat of vapours, in one-atom molecules in the gaseous state there is no motion of rotation. According to the theory of Pictet, the liquid state being the first condensation from the gaseous state must consist of at least two gaseous atoms combined. These two atoms are bound to one another through their ether envelopes. Then the solid state results from the condensation of a liquid, and so a solid molecule must consist of at least two liquid molecules, #.e. at least four gaseous molecules, each surrounded by an atmosphere of ether. M. Pictet imagines these atoms to be centres of attraction; hence in the solid with four such centres the least displace- ment brings into action couples tending to prevent the molecule from twisting as soon as external forces act upon it. All the molecules constituting a solid wiil be rigidly set with regard to one another, for the least displacement sets in action a couple or an opposing force in the molecules on one another. Let us now follow the sketch which M. Pictet has given of changes which we may consider it to undergo when we expend energy upon it. Suppose a solid body is at absolute zero of temperature, which may be regarded as the state in which the molecules of a body are in stable equilibrium and at rest, the application of heat gives a vibratory motion to the molecules of the solid, which increases with the temperature, the mean amplitude of vibration being a measure of the temperature. We may regard the sum of all the molecular forces as the specific heat of the body, and the product of the sum of all the molecular forces by the mean amplitude of the oscillations ; i.e. the product of the specific heat and the temperature will be the quantity of heat or the energy of motion of the body. As more and more heat is applied, the amplitude of vibration of the molecules increases until it is too great for the molecular forces, or forces of cohesion, and the melting point of the solid is reached. Besides their vibratory motion, the molecules are now capable of motions: of translation from place to place among one another. To reduce the solid to the liquid state, 7c. to make the amplitude of vibration of the molecules sufficient to prevent them from coming within the sphere of the forces of cohesion, requires a quantity of heat which does not appear as temperature or molecular motion, and hence it is termed the latent heat of fusion. The temperature remains constant until the melting is complete, the heat bemg spent in bursting the bonds of the solid. Then a further application of heat increases the amplitude of vibration, or raises the temperature of the liquid at a rate depending on its specific heat until the succession of blows of the molecules overcomes the external pressure and the boiling point is. reached. An additional quantity of heat is applied which is spent in changing the body to a gas, te. to a state of higher potential, in which the motion of translation of the molecules is enormously increased. When this state is attained, the tempe- rature of the gas again begins to increase, as heat is applied, until we arrive at a certain point, when dissociation begins, and the molecules of the separate substances of which the body is composed haye so large an amplitude of vibration that the bond which unites them can no longer bring them again into their former positions, 1880. G@ 450 REPORT—1880. The potential of the substances is again raised by a quantity which is proportional to its chemical affinity. Again, we may increase the amplitude of vibration, z.c. the temperature of the molecules, and imagine the possibility of getting higher and higher degrees of dissociation. If temperature means the amplitude of vibration of the molecules, then we might expect that only those bodies which have their temperatures increased hy the same amount when equal amounts of heat are applied to them can possibly combine with one another; and so the fact that the increase of temperature bears a fixed ratio to the increase of heat may be the cause in virtue of which bodies can combine with one another. Were other bodies to begin to combine together at any definite temperature, they would immediately be torn to pieces again when the temperature is even slightly raised, because the amplitudes of vibration of their molecules no longer remain the same. This idea of temperature is supported by the fact that a combining molecule of each substance requires the same amount of heat to raise its temperature by the same number of degrees, the atomic weights being proportional to the masses of the combining molecules. The celebrated dis- covery of Faraday, that in a voltameter the work done by an electric current always decomposes equivalent quantities of different substances, combined with the fact that in the whole range of the physical forces work done is equivalent to the application of heat, is quite in accordance with the view that no molecule can combine with another which has not its amplitude of vibration altered by the same amount when equal quantities of heat are applied to both. As soon as we get any divergence from this state of equal motions for equal increments of heat, then we should expect that a further dissociation of molecules would take place, and that only those which are capable of moving together can remain still associated. Just as in the change of state of a body from the solid to the liquid, or from the liquid to the gas, a great amount of heat is spent in increasing the motion of translation of the molecules without altering the temperature, so a great amount of heat is spent in producing dissociation without increasing the temperature of the dissociated substances, since the principle of conservation of energy has been shown by M. Berthelot to hold for the dissociation of bodies. We may conveniently. male use of the term latent heat of dissociation for the heat required to dissociate a unit of mass of a substance. ‘We may thus sum up the laws of physical and chemical changes :— 1. All the physical phenomena of change of state consist in the subdivision of the body into molecules or particles identical with one another. 2. The reconstitution of a body into a liquid or a solid being independent of the relative position of the molecules, only depends on the pressure and temperature. 3. Dissociation separates bodies into their elements, which are of different kinds, and the temperature remains constant during dissociation. 4, The reunion of dissociated bodies depends on the relative position of the elements, and so depends on the grouping of the molecules. The atomic weight being the mass of a molecule as compared with hydrogen, the specific volume, ze. the atomic weight divided by the density, is the volume or mean free path of a molecule. Building up his theory of heat on these principles, M. Pictet arrives at a de- finite relation between the atomic weight of a body, its density, its melting point, and its coetlicient of expansion, which may be stated thus— The volume of a solid body will be increased as the temperature rises by an amount which is proportional to the number of molecules in it, and inversely as its specific heat. At a certain temperature peculiar to each body, the amplitude of the heat oscillation is sufficient to melt the solid, and we are led to admit that for all bodies the intermolecular distance corresponding to fusion ought to be the same, The higher the point of fusion of a body, the shorter, on this theory, must be its heat-vibrations. The product of the length of swing (the heat-oscillations) by the temperature of fusion ought to be a constant number for all solid bodies. A comparison of the values of the various quantities involved in these state- ments shows a very satisfactory agreement between theory and experiment, from which it appears that the product of the length of swing by the temperature of TRANSACTIONS OF SECTION A. 451 fusion lies between 3°3 and 3:7 for many ‘substances. Not mary values of the latent heat of dissociation have been obtained. ‘In order to determine it, say, for the separation of oxygen and hydrogen, we should have to determine the amount of work required to produce a spark in a mixture of oxygen and hydrogen, and to measure the exact amount of water or vapour of water combined by the spark, as well as the range of temperature through which it had passed after its forma- tion. Very few such determinations have been made. Our usual mode of producing heat is by the combination of the molecules of different substances, and we are limited in the production of high temperatures, and in the quantity of available heat necessary to dissociate any considerable quantity of matter. If we heat vapours or gases, we may raise their temperatures up to a point corresponding to the dissociation of their molecules, and we are limited in our ehemical actions to the temperatures which can be obtained by combining together the most refractory substances, as we are dependent on this combination for our supply of heat. The combination of carbon and hydrogen with oxygen will give us high tem- peratures, so that by the oxyhydrogen blow-pipe most of the salts and oxides are dissociated. The metalloids bromine, iodine, sulphur, potassium, &c., are the results of the combination of two or more bodies bound together by internal forces much stronger than the affinity of hydrogen or carbon for oxygen, for approximately they obey the law of Dulong and Petit. For higher temperatures, in order to dissociate the most refractory substances, we require the electric current, either a continuous current, as in the electric arc from a battery, or a dynamo-machine, or, more intense still, the electrical discharges from an electrical machine or from an induction coil. This electric current may be regarded as the most intense furnace for dissociating large quantities of the most refractory substances, and the electric spark may be regarded as something very much hotter than the oxyhydrogen blow-pipe, and therefore of service in reducing very small quantities of substances which will yield to no other treatment. The temperature of the electric are is limited, and cannot reach above the temperature of dissociation of the conductor, and in the case of the constant current, which will not leap across the smallest space of air unless the carbons have first been brought in contact, the current very soon ceases when the point of fusion has been reached. Yet in the centre of the are we haye the gases of those substances which form the conductor; and, as Professor Dewar has shown, we have the formation of acetylene and cyanogen and other compounds, and there- fore must have attained the temperature necessary for their formation, z.e, the tem- perature of their dissociation. The temperature of the induction spark, or, at least, its dissociating power, is higher than that of the are. We know that the spark will pass across a space of air or a gaseous conductor, and we are limited by the dissociation of the gaseous conductor, and get only very small quantities of the dissociated substances, which immediately recombine, unless they are separated. If the gases formed are of different densities they will diffuse at diflerent rates through a porous diaphragm, and so may be obtained separated from one another. As the molecules of bodies vibrate they produce vibrations of the ether particles ; the period of the oscillations depends on the molecules of the body, and these periodic vibra- tions are taken up by their ether envelopes and by the luminiferous ether, and their wave-length determined by means of the spectroscope. As the temperature is increased, the amplitudes of oscillation of the molecules and of the ether increase, and from the calculations of Lecoq de Boisbaudran, Stoney, Soret, and others, it would appear that many of the lines in the spectra of bodies may be regarded as harmonics of a fundamental vibration. Thus Lecoq de Boisbaudran finds that in the nitrogen spectrum the blue lines seen at a high temperature correspond to the double octave of certain vibrations, and that, at a lower temperature, red and yellow lines are seen which correspond to a fifth of the same fundamental vibrations. The bright line spectrum may be regarded as arising from the vibratory motions of the atoms. A widening of the lines may be produced at a higher temperature by the backward and forward motions of the molecules in the direction of the : GG 2 452 ti gta REPORT— 1880. observer. A widening of the lines may also be produced by increase of pressure, because it diminishes the free path of the molecules, and the disturbances of the ether arising from collisions become more important than vibrations arising from the regular vibrations of the atoms. Band spectra, or channelled space spectra, more readily occur in the case of bodies which are not very readily subject to chemical actions, or, according to Professors Liveing and Dewar, in the case of cooler vapours near the point of liquefaction. The effects of change of temperature on the character of spectra is very well illustrated by an experiment of M. Wiedemann with mixtures of mercury with hydrogen or nitrogen in a Geissler’s tube. At the ordinary temperature of the air the spectrum of hydrogen or nitrogen was obtained alone ; but on heating the tube in an air-bath the lines of mercury appeared and became brighter as the tempera~- ture rose, and at the same time the hydrogen lines disappeared in the wider portion of the tube and at the electrodes. The hydrogen or nitrogen lines disappeared first from the positive electrode and in the luminous tuft, and as the temperature rose disappeared altogether. With nitrogen in a particular experiment, up to 100° C., the nitrogen lines were seen throughout the tube, but from 100° to 230° the nitrogen lines appear towards the negative pole, and the mercury lines are less bright at the negative than at the positive pole, while at about 230° C. no nitrogen lines appear. The experiments of Roscoe and Schuster, of Lockyer and other observers, with potassium, sodium, and other metalloids in vacuum tubes, from which hydrogen is pumped by a Sprengel pump, also show great changes in the molecular condition of the mixture contained in the tubes when they are heated to different temperatures. The changes of colour in the tube are accompanied by changes in the spectrum. Thus, Mr. Lockyer finds that when potassium is placed in the bottom of the tube, and the spark passes in the upper part of it, as the exhaustion proceeds and the tube is slightly heated, the hydrogen lines disappear, and the red potassium line makes its appearance ; then as the temperature is increased, the red line disappears, and three lines in the yellowish-green make their appearance, accompanied by a change in the colour of the tube, and at a higher temperature, and with a Leyden jar joined to a secondary circuit of the induction coil, the gas in the tube becomes of a dull red colour, and with this change a strong line comes out in the spectrum, more refrangible than the usual red potassium line. In this case, on varying the conditions, we get a variation in the character of the spectrum, and the colours and spectra are different in different parts of the tube. In Lockyer’s experiments, at the temperature of the are obtained from a Siemens dynamo-machine, great differences appear in different parts of the are: for instance, with carbon poles in the presence of calcium, the band spectrum of carbon, or the carbon flutings and the lines of calcium, some of them reversed, are seen separated in the same way as mercury and hydrogen, the carbon spectrum appearing near one pole and the calcium near the other, the lines which are strongest near that pole being reversed or absorbed by the quantity of calcium vapour sur- rounding it. On introducing a metal into the are, lines appear which are of different intensities at different distances from the poles, others are strong at one pole and entirely absent at or near the other, while some lines appear as broad as half-spindles in the middle of the arc, but are not present near the poles. Thus, the blue line of calcium is visible alone at one pole, the H and K lines without the blue line at the other. We may probably regard these effects as the result, not of temperature alone, but must take into account that we have powerful electric currents which will act unequally on the molecules of different bodies according as they are more or less electro-positive. It would seem that we have here something analogous to the segregation which is observed in the melting of certain alloys to which I have already referred. The abundance of material in some parts of the arc surrounding the central portion of it gives rise to reversal of the principal lines in varying thicknesses over the are and poles, so that bright lines appear without reversal in some regions, and reversals or absorption lines without bright lines in others. The introduction of a substance into the are gives rise to a flame of great complexity with regard to colour TRANSACTIONS OF SECTION A. 453 and concentric envelopes, and the spectra of these flames differ in different parts of the arc. Thus, in a photograph of the flame given by manganese, the line at wave- length 4234°5 occurs without the triplet near 4030, while in another the triplet is present without the line 4234:5. The lines which are reversed most readily in the arc are generally those the absorption of which is most developed in the flame; thus the manganese triplet in the violet is reversed in the flame, and the blue calcium line is often seen widened when the H and K lines of calcium are not seen at all. In consequence of the numerous changes in spectra at different temperatures, Mr. Lockyer has advanced the idea that the molecules of elementary matter are continually being more and more broken up as their temperature is increased, and has put forward the hypothesis that the chemical elements with which we are acquainted are not simple bodies, but are themselves compounds of some other more simple substances. This theory is founded on Mr. Lockyer’s comparisons of spectra and the maps of Angstrom, Thalén, Young, and others, in which there are coincidences of many of the short lines of the spectra of different substances. These short lines are termed basic lines, since they appear to be common to two or more substances. They appear ut the highest tem- peratures when the longest lines of those substances and those which are considered the test of their presence are entirely absent. Mr. Lockyer draws a distinction between weak lines, which are basic, .e. which would permanently exist at a higher temperature in a more elementary stage, and other weak or short lines which would be more strongly present at a lower tempe- rature, in a more complex stage of the molecules. ‘I'hus, in lithium, the red line is a low temperature line, and the yellow is feeble; ata higher temperature, the red line is weak, the yellow comes out more strongly, and the blue line appears; at a higher temperature still, the red line disappears, and the yellow dies away; whilst at the temperature of the sun the violet lithium line is the only one which comes out strongly. These effects are studied by. first producing the spectrum of the substance in the Bunsen flames, and observing the changes which are produced on assing a spark through the flame; thus, in magnesium a wide triplet or set of three lines (5209°8, b! and b*) is changed into a narrow triplet (b', b?, and b*) of the same character. We have here what some observers regard as a recurrence of the same harmonic relation of the vibrations of the same body at a higher temperature. If the so-called elements are compounds, they must have been formed at a very high temperature, and as higher and higher temperatures are reached the dissocia- tion of these compound bodies will be effected, and the new line spectra, the real basic lines of those substances which show coincidences, will make their appearance as short lines in the spectra. In accordance with this view, Mr. Lockyer holds that the different layers of the solar atmosphere may be regarded as a series of furnaces, in the hottest of which, A, we have the most elementary forms of matter capable of existing only in its uncombined state; at a higher and cooler level, B, this form of matter may form a compound body, and may no longer exist in a free state at the lower temperature; as the cooler and cooler levels, C, D, and B, are reached, the substances become more and more complex and form different combinations, and their spectra become altered at every stage. Since the successive layers are not at rest, but in a state of disturbance, we may get them somewhat mixed, and the lines at the cooler levels D and E may be associated with the lines of the hotter levels; these would be basic or coincident lines in the spectra of two different compounds which exist at the cooler levels D and E. We might even get lines which are not present in the hottest furnace A coming into existence as the lines of compounds in B or C, and then extending among the lines belonging to more complex compounds which can only exist at a lower temperature, when they might be present as coincident weak lines in the spectra of several compound bodies. Thus Mr. Lockyer regards the calcium lines H and K of the solar spectrum as evidence of different molecular groupings of more elementary bodies. In the electric are with a weak current the single line 4226 of calcium, which is easily reversed, is much thicker than the two lines H and K; but the three lines are equally thick with a stronger current, and are all reversed. With a spark from a large coil and using a condenser the line 4226 disappears, and H and K are 454 REPORT—1880. strong lines. In the sun, the absorption bands H and K are very broad, but the band 4226 is weak. Prof. Young, in his observation of the lines of the chromo- sphere, finds that H and K are strongly reversed in every important spot and in solar storms; but the line 4226, so prominent in the arc, was only observed three times in the chromosphere. One of the most interesting features among the most recent researches in Spectrum Analysis is the existence of rhythm in the spectra of bodies, as has been shown by.M. Mascart, Cornu, and others, such as the occurrence and repetition of sets of lines, doublets, and triplets in the spectra of different substances and in different ‘parts of the spectrum of the same body. Professors Liveing and Dewar, using the reversed lines in some cases for the more accurate determination of wave-lengths, have traced out the rhythmical character in the spectra of sodium, potassium, and lithium, They show that the lines of sodium and potassium form groups of four lines each, which vecur ina regular sequence, while lithium gives single lines, which, including the green line, which they show really to belong to lithium, though it was ascribed. to cesium by Thalén, also recur in a similar way. In these three metals the law of recurrence seems to be the same, but the wave-lengths show that the whole series are not simple harmonics of one fundamental, although between some of the terms very simple harmonic relations can be found. Between the lines G and H are two triplets of iron lines, which, according to Mr. Lockyer, do not belong to the same molecular grouping as most of the other lines. In many photographs of the iron spectrum these triplets have appeared almost alone. Also the two triplets are not always in the same relation as to brightness, the more refrangible being harely visible with the spark; combining this with Young’s observatiens, in which some short weak lines near G appear in the chromosphere 30 times, while one of the lines of the less refrangible triplet only appears once, and with the fact that in the solar spectrum the more refrangible triplet is much the more prominent of the two, Mr. Lockyer is led to the conclusion that these two triplets are again due to two distinct molecular groupings. There is one difficulty which must be taken account of in connection with Mr. Lockyer’s theory with regard to the production of successive stages of disso- ciation by means at our command. At each stage of the process there must be a considerable absorption of heat to produce the change of state, and our supply of heat is limited in the electric arc because of the dissociation of the conductors, and more limited still in quantity in the electric spark or in the discharge through a vacuum tube, also we should expect a recombination of the dissociated substances immediately after they have -been first dissociated. Hence it seems easier to suppose that at temperatures which we can command on the earth, the dissociation of molecules by the arc or the spark is accompanied by the formation of new compounds, in the formation of which heat and light, and especially chemical vibrations, would be again given out, giving rise to new spectra, rather than to suppose that we can reach the temperatures neces- sary for successive stages of dissociation. BIR a To the lines C, F, the line near G, and h belonging to hydrogen, which have a certain rhythmical character, Mr. Lockyer adds D, and Kirchoff's line ‘1474,’ regarding ‘1474’ (wave-length 5315:9) as belonging to the coolest or most complex form, rising to F at a higher temperature, which is again subdivided into C and G, using the spark without a condenser, which again gives h with the spark and con- denser, which is again split up and gives D,,a more simple line than h, in the Chro- mosphere. Professors Liveing and Dewar, on the other hand, trace a rhythmical character or ratio between three of the brightest lines of the chromosphere, two of which are lines ‘ 1474’ and ‘f’ of Lorenzoni, similar to the character of C, F, and h of hydrogen, and.also trace a similar relation between the chromospheric line D, and ‘1474’ to the ratio of the wave-lengths of F and the line near @. They infer the probability that these four lines are due to the same at present unknown ‘substance as-had- been suggested by Young with regard to two of them. The harmony of this arrangement is somewhat disturbed by the fact that D, lies onthe wrong side of ‘1474’ to correspond with the line near G of the hydrogen spectrum. If we inquire what our sun and the stars have to say to these changes of iti TRANSACTIONS OF SECTION A. 455 spectra of the same substance at different temperatures, Dr. Huggins gives us the answer. _ In the stars which give a very white light, such as Sirius or a Lyre, we have the lines G and h of hydrogen and also H, which has been lately shown by Dr. Vogel to be coincident with a line of hydrogen ; but the K line of calcium is weak in a Lyre, and does not appear in Sirius. In passing from the white or hottest stars to the yellow stars like our sun, the typical lines diminish in breadth and are better defined, and K becomes stronger relatively to H, and other lines appear. In Arcturus we have a star which is probably cooler than our sun, and in it the line K is stronger in relation to H than it is in the solar spectrum, both being very strong compared with their state in the solar spectrum. Professors Liveing and Dewar find that K is more easily reversed than H in the electrie are, which agrees with the idea that this line is produced at a lower temperature than H. ; Besides the absence or weakness of K, the white stars have twelve strong lines winged at the edges, in which there are three of hydrogen, viz. G, h, and H, and the remaining nine form a group which are so related to one another that Dr. Huggins concludes they probably belong to one substance. Three of these lines are said by Dr. Vogel to be lines of hydrogen. Professors Liveing and Dewar have made considerable progress in determining the conditions and the order of reversal of the spectral lines of metallic vapours. They have adopted methods which allow them to observe through greater thick- nesses of vapour than previous observers have generally employed. For lower temperatures tubes of iron or other material placed vertically in a furnace were used, and the hot bottom of the tube was the source of light, the absorption being produced by vapours of metals dropped into the hot tube and filling it to a greater or less height. By this means many of the more volatile metals, such as sodium, thallium, iridium, cesium, and rubidium, magnesium, lithium, barium, strontium, and calcium, each gave a reversal of its most characteristic line or pair of lines, i.c, the red line of lithium, the violet lines of rubidium and calcium, the blue line of strontium, the sharp green line of barium (5535), and no other lines which can certainly be ascribed to those metals in the elementary state, For higher temperatures tubes bored out in blocks of lime or of gas carbon, and heated by the electric arc, were used. By keeping up a supply of metal and in some eases assisting its volatilisation hy the admixture of a more volatile metal, such as magnesium, and its reduction by some easily oxidisable metal, such as aluminium, or by a current of coal gas or hydrogen, they succeeded in maintaining a stream of vapour through the tube so as to reverse a great many lines. In this way the greater part of the bright lines of the metals of the alkalies and alkaline earths were reversed, as well as some of the strongest lines of manganese, alu- minium, zinc, cadmium, silver, copper, bismuth, and the two characteristic lines of iridium and of gallium. By passing an iron wire into the are through a perforated carbon electrode they succeeded in obtaining the reversal of many of the lines of iron. In observing bright line spectra they have found that the are produced by a De Meritens machine arranged for high tension gives, in an atmosphere of hydrogen, the lines C and F, although the arc of a powerful Siemens machine does not bring them out, and they have observed many metallic lines in the are which had not been previously noticed. The temperature obtained by the De Meritens machine is thus higher than that obtained in the Siemens machine. From observations on weighed quantities of sodium, alone and as an amalgam, introduced into a hot bottle of platinum filled with nitrogen, of which the pressure was varied by an air-pump, they conclude that the width of the sodium lines depends rather on the thickness and temperature of the vapour than upon the whole quantity of sodium present. Very minute quantities diffused into the cool part of the tube give a broad diffuse absorption, while a thin layer of compressed vapour in the hot part of the tube give only narrow absorption lines. Professors ‘Liveing and Dewar have obseryed the reversal of some of the well-known bands of the oxides and chlorides of the alkaline earth metals. The lines produced by -magnesium in hydrogen form a rhythmical series extending all across the well- 456 REPORT—1880. known B group, having a close resemblance in general character to the series of lines produced by an electric discharge in a vacuum tube of olefiant gas. The series appears at all temperatures except when a large condenser is em- ployed along with the induction coil, provided hydrogen is present as well as magnesium, while they disappear when hydrogen is excluded, and never appear in dry nitrogen or carbonic oxide. ‘ From their experiments on carbon spectra they conclude with Angstrom and Thalén that certain of the so-called ‘ carbon bands’ are due to some compound of carbon with hydrogen, probably acetylene, and that certain others are due toa compound of carbon with nitrogen, probably cyanogen. They describe some ultra-violet bands: one of them coincides with the shaded band P of the solar spectrum which accompanies the other violet bands in the flame of cyanogen as well as in the are and spark between carbon electrodes in the nitrogen, All the bands which they ascribe to a compound of carbon and nitrogen disappear when the discharge is taken in a non-nitrogenous gas, and they reappear on the introduction of a minute quantity of nitrogen. They appear in the flame of hydrocyanic acid, or of cyanogen, even when cooled down as much as possible as shown by Watts, or when raised to the highest temperature by burning the cyanogen in nitric oxide; but no flames appear to give these bands unless the burning substance contains nitrogen already united with carbon. As the views of Mr. Lockyer with regard to the multiple spectra of carbon have very recently appeared in the pages of ‘ Nature,’ I need only say that these spectra are looked upon as supporting his theory that the different flutings are truly due to carbon, and that they represent the vibrations of different molecular groupings. The matter is one of very great interest as regards the spectra of comets, for the bands ascribed to acetylene occur in the spectra of comets without the bands of nitrogen, showing that either hydro-carbons must exist ready formed in the comets, in which case the temperature need! not exceed that of an ordinary flame, or else nitrogen must be absent, as the temperature which would produce acetylene from its elements would also produce cyanogen, if nitrogen were present. Quite recently, Professors Liveing and Dewar have, simultaneously with Dr. Huggins, described an ultra-violet emission spectrum of water, and have given maps ‘of this spectrum. It is not a little remarkable that by independent methods these observers should have deduced the same numbers for the wave-lengths of the two strong lines at the most refrangible end of this spectrum. Great attention has been paid by M. Mascart and by M. Cornu to the ultra- violet end of the solar spectrum. M. Mascart was able to fix lines in the solar spectrum as far as the line R (3179), but was stopped by the faintness of the photographic impression. Professor Cornu has extended the spectrum still farther to the limit (2948), heyond which no further effect is produced, owing to complete absorption by the earth’s atmosphere. A quartz-reflecting prism was used instead of a heliostat. The curvature of the quartz lens was calculated so as to give mini- mum aberration for a large field of view. The Iceland spa prism was very care- fully cut. A lens of quartz was employed to focus the sun on the slit. Having photographed as far as possible by direct solar light, Professor Cornu compared the solar spectrum directly by means of a fluorescent eyepiece with the spectrum of iron, and then obtained, by photography, the exact positions of the iron lines which were coincident with observed lines in the solar spectrum. M. Cornu states that the dark absorption lines in the sun and the bright iron lines of the same refrangibility are of the same relative importance or intensity in their spectra, indi- cating the equality between the emissive and the absorbing powers of metallic vapours; and he thinks that we may get by the comparison of bright spectra with the sun some rough approximation to the quantity of metallic vapours present in the absorption layers of the sun’s atmosphere. He draws attention to the abun- dance of the magnetic metals—iron, nickel, and magnesium—and to the fact that these substances form the composition of most meteorites. M. Cornu has studied the extent of the ultra-violet end of the spectrum, and finds that it is more extended in winter than in summer, and that, at different elevations, the gain in length of the spectrum for increase of elevation is very slow, on account of atmospheric absorp- TRANSACTIONS OF SECTION A. 457 tion, so that we cannot hope greatly to extend the spectrum by taking elevated observing stations. The limit of the solar spectrum is reached very rapidly, and the spectrum is sharply and completely cut off at about the line U (wave-length 2948). From photographs taken at Viesch in the valley of the Rhone and at the Riffelberg, 1910 métres above it, M. Cornu finds the limits to be at wave-lengths 2950 and 2930 respectively. In the actual absorption of bright line spectra by the earth’s atmosphere, M. Cornu observed among others three bright lines of aluminium, which M. Soret calls 30, 31, and 32 (wave-lengths about 1988, 1930, and 1860), and he found that 32 could not be seen at the distance of 6 métres; but on using a collimator, and reducing the distance to 1} métres, the line 32 became visible, notwithstand- ing the absorption of the extra lens; at 1 métre, line 32 was brighter than 31, and at a quarter of a métre 32 was brighter than either 30 or 31. With a tube 4 métres in length between the collimator and prism ray 32 is not seen; but when the tube is exhausted, ray 31 gains in intensity and 32 comes into view, and gradually gets brighter than 31, whilst 30 changes very little during the exhaustion. With the same tube he found no appreciable difference between the absorption by air very carefully dried and by moist air, and concludes that this absorption is not due to the vapour of water, and it follows the law of pressure of the atmosphere which shows it to be due to the whole mass or thickness of the air. Also, M. Soret has shown that water acts very differently on the two ends of the spectrum, distilled water being perfectly transparent for the most refrangible rays, since a column of water of 116 cm. allowed the ray 2060 in the spectrum of zinc to pass through: on the other hand, water is so opaque to the ultra- red rays that a length of 1 cm. of it reduces the heat spectra of metals to half their length and one quarter of their intensity. In concluding my address, I wish to draw attention to some of those magnetic changes which are due to the action of the Sun, and which are probably brought about by means of the ether which conveys to us his radiant heat and light. In his discussion of the magnetic effects observed on the earth’s surface, General Sabine has shown the existence of diujnal variations due to the magnetic action of the sun; also the magnetic disturbances, aurora and earth currents, which are now again beginning to be large and frequent, have been set down to disturbances in the sun. Although iron, when raised to incandescence, has its power of attracting a magnet very greatly diminished, we have no proof that it has absolutely no mag- netic power left, and with a slight magnetic action the quantity of iron in the sun would be sufficient to account for the diurnal variations of the magnetic needle. During the last few weeks I have been engaged in examining the declination curyes for the month of March 1879, which have been kindly lent to the Kew Committee by the Directors of the Observatories of St. Petersburg, Vienna, Lisbon, Coimbra, and Stonyhurst. On comparing them with the Kew curves for the the same period, I find the most remarkable coincidences between the curves from these widely distant stations. It was previously known that there was a similarity between disturbances at different stations, and in one or two cases a comparison between Lisbon and Kew had been made many years ago by Senor Capello and Professor Balfour Stewart; but the actual photographic magnetic records from several stations have never heen previously collected, and so the opportunity for such comparisons had not arisen. Allow me to draw attention to a few of the more prominent features of these comparisons which I have made. On placing the declination curves over one another, I find that in many cases there is absolute agreement between them, so that the rate of change of magnetic disturbances at widely distant stations like Kew, Vienna, and St. Petersburg is precisely the same; also similar disturbances take place at different stations at the same absolute time. It may be stated generally, for large as well as small disturb- ances, that the east and west deflections of the declination needle take place at the same time and are of the same character at these widely distant stations. There are exceptions to this law. Some disturbances occur at one or two stations and are not perceived at another station. Many instances occur where, up to a 458 ; REPORT—1880. certain point of time, the disturbances at all the stations are precisely alike, but suddenly at one or two stations the disturbance changes its character: for instance, on comparing Kew and St. Petersburg, we get perfect similarity followed by de- flections of the needle opposite ways at the same instant, and in some such cases the maxima in opposite directions are reached at the same instant, showing that the opposite deflections are produced by the same cause, and that the immediate cause or medium of disturbance in such a case is not far off; probably it is some change of direction or intensity of the earth’s magnetism arising from solar action upon it. Generally, after an hour or two, these differences in the effects of the disturbance vanish, and the disturbances again become alike and simultaneous. In such cases of difference, if the curve-tracing of the horizontal or the vertical force be examined, it is generally found that, at the instant when these opposite movements begin there is an increase or a diminution in the horizontal force, and that the horizontal force continues to change as long as there is any difference in the character of the declination curves. It is clear, then, from these effects that the cause or causes of magnetic disturbances are in general far distant from the earth’s surface, even when those disturbances are large; but that not unfrequently these causes act on magnetic matter nearer to the surface of the earth, and therefore at times between two places of observation, and nearer to one than another, thus producing opposite effects on the declination needle at those places; in such cases, the differences are probably due to changes in the earth’s magnetic force. Now, if we imagine the masses of iron, nickel, and magnesium in the sun to retain even a slight degree of magnetic power in their gaseous state—and we know from the researches of Faraday that gases. are some of them magnetic—we have a sufficient cause for all our terrestrial magnetic changes, for we know that these masses of metal are eyer boiling up from the lower and hotter levels of the sun’s atmosphere to the cooler upper regions,where they must again form clouds to throw out their light and heat, and to absorb the light and heat coming from the hotter lower regions ; then they become condensed and are drawn again back towards the hody of the sun, so forming those remarkable dark spaces or sun-spots by their downrush to- wards the lower levels. In these vast changes, which we know from the science of energy must be taking place, but of the vastness of which we can have no conception, we have abundant cause for those magnetic changes which we observe at the same instant at distant points on the surface of the earth, and the same cause acting by induc- tion on the magnetic matter within and on the earth may well produce changes in the magnitude or in the direction of its total magnetic force. These magnetic changes on the earth will influence the declination needles at different places, and will cause them to be deflected; the direction of the deflection must depend on the situation of the earth’s magnetic axis or the direction of its motion with regard to the stations where the observations are made. Thus both directly and indi- rectly we may find in the Sun not only the cause of diurnal magnetic. variations, but also the cause of these remarkable magnetic changes and disturbances over the surface of the Earth. The following Reports and Papers were read :— l. Report of the Committee for the Measurement of the Lunar Disturbance of Gravity.—See Reports, p. 25. 2. Report of the Committee upon the present state of our Knowledge of Spec- trum Analysis. (Influence of Temperature and Pressure ow the Spectra of Gases.)—See Reports, p. 258. TRANSACTIONS OF SECTION A. 459 8. On determining the Heights and Distances of Clouds by their reflexions in a low pool of water, and in a mercurial horizon. By Francis Gatton, M.A., IRS. The calm surface of a sheet of water may be made to serve the purpose of a huge. mirror in a gigantic vertical range-finder, whereby a sufficiently large parallax may be obtained for the effective measurement of clouds. The observation of the heights and thicknesses of the different strata of clouds, and of their rates of movement, is at the present time perhaps the most promising, as it is the least explored branch of meteorology. As there are comparatively few places in England where the two conditions are found of a pool of water well screened from wind, and of a station situated many feet in height above it, the author hopes by the publication of this memoir to induce some qualified persons who have access to fayourable stations, to interest themselves in the subject, and to make observations. The necessary angles may be obtained with a sextant and mercurial horizon, but itis convenient, for reasons shortly to be explained, to have in addition a tripod stand, with a bar of wood across its top to support the mercurial trough, and some simple instrument for the rapid and rough measurement of altitudes. I have used the little pocket instrument sold by Casella, of Holborn Bars, London, called a ‘pocket alt-azimuth, and have employed Captain George’s mercurial horizon on account of its steadiness and ease in manipulation. The observer has to determine :— 1. The difference of level in feet between the mercury and tke pool of water (call it d). 2. The angle between the reflexions of a part of a cloud in the mercury and in the pool (call itp). This should be carefully measured. 3. The angle between the portion of the cloud and its reflexion in the mercury (call it 2a). This may he roughly measured ; its altitude a may most conveniently be taken at once by the pocket alt-azimuth or other instrument. The subjoined tables will then give the required result with creat ease. If p be not greater than 3°, and if 2 be the number of minutes of a degree in p, the error occasioned by writing n sin 1’ for sin n’, will never exceed six inches in a thousand feet, and may be disregarded. Other errors of similar unimportance, due to the eye not being close to the mercury, may also ke ignored. Under these conditions, since log. sin. 1’ = 646373, it can be easily shown that distance of cloud = x 6875°5 cos (a +p). u vertical height of cloud = distance x sin a. The following table has been calculated for these values when Dove 1. To use n it, multiply the tabular numbers by d (the difference.in feet between the level of ‘the mercury and that of the pool) and divide by (the number of minutes of a degree in the angle between the reflexion in the mercury and that in the pool). The result will be the distance, or height, as required in feet. TaBxe for calculating distances and height of clouds by their reflexions from a mercurial horizon, and from a pool of water at a lower level. a= Altitude of cloud, (being half the sextant angle between the cloud and its reflexion as seen in the mercury, not pool). p= Angle between the reflexion of the cloud in the mercury and that in the pool. d=Vertical height of mercury above fool. n= Number of minutes of a degree in the angle p. Then the distances and heights of clouds = tabular numbers x “ n 460 REPORT—1880. ; Vertical Height of Cloud above Observer Distance we — nop n=60 n=120 ‘| n=180 Observer 1 (orp=0°) | (orp=1°) | (orp=2°) | (orp=8°) 10° 6771 1176 1059 942 825 15° 6641 1719 1607 1494 1381 20° 6461 2210 2103 1997 1889 25° 6231 2633 2534 2435 2334 30° 5954 2977 2886 | 2795 2703 35° . 5632 3230 3149 3067 2985 40° 5267 3386 3314 3243 3170 45° 4862 3438 3377, «|. B8iG 3253 50° 4419 3386 3335 | 3284 3232 55° 3o44 3230 arog. 77 66 10 90 53 65 35 40 83 64 59 45 11 73 #47 75 45 53 68 62 44 173: 12. 68 40 50 44 52 52 47 11 Dec. 29, 1817. 7. Sur la Calculation des Phénoménes périodiques. Par le Professeur RAGONA. L’auteur fait connaitre un perfectionnement qu'il a introduit dans l’usage de la formule de Bessel, c’est-a-dire de la formule des phénoménes périodiques. I] con- siste 4 établir le schema des valeurs calculées par la formule, jusqu’aux secondes différences, et 4 trouver les instants dans lesquels les secondes différences changent de signe. La demi-somme de deux de ces instants successives, donne un maximum en passant d’un changement de + @ — d’un changement de — @ +. Elle donne un minimum en passant d’un changement de — @ +, 4 un changement de + @--. Si on fait usage d’un nombre d’observations pas suffisamment étendues, ou d’ob- servations exécutées dans une époque de disturbations atmosphériques, la formule donne toujours des résultats qui sont plus proches a expression de la véritable loi de phénoméne, si les maximum et les minimum sont déduits par la méthode que Vauteur a proposé, et qu'il appelle méthode des znflexions. L’auteur a plusieurs fois traité, @ priori et a posteriori, de Yutilité de la méthode des inflexions. Une de ces démonstrations est relative 4 la vitesse du vent. La loi annuelle de cette vitesse est exactement connue 4 Modéne. Dans le cours de Vannée se développent trois maximum et trois minimum, qui correspondent inverse- ment au trois maximum et trois minimum que manifeste la pression barométrique dans la période annuelle. En faisant usage d’une série de 12 années de bons obser- vations auteur a établi deux formules, la premiére sur 6 années et la seconde sur tous les 12 années. La derniére donne exactement les trois maz. et trois min. annuels, tandis que la premiére donne, et d’une maniére trés-imparfaite, seulement deux max. et deux min. Mais si dans la premiére pn fait usage de la méthode des inflexions, on obtient d’elle avec beaucoup d’exactitude la véritable distribution des max. et des min. de la vitesse du vent. + : TRANSACTIONS OF SECTION A. 467 L’auteur expose 4 la section un autre exemple de J’utilité de la méthode qu'il @ proposé. Le prof. Mascart, a derniérement publié 4 Paris les résultats d’une série d’observations sur l’électricité atmosphérique. La loi moyenne diurne de I’électricité atmosphérique est bien connue 4 Modéne. II s’agit de deux maa. et deux min. qui correspondent & peu prés aux heures critiques barométriques. M. Mascart dit que ses observations ont été exécutées dans une époque de fortes perturbations atmosphériques. Calculant les observations de M. Mascart par la formule de Bessel, auteur a obtenu seulement un maz. et un mzn., mais en faisant usage de la méthode des inflexions, a obtenu exactement le deux maz. et les deux min. diurnes de ]’électricité atmosphérique. L’auteur donne notice d'une série d’observations qu'il a exécutées sur la période diurne de l’électricité atmosphérique. Ila obtenu les deux maw. et les deux min. presque en coincidence avec les valeurs déduits des observations de M. Mascart par la méthode des inflevions, ce qui est remarquable & cause de la différence des Tieux et des 6poques. Il fait noter qu'il s’agit toujours de la marche diurne de Vélectricité positive, parce que l’auteur a, comme M. Mascart, eliminé tous les jours delectricite négative. L’auteur fait connaitre aussi un résultat digne d’attention de ses observations sur la période diurne de I’électricité dynamique, c’est-d-dire des courants qui montent ou descendent dans les hautes édifices. Sur la tour de l’'Observatoire de Modéne il a placé un excellent galvanométre, dont les deux poles étaient en communication un ayec le terrain et l’autre avec le toit de la tour. En considérant seulement Vintensité du courant ascendant, il a trouvé que son période diurne est exactement inverse de celui de l’électricité atmosphérique ; c’est-d-dire que les max’. d’intensité du courant ascendant correspondent aux min. d’intensité de l’électricité libre positive de l’atmosphére, et inversement. 8. On the Laws of the Change of Speed and Direction of the Wind. By Professor Racona. FRIDAY, AUGUST 27. The following Reports and Papers were read :— 1. Report of the Committee on Underground Temperature. See Reports, p. 26. 2. Report of the Committee appointed to devise and construct an improved form of High Insulation Key for Electrometer Work. See Reports, p. 29. 3. Comparison of Ourves of the Declination Magnetographs at Kew, Stony- hurst, Coimbra, Lisbon, Vienna, and St. Petersburg. By Professor W. Grytis Apams, M.A., F.R.S.—See Reports, p. 201. 4, On the best form of Magnet for Magneto-electric Machines. By W. Uavp, F.R.A.S. At the British Association Meeting at Dundee, in 1867, I made some remarks upon different forms of magnet, and exhibited diagrams, showing by the ‘lines HH 2 468 REPORT—1880. of force ’—naturally arranged—the great superiority of the circular magnet, where an armature is to be employed. Since that time some thousands of that form of magnet have been made for medical, mining, and other purposes. Some months ago, when in conversation with M. Breguet of Paris, I showed him these same diagrams, and he was very much impressed with their importance. He has since then constructed a machine, using the Gramme armature; and witha smaller quantity of steel in the magnets he has made a far more powerful machine than hitherto constructed with either the Jamin or the ordinary horse-shoe form. It is also more symmetrical in appearance and occupies less space. With this machine I can heat to incandescence 19 inches of platinum wire by four turns of the handle; while to heat 14 inches of the same sized wire by a machine haying a Jamin magnet took ten turns of the handle. 5. An Account of some Experiments in Photo-electricity. By G. M. Mincuin, M.A. The two objects aimed at primarily in photo-electricity are— (a) the production, at a distance, of effects due, in the first instance, to the photographic action of light ; (6) the continuous daily registration of the intensity of sunlight of any selected wave-length. The first of these is the problem of constructing what the author has called the Telephotograph, and some of the fundamental conditions of success have been attained. The second problem will, in all probability, soon attain a satisfactory solution, much progress having been already made towards it. The author investigated, in the first instance, the photo-electric currents pro- duced by the action of light on silver plates, coated with the ordinary emulsions Ee silver salts in use among photographers—viz., the chloride, bromide, and iodide of silver. In a cell containing tap water (or slightly acidulated water, or distilled water with a few grains of common salt), if a chloride plate is immersed in presence of an uncoated plate, the current runs from the latter to the former in the cell. The same is the direction of the current when the chloride is replaced by a bromide plate. . But if the sensitised plate is an iodide plate (the conducting liquid being dis- tilled water with a few grains of iodide of potassium), the direction of the current is reversed. In carrying out an idea about phosphorescence as a photo-electric source, it appeared to be of importance to study sulphide of silver. If any emulsion of this salt is made with collodion, and a silver-plate sensitised with it be immersed, as above, ina glass cell, the direction of the current given by magnesium light (or sunlight), agrees with that of the iodide plate; and by passing the light incident on the plate through coloured glasses, it will be found that the red and the blue rays give strong results in the same direction, while the green light gives a com- paratively trifling action. For this salt there is therefore a point of minimum sensibility in the middle of the spectrum. A silver plate coated with nitrate of silver (shaken up in a test-tube with thin photographic gelatine), gave with blue rays a strong current in the iodide and sulphide direction; and with red rays a very small result in the opposite direction, though whether this latter result is due to the action of the red rays on the emulsion or on the plate itself is not certain. . It was found in several of these experiments that the observation of Grove to the effect that light sets up a current in the direction of some previously existing current, being incapable of setting up one of its own, was not confirmed. The experiments of Grove which gave rise to this statement are referred to, From TRANSACTIONS. OF SECTION A. 469 even a purely logical consideration we might conclude that his statement cannot be accepted. The photographic effect of a current which is passed through a sensitised plate is a point of fundamental importance. By placing two plates, each coated with Liverpool Emulsion, in a cell containing distilled water and a few grains of bromide of potassium, and putting this cell into the circuit of a bichromate cell for a few seconds, it will be found that— (a) the plate connected with the carbon pole is, without the employment of a developer, visibly blackened in its immersed portion ; (b) no visible change comes on the other plate ; but when this plate is developed by pyrogallic acid, its immersed portion also becomes dark. This fundamental result was also obtained (though in a less marked degree) by the action of a photo-electric cell, instead of the bichromate cell. To produce the effect with greater ease in this case, expose the two bromide plates to gas-light for about ten seconds before immersion. The localisation of the effect on the plate through which the current passed was further shown by placing several silver strips on the same plate of glass, coating all of them with a layer of Liverpool Emulsion, and throwing some of them out of the circuit of the current. Only those in circuit exhibit the photographic effect. Assuming that fluorescence ought to operate a change of luminous energy into that of an electric current, the author next replaced the silver salts by fluorescent substances. LHosine gave the best results, but it is very easily soluble and it leaves the plate rapidly. A very permanent eosine plate was obtained by making a mixture of eosine solution and thin gelatine, pouring this over the plate, and then pouring a layer of collodion over it. This was exceedingly sensitive to even dull sunlight, and when connected with a galvanometer, indicated the faintest change in the light which it received. As a perfect photometer it has a drawback. When the light is suddenly shut off, the spot on the scale does not immediately return to zero. It was found that this irregularity was due (partly at least) to the action of light on collodion, and this latter was specially examined. A less sensitive, but more regular, plate was made by mixing eosine with thin gelatine and rendering the layer insoluble by immersion in alum solution. Naphthalene red gives also yery good results, and comes near satisfying the requirements of a perfect photometer for continuous registration. Strong light gives opposite results by the action of red and blue rays. Iodine-green—an aniline dye—gives very strong currents, in the direction opposed to that of the current given by an emulsion of iodide of silver—a result for which a theoretical reason may be given. The E.M.F. of this cell for strong but oblique sunlight was in one experiment found to rise so high as 3th of a Daniell. To prevent the solubility of several of the substances employed, mordants— such as chloride of aluminium and borax—were employed ; but though the layers on the plates were rendered insoluble, their sensitiveness to light was almost destroyed. A very curious case of inverse currents presented itself. Two clean silver pe were immersed in a glass cell containing a solution of eosine. When light ell on one plate a current was suddenly set up in the direction opposite that given by a plate coated with eosine and immersed in water. This was a small jerky current, lasting for a second or so, and it was immediately succeeded by a_ large current in the opposite direction which varied with the light intensity. When the light was suddenly shut off a further jerk in the latter direction took place, and then the spot moved towards its zero position. The two plates having been then left immersed in the cell for a fortnight>were again used in the same manner and it was found that the jerk had enormously increased ; but, although the light was kept up, the spot steadily came back and moved in its normal direction beyond its zero position—far beyond it if the light was strong, such as that of a candle at a distance of three or four inches. These contrary currents appear to the author to point to a mechanical action of light on the eosine in solution, as distinct from the chemical action set up between the eosine layer and the silver plate in contact 470 REPORT—1 880. with it. The immersed plates become each coated with a layer of a darkish appear- ance (eoside of silver ?), and this layer will give a current in the same direction as that given by a silver plate coated in the old way with any emulsion of eosine. Platinum plates always give in these experiments much smaller results than silver plates; but this fact may be due to the circumstance that, with the substances: employed, silver may be a better vehicle for the transference of the energy than platinum—apart from the consideration of chemical action. Several other substances, such as fluorescine, fuchsine, sulphate of quinine, &c. were used, the results being less marked. Phosphorescence was studied by coating a platinum plate with a mixture of gelatine and sulphide of calcium, and currents were produced by the action of magnesium light. Experiments of the class last referred to are in progress. 6. Electric Convection-Currents. By Stryanus P. Taompson, D.Sc., B.A.,. Professor of Experimental Physics in University College, Bristol. In a paper ‘On the Action of Magnets on Mobile Conductors of Currents,’ read before this Section a year ago, the author discussed a number of cases of the flow of electricity across a magnetic field. These included cases of true metallic con- duction, of electrolytic conduction, and of those less-understood Jinds of conduc- tivity which occur in the voltaic are, in the discharges in rarefied media, and in the luminous brush-charge at a point. For the case of convection of electricity, either automatically, by self-repulsion between electrified particles of a gas, or mechanically, the electro-magnetic effect is identical with that of a current in which the same quantity of electricity would be transferred in the same time; the ‘ rate of convection ’ “2 being in these cases the equivalent of ‘the strength of the current.’ Maxwell's theory (vol. ii. art. 768) concerning the virtual identity of a current sheet and of an electrified sheet moving in its own plane with a velocity equal to ‘y,’ may be extended to the case of linear currents. The identity may be generalised to all cases of convection-currents. Last year the author predicted that the brush discharge at a point would experience a spiral twist when taking place in the magnetic field. He has since found this to be experimentally the case. The author also pointed out the similarity between the magnetic distortion found by Reitlinger and Wichter in electric ring-figures, and that found by himself to be produced by the presence of a magnet on Nobili’s figures. He also referred to Maxwell’s theory as explaining some of the phenomena observed in the exhausted tubes of Mr. Crookes, in which the discharges from the negative electrode behave like convection-currents haying a velocity less than the velocity of light. 7. On a peculiar behaviour of Copper. By Witu1AM Henry PREECE. From some experiments made in Dr. Warren De La Rue’s laboratory it appeared that in some cases copper wires did not acquire their normal resistance until currents of electricity had passed through them. In several instances the resistance of virgin copper was far higher than it was after electricity had passed through. —_—_— 8. On the proper form of Lightning Conductors. By Wii1AM Henry PREECE. The question of the relative value of surface and sectional area in lightning- conductors never having been satisfactorily solved experimentally, the author, with the aid of Dr. De La Rue’s gigantic battery, endeayoured to do so. He obtained wire tubes and ribbons of copper and lead of similar lengths and weight, and TRANSACTIONS OF SECTION A. 471 passed very powerful charges of electricity through them, observing their thermic effects upon platinum and silver wires. It was found that change of form pro- duced no difference whatever in the character of the discharge, and it was proved that the discharges of electricity of high potential obey the laws of Ohm. No more efficient lightning conductor can be devised than a cylindrical rod or a wire rope. 9. On the necessity for a regular Inspection of Lightning Conductors. By Ricwarp Anperson, £.0.8., A. Inst.C.E. The author referred to a paper by M. W. de Fonvielle, ‘On the advantage of keeping records of Physical Phenomena connected with Thunderstorms, read before this Association in 1872. M. de Fonvielle recommended to the attention of the members the steps which had been taken by the French Government for obtaining information regarding thunderstorms, and suggested that the Association should institute some organisation for the collection of such data; arguing that it would be of much value to science, as well as to the public. Nothing, however, has been done by the Association since 1872; and the author not only confirmed the conclusions at which M. de Fonvielle arrived as to the desirability of collecting such data, but was of opinion that the organisation should go further, and arrange for a regular inspection of all public buildings which had lightning-conductors applied. PP the necessity for this he demonstrated by adducing a number of striking cases where damage, more or less severe, had occurred to buildings, even though having lightning conductors attached to them. The cases.now cited, he explained, were supplementary to those communicated in his paper on a similar subject to the Association in 1878. A few of the cases were as follows :— In October, 1878, an elevated building situated at the back of Victona Station, occupied as a furniture repository, was struck by lightning and sustained damage, although furnished with a 3-inch by }-inch copper-band lightning conductor and a tube of §-inch diameter rising above the iron crestings on tower. The lightning shattered the cresting and bent the point of the lightning-rod, besides doing other damage to the building. On testing, the author found the resistance very great, and on opening out the earth-terminal found it embedded in concrete. In June last St. Mark’s Church, Skelton, was struck by lightning, when the air-terminal of a §-inch diameter copper-rope conductor was slightly bent. On testing, the author found the resistance great, and on opening the ground, the conductor was found to be carried from the building about 14 feet and buried among brick and stone rubbish. The conductivity of the copper was 52°50 instead of 92 to 94 per cent. On June 26 last lightning struck All Saints’ Church, Lambeth, doing con- siderable damage, although there was a 32-inch diameter copper-rope conductor on the west gable, with a copper tube rising 18 inches above. A stone cross about 50 feet from the conductor was thrown down, injuring the roof of the north aisle. On testing the conductor, the author found that it had no ‘earth’ whatever, the rope being simply placed in 2 inches of loose rubbish. The copper was of very inferior quality ; conductivity being 32°10 per cent., or about double that of iron. The author quoted also a few cases from his recent work on ‘ Lightning Con- ductors, their History, &c.’ :— In August, 1878, the Powder Magazine at Victoria Colliery, Burntcliffe, York- shire, was struck by lightning, though furnished with a conductor 13 feet above the building and terminating in 13 feet of clayey soil. The building was blown to pieces. On testing the conductivity of the copper it was found to be 39:2, instead of 92 to 94 per cent. The conductor was insulated from the building and from a large iron door, which it ought not to have been. The author concludes from this evidence that it is not sufficient merely that rods of copper should be attached to a building, but it is necessary that after being fixed they should be regularly inspected, to see if they are in good order, so as to be really efficacious, 472 REPORT—1880. 10, Note on the Theory of the Induction Balance. By Lorv Rayusren, F.R.S., Professor of Experimental Physics in the University of Cambridge. This subject has been treated by Dr. Lodge in the ‘ Phil. Mag.’ for February, 1880, who has arrived at several interesting results. The investigation may be considerably simplified by taking the case of pure tones, as is usual in acoustics. We may also suppose, for distinctness of conception, that the current in the primary circuit (v,) is sensibly unaffected by the reaction of derived currents, though our results will be independent of this hypothesis. If x, ,....be the currents, #, R,... the resistances, M,, M,, M,,..... the coefficients of self-induction, and of mutual induction, the equations for three circuits are Me Ota M. dis Jitsu aaah 4 M dx, dt *8 dt “dt di. da. i dx My, cia + M;, ai ce R, vs = SS M,; dt We now assume that 7, v7,.... are proportional to e”’, where n+27 is the frequency of vibration. Thus:— in (IM, x, + M,, 25) + Ry 2, = —m M,, x, in (M,, t, + Mj,x,) + R, x,= — mM, 2, whence by elimination of 2’, < M?,., v7 . 1? MG Magi 4 in M,, + R, + ——™"__ > = -im M,, 2, — ——8— 841 J in M,, + R, in M,, + Rs From this it appears that a want of balance depending on M,, cannot compen- sate for the action of the tertiary circuit, so as to produce silence in the secondary (telephone) circuit, unless R, be negligible in comparison with x M,,, that is unless the time-constant of the tertiary circuit be very great in comparison with the period of the vibration. Otherwise the effects are of different phases, and therefore in- capable of balancing. We will now introduce a fourth circuit, and suppose that the primary and secondary circuits are accurately conjugate, so that M,,=0, and also that the mutual induction between the third and fourth circuits (M,,) may be neelected. Thus mM (Mogg Xo + Mog Xz, + My, x) + Ry 2%, =0 . nr (Mg ty + Mgz 3) + Ry x, = — in M,, 2, in (Myy 2, + My, v,) + Ry t= —m M,, 2, y(t n*? M*,. n* M*,, ) rain aE as ealgece wk hae STE =~? 2, (Mg Mas Mig Mas) *\in Ma, + R, mM,,+ R, Two conditions must be satisfied to secure a balance, since both the phases and the intensities of the separate effects must be the same. The first condition requires that the time-constants of the third and fourth circuits he equal, unless both be either very great or very small in comparison with the period. If this condition be satisfied, a balance may be obtained by shifting the circuits so as to bring M,, M,, into equality with M,, M,,. For a coil of mean radius a, and radius of section equal to a+ 3:22, the coefficient of self-induction (Z) is * 12 7 n? a, n being the number of turns. Also, if » be the specific resistance, whence Qmna ,,_ 2 (3:22)? n? r wd a * Maxwell, Electricity and Magnetism, § 707. TRANSACTIONS OF SECTION A. 473 For copper 7 = 1640, so that peo eit ails, the C, G. S. system. R 1810 In the case of a shilling the time-constant can scarcely be so high as a ten- thousandth of a second, but periods smaller than this may be concerned when a microphone clock is employed. For similar discs or coins the time-constant varies as a® r—1, a being the linear dimension and r the specific resistance. Equal coins cannot in general be balanced if the specific resistances are different. To obtain a balance, a* should vary as ». In this case M,, M, ; a : a . —_18__28 __ varies as 1 Varles a8 — varies as a, m M,,+R r a~ r on the supposition that the positions of the coins relatively to the primary and secondary coils are the same. A perfect balance is not to be expected in general without two adjustments, though in some cases a fair approximation may be obtained with the sliding wedge employed by Hughes. If the condition of equality of time-constants be satisfied, the remaining condition is independent of the value of n, so that a perfect balance for one pitch secures a perfect balance for all pitches. From this it follows that the results are not limited to simple tones, and that the two conditions are sufficient to secure a balance in all cases. It should be remembered, however, that this indifference to pitch does not apply to approximate balances, which may be satisfactory with one sound, but quite inadequate when another is substituted. SATURDAY, AUGUST 28. The following Reports and Papers were read :— 1, Report of the Committee on Mathematical Tables. See Reports, p. 30. 2. Report of the Committee appointed to calculate Tables of the Funda- mental Invariants of Algebraic Forms.—See Reports, p. 38. 3. Report on the present state of knowledge of the application of Quadratures and Interpolations to Actual Data. By C. W. Murnririexp, F.R.S. See Reports, p. 321. 4, On Maximum and Minimum Energy in Vortex Motion. By Professor Sir Witt1am Tuomson, M.A., F.B.S. I. A finite volume of incompressible inviscid fluid being given, in motion, filling a fixed, simply continuous, rigid boundary, the fact of its being in motion implies molecular rotation, or (as it may he called for brevity) vorticity. ‘Helmholtz’s law of conservation of vorticity shows that, whether the boundary be kept fixed as given, or be moved or deformed in any way, and brought back to its given shape and position, there remains in every portion of the fluid which had molecular rotation a definite constant of vorticity ; and his formula for calculating energy for ‘any given distribution of vorticity allows us to see that the energy may be varied ‘hy the supposed operation on the boundary. 474 REPORT—1880. II. The condition for steady motion of an incompressible inviscid fluid filling a finite fixed portion of space (that is to say, motion in which the velocity and direc- tion of motion continue unchanged at every point of the space within which the fluid is placed) is that, with given vorticity, the energy is a thorough maximum, or a thorough minimum, or a minimax. The farther condition of stability is secured by the consideration of energy alone for any case of steady motion, for which the energy is a thorough maximum or a thorough minimum ; because when the boun- dary is held fixed the energy is of necessity constant. But the mere consideration of energy does not decide the question of stability for any case of steady motion in which the energy is a minimax, III. It is clear that, commencing with any given motion, the energy may be increased indefinitely by properly-designed operation on the boundary (understood that the primitive boundary is returned to). Hence, with given vorticity, there is no thorough maximum of energy in any case. There may also be complete annul- ment of the energy by operation on the boundary (with return to the primitive boundary), as we see by the following illustrations :— 1, The case of two equal, parallel, and oppositely rotating vortex columns terminated perpendicularly by two fixed parallel planes, which, by proper operation on the boundary, may be so mixed (like two eggs ‘whipped’ together) that, in- finitely near to any portion of either, there shall be some of the other. 2. The case of a single Helmholtz ring, reduced by diminution of its aperture to an infinitely long tube coiled within the enclosure. 3. The case of a single vortex column, with two ends on the boundary, bent till its middle meets the boundary; and farther bent and extended, till it is broken into two equal and opposite vortex columns; and then farther dealt with till these two are whipped together to mutual annihilation. IV. To avoid for the present the extremely difficult general question illustrated (or suggested) by the consideration of such cases, confine ourselves now to two- dimensional motions in a space bounded by two fixed parallel planes and a closed cylindric surface perpendicular to them, subjected to changes of figure (but always truly cylindric and perpendicular to the planes). It is obvious that, with the limitation to two-dimensional motion, the energy cannot be either infinitely small or infinitely great with any given vorticity and given cylindric figure. Hence, under the given conditions, there certainly are at least two stable steady motions. We shall, however, see farther (XI. below) that possibly in every case, except cases of a narrow, well-defined character, and certainly in many cases, there is an infinite number of stable steady motions. V. In the present case, clearly, though there are an infinite number of unstable steady motions, there are only two stable steady motions—those of absolute maxi- mum and of absolute minimum energy. VI. In every steady motion, when the boundary is circular, the stream lines are concentric circles, and the fluid is distributed in co-axial cylindric layers of equal vorticity, In the stable motion of maximum energy, the vorticity ‘is greatest at the axis of the cylinder, and is less and less outwards to the circumfer- ence. In the stable motion of minimum energy the vorticity is smallest at the axis, and greater and greater outwards to the circumference. To express the con- ditions symbolically, let 7’ be the velocity of the fluid at distance » from the axis (understood that the direction of the motion is perpendicular to the direction of 7) ; the vorticity at distance 7 is— (2422), yr dr If the value of this expression diminishes from 7 = 0 to r = a, the motion is stable, and of maximum energy. If it increases from 7 = 0 to 7 = a the motion is stable and of minimum energy. If it increases and diminishes, or diminishes and in- creases, as 7 increases continuously, the motion is unstable. VII. As a simplest subcase, let the vorticity be uniform through a given por- tion of the whole fluid, and zero through the remainder. In the stable motion of greatest energy, the portion of fluid haying vorticity will be in the shape of a circular TRANSACTIONS OF SECTION A. 475 cylinder rotating like a solid round its own axis, coinciding with the axis of the enclosure ; and the remainder of the fluid will revolve irrotationally around it, so as to fulfil the condition of no finite slip at the cylindrical interface between the rotational and irrotational portions of the fluid. The expression for this motion in symbols is T=Cr fromr =O0tor = 0b; 2 and T=“ from r = b tor = a. VIII. In the stable motion of minimum energy the rotational portion of the fluid is in the shape of a cylindric shell, inclosing the irrotational remainder, which in this case is at rest. The symbolical expression for this motion is T = 0, when r < ,/ (a? — 6°) and T=¢(r-*=*), when r > / (a? — 6°). IX. Let now the liquid be given in the configuration VII. of greatest energy, and let the cylindrical boundary be a sheet of a real elastic solid, such as sheet-metal with the kind of dereliction from perfectness of elasticity which real elastic solids present; that is to say, let its shape when at rest be a function of the stress applied to it, but let there be a resistance to change of shape depending on the velocity of the change. Let the unstressed shape be truly circular, and let it be capable of slight deformations from the circular figure in cross section, but let it always re- main truly cylindrical. Let now the cylindric boundary be slighly deformed and left to itself, and held so as to prevent it from being carried round by the fluid. The central yortex column is set into vibration in such a manner that longer and shorter wayes travel round it with less and greater angular yelocity.* These waves cause corresponding waves of corrugation to travel round the cylindric bounding sheet, by which energy is consumed, and moment of momentum taken out of the fluid. Let this process go on until a certain quantity of moment of momentum has been stopped from the fluid, and now let the canister run round freely in space, and, for simplicity, suppose its material to be devoid of inertia. The whole moment of momentum is initially n CB? (a?—4 0); 7 CB? (@?-$0*)—M, and continues constantly of this amount as long as the boundary is left free in space. The consumption of energy still goes on, and the way in which it goes on is this: the waves of shorter length are indefinitely multiplied and exalted till their crests run out into fine laminz of liquid, and those of greater length are abated. Thus a certain portion of the irrotationally revolving water becomes mingled with the cen- tral vortex column. The process goes on until what may be called a vortex sponge is formed ; a mixture homogeneous on a large scale, but consisting of portions of rotational and irrotational fluid, more and more finely mixed together as time ad- vances, The mixture is, as indicated above, altogether analogous to the mixture of the substances of two eges whipped together in the well-known culinary operation. Let 5’ be the radius of the cylindric vortex sponge, b being as before the radius of the original vortex column M Cb" It is now $07 =30? + X. Once more, hold the cylindric case from going round in space, and continue holding it until some more moment of momentum is stopped from the fluid. Then leave it to itself again. The vortex sponge will swell by the mingling with it of an additional portion of irrotational liquid. Continue this process until the sponge occupies the whole enclosure. * See Proceedings of the Royal Society of Edinburgh for 1880, or Philosophical Maga- vine for 1880: ‘ Vibrations of a Columnar Vortex:’ Wm. Thomson, 476 REPORT—1880. After that continue the process further, and the result will be that each time the containing canister is allowed to go round freely in space, the fluid will tend to a condition in which a certain portion of the original vortex core gets filtered into a position next to the boundary, and the fluid within it tends to a more and more nearly uniform mixture of vortex with irrotational fluid. This central vortex-sponge, on repetition of the process of preventing the canister from going round, and again leaving it free to go round, becomes more and more nearly irrotational fluid, and the outer belt of pure vortex becomes thicker and thicker. ‘The final condition towards which the whole tends is a belt constituted of the original vortex core now next the boundary; and the fluid which originally revolved irrotationally round it now placed at rest within it, being the condition (VIII. above) of absolute minimum energy. Begin once more with the condition (VII. above) of absolute maximum energy, and leave the fluid to itself, whether with the canister free to go round sometimes, or always held fixed, provided only it is ultimately held from going round in space ; the ultimate condition is always the same, viz., the condition ( VIII.) of absolute minimum energy. XJ. That there may be an infinite number of configurations of stable motions, each of them having the energy of a thorough minimum as said in IV. above, we see, by considering the case in which the cylindric boundary of the containing can- ister consists of two wide portions communicating by a narrow passage, as shown in the sketch. Ifsuch a canister be completely filled with irrotationally moving fluid of uniform vorticity, the stream lines must be something like those indicated in the sketch, Hence if a small portion of the whole fluid is irrotational, it is clear that there may be a minimum energy, and therefore a stable configuration of motion, with the whole of this in one of the wide parts of the canister; or the whole in the other ; or any proportion in one and the rest in the other; or a small portion in the elliptic whirl in the connecting canal, and the rest divided in any proportion between the two wide parts of the canister. 5. On Inverse Figures in Geometry. By Professor H. J. S. Suita, M.A., F.B.S.. 6. On a Mathematical Solution of a Logical Problem. By Professor H. J. 8. Surrs, M.A., F.R.S. 7. On the Distribution of Circles on a Sphere. By Professor H. J. 8. Suirn, M.A., F.R.S. 8. Notes on Non-Euclidian Geometry. By Rosert S. Bau, LL.D., F.R.S. The problem I propose to consider relates to the kinematics of a rigid body in non-Euclidian space. I can hardly say that the communication is exactly novel, as TRANSACTIONS OF SECTION A. 477 the same problem has been considered by Lindemann. I think, however, that a purely geometrical method of looking at the question may be of interest. The most general displacement of a rigid body is a rotation about an axis combined with a rotation about the polar axis with regard to the absolute. These two rotations form the unit of displacement. My problem is the determination of the single unit of displacement, which is equivalent to the joint effect of two displacements, all being small. This, it will be observed, includes every problem of the composition of forces or rotations in non-Huclidian space. Each of the component units involves a pair of conjugate polars, A,A’ and B,B’, and we require to find a pair of conjugate polars 0,0’ the rotations around which shall be equivalent to the given rotations about A,A’ and B,B’. Draw the common transversals X and X’ to the four rays A,B,A’,B’, then it can easily be shown that the effect of the given displacements on four points P Q RS on X will move those points on right of lines directed towards P’ Q/ R’ 8 on X’, so that the anharmonic ratio of PQ RS is equal to that of P’ Q’ RS’. On X there are two critical points, L and M, which are characterised by the circumstance that they start in the same direction whether the displacement be A, A’ or B, B’. It is therefore necessary that C,C’ shall be such as to start L and M in the same direction. This condition will enable C and C’ to be determined. Let the two given displacements convey L and M to L’ and M’, then C and C’ are two generators of the hyperboloid of which X, X’, and L’ M’, are three genera- tors of the other system. But when two hyperboloids are such that a pair of generators of one system on one hyherboloid are conjugate polars of the other, then a pair of generators of the other system are also conjugate polars. Obser- ving that X and X’ are conjugate polars of the absolute we therefore have C and C’ completely determined. 9. On the deduction of Trigonometrical from Elliptic Function Formule. By J. W. UL. Guatsuer, M.A., F.R.S. In any elliptic function identity, connecting sn’s, cn’s, and dn’s, we may, of course, as is well known, put & = 0, when the sn’s and cn’s become respectively sines and cosines and the dn becomes unity. But we may also expand the elliptic functions in powers of k?, and equate the coefficients of A?, k*, &e., to zero. Considering only terms as far as /?, it can be shown that amu =u—tkh*u + df’ sin Qu so that sow = sinu — ¢k?wcosu + $k sin 2ucos u cnu = cosu + +/7usin u — $k sin 2u sin wu dnu=1-—#' sin?u Now the terms — 3/?w cosu and 1 ?wsinu, in which the argument appears, out- side, will generally lead to terms which, on this account, are separately equal to zero, so that in deducing trigonometrical from elliptic function formule (in which the arguments do not appear as external factors), we may put sow = sinu(1 + +h cos? u) enw = cosu(1 — tesa)! par) dnu = 1 — $i? sin? u and equate the powers of i? to zero. As an example, consider the elliptic function identity sn 8 sn ysn(8 — y) + snysnasn(y— a) + snasnfsn (a —§) + sn (8 — y) sn (y — a) sn(a — 8) = 0; putting / = 0, we obtain the well-known trigonometrical identity sin 8 sin y sin (8 -- y) + sinysinasin (y — a) + sinasin sin (a —8) + sin (8 - y) sin(y — a) sin (a — B) = 9,... (2) 478 REPORT—1880. pat substituting for the sn’s by (1), and equating the coefficient of /? to zero, we ao sin 8 siny sin (8 — y) [cos?B8 + cos *y + cos *7(B — y) | + sinysin a gin (y — a) [cos *y + cos*a + cos *(y — a) ] + sinasin f sin (a — 8) [cos *a + cos 78 + cos *(a — ) | + sin (8 — y) sin (y — a) sin (a —8) [cos*(8 — y) + cos*(y—a) + cos*(a — 8) ] = 0, which, in virtue of (2), may be written sin 8 sin ysin (8 — y) [sin?8 + sin*y + sin*(8 — y)] + sinysinasin (y — a) [sin *y + sin*a + sin*(y — a) ] + sina sin #sin(a — #) [sin *a + sin*8 + sin*(a — 8) | + sin (@ — y) sin (y — a) sin (a — 8) [sin*(8 — y) + sin*(y — a) + sin*(a — B)] = 0.,.,..(3) Similarly from snasn (8 — y) + sn@sn(y — a) + snysn(a — f) + k* snasn@snysn(8 — y)sn(y — a) sn(a — 8) = 0 we have, by putting & = 0, sina sin (8 — y) + sin@sin(y — a) + sinysin (a — 8) = 0, and, by equating to zero the coefficient of i’, sina sin (8 — y) [sin?a + sin*(8 — y) | + sin Bsin (y — a) sin’ + sin *(y — a) | + sinysin (a — 8) [sin*y + sin*(a — 8) ] —Asinasinfsiny sin (8 — y) sin(y — a)sin(a — 8B) = 0 If the object be, not to deduce trigonometrical formule from elliptic function formulz, but to verify the latter, the formule deduced by equating to zero the coefficient of k* obtained by means of (1), generally afford a much better verifica- tion than is obtained by merely putting & = 0. It may be mentioned that (3) may be easily verified by use of (2) and of the formula sin2z + sin*y.+ sin?(x — y) = 2 — 2cosxrcosycos(z — y). y 10. On Plane and Spherical Curves of the Fourth Olass with Quadruple Foci. By Henry M. Jerrery, F.R.S. I, On Prane CrAss-QUARTICS. 1, All quartics with quadruple foci may be expressed by the geometrical rela- tion kpt=qr+Xr if the line-coordinates p, g, 7 denote the quadruple focus P, and Q, R the foci of the satellite-conic. It is proposed to examine every possible quartic in a group, in which P,Q, R remain unaltered, while the parameters, x, A, vary indefinitely, 2. When there are critical bitangential quartics in a group, the mutual relation of x, will be exhibited in a plane curve, of which they are the coordinates. This locus will be hereinafter designated the bounding curve, by which plane space will be divided into regions, In some regions no quartic is possible, and if x, A represent points on the bounding curve, critical quartics exist. with real or imaginary bi-tangents. If two branches intersect in a node or unite in a cusp, two bi-tangents will unite to form some higher singularity. In the remaining regions quartics will occur, which alter their character as x or A becomes zero, i.e, as the TRANSACTIONS OF SECTION A. 479 bounding curve intersects the axes, and in other transition-cases, which will be explained in § 8. 8. Order-quartics, whether singular or non-singular, have been classified by Dr. Zeuthen, of Copenhagen (‘ Mathematische Annalen, 1874), according to their depressions, characterised by a bi-tangent and two points of inflexion; such pits are termed by that eminent geometer, folia (although fovee might be thought more expressive). So class-quartics may have four or fewer stirrup-like excrescences. Def.—A stapes or stapete is characterised by two cusps and a erunode. By a stapete-point is meant such an excrescence in its nascent state, just as a folium-point (foveate) or a point of undulation is an incipient depression. The stapetes and folia are reciprocal, and either do or do not constitute singularities, just as the curve is regarded by its class or order. Ex. at + 488y = 0; 27 (ap)* + 64 (bg)% cr = 0. These equations denote the same quartic, with one stapete-point and one folium- point. In passing from one form to the other, 8 dimensions are lost: for (a, 8) isa triple stapete-point with three singularities, and (a, y) is a point of undulation with none. Contrariwise g is the same folium point with a triple tangent, and r a point with no singularity. The same contradiction and parallelism occur in cusped cubics, which are always inflexional. So that these conclusions may be gene- ralised. Since a® + uBr-ly =o) (n a 1)" (ap)” = (- nbgq)"1 cr, denote the same curve, n(n —:2) dimensions are lost by the mergence of cusps and nodes, or of stationary and bi-tangents at the points B, C. 4, The positions of the quadruple focus P, and of the foci Q, R of the satellite- conic, will be distinguished in five families of groups. I. P, Q, R collinear: Q, R coincident in the centre of a satellite circle, Il. P, Q, R collinear: Q, R the foci of a satellite conic. III. P, Q, R not collinear, but Q, R at an infinite distance. IV. P, Q, BR not collinear, but Q or R at a finite distance. V. P, Q, R unrestricted. The special forms should be noted, when P is at an infinite distance. 5. The process adopted will be exemplified in family I., thus represented by the Boothian equation. n= aby? + 9°) +A + 0). P is the origin; PQ = a, the distance of the double focus of the satellite conic. By partial differentiation, o = &(1 — af)? + QE (E + 7°) — a(1 — a) (& + 7’) 0 = (1 — a€)? + 2hy (E+ 77), The factor (n = 0) alone yields bitangential values, If n = 0, 2k = & (1 - a€) 20 + (1 — a€) (1 — 2a€) = 0, Tf it be thought necessary, the equation to this unicursal bounding curve will be found explicitly to be a quintic a = 1 2 (< — 182° + 36x) = (- Be) ON 4) (a? — 8X) K K But hereafter the explicit equation to the bounding curves will be rarely deter- mined. é 6. Ata singular point on the quintic a =0 =, there are two cusps, one at infinity, when & = 0, at the extremity of the (A) axis, and another, when 8a& = 2, 8A = a*, Wak = 2. 480 REPORT— 1880. There is a single asymptote \ + a = 0, when € = ». No points of inflexion, distinct from the cusps, satisfy the condition @kdy ddd dB dé ~ a de 7. By the aid of this bounding quintic all quartics may be exhibited, which have a quadruple focus and a satellite-circle. If in such a group of §5, 8A = a’, 27a’ = 2, so that («,A) is a ceratoid cusp on the bounding quintic, the quartic ahr (4 2EX __ oe alee 2Noee rayt + (Fae 2aé + 1)n + (ag + 2) (¢-2) ae is inflexional. In a family of such groups, the locus of the point of inflexion is the hyperbola (108 kA = 1). For values of («,) on points in the neighbourhood of the cusp, the quartics are veribantangential with two cusps of the cardioid type, or acubitangential, as (x, A) is situated on one or other of the branches which meet at the cusp. For points within this space, the quartics consist of an oval, pierced by the hyperbolic branches of another non-stapete or smooth oval. For points beyond this space the quartics are bistapete with four, two, or no asymptotes, and also become smooth according to the position of (x,A). It may suffice here to state, that for other critical values of (x, A), one or other negative, the quartics are limagonoid, i.e. unistapete in the nascent form, or have bicusped bi-tangents, the reciprocals of biflecnoids, i.e., are bistapete in the nascent state. 8. Non-singular quartics may change their stapetes, without passing through critical values; the stapete-points of transition are determined by aid of the Hessian of the group, or by means of the invariants 8, T, equated to zero, ‘Let the centre of the satellite circle be at infinity. Such a group R= EE +) + AE + 9°)? has no critical bitangential quartics, but its stapetes vary with A. The Hessian of the group is (4A? + 6A + 2) & + (8A? + BA — 1) Ey? + (AA? + 2A) nt = . The real values of these points, which constitute the Hessian, and of the coincident stapete-points, depend upon the auxiliary quadratic 32? + 32d = 1, whose roots are ‘03033 and — 1:038033. Other transition-values of A are 0, — ‘5, —1. If \ = 03 or — 1:03 the quartics have four stapete-points. X = — ‘5, there are two stapete-points. X = 0 or —1, there is a tacnode at infinity, or the quadric is bistapete in its nascent state. For intermediate or external values the quartics are quadristapete, bistapete, or nonstapete. 9. This slight sketch may suffice to explain the plan of this chapter of Plane and a corresponding chapter in Spherical Class-Quartics, which, it is hoped, may shortly find a place in the ‘Quarterly Journal of Mathematics,’ illustrated by the necessary diagrams. 11. On the equations to the real and to the imaginary directrices and latera recta of the general conic (a,b,c,e,f,9,h) (v,y1)? = 0; with a note on a property of the director circle. By Professor R. W. Gunesz, M.A. Let u == aa? + Qhay + by? + 2gn+ 2fy+e=o be the equation to a conic referred to rectangular axes: let (a8) be the codrdinates of a focus, rcos6+ysin 6 = p the corresponding directrix, and e the excentricity of the conic. The equation to the conic may therefore be written (x — a)? + (y—8)? =e? (x cos + ysin 8 — p)? i (= TRANSACTIONS OF SECTION A. 481 comparing with u = o we get 1—e’cos’@ _ 1—e*sin?d _ —e* sin@cosd _ e*pcosd —a a 7 i Shaw “ee h Pe _@psind — B bes a? +B? — e’p* wid say if a c r ; Eliminating e and 6 we get W — (a+b) A+ab—-h? =O..... (A) Since zy are the codrdinates of any point on a directrix, by eliminating p, 6, a8, e from w cos 8+ ysin 6 = p and the above equalities, we shall get the equation to the directrices The result of the elimination is ay" (i) 420 sa et ER I do not exhibit the work, because a quicker method of obtaining it will be given in the note. Using (A), (B) may be shown to represent two parallel straight lines. Thus one value of X from (A) gives the real directrices, and the other the imaginary. I find further that B may be resolved into \ du = ds — VX=b7 + Vi-a Gy = BA tf 12 (0) |ahg where A= |hOf gfe and the sign between the radicals on the left side is that of ~~, It follows that du du — o> ig = 0) re aD MS Ua tia Na 2 (D) is the equation to an axis of the conic. Tn virtue of (A) this is equivalent to =H) M1 = 0 ae y eats CE du du == _— ~ = - ay (A a) dy 0 Having obtained the equations to an axis and to a directrix we can obtain the equation to a latus rectum (the polar of their intersection). Using Dr. Salmon’s notation for the reciprocal coefficients the result is Vi —b (Or — G) + WX —a Cy — F) = + @+b-2) Vac... . ®) The quantity a+b — 2 may be shown to be the expression denoted by R in Dr. Salmon’s conics (Ex. 3, Art 157, and elsewhere). Note. The form of the equation to the director circle of u = 0, viz. with Dr. Salmon’s notation, v=C (a? +y*?) —-2Gax—-2Fy+A+B=0 shows that the straight lines joining any point on it to the circular points at infinity are conjugate with respect to the conic. This is a particular case of the following theorem :—If from two fixed points in the plane of a conic straight lines be drawn conjugate with respect to the conic, the locus of their intersection is, in general, a conic passing through the two given points. Also since a tangent is conjugate to any straight line passing 1880. EY 482 REPORT—1880. through its point of contact, the above locus must pass through the points of contact of the tangents to the conic from the given points. This theorem enables us to write down the equation to the known conic passing through two given points, and the points of contact of tangent from those points to a given conic. To return to the particular case of the director circle. The tangents from the circular points at. infinity intersect in the foci: the points of contact must therefore lie on the polars of the foci, ie. on the directrices. Hence the director circle of a conic passes through the intersections of the directrices with the conic, In other words, the directrices of a conic are the chords of intersection of the conic with its director circle. Their equation is therefore of the form iWin Wi = O}e Laurette eal (Ch) ¢ The conditions that this should represent parallel straight lines are found, after rejecting a factor C, F or G, each to reduce to pw? —p(a+6)+(ab — h*) = 0 the quadratic (A) obtained for A. I have identified (G) with (B), only \ and » must be taken as different roots of the quadratic A. 12. Note on the Skew Surface of the Third Order, By Professor H. J. 8. Suita, M.A., F.R.S. 13. On a kind of Periodicity presented by some Elliptic Functions. By Professor H. J. 8S. Surru, W.A., FBS. 14. On Algebraical Expansions, of which the fractional series for the cotangent and cosecant are the limiting forms. By J. W. L. GuaisHer, V.A., ERS. The expansions in question are :— 1 us pet a(1?—2?) (22—a2"),.. .(n®?—2) nin! wx 1 il 1 (n=l)! (+1)! es =i eel l ( bia 15) (n— 2)! (n +2)! \w-2 w4+2 waaay ] f Re ) (n—r)!(n+r)!\e—9r 2x +r (1 — 282%) (8° 2%)... {Qn 1)?— 2%" } “Tg (Pae) Gar yn os 2 — 2") 1 Cn)! Qn)! = — 2 PPR Q2n~ n! n! ( z a A TRANSACTIONS OF SECTION A. 483 (2n — 2)! (2n + 2)! ( T T 1 ta) BRO eee ere eg aS Ste 2% |@=D1 q+! eho nak I . . . . . (2n — 27)! (2n + 27)! 1 meri | * pe J@=n@antt Bite) HS MRE 8! 1 MO te Al + Oe ) 2m)! + ae “) ee Multiplying (1) and (2) throughout, by :— 1 dee pa ok Ae 2.92 : , at HS Sos Seer (in Ts respectively, they become :— if Sone eS YE bg | PD Po BY = — +- ) r(1-4) (1-%).--(1-4) a ee are = ; caer (1+) (1+2) (1+) a= “+35 nN nv n 1 1 22 (a i Dalsccreity li vw-1l wxr+i1 n Qn + CY ae a Ml + ) TER a ras) (a+2)Q+2 G-+) (1-3) 2 xv+2 n n Qn 2Qn + &e. which, when z is made infinite, give in the limit eS go 2 DD Gil pals 2 i SS Be sin 72 xv “x-1 w+1 vy —2 vt+2 = cot mr = 1 + 1 1 d + L + &e, n z—-l1 x+1 u—2 vt+2 ; ae v“ ‘viz., on writing ~~ for x, sin v v L— 1 Ltr wv — 2 v + Qn : 484 REPORT—1880. I 1 1 1 + + ——— + —— v—T t+ av -— 20 u+ 20 which are the fractional series referred to in the title. The formule (1) and (2) may be established by the ordinary process for re- solying an expression into partial fractions ; or by means of the theorem :—If AG, a + Has ary Bite ah z+1 Te u+n where A,, A,,... An, are any coefficients independent of 2, be denoted by ¢ (x), then + &e. Ph eels + a - af (2) $(-2) =A + Aga) }—ti+— | z+} 1 1 Bes mee | Sef oh ey gia Peat he rs | 1 ee + ma,ot) beri. This theorem applied to the expansions rnd) eR As ee as aN a 1 =p u(vt ly... (v+n) n! « (n—1)! x41 2!(m—2)! x+2 al 1 inl eam (2z'+ 1) (Qh 48)... @n+2n=—1)_ 1 (Qn)t 1 1 21 Q@n=—2)1 1 av + 1)s.. (+7) 2” (n!)? 27 (1! (m—1)!)? +1 _1 @)! Qn — 29)! if 1 (Qn)! 1 To (Fiq@—r)!)? z+r Wal? cen gives at once the formule (1) and (2).* 15. Note on a Trigonometrical Identity involving products of Four Sines. By J. W. L. Guatsuer, M.A., F.B.S. In a paper in the ‘ Messenger of Mathematics’ (vol. x. p. 26), the author had drawn attention to the following identity :— sna sind sine sind = sind sind’ sinc’ sind’ + sina” sin 6” sin ce” sind” where a, 6, c, d are any four quantities, and a’, b’, c’, d’, w”’, b”, c’”’, d’” eight quan= tities derived from them by the equations a=t(-a+bie+d), a’ =4t(a+b+e+d), Hot a—b+e+d), b’=i(a+b-—c-dad), f=4( a+b-c+ad), fm ae eas d@=3( ‘a+b+e-—d), d’=34(a—b-c+r+d), and in this note he pointed out that this was a particular case of a more general formula involving products of four sines. The foregoing identity may be written sin asin b sine sind = sin (o — a) sin(o — 4) sin (o — ¢) sin (o —@) + sing sin(o — b—c)sin(o —b—d)sin(o—e—d)......() * The paper is printed in extenso in the Quarterly Journal of wanes vol.. XVii, pp. 211-226. TRANSACTIONS OF SECTION A. 485 where o=43(a+b+e+ a) and the more general identity is sina sin B sin ysin 8 — sin (a + A) sin(8 + d) sin (y + A) sin (6 + A) + snAsin(a + 6+ A)sn(B +6 +A)sn(y + 6+ dr) — sinSsindsin(S + A)sm(a+B+y+t+4+ 2A) =0 stalbllayenoiieds. a (2) where a, B, y, 5, \ are any five quantities. The formula (1) is the particular case of (2) obtained by putting A= —-t(at+h+y+ 9) The formula (2) may be written sin (a — f) sin (a — g) sin (a — h) sin (6 — ¢) + sin (6 —f) sin (6 — g) sin(b — h) sin (e — a) + sin (c — f) sin (e — g) sin (e — ’) sim (a — b) + sin (b —‘c)sin (¢ — a) sin (a — 6) sm(a +b + € —f-g-h) =9.(3) and in this form it is in effect due to Prof. Cayley and Mr. R. F. Scott: viz., in the ‘Messenger, vol. v. p. 164, Prof. Cayley stated that a certain determinant was equal to zero, if a condition, equivalent to @ + b+ec=f+g +h, was fulfilled ; and in vol. viii. p. 155, Mr. R. F. Scott evaluated this determinant, without this restriction, the developed result being equivalent to (8). 16. On the Periods of the First Class of Hyper-elliptic Integrals. By Wit R. Roserrs, M.A. I investigate the periods of hyper-elliptic functions by a method analogous to that which has been adopted by Schloemilch for the determination of the periods of elliptic integrals. By this method I determine the periodicity of hyper-elliptic integrals without integrating the equations. yn) Akin F (@.) dz 1 . . . . 2 (z,) di, + £4 2) 5. 3 3 @) f (%) 272, * f (Z_) %2"dzy i SF (5) ds 0 0 where il PO = Tame 1 -W#) 18) 2") s a I first determine the general value of the integral f(s)dz, and find it de- pends on four integrals, which I call respectively, 2¥, Dz, 210, and 2i¥ ; and in a similar manner I arrive at the general value of the integral “#(2)e2dz. The mode of investigation which I adopt for the determination of these ‘integrals affords a proof that the equation 1 z= (-1) ae satisfies both the transcendental equations. b4 2 f f (adz + QIN + Amz + 210 + 2 at be f @dz 0 : 0 Zz , st a°f (2)dz + Qv’ + Qmz’ + 2WiO! + Aww’ = St ; of (z)dz ote tt) By a series of transformations I proceed to show that the following equations :— Viet =} ae J/1—2” (2) . JT a We = (-1)**™ STW 486 REPORT—1880. J1-k?@ = (-1L) TF Vine re 1 Vi-Be = (-1)P* Vie are agreeable to both the transcendental equations (2). I then consider the transcendental system :-— (4) Af is (2)dz of cf (s)dz + 2IY + 2nzB + QO + Qniv 0 0 a / ie = f- “f(2)d +f ?f @dz ex 0 tie 2f (a)de of "2 .2f (a)dz + QI! + Qmz’ + QiO! + Qi! 0 0 ~ / oe” cs heey de: ah * fF (2)dz +f aif (s)dz . . . 0 0 and deduce its equivalent algebraic system. Finally I put U = S "1 F (2)de +f "2 P (2)de 0 Ved 5) “1 52 f (2)da +f *2 62 £ (a)da 10) 0 and I write z,z, = F (U,V), and show that F (U,V) is a periodic function of two variables U and V, each of which has four periods, two real and two imaginary ; the nature of the periodicity of which I discuss in the investigation of the general values of the integrals f : Tf (@)dz and fo *2f (2) dz. e’ 0 0 17. On the Integral of Laplace’s Equation in Finite Terms. By the Rey. 8. Earnsuaw, M.A. Tue InTEGRAT oF LAPLACE’s EQuaTIon. The equation to which this title refers is the following :— PE Woo Oy aly da® dy? da? and I am desirous of the three following propositions being communicated to Sec= tion A, at the meeting of the British Association at Swansea. Prop. A.—The independent variables x, y, z are in this equation not necessarily the coordinates of some point P, in space referred to a fixed rectangular system of codrdinate axes Ox, Oy, Oz. We shall, however, hypothetically treat them as such; and therefore we say that . OP = =r gy? + 24, Now from O draw any two lines, OA, OB, at right angles to each other, and let &, 7 represent the lengths of the rectangular projections of OP upon these two arbitrary lines; then will the following be a general integral of Laplace’s equation given above, u = Ae“ cos (an + b).... (2) in which A, a, 6 are arbitrary constants which haye no reference whatever to the arbitrary positions of OA, OB. TRANSACTIONS OF SECTION A. 487 It will also be noticed that, 6 being arbitrary, the integral (2) is equivalent to two conjugate integrals, and may be more completely written thus, u = Be (A cos an + Bsin an). The generality of this integral is due to the circumstance that the two lines OA, OB (on which &, 7 are the projections of 7) are perfectly arbitrary as to their direc- tions in space, while &, 7 are entirely dependent, for their values in terms of 2, y, 2, on the positions of OA, OB. Every different position of OA, OB, or of either of them, will give a special integral, though every such special integral will be of the common type (2). Each special integral will have its own arbitrary (or special) constants in the place of A, a, b; and any of such special integrals may be formed by addition into a group, which group will be an integral of equation (1). There is no limit to the number of groups, but every group will be composed of integrals of the type (2); and it is in reference to this property that we designate (2) the general integral. We may mention that € = rcos AOP andy = rcos BOP, and these cosines are easily expressed in terms of 2, y, 2, and the arbitrary angles which OA, OB make with the codrdinate axes. Prop. B.—If now a third line OC be drawn at right angles to both the lines OA, OB; and if ¢ be the length of the projection of 7 on OC, then will the following differential equation hold good always, t.e. whatever be the positions of OA, OB, OC, Mu , du i du _¢ 2 an de : from which it follows, that if we possess any integral F (x,y,z) of the equation (1) we may write in this integral, instead of x, y, x, the values of &, 7, ¢ in terms of x, y,2; and the integral F, though much changed thereby, will still be an integral of the equation (1). As a very simple example we may mention this, that if F(a, y,z) be an integral, so likewise will F (wcosa + ysina,ycosa — xsina,z) be an integral of equation (1), though we have written «cosa + ysina andy cosa — «sina instead of « and y; and a= is an arbitrary constant. And, thus, if the integral F (x,y, 2) be only a particular integral this introduction of an additional arbitrary constant a, which it did not possess before, will advance it a step towards generality. Prop. C_—The independent variables of equation (1) have usually been changed by assuming two angles, 6, d, such that « =7sn@cosd,y = rsinésing, and s=rcos@. It is somewhat more convenient in the work of integration to change the angle @ for its complement to a right angle. Thus we shall make the following change of independent variables, x = rcosécosdh,y = 7 cos @ sind, 2 = 7 sin 8. The transformed equation on these assumptions is du. du du au tease eet eed EE ee 26 — = ir or * dB and =, + sec OG ,=9, and of this the following is the general integral, uw=F (r-cos 6 : “'?) + =f (r sec 6 : e?) aiatere| (a) 7 is defined by the equation 7? = — 1, and F, f are arbitrary functions, The form of the transformed differential equation shows that oe is also an in- tegral of it. Hence we may replace the second term of (3) by its differential coefficient with regard to @; so that we may present (8) in the following form :— “= F (reoso. <'?) +e ~% sec 6 f(r sec 6. %), -+e(4), 488 REPORT—1880. I am not aware that the integral of the above equation has ever before been presented in finite terms; on which account I make this communication to the British Association.! MONDAY, AUGUST 30. The following Reports and Papers were read :— 1. Report of the Committee on Tidal Observations in the English Channel, fe. See Reports, p. 390. 2. Report of the Committee on Luminous Meteors.—See Reports, p. 39. 3. Report of the Committee on the question of Improvements in Astronomical Olocks.—See Reports, p. 56. 4. On a Septum permeable to Water and impermeable to Air, with practical applications to a Navigational Depth-gauge. By Professor Sir WILLIAM Tomson, M.A., F.B.S. A small quantity of water in a capillary tube, with both ends in air, acts as a perfectly air-tight plug against difference of pressure of air at its two ends, equal to the hydrostatic pressure corresponding to the height at which water stands in the same capillary tube when it is held upright, with one end under water and the other in air. And if the same capillary tube be held completely under water, it is perfectly permeable to the water, opposing no resistance except that due to viscidity, and permitting a current of water to flow through it with any difference of pressure at its two ends, however small. In passing it may be remarked that the same capillary tube is, when not plugged by liquid, perfectly permeable to air. A plate of glass, or other solid, capable of being perfectly wet by water, with a hole bored through it, acts similarly in letting air pass freely through it when there is no water in the hole; and letting water pass freely through it when it is held under water; and resisting a difference of air-pressures at the two sides of it when the hole is plugged by water. The difference of air-pressures on the two sides which it resists is equal to the hydrostatic pressure corresponding to the rise of water in a capillary tube of the same diameter as the narrowest part of the hole. Thus a metal plate with a great many fine perforations, like a very fine rose for a watering-can for flowers, fulfils the conditions stated in the title to this com- munication. So does very fine wire cloth. The finer the holes, the greater is the difference of air-pressures balanced, when they are plugged with water. The shorter the length of each hole the less it resists the passage of water when com- pletely submerged; and the greater the number of holes, the less is the whole re- sistance to the permeation of water through the membrane. Hence, clearly, the object indicated in the title is more perfectly attained the thinner the plate and the smaller and more numerous the holes. Very fine wire cloth would answer the purpose better than any metal plate with holes drilled ‘through it; and very fine closely-woven cotton cloth, or cambric, answers better than the finest wire cloth. The impenetrability of wet cloth to air is well known to laundresses, and to every naturalist who has ever chanced to watch their operations. The quality of dry cloth to let air through with considerable freedom, and wet cloth to resist it, is well known to sailors, wet sails being sensibly more 1 The original paper is ready for the press, and will shortly be published. TRANSACTIONS OF SECTION A. 489 ‘effective than dry sails (and particularly so in the case of old sails, and of sails of thin and light material). An illustration was shown to the meeting by taking an Argand lamp-funnel, with a piece of very fine closely-woven cotton cloth tied over one end of it. When the cloth was dry, and the other end dipped under water, the water rose with perfect freedom inside, showing exceedingly little resistance to the passage of air through the dry cloth. When it was inverted, and the end guarded by the cloth held under water, the water rose with very great freedom, showing exceed- ingly little resistance to the permeation of water through the cloth. The cloth being now wet, and the glass once more held with its other end under water, the cloth now seemed perfectly air-tight, even when pressed with air-pressure corre- sponding to nine inches of water, by forcing down the funnel, which was about nine inches long, till the upper end was nearly submerged. When it was wholly ‘submerged, so that there was air on one side and water on the other the resistance to permeation of air was as decided as it was when the cloth, very perfectly wet, had air on each side of it. Once more, putting the cloth end under water; holding the tube nearly hori- zontal, and blowing by the mouth applied to the other end :—the water which had risen into the funnel before the mouth was applied, was expelled. After that no air escaped until the air-pressure within exceeded the water pressure on the outside of the cloth by the equivalent of a little more than nine inches of water ; and when blown with a pressure just a very little more than that which sufficed to produce a bubble fronfany part of the cloth, bubbles escaped in a copious torrent from the whole area of the cloth. Water indicated by horizontal shading ; air by white paper. The accompanying sketch represents the application to the Navigational Depth- gauge. The wider of the two communicating tubes, shown uppermost in the sketch, has its open mouth guarded by very fine cotton cloth tied across it. The tube shown lower in the diagram is closed for the time of use by a stopper at its lower end. A certain quantity of water (which had been forced into it during the descent of the gauge to the bottom of the sea) is retained in it while the gauge is being towed up to the surface in some such oblique position as that shown in the sketch. While this is being done the water in the wide tube is expelled by the expanding air. The object of the cloth guard isto secure that this water is expelled to the last drop before any air escapes; and that afterwards, while the gauge is being towed wildly along the surface from wave to wave by .a steamer running at fourteen or sixteen knots, not a drop of water shall re-enter the instrument. 5. On the Effect of Oil in destroying Waves on the Surface of Water. By Professor Osporne Reynoups, M.A., F.R.S. This paper contained a short account of an investigation from which it ap- peared that the effect of oil on the surface of water to prevent wind-waves and destroy waves already existing, was owing to the surface-tension of the water over which the oil spread varying inversely as the thickness of the oil, thus introducing 490 REPORT—1880. tangential stiffness into the oil-sheet, which prevented the oil taking up the tan+ gential motion of the water beneath. Several other phenomena were also men- tioned, The author hopes shortly to publish a full account of the investigation. 6. Experiments on thin Films of Water, with regard to their absorption of Radiant Heat. By the Hon. F. A. R. Russet. The experiments, the general results of which are given below, were made with the object of ascertaining the diathermancy of water in yery thin films, and these experiments afforded incidentally an opportunity of observing the behaviour of films subject to varying conditions. The arrangement of instruments was similar to that illustrated at p. 383 of Prof. Tyndall’s ‘ Heat as a Mode of Motion,’ The instruments used were: a dead- beat mirror galyanometer and scale, a thermopile, and a screen. The soap film was carried by a piece of a cork sole perforated by a hole slightly larger than the hole inthe screen, about 13 inches in diameter. The sources of heat were (1) a copper or iron ball heated from behind by a small gas flame ; (2) a common gas flame from a Bunsen burner, and (3) a hydrogen flame in air. The film was mostly made from a solution of about half a drachm of shavings of Castile soap, dissolved 5 to 15 minutes in about 5 cubic inches of water, at 60° Fahrenheit. The film soon after being placed perpendicularly at the orifice im the screen exhibited coloured bands, which descended in regular succession until the last band appeared, which contained a bright blue line. The descent of the bands continued at a slackened rate till the grey, and finally the black, occupied a portion of the upper half of the film, which half was alone subject to experiment. A condition more or less of equilibrium then prevailed, the tension of the black portion counteracting the force of gravity. A light yellow or bronze was always the last colour to appear, and preceded the white or grey, which again was succeeded by black. When there was any black in the film, the bursting of the film was marked by a slight click or snapping sound. The best films lasted frequently between 10 and 30 minutes, and sometimes the black portion alone was under observation 15 or 20 minutes. The following table shows the absorption per cent. for each of the three sources of heat, and the thickness of the film, as derived from a table in Watts’s ‘ Dictionary of Chemistry,’ giving Newton’s thicknesses of thin films of air, water, and glass. A table in Cooke’s ‘ New Chemistry’ gives the thicknesses of soap-films as consider- ably greater than those stated in Newton's table. The ‘light film’ of Cooke corresponds to my ‘grey,’ and his ‘grey’ to my ‘fine grey.’ Newton’s ‘ white’ corresponds to my ‘grey.’ The refractive index of the solution used by me was 1:34 and 1°35, a little higher than that of pure water. Coal Thickness of Film State of Film Metal Gas Hydrogen in millionths of an inch Last band alone! . 5 : 4 9? 82 — 8:3 Bronze . : . ; 6 57 —_— 52 All grey (white) . : Fs : 4-7 — 4:5 39 Fine grey ‘ : . - ‘ — 3-4 — 18 Half grey, half black. : : — 2°9 -- 2°3 Two-thirds black, one-third grey . — 16 16 1:8 Half fine grey, half black A : 0-7 — — 134 Black and slight fine grey . ; — aa 12 ; Fine grey and black, or all black . 0:29 — — 0-75 All black F 5 : . ; 0:29 15 06 \ 1 The absorption in this case is deduced from that of a film containing a portion of grey, the absorption of the grey being known, TRANSACTIONS OF SECTION A. 491 7. On an Experimental Illustration of Minimum Energy in Vortex Motion. By Professor Sir Wiiutiam Tuomson, M.A., F.R.S. This illustration consists of a liquid gyrostat of exactly the same construction as that described and represented by the annexed drawing, repeated from ‘ Nature,’ February 1, 1877, pp. 297-298, with the difference that the figure of the shell is prolate instead of oblate. The experiment was in fact conducted with the actual apparatus which was exhibited to the British Association at Glasgow in 1876, altered by the substitution of a shell having its equatorial diameter about = of its axial diameter, for the shell with axial diameter 3; of equato- rial diameter which was used when the apparatus was shown as a successful gyrostat. The oblate and prolate shells were each of them made from the two hemispheres of sheet copper which plumbers solder together to make their globular floaters. By a little hammering it is easy to alter the hemispheres to the proper shapes to make either the ~--------------- DNMINGHE Sara prolate or the oblate figure. ? “euctats ie Theory had pointed out that the rotation of a liquid in a rigid shell of oval figure, being a configuration of maximum energy for given vorticity, would be unstable if the containing vessel is left to itself supported on imperfectly elastic supports, although it would be stable if the vessel were held absolutely fixed, or borne by per- fectly elastic supports, or left to itself in space unacted on by ex- ternal force ; and it was to illus- trate this theory that the oval shell was made and filled with water and placed in the appara- tus. The result of the first trial was literally startling, although it ought not to have been so, as it was merely a realisation of what had been anticipated by theory. The framework was held as firmly as possible by one per- son with his two hands, keeping it as steady as he could. The spinning by means of a fine cord' round a small 1 Instead of using along cord first wound on a bobbin, and finally wound up on the circumference of the large wheel, as described in Watwre, February 1, 1877, p. 297, I have since found it much more convenient to use an endless cord a little more than half round the circumference of the large wheel, and less than half round the circumference of the V pulley of the gyrostat ; and to keep it tight enough to exert whatever tangential force on the V pulley is desired by the person holding the framework in his hand, After continuing the spinning by turning the fly-wheel for 492 REPORT—1880. V pulley of 3-inch diameter on the axis of the oval shell, and passing round a large fly-wheel of three feet diameter turned at the rate of about one round per second, was continued for several minutes. This in the case of the oblate shell, as was known from previous experiments, would have given amply sufficient rota- tion to the contained water to cause the apparatus to act with great firmness like a solid gyrostat. In the first experiment with the oval shell the shell was seen to be rotating with great velocity during the last minute of the spinning ; but the moment it was released from the cord, and when, holding the framework in my hands, I com- menced carrying it towards the horizontal glass table to test its gyrostatic quality, the framework which I held in my hands gave a violent uncontrollable lurch, and in a few seconds the shell stopped turning. I saw that one of the pivots had become bent over, by yielding of the copper shell in the neighbourhood of the stiff pivot-carrying disk, soldered to it, showing that the liquid had exerted a very strong couple against its containing shell, in a plane through the axis, the effort to resist which by my hands had bent the pivot. The shell was refitted with more strongly attached pivots, and the experiment has been repeated several times. In every case a decided uneasiness of the framework is perceived by the person holding it in his hands during the spinning; and as soon as the cord is cut and the person holding it carries it towards the experimental table, the framework begins, as it were, to wriggle round in his hands, and by the time the framework is placed on the table the rotation is nearly all gone. Its utter failure as a gyrostat is pre- cisely what was expected from the theory, and presents a truly wonderful contrast to what is observed with the apparatus and operations in every respect similar, except having an oblate instead of a prolate shell to contain the liquid. 8. On a Disturbing Infinity in Lord Rayleigh’s Solution for Waves in a Plane Vortex Stratum. By Professor Sir Wituiam Tuomson, W.A., ERS. Lord Rayleigh’s solution involves a formula equivalent to &T 2 ape = m* + dy v=0 dy Ta% \ m Where v denotes the maximum value of the y-component of velocity ; » my, aconstant such that 27 is the wave-length ; m T ,, the translational velocity of the vortex-stratum when undis- turbed, which is in the z-direction, and is a function of y ; n ,, the vibrational speed, or a constant such that 27 is the period. n ” Now a vortex stratum is stable, if on one side it is bounded by a fixed plane, and if the vorticity (or value of a) diminishes as we travel (ideally) from this c plane, except in places (if any) where it is constant. To fulfil this condition, suppose a fixed bounding plane to contain ox and be perpendicular to oy; and let oe have its greatest value when y = 0, and decrease 4 continuously, or by one or more abrupt changes, from this value, to zero at y = a and for all greater values of y. It is easily proved that the wave-velocity, whatever be the wave-length, is in- termediate between the greatest and least values of 7. Hence for a certain value of y between 0 and a, the translational velocity is equal to the wave-velocity, or as long a time as is judged proper, the endless cord is cut with a pair of scissors and the gyrostat is released. TRANSACTIONS OF SECTION A. 493, T= ™. Hence for this value of y the second term within the bracket in Lord m 2 We evade entirely the consideration of this infinity if we take only the case of a layer of constant vorticity (~ = constant from y = 0 toy = a) , as for this case y the formula is simply = = m?v, but the interpretation of the infinity which Rayleigh’s formula is infinite unless, for the same value of y, es vanishes. occurs in the more comprehensive formula suggests an examination of the stream- lines by which its interpretation becomes obvious, and which proves that even in the case of constant vorticity the motion has a startlingly peculiar character at the place where the translational velocity is equal to the wave-velocity. This pecu- liarity is represented by the annexed diagram, which is most easily understood if SSS SS SS oe ee ee —> Y/ we imagine the translational velocities at y = 0 and y =a to be in opposite direc- tions, and of such magnitude that the wave-velocity is zero; so that we have the case of standing waves. For this case the stream lines are as represented in the annexed diagram, in which the region of translational velocity greater than wave- propagational velocity is separated from the region of translational velocity less than waye-propagational velocity by a cat’s-eye border pattern of elliptic whirls. 9. Supplement to a Paper on the Synchronism of Mean Temperature and Rainfall in the Climate of London. By H. Courrmnay Fox, M.R.C.8. In the Report of the British Association for 1879, page 277, is an abstract of a paper on the above subject which I had the pleasure of reading last year. The yainfall-data which I then used were of two kinds—namely, first, the monthly yainfall at the Royal Observatory back to the year 1841; and, secondly (for the years 1813 to 1840), the rainfall for every month collected by Mr. Dines from sundry observations about London. After I had presented this paper, Mr. Glaisher kindly favoured me with a table of the monthly rainfall at Greenwich, going back to the year 1815. I have since gone carefully through my paper with it, and am glad to state that the results which I ventured to offer to the Association are, with small excep- tion, fully confirmed. Conclusion No. 1 is confirmed, with the exception that February loses the synchronism of cold with dry, although that of warm with wet is retained. Conclusions Nos. 2 and 3 are confirmed. Conclusion No. 4:—The results for April and November are unchanged. The four remaining months, though in some respects they presented ‘slight’ tendencies to the association of extremes of rainfall and temperature, were more or less indefinite in character. This is still the case as regards March, September, and October, but in May the tendency is for the synchronism of cold with wet to prevail. A94 REPORT—1880. ' TUESDAY, AUGUST 31. The following Reports and Papers were read :— 1. Report of the Committee for commencing Secular Huperiments on the Elasticity of Wires.—See Reports, p. 61. 2. On the Elasticity of Wires. By J. T. Borromtzy, M.A., F.R.S.L. 3. Report of the Committee on the Specific Inductive Capacity of a good Sprengel Vacuum.—See Reports, p. 197. 4. On a method of measuring Contact Electricity. By Professor Sir Witu1Am Tuomson, M.A., F.R.S. In my reprint of Papers on ‘ Electrostatics and Magnetism,’ section 400 (of date January 1862), I described briefly this method, in connection with a new physical principle, for exhibiting contact electricity by means of copper! and zinc quadrants substituted for the uniform brass quadrants of my quadrant electrometer. I had used the same method, but with movable discs for the contact electricity, after the method of Volta, and my own quadrant electrometer substituted for the gold-leaf electroscope by which Volta himself obtained his electric indications, in an extended series of experiments which I made in the years 1859-61. I was on the point of transmitting to the Royal Society a paper which I had written describing these experiments, and which I still have in manuscript, when I found a paper by Hankel in Poggendorff’s ‘ Annalen’ for January 1862, in which results altogether in accordance with my own were given, and I withheld my paper till I might be able not merely to describe a new method, but, if possible, add some- thing to the available information regarding the properties of matter to be found in Hankel’s paper. I have made many experiments from time to time since 1861 by the same method; but have obtained results merely confirmatory of what had been published by Pfaff in 1820 or 1821, showing the phenomena of contact electricity to be independent of the surrounding gas, and agreeing in the main with the numerical values of the contact differences of different metals which Hankel had published ; and I have therefore hitherto published nothing except the slight state- ments regarding contact electricity which appear in my ‘ Electrostatics and Magne- tism.’ As interest has been recently revived in the subject of contact electricity, the following description of my method may possibly prove useful to experimenters. The same method has been used to very good effect, but with a Bohnenberger electroscope instead of my quadrant electrometer, in researches on contact electricity by Monsieur H. Pellat, described in the ‘ Journal de Physique’ for May 1880. The apparatus used in these experiments was designed to secure the following conditions :—To support two circular discs of metal about four inches in diameter in such a way that the opposing surfaces should be exactly parallel to each other and approximately horizontal; and that the distance between them might be varied at pleasure from a shortest distance of about =; of an inch to about a quarter or half an inch. The lower plate, which was the insulated one, was fixed in a glass stem rising from the centre of a cast-iron sole plate. The upper plate was suspended by a chain to the lower end of a brass rod sliding through a steady- ing socket in the upper part of the case. A stout brass flange fixed to the lower end of this rod bears three screws, one of which, S, is shown in the drawing, by which the upper plate can be adjusted to parallelism to the lower plate. The other apparatus used consisted of a quadrant electrometer and a gravity Daniell’s cell of the form which I described in ‘ Proce. R.S.’ 1871 (pp. 253-259) with a divider by which any integral number of per cents. from 0 to 100 of the electromotive force of the cell could be established between any two mutually insulated homogeneous metals in the apparatus, TRANSACTIONS OF SECTION A, 495 496 ; REPORT—1880. I had a smaller apparatus, with Volta discs of only about half an inch diameter,. and with gas-tight enclosing case, constructed in the year 1871; and I have made many experiments with it, of which I hope soon to publish an account. Connections. The insulated plate was connected by a stiff brass wire passing through a wide- enough hole-in the case of the Volta condenser to the electrode of the insulated pair of quadrants. The upper plate was connected to the metal case of the Volta condenser and to the metal case of the electrometer, one pair of quadrants of which were also connected to the case. One of the terminals of the divider, which con- nected the poles of the cell through a graduated resistance coil, was connected to the case of the electrometer, and to the other terminal was attached one of the con- tact wires, which was a length of insulated copper wire having soldered to its outer end a short piece of platinum. The other contact piece was a similar short piece of platinum fixed to the insulated electrode of the electrometer. Hence it will be seen that metallic communication between the two plates was effected by putting the divider at zero and bringing into contact the two pieces of platinum wire. Order of Experiment. The sliding piece of the divider was put to zero, and contact made and broken and the upper plate raised, and the deflection of the spot of light was observed. These operations were repeated with the sliding piece at different numbers on the divider scale until one was found at which the make-break and separation caused no perceptible deflection. The number thus found on the divider scale was the number of hundredths of the electro-motive force of the cell, which was equal to the contact electric difference of the discs in the Volta condenser. [ Addendum, November 23, 1880.—Since the communication of this paper to the British Association, I have found that a dry platinum disc, kept for some time in dry hydrogen gas, and then put into its position in dry atmospheric air in the apparatus for contact electricity, becomes positive to another platinum dise which had not been so treated, but had simply been left undisturbed in the apparatus. The positive quality thus produced by the hydrogen diminishes gradually, and becomes insensible after two or three days. | 5. On a method of determining without mechanism the limiting Steam- Liquid Temperature of a Fluid. By Professor Sir Wit1iam THomson, M.A., FBS. A piece of straight glass tube—60 centimétres is a convenient length—is to be filled with the substance in a state of the greatest purity possible. It is to contain such a quantity of the substance that, at ordinary atmospheric temperatures, about 3 or 4 centimétres of the tube are occupied by steam of the substance, and the re- mainder liquid. Fix the tube in an upright position, with convenient appliances for warming the upper 10 centimétres of the length to the critical temperature, or to whatever higher or lower temperature may be desired; and for warming a length of 40 centimétres from the bottom to some lower temperature, and varying its temperature conveniently at pleasure. Commence by warming the upper part until the surface of separation of liquid and steam sinks below 5 centimétres from the top. Then warm the lowest part until the surface rises again to a conyenient position. Operate thus, keeping the surface of separation of liquid and solid at as nearly as possible a constant position of 3 centimétres below the top of the tube, until the surface of separation disappears. The temperature of the tube at the place where the surface of separation was seen immediately before disappearance is the critical temperature. It may be remarked that the changes of bulk produced by the screw and mercury in Andrews’ apparatus are, in the method now described, produced by elevations and depressions of temperature in the lower thermal vessel. By proper arrange- ments these elevations and depressions of temperature may be made as easily, and in some cases as rapidly, as by the turning of a screw. The dispensing with all mechanism and joints, and the simplicity afforded by using the substance to be ex- TRANSACTIONS OF SECTION A. 497 perimented upon, and no other substance in contact with it, in a hermetically sealed glass vessel are advantages in the method now described. It is also interesting to remark that in this method we have continuity through the fluid itself all at one equal pressure exceeding the critical pressure, but at different temperatures in different parts, varying continuously from something above the critical temperature at the top of the tube to a temperature below the critical temperature in the lower part of the tube. The pressure may actually be measured by a proper appliance on the outside of the lower part of the tube to measure its augmentation of volume under applied pressure. If this is to be done, the lower thermal vessel must be applied, not round the bottom of the tube, but round the middle portion of it, leaving, as already described, 10 or 20 cms. above for observation of the surface of separation between liquid and vapour, and leaving at the bottom of the tube 20 or 30 cms. for the pressure-measuring appliance. : This appliance would be on the same general principle as that adopted by Pro- fessor Tait in his tests of the Challenger thermometers under great pressure (‘ Proceed- ings Royal Soc. Edin.,’ 1880); a principle which I have myself used in a form of depth-gauge for deep-sea soundings ; in which the pressure is measured, not by the compression of air, but by the flexure or other strain produced in brass or glass or other elastic solid. 6. On the possibility of originating Wave-disturbances in the Ether by Electro-magnetic Forces. By G. F. FivzGERawp. 7. On the Number of Electrostatic Units in the Electro-magnetic Unit. By R. Sura, M.L., Imperial College of Engineering, Tokio, Japan. The object of this paper is to explain measurements made during the month of July last for an evaluation of ‘»,’ the number of electrostatic units in the electro- magnetic unit—a question which has much engaged the attention of the British Association. We can evaluate ‘v’ by determining the electrostatic and also the electro-magnetic measure of any one of the following terms: Electro-motive Force, Resistance, Current, Quantity and Capacity. It is the first of these terms that I measured in the two systems of units, and the EH. M. F. was that of Sir Wm. Thomson’s gravity Daniell, which is very constant. The question divides itself into two parts. (A). Absolute electrostatic measurement of the K. M. F. This measurement was made by means of Sir Wm. Thomson’s Absolute Electrometer, the most perfect instrument of the kind hitherto invented. As the description and principle of this instrument will be found fully given in Sir Wm. Thomson’s ‘Electrostatics and Magnetism,’ I need not enter into these explanations. I may mention, however, that the instrument, perfect as it is, will not give accurate results unless considerable care be taken in using it. In measuring an E. M. F. by this instrument, it is important that the potential of the jar or the guard ring or disc should be kept constant during the experiment. It was observed, however, that the jar was losing its charge, though very slowly, on account of the pieces of ebonite in the replenisher insulating imperfectly. Of course I could keep the potential of the jar the same during the experiment by means of the replenisher; but I found it very difficult to work the replenisher, and to take at the same time accurate readings. For this reason I thought it better, when the experimentis done by one experimenter, (oreven when, I venture to think, there are more experimenters thun one) to proceed in the following manner. First, connect one pole, say zinc, to the continuous plate, and the other pole to the outside of the jar, and take a reading; then reverse the poles and take another reading. Repeat the same operation—that is to say, take a great number of readings by successive reversals. If the experimenter be well practised, the time each reading will take him will be very nearly the same. Let D,, D,, D,, &c., be the readings 1880. KK 498 REPORT—1 880. corresponding to zinc, and D’,, D’,, D’,, &c. be those corresponding to copper, then the difference of the two readings of zinc and copper would be the difference between the mean of any consecutive readings of one pole and the reading of the other taken between those two consecutive readings, such, for example, as / / mats — D’,,or mat — D,,&c. Thus we get many yalues very nearly the same, if not exactly the same, of the true difference in question; if, therefore, we take the mean of all these, the error due not only to a small loss of charge, but also to a little inaccuracy in the readings, will be avoided. This is the method I used in measuring the E. M. F. of 30 Daniell cells, and the result I obtained is the mean defined as above = 13:283 divisions of the micrometer screw-head, As regards the mathematical calculation we have V-W=20-D)/7 4, 1 2 where V — V’ is the E. M. F. of the battery, D — D! the difference of the distances corresponding to the readings of the two poles, F the attracting force of the continuous plate on the disc, R, the radius of the disc, and R, that of the aperture. Since, now, one division of the micrometer screw-head corresponds to a distance of aon cm, we get, V — V’ = ‘904187 (C. G. 8.) ? The E. M. F. of Thomson’s gravity Daniell was measured by comparing it before and after the above experiment directly with that of the above battery by means of Sir Wm. Thomson's Quadrant Electrometer. The E. M. F. e of the cell was - V—V" _ 0.034381 (C. G. 8.) electrostatic unit £1 .961909 = 0:03 (C. G. 8.) electrostatic units, (B). Absolute electro-magnetic measurement of the E. M. F. This measurement was made by determining the strength of the current given by the E. M. F. by means of a tangent galvanometer, and then measuring the resistance of the circuit in the way to be described presently. The tangent galyanometer employed consists of a circular coil of mean radius 18:2 c.m., containing 400 turns in 19 layers of insulated copper wire, the breadth and the depth of the coil being 2 and 1:5 ¢.m. respectively. The needle of the galvanometer consists of a magnet only about 3 c.m. long, made of hard tempered steel wire, and suspended in the centre of the coil by a single silk fibre. To the needle is attached a very fine straight glass fibre, of such a leneth that its ends travel round a graduated dial of radius a little less than that of the coil, thus serving for taking readings. The mathematical theory show: that in a tangent galvanometer, . BA 7, + 6 tana ee Gatne (1); 2a n HGS est ge eee ‘ where ¢ is the current streneth, H the horizon comp. of earth magnetism, a the angle of deflection, » the number of turns of wire in the coil, 7, the mean radius of the coil, 6 half the breadth of the coil in the plane at right angles to the plane of the coil, d half the depth of the coil in its plane, g the number of layers in the coil. If E be the E. M. F. producing the current ¢ in a circuit of resistance R, then by Ohm’s law and from the preceding equation we get ec uh _'RH Jr + b? tana : = Bd He - eeee (2) oe Bere + GF — The formula (2) shows that in order to measure an HK. M. F. in absolute electro-magnetic units we have to determine, (a) the deflection a, (6) the resistance R, and (ce) the horizontal component of earth-magnetism H. (a) To determine a. The formula (2) also shows that whatever be the value of R the product R tan a is a constant quantity as long as E is kept constant, which furnishes this important suggestion that by varying the resistance R we TRANSACTIONS OF SECTION A. 499 vary a and thus get many values, very nearly equal, if not equal, of the product R tan a, the mean of which would be the more accurate value of the product. The determination of a therefore was performed as follows. The current from the gravity cell was passed through the tangent galvanometer g and a variable re- sistance 7, and the deflection a was noted. The object of introducing the variable resistance is (1) to enable us to alter the resistance R, and (2) to obtain the deflection giving minimum error, which is 45°. (6) To determine R(= 9 +6+ 7). The resistance g of the galvanometer was measured by Wheatstone’s bridge-method, and was equal to 30°86 ohms. The resistance b of the battery was measured by measuring the deflections produced on the scale of Sir Wm. Thomson’s Quadrant Electrometer by connecting the electrodes of the cell to those of the electrometer—first when the cell was unshunted ; and, secondly, when it was shunted by a known resistance; the resistance b in this case is equal to the product of the difference of the two readings into the shunt divided by the second reading. It was exactly equal to 202 ohms, So that we have a iE R 45°—15' . 80o0hms. 107'88 42° — 45’ . 100 ,, . Has th mean value of R tana = 104-73 x 10°. igre BO), 82588 It must, however, be remembered that in all these measurements the ohm, or B.A. unit of resistance, is assumed to be exactly 10° C. G. S. units, which is unfortunately doubtful, as was well remarked by Professor Adams, the President of this Section, in his address. (c) To determine H. The method of determining this element consisted in (1) observing the period of vibration of a magnet under H; and (2), observing the deflection of a magnetometer placed in the magnetic meridian by the action of the magnet placed at a fixed distance in a line at right angles to the magnetic meridian and passing through the centre of the magnetometer. . I made the experiment with two different magnets made out of very hard tempered steel wire about 0:97 ¢.m. in diameter, and also experimented with each magnet by varying the distance of the magnet, and found the results to agree very closely with one another. The mean value of H obtained with one magnet is ‘15955, and the mean value obtained with the other is ‘15937, so that the mean of these two is H = '15947 The formula used in the calculation of H is 2 Tha H = a OUND ‘ t(k — 2) (k + 1) tan p where ¢ is period of vibration of magnet under H; & distance of the centre of the magnet from the magnetometer; 7 half the length of magnet; 7 the moment of inertia of the magnet; the angle of deflection of the magnetometer. We haye now come to the evaluation of ‘v.’ The formula (II.) gives e = 101172 x 10° (C. G. S.) electro-magnetic units. Hence v = 294-4 x 10® centimétres per second, which agrees well with the latest value obtained hy Sir Wm. Thomson, namely, 293° x 10°. Although I took as much care as possible in making all the above measurements leading to this evaluation of ‘ v,’ yet since, from want of time, it was only on one occasion that I was able to make the complete measurements, there may have heen some cause or causes of error unnoticed. I intend, therefore, to repeat the whole experiment, and hope to be able to make a further communication. In conclusion, I must say—and I say with extreme gratitude—that if the experiment be in any way satisfactory, it is chiefly due to the very able and kind instructions given me by Sir Wm, Thomson and his assistants in carrying out the experiment, KK2 500 REPORT—1880. 8. On an Hlectro-magnetic Gyroscope. By W. DE FonvigLLe. 9, Sur les Transformations successives desImag es photographiques, et les Applications al Astronomie. ParM. J. Janssun, de V Institut, Directeur de V Observatoire de Meudon. Les études que je poursuis 4 Meudon sur l’application de la photographie a V’étude de la constitution du soleil, m’ont conduit 4 étendre nos connaissances sur les transformations de image photographique par l’action seule de la lumiére. On avait déji reconnu depuis longtemps que l'image photographique pouvait étre renversée, soit par l’effet de certains réactifs, soit par l'action simultanée ou succes- sive de lumiéres de réfrangibilité différentes. MM. Draper, C* Abney, Vogel, notamment ont accompli, dans cette direction, de remarquables travaux. Tout derniérement on reconnut en Allemagne que la seule prolongation d’action de la lumiére pouvait amener l’inversion de limage pour des plaques au gélatino-bromure ou au tannin. De notre coté, & Meudon, nous obtenions, en juin dernier, des images positives du soleil sur plaques au gélatino-bromure, au tannin, etc., par la seule action pro- longée de la lumiére méme qui donne l'image. Mais bientdt ce premier résultat fut complété, et nous avons été conduit 4 reconnaitre que la seule action prolongée, ou suffisamment intense, de la lumiére, améne six phases successives et bien distinctes dans l’état de la plaque photographique. 1° La phase de négativité, c’est la phase de l'image ordinaire. 2° La premiére phase de neutralité. Dans cette phase, image négative a disparu ; la plaque est presque uniformément obscure. 3° La phase de positivité. Pendant cette phase, l'image négative a_été rem- placée par une image exactement inverse, c’est-i-dire positive. Cette phase est beaucoup plus longue que la phase négative qui précéde. 4° A cette phase succéde une nouvelle phase de neutralité, mais qui différe de la premiére en ce que la plaque devient ici uniformément claire au développement, au lieu d’étre obscure. 5° L’action lumineuse continuant, une nouvelle image négative apparait, image que nous nommons du second ordre, pour la distinguer de la premiére image négative qui s'est formée sur la plaque. Cette phase est encore beaucoup plus longue que la positive précédente. 5 6° Enfin, l’action lumineuse se prolongeant toujours, cette image disparait a son tour, et la plaque devient, aprés développement, presque uniformément obscure. C’est la phase d’obscurité du second ordre. Tl suit de ces résultats que l’action de la lumiére sur les substances examinées est périodique ; que pour une certaine durée de son action elle provoque, par le développement, un dépdt métallique ; que pour une action plus longue, elle cesse de le provoquer ; qu'elle le provoque de nouveau pour un temps d’action encore plus considérable, etc. Je me propose de déterminer les rapports qui existent entre ces durées d’actions différents et si remarquables. Déja j’ai pu constater approximativement que le temps d’action qui donne l'image négative du deuxiéme ordre doit étre plus d’un million de fois celui qui donne celle du premier. C'est la puissance de nos appareils de photographie céleste qui nous a permis de réaliser, dans de courtes périodes, des différences aussi considérables dans les actions lumineuses. Nous avons obtenu, 4 l’observatoire de Meudon, des images positives directes du soleil de 4, 10, 830 centimétres de diamétre. Ces images directes montrent le soleil comme il est vu dans les lunettes. Ces images sont entourées d’un cercle noir, sur la signification duquel nous aurons & reyenir. En variant convenablement le temps de l’action lumineuse par une disposition TRANSACTIONS OF SECTION A. 501 spéciale, nous avons pu obtenir des images solaires ou une partie est positive, une |i Saad . : imp Ee ee et ad ’ partie neutre-claire, une partie négative du deuxiéme ordre, etc. J’ai Vhonneur de joindre a cette note: 1° Une image solaire de 10 centimétres (boite) de diamétre, positive. 2° Une image solaire de 4 centimétres de diamétre, positive. . 5 . . . ? 3° Une image solaire avec partie neutre-claire. 4° Une image solaire ayant une partie positive, une neutre-claire, une négative A taf J / ’ ? o du deuxiéme ordre, ete, 5° Un paysage négatif avec soleil positif dans un ciel négatif. 6° Un paysage coupé en trois parties, obtenu par contact avec un cliché négatif. Premier tiers : négatif 1° ordre. Deuxiéme tiers: positif. Troisiéme tiers: négatif, 2™° ordre (les apparences sont inverses, parce ae tof ? AN 7 que le cliché producteur est négatif). 7° Une photographie de taches solaires obtenue d’un cliché de 50 centimétres de diamétre pour un grossissement de trois fois. Cette photographie montre les stries P i PONE de la pénombre et les granulations de la surface. envirennante. fo} 10. On Improvements in Electro-Motors.! By THEODOR WIESENDANGER. 1. The inventors of the most recent electro-motive engines have worked— perhaps unconsciously—upon the idea, that the construction and action of electro- motors are based altogether upon the same laws as those of dynamo and magneto- machines and in accordance with that assumption the field-magnets of the Desprez- Motor are made to consist of large and heavy masses of magnetised steel. 2. Experimenters have also for a long time past clung to the idea that the efficiency of an electro-motor, or the amount of energy to be obtained from such a machine, by means of a current of given strength circulating in the coils of its armature only, bears a definite and direct proportion to the magneto-inductive power of its field-magnets, and that an increase of power in the field-magnets alone must necessarily produce greater capabilities of the machine. 3. This, however, is a mischievous theory, because erroneous in its very principles, and its development would only lead to the hypothesis of perpetual motion. On the contrary, starting from a consideration of the facts that a very small magnetic needle, if acted upon by one of the poles of another and very powerful magnet, has its polarity destroyed or reversed, and that, if one of its poles, say the N pole, is presented to a similar (N) pole of the large magnet, the former will completely lose its characteristic qualities and be attracted by its over- powering opponent, we can only come to the one rational conclusion, that the power of the field-magnets of an electro-motor, as compared with that of the magnet or magnets constituting its armature, should not surpass the limit of some certain ratio, yet to be determined by experiments carefully conducted, and that, if it sur- passes that limit, the capabilities of the machine must be impaired. Acting on this principle the inventor constructed a motor (the motor was shown in motion) in which the power of the field-magnets is as nearly as possible equal to that of the armature, the core of the former being very light and made entirely of soft iron; and the satisfactory results obtained from this machine are a sure sign that a further investigation of the subject, and experiments made with a view of deter- mining the exact ratio, will lead to further improvement. Another very important consideration in the construction of electro-motors is the method of motion of the revolving armature, with regard to the approach to, or the receding of its poles from the poles of the field magnets. The greatest amount of power will be derived from a motor if attention is paid, not merely to the one condition that the armature should revolye in the most highly concentrated magnetic 1 Published in exrtenso, with illustrations, in the Hnglish Mechanic; also in Design and Work, September 18, 1880. 502 REPORT—1880. field possible, but also to the other, of no less moment, that nearly the entire motion of the revolving armature should be either one of approach to or of withdrawal from the poles of the field-magnets. [Various methods of accom- plishing this object were described and illustrated by drawing models.] Electro- motive engines with field-magnets of more than two poles are more _ perfect in their action than others with field-magnets of two poles only, mainly be- cause in the former the line of attraction, as exercised between the two systems of poles is at angles varying from 80 to 1 degrees from the motion of the poles of the armature, while in the latter the line of attraction very nearly coincides with the line of motion. The relative positions to each other of the axes of the systems of field-magnets and the magnets constituting the armature, and the ratio of power of the two systems, are both matters awaiting careful investigation from men of science, and further researches in this most important and interesting field of work must lead to immediate progress. With regard to the former question we have as yet only the vague, unsatisfactory hypothesis of ‘lines of force,’ and the latter point appears to have escaped altogether the notice of hoth inventors and investigators. 11. On a New Mode of Illuminating Microscopic Objects, By Purr Brana, F.C.S. 12. On an Instrument for the Detection of Polarised Light. By Pup Brann, F.C.S. TRANSACTIONS OF SECTION B. 503 Section B.—CHEMICAL SCIENCE. PRESIDENT OF THE SECTION—JOSEPH HENRY GILBERT, Ph.D., F.B.S., F.C.S., F.L.S. [For Dr. Gilbert’s Address see page 507. ] THURSDAY, AUGUST 26. The following Reports and Papers were read :— 1. Report of the Committee on the Best Means for the Development of Light from Coal Gas of different qualities. Part II.—See Reports, p. 241. 2. On some Relations between the Atomic Volumes of Certain Elements and the Heats of Formation of some of their Compounds. By WATER WELDON, F.R.S.L. 3. On the Influence of Water on the Union of Carbonic Oxide with Oxygen at High Temperatures. By Haronp B. Dixon, M.A., F.C.8. When a spark from a Leyden jar is passed through a mixture of two volumes of carbonic oxide and one volume of oxygen, which has been thoroughly dried, no explosion is caused. It is very difficult to dry the gases thoroughly enough to prevent the explosion under atmospheric pressure; but by a reduction of pressure it is easy to show that a mixture of dry gases will not explode under the influ- ence of the spark, which mixture readily explodes on addition of a minute trace of moisture. It was found that, when the pressure in a dried eudiometer was gra- dually increased until the passage of the spark caused the gases to combine, the disc of flame passed quite slowly down the tube, whereas when the tube was satu- rated with moisture the flame travelled too quickly to be followed by the eye. Some of the mixture sealed up in a glass tube with anhydrous phosphoric acid under atmospheric pressure, would not explode on passing a succession of sparks through it. On opening the sealed end under water, the spark caused the gases to unite. Into a similar tube containing anhydrous phosphoric acid, a piece of potash was fused to the glass; when filled with the mixture and sealed up, the gases would not combine on passing the spark. On gently heating the potash with a Bunsen flame, the spark caused an explosion. It was found that a small admixture of dry carbonic acid with the gases had no effect in determining the explosion. Neither dry nitrogen nor dry cyanogen had any effect, while the smallest admixture of hydrogen or ether vapour caused the gases to explode on passing a spark. From these experiments it appears probable that the oxidation of carbonic oxide is really caused by the alternate re- duction and oxidation of water molecules, according to the equations :— (1) CO + H,O = CO, + H, (2) 2H, +0, = 2H,0. A comparatively small number of water molecules suffices to determine the explo- sion; but the explosion gains in intensity the greater the number of water molecules present, It was shown by experiments at 52°C. that the force of the explosion was 504 REPORT— 1880. greater when the number of water molecules was equal to the number of carbonic oxide molecules, than when a fewer number of water molecules were present, and their place taken by molecules of nitrogen, whose specific heat is less than half that of steam, 4. On Metallic Compounds containing Divalent Organic Radicals. Part I. By J. Saxurat.! With the view of isolating metallic combinations of olefiant gas, Wanklyn and Von Than (‘ Jour. Chem. Soc.’ xii, 258) studied the action of mercury and zinc upon ethylene iodide ; but they failed in obtaining even a trace of organometallic com- pounds. I repeated their experiments not only with iodide and chloride of ethylene, but also with the bromide and the chloriodide, and under various conditions; but the results obtained are essentially the same as those described by the above-named chemists. Olefiant gas is given off in abundance, and metallic chloride, bromide, or iodide is formed at the same time. At the suggestion of Professor Williamson, methylene iodide was next tried ; for it appeared probable that with this compound the decomposition into metallic iodide on the one hand, and into the hydrocarbon on the other, would be impos- sible, or, at any rate, would not take place under such circumstances as those which, while easily allowing the ethylene compound to decompose, are, at the same time, favourable for, or essential to, the formation of organometallic compounds. This anticipation was realised. By leaving methylene iodide in contact with metallic mercury and some mercurous iodide for a few days, combination takes place without any evolution of gas. One point of interest in’ the reaction consists in the part played by the mercurous iodide. This, under the influence of light, decomposes into metallic mercury and mercuric iodide: the former enters into combination with methylene iodide ; and the latter, taking up fresh mercury, repro- duces mercurous iodide ready for decomposition. Chiefly two products are formed. One of these, when properly purified, is a white crystalline substance, insoluble in water, cold alcohol, ether, chloroform, ethylic iodide, or benzene. It is somewhat soluble in boiling alcohol, from which it erystallises out, on cooling, in white slender needles. But by far the best solvent for it is methylene iodide, which, when hot, takes up a considerable quantity of the substance, and allows a part of it to crystallise out on cooling. From the mother liquor, ether precipitates it almost completely in the form of fine crystals. The substance melts at 108° to 109° C. to a clear yellow liquid, in which state it remains up to a considerably higher temperature. On cooling, it solidifies to a yellow crystalline mass, and re-melts at the original temperature. The following numbers were obtained on analysis :— I. 0:2075 gr. of the substance gave 0:1030 gr. of mercuric sulphide. TT MO:09100 5 x55 5 0:0455_—,, - and 0:0910__,, __ silver iodide, Thus— Found. _ —--—_ + Cale. for I. u. CH,Hgl, Mercury . . 42-790 43:100 42735 Iodine . . = 54.040 54-273 Heated with iodine, the substance is decomposed into mercuric and methylene iodide. Quantitative determinations show that for every 100 parts by weight of the substance, 54°54 parts by weight of iodine are needed ; that is, as much iodine as is contained in 100 parts of the substance. Now, if the compound contains in its molecule nothing but a molecule of methylene iodide and an atom of mercury, it ought to require, as it does, for the completion of the reaction, ze. for the pro- duction of methylene iodide and mercuric iodide, just as much iodine as it contains, apraarr CH,Hgl, + I, = CH,J, + Hel,. . Bromine and chlorine act upon the body in a manner similar to that of iodine. 1 Journal of Chemical Society, September 1880. TRANSACTIONS OF SECTION B. 505 The simplest, and indeed the most reasonable, constitutional formula that can be assigned to this new body, which may be termed monomercurie methylene iodide, is I(CH,)’Hgl, the divalent radical methylene (CH,)”, combining to the extent of half of its power with iodine on the one hand, and to the same extent on the other, with Hel, which plays the part of a monatomic radical. The novelty of the com- pound is revealed in the fact just stated, inasmuch as all the so-called organo- metallic bodies hitherto known are characterised by the monatomic nature of the alcohol radicals which they contain, viz. methyl, ethyl, amyl, and allyl. It has already been stated that two products are formed by the action of mer- cury upon methylene iodide. This second compound has not yet been obtained in the pure state. It was, however, analysed; and from the results, as well as from some of its reactions, there is reason to believe that this body is dimercuric methylene todide, CH,(Hgl),. The action of zinc, as well as of sodium amalgam in presence of acetic ether, upon methylene iodide were tried, and the results of these experiments will be the subject of a future paper. Ifthe zinc compound be successfully isolated, it cannot fail to be of great service in building up bodies of the homologous series, where the consecutive members differ by CH,, and we may thus be able to synthesise higher alcohols by a comparatively simple process. 5. On the Application of Organic Acids to the Buamination of Minerals. By Professor H. Carrinaton Bourton, Ph.D. The following research into the behaviour of the commoner minerals with or- ganic acids was prompted by the difficulty of transporting the liquid mineral acids on mineralogical and geological journeys. A careful study of the action of citric acid on 200 mineral species has established the fact that this organic acid possesses a power of decomposing minerals only slightly less than that of hydrochloric acid. The manner of conducting the investigation was briefly as follows: the mineral to be examined was yery finely pulverised, and treated in a test-tube with a satu- rated solution of the organic acid in the cold, and then the contents were heated to boiling. Preference is given to citric acid, because it appears to have greater decomposing power than either tartaric or oxalic, owing probably to the greater solubility of metallic citrates. In order to increase the power of the organic acid, two other reagents have been employed in connexion with it; these are sodium nitrate and potassium iodide. These are added, in solid form, to saturated solutions of the citric acid at the moment of using. Minerals belonging to several groups were submitted to these processes, and gave phenomena which may be summarised as follows:— Ist. More or less complete decomposition and solution of oxides, phosphates, &c., without formation of precipitates or liberation of gases. 2nd. Complete solution of carbonates, with liberation of carbonic anhydride. 8rd, Decomposition of certain sulphides with evolution of sulphuretted hydrogen. 4th. Decomposition of certain sulphides, with oxidation of the sulphur. 5th. More or less perfect decomposition of silicates, with separation of either slimy or gelatinous silica. 6th. Decomposition of certain species by reagents forming characteristic pre- cipitates. 7th. Wholly negative action. The exact behaviour of each species is shown in the annexed table. The application of this method of examining minerals to field work is obvious ; and this newly developed power of organic acids has undoubtedly an important bearing on the chemistry of geological changes. The quiet work of the organic acids of the soil in decomposing rocks and minerals demands greater recognition than is usually accorded. 1880. REPORT 506 “sozturyepoy), } ‘aqtooyos “ozrysiwueg ‘opquinjoy “oyopldryy ‘uoey ‘oper, ‘oyMomog ‘oqrjomeyg ‘oplUegL Ty, ‘zedoy, ‘oymud yy -O51[0 ‘azttopraquy ‘oqyryytowy ‘oyJoneT ‘oqeuIO MA ‘oyTjopIderT ‘ayAoosnyy ‘071901 “OF 1[OT ‘aqtsto7, ‘oqrWBLANS A ‘opm ‘ogrreqissup “TAroqosarp ‘aqrmo.xyH ‘aurdg “umpuns0g ‘aytokapy ‘agtonpy ‘oQSNorg ‘ayruapqAToy "POV OFGIO el} Wry paatsap st poapoaa “OD on, + ‘T pun Ty “YT A‘ ‘0 ‘a ut a80y} Jo ysou pun ‘oqoprd gy ‘ayruoydopop ‘adoas gq ‘ayIpurwpy “OUTATI() « O}ISVILVT + OPOUTO VW » OpUaTquIo;T , ouauinpodg ‘ayiony ‘guoyysrad (Fy ‘oyTUIsUTT ‘opruneag “OUT ULAYT + O}JOUSe YY 4097004 ~BUryse AA » 8} TawOOUT Ne + OW POWO TT j Steqvaaip x Juaw1d1g IBS [VOT M+) UQTAN Suyprog &q pasoduosaq x Peri UL asoyy pun ‘aqrouqn iy j ‘oyruruet yy j ayLore Uy j ‘ayisuq Apog ‘ayruvydayg { ‘oyjuvauay, j OJLIpayRayay, aq (S.eld gq jo MOryI0g jOMT[IAoD ‘ay SvADV N j eyttAdoues.ry j eVISBoIe pT j oyrameu i eqaTeqoD j ‘ay greutg ‘oylovuULy j ‘oyttAdoopeyd, j fayd gy ‘}1T0901N 1 SPOT j ‘oyrUUB WOT, j eypoooe yD) ‘OUISSOT] ‘ayquesiy j oyryAout0g OPUTY NST x tnydng “yqnuustg, ‘Auoupuy ‘otuas1y ‘raddoy ‘AMO. STOATIS *ON®N +0 TTA BuTog Aq peaTossi(y I *squahna, “payougqe A[qQoaT x UFIA POULUUX 2.18 paAlOAd SosUs OL L—"A "No —— — ——-'0006WO 8 HH ——— eee *“paafosstp 10 pasoduioosap Ajaqarduroy j (‘sorods parpuny oT) oypAyy ‘oy 4sa[99 ‘opLeg, PNITIOR NO *OILOTYOO.A J " MW asoyp ‘0 uw asoyz "g U1 asoyy “FUL asoyy. ‘opp AOMacy pup pun pun a) “OUIQTS t ‘oytpoyoss0 fy ‘aqisequyd ‘ayo[euy i OP }0Se TN. x OJTUOSL TT tj foytporqenr 4 VL ‘AyIStIAya sr: j ‘o}TWOSUIOY J, j foUTORTR « 2} EOasary) ,gumsday | ‘ayrpAqdody j ‘ayIssn.1a(-), “aq TyJUaL) ‘ayooory | tj fourteen jo} T8003 Avg ‘ayyseg ‘aytuazn AA | [SB ]fooosAg j ‘egluviyu0y4g ‘OyTRULIaYy sopra | f j‘eyQuOMINET {‘OOqIE A ‘attosAayyy | OVApIS ~waoA | Tj *e9t[0}00g | ‘oyuosvry ‘auiquad.aag j ‘opIsouSe oud y ayporipuoyy x OPLUOSTALUG | oypurpnoyy +i Pear | Ce)‘ouuerry | “Huzey sidey 4 O}18 , OPTUYaL ‘oyIsouloy | | jfeurpauopisg | ,‘oyruowryT ‘anpoydan | ‘oyoymadg -orooporyy | fy ‘oqroyeq | ‘opwesuemog | j‘ayruvsueyy | ,‘oynpjoorn | tj foyrmoarytAy | ‘oztaopeydg 4 O}LOYUV |, eytdosopyg | ,‘o}ytuoumog | {j oysnpor 6,400 | 3 0 0 30,000 21,300,000 B05 10,600 | 210 0 25,000 17,750,000 90 years — — 2,663,164 | 1,890,846,440 Plan No. 3. 40 years 5,000 |} 310 0 35,000 24,850,000 A AY se 6,300 | 210 0 25,000 17,750,000 87 years — — 2,564,185 | 1,820,571,135 Plan No. 5. 30 years 5,000 | 310 0 35,000 24,850,000 30. =(Cs, 7,100 3 0 0 30,000 21,300,000 24 4, 12,300 | 210 O 25,000 17,750,000 84 years — —= 2,547,752 | 1,808,903,920 Plan No. 6. 10 years 5,000} 310 0 35,000 24,850,000 NO! Sie 5,700 SCS KO 34,000 24,140,000 LO ass 6,700 | 3 6 0 33,000 23,430,000 LOR 8,000 3 «4? 0 32,000 22,720,000 LOD ess 8,700 | 3 0 0 30,000 21,300,000 TO): ese 10,700 | 218 0 29,000 20,590,000 We 12,400 214 0 27,000 19,170,000 NOs; 14,700 210 0 25,000 17,750,000 Diiueryy 17,200} 2 5 0 22,500 15,975,000 89 years -> — 2,652,127 | 1,883,010,170 Plan No. 7. For the first eight periods as Plan No. 6. 10 years 14,700 | 2 0 0 20,000 14,200,000 1 year 6,200 013 0 6,400 4,530,000 91 years _ —- | 2,655,982 | 1,885,747,220 Annual charge on £780,000,000 £ about 26,910,000 23,400,000 19,500,000 2,077,267,920 27,300,000 19,500,000 2,000,064,300 27,300,000 23,400,000 19,500,000 1,986,846,560 27,300,000 26,520,000 25,740,000 24,960,000 23,400,000 22,620,000 21,060,000 19,500,000 17,550,000 2,068,659,060 15,600,000 4,980,000 | 2,071,665,960 Comparison of Cost of Different Systems. Plan No. 6, Diminishing Sinking Fund or Annuities Perpetual Annuities £30,000 x 89 years = £2,670,000 Add debt still owing . Annuities for terms of years, £3 4s. ‘gd. each x 89 years = £287 15s. 4d. x 10,000 1 000, 000 £2,652,127 3,670,000 2,877, 6662 TRANSACTIONS OF SECTION F. 679 Plan No. 7. Diminishing Sinking Fund or Annuities . 3 A : 2,655,982 Perpetual Annuities £30,000 x 91 years = £2,730,000 Add debt stillowing . 3 i 1,000,000 3,730,000 Annuities for terms of years, £3 4s. 4d. each x 91 years = £292 14s. 4d. x 10,000 : A A 2,927,1662 I now request your attention to plans 6 and 7, which are drawn up especially for practical purposes, not to demonstrate the capacity for modification of my principle, or the vastness of the economies to be effected. Examining plan No. 6, it is noticeable that after 40 years the excess for sinking fund entirely ceases. From the 41st to 50th year the annual payment is the same as for perpetual in- terest, and from the 51st to the last year it is decreasingly less. The total disburse- ment on account of the sinking fund is, in the forty years, some 140,000/. per million, or 99,400,0007. for the funded debt ; while in the last 39 years the total saving is 165,000. and 117,150,000/. respectively, which more than compensates for the early sacrifice. If we study the problem from an every-day, instead of a theoretical, standpoint, it is evident that to redeem the debt need cost the country NnoTHine. This generation lays out 99,400,000/. by 40 instalments, to be returned with interest to its successors. If 89 years is considered too long a term, the payments from the 4lst year can be equalised at 3 per cent. on the capital, and the debt annihilated in 81} years, The net cost of redemption will then be 99,400,0002, or 14 per cent. I will now ask you to inspect plan 7. You will observe that the same method of repayment is continued up to the 80th year, but that from the 81st the annuity is 2/7. instead of 2/. 5s.,and the annual payment is fixed at 20,0002. instead of 22,5001. per million. In introducing this variation my object is to impress upon the mind, with redoubled force, the extraordinary potency of compound interest, when judiciously applied. Although the funded debt charge for the final period averages 1,775,000/. less by the last plan, liquidation occupies little more than a year longer; while the aggregate sum required for interest and sinking fund is augmented by 2,737,050/. only. Prolonging the term of redemption has the effect of showing up the new philosophy in more brilliant colours—the saving when compared with perpetual annuities being 63,145/. per million more, or when compared with annuities for terms of years or cumulative sinking funds, 271,184/. 13s, 4d. against 225,539/. 13s. 4d. The correct figures for the funded debt are, as against perpetual annuities, 12,689,830/. by plan No. 6, and 52,552,7801. by plan No. 7. This is excluding the 710,000,000/. capital paid off. When com- pared with annuities or cumulative sinking fund loans terminating in 89 or 91 years, the net savings are over 160 and 192 millions respectively. The limitation of time prevents notice being taken of many other important phenomena which occur to my mind, but I trust sufficient information has been given to enable economists and financiers to thoroughly investigate this neo-philosophy in sinking funds and annuities, and that sooner or later we may see its principles adopted in this and other countries. TUESDAY, AUGUST 31. The following Papers were read :— 1. What is Capital? The Contradictory Responses of Economists to this question examined from the ground of Aciual Fact and Life. By W. WESTGARTH. The author, after alluding to the late Mr. Bagehot’s remark, that many who were conversant with economic theory were not so with economic facts, and vice versd, went on to illustrate this by the case of capital, which is still so disputed a 680 REPORT—1880. subject in Political Economy. The question What is Capital? is still answered by economists in a most various and unsatisfactory way. Approaching the question from the side of a large conversancy with economic facts, he would point out where the conclusions of economic theory appeared to him at variance with the facts of life. He first gave the prevailing theories as to capital, and then contrasted them with what capital actually was in the world of fact and life. Adam Smith’s view was, that everything dealt with to yield revenue or profit was Capital. This view, although still partially held, had been largely departed from since, and the prevailing view now was, that capital was that only which was concerned in pro- duction. Then again arose the question of two kinds of capital, the fixed and the circulating, and what rule or principle distinguished them. Here Smith’s criterion was fixity as distinguished from mobility ; but Ricardo had suggested rather relative durability, and in this had carried most economists with him, so that the prevail- ing view now was that things of a durable kind, as land, buildings, railways, were of fixed capital, while perishable or renewable things, as food, clothing, furniture, were of circulating capital. But as Professor Jevons and others admit, there is no clear line between a throng of things which are neither very durable nor yet very perishable. He then passed to a suggestion of Mr. Jevons, which he noticed favourably as tending to a correct view of capital. This is in effect that the so- called fixed capital is not itself capital, but is that which has had capital spent upon or sunk in it. He proposes thus to distinguish a ‘ free’ from an invested capital. But as to this free capital, he falls back upon the ‘ production’ idea, already adverted to, and limits capital to articles of food, clothing, furniture, and such direct needs of ‘labour of all kinds and classes.’ Lastly, as to the origin, maintenance, and increase of capital, most economists are agreed that these all result from saving, abstinence, and improving industry, so that the less the spend- ing of what is produced, the more the capital, and on apparently to indefinite increase, All these views Mr. Westgarth considered to differ more or less from that of the capital of fact as confronting us in actual life. This capital we see to be one fund—one homogeneous fund we might call it—which supports indiscriminately not production only, but all exchange or business life. He insisted, as speaking from the world of fact, that exchange was essential to the idea of capital. What caused exchange was the subdivision, or, to speak more comprehensively, the association of labour. With the association of labour, he remarked, we enter upon Economic Science, and it has thus, in this its limitation, a sufficiently marked distinction from the far wider Sociology, or the Science of Society. Capital, then, is the fruit of exchange. It consists of the stock of things which arise and are maintained as the needs of exchange. These stocks are mainly of three kinds : first, raw materials, or things in preparation for our use; second, the things pre- pared, and for sale in the shops and markets; and third, the prepared things which are not passed out of exchange for ‘ consumption,’ but kept as the ‘ rolling stock’ of trading or exchanging life. The chief and most notable item of this third lind is money. Money is simply one kind of goods used to value the other kinds, and where independently originated, it has always made its first appearance in this simple way. Coinage and the change of material for the ‘ precious metals’ were afterthoughts to increase convenience, but they noways altered relationships. The fund of capital then consisted of goods and money—ot these indiscriminately, as one and the same class of things. This fund was distinguished from the so-called fixed capital, which, as to its leading idea, was not capital at all, but only agency, which agency, in conjuction with that of man himself, enabled us to produce the real things of capital, namely the requisites of our direct use. Land, for instance, is such agency, and only its crop belongs to capital. These direct requisites are. capital while within the sphere of exchange; outside of exchange they cease to be capital. Thus the limitation or law of capital is that it constitutes the stocks required for the time being by exchange. As exchange extends in a country and larger stocks are needed, there is more capital to the country. What causes ex- change or trading to extend, in spite of this cost of larger capital, is the increased economy of production gained by the larger scale of business. All trade extension. TRANSACTIONS OF SECTION F. 68 is an everlasting battle between, on the one hand, the increased profit by cheaper production, and on the other, the increased cost of the larger capital requirement. Successful trade extension is that which, in increasing a country’s income, increases concurrently also the total of its capital. There is then a ‘ Law of Capital,’ and these are its chief elements. 2. Remarks and Statistics relating to Swansea Usages and Customs as they affect the Sellers of Foreign or Colonial Copper Ores. By Wm. Hen- DERSON. I have chosen the occasion of the meeting of the British Association at Swansea as a fitting time and place for the discussion of this very important subject. It is a matter of great local importance, and here it is most likely to receive an intelli- gent and practical treatment. No doubt from the standpoint of the sellers of foreign ores, the clamant evils of the system have long ago called for redress. For many years we have suffered from delays, inaccuracies, and all the evils inherent in this antiquated system, and striven to remedy it as best we could, and have succeeded, where we had to deal with rich ore, reguluses, or precipitate, to a certain extent, and completely, so far as Chili bars are concerned; but to the very large quantity of poor ores, such as the Spanish and Portuguese ores, the whole of the Swansea system applies in all its inconsistency and rigour; and my object in this paper is to show the hardships we are altogether unnecessarily subjected to, and to propose a remedy. I may also here premise that we do not complain of the actual price paid us for our ores, as I do not believe that we should get a penny more were the system changed to-morrow. But what we complain of is the system by which that price is arrived at, and the enormous waste of time before we get ‘agreed’ results. I purpose treating this subject under the following heads :— 1. Swansea public sales or ‘ ticketings.’ 2. Sales by private bargain at Swansea and elsewhere based on Swansea sales. 3. Sales by private bargain based otherwise than Swansea. 4, Weights and allowances. 5. Dry assay and its relations to the truth, as shown by actual results by smelting and wet process. Time consumed in getting settled results— differences. 6. Wet assay. 7. What ought to be the simple basis of price ? 1. Swansea Public Sales or Ticketings. Public sales of copper ores at Swansea, several years ago, used to be very regu- larly held once a fortnight, and the quantities of ore were then very large and important. This is now no longer the case. For the year 1877 there were only twenty-three sales; for 1878, only eighteen sales; and for 1879, only fifteen sales. The quantities sold were insignificant—being for the three years collectively 112,504 tons. The usual custom with foreign ores which are to be disposed of by public sales is as follows:—They are usually consigned to one or other of the ore yards, such as those of Messrs, Bath & Sons, or Messrs. Richardson & Sons, where the ore is landed, and, if necessary, crushed and put out in square or oblong piles about 2 to 23 feet deep, and in parcels of from 50 to 100 tons and less. These are generally put forward for next sale, and a day is appointed for sampling, when intended purchasers are represented as well as the seller. A period of fourteen days is allowed between the date of sampling and the day of sale, which is considered necessary to allow the assays to be made. On an average it takes fourteen days more to prepare and crush the ore previous to sampling, and all this is attended with a very serious expense, besides the delay. As we do not know when another sale will take place at Swansea, we save time and lose nothing by adhering to previous sale. 682 REPORT—1880. Two tables were here given, showing what time is lost between the delivery of the ore and the settlement of the assay and price. During the whole of these numbers of days, ranging from sixteen, which appears to be the shortest, up to sixty-two days, we cannot deliver our invoices, and have to wait for our money all that time. This great hardship is further aggravated to the importer who sells his raw ore to the sulphuric acid makers for sulphur value only, and takes back the cinders. These have to be again sampled and assayed, with the delays repeated. If he is also a copper extractor, as I am, and sells his precipitate, that has again to be sampled and assayed, and the same delays re- peated, so that it may be quite a common event that from the time of landing till the time of realisation eight months may elapse, and the same copper be assayed. three times. The costs by sale at public ticketings are very considerable, amounting in Spanish ores to fully half the freight, which, with present low prices of copper, may be all the profit. This is not the custom when sold by private bargain, as these sales as a rule are generally ex ship. It is, therefore, evident that if an importer can sell his ores to arrive ex ship by private bargain, he will not send them to the Swansea sales ; and surely this is not a state of things conducive to the prosperity of Swansea or its industries. 2, 3. Sales by private bargain at Swansea and elsewhere based on Swansea sales. The great bulk and value of these sales are made elsewhere than at Swansea and the preceding sale ; or, if any Swansea sale takes place on the day of sampling, that sale is taken as the basis of price. The object is, of course, to save time, and one has to take the risk of a rise or fall in the price of copper between the dates of sale and that of delivery. Our friends the copper-smelters at Swansea will, how- ever, admit that so far as the produce of Spain and the economical treatment of the raw Spanish or Portuguese ores are concerned, or even for the smelting of the burnt ores, the processes of Swansea were quite unable to deal with the large quantities in any economical way. With the raw ores, asa rule, the very large percentage of sulphur, viz. 48 per cent., would have been worse than wasted, as it would have cost something considerable to calcine such ores, rich in sulphur and poor in copper, down to the point to make them produce per se (or even mixed with other calcined ores) a sufficiently rich regulus, Besides the enormous increase of nuisance, and even when in later days the sulphuric acid manufacturers came to use the sulphur, the cinders still contained 60 per cent. of metallic iron, and which when sent to Swansea, from such distant places as Newcastle and Glasgow, at heavy freights, only 4 per cent, to 6 percent. of the weight was paid for, and the whole of the iron contents were lost. By the introduction of my wet process at this juncture, the shipment of these burnt ores from all the districts of large consumption was rapidly stopped, and the ores treated on the spot, saving the freights and iron ore, and yielding much more perfect results for copper—thus preventing very large quantities of ores coming to Swansea. Andso in like manner the enormous yields of the Spanish and Portuguese mines (which are constantly increasing), over and above their possible sales for sulphuric acid purposes at home and on the Con- tinent has gradually led to great extension of the slow process of cementation from the poorer grades of ore, produced at very small cost, in enormous quantities, reckoned by hundreds of thousands of tons, for each of the uncovered mines per annum a very large and increasing annual production of copper, as precipitate, of from 50 to 75 per cent. produce is annually obtained. Another reason why the public sales at Swansea have decreased, and are there- fore no longer a fair basis for private sales made elsewhere, is the most serious of all. By the opening up of short railways to the mines, and the great development of coal mining, Chili now sends most of her produce to this country, as Chili bars, or in blocks containing about 96 per cent. pure copper. So serious is this production, that it may be stated roughly as a fact that Chili exports as much copper in ores, reguluses, bars, and ingots as all the rest. of the world produces, and almost the whole of this is sold by private bargain, and the price is regularly quoted every busi- ness day, and virtually rules the price of copper. fest EEE LL— ll TRANSACTIONS OF SECTION F. 683 The statistics given below from the Board of Trade returns for the last three years amply prove what a small proportion of the copper imported is sold at Swansea public sales, and how much by private bargain. Board of Trade Returns of Imports for Years 1877, 1878, 1879. Specification and Country Quantities Values 1877 1878 1879 1877 1878 1879 Tons | Tons | Tons = £ £ Copper Ore from Chili . : 7,949) 2,349 461) 115,933) 30,694 8,355 Do. Cape of Good Hope . . | 14,060) 12,789) 13,629) 258,839) 241,373) 232,956 Do. British North America . | 38,612) 34,630} 25,054) 256,215) 191,505) 127,581 Do. other countries 5 . | 54,845) 53,177| 48,685) 533,723) 456,561) 395,605 Total ; z . (115,466)102,945| 87,829)1,164,710) 915,133) 764,497 Regulus (incl. Precipitate) from Chili 2 : . | 17,031] 11,455) 15,666) 531,237) 342,363) 415,996 Do. other countries : . | 16,670} 21,955] 30,264! 667,312) 798,574/1,073,160 Total . . - . | 33,701) 33,410) 45,930/1,198,549)1,140,937| 1,489,156 Unwrought or part wrought from Chili . : 3 . | 25,958) 22,785) 33,534/1,810,859/1,434,403)1,957,049 Do. from Australia . ; . | 11,010) 8,661) 9,845) 851,759} 610,640) 638,632 Do. other countries F 3,248] 7,914} 3,291} 225,753) 513,232) 207,494 Totals . . . | 40,216) 39,360) 46,670)2,888,371|2,558,275|2,803,175 Pyrites ' ‘ . ° . |680,033/577,719)481,622/1,646,132/1,332,934)1,051,015 Grand Totals . . |869,422|753,434|662,051|/6,897,762/5,947,279|6,107,933 Public Sales at Swansea . . | 45,674) 35,581) 31,249) 407,969) 164,914) 134,069 Sales elsewhere by private bar- gain . : ; ; . §23,748]717,853/630,802/6,489,793)5,782,365/5,973,864 4, Weights and Allowances.—It used to be the custom at Swansea and elsewhere to weigh the ores, reguluses, and precipitate in hand barrows of 3 ewt. each, by beam and scale, thus giving seven weighings to the ton of 21 cwt. For some years, how- ever, this custom has been departed from, and 2 cwt. barrows substituted, thus requiring 103 turns of the scale for every ton of 21 ewt. But over and above this allowance a draftage of 244 Ibs. per ton of 21 ewt.is demanded from sellers of foreign or colonial ores. Why this anomaly exists it is impossible to guess, when no such allowance is asked for in Cornish ores. "What even is the use of maintain- ing the 21 ewt. to the ton except to complicate and obscure accounts? Refined copper is not sold at 21 ewt. to the ton; and no such absurd allowances as 244 lbs. per ton, nor is it weighed in 2 or 8 ewt. lots. Ingots, cakes, and tiles are all weighed carefully in 10 ewt. lots with just the turn of the scale, and the seller makes an allowance at the time of about two pounds to the ton, as it is found by experience that a certain amount of scale comes off in handling and transit, and this allowance is to insure delivery of nett weight to the purchaser on delivery, and experience shows that this allowance is ample. In selling or buying Chili bars, which are partially refined copper of about 96 per cent., an allowance of 4 Ibs. on the ton of 20 ewt. is all that is allowed, and I think this is perfectly fair, for ne refiner has to sustain the risk of scaling and abrasion both to and from his refinery. 684 REPORT— 1880. There can be no argument in favour of the maintenance of the 21-cwt. ton and allowance, except some antiquated custom, and there is much in favour of its imme- diate abolition. We, the sellers of foreign ores, do not for a moment suppose that so far as price is concerned the abolition of these absurd and antiquated customs will secure us any advantage whatever. We are perfectly aware that the receiving of these allowances by the buyer, and the giving of them by the seller, have all been taken into calculation by both. Our only argument here is, what is the use of introducing gratuitously into a simple calculation complications of this sort, which are admittedly discounted previously? We consider this a grievance that only requires to be stated to be admitted, and as its maintenance benefits no one, but wastes time and leads to needless book-keeping, we earnestly trust our friends the smelters will agree to their early discontinuance. 5,6. The Dry Assay and its relations to the truth, as shown by actual results, «s obtained by Smelting and by the Wet Process with works where the Precipitate is refined, and Copper sold as B. S. or Tough Cale. The Wet Assay tested in the same manner, and as compared with the Dry Assay. It will be more convenient to treat these two divisions of my subject together. I do not intend here to enter into any description of either the dry or the wet assay, and their modes of operation. In the Chemical Sections of this, or a future meeting, I hope to have an opportunity of discussing these fully. What we importers of foreign ores have chiefly to complain of in the method of the dry assay is the unreasonably long time it takes to get agreed results, and the constant disputes, which require a considerable amount of very unpleasant and vexatious correspondence, which generally ends in a reference; and all this con- sumes valuable time. I have enough and to spare of statistics to prove this argu- ment against the dry assay method—the long and inconsistent delay in settling results—a delay and uncertainty in which the disputes are so chronic that I venture to say no other class of merchants would have endured them one year without seeking some remedy. A set of results furnished me by Messrs. Mason & Barry show that no possible reliance can be placed upon the dry assay, as in the same cargo, delivered from the same ship, but divided amongst several customers, totally ditferent results are ob- tained. Now, I am not prepared to go so far as this, as it goes quite against my general experience. In my view, it is a perfect proof that the mode of sampling is utterly wrong, when the sampler for the buyer and the sampler for the seller are permitted to take their samples by running over a series of loaded trucks and each chip off about a shovelful from a six or ten ton truck from large pieces of ore. Mix them together and call this a sample!!| The results of divided cargoes—which, if properly sampled, would go to prove the dry assay utterly worthless, are, when not certain on the point of sampling, misleading—are yet so instructive, that I have ventured to give them here as facts which bear somewhat of an important argument against the dry assay. Then against the dry assay we have a special charge that the assayers very often disagree, and the result is a reference to a third assayer with a corresponding loss of time. This has very frequently to be undergone, especially with burnt ores, and in most cases the third assayer agrees with neither of the others. As a contrast to this, I recently caused the Seville Sulphur and Copper Company to send a sample from their usual imports from their two mines, one comparatively rich and the other very poor, to five of the best known chemists who make’a speci- ality of analysis of minerals, and I give below their results, and it will be seen how closely they agree. cx Betty Russell. ex Bella Rosa. if II. Ill. Edward Riley, London , i : 6752 6°808 3-42 Fred Claudet, London 4 F F 6°830 6825 6°835 3-48 James 8. Merry, Swansea . 5 : 675 685 6:90 3°47 Alfred H. Allen, Sheffield . : a“ 6°82 3°30 John Clark, Ph. D., Glasgow. 4 6°81 3°42 Average . * = “ 6°80%, 3°42% TRANSACTIONS OF SECTION F. 685 It will also be seen that the dry assay is uniformly too low, and always con- siderably short of the truth. This is proved not only by its difference from the wet assay, but also by actual results obtained by smelting, where the surplus copper forms a very considerable portion of the profit. But the wet assay is proved to be the true assay by results obtained on the large scale when my process of extraction is used, and the precipitate produced refined. I give the results from four different works, in situations far distant from each other, and all for the same year. The works are placed in the order of their erection, D being the most recent and the most perfect in construction. { Specification A B Cc D eee Ore Calcined . : 7,940°65 | 9,833°063 | 23,074:76 | 14,485°975 | 55,964°448 Copper—Dry Assay . 311°89 252°333 690:053 466°465 | 1,720°741 Do., Wet Assay 416:356| 382-110 984-830 650°210| 2,433°506 Copper produced 387:069 | 338-855 919°284 636°768 | 2,281-976 Gain on Dry Assay . 75179 86°522 229-231 170°303 561°235 Loss on Wet Assay . 29-287 43°255 65°546 13°442 151530 Percentage—Dry Assay . 3°93 2°57 2°91 3°22 3°07 Do., Wet Assay : 5:24 3°89 4-15 4:49 4°35 Produced. : : 4:87 3°45 3°88 4:39 4:08 Difference between Wet and Dry Assay 1:31 1:32 1-24 1:27 1:28 Gain on Dry Assay . “94 88 HSI 117 101 Loss on Wet Assay . BT “44 27 10 27 Surplus r : 23°9 34:2 33°3 36:3 32°90 These results were obtained ten years ago; but with increased experience and better plant the produce by the wet assay has been obtained with great regularity to within the second place of decimals. The results shown in the above table prove con- clusively that the dry assay is not within 33 per cent. of the truth; for these four works in one year, by the treatment of nearly 56,000 tons of ore, actually refined and sold no less than 561 tons of copper more than the dry assay declared existed in the ore. There can be no mistake about a reality of this kind; and what are we to say in fayour of a system which is so misleading? In any other branch of business such proved inaccuracies would never be tolerated a moment; and the worst of it is, that the lower the percentage of copper in the ore the greater the proportional difference. By reference to tables supplied by Messrs. Mason & Barry, we see that when the dry assay says the ore contains | per cent. copper, the wet assay says at least 2 per cent. ; so that if these four works had been working ores of what the dry assay called 1 per cent., they would most assuredly have got 2 per cent. out, or 100 per cent. surplus. A very amusing instance of the utter uselessness of the dry assay for poor ores was shown in the case of the Alderley Edge ores, which were a very pure sandstone mixed with a good deal of sulphate of barytes, and just stained green with carbonate of copper. The wet assay gave readily 1 to 13 per cent., but the average of the ore treated was 0:92 percent. I knew, of course, that the ore would be extremely difficult to assay by the dry way—in fact, I could get nothing. We sent two samples to two Cornish assayers, and they could find no- thing either. Now, here was an extraordinary thing. A copper mine raising 1200 tons a month, paying a lordship of nearly £3000 a year, and dividing handsome dividends for eighteen years, all out of nothing. We cannot push the argument against the dry assay further; it stands self-convicted. ; 7. What ought to be the simple basis of price? I am quite aware I approach the most difficult part of my subject, but I believe there is a clear way out of the difficulty. I have, I think, proved that—so far at least as poor ores are concerned—the dry assay is utterly worthless, Of course I assume that no one of any intelligence will be found to maintain that 686 REPORT— 1880. 21-cwt. tons and 243 Ibs. draft per ton can possibly be retained with any show of reason. As to the dry assay on rich ores and reguluses, I think I have clearly proved that, at all events as far as precipitate is concerned, it is always below the truth by a good many per cents., and the same must be said of all ores between 10 and 90 per cent. On the other hand, Chili bars, which have only to be refined, should be refined by the process they have to go through to make them fine copper, and I think the dry assay is the nearest corresponding pro- cess they could be subjected to. At all events, the wet and the dry assays almost entirely agree in Chili bars; an occasional difference of 4 per cent. is éntirely due to the opinion of the refiner whether he has actually got refined copper or not— ‘BS! or ‘T.C.’ But with precipitate it is very different, particularly that pro- duced by the ‘ salt process ;’ there is always a difference of at least 4 per cent. In the early days there used regularly to be 11 per cent. difference, but now, though not satisfactory, it is much better. Still, I think all ores and reguluses, including pre- cipitate, ought to be assayed by the wet method, and the results stated in whole numbers and decimal fractions, and be paid for including the second place of deci- mals. The basis of price should be in proportion to the official price of refined copper as quoted on the day of sampling, or if there is no official or quoted market price on that day, then the last preceding quotation. As there are several qualities of refined copper, the medium quality, or what is known as ‘ Tough Cake,’ would, I think, be fairest. Chili bars, which form such a large proportion of the material out of which refined copper is produced, and are officially quoted every market day, might also be taken; but as these may cease to be produced, it would be better, I think, to base the price on the price of ‘Tough Cake.’ Then, as to the proportional price for all percentages of ores, leaving a fair margin to smelters and extractors, this can be arrived at very much as is done at present. A complete set of tables, I would suggest, could be constructed by a committee of smelters, extractors, and importers, and these should be printed by authority of this committee, and available to any purchaser. I would suggest also that a committee of chemists should also settle and publish with the book a very minute description of the best known wet method of assay, and that this method of assay be, and remain until altered by authority, the standard method of assay. It would not be necessary in these tables, in my opinion, to go further than to state opposite each percentage or bracketed set of produces how many shillings and pence per wnit these produces are worth. Anyone with the most rudimentary knowledge of figures from these data would find the price per ton of ore. By means of the wet assay, which can be made with great rapidity and exactness, and with this authoritative data as to the value per unit, invoices could be rendered within a few days, or even hours, after sampling, with perfect confidence. 3. Progress of the English Stations in the Hill Regions of India. By Hyper Crarxt, V.P.S.S. Mr. Clarke stated that the Himalayan ranges to the north possess the cool climate of England, and that Englishmen thrive there, This had early attracted the atten- tion of our great administrators, who, beginning with Simla in 1818 and Darjeeling in 1828, had formed a series of stations, which had performed the functions of sanitaria, watering-places, and military posts, of metropolis and capitals, and latterly also of centres of tea-culture. A chain of hills passed as a backbone through India on the west, in which were seated some minor stations. He had shown how by tele- graph connection these towns were as well suited as the unhealthy cities of the plains for governmental and military purposes. In a series of statistics he illus- trated the condition of the tea and cinchona plantations and the breweries. He estimated the hill products as approaching a million in value, including 10,000,000 Ibs. of tea and 3,500,000 Ibs. of coffee. The gross imports from the foreign hill states he estimated at about 2,000,000/. yearly. All this trade was capable of exten- sion by careful administration. Thibet and China are closed to us; where Russian power extends our trade ceases. Nepaul excludes us, and our own feudatory in Kashmere but grudgingly allows us access. The oppression and misgovernment of TRANSACTIONS OF SECTION F. 687 the latter country require a removal of the ruler. In a political point of view it was admitted that the hills, although so little used, afforded suitable quarters for a large portion of our English army, which would greatly increase its efficiency. The development of the hill regions would create an available reserve, while India would obtain what was essential for its welfare, greater security from aggression from without and from dissension among the various conflicting races within the peninsula. It was, however, chiefly in reference to the interests of civilisation in the advancement of India that the development of the English population in the hill countries of India was to be regarded. He showed too that the aboriginal races might in this respect receive great benefit. The progress which had heen made in the hills within the last twenty years, almost without care, showed what was to be effected in the future. 688 REPORT— 1880. Section G.—MECHANICAL SCIENCE. PRESIDENT OF THE SECTION—JAMES ABERNETHY, V.P. Inst.C.E., F.R.S.E. THURSDAY, AUGUST 26. The Section did not meet. FRIDAY, AUGUST 27. The PresipEnT delivered the following Address :— As time will not permit of a generally detailed description, I propose, in the Address which I have the honour and pleasure to make as President of your Section, to describe generally the past and present condition of the port of Swansea, as typical of the rise and progress of the various ports in the Bristol Channel within the last half-century, and the vast improvements which have been effected in the nature and extent of the accommodation provided to meet the requirements of the shipping of the present day as regards dock facilities and appliances for the rapid and economi- cal loading and discharging of their cargoes rendered necessary by the amount of active competition in every branch of commerce, both export and import. I propose to confine myself in this address generally to the engineering history of Swansea Harbour, but I think it necessary, in the first place, briefly to describe certain features of the Bristol Channel, resulting in the peculiar advantages its harbours possess over those of the eastern coast, due to the greater tidal range. At its entrance between St. Govan’s Head on the north and Hartland Point on the south, its width is 42 miles, gradually contracting, until at King Road at the mouth of the River Avon, 92 miles distant, its width is only 44 miles, the result being a proportionate elevation of the tidal wave in its progress upward, so that in Swansea Bay spring tides rise 28 feet, at Cardiff 35 feet, and at Avonmouth 40 feet, and in consequence engineers have been enabled to provide for the entrance of the largest class of shipping by providing at the various docks recently constructed a greater depth of water than is generally practicable on the eastern coast. The eill of the dock at present in process of construction at Swansea will have a depth over it at spring tides of 32 feet, while the existing cill of the Roath Dock at ‘Cardiff has 35 feet 83 inches over it; that of the Alexandra Deck at Newport 35 feet, and the Avonmouth Dock 39 feet—greater depths than exist over the lock cills of any of the ports on the eastern coast generally. It would extend my address to an unnecessary length to describe the vast im- provements which have taken place at all the ports in the Bristol Channel within the past half-century. The port of Swansea may fairly be taken as a type, inas- much as from its position it has natural difficulties to contend with, requiring, as at Cardiff, extensive works seaward in order to provide the requisite depth of water, such works not being necessary in the case of the docks at Newport, Ayon- mouth, or Portishead. As regards its situation, the port is placed nearly in the centre of Swansea Bay, TRANSACTIONS OF SECTION G. 689 at the mouth of the river Tawe, partially sheltered from prevailing winds by the Mumbles Headland bearing from the harbour entrance south-west three-quarters west, the shelter from that headland affording good anchorage as regards holding ground, but subject to the range of the sea in south-westerly gales. The entrance to the port is exposed from south-west three-quarters west to south-east, the heaviest seas occurring when the wind is south-westerly or directly up the Channel. Previous to the year 1794 no engineers appear to have been consulted as to the improvement of the port, which at that period simply consisted of the bed of the River Tawe, the latter discharging over the flat foreshore after passing through a small subsidiary bay, termed Fabian’s Bay, lying between two points of land ealled Black Point and Salthouse Point, the entrance being fully exposed to the range of the sea from the points of the compass before enumerated, and con- sequently blocked up by sand driven into it by the action of south-westerly seas, and only accessible at spring tides in fair weather by a small class of coasting vessels. In the year 1794 the then Trustees consulted Captain John Huddard, F.R.S., who at that time had the reputation of being an eminent marine engineer, and a perusal of whose report shows that, having regard to the meagre knowledge of harbour improvements at that period, he possessed great powers of observation and considerable practical engineering knowledge. In his first report, which is of con- siderable length, dated 24th September 1794, he states that he was called upon by the Trustees to answer various queries generally bearing on the possibility of providing an increased depth of water by improving what is termed the ‘bar’ or sand carried into the navigable channel by the tidal action in south-westerly gales, and the protection of the harbour entrance from the inrun of the sea during those winds. The condition of the harbour at that period in regard to depth can be inferred from the following passage in his report—‘On the 5th August I found only 8 feet of water in the harbour, and in the evening of the 31st July a vessel of about 13 feet draught of water, in sailing out of the harbour, grounded upon the bar, where she remained till the 10th August, when the tide rose to take her off; and eyery ship in the harbour loaded to that draught of water, and ready to sail at that time, must suffer the same detention.’ Captain Huddard gave as his opinion that a greater depth of water could not be obtained, nor the drifting of the sand from the effect of the sea into the entrance channel prevented, without the construction of piers, which he termed the eastern and western piers, the first extending from Black Point and the latter from Salt- house Point, which piers in consequence of his recommendation were subsequently constructed. Captain Huddard further observes that the increased depth antici- pated consequent on their construction ‘would continue so long as the tide is Suffered to flow up the river as at present,’ but at the same time it would appear _ that a project was then entertained, often since revived, for damming the river and converting it into a floating dock, as his report contains the following passage— ‘Should the river be embanked for a floating dock, sluices will be necessary to clear ‘away the silt out of the channel which the sea will deposit in the outer harbour; for though the harbour of Swansea will not be so liable to silt as many others from the strength of the tide in the Severn being thrown off by the Mumbles and Nash Points ; yet, in fresh gales, the same being impregnated with mud, will deposit it in the harbour and require a current to clear it out of the channel.’ The construction of the West Pier, as recommended by Captain Huddard, was carried out, and in May 1804 he was again called on to report. He states that the only alteration which he observed on his second visit was that the sand to the extent of 270 yards south of the pier head was worn down nearly one foot, but that what was termed the ‘Bar’ seaward was higher than the harbour entrance, and that it was absolutely necessary to complete the Eastern Pier in order to secure a permanent depth of water and to afford the necessary protection from south- westerly winds. The Eastern Pier was in consequence constructed, the result being the prolongation of the river current and the driving of the bar further seaward, end in the year 1831 it was reported that a depth of 21 feet existed over it at apring tides, as anticipated in Captain Huddard’s report of 1794, 0. 2x 690 REPORT—1880. In the year 1826 the Trustees consulted Mr. Telford, and he reported on Feb- ruary 5 of the following year. At that period what was termed the harbour was simply the bed of the river Tawe; the shipping lying within it were endangered by exposure to the action of heavy floods, and he recommended that the present new cut should be made as achannel for the river—no doubt an important and necessary work; but he again revived the old engineering heresy of recommending the conversion of this new cut and of the old harbour into floats with a river overflow and draw sluices. He further recommended the direction of the ebbing current seaward by slag banks, in order to act upon the bar. These propositions of Mr. Telford were generally approved of by Mr. H. R. Palmer in a report addressed to the Trustees in January 1831, and he further recommended the prolongation of the Western Pier. Similar propositions were recommended by other engineers, among them the late Mr. Jesse Hartley ; but fortunately for the future of the port of Swansea, none of the works for the conversion of the river into a float were executed. The new cut, or channel, for the river was commenced in 1840, and finished in 1844, the eflect being to materially lessen the risk to shipping lying within the harbour or original bed of the river during floods, and in giving a better direction to the ebbing current. In 1845, what is termed the Pottery Entrance was constructed under the direc- tion of Mr. Rendel, with a double cill, as a provision for the canalising of the river or the new cut at a future period. The masonry of this entrance I found completed at the period of my first visit to Swansea in the month of February 1849, and the project was still entertained of converting the river and new cut into a float, rela- tive to which. I reported in the following words:—‘ Any interference with the channel of the river or new cut which would prevent the free influx and reflux of the tide, would, I am of opinion, be most prejudicial to the harbour entrance. In times of flood, the river current is no doubt an active agent in deepening and removing obstruction from the entrance channel; but, under ordinary circumstances, its volume is too small to haye any material effect. On reference to sections taken by the late Mr. Price, I find that 40,000,000 cubic feet or thereabouts of tidal water ebbs each tide from the river channel alone, independent of the backwater from Fabian’s Bay, and I am of opinion that, although the land-floods are active agents in deepening and removing obstructions from the entrance channel, the tidal water is the main agent in maintaining and keeping it clear, and that every facility should be given by deepening the bed of the river to aid its upward flow, and that in pro- portion as the bed of the river is lowered the entrance channel will be deepened.’ To that opinion, expressed upwards of thirty years ago, I still adhere. The system of discharging a volume of water at the period of low tide from reservoirs, and thereby creating a shallow stream as a means of preserving a navigable channel and a sandy foreshore, is, in my opinion, entirely futile, and in the case of several important Continental harbours threatens seriously to interrupt the regular postal service between this country and the Continent. Upon my visit in 1849, with the exception of the masonry of what is termed the Pottery Entrance and the various wharves on each side of the old river-bed and of the New Cut, no works had been executed of any magnitude; the harbour still con- sisted of the original river-bed composed of hard gravel worn into irregularities by the occasional action of floods, and the superior class of shipping engaged in the copper ore trade was constantly strained in taking the uneven ground. As regards communication with the harbour, no railways were in existence, and I used to make the journey from Aberdeen, in Scotland, to Swansea, entirely by coach. The gross revenue of the harbour was about 7000/. per annum at that time; during the present year it is estimated at about 60,0007. After considerable discussion, the Trustees determined in November 1849 to convert the tidal harbour, or old bed of the river, into a floating dock with an outer half-tide basin, of the respective areas of 11 and 23 acres, the half-tide basin entrance being 60 feet in width, with a depth over the cill of 25 feet 6 inches, at high water spring tides. Between the half-tide basin and dock, a lock was constructed, 160 feet in length and 60 feet wide, with a depth over the cill of 22 feet 6 inches; these TRANSACTIONS OF SECTION G. 691 dimensions were considered, at the time, ample for the largest class of shipping frequenting the port. At that period the number of steam in comparison with sailing vessels was insignificant, and the Transatlantic service between this country and America was only in contemplation. Some difficulty was encountered in the construction of these works, as they had to be carried out without impeding the traffic in the harbour, They were com- leted in December 1851, so far as the dock was concerned. An additional half-tide asin and lock, at the upper end of the dock, was commenced in 1856, and completed in 1861. An immediate effect was felt in the increased tonnage of the shipping, and in the superior description and size of the vessels frequenting the port. In the year 1853, Mr. Armstrong (now Sir William Armstrong) was consulted, and in 1856 hydraulic power was first applied to work the existing hand gearing of the lock by a system of shafting, which has since been superseded by more perfect adaptation of the power, but the machinery, nevertheless, has worked without failure up to the present time. As far back as the year 1846, attention was directed to the foreshore of the sea, westward of the harbour entrance, as a site for floating dock accommodation, and His Grace the late Duke of Beaufort consulted Mr. Brunel on the subject, and in his report of October 1846, whilst strongly condemning a project again revived for conyerting the river into a float, he strongly recommended the construction of a dock on the foreshore, on the site of the present South Dock. An Act was obtained in 1847 for its construction, and in 1850 the works were commenced. These docks are constructed in great part seaward of the original high-water mark, and the geological features of the strata, exposed in the excavation, were somewhat of an extraordinary character, consisting :— 1. Of made ground, ranging in depth from 20 to 26 feet, composed of gravel and boulder stones, which must have been transported from a considerable distance, by the action of river floods, probably from the neighbourhood of Llandore. 2. Peat, with leaves, trees, &c., 2 feet. 8. Blue or marine clay, 8 feet 6 inches, containing shells imbedded in it, ‘ Scrobicularia piperata,’ stated to be still living on the coast. 4, Peat, 2 feet 10 inches. 5. Blue marine clay, 4 feet 1 inch. 6. Peat with trees, 3 feet 1 inch, overlying the gravel foundation upon which the works are founded. At two points the foundations had to be taken to an extraordinary depth in the lower peat, arising from the depression of the gravel at those points, apparently ancient river beds, and in the peat were found various trees supposed to be the remains of an ancient forest. Antlers of the red deer were also found in this stratum, The existence of this upper bed of marine clay beneath the made ground indi- cated that a dock might be constructed on the site with great facility without danger of percolation from the tidal waters, and the result proved the accuracy of this conclusion. The works were commenced in 18564 and completed in 1859. They consist of a trumpet-mouth entrance basin leading to a half-tide basin en- trance 70 feet in width, with a depth of water over the cill of 24 feet at H.W.O.S.T., a half-tide basin or outer dock of 4 acres area leading to an entrance lock 300 feet in length and 60 feet in width, with a depth over the inner cill of 22 feet 6 inches, the dock level being kept level with the tide of the day by pump- ing from the half-tide basin in order to prevent accretion in the dock by the admission of the tidal water heavily charged with detritus. In 1860 the Great Western Railway Company completed their line into Swan- sea, together with certain provisions for shipping coal by hydraulic machinery in the North Dock, and in 1863 a railway was completed from Neath to Swansea, by which the great Welsh coal-field was brought into immediate communication with the port, and it became a matter of great importance that this coal should be conveyed to the South Docks for shipment, This involved the construction of two massive opening bridges for a double line of broad gauge railway, one across the New Cut we? 692 REPORT— 1880. or river Tawe, with an opening portion of 60 feet span; and another across the lock of the North Dock of 72 feet span, both of which were executed by the firm of Sir William Armstrong and Co., and are worked by hydraulic power. Tn connection with these works extensive viaducts had to be constructed through the town and along the quay of the South Dock, for the shipment of coal from the high level by hydraulic drops, also constructed by Sir W. Armstrong and Co. These works were all completed about the year 1863, and the immediate result was an increase in the tonnage of the port from the year 1851, the period of the com- pletion of the first or North Dock, from 269,554 tons to 847,823 tons during the ast year. Tuning south-westerly gales it was found that the Western Pier, from its ter- mination being slightly within or landward of that of the Eastern Pier, afforded inade- quate protection from those gales, and in consequence a considerable inrun of the sea existed within the Harbour, and the sand also driven coastward during south- westerly winds occasionally blocked up the entrance. In order to remedy these defects, and to form a defined channel over the foreshore to low-water mark, an extension of the Western Pier was decided upon and completed for a length of 1000 feet in 1863, the result being that the inrun of the sea no longer existed, and the entrance channel formed by dredging pat passu with the extension of the pier maintained its depth by the prolonged defined direction of the ebbing tidal current. Subsequently, in 1875, it was determined to further prolong the pier an additional 1000 feet, which was completed in 1877, the effect being a still further increase in the depth of the channel, which has been. maintained ; so that, at present, instead of 20 feet at spring tides, which existed in 1849, there is now an available depth of about 28 feet, which is conserved by the prolonged and defined action of the out- going tidal current, aided, to a certain extent, by the river floods. In consequence of the great increase in the size and number of the shipping frequenting the port, particularly steam vessels, it has been found indispensable to provide an entrance lock of greater size and depth of water over the cill, with an additional extensive dock and spacious quays so as to furnish ample siding accom- modation for the shipment of coal and increased facilities generally for the rapid and economical loading and discharging of cargoes. In consequence, the Trustees have entered into a contract for the construction of a dock in Fabian’s Bay of 231 acres area of water space, together with an entrance lock 450 feet in length, and 60 feet in width, with 32 feet of water over the outer cill at H.W.O.S.T.; the dock to be kept (as in the case of the South Dock) above the tide of the day by the surplus water from Port Tennant Canal and other sources discharging into it. As regards the shipment of coal it is proposed to be conducted on the same system as that at the Alexandra Dock at Newport, viz. by gravitation from the sidings to the hoists both for the loaded and empty waggons, the whole machinery of the dock appliances to be worked by hydraulic power, it having been found possible by this system at a very moderate cost to ship from 150 to 200 tons of coal per hour at each hoist. In addition to providing this extensive dock accommodation the embanking of the indent termed ‘ Fabian’s Bay ’ within the Eastern Pier will, it is anticipated, as in other well-known cases, tend to accelerate the tidal flow into the upper reaches of the river, and give a better direction and greater force to the ebbing tidal current for the future maintenance of the entrance channel at present in progress of being further deepened by dredging. These various works are now in course of construction, and in conclusion I have to state that it will afford me pleasure to conduct you over them and to explain in detail their features, and those of the works executed during past years. The following Papers were read :— 1. On the Bute Docks, Cardiff, By J. McCoynocum, M.Inst.0.L. The construction of the Bute Docks at Cardiff, and the consequent rapid growth of the town, are due to the remarkable foresight and public spirit of the late = «<*>? TRANSACTIONS OF SECTION G. 693 Marquess of Bute, who, in the year 1830, finding the great mineral wealth of the adjoining district of South Wales locked up by the want of railway conveyance to the sea-coast, and proper means of shipment, resolved upon the construction of a dock on the foreshore at Cardiff, the only accommodation then existing for vessels being the Glamorganshire Canal, with a limited capacity available only for vessels up to 200 tons. The original design of the engineer, Mr. Green of Exeter, was to place the entrance gates on the foreshore at a point near the end of the present low-water pier, and to construct a ship canal across the foreshore to the intended dock on the mainland. The expense and difficulty of constructing such a work at that time led to a modification, and it was ultimately decided, under the advice of the late Sir William Cubitt, to cut an open tidal channel across the foreshore to the mainland, and then construct an entrance basin communicating with the dock by means of a lock. This dock, now called the ‘Bute West Dock,’ was, with its sea approach, com- pleted in 1839, at a cost of about 400,000/7., an expenditure which even then displayed the public spirit of the late Marquess of Bute, when the total import and export trade amounted to less than 7000 tons per annum, as compared with 5,000,000 tons per annum at the present time, showing an increase of over 700 times. The tidal water of this part of the Bristol Channel contains a very large quan- tity of mud in suspension, which would have involved a heavy expenditure for dredging the deposit if the tidal water had been impounded in the dock. This consideration led the engineer to fix the level of the dock water at several feet above the high-water level of the Channel, and to supply the dock with fresh water from the river 'l'aff. The water is drawn from the river for this purpose about two miles inland, and the feeder passes through the town, and delivers the ‘fresh water at the north end of the dock. The entrance channel across the fore- shore is three-quarters of a mile long and about 200 feet wide. The basin is 300 feet long and 200 feet wide, with an entrance of 47 feet wide from the sea; the lock between the basin and the dock is 152 feet long and 36 feet wide. The dock is 4000 feet long and 200 feet wide, with 19 feet depth of water for a length of about 1500 feet, and 15 feet for the remaining leneth of about 2500 feet. The depth of water on the sill of the entrance gates is 28 ft. 9 in. at high water of ordinary spring tides, and the gates are opened only for one hour before, and about two hours after high water. The gates are constructed of timber. The water area of the dock and basin amounts to 20 acres. So great and rapid was the increase of traffic after the opening of the Bute West Dock, that in 1851 it was decided by the trustees of the Marquess of Bute to construct a new dock of larger capacity, now called the ‘ Bute East Dock.’ This dock has a sea-basin 380 feet long by 250 feet wide, approached from the entrance channel on the foreshore by a lock 220 feet long by 55 feet wide, having a depth of 31 feet 9 inches on the sill, or 3 feet more than in the West Dock. The inner lock from the sea basin to the dock is 200 feet long by 50 feet wide. The dock is 4300 feet long by 300 feet wide for the first 1000 feet, and 50U feet wide for the remaining 3300 feet. The uniform depth of water is 25 feet, the water-level in ‘this dock being maintained at the same level as in the West Dock, by water drawn from the river Taff. The water area of the East Dock and basin amounts to 45 acres. The lock gates were originally constructed of German and English oak; but haying ultimately proved too weak to resist the great pressure of water to which they were subjected, the gates of the outer lock were replaced in 1863 by new gates, constructed of wrought-iron ribs, English oak heel and meeting posts, and Dantzic fir planking. The gates of the inner lock were replaced in 1878 by new gates constructed of wrought-iron ribs, heel and meeting posts with green- heart facings, and Dantzic fir planking on both sides of the lower gates; the up r gates were faced on the dock side with wrought-iron plates, and Dantzic fir p g on the lock side ; both upper and lower gates being on the buoyant principle, this construction being rendered necessary by the limited space provided in the masonry for wooden gates, and has proved perfectly satisfactory. A junction canal connects the East and West Docks with the Glamorganshire Canal. 694 REPORT—1880. The basin and first portion of the East Dock were opened for traffic in 1855, and the remaining length of the dock was completed in 1859. The East Dock was commenced from the designs of Sir John Rennie and Mr. John Plews, and com- pleted from the designs of Messrs. Walker, Burges, and Cooper. New Basin.—Notwithstanding this large accession to the dock area of the port, the continued increase of traffic called for further accommodation; and in 1864 application was made to Parliament by the Bute Trustees for powers to construct additional dock accommodation; but it was not until 1866 that an Act was ob-- tained for the construction of an additional basin, which has been completed from the author’s designs, and was opened for traffic in 1874, This basin is intended as a preliminary to an additional dock of 54 acres area, for which Parliamentary powers have been obtained; and while serving the new dock, it also relieves and facilitates the working of the traffic of the Bute East Dock. The New Basin is 1000 feet long by 525 feet wide, having a water area of 12° acres. It is entered from the channel on the foreshore, which has been widened for this purpose by a sea-lock 350 feet long and 80 feet wide, having 35 feet 9 inches. depth of water on the sill. A junction lock 370 feet long, with gates 60 feet wide, connects this basin with the East Dock. The chamber of the lock is 120 feet wide,. so as to pass three or four vessels at the same time. The existing dock accommodation provided by the Marquess of Bute and his Trustees now amounts to 77 acres, and the Parliamentary powers recently obtained will enable the Trustees still further to increase this accommodation by 54 acres to meet the growing requirements of the port. The gates of the Sea Lock of the New Basin are 80 feet wide, and are believed to. be the largest gates hitherto constructed. They are of wrought iron, on the buoyant principle, with skin plates, diaphragms, and lattice ribs, and with greenheart heel posts, meeting posts, and sills. Each leaf of these gates weighs 145 tons. They were constructed by Sir William Armstrong & Co., the arrangement of lattice ribs being adopted at the suggestion of Sir William Armstrong, as affording more con-- venient access to the interior for examination and repair, and also diminishing the weight in comparison with solid plate ribs. The gates of the Junction Lock between the New Basin and the East Dock are 60 feet wide, and are of wrought iron, similar in design to the gates of the Sea Lock, but with solid plate ribs in place of lattice ribs. They were constructed by Messrs. Maudsley Brothers, of the Bute Iron Works, Cardiff. The lock gates,. capstans, bridges, and sluices connected with the New Basin are worked by hydraulic machinery ; those at the East and West Docks were arranged for hand power, and are still so worked. The provisions for the examination and repair of vessels entering the port con-- sist of four graving docks—one 200 feet long, entered from the West Dock; one 400 feet long, entered from the East Dock, both the property of Messrs. C. Hill & Sons, on ground leased to them by the Bute Trustees. The third graving dock,. 320 feet long, is outside the entrance of the docks, and is the property of Messrs. Gunn & Co. The fourth graving dock, 600 feet long, with an entrance 60 feet wide, has been constructed by the Bute Trustees, and is entered from the New- Basin. It is available for use by the public on payment of dockage rates, as at Liverpool. ua Relative ua Pres- E P BS |. Sam & | Strains on Pi sure |~Xpan-| Pressure | % 6 2 F | py gi iston sion S2ae speed a i 31 16 600 36 | 100 . : 1 3 ; Cornish Engine. : . 19 45 45 19 500 4B 80 : 3 . 43 6°25 13 228 14 168 Compound Differential Engine . 80 | 8 24 290 137. | 150 698 REPORT— 1880. In the diagrams (Plate XIII, figs. 2 and 3) the abscisse of the curves represent the spaces passed over by the piston, and the corresponding ordinates the times in which those spaces were described. : The Differential Engine received its name because of its peculiar valve-gear—a gear which automatically effects the distribution of steam by the differential motion produced in combining the motion of the engine-piston with that of a uniformly moving subsidiary piston. In Plate XIL., fig. 3, D is the differential lever, and c the connection to the engine ‘valves, The point R is attached to the subsidiary piston E. The motions of the points R and c are opposite in direction, and when the motions are equal, there is no motion of the point p. When the motion of £ is quicker than that of c, the valves are being opened—this occurs at the beginning of the stroke; but as soon as the engine motion c becomes quicker than that of the subsidiary piston 8, the valves are being closed. The initial velocity of the engine-piston varies according to the resistance it has to overcome, and the resistance therefore determines the distribu- tion of the steam. The Differential Engine is double-acting, and the weights w w, Plate XII. fig. 2, support each other, and cannot move except when moved by the engine. Should there be a vacant space in the pump at the commencement of the stroke, the engine would have no resistance to encounter except its own inertia and friction, and would move off very readily on the opening of the steam valve, so much so that its initial motion would be greater than that of the subsidiary engine, and the steam valve would be closed again; but immediately the plunger came in contact with the water, the fulldoad would be upon the engine, and a halt would be produced until the subsidiary engine had gained a lead sufficient to have fully opened the steam valve. Plate XIIL., fig. 1,is a steam diagram taken under the conditions just described. This element of safety is most important. Referring to the Cornish Engine, Plate XII, fic. 1, the more the steam is expanded in the cylinder, the greater the initial velocity of the plunger, and the more difficult it is for the water to follow up the plunger closely, and the greater the unsupported weight at the end of the stroke, With an eightfold expansion, the plunger would have an initial velocity of 600: feet per minute, and at the end of the stroke the steam-pressure would only support one-third of the weight w. Should there be a vacant space in the pump, the plunger would fall back with a great shock. This is one of the greatest sources of accident in the Cornish Engine. All the early compound engines were single-acting, that is to say, they were Compound Cornish Engines, and in addition to possessing defects in principle and construction, were very cumbersome and costly for a given power. Plate XII, fig. 4, illustrates Sims’s engine, which wasa development of Trevet- hick’s Pole Engine, Plate XIII., figs, 4 and 5 give respectively the relative strains and velocities in the two engines. As a question of weight and first cost for a given power, the following is a comparison of the three systems of engines described in the paper :— Power. Weight. Cost. The Compound Cornish Engine , 1 100 100 per cent. The Single Cylinder ,, pe 1 70 70 The Compound Differential,, . 1 45 50 ” ” 5. Project for a Channel Railway.1 By BraprorD Lesuin, MInst.0.£., Agent and Chief Engineer, East Indian Railway. This was a pamphlet submitted by Mr. Ernest Benedict, M.Inst.C.E., M.LE. & S.. Scotland, accompanied by two drawings, and describing a project for establishing” railway communication between France and England in the neighbourhood of Calais: and Dover. The author proposes to lay a single line of rails within a straight cylindrical steel tube, 16 feet in diameter and 23 inches thick, smooth outside andi 1 Pamphlet printed at the Stanhope Press, Calcutta.’ TRANSACTIONS OF SECTION G. 699 properly stiffened within, This tube is to be ballasted, so as to make it weigh 12 ton to the foot-run less than the water displaced, and is to be held down to within 35 feet of the lowest water level by two 3-in. chains passed over the tube, and attached to caissons weighing 500 tons each, and sunk a sufficient distance each side of the centre line to give the requisite angle to the four parts of the chain. These moorings will occur at every 250 feet along the tube, and will be at such an angle and so rigid that the tide will not affect them. The passage of trains through the tube will relieve the chains of part of the strain on them. f Ventilating shafts to be provided if found necessary, to act as block-signal stations, and to be protected by light-ships moored on either side. The shore ends of the tube are to be laid in channels dredged and excavated to receive them, and afterwards filled with concrete. The ends are to be laid in these channels on the hottest day that can be con- veniently chosen, and angle-iron rings projecting from the tube, and held firm by oe concrete, will prevent any movement from the expansion or contraction of the tube. The tube to be commenced in the centre, and to be gradually submerged and anchored as the work proceeds. The two ends during construction will rest on pontoons, whereon the work of adding to the tube will be carried on above water, the tube being flexible enough to allow of this being done. The time required for constructing the tube is estimated at three years, and the cost at eight millions sterling. The working expenses would probably not exceed 20 per cent. of the gross receipts. Twenty-seven trains a day in each direction, at li. a train mile, would yield 5 per cent.; and three times this number of trains could be worked through the tube in the twenty-four hours. 6. On Combined Elliptical, Parallel, and Angular Motion. By Guorce Fawevs. 7. On the Shakespear Safety Lamp. By Colonel SHaKEsprar. TUESDAY, AUGUST 31. The following Papers were read :— 1. On the Loading of Ships. By W. E. Haun. | 2. On the Steering of Ships. By Professor Osporne Reynotps, F.R.S. Ihave received an important communication from the Admiralty, upon the steering qualities and turning powers of H.M.S. Minotaur and Defence. As the experiments therein described were made in accordance with the request of the Committee of the British Association upon the Steering of Ships, and as the results obtained are very definite and important, I think it desirable that they should be Poe upon record, Itherefore append them to this notice. (See Tables, pp. 700- Admiralty, S.W., 19th September, 1879. 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The Owens College, Manchester, S. 8087, ’79. STEERING QuALITIES AND TURNING Powers or ScREw SHIPs. ‘Minotaur’ at Vigo, ‘No. 165, 3lst July, 79. Sir, With reference to your letter of the 25th April, 77, S. 7735, addressed to my predecessor, Vice-Admiral Sir Beauchamp P. Seymour, relative to the Steering ‘Qualities and Turning Powers of Screw Ships, I have now the honour to enclose for the information of the Lords Commissioners of the Admiralty the results of experiments that have, under my direction, taken place in,H.M. Ships ‘ Minotaur ’ and ‘Defence,’ together with a summary of the same—observing that these experiments, so far as they go, seem to be useful as illustrating the views of the British Association. I haye, &c., Joun Hay, To the Secretary of the Admiralty. Vice-Admiral Commanding. 3. On an improved Sounding Machine. By Professor Sir W. THomson, A., FBS. [This machine was exhibited on the steamer ‘ Flying Oloud,’ during an excursion trip to the Worm’s Head, on September 1. Various soundings were taken with it, and the depths registered (from 12 to 21 fathoms) agreed closely with those marked on the Admiralty Charts. | 4. On the Incrustation of Steam Boilers. By W. THomson. eit aa eee bgor =o Oy as i Ae Bote es: : am SN OLSIA NT ripe wae Suan a i v sunkioaiel att) +6 what " Ve ig Prana ne Bc Ei Bete" seats: fi eB Uh Tia venA tegail AGN ia Saks ner - vee: Y $ z . - ’ % eo ee, b Pereage Fhe a “S 3 bh oe < ma ¥: sit £5 ' ais we fan ttt ae swewot deine? RAN geen ; ‘ 3 \ Rae re a apie i ERE ee ee een | Bee seh. nO eae ae eee se ae oF Boab cre A De A ites meh 1 in ‘Shek ai ere ke a of Sedalia ai MPSA. (ha hoe aptly 2) Mehl: © ‘Th Gi oghhe wie ert T weil ae ted ak een Wait ‘al iy habr inte Divi ath Sth. peter nquitotis Dp ares Ver atomih® gqid@ JRE al: pet wawe} wahstity Joep jel? tore Bray: sneNGuedNe a it wat Wy yiacdnene a tet Se ‘rere ay wiibctectitvre bituanr a OF bed Mes ghee nt F . ox Ty. ieee J ‘ e , a) wed t by ‘ ; dadtienot © » ail j & ppb ie NRT) Da + mt fi iy a: see : J . “ me bg es, dat Muon A sig fe otis eh 0 i y is i 0d. ee a pis i 7 +E i er neh wen iad | baer Durr p toa rite sii ath th } at tai rk delet Dadat ow ahaa canta’ reat < de Mexinweo dt ay 1 Tem io paren {arteaiig? ig ss Claes i casead pee heey a . < ‘senquowt We cag ie sonteat sient’ e pee phe INDEX. [An asterish (*) signifies that no abstract of the communication is given. | BJECTS and rules of the Association, xxi. Places and times of meeting, with names of officers from commencement, xxviii. List of former Presidents and Secretaries of the Sections, xxxv. List of evening lectures, xlviii. Lectures to the Operative Classes, 1. Officers of Sectional Committees present at Swansea, li. Treasurer’s account, liii. Table showing the attendance and re- ceipts at the annual meetings, liv. Officers and Council for 1880-81, lvi. Report of the Council to the General Committee at Swansea, lvii. Recommendations adopted by the General Committee at Swansea :—Involving grants of money, lx.; not involving grants of money, Ixiii.; communica- tions ordered to be printed im extenso, Ixv. Synopsis of grants of money appropriated to scientific purposes, Ixvi. Places of meeting for 1881 and 1882, lxvii. General statement of sums which have been paid on account of grants for scientific purposes, lxviii. General meetings, Ixxvii. Address by the President, A. C. Ramsay, Esq., LL.D., F.R.S., V.P.G.S., Director- General of the Geological Survey of the United Kingdom, and of the Museum of Practical Geology, 1. Abel (Prof.) on patent legislation, 318. Abernethy (J.), Address by, to the Me- chanical Section, 688, Abney (Capt.) on an investigation for the purpose of fixing a standard of white light, 119; on the present state of our knowledge of spectrum analy- sis, 258. Ace (Rev. Dr.) on the required amend- ment in the Marriage Laws of the United Kingdom, 672. Adams (Prof, A. Leith) on the explora- 1880. tion of the caves of the South of Ire- land, 209. Adams (Prof. W. G.) on an investigation for the purpose ot fixing a standard of white light, 119; comparison of curves of the declination magnetographs at Kew, Stonyhurst, Coimbra, Lisbon, Vienna and St. Petersburg, 201; Ad- dress by, to the Mathematical and Physical Section, 447. Admiralty monies and accounts, F. P. Fellows on, 668. Africa, South, the stone age in, W. D. Gooch on, 622. *___, West Central, the results of the Portuguese expedition in, Capt. H. Capello and Lieut. R. Ivens on, 659. Agricultural education and research, the position of, in this country and on the continent of Europe, J, M. Cameron on, 537. Agricultural statistics and the land ques- tion, by W. Botly, 668. Alexander (Lieut.-Gen. Sir J. E.) on the preservation of fish and preventing the pollution of rivers, 672. Algebraical expansions, of which the fractional series for the cotangent and cosecant are the limiting forms, J. W. L. Glaisher on, 482. *Alkaline fermentation of urine, A. S. Lea on the, 644. Allen (A. H.) on the specific rotatory power of cane and invert sugar, 541; further notes on petroleum spirit and analogous liquids, 547; *on the so- called ‘normal’ solutions of volumetric analysis, 549. Allman (Prof.) on paleontological and zoological researches in Mexico, 254, Anatomy and Physiology, Address by F. M. Balfour to the Department of, 636. Ancient settlement found beneath the surface of the peat in the coal-bog near Boho, co. Fermanagh, T, Plunkett on an, 623, Anderson (R.) on the necessity for a regular inspection of lightning con- ductors, 471. ZZ 706 Anderson (Dr. T.), an improved helio- graph or sun signal, 461; improved apparatus for the objective estimation of astigmatism, 463. Annuities, diminishing, F. N. Newcome on, 675. Anthracite coal and coal-field of South Wales, C. H. Perkins on the, 220. Anthropological colour phenomena in Belgium and elsewhere, Dr. Beddoe on, 629. Anthropology, Address by F. W. Rudler to the Department of, 609. Anthropometric Committee, report of the, 120. Astigmatism, improved apparatus for the objective estimation of, by Dr. T. Anderson, 463. Astronomical clocks, on the question of improvements in, first report, 56; second report, 58. Atchison (A. T.) on patent legislation, 318. *Atomic volumes of certain elements and the heats of formation of some of their compounds, some relations between the, W. Weldon on, 503. *Australian autochthony, W. Forster on, 620. *Autochthony, Australian, W. Forster on, 620. Ayrton (Prof. W. E.) on devising and constructing an improved form of high insulation key for electrometer work, 29; on accurately measuring the speci- fic inductive capacity of a good Spren- gel vacuum, and the specific resistance of gases at different pressures, 197, Baden-Powell (G.) on protection in the United States and its lessons, 671. Baily (W. H.) on the Tertiary (Miocene) flora, &¢c., of the basalt of the North of Treland, 107. Balearic Islands, an examination of the, Dr. Phené on, 663. —, the geology of the, Dr. Phené on, 585. Balfour (Prof. Bayley), report on the natural history of Socotra, 212. Balfour (F. M.) on the occupation of a table at the zoological station at Naples, 161; Address by, to the De- partment of Anatomy and Physiology, 636. — and W. N. Parker on the develop- ment of Lepidosteus, 599. Ball (Prof. R. 8.) on observations of luminous meteors during the year 1879-80, 39; notes on non-Euclidian geometry, 476. *Bamfield (J.) on the spontaneous com- bustion of coals in ships, 696. INDEX. Barlow (W. H.) on patent legislation, 318. Barnes-Lawrence (Rev. H. F.) on the possibility of establishing a close time for indigenous animals, 257. *Barrows, long, the structure of, Prof. G. Rolleston on, 623. , *___, round, the structure of, Prof. G. Rolleston on, 623. Bate (C. Spence) on the exploration of the marine zoology of South Devon, 160; on the present state of our knowledge of the Crustacea: Part V. On fecundation, respiration, and the green gland, 230 ; on the possibility of establishing a close time for indi- genous animals, 257. Beddoe (Dr.) on the work of the Anthro-— pometric Committee, 120; on anthro- pological colour phenomena in Belgium and elsewhere, 629. Bennett (A. W.) on the classification of cryptogams, 599. —— and G. Murray, a reformed system of terminology of the reproductive organs of thallophytes, 600. ; Bi-lingual seal in Cuneiform and Khita, the discovery of a, Hyde Clarke on, 633. Biological Section, Address by Dr. Giin- ther to the, 591. Birds, the classification of, P. L. Sclater on, 606. , the migration of, and Messrs. Brown and Cordeaux’s method of ob- taining systematic observations of the same at lighthouses and lightships, A, Newton on, 605. Bismuth, fluid, the density of, W. C. Roberts and T. Wrightson on, 543. Blanford (W. T.) on the geological age and relations of the Siwalik and Pi- kermi vertebrate and invertebrate faunas, 577. Bleaching powder residue, F. W. Hodges on, 560. Bock (Carl) on the Dutch Indian Go- vernment exploring expedition in Borneo, 661. Bolton (Prof. H. C.) on the application of organic acids to the examination of minerals, 505. Bonney (Prof. T. G.) on the ‘Geological Record,’ 87; on the erratic blocks of England, Wales, and Ireland, 110. Borneo, the Dutch Indian exploring ex- pedition in, Carl Bock on, 661. Boscawen (W. St. C.) on the Hittites, 632. Botly (W.), agricultural statistics and the land question, 668. Bottomley (J. T.) on secular experiments on the elasticity of wires, 61; * on the elasticity of wires, 494. INDEX. Bourne (Rev. A.) on the German and other systems of teaching the deaf to speak, 216. Bourne (8.) on the German and other systems of teaching the deaf to speak, 216; on the appointment of H.M. in- spectors of elementary schools, 219; on the present appropriation of wages and sources of income, 318; on the recent revival in trade, 436. ‘Brabrook (Mr.) on the work of the An- thropometric Committee, 120. Braham (P.) *on a new mode of illu- minating microscopic objects, 502; *on an instrument for the detection of polarised light, 502 ; *on crystals of mercury, 544; note on silver sulphate, 550. Bramwell (F. J.) on secular experiments on the elasticity of wires, 61; on patent legislation, 318. ‘Bristol coalfield, the sandstones and grits of the lower and middle series of the, E. Wethered on, 579. British Columbia, sketch of the geology of, by G. M. Dawson, 588. Brittain (Mr.) on the present appropria- tion of wages and sources of income, 318. Brown and Cordeaux’s, Messrs., method of obtaining systematic observations of the migration of birds at lighthouses and lightships, A. Newton on, 605. Buckland (Miss A. W.) on surgery and superstition in neolithic times, 630. *Bushmen crania, Prof, G. Rolleston on, 631. Busk (G.) on the exploration of Kent’s Cavern, 62. Bute Docks, Cardiff, J. McConnochie on the, 692. *Butler (G. G.) on pictorial aid to geo- graphical teaching, 660. ‘Cameron (J. M.) on the position of agri- cultural education and research in this ane and on the continent of Europe, Campbell (Sir G.) on the work of the Anthropometric Committee, 120. *Candahar, the high road from the Indus to, by Sir R. Temple, 658. “Canton, a journey from, to Kwei-Yang-Fu a the Canton river, W. Mesny on, *Capello (Capt. H.) and Lieut. R. Ivens on the results of the Portuguese ex- pedition in West Central Africa, 659. ‘Capital, what is? by W. Westegarth, 679. Carbonic acid, the action of, on lime- stone, Prof. W. Boyd Dawson on, 573. Carbonic oxide, the influence of water - on the union of, with oxygen at high temperatures, H. B. Dixon on, 503. 707 Carboniferous polyzoa, report on the, 76, Carbutt (E. H.) on patent legislation, 318. Carpenter (Dr.) on the occupation of a table at the zoological station at Naples, 161. Carruthers (W.) on the ‘ Geological Re- cord,’ 87. Caves of the South of Ireland, first report on the exploration of the, 209; R. J. Ussher on the caves and kitchen- midden at Carrigagower, co. Cork, 210; R. Day on the implements found at Carrigagower, co. Cork, 211. Cayley (Prof.) on mathematical tables, 30; on the calculation of tables of the fundamental invariants of algebraic forms, 38. ‘Challenger’ expedition, exhibition of some of the zoological reports of the, by P. L. Sclater, 606. Channel railway, project for a, by B. Leslie, 698. Chemical Section, Dr. J. H. Gilbert’s Ad- dress to the, 507. *Chilian tumulus, J. H. Madge ona, 636. Chiroptera, report on accessions to cur knowledge of the, during the past two years (1878-80), by G. E. Dobson, 169. *Oircles on a sphere, the distribution of, Prof. H. J. 8. Smith on, 476. Circulation of the underground waters in the Permian, New Red Sandstone, and Jurassic formations of England, and the quantity and character of the water supplied to towns and districts from those formations, sixth report on the, 87. Clarke (Hyde) on drum-signalling in Africa, 620; on a manuscript, perhaps Khita, discovered by Capt. Gill in Western China, 621; recent doubts on monosyllabism in philological classifi- cation, 621; on the pre-Cymric epoch in Wales, 629; on the antiquity of gesture and sign language, and the origin of characters and speech, 630 ; on the discovery of a bi-lingual seal in Cuneiform and Khita, 633; further re- searches on the prehistoric relations of the Babylonian, Chinese and Egyptian characters, language and culture, and their connection with sign and gesture language, 635 ; on the * Vei Syllabary ’ of Liberia, West Africa, 635; on the progress of the English stations in the hill regions of India, 686. Close time for indigenous animals, re- port on the possibility of establishing a, 257. Clouds, on determining the heights and distances of, by their reflexions in a low pool of water, and in a mercurial horizon, by F. Galton, 459. Z2Z2 708 Coal-gas of different qualities, report on | the best means for the development of light from: Part II., 241. *Coal seams of the eastern portion of the South Wales basin, the, and their chemical composition, J. W. Thomas on, 534. Coal-tar colours, the identification of the, J. Spiller on, 542. *Coals in ships, the spontaneous com- bustion of, J. Bamfield on, 696. Coast-line directions represented by great circles on the globe and the localities marked by earthquakes in Europe, the relation to be established between, Prof. J. P. O’Reilly on, 576. Collins (J. H.) on the fault systems of Central and West Cornwall, 584 *Combined elliptical, parallel, and an- gular motion, G. Faweus on, 699. Contact electricity, a method of measur- ing, Prof. Sir W. Thomson on, 494. Copper, a peculiar behaviour of, W. H. Preece on, 470. — contained in copper ores and regu- luses, a new process for separating silver from, W. Henderson on, 546. *Coppinger (R. W.) on a visit to Skyring Water, Straits of Magellan, 665. Cork, West, the hiatus said to have been found in the rocks of, G. H. Kinahan on, 574. Cornwall, Central and West, the fault | systems of, J. H. Collins on, 584. Crosskey (Rev. H. W.) on the circulation | of underground waters, 87; on the erratic blocks of England, Wales, and Treland, 110. Crustacea, report on the present state of | our knowledge of the: Part V. On fe- cundation, respiration, and the green gland, 230. Cryptogams, the classification of, A. W. Bennett on, 599. *Crystals of mercury, P. Braham on, | 544, Curves of the declination magnetographs at Kew, Stonyhurst, Coimbra, Lisbon, Vienna, and St. Petersburg, comparison of the, by Prof. W. G. Adams, 201. Dalton (W. H.) on the range of the lower tertiaries of East Suffolk, 575. *Dara Nur, Northern Afghanistan and its inhabitants, Lieut.-Col. H.C. B. Tanner on the, 665. Darwin (G. H.) on the measurement of the lunar disturbance of gravity, 25. Darwin (H.) on the measurement of the lunar disturbance of gravity, 25. Davey (H.) on the expansion of steam in non-rotative pumping engines, 697. Dawkins (Prof. W. Boyd) on the explo- ration of Kent’s Cavern, 62; on the INDEX. mode of reproduction of certain species- of Ichthyosaurus from the lias of England and Wiirtemberg, 68 ; on the erratic blocks of England, Wales, and Treland, 110; on the exploration of the caves of the South of Ireland, 209 ; on the action of carbonic acid on lime- stone, 573. Dawson (G. M.), sketch of the geology of British Columbia, 588. Day (R.) on the implements found at Carrigagower, Co. Cork, 211. Day (St. J. V.) on patent legislation, 318. Deacon (G. F.) on underground tempera- ture, 26. Deacon (J. F.) on the phenomena of the stationary tides inthe English Channel . and the North Sea, and the value of tidal observations in the North Atlantic Ocean, 390. Deaf, the German and other systems of teaching the, to speak, report on, 216. Deane (Dr.) on the erratic blocks of England, Wales, and Ireland, 110. *De Fonveille (W.) on an electro-mag- netic gyroscope, 500. Delany (Rev. W.) on the appointment of H.M. inspectors of elementary schools, 219. De Rance (C. E.) on the circulation of underground waters, 87; on the pre- glacial contours and post-glacial de- nudation of the north-west of England, 590. Dewar (Prof.) on the present state of our knowledge of spectrum analysis, 258. Dew-Smith (Mr.) on the occupation of a table at the zoological station at Naples 161. Dickinson (J.) on underground tempera- ture, 26. Dittmar (Prof.) on the best means for the development of light from coal- gas, 241. Dixon (H. B.) on the influence of water on the union of carbonic oxide with oxygen at high temperatures, 503. Dobson (G. E.) report on accessions to: our knowledge of the Chiroptera during the past two years (1878-80), 169. Doncaster (C.) on the German and other systems of teaching the deaf to speak, 216. *Double malar bone, Prof. G. Rolleston on the, 604. | Dresser (H. E.) on the possibility of establishing a close time for indige- nous animals, 257. Drew (F.) on the ‘ Geological Record,” 87. ‘Drumming’ of the snipe, Capt. W. Ve Legge on the, 604. INDEX. Drum-signalling in Africa, Hyde Clarke on, 620. Duncan (Prof. P. M.) on the carboniferous polyzoa, 76. Earnshaw (Rev. 8.) on the integral of ee equation in finite terms, 86. *Hast African expedition, the Royal Geographical Society’s, under Mr, J. Thomson, latest news of, 656. *Economic Science and Statistics, Ad- dress by G. W. Hastings to the Section of, 671. *Elasticity of wires, J. T. Bottomley on the, 494. —, secular experiments upon the, re- port of the Committee for commencing, 61. Electric convection-currents, Prof. 8. P. Thompson on, 470. *Hlectro-magnetic gyroscope, W. de Fon- vielle on an, 500, Electro-magnetic unit, the number of electrostatic units in the, R. Shida on, 497. Electro-motors, improvements in, T. Wiesendadger on, 501. Electrostatic units, the number of, in the electro-magnetic unit, R. Shida on, 497. Elliptic function formule, the deduction of trigonometrical from, J. W. L. Glaisher on, 477. *Elliptic functions, a kind of periodicity presented by some, Prof. H. J. S. Smith on, 482. Elwes (Capt. H. J.) on the relation of the Lepidoptera of Great Britain to those of other countries, 604. English stations in the hill regions of India, the progress of the, Hyde Clarke on, 686. Eozoon Canadense, proofs of the organic nature of, by C. Moore, 582. Equations to the real and to the imagi- nary directrices and latera recta of the general conic (a, b, c, e, f, g, h) (a, y1)?=0, Prof. R. W. Genese on the, with a note on aproperty of the director circle, 480. Erratic blocks of England, Wales, and Treland, eighth report on the, 110. Etheridge (R., jun.) on the ‘ Geological Record,’ 87, Evans (Dr. J.) on the exploration of Kent’s Cavern, 62; on the ‘ Geological Record,’ 87 ; on the exploration of the caves of the South of Ireland, 209. Everett (Prof.) on underground tempera- ture, 26. Expansion of steam in non-rotative pumping engines, H. Dayey on the, 709 Farr (Dr.) on the work of the Anthropo- metric Committee, 120. Fault systems of Central and West Cornwall, J. H. Collins on the, 584. *Fawcus (G.) on combined elliptical, parallel, and angular motion, 699. Fellows (F. P.) on the work of the Anthro- pometric Committee, 120; on the pre- sent appropriation of wages and sources of income, 318; on Admiralty monies and accounts, 668. Field (R.) on the phenomena of the stationary tides inthe English Channel and the North Sea, and the value of tidal observations in the North Atlantic Ocean, 390. Films of water, thin, experiments on, with regard to their absorption of yadiant heat, by the Hon. F. A. R. Russell, 490. Fish, the preservation of, and preventing the pollution of rivers, Lieut.-Gen. Sir J. E. Alexander on, 672. *Fitzgerald (G. F.) on the possibility of originating wave-disturbances in the ether by electro-magnetic forces, 497. Flight (W.) on observations of luminous meteors during the year 1879-80, 39. Flint-workers, the British, at Brandon, J. P. Harrison on, 626. Foote (R. B.) on the occurrence of stone implements in the coast laterite, south of Madras, and in high-level gravels and other formations in the South Mahratta country, 589. Forbes (Prof. G.) on the measurement of the lunar disturbance of gravity, 25; on observations of luminous meteors during the year 1879-80, 39; on im- provements in astronomical clocks, 56. *Forster (W.) on Australian autochthony, 620. Foster (Dr. C. Le Neve) on underground temperature, 26. Foster (Prof. G. C.) on an investigation for the purpose of fixing a standard of white light, 119; on the present state of our knowledge of spectrum analysis, 258. Foster (Prof. M.) on the influence of bodily exercise on the elimination of nitrogen, 159; on the occupation of a table at the zoological station at Naples, 161. Fox (H. C.) supplement to a paper on the synchronism of mean temperature and rainfall in the climate of London, 493. French deep-sea exploration in the Bay of Biscay, J. Gwyn Jeffreys on the, 378. ——, the Rev. A. M. Norman on the, 387. Fundamental invariants of algebraic forms, the calculation of tables of the, report on, 38. 710 Galapagos Islands, a visit to the, in H.M.S. ‘Triumph,’ 1880, by Capt. Markham, 665. Galloway (Mr.) on underground tem- perature, 26. Galton (Capt. D.) on the circulation of underground waters, 87; on patent legislation, 318 ; on the phenomena of the stationary tides in the English Channel and the North Sea, and the value of tidal observations in the North Atlantic Ocean, 390. Galton (F.) on the work of the Anthro- pometric Committee, 120; on determin- ing the heights and distances of clouds by their reflexions in a low pool of water, and in a mercurial horizon, 459 ; on a pocket registrator for anthro- pological purposes, 625. Gamgee (Dr.) on paleontological and zoological researches in Mexico, 254. Gases, the specific resistance of, at dif- ferent pressures, and the specifie in- ductive capacity of a good Sprengel vacuum, preliminary report of the Committee for accurately measuring, LO: Geddes (Mr.) on paleontological and _ zoological researches in Mexico, 254. Geikie (Prof.) on underground tempera- ture, 26. Genese (Prof. R. W.) on the equations to the real and to the imaginary direc- trices and latera recta of the general conic (a, b,c, e, f, g, h) (a, yl)?=0; with a note on a property of the director circle, 480. Geographical Section, Address by Lieut.- Gen. Sir J. H. Lefroy to the, 646. *Geographical teaching, pictorial aid to, G. G. Butler on, 660. Geological age and relations of the Siwalik and Pikermi vertebrate and invertebrate faunas, W. T. Blanford on the, 577. Geological evidence of the temporary sub- mergence of the South-west of Europe during the early human period, Prof. Prestwich on the, 581. ‘Geological Record,’ report on the, 87. Geological Section, H. C. Sorby’s Address to the, 565. Geology, mineralogy, and paleontology of Wales, list of works on the (to the end of 1873), by W. Whitaker, 397. —— of British Columbia, sketch of the, by G. M. Dawson, 588. of the Balearic Islands, Dr. Phené on the, 585. , the submarine, of the English Channel off the coast of South Devon, A. R. Hunt on, 573. *Geometry, inverse figures in, Prof. H. J. 8. Smith on, 476. INDEX. eometry, non-EKuclidian, notes on, by R. 8. Ball, 476. Gesture and sign language, the antiquity of, and the origin of characters and speech, Hyde Clarke on, 630. Gilbert (Dr. J. H.) Address by, to the Chemical Section, 507. Gill (D.) on improvements in astro- nomical clocks, 56. Gimingham (C. H.) on improvements in astronomical clocks, 56. Gladstone (Dr. J. H.) on the appoint- ment of H.M. inspectors of elementary schools, 219; on the refraction-equiva-- lent of diamond and the carbon com- pounds, 535. Glaisher (J.) on underground tempera- ture, 26; on mathematical tables, 30; on observations of luminous meteors. during the year 1879-80, 39; on the circulation of 87. Glaisher (J. W. L.) on mathematical tables, 30; on the deduction of trigo- nometrical from elliptic function for- mulz, 477; on algebraical expansions, of which the fractional series for the cotangent and cosecant are the limiting forms, 482; note on a trigonometrical identity involving products of four sines, 484. Godwin-Austen (Lieut.-Col. H. H.) on the steps taken for investigating the natural history of Socotra, 212; on the post-tertiary and more recent deposits of Kashmir and the Upper Indus Valley, 589. Gooch (W. D.) on the stone age in South Africa, 622. Gordon (J. E. H.) on accurately measur- ing the specific inductive capacity of a good Sprengel vacuum, and the specific resistance of gases at different pres- sures, 197. Grant (Prof.) on the measurement of the lunar disturbance of gravity, 25. Greek profile (incorrectly so called),. additional remarks on the, by J. Park Harrison, 625. Grubb (H.) on improvements in astro-. nomical clocks, 56. Giinther (Dr.) Address by, to the Biolo- gical Section, 591. *Hall (W. E.) on the loading of ships,. 699. Hallett (P.) on the work of the Anthro-. pometrie Committee, 120. Hancock (Dr. N.) on the German and other systems of teaching the deaf to speak, 216; on patent legislation, 318 ; on the present appropriation of wages and sources of income, 318. Harlech Mountains, Merionethshire, some: underground waters,. — ow © INDEX. pre-Cambrian rocks in the, Dr. H. Hicks on, 584. Harrison (J. Park) on the work of the Anthropometric Committee, 120; ad- ditional remarks on the Greek profile (incorrectly so called), 625; on the British flint-workers at Brandon, 626. Harting (J. EH.) on the possibility of establishing aclose time for indigenous | animals, 257. Hartlaub (Lr. G.) on the steps taken for investigatmg the natural history of Socotra, 212 olde Hartley (Prof.) on the present state of our | knowledge of spectrum analysis, 258. *Hastings (G. W.), Address by, to the Section of Economic Science and Statistics, 671. Haughton (Rev. Prof.) on the exploration | of the caves of the South of Ireland, 209. Head-kidney, the origin of the, A. Sedg- wick on, 644. Heat, the loss of, in steam boilers arising from incrustation, the determination of, W. Thomson on, 549. Heliograph or sun sigtal, an improved, by Dr. T. Anderson, 4¢1. Henderson (W.) on a new process for separating silver from copper contained in copper ores and reguluses, 546; remarks and statistics relating to Swansea usages and customs as they affect the sellers of foreign or colonial copper ores, 681. Herschel (Prof. A. 8.) on underground temperature, 26; on observetions of luminous meteors during the year 1879-89, 39. Heywood (J.) on the work of the Anthro- pometric Committee, 120; on the German and other systems of teaching the deaf to speak, 216 ; on thle appoint- ment of H.M. inspectors of elementary schools, 219 Hicks (Dr. H.) on some pre-Cambrian rocks in the MHarlech Mountains, Merionethshire, 584. High insulation key for electiometer work, an improved form of, rejort of the Committee for devising anc con- structing, 29. Hittites, W. St. C. Boscawen on the. 632. Hodges (F.- W.) on bleaching powder residue, 560. Hooker (Sir J.) on the steps taken for investigating the natural history of Socotra, 212. Hughes (Prof.) on the erratic blocks of England, Wales, and Ireland, 110. Hull (Prof. E.) on underground tempera- ture, 26; on the circulation of unde- ground waters, 87. Hunt (A. RB.) on the submarine geology | 711 of the English Channel off the coast of South Devon, 573. Hunter (Capt. F. M.) on the steps:taken for investigating the natural history of Socotra, 212. Huntington (Prof. A. K.) on the present state of our knowledge of spectrum analysis, 258. Huxley (Prof.) on the occupation of a table at the zoological station at Naples, 161. Hyper-elliptic integrals, the periods of the first class of, W. R. Roberts on, 485. Ichthyosaurus from the lias of England and Wiirtemberg, report on the mode of reproduction of certain species of, 68. Images photographiques, les transforma- tions successives des, et les appli- cations a l’astronomie, J. Janssen sur, 500. *Incrustation of steam boilers, W. Thom- son on the, 703. *India the home of gunpowder, on philo- logical evidence, by Dr. G. Oppert, 636. Induction balance, note on the theory of, by Lord Rayleigh, 472. *Indus, the, to Candahar, the high road from, by Sir R. Temple, 658. Influence of bodily exercise on the elimi- nation of nitrogen, report on the, 159 Ink used in writing letters and docu- ments, the identification of, W. Thom- son on, 549. : Inspectors, H.M., of elementary schools, report as to whether it is important that they should be appointed with reference to their ability for examining in the scientific specific subjects of the Code in addition to other matters, 219. *Ivens (Lieut. R.) and Capt. H. Capello on the results of the Portuguese ex- pedition in West Central Africa, 659. Janssen (J.) sur les transformations suc- cessives des images photographiques, et les applications 4 l’astronomie, 500. Jeffery (H.M.) on plane and spherical curves of the fourth class with quad- ruple foci, 478. Jeffreys (Dr. J. Gwyn) on the occupation of a table at the zoological station at Naples, 161; on the possibility of es- tablishing a close time for indigenous animals, 257; on the French deep-sea exploration in the Bay of Biscay, 378 ; list of the mollusca procured, 382; further remarks on the mollusca of the Mediterranean, 601. Jevons (Prof.) on the present appropria- tion of wages and sources of income, 318. Jones (B.) on the antiquities of Loughor Castle, 620. 712 Kashmir and the Upper Indus Valley, the post-tertiary and more recent deposits of, Lieut.-Col. H. H. Godwin-Austen on, 589. Kent’s Cavern, Devonshire, sixteenth and concluding report of the Committee for exploring, 62. Kinahan (G. H.) on the hiatus said to have been found in the rocks of West Cork, 574. ‘Knight Errant,’ the cruise of the, Prof. Sir C. Wyville Thomson on, 603. Kwei-Yang-Fu, a journey from Canton to, up the Canton river, W. Mesny on, 660. Kynaston (J. W.) on a new process for the production, from aluminous metals containing iron, of sulphate of alumina free from iron, 545. Ladd (W.) on the best form of magnet for magneto-electric machines, 467. Land question, agricultural statistics and the, by W. Botly, 668. Lankester (Prof. Ray) on the occupation of a table at the zoological station at Naples, 161. Lansdell (Rev. H.), through Siberia, vid the Amur and the Ussuri, 656. Laplace’s equation in finite terms, the integral of, Rev. 8. Earnshaw on, 486. Lapps, the mountain, Lieut. G. T. Temple on, 631. Latham (B.) on the temperature of town water-supplies, 696. Lawes (Rev. W.G.) three years in South- east New Guinea, 658. *Lea (A. 8.) on the alkaline fermentation of urine, 644. Lebour (Prof. G. A.) on underground temperature, 26; on the ‘ Geological Record,’ 87; on the circulation of underground waters, 87. Lee (J. E.) on the exploration of Kent’s Cavern, 62; on the erratic blocks of England, Wales, and Ireland, 110. Lefevre (J. G. Shaw) on the possibility of establishing a close time for indi- genous animals, 257. Lefroy (Lieut.-Gen. Sir J. H.) Address by, to the Geographical Section, 646. Legge (Capt. W. V.) on the ‘drumming’ of the snipe, 604. Lepidoptera of Great Britain, the relation of, to those of other countries, Capt. H. J. Elwes on, 604, Lepidosteus, the development of, F. M. Balfour and W. N. Parker on, 599. Leslie (B.) project for a Channel railway, 698 Levi (Prof. L.) on the work of the An- thropometric Committee, 120; on the present appropriation of wages and sources of income, 318. INDEX. Lichen, the action of a, on limestone, Prof. W. J. Sollas on, 586. Lightning conductors, the necessity for a regular inspection of, R. Anderson on, 471. —, the proper form of, W. H. Preece on, 470. Limestone, the action of a Jichen on, Prof. W. J. Sollas on, 586. —, the action of carbonic acid on, Prof. W. Boyd Dawkins on, 573. Liveing (Prof.) on the present state of our knowledge of spectrum analysis, 258. *Loading of ships, W. E. Hall on the, 699. ; Lodge (Dr. O. J.) on devising and con- structing an improved form of high in- sulation key for electrometer work, 29; on accurately measuring the specific inductive capacity of a good Sprengel vacuum, and the specific resistance of gases at different pressures, 197. London, the synchronism of mean tem- perature and rainfall in the climate of, supplement to a paper on, by H. C. Fox, 493. Loughor Castle, the antiquities of, B. Jones on, 620, Lowe (E. J.) or observations of luminous meteors durjng the year 1879-80, 39. Lubbock (SirJ.) on the exploration of Kent’s Cayern, 62. Luminous meteors, report on observations of, during the year 1879-80, 39. Lunar disturbance of gravity, measurement of the, report on, 25. the McConnochie (J.) on the Bute Docks, Cardiff, 692. Mackintosh (D.) on the erratic blocks of England, Wales, and Ireland, 110. McLeod (Pyof.) on the present state of our knowledge of spectrum analysis, 258. Macrory (Mr.) on patent legislation, 318. *Madge J. H.) on a Chilian tumulus, 636. Magnesia, the effects of, on vegetation, Maj.-fen. Scott on, 550. Magnei for magneto-electric machines, the best form of, W. Ladd on, 467. Maeneto-electric machines, the best form of nagnet for, W. Ladd on, 467. Mahomed (Dr. F. A.) on the work of the Anthropometric Committee, 120. Malagasy, the origin of, C. S. Wake on, 626. Manuscript, a, perhaps Khita, discovered by Capt. Gill in Western China, Hyde Chrke on, 621. Manne zoology of South Devon, second report on the exploration of the, 160. Maikham (Capt.) on a visit to the Gala- INDEX. pagos Islands in H.M.S. ‘Triumph,’ | 1880, 665. Marriage Laws of the United Kingdom, the required amendment in the, the Rev. Dr. Ace on, 672. Masaki (Taiso) on the German and other systems of teaching the deaf to speak, 216. Mathematical and Physical Section, Ad- dress by Prof. W. G. Adams to the, 447. *Mathematical solution of a logical pro- blem, Prof. H. J. 8. Smith on a, 476. —— tables, report on, 30. Mechanical Section, Address by J. Aber- nethy to the, 688. Mediterranean, the mollusca of the, fur- ther remarks on, by J. Gwyn Jeffreys, 601. *Mercury, crystals of, P. Braham on, 544. Merrifield (C. W.) on patent legislation, 318 ; on the present state of knowledge of the application of quadratures and interpolation to actual data, 321. Merrifield (Dr. J.) on the phenomena of the stationary tides in the English Channel and the North Sea, and the value of tidal observations in the North Atlantic Ocean, 390. “Mesny (W.) on a journey from Canton to | | Neolithic times, surgery and superstition Kwei-Yang-Fu up the Canton river, ‘660. Metallic compounds containing divalent organic radicals, J. Sakurai on: Part I., 504. Metals, the action of oils on, W. H. Wat- son on, 560. Mexico, paleontological and zoological researches in, report of the Committee for conducting, 254. Miall (Prof. L. C.) on the ‘Geological | Record,’ 87; on the erratic blocks of England, Wales, and Ireland, 110. Mica schist, a fragment of, Prof. W. J. Sollas on, 577. ‘Microscopic objects, a new mode of illu- minating, P. Braham on, 502. Minchin (G. M.), an account of some ex- periments in photo-electricity, 468. ‘Mineralogy of Wales, list of works on the (to the end of 1873), by W. Whita- ker, 397. ‘Minerals, the application of organic C. Bolton on, 505. Molloy (C.) on the German and other | systems of teaching the deaf to speak, 216. Mollusca, a list of the, procured during | the eruise of the ‘ Travailleur’ in the Bay of Biscay, 1880, by J. Gwyn Jef- | | Oils, the action of, on metals, W. H. freys, 382. of the Mediterranean, further re- marks on the, by J. Gwyn Jeffreys, 601. 713 Molyneux (W.) on the circulation of underground waters, 87; on the erratic blocks of England, Wales, and Ireland, 110. Monosyllabism in philological classifica- tion, recent doubts on, Hyde Clarke on, 621. Moore (C.) on the mode of reproduction of certain species of Ichthyosaurus from the lias of England and Wiirtem- berg, 68; proofs of the organic nature of Hozoon Canadense, 582. Morton (Mr.) on the circulation of under- ground waters, 87. Muirhead (Dr. H.) on the work of the Anthropometric Committee, 120; on the length of the sun-spot period, 465. Mundella (Rt. Hon. A. J.) on the German and other systems of teaching the deaf to speak, 216. Murray (G.) and A. W. Bennett, a re- formed system of terminology of the reproductive organs of thallophytes, 600. Musicians, vital and other statistics ap- plicable to, by P. M. Tait, 666, Neanderthal skull, the original, Prof. Schaaffhausen on, 624. in, Miss A. W. Buckland on, 630. | New Britain and neighbouring islands, six years’ exploration in, by W. Powell, 658. Newcome (F. N.) on diminishing annui- ties, 675. New Guinea, South-east, three years in, by the Rev. W. G. Lawes, 658. Newmarch (Mr.) on patent legislation, 318, Newton (Prof. A.) on the possibility of establishing a close time for indigenous animals, 257; on the migration of birds, and Messrs. Brown and Cor- deaux’s method of obtaining systematic observations of the same at lighthouses and lightships, 605. Nicholson (Prof. H. A.) on the ‘Geologi- cal Record,’ 87. Non-rotative pumping engines, the ex- pansion of steam in, H. Davey on, 697. | Norman (Rey. A. M.) on the French acids to the examination of, Prof. H. | deep-sea exploration in the Bay of Biscay, 387. North-East Passage, Lieut. G. T. Temple on the, 663. Oil, the effect of, in destroying waves on the surface of water, Prof. O. Reynolds on, 489. Watson on, 560. Oliphant (L.), recent travels in trans- Jordanic Palestine, 659. 714 *Oppert (Dr. G.), India the home of gun- powder, on philological evidence, 686. O'Reilly (Prof. J. P.) on the relation to be established between coast-line direc- tions represented by great circles on the globe and the localities marked by earthquakes in Europe, 576. Ores, complex, containing zinc, a new process for the metallurgic treatment of, E. A. Parnell on, 544. Organic acids, the application of, to the examination of minerals, Prof. H. C. . Bolton on, 505. Paleolithic flint implement from Pales- tine, H. Stopes on a, 624. —— implement manufactory, the site of a, at Crayford, Kent, F. C. J. Spurrell on, 574. stone implement from Egypt, H. Stopes on a, 624. Palzontological and zoological researches in Mexico, report of the Committee for conducting, 254. Paleontology of Wales, list of works on the (to the end of 1873), by W. Whitaker, 397. Palestine, trans-Jordanic, recent travels in, by L. Oliphant, 659. Parker (W. N.) and F. M. Balfour on the development of Lepidosteus, 599. Parnell (EH. A.), a new process for the metallurgic treatment of complex ores containing zine, 544. Patent legislation, report of the Com- mittee appointed to watch and report to the Council on, 318. Pattinson (J.) on the best means for the development of light from coal-gas, 241. Pengelly (W.) on underground tempera- ture, 26; on the exploration of Kent's Cavern, 62; on the circulation of underground waters, 87 ; on the erratic blocks of England, Wales, and Ireland, 110. Perkins (C. H.) on the anthracite coal -and coal-field of South Wales, 220. Perry (Prof. J.)on devising and construct- ing an improved form of high insu- lation key for electrometer work, 29 ; on accurately measuring the specific inductive capacity of a good Sprengel vacuum, and the specific resistance of gases at different pressures, 197. Petroleum spirit and analogous liquids, further notes on, by A. H. Allen, 547. Phené (Dr.) on the geology of the Ba- learic Islands, 585; on the retention of ancient and prehistoric customs in the Pyrenees, 627 ; on an examination of the Balearic Islands, 663; on a re- cent examination of the topography of the Troad, 664. INDEX. Phénoménes periodiques, la calculation des, Prof. Ragona sur, 466. Photo-electricity, an account of some ex- periments in, by G. M. Minchin, 468. Physical Section, Address by Prof. W. G. Adams to the Mathematical and, 447. Physiology, Anatomy and, Address by F. M. Balfour to the Department of, 636. Pikermi vertebrate and invertebrate faunas, the geological age and relations of the Siwalik and, W. T. Blanford on,. 577. Pitt-Rivers (Major-Gen.) on the work of the Anthropometric Committee, 120. Plane and spherical curves of the fourth class with quadruple foci, H. M. Jeffery on, 478. Plant (J.) on the circulation of under- ground waters, 87; on the erratic blocks of England, Wales, and Ireland, 110. Plunkett (T.) on an ancient settlement found beneath the surface of the peat in the coal-bog near Boho, Co, Fer- managh, 623. Pocket registrator for anthropological purposes, fF. Galton on a, 625. *Polarised light, an instrument for the detection of, P. Braham on, 502. *Portuguese expedition in West Central Africa, the results of the, Capt. H.. Capello and Lieut. R. Ivens on, 659. Post-tertiary and more recent deposits of Kashmir and the Upper Indus Valley, Lieut.-Col. H. H. Godwin-Austen on the, 589. Powell (W.) six years’ exploration in New Britain and neighbouring islands,. 658. Pre-Cambrian rocks in the Harlech Mountains, Merionethshire, Dr. H. Hicks on the, 584. Pre-Cymric epoch in Wales, Hyde Clarke on the, 629. Preece (W. H.) on a peculiar behaviour of copper, 470; on the proper form of lightning conductors, 470. Pre-glacial contours and post-glacial de- nudation of the North-west of England, C. E. De Rance on the, 590. Prehistoric relations of the Babylonian, Chinese, and Egyptian characters, lan-- guage, and culture, and their connec- tion with sign and gesture language, further researches on the, by Hyde Clarke, 635. — times in the Valley of the Rhine, Prof. Schaaffhausen on, 624. Prestwich (Prof.) on the cireulation of underground waters, 87; on the erratic: blocks of England, Wales, and Ireland, 110; on a raised beach in Rhos Sili - Bay, Gower, 581; on the geological evidence of the temporary submer- ee INDEX. . gence of the south-west of Europe during the early human period, 581. Protection in the United States and its lessons, G. Baden-Powell on, 671. Purser (Prof. ) on the measurement of the lunar disturbance of gravity, 25. Pye-Smith (Dr.) on the influence of bodily exercise on the elimination of nitrogen, 159. Pye-Smith (R. J.) on the German and _ other systems of teaching the deaf to speak, 216. Pyrenees, the retention of ancient and . prehistoric customs in the, Dr. Phené on, 627. Quadratures and interpolation, the ap- plication of, to actual data, C. W. Mer- rifield on the present state of knowledge of, 321. Ragona (Prof.) sur la calculation des phénoménes periodiques, 466; *on the laws of the change of speed and direc- tion of the wind, 467. Raised beach in Rhos Sili Bay, Gower, Prof. Prestwich on a, 581. Ramsay (Prof.) on underground tempera- ture, 26. Rawson (Sir R.) on the work of the An- thropometric Committee, 120. Rayleigh (Lord) on the present state of our knowledge of spectrum analysis, 258 ; note on the theory of the induc- tion balance, 472. Rayleigh’s, Lord, solution for waves in a plane vortex stratum, a disturbing infinity in, Prof. Sir W. Thomson on, 492. Reade (M.) on the circulation of under- ground waters, 87. Refraction-equivalent of diamond and the carbon compounds, Dr. J. H. Glad- _ Stone on the, 535. Reinold (Prof.) on the present state of our knowledge of spectrum analysis, 258. Revival in trade, the recent, S. Bourne on, 436. Reynolds (Prof. E.) on the present state of our knowledge of spectrum analysis, 258. Reynolds (Prof. 0.) on the phenomena of the stationary tides in the English | Channel and the North Sea, and the | in the | value of tidal observations North Atlantic Ocean, 390; on the ef- fect of oil in destroying waves on the surface of water, 489; on the steering of ships, 699. Rhine, the Valley of the, prehistoric times in, Prof. Schaaffthausen on, 624. Rhos Sili Bay, Gower, a raised beach in, Prof. Prestwich on, 581. 715. Roberts (C.) on the work of the Anthro~ pometric Committee, 120. Roberts (Mr.) on the circulation of underground waters, 87. Roberts (W. C.) on the present state of our knowledge of spectrum analysis, 258. and T. Wrightson on the density of fluid bismuth, 543. Roberts (W. R.) on the periods of the first class of hyper-elliptic integrals, 485, *Rodents, the classification of, Prof. G.. Rolleston on, 604. Rolleston (Prof. G.) on the work of the Anthropometric Committee, 120; on the occupation of a table at the zoo- logical station at Naples, 161; *on the double malar bone, 604; *on the classi- fication of rodents, 604; on the struc- ture of round barrows, 623; *on the structure of long barrows, 623; *on Bushmen crania, 631. Rowe (J. b.) on the exploration of the marine zoology of South Devon, 160. Rudler (F. W.) on the ‘Geological Record,’ 87 ; Address by, tothe Depart- ment of Anthropology, 609. | Russell (Hon. F, A, R.), experiments on thin films of water, with regard to their absorption of radiant heat, 490. *Safety lamp, the Shakespear, Colonel Shakespear on, 699. Sakurai (J.) on metallic compounds con= taining divalent organic radicals> Part I., 504. Salmon (Prof.) on the calculation of tables of the fundamental invariants of algebraic forms, 38. Salting mounds of Essex, H. Stopes on the, 631. Sanderson (Prof. B.) on the influence of bodily exercise on the elimination of nitrogen, 159. Sanford (W. A.) on the exploration of Kent’s Cavern, 62. Schaaffhausen (Prof.) on prehistoric times in the Valley of the Rhine, 624 ;: on the original Neanderthal «skull, 624, Schiifer (Prof.) on paleontological and zoological researches in Mexico, 254. Schuster (Dr.) on the present state of our knowledge of spectrum analysis, 258. Sclater (P. L.) on the occupation of a table at the zoological station at Naples, 161; on the steps taken for investigating the natural history of Socotra, 212 ; exhibition of some of the zoological reports of the ‘Challenger * expedition, 606; on the classification: of birds, 606. 716 Scott (Maj.-Gen.) on the effects of mag- nesia on vegetation, 550. Sedgwick (A.) on the origin of the head- kidney, 644. Seeley (Prof. H. G.) on the mode of reproduction of certain species of Ichthyosaurus from the lias of England and Wiirtemberg, 68. Septum permeable to water and imper- meable to air, Prof. Sir W. Thomson on a, with practical applications to a navigational depth-gauge, 488. Sewage, a new mode for the purification of, P. Spence on, 534. Shaen (Mr.) on the appointment.of H. M. inspectors of elementary schools, 219. *Shakespear (Col.) on the Shakespear safety lamp, 699. Shida (R.) on the number of electro- static units in the electro-magnetic unit, 497. “Ships, the loading of, W. E. Hall on, 699. -——, the steering of, Prof. O. Reynolds on, 699. -Shoolbred (J. N.) on the phenomena of the stationary tides in the English Channel and the North Sea, and the value of tidal observations in the North Atlantic Ocean, 390. Siberia, through, vid the Amur and the Ussuri, by the Rey. H. Lansdell, 656. -Siemens (Dr. C. W.) on the measurement of the lunar disturbance of gravity, 25; on secular experiments on the ‘elasticity of wires, 61; on patent legislation, 318. Silver, a new process for separating, from copper contained in copper ores and reguluses, W. Henderson on, 546. Silver sulphate, note on, by P. Braham, 550. Siwalik and Pikermi vertebrate and invertebrate faunas, the geological age and relations of the, W. T. Blanford on, 577. *Skew surface of the third order, note on the, by Prof. H. J. S. Smith, 482. ~“*Skyring Water, Straits of Magellan, a visit to, R. W. Coppinger on, 665. Sladen (P.) on the occupation of a table at the zoological station at Naples, 161. Smith (Prof. H. J. 8.) on mathematical tables, 30; *on inverse figures in geometry, 476; *on a mathematical solution of a logical problem, 476; *on the distribution of circles on a sphere, 476; *note on the skew surface of the third order, 482; *on a kind of periodicity presented by some elliptic functions, 482. Snipe, the ‘drumming’ of the, Capt. W. V. Legge on, 604. Socotra, the natural history of, report on | INDEX. the steps taken for investigating, 212 ; report to the Committee by Prof. Bayley Balfour, 212. Sollas (Prof. W. J.) on the island of Tor- ghatten, 576; on a fragment of mica schist, 577; 6n a striated stone from the trias of Portishead, 586; on the action of a lichen on limestone, 586; on sponge-spicules from the chalk of Trimmingham, Norfolk, 586. Sorby (H. C.) Address by, to the Geo- logical Section, 565. *Sounding machine, an improved, Sir W. Thomson on, 703. Specific rotatory power of cane and in- vert sugar, A. H. Allen on the, 541. Spectrum analysis, report on the present state of our knowledge of, 258. Spence (P.) on a new mode for the puri- fication of sewage, 534. Spiller (J.) on the identification of the coal-tar colours, 542. Sponge-spicules from the chalk of Trim- mingham, Norfolk, Prof. W.J.Sollas on, 586. *Spontaneous combustion of coals in ships, J. Bamfield on the, 696. Sprengel vacuum, a good, the specific in- ductive capacity of, and the specific resistance of gases at different pres- sures, preliminary report of the Com- mittee for accurately measuring, 197. Spurrell (F. C. J.) on the site of a paleolithic implement manufactory at Crayford, Kent, 574. *Starling (J. W.), exhibition of an im- proved volumetric apparatus, 534. Stationary tides in the English Channel and the North Sea, the phenomena of the, third report on, 390. *Statistics, Economic Science and, Address by G. W. Hastings to the Section of, 671. *Steam boilers, the incrustation of, W. Thomson on, 703. Steam-liquid temperature of a fluid, a method of determining the, without mechanism, Sir W. Thomson on, 496. Steering of ships, Prof. O. Reynolds on the, 699. Stokes (Prof. G. G.) on mathematical tables, 30. Stone age in South Africa, W. D. Gooch on the, 622. implements, the occurrence of, in the coast laterite, south of Madras, and in high-level gravels and other formations in the South Mahratta country, R. B. Foote on, 589. Stoney (Mr.) on the present state of our knowledge of spectrum analysis, 258. Stopes (H.) on a palzolithic stone im- plement from Egypt, 624; on a paleo- lithic flint implement from Palestine, — — INDEX. 624; on the salting mounds of Essex, 631. Striated stone from the trias of Portis- head, Prof. W. J. Sollas on a, 586. Suffolk, East, the range of the lower ter- tiaries of, W. H. Dalton on, 575. Sugar, cane and invert, the specific rota- tory power of, A. H. Allen on, 541. Sulphate of alumina free from iron, a new process for the production of, from aluminous minerals containing iron, J. W. Kynaston on, 545. Sun-spot period, the length of the, Dr. H. Muirhead on, 465. a Surgery and superstition in neolithic times, Miss A. W. Buckland on, 630. Swansea usages and customs, remarks and statistics relating to, as they affect the sellers of foreign or colonial copper ores, by W. Henderson, 681. : Sylvester (Prof.) on the calculation of tables of the fundamental invariants of algebraic forms, 38. Symons (G. J.) on underground tempera- ture, 26. Tait (Prof.) on the measurement of the lunar disturbance of gravity, 25; on secular experiments on the elasticity of wires, 61. he Tait (P. M.), vital and other statistics applicable to musicians, 666, *Tanner (Lieut.-Col. H. C. B.) on the Dara Nur, Northern Afghanistan and its inhabitants, 665. : Tawney (E. B.) on the ‘Geological Record,’ 87. u Temperature, underground, thirteenth report on the rate of increase of, down- wards in various localities of dry land and under water, 26. ‘ Temple (Lieut. G. T.) on the mountain Lapps, 631; on the North-Hast Pas- sage, 663. ‘ *Temple (Sir R.), the high road from the Indus to Candahar, 658. Tertiaries, the lower, of East Suffolk, the range of, W. H. Dalton on, 575. Tertiary (Miocene) flora, &c., of the ba- salt of the North of Ireland, second report on the, 107. Thallophytes, a reformed system of ter- minology of the reproductive organs of, by A. W. Bennett and G. Murray, 600. *Thomas (J. W.) on the coal seams of the eastern portion of the South Wales basin, and their chemical composition, 534. Thompson (Prof. S. P.) on electric con- vection-currents, 470. Thomson (Prof. Sir C. Wyville) on the occupation of a table at the zoological station at Naples, 161; on the cruise of the ‘ Knight Errant,’ 603. 717 *Thomson, Mr. J., latest news of the Royal Geographical Society’s Hast- African expedition under, 656. Thomson (Prof. Sir Wm.) on the mea- surement of the lunar disturbance of gravity, 25; on underground tempera- ture, 26 ; on mathematical tables, 30 ; on secular experiments on the elasti- city of wires, 61 ; on patent legislation, 318; on the phenomena of the sta- tionary tides in the English Channel and the North Sea, and the value of tidal observations in the North Atlan- tie Ocean, 390; on maximum and mini- mum energy in vortex motion, 473 : on a septum permeable to water and impermeable to air, with practical applications to a navigational depth- gauge, 488 ; on an experimental illns- tration of minimum energy in vortex motion, 491; on a disturbing infinity in Lord Rayleigh’s solution for waves. in a plane vortex stratum, 492; on a method of measuring contact electri- city, 494; on a method of determin- ing without mechanism the limiting steam-liquid temperature of a fluid, 496; on an improved sounding machine, 703. : Thomson (W.) on the determination of the loss of heat in steam-boilers aris- ing from incrustation, 549; on the identification of the ink used in writ- ing letters and documents as evidence in cases of libel, forgery, &c., 549. *Thomson (W.) on the incrustation of steam boilers, 703. Tidal observations at Madeira or other islands in the North Atlantic Ocean, on the value of, 390. Tiddeman (R. H.) on the erratic blocks of England, Wales, and Ireland, 110. Tides, the stationary, in the English Channel and the North Sea, the pheno- mena of, third report on, 390. Topley (W.) on the ‘ Geological Record,” 87 Torghatten, the island of, Prof. W. J. Sollas on, 576. Town water-supplies, the temperature of,. B. Latham on, 696. Trade, the recent revival in, 8. Bourne. on, 436. Trigonometrical from elliptic function formule, the deduction of, J. W. L. Glaisher on, 477. —— identity involving products of four sines, note on a, by J. W. L. Glaisher,. 484. Tristram (Rev. Canon) on the possibility- of establishing a close time for indi- genous animals, 257. Troad, a recent examination of the topo~ graphy of the, Dr, Phené on, 664. 718 Underground temperature, thirteenth re- port on the rate of increase of, down- wards in various localities of dry land and under water, 26. waters in the Permian, New Red Sandstone, and Jurassic formations of England, the circulation of the, and the quantity and character of the water supplied to towns and districts from those formations, sixth report on, 87. United States, Protection in the, and its lessons, G. Baden-Powell on, 671. Urine, the alkaline fermentation of, A. S. Lea on, 644, Ussher (R. J.) on the caves and kitchen- midden at Carrigagower, co. Cork, 210. “Vei Syllabary’ of Liberia, West Africa, Hyde Clarke on the, 635. Vine (G. R.) on the carboniferous poly- zoa, 76. Vital and other statistics applicable to musicians, by P. M. Tait, 666. Vivian (E.) on the exploration of Kent’s Cavern, 62. *Volumetric analysis, the so-called ‘ nor- mal’ solutions of, A. H. Allen on, 549. apparatus, an improved, exhibition of, by J. W. Starling, 534. Vortex motion, an experimental illus- tration of minimum energy in, Sir W. Thomson on, 491, ——, maximum and minimum energy in, Prof. Sir W. Thomson on, 473. ok ‘Wages, and sources of income, the pre- sent appropriation of, and how far it is consonant with the economic progress of the people of the United Kingdom, report on, 318. Wake (C. 8.) on the origin of the Mala- gasy, 620. Wallace (Dr. W.) on the best means for the development of light from coal- gas, 241. ‘Waters (A. W.) report on the occupation of a.table at the zoological station at Naples, 163. Watson (W. H.) on the action of oils on metals, 560. Watts (Dr. M.) on the present state of our knowledge of spectrum analysis, 258. *Wave-disturbances in the ether, the possibility of originating, by electro- INDEX. magnetic forces, G. F. Fitzgerald on, 497. Waves on the surface of water, the effect of oil in destroying, Prof. O. Reynolds on, 489. Weldon (W.) *on some relations between the atomic volumes of certain elements and the heats of formation of some of their compounds, 503. Westgarth (W.), What is capital? 679. Wethered (H.) on underground tempera- ture, 26; on the sandstones and grits of the lower and middle series of the Bristol coalfield, 579. Whitaker (W.) on the ‘Geological Re- cord,’ 87 ; on the circulation of under- ground waters, 87; list of works on the geology, mineralogy, and paleon- tology of Wales (to the end of 1873), 397. White light, a standard of, report on an investigation for the purpose of fixing, ILS: Wiesendanger (T.) on improvements in electro-motors, 501. Wilkinson (R.) on the German and other systems of teaching the deaf to speak, 216; on the appointment of H.M. in- spectors of elementary schools, 219. Williamson (Dr. A. W.) on the present state of our knowledge of spectrum analysis, 258; on patent legislation, 318. Williamson (Prof. W. C.) on the Tertiary (Miocene) flora, &e., of the basalt of the North of Ireland, 107. *Wind, the laws of the change of speed and direction of the, Prof. Ragona on, 467. Wood (H. T.) on patent legislation, 318. Wrightson (T.) and W. C. Roberts on the density of fluid bismuth, 543. Wynne (A. B.) on underground tempera- ture, 26. Zoological and paleontological researches in Mexico, report of the Committee for conducting, 254. Zoological reports of the ‘Challenger’ expedition, exhibition of some of the, by P. L. Sclater, 606. Zoological station at Naples, report of the Committee appointed to arrange for the occupation of a table at the, 161; report to the Committee by A. W. Waters, 163. BRITISH ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE. Life Members (since 1845), and all Annual Members who have not intermitted their Subscription, receive gratis all Reports published after the date of their Membership. Any other volume they require may be obtained on application at the Office of the Association, 22 Albemarle Street, Piccadilly, London, W., at the following prices, viz.—Reports for 1831 to 1874 (of which more than 15 copies remain), at 2s. 6d. per volume ; after that date, at two-thirds of the Publication Price. A few sets, from 1831 to 1874 inclusive, may also be obtained at £10 per set. Associates for the Meeting in 1880 may obtain the Volume for the Year at two-thirds of the Publication Price. PROCEEDINGS ortase FIRST anp SECOND MEETINGS, at York and Oxford, 1831 and 1832, Published at 13s. 6d. CONTENTS :—Prof. Airy, on the Progress of Astronomy ;—J. W. Lubbock, on the Tides ;—Prof. Forbes, on the Present State of Meteorology ;—Prof. Powell, on the Present State of the Science of Radiant Heat ;—Prof. Cumming, on Thermo-Electri- city ;—Sir D. Brewster, on the Progress of Optics ;—Rev. W. Whewell, on the Present State of Mineralogy ;—Rev. W. D. Conybeare, on the Recent Progress and Present State of Geology ;—Dr. Pritchard’s Review of Philological and Physical Researches. Together with Papers on Mathematics, Optics, Acoustics, Magnetism, Electricity, Chemistry, Meteorology, Geography, Geology, Zoology, Anatomy, Physiology, Botany, and the Arts; and an Exposition of the Objects and Plan of the Association, &c. PROCEEDINGS or tar THIRD MEETING, at Cambridge, 1833, Published at 12s. (Out of Print.) CONTENTS :—Proceedings of the Meeting ;—John Taylor, on Mineral Veins ;—Dr. Lindley, on the Philosophy of Botany ;—Dr. Henry, on the Physiology of the Nervous System ;—P. Barlow, on the Strength of Materials ;—S. H. Christie, on the Magnetism of the Earth ;—Reyv. J. Challis, on the Analytical Theory of Hydrostatics and Hy- drodynamics ;—G. Rennie, on Hydraulics as a Branch of Engineering, Part I.;—Rev. G. Peacock, on certain Branches of Analysis. Together with Papers on Mathematics and Physics, Philosophical Instruments and Mechanical Arts, Natural History, Anatomy, Physiology, and History of Science. 720 PROCEEDINGS or rus FOURTH MEETING, at Edinburgh, 1834, Published at 15s. CONTENTS :—H. G. Rogers, on the Geology of North America ;—Dr. 0. Henry, on the Laws of Contagion ;—Prof. Clark, on Animal Physiology ;—Rev. L. Jenyns, on Zoology ;—Reyv. J. Challis, on Capillary Attraction ;—Prof. Lloyd, on Physical Optics ; —G. Rennie, on Hydraulics, Part I1. Together with the Transactions of the Sections, and Recommendations of the Association and its Committees. PROCEEDINGS or tae FIFTH MEETING, at Dublin, 1835, Pub- lished at 13s. 6d. CONTENTS :—Rev. W. Whewell, on the Recent Progress and Present Condition of the Mathematical Theories of Electricity, Magnetism, and Heat ;—A. Quetelet, Apercu de l’Etat actuel des Sciences Mathématiques.chez les Belges ;—Capt. E. Sabine, on the Phenomena of Terrestrial Magnetism. Together with the Transactions of the Sections, Prof. Sir W. Hamilton’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or THE SIXTH MEETING, at Bristol, 1836, Pub- lished at 12s. CONTENTS :—Prof. Daubeny, on the Present State of our Knowledge with respect to Mineral and Thermal Waters ;—Major E. Sabine, on the Direction and Intensity of the Terrestrial Magnetic Force in Scotland ;—J. Richardson, on North American Zoo- logy ;—Rev. J. Challis, on the Mathematical Theory of Fluids;—J. T. Mackay, a Comparative View of the more remarkable Plants which characterize the neighbour- hood of Dublin and Edinburgh, and the South-west of Scotland, &c.;—J. T. Mackay, Comparative Geographical Notices of the more remarkable Plants which characterize Scotland and Ireland ;—Report of the London Sub-Committee of the Medical Section on the Motions and Sounds of the Heart ;—Second Report of the Dublin Sub-Com- mittee on the Motions and Sounds of the Heart ;—Report of the Dublin Committee on the Pathology of the Brain and Nervous System ;—J. W. Lubbock, Account of the Recent Discussions of Observations of the Tides ;—Rev. B. Powell, on deter- mining the Refractive Indices for the Standard Rays of the Solar Spectrum in various media;—Dr. Hodgkin, on the Communication between the Arteries and Ab- sorbents ;—Prof. Phillips, Report of Experiments on Subterranean Temperature ; —FProf. Hamilton, on the Validity of a Method recently proposed by G. B. Jerrard, for Transforming and Resolving Equations of Elevated Degrees. Together with the Transactions of the Sections, Prof. Daubeny’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or tas SEVENTH MEETING, at Liverpool, 1837, Published at 16s. 6d. CONTENTS :—Major E. Sabine, on the Variations of the Magnetic Intensity ob- served at different points of the Earth’s Surface ;—Rey. W. Taylor, on the various modes of Printing for the Use of the Blind ;—J. W. Lubbock, on the Discussions of Observations of the Tides ;—Prof. T. Thompson, on the Difference between the Com- position of Cast Iron produced by the Cold and Hot Blast ;—Rey. T. R. Robinson, on the Determination of the Constant of Nutation by the Greenwich Observations ;— R. W. Fox, Experiments on the Electricity of Metallic Veins, and the Temperature of Mines ;—Provisional Report of the Committee of the Medical Section of the British Association, appointed to investigate the Composition of Secretions, and the Organs producing them ;—Dr. G. O. Rees, Report from the Committee for inquiring into the Analysis of the Glands, &c., of the Human Body ;—Second Report of the London Sub-Committee of the British Association Medical Section, on the Motions and Sounds of the Heart ;—Prof. Johnston, on the Present State of our Knowledge in re- gard to Dimorphous Bodies ;—Lieut.-Col. Sykes, on the Statistics of the four Collec- torates of Dukhun, under the British Government ;—E, Hodgkinson, on the relative 721 Strength and other Mechanical Properties of Iron obtained from the Hot and Cold Blast ;—W. Fairbairn, on the Strength and other Properties of Iron obtained from the Hot and Cold Blast ;—Sir J. Robinson and J. §. Russell, Report of the Committee on Waves ;—Note by Major Sabine, being an Appendix to his Report on the Varia- tions of the Magnetic Intensity observed at different Points of the Earth’s Surface ; —J, Yates, on the Growth of Plants under Glass, and without any free communica- tion with the outward Air, on the Plan of Mr. N. J. Ward, of London. Together with the Transactions of the Sections, Prof, Traill’s Address, and Recom- mendations of the Association and its Committees. PROCEEDINGS or trxz EIGHTH MERTING, at Newcastle, 1838, Published at 15s. CONTENTS :—Rev. W. Whewell, Account of a Level Line, measured from the Bristol Channel to the English Channel, by Mr. Bunt ;—Report on the Discussions of Tides, prepared under the direction of the Rev. W. Whewell ;—W. 8. Harris, Account of the Progress and State of the Meteorological Observations at Plymouth ;—Major E. Sabine, on the Magnetic Isoclinal and Isodynamic Lines in the British Islands ; Dr. Lardner, on the Determination of the Mean Numerical Values of Rail- way Constants ;—R. Mallet, First Report upon Experiments upon the Action of Sea and River Water upon Cast and Wrought Iron ;—R. Mallet, on the Action of a Heat of 212° Fahr., when long continued, on Inorganic and Organic Substances. Together with the Transactions of the Sections, Mr. Murchison’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or tae NINTH MEETING, at Birmingham, 1839, Published at 13s. 6d. (Out of Print.) CONTENTS :—Rey. B. Powell, Report on the Present State of our Knowledge of Refractive Indices, for the Standard Rays of the Solar Spectrum in different media ; Report on the Application of the Sum assigned for Tide Calculations to Rev. W. Whewell, in a letter from T., G. Bunt, Esq. ;—H. L. Pattinson, on some Galvanic Experiments to determine the Existence or Non-Existence of Electrical Currents among Stratified Rocks, particularly those of the Mountain Limestone formation, constituting the Lead Measures of Alton Moor ;—Sir D. Brewster, Reports respecting the Two Series of Hourly Meteorological Observations kept in Scotland ;—Report on the subject of a series of Resolutions adopted by the British Association at their Meeting in August 1838, at Newcastle ;—R. Owen, Report on British Fossil Reptiles ; —E. Forbes, Report on the Distribution of the Pulmoniferous Mollusca in the British Isles ;—W. 8. Harris, Third Report on the Progress of the Hourly Meteorological Register at Plymouth Dockyard. Together with the Transactions of the Sections, Rev. W. Vernon Harcourt’s Ad- dress, and Recommendations of the Association and its Committees. PROCEEDINGS or tras TENTH MEETING, at Glasgow, 1840, Published at 15s. (Out of Print.) CONTENTS :—Reyv. B. Powell, Report on the Recent Progress of discovery relative to Radiant Heat, supplementary to a former Report on the same subject inserted in the first volume of the Reports of the British Association for the Advancement of Science ;—J. D. Forbes, Supplementary Report on Meteorology ;—W. S. Harris, Re- port on Prof, Whewell’s Anemometer, now in operation at Plymouth ;—Report on *The Motion and Sounds of the Heart,’ by the London Committee of the British Association, for 1839-40;—Prof. Schénbein, an Account of Researches in Electro- Chemistry ;—R. Mallet, Second Report upon the Action of Air and Water, whether fresh or salt, clear or foul, and at various temperatures, upon Cast Iron, Wrought Tron, and Steel ;—R. W. Fox, Report on some’Observations on Subterranean Tempe- rature ;—A. F. Osler, Report on the Observations recorded during the years 1837, 1838, 1839, and 1840, by the Self-registering Anemometer erected at the Philosophical Institution, Birmingham ;—Sir D. Brewster, Report respecting the Two Series of Hourly Meteorological Observations kept at Inverness and Kingussie, from Nov. Ist, ean Noy, Ist, 1839 :—W. Thompson, Report on the Fauna of Ireland: Div. Verte- 0. 3A 722 brata;—C. J. B. Williams, M.D., Report of Experiments on the Physiology of the Lungs and Air-Tubes ;—Rev. J. 8. Henslow, Report of the Committee on the Preservation of Animal and Vegetable Substances. Together with the Transactions of the Sections, Mr. Murchison and Major E. Sabine’s Address, and Recommendations of the Association and its Committees, PROCEEDINGS or tHe ELEVENTH MEETING, at Plymouth, 1841, Published at 13s. 6d. ContTENTS :—Rev. P. Kelland, on the Present State of our Theoretical and Expe- rimental Knowledge of the Laws of Conduction of Heat ;—G. L. Roupell, M.D., Re- port on Poisons ;—T. G. Bunt, Report on Discussions of Bristol Tides, under the direction of the Rev. W. Whewell;—D. Ross, Report on the Discussions of Leith Tide Observations, under the direction of the Rev. W. Whewell;—W. 8S. Harris, upon the working of Whewell’s Anemometer at Plymouth during the past year ;— Report of a Committee appointed for the purpose of superintending the scientifie co-operation of the British Association in the System of Simultaneous Observations in Terrestrial Magnetism and Meteorology ;—Reports of Committees appointed to provide Meteorological Instruments for the use of M. Agassiz and Mr. M‘Cord ;—Report of a Committee appointed to superintend the Reduction of Meteorological Observations ; —Report of a Committee for revising the Nomenclature of the Stars ;—Report ofa Committee for obtaining Instruments and Registers to record Shocks and Earthquakes in Scotland and Ireland ;—Report of a Committee on the Preservation of Vegetative Powers in Seeds ;—Dr. Hodgkin, on Inquiries into the Races of Man ;—Report of the Committee appointed to report how far the Desiderata in our knowledge of the Con- dition of the Upper Strata of the Atmosphere may be supplied by means of Ascents in Balloons or otherwise, to ascertain the probable expense of such Experiments, and. to draw up Directions for Observers in such circumstances ;--R. Owen, Report on British Fossil Reptiles ;—Reports on the Determination of the Mean Value of Rail- way Constants ;—Dr. D. Lardner, Second and concluding Report on the Determi- nation of the Mean Value of Railway Constants;—E. Woods, Report on Railway Constants ;—Report of a Committee on the Construction of a Constant Indicator for Steam Engines. Together with the Transactions of the Sections, Prof. Whewell’s Address, and Recommendations of the Association and its Committees, . PROCEEDINGS or tose TWELFTH MEETING, at Manchester, 1842, Published at 10s. 6d. ConTENTS :—Report of the Committee appointed to conduct the co-operation of the British Association in the System of Simultaneous Magnetical and Meteorological Observations ;—Dr. J. Richardson, Report on the present State of the Ichthyology of New Zealand ;—W. 8. Harris, Report on the Progress of Meteorological Observa- tions at Plymouth ;—Second Report of a Committee appointed to make Experiments on the Growth and Vitality of Seeds ;—C. Vignoles, Report of the Committee on Railway Sections ;—Report of the Committee for the Preservation of Animal and Vegetable Substances;—Dr. Lyon Playfair, Abstract of Prof. Liebig’s Report on Organic Chemistry applied to Physiology and Pathology ;—R. Owen, Report on the British Fossil Mammalia, Part I. ;—R. Hunt, Researches on the Influence of Light on the Germination of Seeds and the Growth of Plants;—L. Agassiz, Report on the Fossil Fishes of the Devonian System or Old Red Sandstone ;—W. Fairbairn, Appen- dixtoa Report on the Strength and other Properties of Cast Iron obtained from the Hot and Cold Blast ;— D. Milne, Report of the Committee for Registering Shocks of Earth- quakes in Great Britain ;—Report of a Committee on the construction of a Constant Indicator for Steam-Engines, and for the determination of the Velocity of the Piston of the Self-acting Engine at different periods of the Stroke ;—J. 8. Russell, Report of a Committee on the Form of Ships ;—Report of a Committee appointed ‘to consider of the Rules by which the Nomenclature of Zoology may be established on a uniform and permanent basis ;’—Report of a Committee on the Vital Statistics of Large Towns in Scotland ;—Provisional Reports, and Notices of Progress in Special Researches entrusted to Committees and Individuals. Together with the Transactions of the Sections, Lord Francis Egerton’s Address, and Recommendations of the Association and its Committees, 723 PROCEEDINGS or raz THIRTEENTH MEETING, at Cork, “1843, Published at 12s. CONTENTS :—Robert Mallet, Third Report upon the Action of Air and Water, whether fresh or salt, clear or foul, and at Various Temperatures, upon Cast Iron, Wrought Iron, and Steel ;—Report of the Committee appointed to conduct the Co- operation of the British Association in the System of Simultaneous Magnetical and Meteorological Observations ;—Sir J. F. W. Herschel, Bart., Report of the Committee -appointed for the Reduction of Meteorological Observations ;—Report of the Com- mittee appointed for Experiments on Steam-Engines ;—Report of the Committee ap- pointed to continue their Experiments on the Vitality of Seeds ;—J. S. Russell, Report of a Series of Observations on the Tides of the Frith of Forth and the East Coast of Scotland ;—J. 8. Russell, Notice of a Report of the Committee on the Form of Ships; —J. Blake, Report on the Physiological Action of Medicines ;—Report of the Com- mittee on Zoological Nomenclature ;—Report of the Committee for Registering the Shocks of Earthquakes, and making such Meteorological Observations as may appear to them desirable ;—Report of the Committee for conducting Experiments with Cap- tive Balloons ;—Prof. Wheatstone, Appendix to the Report;—Report of the Com- “mittee for the Translation and Publication of Foreign Scientific Memoirs;—C. W. Peach, on the Habits of the Marine Testacea ;—E. Forbes, Report on the Mollusca -and Radiata of the #igean Sea, and on their distribution, considered as bearing on Geology ;—L. Agassiz, Synoptical Table of British Fossil Fishes, arranged in the order of the Geological Formations ;—R. Owen, Report on the British Fossil Mam- malia, Part I. ;—E. W. Binney, Report on the excavation made at the junction of the Lower New Red Sandstone with the Coal Measures at Collyhurst ;—W. Thomp- son, Report on the Fauna of Ireland: Div. Invertebrata ;—Provisional Reports, and Notices of Progress in Special Researches entrusted to Committees and Individuals. Together with the Transactions of the Sections, the Earl of Rosse’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or raz FOURTEENTH MEETING, at York, 1844, Published at £1. CONTENTS :—W. B. Carpenter, on the Microscopic Structure of Shells ;—J. Alder and A. Hancock, Report on the British Nudibranchiate Mollusca;—R. Hunt, Researches on the Influence of Light on the Germination of Seeds and the Growth of Plants ;—Report of a Committee appointed by the British Association in 1840, for revising the Nomenclature of the Stars ;—Lt.-Col. Sabine, on the Meteorology of Toronto in Canada ;—J. Blackwall, Report on some recent researches into the Structure, Functions, and Economy of the Avaneidea made in Great Britain ;—EKar? of Rosse, on the Construction of large Reflecting Telescopes ;—Rev. W. V. Harcourt, Report on a Gas-furnace for Experiments on Vitrifaction and other Applications of High Heat in the Laboratory ;—Report of the Committee for Registering Earth- quake Shocks in Scotland ;—Report of a Committee for Experiments on Steam- Engines ;—Report of the Committee to investigate the Varieties of the Human Race ;—Fourth Report of a Committee appointed to continue their Experiments on the Vitality of Seeds ;—W. Fairbairn, on the Consumption of Fuel and the Preven- tion of Smoke ;—F. Ronalds, Report concerning the Observatory of the British Association at Kew;—Sixth Report of the Committee appointed to conduct the Co-operation of the British Association in the System of Simultaneous Magnetical and Meteorological Observations ;—Prof. Forchhammer on the influence of Fucoidal Plants upon the Formations of the Earth, on Metamorphism in general, and par- ticularly the Metamorphosis of the Scandinavian Alum Slate ;—H. E. Strickland, Report on the Recent Progress and Present State of Ornithology ;—T, Oldham, Report of Committee appointed to conduct Observations on Subterranean Tempera- ture in Ireland ;—Prof. Owen, Report on the Extinct Mammals of Australia, with descriptions of certain Fossils indicative of the former existence in that continent of large Marsupial Representatives of the Order Pachydermata;—W. 8S. Harris, Report on the working of Whewell and Osler’s Anemometers at Plymouth, for the years 1841, 1842, 1843 ;—W. R. Birt, Report on Atmospheric Waves ;—L. Agassiz, Rapport sur les Poissons Fossiles de l’Argile de Londres, with translation ;—J. S. 3a2 724 Russell, Report on Waves ;—Provisional Reports, and Notices of Progress in Special Researches entrusted to Committees and Individuals. Together with the Transactions of the Sections, the Dean of Ely’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or tus FIFTEENTH MEETING, at Cambridge,. 1845, Published at 12s. ConTENTS :—Seventh Report of a Committee appointed to conduct the Co-opera- tion of the British Association in the System of Simultaneous Magnetical and Meteorological Observations ;—Lieut.-Col. Sabine, on some Points in the Meteorology of Bombay ;—J. Blake, Report on the Physiological Actions of Medicines ;—Dr. Von Boguslawski, on the Comet of 1843 ;—R. Hunt, Report on the Actinograph ;—Prof. Schénbein, on Ozone ;—Prof. Erman, on the Influence of Friction upon Thermo- Electricity ;—Baron Senftenberg, on the Self-registering Meteorological Instru- ments employed in the Observatory at Senftenberg ;—W. R. Birt, Second Report on Atmospheric Waves ;—G. R. Porter, on the Progress and Present Extent of Savings” Banks in the United Kingdom ;—Prof. Bunsen and Dr. Playfair, Report on the Gases evolved from Iron Furnaces, with reference to the Theory of Smelting of Iron ;— Dr. Richardson, Report on the Ichthyology of the Seas of China and Japan ;— Report of the Committee on the Registration of Periodical Phenomena of Animals and Vegetables;—Fifth Report of the Committee on the Vitality of Seeds ;— Appendix, &c. Together with the Transactions of the Sections, Sir J, F, W. Herschel’s Address,. and Recommendations of the Association and its Committees. PROCEEDINGS or raz SIXTEENTH MEETING, at Southampton,. 1846, Published at 15s. ContTENTS :—G. G. Stokes, Report on Recent Researches in Hydrodynamics ;— Sixth Report of the Committee on the Vitality of Seeds;—Dr. Schunck, on the Colouring Matters of Madder ;—J. Blake, on the Physiological Action of Medicines ;- —R. Hunt, Report on the Actinograph ;—R. Hunt, Notices on the Influence of Light on the Growth of Plants ;—R. L, Ellis, on the Recent Progress of Analysis ;—Prof. Forchhammer, on Comparative Analytical Researches on Sea Water ;—A, Erman, on. the Calculation of the Gaussian Constants for 1829;—G. R. Porter, on the Progress, present Amount, and probable future Condition of the Iron Manufacture in Great Britain ;—W. R. Birt, Third Report on Atmospheric Waves ;—Prof. Owen, Report on the Archetype and Homologies of the Vertebrate Skeleton ;—J. Phillips, on Anemometry ;—Dr. J. Percy, Report on the Crystalline Flags ;—Addenda to Mr. Birt’s Report on Atmospheric Waves. Together with the Transactions of the Sections, Sir R. I. Murchison’s Address, . and Recommendations of the Association and its Committees. PROCEEDINGS or tas SEVENTEENTH MEETING, at Oxford,. 1847, Published at 18s. ConTENts :—Prof, Langberg, on the Specific Gravity of Sulphuric Acid at different degrees of dilution, and on the relation which exists between the Develop-. ment of Heat and the coincident contraction of Volume in Sulphuric Acid when mixed with Water ;—R. Hunt, Researches on the Influence of the Solar Rays on the Growth of Plants;—R. Mallet, on the Facts of Earthquake Phenomena ;—Prof,. Nilsson, on the Primitive Inhabitants of Scandinavia ;—W. Hopkins, Report on the Geological Theories of Elevation and Earthquakes ;—Dr. W. B. Carpenter, Report on the Microscopic Structure of Shells ;—Rev. W. Whewell and Sir James C. Ross,. Report upon the Recommendation of an Expedition for the purpose of completing our Knowledge of the Tides ;—Dr. Schunck, on Colouring Matters ;—Seventh Report of the Committee on the Vitality of Seeds ;—J. Glynn, on the Turbine or Horizontal Water-Wheel of France and Germany ;—-Dr. R, G. Latham, on the present state and 725 ‘recent progress of Ethnographical Philology ;—Dr. J. C. Prichard, on the various ‘methods of Research which contribute to the Advancement of Ethnology, and of the relations of that Science to other branches of Knowledge ;—Dr. C. C. J. Bunsen, on ‘the results of the recent Egyptian researches in reference to Asiatic and African Ethnology, and the Classification of Languages ;—Dr. C. Meyer, on the Importance of the Study of the Celtic Language as exhibited by the Modern Celtic Dialects still extant ;—Dr. Max Miiller, on the Relation of the Bengali to the Aryan and Aboriginal Languages of India ;—W. R. Birt, Fourth Report on Atmospheric Waves ;—Prof. W. H. Dove, Temperature Tables, with Introductory Remarks by Lieut.-Col. E. Sabine ; —A. Erman and H, Petersen, Third Report on the Calculation of the Gaussian Con- ‘stants for 1829. Together with the Transactions of the Sections, Sir Robert Harry Inglis’s Address, -and Recommendations of the Association and its Committees. PROCEEDINGS or tus EIGHTEENTH MEETING, at Swansea, 1848, Published at 9s. CONTENTS :—Rev. Prof. Powell, A Catalogue of Observations of Luminous Meteors ;—J. Glynn, on Water-pressure Engines;—R. A. Smith, on the Air and Water of Towns ;—Eight Report of Committee on the Growth and Vitality of Seeds ; —W. R. Birt, Fifth Report on Atmospheric Waves ;—E. Schunck, on Colouring Matters ;—J. P. Budd, on the advantageous use made of the gaseous escape from the Blast Furnaces at the Ystalyfera Iron Works ;—R. Hunt, Report of progress in the Investigation of the Action of Carbonic Acid on the Growth of Plants allied to those of the Coal Formations ;—Prof. H. W. Dove, Supplement to the Temperature Tables printed in the Report of the British Association for 1847 ;—Remarks by Prof. Dove on his recently constructed Maps of the Monthly Isothermal Lines of the Globe, and on some of the principal Conclusions in regard to Climatology deducible from them; with an introductory Notice by Lieut.-Col. E. Sabine ;—Dr. Daubeny, on the progress of the investigation on the Influence of Carbonic Acid on the Growth of Ferns ;—J. Phillips, Notice of further progress in Anemometrical Researches;—Mr. Mallet’s Letter to the Assistant-General Secretary ;—A. Erman, Second Report on the 4zaussian Constants ;—Report of a Committee relative to the expediency of recom- mending the continuance of the Toronto Magnetical and Meteorological Observatory until December 1850. Together with the Transactions of the Sections, the Marquis of Northampton’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or raz NINETEENTH MEETING, at Birmingham, 1849, Published at 10s. CONTENTS :—Rey. Prof. Powell, A Catalogue of Observations of Luminous Meteors ;—Earl of Rosse, Notice of Nebulz lately observed in the Six-feet Reflector ; —Prof. Daubeny, on the Influence of Carbonic Acid Gas on the health of Plants, especially of those allied to the Fossil Remains found in the Coal Formation ;—Dr. Andrews, Report on the Heat of Combination ;—Report of the Committee on the Registration of the Periodic Phenomena of Plants and Animals ;—Ninth Report of Committee on Experiments on the Growth and Vitality of Seeds;—F. Ronalds, Report concerning the Observatory of the British Association at Kew, from Aug. 9, 1848 to Sept. 12, 1849 ;—R. Mallet, Report on the Experimental Inquiry on Railway ‘Bar Corrosion ;—W. R. Birt, Report on the Discussion of the Electrical Observations at Kew. Together with the Transactions of the Sections, the Rev. T. R. Robinson’s Address, and Recommendations of the Association and its Committees. _ PROCEEDINGS or tae TWENTIETH MEETING, at Edinburgh, 1850, Published at 15s. (Out of Print.) CoNTENTS:—R. Mallet, First Report on the Facts of Earthquake Phenomena ;— Rev. Prof. Powell, on Observations of Luminous Meteors ;—Dr. T. Williams, on the Structure and History of the British Annelida ;—T, C. Hunt, Results of Meteoro- 726 logical Observations taken at St. Michael’s from the Ist of January, 1840, to the 31st of December, 1849;—R. Hunt, on the present State of our Knowledge of the- Chemical Action of the Solar Radiations ;—Tenth Report of Committee on Experi- ments on the Growth and Vitality of Seeds ;—Major-Gen. Briggs, Report on the Aboriginal Tribes of India ;—F. Ronalds, Report concerning the Observatory of the British Association at Kew ;—E. Forbes, Report on the Investigation of British Marine Zoology by means of the Dredge ;—R. MacAndrew, Notes on the Distribution and Range in depth of Mollusca and other Marine Animals, observed on the coasts of Spain, Portugal, Barbary, Malta, and Southern Italy in 1849 ;—Prof. Allman, on the Present State of our Knowledge of the Freshwater Polyzoa ;—Registration of the Periodical Phenomena of Plants and Animals ;—Suggestions to Astronomers for the Observation of the Total Eclipse of the Sun on July 28, 1851. Together with the Transactions of the Sections, Sir David Brewster’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or tHe TWENTY-FIRST MEETING, at Ipswich, 1851, Published at 16s. 6d. CONTENTS :—Rey. Prof. Powell, on Observations of Luminous Meteors ;— Eleventh Report of Committee on Experiments on the Growth and Vitality of Seeds ;—Dr. J. Drew, on the Climate of Southampton ;—Dr. R. A. Smith, on the Air and Water of Towns: Action of Porous Strata, Water, and Organic Matter ;— Report of the Committee appointed to consider the probable Effects in an Econo- mical and Physical Point of View of the Destruction of Tropical Forests ;—A.. Henfrey, on the Reproduction and supposed Existence of Sexual Organs in the Higher Cryptogamous Plants ;—Dr. Daubeny, on the Nomenclature of Organic Com-- pounds ;—Rey. Dr. Donaldson, on two unsolved Problems in Indo-German Philology ; —Dr. T. Williams, Report on the British Annelida ;—R, Mallet, Second Report on ‘the Facts of Earthquake Phenomena ;—Letter from Prof. Henry to Col. Sabine, on the System of Meteorological Observations proposed to be established in the United. States ;—Col. Sabine, Report on the Kew Magnetographs ;—J. Welsh, Report on the Performance of his three Magnetographs during the Experimental Trial at the Kew Observatory ;—F. Ronalds, Report concerning the Observatory of the British Association at Kew, from September 12, 1850, to July 31, 1851 ;—Ordnance Survey of Scotland. Together with the Transactions of the Sections, Prof. Airy’s Address, and Recom-- mendations of the Association and its Committees. PROCEEDINGS or taps TWENTY-SECOND MEETING, at Belfast,. 1852, Published at 15s. ConTENTS :—R. Mallet, Third Report on the Facts of Earthquake Phenomena ;— Twelfth Report of Committee on Experiments on the Growth and Vitality of Seeds; —Reyv. Prof. Powell, Report on Observations of Luminous Meteors, 1851-52 ;—Dr. Gladstone, on the Influence of the Solar Radiations on the Vital Powers of Plants ; —A Manual of Ethnological Inquiry ;—Col. Sykes, Mean Temperature of the Day, and Monthly Fall of Rain at 127 Stations under the Bengal Presidency ;—Prof. J. D. Forbes, on Experiments on the Laws of the Conduction of Heat ;—R. Hunt, on the Chemical Action of the Solar Radiations ;—Dr. Hodges, on the Composition and Economy of the Flax Plant ;—W. Thompson, on the Freshwater Fishes of Ulster ;— W. Thompson, Supplementary Report on the Fauna of Ireland ;—W. Wills, on the Meteorology of Birmingham ;—J. Thomson, on the Vortex-Water-Wheel ;—J. B. Lawes and Dr. Gilbert, on the Composition of Foods in relation to Respiration and the Feeding of Animals. Together with the Transactions of the Sections, Colonel Sabine’s Address, and: Recommendations of the Association and its Committees. 727 PROCEEDINGS or tuz TWENTY-THIRD MEETING, at Hull, 1853, Published at 10s. 6d. ConTENTS :—Rey. Prof, Powell, Report on Observations of Luminous Meteors, 1852-53 ;—James Oldham, on the Physical Features of the Humber ;—James Old- ham, on the Rise, Progress, and Present Position of Steam Navigation in Hull ;— William Fairbairn, Experimental Researches to determine the Strength of Locomo- tive Boilers, and the causes which lead to Explosion ;—J. J. Sylvester, Provisional ’ Report on the Theory of Determinants ;—Professor Hodges, M.D., Report on the Gases evolved in Steeping Flax, and on the Composition and Economy of the Flax Plant ;—Thirteenth Report of Committee on Experiments on the Growth and Vitality of Seeds ;—Robert Hunt, on the Chemical Action of the Solar Radiations ; —Dr. John P. Bell, Observations on the Character and Measurements of Degrada- tion of the Yorkshire Coast ;—First Report of Committee on the Physical Character of the Moon’s Surface, as compared with that of the Earth ;—R. Mallet, Provisional Report on Earthquake Wave-Transits; and on Seismometrical Instruments ;- - William Fairbairn, on the Mechanical Properties of Metals as derived from repeated Meltings, exhibiting the maximum point of strength and the causes of deterioration ; "Robert Mallet, Third Report on the Facts of Earthquake Phenomena (continued). Together with the Transactions of the Sections, Mr, Hopkins’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or tus TWENTY-FOURTH MEETING, at Liver- pool, 1854, Published at 18s. Conrents:—R. Mallet, Third Report on the Facts of Earthquake Phenomena (continued) ;—Major-General Chesney, on the Construction and General Use of Efficient Life-Boats ;—Rev. Prof. Powell, Third Report on the present State of our Knowledge of Radiant Heat ;—Colonel Sabine, on some of the results obtained at the British Colonial Magnetic Observatories ;—Colonel Portlock, Report of the Committee on Earthquakes, with their proceedings respecting Seismometers ;—Dr. Gladstone, on the Influence of the Solar Radiations on the Vital Powers of Plants, Part 2;—Reyv. Prof. Powell, Report on Observations of Luminous Meteors, 1853-54 ; —Second Report of the Committee on the Physical Character of the Moon’s Surface ; —W. G. Armstrong, on the Application of Water-Pressure Machinery ;—J,. B. Lawes and Dr. Gilbert, on the Equivalency of Starch and Sugar in Food ;—Archibald Smith, on the Deviations of the Compass in Wooden and Iron Ships ;—Fourteenth Report of Committee on Experiments on the Growth and Vitality of Seeds. - Together with the Transactions of the Sections, the Earl of Harrowby’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or tas TWENTY-FIFTH MEETING, at Glasgow, 1855, Published at lds. ConrENtS:—T. Dobson, Report on the Relation between Explosions in Coal- Mines and Revolving Storms ;—Dr. Gladstone, on the Influence of the Solar Radia- tions on the Vital Powers of Plants growing under different Atmospheric Conditions, Part 3;—C. Spence Bate, on the British Edriophthalma ;—J. F. Bateman, on the present state of our knowledge on the Supply of Water to Towns ;—Fifteenth Report of Committee on Experiments on the Growth and Vitality of Seeds ;—Rev. Prof. Powell, Report on Observations of Luminous Meteors, 1854-55 ;—Report of Committee appointed to inquire into the best means of ascertaining those properties of Metals and effects of various modes of treating them which are of importance to the durability and efficiency of Artillery ;—Rey. Prof. Henslow, Report on Typical Objects in Natural History ;—A. Follett Osler, Account of the Self-registering Anemometer and Rain-Gauge at the Liverpool Observatory ;—Provisional Reports. Together with the Transactions of the Sections, the Duke of Argyll’s Address, and Recommendations of the Association and its Committees. 728 ‘PROCEEDINGS or tur TWENTY-SIXTH MEETING, at Chel- tenham, 1856, Published at 18s. CONTENTS :—Report from the Committee appointed to investigate and report upon the effects produced upon the Channels of the Mersey by the alterations which within the last fifty years have been made in its Banks;—J. Thomson, Interim Report on progress in Researches on the Measurement of Water by Weir Boards ;— Dredging Report, Frith of Clyde, 1856;—Rev. B. Powell, Report on Observations of Luminous Meteors, 1855-1856 ;-—Prof. Bunsen and Dr. H. E. Roscoe, Photochemical Researches ;—Rev. James Booth, on the Trigonometry of the Parabola, and the Geometrical Origin of Logarithms;—R. MacAndrew, Report on the Marine Testaceous Mollusca of the North-east Atlantic and neighbouring Seas, and the physical conditions affecting their development ;—P. P. Carpenter, Report on the present state of our knowledge with regard to the Mollusca of the West Coast of North America ;—T. C. Eyton, Abstract of First Report on the Oyster Beds and Oysters of the British Shores ;—Prof. Phillips, Report on Cleavage, and Foliation in Rocks, and on the Theoretical Explanations of these Phenomena, Part 1 ;—Dr. T. Wright, on the Stratigraphical Distribution of the Oolitic Echinodermata ;—W. Fairbairn, on the Tensile Strength of Wrought Iron at various Temperatures ; —C. Atherton, on Mercantile Steam Transport Economy ;—J. 8. Bowerbank, on the Vital Powers of the Spongiadz ;—Report of a Committee upon the Experiments con- ducted at Stormontfield, near Perth, for the artificial propagation of Salmon ;—Pro- visional Report on the Measurement of Ships for Tonnage ;—-On Typical Forms of Minerals, Plants and Animals for Museums ;—J. Thomson, Interim Report on Pro- gress in Researches on the Measurement of Water by Weir Boards ;—R. Mallet, on Observations with the Seismometer;—A. Cayley, on the Progress of Theoretical Dynamics ;—Report of a Committee appointed to consider the formation of a Catalogue of Philosophical Memoirs, Together with the Transactions of the Sections, Dr. Daubeny’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or tus TWENTY-SEVENTH MEETING, at Dublin, 1857, Published at 15s. ConTENTS :—A. Cayley, Report on the recent progress of Theoretical Dynamics ; —Sixteenth and Final Report of Committee on Experiments on the Growth and Vitality of Seeds ;—James Oldham, C.E., continuation of Report on Steam Navigation at Hull;—Report of a Committee on the Defects of the present methods of Measur- ing and Registering the Tonnage of Shipping, as also of Marine Engine-Power, and to frame more perfect rules, in order that a correct and uniform principle may be adopted to estimate the Actual Carrying Capabilities and Working-power of Steam Ships ;—Robert Were Fox, Report on the Temperature of some Deep Mimes in Corn- —a at) + 1BH) + 19t) 41 le+ Iyt + let+1 a étant entier négatif, et de quelques cas dans lesquels cette somme est exprimable par une combinaison de factorielles, la notation a‘|+!désignant le produit des facteurs a (a+1) (a+2) &e....(a+t -1) ;—G. Dickie, M.D., Report on the Marine Zoology of Strangford Lough, County Down, and corresponding part of the Irish Channel ;—Charles Atherton, Suggestions for Statistical Inquiry into the Extent to which Mercantile Steam Transport Economy is affected by the Constructive Type of Shipping, as respects the Proportions of Length, Breadth, and Depth ;—J. 8. Bower- bank, Further Report on the Vitality of the Spongiadez ;—Dr. John P. Hodges, on Flax ;—Major-General Sabine, Report of the Committee on the Magnetic Survey of Great Britain ;—Rev. Baden Powell, Report on Observations of Luminous Meteors, 1856-57 ;—C. Vignoles, on the Adaptation of Suspension Bridges to sustain the passage of Railway Trains;—Prof. W. A. Miller, on Electro-Chemistry ;—John Simpson, Results of Thermometrical Observations made at the Plover’s Wintering- place, Point Barrow, latitude 71° 21’ N., long. 156° 17’ W., in 1852-54 ;—Charles James Hargreave, on the Algebraic Couple; and on the Equivalents of Indetermi- nate Expressions ;—Thomas Grubb, Report on the Improvement of Telescope and Equatorial Mountings ;—Prof. James Buckman, Report on the Experimental Plots wall ;—Dr. G. Plarr, de quelques Transformations de la Somme 3% 729 in the Botanical Garden of the Royal Agricultural College at Cirencester ;—William Fairbairn, on the Resistance of Tubes to Collapse ;—George C. Hyndman, Report of the Proceedings of the Belfast Dredging Committee ;—Peter W. Barlow, on the Mechanical Effect of combining Girders and Suspension Chains, and a Comparison of the Weight of Metal in Ordinary and Suspension Girders, to produce equal de- flections with a given load ;—J. Park Harrison, Evidences of Lunar Influence on Temperature ;—Report on the Animal and Vegetable Products imported into Liver- pool from the year 1851 to 1855 (inclusive) ;—Andrew Henderson, Report on the Sta- tistics of Life-boats and Fishing-boats on the Coasts of the United Kingdom. Together with the Transactions of the Sections, the Rev. H. Lloyd’s Address, and Recommendations of the Association and its Committees, PROCEEDINGS or rus TWENTY-EIGHTH MEETING, at Leeds, September 1858, Published at 20s. CONTENTS :—R. Mallet, Fourth Report upon the Facts and Theory of Earthquake Phenomena ;—Reyv. Prof. Powell, Report on Observations of Luminous Meteors, 1857, 1858 ;—R. H. Meade, on some Points in the Anatomy of the Araneidea or true Spiders, especially on the internal structure of their Spinning Organs ;—W. Fairbairn, Report of the Committee on the Patent Laws ;—S. Eddy, on the Lead Mining Districts of Yorkshire ;—W. Fairbairn, on the Collapse of Glass Globes and Cylinders ;—Dr. E. Perceval Wright and Prof. J. Reay Greene, Report on the Marine Fauna of the South and West Coasts of Ireland ;—Prof. J. Thomson, on Experiments on the Measurement of Water by Triangular Notches in Weir Boards ;—Major-General Sabine, Report of the Committee on the Magnetic Survey of Great Britain ;—Michael Connel and William Keddie, Report on Animal, Vegetable, and Mineral Substances imported from Foreign Countries into the Clyde (including the Ports of Glasgow, Greenock, and Port Glasgow) in the years 1853, 1854, 1855, 1856, and 1857 ;—Report of the Committee on Shipping Statistics ;—Rev. H. Lloyd, D.D., Notice of the Instruments employed in the Magnetic Survey of Ireland, with some of the Results ;—Prof. J. R. Kinahan, Report of Dublin Dredging Committee, appointed 1857-58 ;—Prof. J. R. Kinahan, Report on Crustacea of Dublin District ;—Andrew Henderson, on River Steamers, their Form, Construction, and Fittings, with reference to the necessity for improving the present means of Shallow-Water Navigation on the Rivers of British India ;—George C. Hyndman, Report of the Belfast Dredging Committee ;—Appendix to Mr. Vignoles’ Paper ‘On the Adaptation of Suspension Bridges to sustain the passage of Railway Trains;’—Report of the Joint Committee of the Royal Society and the British Association, for procuring a continuance of the Magnetic and Meteorological Observatories ;—R. Beckley, Description of a Self-recording Ane- mometer. Together with the Transactions of the Sections, Prof. Owen’s Address, and Re- commendations of the Association and its Committees. PROCEEDINGS or trxp TWENTY-NINTH MEETING, at Aberdeen, September 1859, Published at 15s. ConTENTS :—George C. Foster, Preliminary Report on the Recent Progress and Present State of Organic Chemistry ;—Professor Buckman, Report on the Growth of Plants in the Garden of the Royal Agricultural College, Cirencester ;—Dr. A. Voelcker, Report on Field Experiments and Laboratory Researches on the Constituents of Manures essential to Cultivated Crops;—A. Thomson, of Banchory, Report on the Aberdeen Industrial Feeding Schools ;—On the Upper Silurians of Lesmahagow, Lanarkshire ;—Alphonse Gages, Report on the Results obtained by the Mechanico- ‘Chemical Examination of Rocks and Minerals ;—William Fairbairn, Experiments to determine the Efficiency of Continuous and Self-acting Breaks for Railway Trains ;— Professor J. R. Kinahan, Report of Dublin Bay Dredging Committee for 1858-59 ;— Rev. Baden Powell, Report on Observations of Luminous Meteors for 1858-59 ;— Professor Owen, Report on a Series of Skulls of various Tribes of Mankind inhabiting Nepal, collected, and presented to the British Museum, by Bryan H. Hodgson, Esq., late Resident in Nepal, &c., &c. ;—Messrs. Maskelyne, Hadow, Hardwich, and Llewelyn, Report on the Present State of our Knowledge regarding the Photographic Image ;— 730 G. C. Hyndman, Report of the Belfast Dredging Committee for 1859 ;—James. Oldham, Continuation of Report of the Progress of Steam Navigation at Hull ;— Charles Atherton, Mercantile Steam Transport Economy as affected by the Con- sumption of Coals;—Warren De La Rue, Report on the present state of Celestial Photography in England ;—Professor Owen, on the Orders of Fossil and Recent Reptilia, and their Distribution in Time ;—Balfour Stewart, on some Results of the Magnetic Survey of Scotland in the years 1857 and 1858, undertaken, at the request of the British Association, by the late John Welsh, Esq., F.R.S.;—W. Fairbairn, The Patent Laws: Report of Committee on the Patent Laws;—J. Park Harrison, Lunar Influence on the Temperature of the Air :—Balfour Stewart, an Account of the Con- struction of the Self-recording Magnetographs at present in operation at the Kew Observatory of the British Association ;—Professor H. J. Stephen Smith, Report on the Theory of Numbers, Part I.;—Report of the Committee on Steamship Performance;: —Report of the Proceedings of the Balloon Committee of the British Association appointed at the Meeting at Leeds ;—Prof. William K. Sullivan, ,Preliminary Report on the Solubility of Salts at Temperatures above 100° Cent., and on the Mutual Action of Salts in Solution. Together with the Transactions of the Sections, Prince Albert’s Address, and Recommendations of the Association and its Committees. ; PROCEEDINGS or tos THIRTIETH MEETING, at Oxford, June and July 1860, Published at 15s. CONTENTS :—James Glaisher, Report on Observations of Luminous Meteors,. 1859_60 ;—J. R. Kinahan, Report of Dublin Bay Dredging Committee ;—Rev. J. Anderson, Report on the Excavations in Dura Den;—Prof. Buckman, Report on the Experimental Plots in the Botanical Garden of the Royal Agricultural College, Cirencester ;—Rey. R. Walker, Report of the Committee on Balloon Ascents ;—Prof. W. Thomson, Report of Committee appointed to prepare a Self-recording Atmo- spheric Electrometer for Kew, and Portable Apparatus for observing Atmospheric Electricity ;—William Fairbairn, Experiments to determine the Effect of Vibratory Action and long-continued Changes of Load upon Wrought-iron Girders ;—R. P. Greg, Catalogue of Meteorites and Fireballs, from A.D. 2 to A.D. 1860;—-Prof. H. J. S.. Smith, Report on the Theory of Numbers, Part IJ.;—Vice-Admiral Moorsom, on the Performance of Steam-vessels, the Functions of the Screw, and the Relations of its Diameter and Pitch to the Form of the Vessel ;—Rey. W. V. Harcourt, Report on the Effects of long-continued Heat, illustrative of Geological Phenomena ;—Second Report of the Committee on Steamship Performance ;—Interim Report on the Gauging of Water by Triangular Notches ;—List of the British Marine Invertebrate Fauna. Together with the Transactions of the Sections, Lord Wrottesley’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or tar THIRTY-FIRST MEETING, at Manches- ter, September 1861, Published at £1. CoNTENTS :—James Glaisher, Report on Observations of Luminous Meteors ;— Dr. E. Smith, Report on the Action of Prison Diet and Discipline on the Bodily Functions of Prisoners, Part I. ;—Charles Atherton, on Freight as affected by Differ- ences in the Dynamic Properties of Steamships;—Warren De La Rue, Report on the Progress of Celestial Photography since the Aberdeen Meeting ;—B. Stewart, on the Theory of Exchanges, and its recent extension ;—Drs. E. Schunck, R. Angus Smith, and H. E. Roscoe, on the Recent Progress and Present Condition of Manufacturing Chemistry in the South Lancashire District ;—Dr. J. Hunt, on Ethno-Climatology ; or, the Acclimatization of Man ;—Prof. J. Thomson, on Experiments on the Gauging of Water by Triangular Notches;—Dr. A. Voelcker, Report on Field Experiments and Laboratory Researches on the Constituents of Manures essential to cultivated: Crops ;—Prof. H. Hennessy, Provisional Report on the Present State of our Knowledge respecting the Transmission of Sound-signals during Fogs at Sea ;—Dr. P. L. Sclater: and F, von Hochstetter, Report on the Present State of our Knowledge of the Birds. of the Genus Apteryx living in New Zealand ;—J. G. Jeffreys, Report of the Results. of Deep-sea Dredging in Zetland, with a Notice of several Species of Mollusca new to Science or to the British Isles ;—Prof, J. Phillips, Contributions to a Report on j 731 the Physical Aspect of the Moon ;—W. R. Birt, Contribution to a Report on the Phy~ sical Aspect of the Moon;—Dr. Collingwood and Mr. Byerley, Preliminary Report of the Dredging Committee of the Mersey and Dee ;—Third Report of the Committee on Steamship Performance ;—J. G. Jeffreys, Preliminary Report on the Best Mode of preventing the Ravages of Zeredo and other Animals in our Ships and Harbours ;— R. Mallet, Report on the Experiments made at Holyhead to ascertain the Transit- Velocity of Waves, analogous to Earthquake Waves, through the local Rock Formations ;- —tT., Dobson, on the Explosions in British Coal-Mines during the year 1859 ;—J. Old- ham, Continuation of Report on Steam Navigation at Hull ;—Prof. G. Dickie, Brief Summary of a Report on the Flora of the North of Treland ;—Prof. Owen, on the Psychical and Physical Characters of the Mincopies, or Natives of the Andaman Islands, and on the Relations thereby indicated to other Races of Mankind ;—Colonel Sykes, Report of the Balloon Committee ;—Major-General Sabine, Report on the Re- petition of the Magnetic Survey of England ;—Interim Report of the Committee for Dredging on the North and East Coasts of Scotland ;—W. Fairbairn, on the Resist- ance of Iron Plates to Statical Pressure and the Force of Impact by Projectiles at High Velocities ;—W. Fairbairn, Continuation of Report to determine the effect of Vibratory Action and long-continued Changes of Load upon Wrought-Iron Girders ;. —Report of the Committee on the Law of Patents;—Prof. H. J. S. Smith, Report on: the Theory of Numbers, Part III. Together with the Transactions of the Sections, Mr. Fairbairn’s Address, and Re= commendations of the Association and its Committees. PROCEEDINGS or rar THIRTY-SECOND MEETING at Cam- bridge, October 1862, Published at £1. ConTENTS :—James Glaisher, Report on Observations of Luminous Meteors, 1861~— 62 ;—G. B. Airy, on the Strains in the Interior of Beams ;—Archibald Smith and F._ J. Evans, Report on the three Reports of the Liverpool Compass Committee ;—Report on Tidal Observations on the Humber;—T. Aston, on Rifled Guns and Projectiles. adapted for Attacking Armour-plate Defences ;—Extracts, relating to the Observa- tory at Kew, from a Report presented to the Portuguese Government, by Dr. J. A.. de Souza ;—H. T. Mennell, Report on the Dredging of the Northumberland Coast and Dogger Bank ;—Dr. Cuthbert Collingwood, Report upon the best means of ad~ vancing Science through the agency of the Mercantile Marine ;—Messrs. Williamson, . Wheatstone, Thomson, Miller, Matthiessen, and Jenkin, Provisional Report on Stan- dards of Electrical Resistance ;—Preliminary Report of the Committee for investiga~- ting the Chemical and Mineralogical Composition of the Granites of Donegal ;— Prof. H. Hennessy, on the Vertical Movements of the Atmosphere considered in connec ‘tion with Storms and Changes of Weather ;— Report of Committee on the application of Gauss’s General Theory of Terrestrial Magnetism to the Magnetic Variations ;— Fleeming Jenkin, on Thermo-electric Currents in Circuits of one Metal ;—W. Fair- bairn, on the Mechanical Properties of Iron Projectiles at High Velocities ;—A. Cay- ley, Report on the Progress of the Solutionof certain Special Problems of Dynamics ;.. —Prof. G. G. Stokes, Report on Double Refraction ;—Fourth Report of the Committee on Steamship Performance ;—G. J. Symons, on the Fall of Rain in the British Isles. in 1860 and 1861 ;—J. Ball, on Thermometric Observations in the Alps; J. G. Jeffreys, Report of the Committee for Dredging on the North and East Coasts of Scotland ;—Report of the Committee on Technical and Scientific Evidence in Courts of Law ;—James Glaisher, Account of Eight Balloon Ascents in 1862 ;—Prof. H. J.S.. Smith, Report on the Theory of Numbers, Part IV. ’ Together with the Transactions of the Sections, the Rev. Prof. R. Willis’s Address. and Recommendations of the Association and its Committees. PROCEEDINGS or tae THIRTY-THIRD MEETING, at New-. castle-upon-Tyne, August and September 1863, Published at £1 5s. CoNnTENTS :—Report of the Committee on the Application of Gun-cotton to War-.- like Purposes ;—A. Matthiessen, Report on the Chemical Nature of Alloys ;-—Report of the Committee on the Chemical and Mineralogical Constitution of the Granites of* Donegal, and on the Rocks associated withthem ;—J. G. Jeffreys, Report of the Com-- mittee appointed for exploring the Coasts of Shetland by means of the Dredge ;— 732 \G. D. Gibb, Report on the Physiological Effects of the Bromide of Ammonium ;—C. K. Aken, on the Transmutation of Spectral Rays, Part I. ;—Dr. Robinson, Report of the Committee on Fog Signals ;—Report of the Committee on Standards of Electrical Resistance ;—E. Smith, Abstract of Report by the Indian Government on the Foods used by the Free and Jail Populations in India ;—A. Gages, Synthetical Researches on the Formation of Minerals, &c.;—R. Mallet, Preliminary Report on the Experi- mental Determination of the Temperatures of Volcanic Foci, and of the Temperature, State of Saturation, and Velocity of the issuing Gases and Vapours;—Report of the Committee on Observations of Luminous Meteors ;—Fifth Report of the Committee on Steamship Performance ;-—G. J. Allman, Report on the Present State of our Know- ledge of the Reproductive System in the Hydroida;—J. Glaisher, Account of Five Bal- loon Ascents made in 1863 ;—P. P. Carpenter, Supplementary Report on the Present State of our Knowledge with regard to the Mollusca of the West Coast of North America ;—Prof. Airy, Report on Steam Boiler Explosions ;—C, W. Siemens, Obser- vations on the Electrical Resistance and Electrification of some Insulating Materials ander Pressures up to 300 Atmospheres ;—C. M. Palmer, on the Construction of Iron Ships and the Progress of Iron Shipbuilding on the Tyne, Wear, and Tees ;—Messrs. Richardson, Stevenson, and Clapham, on the Chemical Manufactures of the Northern Districts ;—Messrs. Sopwith and Richardson, on the Local Manufacture of Lead, Copper, Zinc, Antimony, &c. ;—Messrs. Daglish and Forster, on the Magnesian Lime- stone of Durham ;—I. L. Bell, on the Manufacture of Iron in connexion with the Northumberland and Durham Coal-field ;—T. Spencer, on the Manufacture of Steel in the Northern District ;—Prof. H. J.S. Smith, Report on the Theory of Numbers, Part V. Together with the Transactions of the Sections, Sir William Armstrong’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or tus THIRTY-FOURTH MEETING, at Bath, September 1864, Published at 18s. CONTENTS :—Report of the Committee for Observations of Luminous Meteors ;-— Report of the Committee on the best means of providing for a Uniformity of Weights and Measures ;—T. 8. Cobbold, Report of Experiments respecting the Development -and Migration of the Entozoa;—B. W. Richardson, Report on the Physiological Action of Nitrite of Amyl ;—J. Oldham, Report of the Committee on Tidal Observa- tions ;—G. §. Brady, Report on Deep-sea Dredging on the Coasts of Northumberland and Durham in 1864 ;—-J. Glaisher, Account of Nine Balloon Ascents made in 1863 and 1864 ;—J. G. Jeffreys, Further Report on Shetland Dredgings;—Report of the Committee on the Distribution of the Organic Remains of the North Staffordshire Coal-field ;—Report of the Committee on Standards of Electrical Resistance ;—G. J. Symons, on the Fall of Rain in the British Isles in 1862 and 1863;—W. Fairbairn, Preliminary Investigation of the Mechanical Properties of the proposed Atlantic Cable. Together with the Transactions of the Sections, Sir Charles Lyell’s Address, and Recommendations of the Association and its Committees, PROCEEDINGS or tHe THIRTY-FIFTH MEETING, at Birming- ham, September 1865, Published at £1 5s. CONTENTS :—J. G. Jeffreys, Report on Dredging among the Channel Isles ;—F, Buckland, Report on the Cultivation of Oysters by Natural and Artificial Methods ;— Report of the Committee for exploring Kent’s Cavern ;—Report of the Committee on Zoological Nomenclature ;—Report on the Distribution of the Organic Remains -of the North Staffordshire Coal-field ;—Report on the Marine Fauna and Flora of the South Coast of Devon and Cornwall ;—Interim Report on the Resistance of Water to Floating and Immersed Bodies ;—Report on Observations of Luminous Meteors ;—Report on Dredging on the Coast of Aberdeenshire ;—J. Glaisher, Account -of Three Balloon Ascents;—Interim Report on the Transmission of Sound under Water ;—G. J. Symons, on the Rainfall of the British Isles ;—W. Fairbairn, on the Strength of Materials considered in relation to the Construction of Iron Ships ;— Report of the Gun-Cotton Committee ;—A. F. Osler, on the Horary and Diurnal ‘Variations in the Direction and Motion of the Air at Wrottesley, Liverpool, and 733 Birmingham ;—B, W. Richardson, Second Report on the Physiological Action of certain of the Amyl Compounds ;—Report on further Researches in the Lingula- flags of South Wales ;—Report of the Lunar Committee for Mapping the Surface of the Moon ;—Report on Standards of Electrical Resistance ;—Report of the Com- mittee appointed to communicate with the Russian Government respecting Mag- netical Observations at Tiflis ;—Appendix to Report on the Distribution of the Verte- brate Remains from the North Staffordshire Coal-field ;—H. Woodward, First Report on the Structure and Classification of the Fossil Crustacea ;—Prof. H. J. S. Smith, Report on the Theory of Numbers, Part VI. ;—Report on the best means of providing for a Uniformity of Weights and Measures, with reference to the interests of Science ; —A. G. Findlay, on the Bed of the Ocean ;—Prof. A. W. Williamson, on the Com- position of Gases evolved by the Bath Spring called King’s Bath. Together with the Transactions of the Sections, Prof, Phillips’s Address, and Re~ commendations of the Association and its Committees, PROCEEDINGS or raz THIRTY-SIXTH MEETING, at Notting ham, August 1866, Published at £1 4s. CONTENTS :—Second Report on Kent’s Cavern, Devonshire ;—A. Matthiessen, Preliminary Report on the Chemical Nature of Cast Iron ;—Report on Observations of Luminous Meteors;—W. S. Mitchell, Report on the Alum Bay Leaf-bed ;— Report on the Resistance of Water to Floating and Immersed Bodies ;—Dr. Norris.. Report on Muscular Irritability ;—Dr. Richardson, Report on the Physiological Action of certain compounds of Amy] and Ethyl ;—H. Woodward, Second Report on the Structure and Classification of the Fossil Crustacea ;—Second Report on the ‘Menevian Group,’ and the other Formations at St. David’s, Pembrokeshire ; —J.G. Jeffreys, Report on Dredging among the Hebrides;—Rev. A. M. Norman, Report on the Coasts of the Hebrides, Part II. ;—J. Alder, Notices of some Inverte- brata, in connexion with Mr. Jeffreys’s Report;—G. 8S. Brady, Report on the Ostracoda dredged amongst the Hebrides ;—Report on Dredging in the Moray Firth ; —Report on the Transmission of Sound-Signals under Water ;—Report of the Lunar Committee ;—Report of the Rainfall Committee ;—Report on the best means of providing for a Uniformity of Weights and Measures, with reference to the Interests. of Science ;—J. Glaisher, Account of Three Balloon Ascents ;—Report on the Extinet Birds of the Mascarene Islands ;—Report on the Penetration of Iron-clad Ships by Steel Shot ;—J. A. Wanklyn, Report on Isomerism among the Alcohols ;—Report on Scientific Evidence in Courts of Law ;—A, L. Adams, Second Report on Maltese Fossiliferous Caves, «ce. Together with the Transactions of the Sections, Mr, Grove’s Address, and Recom-- mendations of the Association and its Committees, PROCEEDINGS or tue THIRTY-SEVENTH MEETING, at Dundee, September 1867, Published at £1 6s. CONTENTS :—Report of the Committee for Mapping the Surface of the Moon ;— Third Report on Kent’s Cavern, Devonshire ;—On the present State of the Manu-~ facture of Iron in Great Britain ;—Third Report on the Structure and Classification of the Fossil Crustacea ;—Report on the Physiological Action of the Methyl Com- pounds ;—Preliminary Report on the Exploration of the Plant-Beds of North Green-- land ;—Report of the Steamship Performance Committee ;—On the Meteorology of Port Louis, in the Island of Mauritius ;—On the Construction and Works of the: Highland Railway ;—Experimental Researches on the Mechanical Properties of Steel ;—Report on the Marine Fauna and Flora of the South Coast of Devon an& Cornwall ;—Supplement to a Report on the Extinct Didine Birds of the Mascarene Islands ;—Report on Observations of Luminous Meteors ;—Fourth Report on Dredging among the Shetland Isles ;—Preliminary Report on the Crustacea, &c., procured by the Shetland Dredging Committee in 1867 ;—Report on the Foraminifera obtained: in the Shetland Seas ;—Second Report of the Rainfall Committee ;—Report on the best means of providing for a Uniformity of Weights and Measures, with reference to the interests of Science ;—Report on Standards of Electrical Resistance. Together with the Transactions of the Sections, and Recommendations of the: Association and its Committees, 734 PROCEEDINGS or raz THIRTY-EIGHTH MEETING, at Nor- wich, August 1868, Published at £1 ds. ConTENTS:—Report of the Lunar Committee ;—Fourth Report on Kent’s “Cavern, Devonshire ;—On Puddling Iron ;—Fourth Report on the Structure and “Classification of the Fossil Crustacea ;—Report on British Fossil Corals ;—Report on ‘Spectroscopic Investigations of Animal Substances ;—Report of Steamship Perform- sance Committee ;—Spectrum Analysis of the Heavenly Bodies ;—On Stellar Spectro- “metry ;—Report on the Physiological Action of the Methyl and allied Compounds ;— Report on the Action of Mercury on the Biliary Secretion ;—Last Report on Dredg- ing among the Shetland Isles ;—Reports on the Crustacea, &c., and on the Annelida sand Foraminifera from the Shetland Dredgings ;—Report on the Chemical Nature of ‘Cast Iron, Part I.;—Interim Report on the Safety of Merchant Ships and their Passengers ;—Report on Observations of Luminous Meteors ;—Preliminary Report “on Mineral Veins containing Organic Remains;—Report on the Desirability of Explorations between India and China;—Report of Rainfall Committee ;—Re- port on Synthetical Researches on Organic Acids ;—Report on Uniformity of Weights sand Measures ;—Report of the Committee on Tidal Observations ;—Report of the “Committee on Underground Temperature ;—Changes of the Moon’s Surface ;—Re- port on Polyatomic Cyanides. : Together with the Transactions of the Sections, Dr. Hooker’s Address, and Recom- mendations of the Association and its Committees. PROCEEDINGS or tas THIRTY-NINTH MEETING, at Exeter, August 1869, Published at £1 2s. ConTENTS :—Report on the Plant-beds of North Greenland ;—Report on the existing knowledge on the Stability, Propulsion, and Sea-going qualities of Ships ; —Report on Steam-boiler Explosions ;—Preliminary Report on the Determination -of the Gases existing in Solution in Well-waters;—The Pressure of Taxation on Real Property ;—On the Chemical Reactions of Light discovered by Prof. Tyndall ;— ‘On Fossils obtained at Kiltorkan Quarry, co. Kilkenny ;—Report of the Lunar Com- mittee ;—Report on the Chemical Nature of Cast Iron ;—Report on the Marine Fauna sand Flora of the South Coast of Devon and Cornwall ;—Report on the Practicability -of establishing a ‘Close Time ’ for the Protection of Indigenous Animals ;—Experi- ‘mental Researches on the Mechanical Properties of Steel;—Second Report on British Fossil Corals ;—Report. of the Committee appointed to get cut and prepared Sections of Mountain-Limestone Corals for Photographing ;—Report on the Rate of Increase of Underground Temperature ;—Fifth Report on Kent’s Cavern, Devon- shire ;—Report on the Connexion between Chemical Constitution and Physiological Action;—On Emission, Absorption, and Reflection of Obscure Heat ;—Report on ‘Observations of Luminous Meteors ;—Report on Uniformity of Weights and Measures ; —Report on the Treatment and Utilization of Sewage ;—Supplement to Second Report of the Steamship-Performance Committee ;—Report on Recent Progress in Elliptic and Hyperelliptic Functions ;—Report on Mineral Veins in Carboniferous Limestone and their Organic Contents ;—Notes on the Foraminifera of Mineral Veins and the Adjacent Strata ;—Report of the Rainfall Committee ;—Interim Re- port on the Laws of the Flow and Action of Water containing Solid Matter in Suspension ;—Interim Report on Agricultural Machinery ;—Report on the Physio- logical Action of Methyl and Allied Series ;—On the Influence of Form considered in Relation to the Strength of Railway-axles and other portions of Machinery sub- jected to Rapid Alterations of Strain;—On the Penetration of Armour-plates with Long Shells of Large Capacity fired obliquely ;—Report on Standards of Electrical Resistance, Together with the Transactions of the Sections, Prof. Stokes’s Address, and Re- ‘ommendations of the Association and its Committees. 735 PROCEEDINGS or tut FORTIETH MEETING, at Liverpool, Sep- tember 1870, Published at 18s. CONTENTS :—Report on Steam-boiler Explosions ;—Report of the Committee on the Hematite Iron-ores of Great Britain and Ireland ;—Report on the Sedimentary Deposits of the River Onny ;—Report on the Chemical Nature of Cast Iron ;—Re- port on the practicability of establishing a ‘Close Time’ for the protection of Indigenous Animals ;—Report on Standards of Electrical Resistance ;—Sixth Report on Kent’s Cavern ;—Third Report on Underground Temperature ;—Second Report of the Committee appointed to get cut and prepared Sections of Mountain-Limestone Corals ;—Second Report on the Stability, Propulsion, and Sea-going Qualities of Ships ;—Report on Earthquakes in Scotland ;—Report on the Treatment and Utili- zation of Sewage ;—Report on Observations of Luminous Meteors, 1869-70 ;—Report on Recent Progress in Elliptic and Hyperelliptic Functions;—Report on Tidal Ob- servations ;—On a new Steam-power Meter ;—Report on the Action of the Methyl and Allied Series;—Report of the Rainfall Committee;—Report on the Heat generated in the Blood in the Process of Arterialization;—Report on the best means of providing for Uniformity of Weights and Measures. Together with the Transactions of the Sections, Prof. Huxley’s Address, and Re- commendations of the Association and its Committees. PROCEEDINGS or tar FORTY-FIRST MEETING, at Edinburgh, August 1871, Published at 16s. CONTENTS :-——Seventh Report on Kent’s Cavern;—Fourth Report on Under- ground Temperature ;—Report on Observations of Luminous Meteors, 1870-71 ;— Fifth Report on the Structure and Classification of the Fossil Crustacea ;—Report. of the Committee appointed for the purpose of urging on Her Majesty’s Government the expediency of arranging and tabulating the results of the approaching Census in the three several parts of the United Kingdom in such a manner as to admit of ready and effective comparison ;—Report of the Committee appointed for the purpose of Superintending the Publication of Abstracts of Chemical Papers ;—Report of the Committee for discussing Observations of Lunar Objects suspected of change ;— Second Provisional Report on the Thermal Conductivity of Metals ;—Report on the Rainfall of the British Isles;—Third Report on the British Fossil Corals ;— Report on the Heat generated in the Blood during the Process of Arterialization ; —Report of the Committee appointed to consider the subject of Physiological Experimentation ;—Report on the Physiological Action of Organic Chemical Com- pounds ;—Report of the Committee appointed to get cut and prepared Sections of Mountain-Limestone Corals ;—Second Report on Steam-Boiler Explosions ;—Re- port on the Treatment and Utilization of Sewage ;—Report on promoting the Foun- ‘dation of Zoological Stations in different parts of the World ;—Preliminary Report on the Thermal Equivalents of the Oxides of Chlorine ;—Report on the practi- eability of establishing a ‘Close Time’ for the protection of Indigenous Animals ;—Report on Earthquakes in Scotland ;—Report on the best means of pro- viding for a Uniformity of Weights and Measures ;—Report on Tidal Observations. Together with the Transactions of the Sections, Sir William Thomson’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or tus FORTY-SECOND MEETING, at Brighton, August 1872, Published at £1 4s. CONTENTS :—Report on the Gaussian Constants for the Year 1829 ;—Second Sup- plementary Report on the Extinct Birds of the Mascarene Islands ;—Report of the Committee for Superintending the Monthly Reports of the Progress of Chemistry ;— Report of the Committee on the best means of providing for a Uniformity of Weights and Measures ;—Kighth Report on Kent’s Cavern ;—Report on promoting the Foundation of Zoological Stations in different parts of the World ;—Fourth Report on the Fauna of South Devon ;—Preliminary Report of the Committee appointed to Construct and Print Catalogues of Spectral Rays arranged upon a Scale of Wave- numbers ;—Third Report on Steam-Boiler Explosions ;—Report on Observations of 736 Luminous Meteors, 1871-72 ;—Experiments on the Surface-friction experienced by- a Plane moving through Water ;—Report of the Committee on the Antagonism be~ tween the Action of Active Substances ;—Fifth Report on Underground Tempera-- ture ;—Preliminary Report of the Committee on Siemens’s Elecirical-Resistance Pyrometer :—Fourth Report on the Treatment and Utilization of Sewage ;—Interim Report of the Committee on Instruments for Measuring the Speed of Ships and Currents ;—Report on the Rainfall of the British Isles ;—Report of the Committee on a Geographical Exploration of the Country of Moab ;—Sur 1élimination des Fonctions Arbitraires ;—Report on the Discovery of Fossils in certain remote parts. of the North-western Highlands ;—Report of the Committee on Earthquakes in Scotland ;—Fourth Report on Carboniferous-Limestone Corals ;—Report of the Com- mittee to consider the mode in which new Inventions and Claims for Reward in respect of adopted Inventions are examined and dealt with by the different Depart ments of Government ;—Report of the Committee for discussing Observations of Lunar Objects suspected of change ;—Report on the Mollusca of Europe ;—Report of the Committee for investigating the Chemical Constitution and Optical Properties. of Essential Oils ;—Report on the practicability of establishing a ‘Close Time’ for the preservation of Indigenous Animals ;—Sixth Report on the Structure and Classi- fication of Fossil Crustacea ;—Report of the Committee appointed to organize an Ex- pedition for observing the Solar Eclipse of Dec. 12, 1871 ;—Preliminary Report of a Committee on Terato-embryological Inquiries ;—Report on Recent Progress in Elliptic and Hyperelliptic Functions ;—Report on Tidal Observations ;—On the Brighton Waterworks ;—On Amsler’s Planimeter. Together with the Transactions of the Sections, Dr. Carpenter’s Address, and Recommendations of the Association and its Committees, PROCEEDINGS or tas FORTY-THIRD MEETING, at Bradford, September 1873, Published at £1 5s. CoNTENTS :—Report of the Committee on Mathematical Tables ;—Observations on the Application of Machinery to the Cutting of Coal in Mines ;—Conceluding Re- port on the Maltese Fossil Elephants ;—Report of the Committee for ascertaining the Existence in different parts of the United Kingdom of any Erratic Blocks or Boulders ;—Fourth Report on Earthquakes in Scotland ;—Ninth Report on Kent's Cavern ;—On the Flint and Chert Implements found in Kent’s Cavern ;—Report of the Committee for Investigating the Chemical Constitution and Optical Properties of Essential Oils ;—Report of Inquiry into the Method of making Gold-assays ; —Fifth Report on the Selection and Nomenclature of Dynamical and Electrical Units ;—Report of the Committee on the Labyrinthodonts of the Coal-measures ;— Report of the Committee appointed to construct and print Catalogues of Spectral Rays ;—Report of the Committee appointed to explore the Settle Caves;—Sixth Report on Underground Temperature ;—Report on the Rainfall of the British Isles ;—Seventh Report on Researches in Fossil Crustacea ;—Report on Recent Progress in Elliptic and Hyperelliptic Functions ;—Report on the desirability of establishing a ‘ Close Time’ for the preservation of Indigenous Animals ;—Report on Luminous Meteors ;. - -On the Visibility of the Dark Side of Venus ;—Report of the Committee for the Foundation of Zoological Stations in different parts of the World ;—Second Report of the Committee for collecting Fossils from North-western Scotland ;—Fifth Report on the Treatment and Utilization of Sewage ;—Report of the Committee on Monthly Reports of the Progress of Chemistry ;—On the Bradford Waterworks ;—Report on the possibility of Improving the Methods of Instruction in Elementary Geometry ; —Interim Report of the Committee on Instruments for Measuring the Speed of Ships, &c.;—Report of the Committee for Determinating High Temperatures by means of the Refrangibility of Light evolved by Fluid or Solid Substances ;—On a periodicity of Cyclones and Rainfall in connexion with Sun-spot Periodicity ;—Fifth Report on the Structure of Carboniferous-Limestone Corals ;—Report of the Com- mittee on preparing and publishing brief forms of Instructions for Travellers, Ethnologists, &c. ;—Preliminary Note from the Committee on the Influence of Forests. on the Rainfall ;—Report of the Sub-Wealden Exploration Committee ;—Report of the Committee on Machinery for obtaining a Record of the Roughness of the Sea and Measurement of Waves near shore ;—Report on Science Lectures and Organi- ‘zation ;—Second Report on Science Lectures and Organization. Together with the Transactions of the Sections, Prof. A. W. Williamson’s Address, and Recommendations of the Association and its Committees, 737 PROCEEDINGS or tur FORTY-FOURTH MEETING, at Belfast, August 1874, Published at £1 5s. ConrENTS:—Tenth Report on Kent’s Cavern ;—Report for investigating the Chemical Constitution and Optical Properties of Essential Oils ;—Second Report of the Sub-Wealden Exploration Committee ;—On the Recent Progress and Present State of Systematic Botany ;—Report of the Committee for investigating the Nature of Intestinal Secretion ;—Report of the Committee on the Teaching of Physics in Schools ;—Preliminary Report for investigating Isomeric Cresols and their Deriva- tives ;—Third Report of the Committee for collecting Fossils from localities in North-western Scotland ;—Report on the Rainfall of the British Isles ;—On the Bel- fast Harbour ;—Report of Inquiry into the Method of making Gold-assays ;—Report of a Committee on Experiments to determine the Thermal Conductivities of certain Rocks ;—Second Report on the Exploration of the Settle Caves ;—On the Industrial uses of the Upper Bann River;—Report of the Committee on the Structure and Classification of the Labyrinthodont ;—Second Report of the Committee for record- ing the position, height above the sea, lithological characters, size, and origin of the Erratic Blocks of England and Wales, &c. ;—Sixth Report on the Treatment and Utilization of Sewage ;—Report on the Anthropological Notes and Queries for the use of Travellers ;—On Cyclone and Rainfall Periodicities ;—Fifth Report on Harth- quakes in Scotland ;—Report of the Committee appointed to prepare and print Tables of Wave-numbers ;—Report of the Committee for testing the new Pyrometer of Mr. Siemens ;—Report to the Lords Commissioners of the Admiralty on Experi- ments for the Determination of the Frictional Resistance of Water on a Surface, &ce. ;—Second Report for the Selection and Nomenclature of Dynamical and Elec- trical Units ;—On Instruments for measuring the Speed of Ships;—Report of the Committee on the possibility of establishing a ‘Close Time’ for the Protection of Indigenous Animals ;—Report of the Committee to inquire into the economic effects of Combinations of Labourers and Capitalists ;—Preliminary Report on Dredging on the Coasts of Durham and North Yorkshire ;—Report on Luminous Meteors ;—Re- port on the best means of providing for a Uniformity of Weights and Measures. Together with the Transactions of the Sections, Prof. John Tyndall’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or tat FORTY-FIFTH MEETING, at Bristol, August 1875, Published at £1 5s. _ ConTEeNntTs:—Eleventh Report on Kent’s Cavern ;—Seventh Report on Under- ground Temperature ;—Report on the Zoological Station at Naples ;—Report of a Committee appointed to inquire into the Methods employed in the Estimation of Potash and Phosphoric Acid in Commercial Products ;—Report on the present state of our Knowledge of the Crustacea;—Second Report on the Thermal Conduc- tivities of certain Rocks ;—Preliminary Report of the Committee for extending the Observations on the Specific Volumes of Liquids ;—Sixth Report on Earthquakes in Scotland ;—Seventh Report on the Treatment and Utilization of Sewage ;—Re- port of the Committee for furthering the Palestine Explorations ;—Third Report of the Committee for recording the position, height above the sea, lithological characters, size, and origin of the Erratic Blocks of England and Wales, &c. ;— Report of the Rainfall Committee ;—Report of the Committee for investigating Isomeric Cresols and their Derivatives ;—Report of the Committee for investigating the Circulation of the Underground Waters in the New Red Sandstone and Permian Formations of England ;—On the Steering of Screw-Steamers ;—Second Report of the Committee on Combinations of Capital and Labour ;—Report on the Method of making Gold-assays ;—Eighth Report on Underground Temperature ;—Tides in the River Mersey ;—Sixth Report of the Committee on the Structure of Carboniferous Corals ;—Report of the Committee appointed to explore the Settle Caves ;—On the River Avon (Bristol), its Drainage-Area, &c.;—Report of the Committee on the possibility of establishing a ‘Close Time’ for the Protection of Indigenous Animals ;—Report of the Committee appointed to superintend the Publication of the Monthly Reports of the Progress of Chemistry ;—Report on Dredging off the Coasts of Durham and North Yorkshire in 1874 ;—Report on Luminous Meteors ;—On the Analytical Forms called Trees ;—Report of the Committee on Mathematical 1880, 3B 738 Tables ;—Report of the Committee on Mathematical Notation and Printing ;—Second Report of the Committee for investigating Intestinal Secretion ;—Third Report of the Sub-Wealden Exploration Committee. Together with the Transactions of the Sections, Sir John Hawkshaw’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or tat FORTY-SIXTH MEETING, at Glasgow, September 1876, Published at £1 5s. CONTENTS :—Twelfth Report on Kent’s Cavern;—Report on Improving the Methods of Instruction in Elementary Geometry ;—Results of a Comparison of the British-Association Units of Electrical Resistance ;—Third Report on the Thermal Conductivities of certain Rocks ;—Report of the Committee on the practicability of adopting a Common Measure of Value in the Assessment of Direct Taxation ;— Report of the Committee for testing experimentally Ohm’s Law ;—Report of the Committee on the possibility of establishing a ‘Close Time’ for the Protection of Indigenous Animals ;—Report of the Committee on the Effect of Propellers on the Steering of Vessels ;—On the Investigation of the Steering Qualities of Ships ;— Seventh Report on Earthquakes in Scotland ;—Report on the present state of our Knowledge of the Crustacea ;—Second Report of the Committee for investigating the Circulation of the Underground Waters in the New Red Sandstone and Permian Formations of England ;—Fourth Report of the Committee on the Erratic Blocks of England and Wales, &c.;—Fourth Report of the Committee on the Exploration of the Settle Caves (Victoria Cave) ;—Report on Observations of Luminous Meteors, 1875-76 ;—Report on the Rainfall of the British Isles, 1875-76 ;—Ninth Report on Underground Temperature ;—Nitrous Oxide in the Gaseous and Liquid States ;— Eighth Report on the Treatment and Utilization of Sewage ;—Improved Investiga- tions on the Flow of Water through Orifices, with Objections to the modes of treat- ment commonly adopted ;—Report of the Anthropometric Committee ;—On Cyclone and Rainfall Periodicities in connexion with the Sun-spot Periodicity ;—Report of the Committee for determining the Mechanical Equivalent of Heat ;—Report of the Committee on Tidal Observations ;—Third Report of the Committee on the Condi- tions of Intestinal Secretion and Movement ;—Report of the Committee for collect- ing and suggesting subjects for Chemical Research. Together with the Transactions of the Sections, Dr. T. Andrews’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or tHe FORTY-SEVENTH MERTING, at Ply- mouth, August 1877, Published at £1 4s. CONTENTS :—Thirteenth Report on Kent’s Cavern ;—Second and Third Reports on the Methods employed in the estimation of Potash and Phosphoric Acid in Com- mercial Products ;—Report on the present state of our Knowledge of the Crustacea (Part III.) ;—Third Report on the Circulation of the Underground Waters in the New Red Sandstone and Permian Formations of England ;—Fifth Report on the Erratic Blocks of England, Wales, and Ireland ;—Fourth Report on the Thermal Conducti- vities of certain Rocks ;—Report on Observations of Luminous Meteors, 1876-77 ;— Tenth Report on Underground Temperature ;—Report on the Effect of Propellers on the Steering of Vessels ;—Report on the possibility of establishing a ‘Close Time’ for the Protection of Indigenous Animals ;-—Report on some Double Compounds of Nickel and Cobalt ;—Fifth Report on the Exploration of the Settle Caves (Victoria Cave) ;—Report on the Datum Level of the Ordnance Survey of Great Britain ;— Report on the Zoological Station at Naples ;—Report of the Anthropometric Com- mittee ;—Report on the Conditions under which Liquid Carbonic Acid exists in Rocks and Minerals. Together with the Transactions of the Sections, Prof. Allen Thomson’s Address, and Recommendations of the Association and its Committees. 739 PROCEEDINGS or tum FORTY-EIGHTH MEETING, at Dublin, August 1878, Published at £1 4s. ConrTENTS :—Catalogue of the Oscillation-Frequencies of Solar Rays ;—Report on Mr. Babbage’s Analytical Machine ;—Third Report of the Committee for deter- mining the Mechanical Equivalent of Heat ;—Report of the Committee for arrang- ing for the taking of certain Observations in India, and Observations on Atmospheric Electricity at Madeira ;—Report on the commencement of Secular Experiments upon the Elasticity of Wires ;—Report on the Chemistry of some of the lesser-known Alkaloids, especially Veratria and Bebeerine ;—Report on the best means for the Development of Light from Coal-Gas ;—Fourteenth Report on Kent’s Cavern ;— Report on the Fossils in the North-west Highlands of Scotland ;—Fifth Report on the Therma! Conductivities of certain Rocks ;—Report on the possibility of estah- lishing a ‘Close Time’ for the Protection of Indigenous Animals ;—Report on the occupation of a Table at the Zoological Station at Naples;—Report of the Anthro- pometric Committee ;—Report on Patent Legislation ;—Report on the Use of Steel for Structural Purposes ;—Report on the Geographical Distribution of the Chiro- ptera ;—Recent Improvements in the Port of Dublin;—Report on Mathematical Tables ;—Eleventh Report on Underground Temperature ;—Report on the Explora- tion of the Fermanagh Caves ;—Sixth Report on the Erratic Blocks of England, Wales, and Ireland ;—Report on the present state of our Knowledge of the Crus- tacea (Part IV.) ;—Report on two Caves in the neighbourhood of Tenby ;—Report on the Stationary Tides in the English Channel and in the North Sea, &c. ;—Second Report on the Datum-level of the Ordnance Survey of Great Britain ;—Report on Instruments for measuring the Speed of Ships ;—Report of Investigations into a Common Measure of Value in Direct Taxation ;—Report on Sunspots and Rainfall ; —Report on Observations of Luminous Meteors ;—Sixth Report on the Exploration of the Settle Caves (Victoria Cave) ;—Report on the Kentish Boring Exploration ;— Fourth Report on the Circulation of Underground Waters in the Jurassic, New Red Sandstone, and Permian Formations, with an Appendix on the Filtration of Water en Triassic Sandstone ;—Report on the Effect of Propellers on the Steering of essels. Together with the Transactions of the Sections, Mr. Spottiswoode’s Address, and Recommendations of the Association and its Committees. PROCEEDINGS or tar FORTY-NINTH MERTING, at Sheffield, August 1879, Published at £1 4s. CONTENTS :—Report on the commencement of Secular Experiments upon the Elasticity of Wires ;—Fourth Report of the Committee for determining the Mechan- ical Equivalent of Heat ;—Report of the Committee for endeavouring to procure reports on the Progress of the Chief Branches of Mathematics and Physics ;—Twelfth Report on Underground Temperature ;—Report on Mathematical Tables ;—Sixth Report on the Thermal Conductivities of certain Rocks ;—Report on Observations of Atmospheric Electricity at Madeira ;—Report on the Calculation of Tables of the Fundamental Invariants of Algebraic Forms ;—Report on the Calculation of Sun- Heat Coefficients ;—Second Report on the Stationary Tides in the English Channel and in the North Sea, &c. ;—Report on Observations of Luminous Meteors ;—Report on the question of Improvements in Astronomical Clocks ;—Report of the Committee for improving an Instrument for detecting the presence of Fire-damp in Mines ;— Report on the Chemistry of some of the lesser-known Alkaloids, especially Veratria and Beeberine ;—Seventh Report on the Erratic Blocks of England, Wales, and Ire- land ;—Fifteenth Report on Kent’s Cavern ;—Report on certain Caves in Borneo ;— Fifth Report on the Circulation of Underground Waters in the Jurassic, Red Sand- stone, and Permian Formations of England ;—Report on the Tertiary (Miocene) Flora, &c., of the Basalt of the North of Ireland ;—Report on the possibility of Establishing a ‘Close Time’ for the Protection of Indigenous Animals ;—Report on the Marine Zoology of Devon and Cornwall ;—Report on the Occupation of a Table at the Zoological Station at Naples;—Report on Excavations at Portstewart and elsewhere in the North of Ireland ;—Report of the Anthropometric Committee ;— Report on the Investigation of the Natural History of Socotra ;—Report on Instru- 740 ments for measuring the Speed of Ships;—Third Report on the Datum-level of the Ordnance Survey of Great Britain ;—Second Report on Patent Legislation ;—On Self-acting Intermittent Siphons and the conditions which determine the com- mencement of their Action ;—On some further Evidence as to the Range of the Paleozoic Rocks beneath the South-east of England ;—Hydrography, Past and Present, Together with the Transactions of the Sections, Prof. Allman’s Address, and Recommendations of the Association and its Committees. BRITISH ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE. LIstT OFFICERS, COUNCIL, AND MEMBERS, CORRECTED TO NOVEMBER 30, 1880. i “ bs ry a as é ay Bee MERA 0GGa REE vial X! “5 : 7 . ae EG . hep be Oe: TO TAMAR: , ees ® - ea 4 rod OFFICERS AND COUNCIL, 1880-81. PRESIDENT. ANDREW CROMBIE RAMSAY, Esq., LL.D., F.R.S., V.P.G.S., Director-General of the Geological Survey of the United Kingdom, and of the Museum of Practical Geology. VICE-PRESIDENTS, “The Right Hon. the Ean or Jersey, L. Li. Dittwyn, Esq., M.P., F.L.S., F.G.S. “The Mayor or SWANSEA, J. Gwyn _ JEFFREYS, Esq., LL.D., F,R.S., F.L.S., "The Hon. Sir W. R. Grove, M.A., D.C.L., F.R.S, Treas. G.S., F.R.G.S, HH, Hussey Vivian, Esq., M.P., F.G.S, PRESIDENT ELECT. SIR JOHN LUBBOCK, Bart., M.P., D.C.L., LL.D., F.R.S., F.L.S., F.G.S, VICE-PRESIDENTS ELECT. His Grace the ARCHBISHOP oF York, D.D., F.R.S. | W. B. CARPENTER, Esq., C.B., M.D., LL.D., ‘The Hon. Sir W. R. Grove, M.A., D.C.L., F.B.S. F.R.S., F.G.S. fessor G. G. STOKES, M.A., D.C.L., LL.D., | Sir Jonny HawksuHaw, C.E., F.R.S., F.G.S., F.R.G.S. Sec, R.S. ALLEN THOMSON, Esq., M.D., LL.D., F.R.S. L. & Ex Professor ALLMAN, M.D., LL.D., F.R.S. L, & E., F.LS. LOCAL SECRETARIES FOR THE MEETING AT YORK, Rey. THoMAS ADAMs, M.A. TEMPEST ANDERSON, Esq., M.D., B.Sc. LOCAL, TREASURER FOR THE MEETING AT YORK. W. W. WILBERFORCE, Esq. ORDINARY MEMBERS OF THE COUNCIL. ABEL, F. A., Esq., O.B., F.R.S. NEWMARCH, W., Esq., F.R.S. ADAMS, Professor W. G., F.R.S. NEWTON, Professor A., F.R.S, BATEMAN, J. F., Esq., C.E., F.R.S, PENGELLY, W., Esq., F.R.S. CAYLEY, Professor, F.R.S. PERE, W. H., Esq., F.R.S. Easton, E., Esq., C.E. Pitt-RIvers, Gen. A., F.R.S, Evans, Captain, C.B., F.R.S. RAYLEIGH, Lord, F.R.S. Evans, J., Esq., F.R.S. ROLLESTON, Professor G., F.R.S. Foster, Professor G. C., F.R.S. Roscok, Professor H. E., F.R.S. GLAISHER, J. W. L., Esq., F.R.S, SANDERSON, Prof. J. S. BURDON, F.R.S. Heywoop, J., Esq., F.R.S. SmyTH, WARRINGTON W., Esq., F.R.S. Hueerys, W., Esq., F.R.S. Sorsy, Dr. H. C., F.R.S. HUGHES, Professor T. McK., M.A. THUILLIER, Gen. Sir H. E. L., C.8.1., F.R.S. JEFFREYS, J. GwYN, Esq., F.R.S. GENERAL SECRETARIES. “Capt. Douaias Garon, O.B., D.C.L., F.B.S., F.G.S., 12 Chester Street, Grosvenor Place, London, S.W. Puivip Luriey ScuaTer, Esq., M.A., Ph.D., E.RS., F.LS., F.G.S., 11 Hanover Square, London, W. ASSISTANT SECRETARY. J. H, H. Gorpon, Esq., B.A., 22 Albemarle Street, London, W. GENERAL TREASURER, Professor A. W, WILLIAMSON, Ph.D., LL.D., F.R.S., F.C.S., University College, London, W.C, EX-OFFICIO MEMBERS OF THE COUNCIL. ‘The Trustees, the President and President Elect, the Presidents of former years, the Vice-Presidents and ‘Vice-Presidents Elect, the General and Assistant General Secretaries for the present and former years, the General Treasurers for the present and former years, and the Local Treasurer and Secretaries for the -ensuing Meeting. TRUSTEES (PERMANENT). General Sir EDWARD SABINE, K.C.B., R.A., D.C.L., F.R.S. Sir Pompe DE M. Grey EGERTON, Bart., M.P., F.R.S., F.G.S. Sir JouN Lupsock, Bart., M.P., D.C.L., LL.D., F.R.S, F.LS PRESIDENTS OF FORMER YEARS. The Duke of Devonshire. Sir W. G. Armstrong, C.B., LL.D. | Prof. Williamson, Ph.D., F.R.S, “The Rey. T. R. Robinson, D.D. Sir William R, Grove, F.R.S. Prof. Tyndall, D.C.L., F.R.S. Sir G. B, Airy, Astronomer Royal, | The Duke of Buccleuch, K.G. Sir John Hawkshaw, C.E., F.R.S, “General Sir E. Sabine, K.C.B, Sir Joseph D. Hooker, D.C.L. Prof. T. Andrews, M.D., F.R.S. The Earl of Harrowby,. Prof, Stokes, M.A., D.C.L, Allen Thomson, Esq., F.R.S. “The Duke of Argyll. Prof. Huxley, LL.D., Sec. R.S. W. Spottiswoode, Esq., Pres. B.S, ‘The Rev. H. Lloyd, D.D. Prof. Sir Wm. Thomson, D.C.L. | Prof. Allman, M.D., F.R.S. Richard Owen, M.D., D.C.L. Dr. Carpenter, C.B., F.R.S. GENERAL OFFICERS OF FORMER YEARS. B. Galton, Esq., F.R.S, | Gen. Sir E. Sabine, K.C.B., F.R.S. | Dr. Michael Foster, F.R.S. Dr. T, A. Hirst, F.R.S, W. Spottiswoode, Esq., Pres. R.S, | George Griffith, Esq., M.A, A2 Aa ok 10:59 se 1 Seaatows's Yo pie mall itt 18 Sie dtnatiensy rae jest We ALL ae PY 4 : an met a AP, ot as ot 7 an nv 4° “h 1 ee ia +i w enpid ns. at Ae roe HM ott TOG yer soit HN aa ve ice ‘Seam pruncaunde adel! ee i AN pttatle aif vit aft.) ot arb aniingt A h N | rye at ake ' tot stalk ALI Boyeiiganraianet wi jad : we Fs oh AEE ellie eae.) (fh 7" Woy 7a a is iNeed rn vi ak, Gt ere a eee y ty LK as Oo Faiebn Ls ‘ } > Ray TA OWITHEM ENT,.0O4 OaRA ayioee 2+ wed LAL Aneto ALAA th xT! * 1 ated h «rivals As Brie Fh omer’ tA oer aaM BHT eT rg aN UNE i ae owl wt a cled et 1 wl NF 4 Ss 7 in ~ hay) ) LAAN ane 4a etna 404 WSR rye N rt % weld eee #4, iM 1 a ve aaperatice v he Wat ti At Soe OL, 2 sf ny) yan hPa’ i, unt Pe ar aes, FF oeMy te f i ae) i CoS hb, vind plan? ehh 8 1 well 2 ; ae . re REA end wae Saber Hee Lit AALS al! Atak Ptpops ray vipik Vi ve RHE maze aa’ Ww ivan deena tts dtd Ket ft ORO at ® fh uf Aa pe 7) Owe hut sation ganas PA ah etd aah bane : Sipndoos anim Se aats: cro renee Rev vet YY ova > serie? Sav nee Ny mete DOOnt te awed fotan pled Fe q Lge, WAPOTE fi. Leperetny fir het annaeep res tears? Caratette ts faiy reared cart Waal aay Ulta ot hire Coat why, UE Deh me eee A ys’ Ret eo ore tier ee ee ah Swe Ray ; i ye te ee gt aigk 2 Garay oe ee 5 (4 vanh) bd Be Pee re Pasi let thal ge, ve yah - ve | wan miners anevrt Mas hei ixtiais en. an K, J ih See Maes se , OME ym | AEE ee icky wh ied ade ts ' Mr AA iter , Dighdes , ease | pak +. FGI r) ive waar: od int z ‘ eee pracy nt - venient LIST OF MEMBERS OF THE BRITISH ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE. 1880. * indicates Life Members entitled to the Annual Report. § indicates Annual Subscribers entitled to the Annual Report. §§ indicates Annual Subscribers who will be entitled to the Report if their Subscriptions are paid by December 31, 1880. ¢ indicates Subscribers not entitled to the Annual Report. Names without any mark before them are Life Members not entitled to the Annual Report. Names of Members of the GENERAL COMMITTEE are printed in SMALL CAPITALS. Names of Members whose addresses are incomplete or not known are in italics. Notice of changes of Residence should be sent to the Assistant Seerctary, 22 Albemarle Street, London, W. : Year of 1866. 1863. 1856. 1863. 1873. 1860. 1873. 1854. 1877. 1873. 1869, 1877. 1873. ‘Election. Abbatt, Richard, F.R.A.S, Marlborough House, Burgess Hill, Sussex. tAbbott, George J., United States Consul, Sheffield and Nottingham, *ApeL, FREDERICK Aveustus, C.B., F.R.S., F.C.S., Director of the Chemical Establishment of the War Department. Royal Arsenal, Woolwich. tAbercrombie, John, M.D. 13 Suffolk-square, Cheltenham. *A BERNETHY, JAMES, M.Inst.C.E., F.R.S.E. ‘4 Delahay-street, West minster, 8. W. tAbernethy, James. Ferry-hill, Aberdeen. tAbernethy, Robert. Ferry-hill, Aberdeen. *Apney, Captain W. de W., R.E., F.RS., FRAS., FCS. 3 St. Alban’s-road, Kensington, London, W. tAbraham, John. 87 Bold-street, Liverpool. §Ace, Rev. Daniel, D.D., F.R.A.S. Laughton, near Gainsborough, Lincolnshire. tAckroyd, Samuel. Greayes-street, Little Horton, Bradford, York shire. tAcland, Charles T. D. Urea Exeter. *Acland, Francis E. Dyke, R.A. Oxford. *Acland, Rev. H. D. Loughton, Essex. AcLAND, Henry W. D., M.A., M.D., LL.D., F.R.S., F.R.GS., Radcliffe Librarian and Regius Professor of Medicine in the University of Oxford. Broad-street, Oxford. : 6 LIST OF MEMBERS. Year of Election. 1877, *Acland, Theodore Dyke, M.A. 13 Vincent-square, Westminster, W. S.W. 1860, tActanD, Sir Toomas Dyxr, Bart., M.A., D.O.L., M.P. Sprydon- cote, Exeter ; and Athenzeum Club, London, S.W. Adair, John. 13 Merrion-square North, Dublin. 1872. tApams, A. Lerrn, M.A., M.B., F.R.S., F.G.S., Professor of Natural History in Queen’s College, Cork. 18 Clarendon-gardens, Maida Hill, London, W. 1876. Adams, James. 9 Royal-crescent West, Glasgow. *Apams, JoHn Coucn, M.A., LL.D., F.R.S., F.R.A.S., Director of the Observatory and Lowndsean Professor of Astronomy and Geometry in the University of Cambridge. The Observatory,. Cambridge. 1871. {Adams, John R. 3 Queen’s-gate-terrace, London, S.W. 1879. §ApAms, Rev. THomas, M.A, Clifton Green House, York. 1877. {Apams, Wii11AM. 3 Sussex-terrace, Plymouth. 1869, *Apams, Witt1AM Grytts, M.A., F.R.S., F.G.S., F.C.P.S., Professor of Natural Philosophy and Astronomy in King’s College, London. La 43 Notting Hill-square, London, W. 1873. tAdams-Acton, John. Margutta House, 103 Marylebone-road, London, N.W. 1879.§§Adamson, Robert, M.A., Professor of Logic and Political Economy in Owens College, Manchester. 60 Parsonage-road, Withing= ton, Manchester. ADDERLEY, The Right Hon. Sir Coartus Bowyer, M.P. Hams-< hall, Coleshill, Warwickshire. Adelaide, The Right Rey. Augustus Short, D.D., Bishop of. South, Australia. 1865. *Adkins, Henry. Northfield, near Birmingham. 1864, *Ainsworth, David. The Flosh, Cleator, Carnforth. 1871. *Ainsworth, John Stirling. The Flosh, Cleator, Carnforth. Ainsworth, Peter. Smithills Hall, Bolton. 1842. *Ainsworth, Thomas. The Flosh, Cleator, Carnforth. 1871. {Ainsworth, William M. The Flosh, Cleator, Carnforth. 1859. {Arriig, The Right Hon. the Earl of, K.T. Holly Lodge, Campden Hill, London, W.; and Airlie Castle, Forfarshire. Airy, Sir GroreE Bropett, K.C.B., M.A., LL.D., D.C.L., F.R.S.,, F.R.A.S., Astronomer Royal. The Royal Observatory, Green-. : wich, S.E. 1871. §Aitken, John, F.R.S.E. Darroch, Falkirk, N.B. : Alkvroyd, Edward. Bankfield, Halifax. 1862. t{Atcocx, Sir Rurwerrorp, K.C.B., D.C.L., F.R.G.S. The Athe= neeum Club, Pall Mall, London, S.W. 1861. tAlcock, Thomas, M.D. Side Brook, Salemoor, Manchester. 1872. *Alecock, Thomas, M.D. Oakfield, Sale, Manchester. *Aldam, William. Frickley Hall, near Doncaster. ALDERSON, Sir Jamzs, M.A., M.D., D.C.L., F.R.S., Consulting Phy=- sician to St. Mary’s Hospital. 17 Berkeley-square, London, W.. 1859. {ALEXANDER, General Sir James Epwarp, K.O.B., K.C.LS., ; F.R.S.E., F.R.A.S., F.R.G.S. Westerton, Bridge of Allan, N.B.. 1873. {Alexander, Reginald, M.D. 13 Hallfield-road, Bradford, Yorkshire. 1858. {ALExanpER, Wittr1AM, M.D. Halifax. 1850. Alexander, Rey. William Lindsay, D.D.,F.R.S.E. Pinkieburn, Mus— selburgh, by Edinburgh. 1867. {Alison, George L. C. Dundee. 1859. {Allan, Alexander. Scottish Central Railway, Perth. 1871. {Allan, G., C.E. 17 Leadenhall-street, London, E.C. LIST OF MEMBERS. 7 Year of Election. 1871. 1879. 1878. 1861. 1852. 1863. 1875. 1873. 1876. 1878. 1850. 1850. 1874. 1876. 1859. 1880. 1875. 1880. 1880. 1880. 1857. 1877. 1859. 1878. 1868. 1870. 1855. 1874. 1851. 1861. 1867. 1879. §Atten, Atrrep H., F.C.S. 1 Surrey-street, Sheffield. *Allen, Rev. A. J.C. Peterhouse, Cambridge. tAllen, John Romilly. 5 Albert-terrace, Regent’s Park, London, N.W. fAllen, Richard. Didsbury, near Manchester. *AtLen, Witt1aM J. C., Secretary to the Royal Belfast Academical Institution. Ulster Bank, Belfast. tAllhusen, O. Elswick Hall, Newcastle-on-Tyne. *AttmaNn, GeorcE J., M.D., LL.D., F.R.S. L. & E., M.R.LA., Pres. L.S., Emeritus Professor of Natural History in the University of Edinburgh. Parkstone, Dorset. *Arston, Epwarp R., F.L.S., F.Z.S. 14 Maddox-street, Regent- street, London, W. tAmbler, John. North Park-road, Bradford, Yorkshire. tAnderson, Alexander. 1 St. James’s-place, Hillhead, Glasgow. tAnderson, Beresford. Saint Ville, Killiney. tAnderson, Charles William. Cleadon, South Shields. tAnderson, John. 31 St. Bernard’s-crescent, Edinburgh. tAnderson, John, J.P., F.G.S. Holywood, Belfast. tAnderson, Matthew. 187 St. Vincent-street, Glasgow. tAnpERSON, Patrick. 15 King-street, Dundee. §Anderson, Richard. New Malden, Surrey. tAnderson, Captain 8., R.E. Junior United Service Club, Charles- street, St. James's, London, S.W. *AnpeErson, TempEst, M.D., B.Sc. 17 Stonegate, York. §Andrew, Mrs. 126 Jamaica-street, Stepney, London, E. *Andrew, Thornton, M.I.C.E. Cefn Eithen, Swansea. *AnpREws, THomas, M.D., LL.D., F.R.S., Hon. F.R.S.E., M.R.1LA., F.C.S. Fortwilliam Park, Belfast. tAndrews, William. The Hill, Monkstown, Co. Dublin. §Angell, John. 81 Ducie-grove, Oxford-street, Manchester. tAngus, John. Town House, Aberdeen. tAnson, Frederick H. 9 Delahay-street, Westminster, S.W. Anthony, John, M.D. 6 Greentield-crescent, Edgbaston, Birming- ham. Apsoun, James, M.D., F.R.S., F.C.S., M.R.LA., Professor of Mineralogy at Dublin University. South Hill, Blackrock, Co. Dublin. tAppleby, C.J. Emerson-street, Bankside, Southwark, London, 8.E. tArcher, Francis, jun. 3 Brunswick-street, Liverpool. *ArcHER, Professor THomas ©., F.R.S.E., Director of the Museum u paance and Art, Edinburgh. West Newington House, Edin- ureh. tArcher, William, F.R.S., M.R.I.A. St. Brendan’s, Grosvenor-road East, Rathmines, Dublin. tAReYLL, His Grace the Duke of, K.T.,D.C.L., F.R.S. L.&E., F.G.S. Argyll Lodge, Kensington, London, W. ; and Inveraray, Argyle- shire. tArmitage, William. 95 Portland-street, Manchester. *Armitstead, George. Errol Park, Errol, N.B. *Armstrong, Sir Alexander, K.C.B., M.D., LL.D., F.R.S., F.R.G.S. The Albany, London, W. 1873.§§ Armstrong, Henry E., Ph.D., F.R.S., F.0.8. London Institution, 1878. 1874. Finsbury-circus, London, E.C. tArmstrong, James. 28 Renfield-street, Glasgow. tArmstrong, Jumes T., F.CS. Plym Villa, Clifton-road, Tuebrook, Liverpool. 8 LIST OF MEMBERS. Year of Election. Armstrong, Thomas. Higher Broughton, Manchester. 1857. *ArMstROoNG, Sir WitLiAM Gezorex, O.B., LL.D., D.O.L., F.R.S. 8 Great George-street, London, 8S. W. 5 and Jesmond Dene, Newcastle-upon-Tyne. 1871. tArnot, William, F.C.S. St. Margaret’s, Kirkintilloch, N.B. 1870. tArnott, Thomas Reid. Bramshill, Harlesden Green, London, N.W. 1853. 1870. 1874. 1873. 1842, 1866. 1861. 1875. 1861. 1861. 1872. 1858. 1866. 1865. 1861. 1865. 1863. 1861. 1858. 1842, 1858. 1863. 1860. 1865. 1878. 1877. 1853. 1863. 1877. 1870. 1878. 1865. 1855. 1866. 1866, *Arthur, Rev. William, M.A. Clapham Common, London, 8. W. *Ash, Dr. T. Linnington. Holsworthy, North Devon. {Ashe, Isaac, M.B. ~ Dundrum, Co. Dublin. §Ashton, John. Gorse Bank House, Windsor-road, Oldham. *Ashton, Thomas, M.D. 8 Royal Wells-terrace, Cheltenham, Ashton, Thomas. Ford Bank, Didsbury, Manchester. tAshwell, Henry. Mount-street, New Basford, Nottingham. *Ashworth, Edmund. Egerton Hall, Bolton-le-Moors. ‘Ashworth, Henry. Turton, near Bolton. tAspland, Alfred. Dukinfield, Ashton-under-Lyne. *Aspland, W. Gaskell. Care of Mrs. Houghton, Moorfield, Knuts- ford. §Asquith, J. R. Infirmary-street, Leeds. tAston, Theodore. 11 New-square, Lincoln’s Inn, London, W.C. §Atchison, Arthur T., M.A. 60 Warwick-road, Earl’s Court, London, S.W tAtherton, Charles. Sandover, Isle of Wight. ft Atherton, J. H., F.C.S: Long-row, Nottingham. tAtkin, Alfred. ’ Griffin’s Hil), Birmingham. tAtkin, Eli. Newton Heath, "Manchester. *Arkinson, Epmunpb, Ph.D., F.C.S. Portesbery Hill, Camberley, Surrey. *Athinson, & Clayton. 21 Windsor-terrace, Newcastle-on-Tyne, tAtkinson, Rey. J. A. Longsight Rectory, near Manchester. *Atkinson, John Hastings. "12 East Parade, Leeds. *Atkinson, Joseph Beavington. Stratford House, 113 Atitagdonteaie Kensington, London, W. Atkinson, William. Claremont, Southport. *ATTFIELD, Professor J., Ph.D., F.R.S., F.C.S. 17 Bloomsbury- square, London, W.C. *Austin-Gourlay, Rey. William E.C., M.A. The Rectory, Stanton St. John, near Oxford. *Avery, Thomas. Church-road, Edgbaston, Birmingham. *Aylmer, Sir Gerald George, Bart. Donadea Castle, Kilcock, Co. Kildare. *Ayrton, Professor W. E. 68 Sloane-street, London, S.W. *Ayrton, W.5S., F.S.A. a Saltburn-by-the-Sea. *BaBINGTON, CHARLES Carparz, M.A., F.R.S., F.L.S., F.G.S., Pro- fessor of Botany in the University of Cambridge. 5 Brookside, Cambridge. Backhouse, Hdmeai Darlington. Backhouse, Thomas James. Sunderland. : {Backhouse, T. W. West Hendon House, Sunderland. tBadock, W. F. Badminton House, Clifton Park, Bristol. §Bailey, Dr. F. J. 51 Grove-street, Liverpool, tBailey, John, 3 Blackhall-place, Dublin. {Bailey, Samuel, F.G.S. The Peck, Walsall. tBailey, William. Hor seley Fields Chemical Works, Wolverhampton. {Baillon, Andrew. St. Mary’s Gate, Nottingham. tBaillon, L. St. Mary’s Gaie, Nottingham. Year of Election. 1878, 1857, 1873. 1865. 1858. 1858. 1866, 1865, 1861. 1865. 1849, 1863. 1875. 1875, 1871, 1871. 1875. 1878, 1866. 1878. 1876. 1869, 1874. 1852. 1879.§ 18 LIST OF MEMBERS. 9 {Baily, Walter. 176 Haverstock-hill, London, N.W. {Barty, Wrrr1am Herrimer, F.L.S., E.G. S., Acting Palzontologist to the Geological Survey of Ireland, 14 Hume-street ; and Apsley Lodge, 92 Rathgar-road, Dublin. §Bain, Sir James. 3 ‘Park-terrace, Glasgow. tBan, Rev. W. J. Glenlark Villa, Leamington. *Bainbridge, Robert Walton. Middleton House, Middleton-in-Tees- dale, by Darlington. *Baines, Epwarp, J.P. Belgrave Mansions, Grosyenor-gardens, London, S. W.; ; and St. Ann’s Hill, Burley, Leeds. {Baines, Frederick. Burley, near Leeds. {Baines, T. Blackburn. ‘Mercury’ Office, Leeds. {Baker, Francis B. Serre odie Nottingham. {Baker, James P. Wolverhampton. *Baker, John. St. John’s-road, Buxton. tBaker, Robert L. Barham House, Leamington. *Baker, William. 63 Gloucester-place, Hyde Park, London, W, {Baker, William. 6 Taptonville, Sheffield. *Baker, W. Mills. Moorland House, Stoke Bishop, near Bristol. {Baxer, W. Procror. Brislington, Bristol. ve Francis MAITLAND, MM. AS F.R.S. Trinity College, Cam- ridge, tBalfour, G. W. Whittinghame, Prestonkirk, Scotland. {Balfour, Isaac Bayley, D.Sc. 27 Inverleith-1 ow, Edinburgh. *Batrour, JoHn Hurron, M.A., M.D., UL.D., F.R.S. L. & E., F.L.S. Emeritus Professor of Botany. Tnverleith House, Edinburgh. *Ball, Charles Bent, M.D. 16 Lower Fitzwilliam-street, Dublin. *Baxt, Joun, M.A., F.R.S., F.L.S., M.R.LA. 10 Southwell-gardens, South Kensington, London, S.W. *Batz, Ropert StaweEtt, M. A., LL.D., F.R.S., F.R.A.S., Andrews Professor of Astronomy in ‘the University of Dublin, and Astro- nomer Royal for Ireland. The Observatory, Dunsink,’ Co. Dublin. §Bati, VaLEenTINE, M.A., F.G.S. Calcutta. (Care of Messrs. 8, H. King & Co., Pall Mall, London, S.W.) t Ballantyne, James. Souther oft, Rutherglen, Glasgow. {Bamber, Henry K., F.C.S. 5 Westminster-chambers, Victoria- street, Westminster, S.W. *Bangay, Frederick Arthur. Cheadle, Cheshire. tBangor, Viscount. Castleward, Co. Down, Ireland. §Banham, H. French. Mount View, Glossop-road, Sheffield. 70. {BantstER, Rey. Wittt1am, B.A. St. James’s Mount, Liverpool. 1866. 1861. 1859. 1855. 1871. 1852. 1860. 1876. 1868. 1863. 41860, {Barber, John. Long-row, Nottingham. *Barbour, George. Bankhead, Broxton, Chester. {Barbour, George F. 11 George-square, Edinburgh. *Barbour, Robert. Bolesworth Castle, Tattenhall, Chester. {Barclay, ” Andrew. Kilmarnock, Scotland. Barclay, Charles, F.S.A. Bury Hill, Dorking. tBarclay, George. 17 Coates-crescent, Edinburgh. *Barclay, J. Gurney. 54 Lombar d-street, London, E.C, *Barclay, Robert. High Leigh, Hoddesden, Herts. *Barclay, Robert. 21 ‘Park-terrace, Glasgow. *Barclay, W. L. 54 Lombard-street, London, E.C. *Barford, James Gale, F.C.S. Wellington College, Wokingham, Berkshire. *Barker, Rev. Arthur Alcock, B.D. East Bridgford Rectory, Nottingham. 10 LIST OF MEMBERS. Year of Election. 1879.§§Barker, Elliott. 2 High-street, Sheffield. 1879. *Barker, Rev. Philip C., M.A., LL.B. Rotherham, Yorkshire. 1865. tBarker, Stephen. 30 Frederick-street, Edgbaston, Birmingham. 1870. §Barxty, Sir Henry, G.C.M.G., K.C.B., F.R.S., F.R.G.S. 1 Bina- gardens, South Kensington, London, $.W. 1873. tBarlow, Crawford, B.A. 2 Old Palace-yard, Westminster, 8.W. 1878, {Barlow, John, M.D. The University, Glasgow. Barlow, Lieut.-Col. Maurice (14th Regt. of Foot). 5 Great George- street, Dublin. 1857. {Bartow, Perer WILLIAM, F.R.S., F.G.S. 26 Great George-street, Westminster, S. W. : 1878. Bartow, W. H., C.E., F.R.S. 2 Old Palace-yard, Westminster, S.W 1861. *Barnard, Major R. Cary, F.L.S. Bartlow, Leckhampton, Chelten- ham. 1868.§§Barnes, Richard H. (Care of Messrs. Collyer, 4 Bedford-row, London, W.C Barnes, Thomas Addison. Brampton Collieries, near Chesterfield. *Barnett, Richard, M.R.CS. 3 Heath-terrace, Leamington. 1859. {Barr, Lieut.-General. Apsleytoun, East Grinstead, Sussex. 1861. *Barr, William R., F.G.S8. Fernside, Cheadle Hulme, Cheshire. 1860. {Barrett, T. B. High-street, Welshpool, Montgomery, 1872. *Barrert, W. F., F.R.S.E., M.R.LA., F.C.8S., Professor of Physics- in the Royal College of Science, Dublin. 1874. {Barrington, R. M. Fassaroe, Bray, Co. Wicklow. 1874. §Barrington-Ward, Mark J., M.A., F.L.S., F.R.G.S., H.M. Inspector of Schools. Salwarpe End, Droitwich. eg 1866. {Barron, William. Elvaston Nurseries, Borrowash, Derby. 1858. {Barry, Rev. Canon, D.D., D.C.L., Principal of King’s’ College, London, W.C. 1862. *Barry, Charles. 15 Pembridge-square, Bayswater, London, W. 1875. {Barry, John Wolfe. 23 Delahay-street, Westminster, 8. W. Barstow, Thomas. Garrow Hill, near York. 1858. *Bartholomew, Charles. Castle Hill House, Ealing, Middlesex, W. 1855. {Bartholomew, Hugh. New Gasworks, Glasgow. 1858. *Bartholomew, William Hamond. Ridgeway House, Cumberland-road,, Headingley, Leeds. 1873. §Bartley, George C. T. St. Margaret’s House, Victoria-street, London, 8. W. 1868. *Barton, Edward (27th Inniskillens). Clonelly, Ireland. 1857. {Barton, Folloit W. Clonelly, Co. Fermanagh, 1852. {Barton, James. Farndree, Dundalk. 1864. {Bartrum, John 8. 41 Gay-street, Bath. *Bashforth, Rey. Francis, B.D. Minting Vicarage, near Horncastle. 1876. {Bassano, Alexander. 12 Montagu-place, London, W. 1876. {Bassano, Clement. Jesus College, Cambridge. 1866. *Bassrrr, Hunyry. 26 Belitha-villas, Barnsbury, London, N. 1866. {Bassett, Richard. Pelham-street, Nottingham. 1869. {Bastard, 8.8. Summerland-place, Exeter. 1871. {Bastran, H. Cuartron, M.D., M.A., F.R.S., F.L.S., Professor of* Pathological Anatomy at University College. 20 Queen Anne— street, London, W. 1848. {Bars, C. Spence, F.R.S., F.L.S. 8 Mulgrave-place, Plymouth. 1873. *Bateman, Daniel. Low Moor, near Bradford, Yorkshire. 1868. {Bateman, Frederick, M.D. Upper St. Giles’s-street, Norwich. Bateman, James, M.A., F.R.S., F.R.GS., F.L.S. 9 Hyde Park— gate South, London, W. LIST OF MEMBERS. 1k Year of Election. 1842. 1864. 1852, 1851. 1869. 1863. 1861. 1867. 1867. 1867. 1868. 1851. 1866. 1875. 1876. 1860. 1872. 1870. 1855. 1861. 1871. 1859. 1864. 1860. 1866. 1870. 1878. 1873. 1874. 1873. 1871. 1859. 1860. 1855. 1880. *BaTeMAN, JOHN FrepERIC, C.E., F.R.S., F.G.S., F.R.G.S. 16 Great George-street, London, 8. W. {Barrs, Henry WAtrTeER, Assist.-Sec. R.G.S., F.L.S. 1 Savile-row, London, W. {Bateson, Sir Robert, Bart. Belvoir Park, Belfast. {Barn and WELLS, The Right Rev. Lord Arruur Hervey, Lord Bishop of. The Palace, Wells, Somerset. {Batten, John Winterbotham. 35 Palace Gardens-terrace, Kensing- ton, London, W. §BavERMAN, H., F.G.S. 41 Acre-lane, Brixton, London, S.W. {Baxendell, Joseph, F.R.A.S. 108 Stock-street, Manchester, {tBaxter, Edward. Hazel Hall, Dundee. {Baxter, John B. Oraig Tay House, Dundee. {Baxter, The Right Hon. William Edward, M.P. Ashcliffe, Dundee.. tBayes, William, M.D. 58 Brook-street, London, W. Seen, George. 16 London-street, Fenchurch-street, London,. E. {Bayley, Thomas. Lenton, Nottingham. Bayly, John. Seven Trees, Plymouth. *Bayly, Robert. Torr-grove, near Plymouth. *Baynes, Robert E., M.A. Christ Church, Oxford. Bazley, Thomas Sebastian, M.A. Hatherop Castle, Fairford, Glou- cestershire. *BEALE, Lionzt S., M.D., F.R.S., Professor of Pathological Anatomy in King’s College. 61 Grosvenor-street, London, W. Spero Edward, F.C.S. The White House, North Dulwich, Surrey, S {Beard, Rey. Charles. 13 South-hill-road, Toxteth Park, Liverpool. *Beatson, William. Ash Mount, Rotherham. *Beaufort, W. Morris, F.R.A.S., F.R.G.S., F.M.S., F.S.S. 18 Picca- dilly, London, W. *Beaumont, Rey. Thomas George. Chelmondiston Rectory, Ips- wich. *Beazley, Major George G., F.R.G.S. 16 Holles-street, Cavendish-. square, London, W. *Beck, Joseph, F.R.A.S. 68 Cornhill, London, E.C. §Becker, Miss Lydia E. Whalley Rance, Manchester. }Becxtss, Samvet H., F.R.S., F.G.S. 9 Grand-parade, St. Leonard’s-. on-Sea. tBeddard, James. Derby-road, Nottingham. §Brppog, Joun, M.D., F.R.S. Clifton, Bristol. {Bedson, P. Phillips, D.Sc. Oak Leigh, Marple, near Stockport. ee Jacob. Springfield House, North-parade, Bradford, York~ shire. {Belcher, Richard Boswell. Blockley, Worcestershire. tBell, A. P. Royal Exchange, Manchester. §Bell, Charles B. 6 Spring-bank, Hull. Bell, Frederick John. Woodlands, near Maldon, Essex. tBell, George. Windsor-buildings, Dumbarton. {Bell, Rev. George Charles, M.A. Marlborough College, Wilts. {Bell, Capt. Henry. Chalfont Lodge, Cheltenham. §Bell, Henry Oswin. 13 Northumberland-terrace, Tynemouth, 1879.§§Bell, Henry 8. Kenwood Bank, Sharrow, Sheffield, 1862. *Betx, Isaac Lowruran, F.R.S., F.0.S., M.I.C.E, Rounton Grange,, Northallerton. ; 1875.§§ Bell, Ba F.C.8. The Laboratory, Somerset House, London, 12 1876. 1863. 1867. 1875. 1842. 1864, 1870. 1836. 1870. 1870. 1852. 1848. 1870. 1863. 1848, 1842, 1863. 1875. 1876, 1868. 1863. 1848, 1870. 1862, 1865. 1858. 1876, 1880. 1859. 1874. 1863. 1870. 1868. 1864, 1877. 1842, 1873. LIST OF MEMBERS. f lection. 1871. *Bell, J. Carter, F.C.\S. Kersal Clough, Higher Broughton, Man- chester. 1853. {Bell, John Pearson, M.D. Waverley House, Hull. 1864, {Bell, R. Queen’s College, Kingston, Canada. §Bell, R. Bruce. 2 Clifton-place, Glasgow. *Bell, Thomas. Crosby Court, Northallerton. {Bell, Thomas. Belmont, Dundee. tBell, William. Witford House, Briton Ferry, Glamorganshire. Bellhouse, Edward Taylor. Eagle Foundry, Manchester. ‘Bellingham, Sir Alan. Castle Bellingham, Ireland. *“Bendyshe, T. 3 Sea-View-terrace, Margate. {Benyert, ALFRED W., M.A., B.Sc., F.L.S. | 6 Park Village East, Regent’s Park, London, N.W. §Bennett, Henry. Bedminster, Bristol. *Bennett, William. 109 Shaw-street, Liverpool. *Bennett, William, jun. Oak Hill Park, Old Swan, near Liver- ool, Bowne, Francis, F.S:A. 5 Tavistock-square, London, W.C. Benson, Robert, jun. Fuirfield, Manchester. tBenson, Starling, F.G.S. Gloucester-place, Swansea, tBenson, W. Alresford, Hants. tBenson, William. Fourstones Court, Newcastle-on-Tyne. {BentHam, Grorer, F.R.S., F.R.G.S., F.L.S. 25 Wilton-place, Knightsbridge, London, 8. W. Bentley, John. 2 Portland-place, London, W. §BentLey, Ropert, F.L.S., Professor of Botany in King’s College, London. 1 Trebovir-road, South Kensington, London, 8, W. }Beor, Henry R. Scientific Club, Savile-row, London, W. tBergius, Walter C. 9 Loudon-terrace, Hillhead, Glasgow. {BERKELEY, Rey. M. J., M.A., F.R.S., F.L.S. Sibbertoft, Market Harborough. {Berkley, C. Marley Hill, Gateshead, Durham. ;Berrington, Arthur V. D. Woodlands Castle, near Swansea. {Berwick, George, M.D. 36 Fawcett-street, Sunderland. tBesant, William Henry, M.A., F.R.S. St. John’s College, Cam- bridge. *BussEMER, Sir Heyry, F.R.S. Denmark Hill, London, 8.E. {Best, William. Leydon-terrace, Leeds. Bethune, Admiral, C.B., F.R.G.S. Balfour, Fifeshire. *Bettany, G. T., M.A., B.Se., Lecturer on Botany at Guy’s Hospital, London, 8.E. *Bevan, Rey. James Oliver, M.A. 72 Beaufort-road, Edgbaston, Birmingham. tBeveridge, Robert, M.B. 36 King-street, Aberdeen. *Bevington, James B. Merle Wood, Sevenoaks, {Bewick, Thomas John, F.G.8. Haydon Bridge, Northumberland. *Bickerdike, Rev. John, M.A. Shireshead Vicarage, Garstang. tBickerton, A.W., F.C.S. Christchurch, Canterbury, New Zealand. {Bigger, Benjamin. Gateshead, Durham. {Biges, Robert. 16 Green Park, Bath. Bilton, Rev. William, M.A.,F.G.S8. United University Club, Suffolk- street, London, S.W. tBinder, W. J., B.A. Barnsley. Brynzy, Epwarp WittiaM, F.R.S., F.G.S. Cheetham Hill, Man- chester. : }Binns, J. Arthur. Manningham, Bradford, Yorkshire. 1879.§§Binns, E. Knowles. 216 Heavygate-road, Sheffield. LIST OF MEMBERS. 18 Year of Election. Birchall, Edwin, F.L.S. Douglas, Isle of Man. Birchall, Henry. College House, Bradford. 1880. §Bird, Henry, F'.C.S. South Down, near Devonport, 1866, *Birkin, Richard. Aspley Hall, near Nottingham. *Birks, Rev. Thomas Rawson, M.A., Professor of Moral Philosophy in the University of Cambridge. 6 Salisbury-villas, Cambridge. 1841, *Brar, Wintram Rancrirr, F.R.A.S. 3 Shrewsbury-villas, Water- lane, Stratford, E. 1871. *Biscuor, Gustav. 4 Hart-street, Bloomsbury, London, W.C. 1868. {Bishop, John. Thorpe Hamlet, Norwich. 1866. {Bishop, Thomas. Bramcote, Nottingham. 1877. {Biacurorp, The Right Hon. Lord, K.C.M.G. Cornwood, Ivy~ bridge. 1869. {Blackall, Thomas. 13 Southernhay, Exeter. 1834, Blackburn, Bewicke. 14 Victoria-road, Kensington, London, W. 1876, {Blackburn, Hugh, M.A. Roshven, Fort William, N.B. Blackburne, Rev. John, M.A. Yarmouth, Isle of Wight. Blackburne, Rey. John, jun., M.A. Rectory, Horton, near Chip- enham. 1877, tBlackie, J. Alexander. 17 Stanhope-street, Glasgow. 1859, {Blackie, John Stewart, M.A., Professor of Greek in the University of Edinburgh. 1876. {Blackie, Robert. 7 Great Western-terrace, Glasgow. 1855, *Brackxiz, W. G., Ph.D., F.R.G.S. 17 Stanhope-street, Glasgow, 1870, {Blackmore, W. Founder’s-court, Lothbury, London, E.C. *BLACKWALL, Rey. Jonn, F.L.S. Hendre House, near Llanrwst, Denbighshire. 1878.§§Blair, Matthew. Oakshaw, Paisley. 1863. {Blake, C. Carter, D.Sc. Westminster Hospital School of Medi~ cine, Broad Sanctuary, Westminster, S.W. 1849, *Braxrn, Henry Wottaston, M.A., F.R.S., F.R.G.S. 8 Devonshire- place, Portland-place, London, W. 1846. *Blake, William. Bridge House, South Petherton, Somerset. 1878.§§Blakeney, Rey. Canon, M.A., D.D. The Vicarage, Sheffield. 1861. §Blakiston, Matthew, F.R.G.S. 18 Wilton-crescent, London, S.W. 1869. {Blanford, W. T., F.R.S., F.G.S., F.R.G.S. Geological Survey of India, Calcutta. *BLOMEFIELD, Rey. Lronarp, M.A., F.L.S., F.G.S. 19 Belmont, Bath. 1878. tBlood, T. Lloyd. 1880. §Bloxam, G. W., M.A., F.L.S. 44 Dacre-park, Lee, Kent. 1870. {Blundell, Thomas Weld. Ince Blundell Hall, Great Crosby, Lan- cashire. 1859. {Blunt, Sir Charles, Bart. Heathfield Park, Sussex. 1859. {Blunt, Capt. Richard. Bretlands, Chertsey, Surrey. - Blyth, B. Hall. 135 George-street, Edinburgh. 1858. *Blythe, William. Holland Bank, Church, near Accrington. 1867. {Blyth-Martin, W. Y. Blyth House, Newport, Fife. 1870. {Boardman, Edward. Queen-street, Norwich. 1866. §Bogg, Thomas Wemyss. 2 East Ascent, St. Leonard’s. 1859, *Bonn, Hunry G., F.LS., F.R.A.S., F.R.G.S., F.S.S. North End House, Twickenham. 1871. {Bohn, Mrs. North End House, Twickenham. 1859. {Bolster, Rev. Prebendary John A. Cork. 1876, {Bolton, J.C. Carbrook, Stirling. Bolton, R. L. Laurel Mount, Aigburth-road, Liverpool. 1866, {Bond, Banks, Low Pavement, Nottingham, 44 LIST OF MEMBERS, _ Year of lection. 1871. 1866, 1861, 1861. 1876. 1880, 1861. 1849, 1876. 1863. 1876. 1867. 1872. 1868, 1871. 1876. 1870. 1868. 1866, 1872. 1870. 1867. 1856. 1880. 1863. 1869. 1863. 1871. 1865. 1872. 1869. 1870. 1880. 1861. 1842, 1857. 1863. Bond, Henry John Hayes, M.D. Cambridge. §Bonney, Rev. Thomas George, M.A., F.R.S., F.S.A., F.G.S., Pro- fessor of Geology in University College, London. St. John’s College, Cambridge. i tBooker, W. H. Cromwell-terrace, Nottingham. §Booth, James. Elmfield, Rochdale. *Booth, William. Hollybank, Cornbrook, Manchester. tBooth, William H. Trinity College, Oxford. §Boothroyd, Samuel. Warley House, Southport. *Borchardt, Louis, M.D. Barton Arcade, Manchester. Bora William W., F.R.A.S. The Mount, Haverhill, New- market. *Borland, William. 260 West George-street, Glasgow. {Borries, Theodore. Lovaine-crescent, Newcastle-on-Tyne. ecae ste a H.M., M.A., F.C.S., F.R.S.A. St. John’s College, Oxfor *Bossey, Francis, M.D. Mayfield, Oxford-road, Redhill, Surrey. §Botly, William, F.S.A. Salisbury House, Hamlet-road, Upper Norwood, London, 8.E. {Bottle, Alexander. Dover. tBottle, J. T. 28 Nelson-road, Great Yarmouth. *BorroMLEY, JAMES THOMSON, M.A., F.RS.E., F.C.S. 2 Hijow terrace, Hillhead, Glasgow. Bottomley, William. 14 Brunswick-gardens, Kensington, London; WwW tBottomley, William, jun. 14 Brunswick-gardens, Kensington, London, W TBoult, Swinton. 1 Dale-street, Liverpool. tTBoulton, W. 8. Norwich. § Bourne, STEPHEN, F.S.8. Abberley, Wallington, Surrey. — TBovill, William Edward. 29 James-street, Buckingham-gate, London, 8. W. tBower, Anthony. Bowersdale, Seaforth, Liverpool. tBower, Dr. John. Perth. *Bowlby, Miss F. E. 23 Lansdowne-parade, Cheltenham. §Bowly, Christopher. Cirencester. tBowman, R. Benson. Neweastle-on-Tyne. Bowman, William, F.R.S., F.R.C.S. 5 Clifford-street, London, WwW tBowring, Charles T. Elmsleigh, Prince’s-park, Liverpool. §Boyd, Edward Fenwick. Moor House, near Durham. {Boyd, Thomas J. 41 Moray-place, Edinburgh. tBortz, Rev. G. D. Soho House, Handsworth, Birmingham. *BraBrook, KE. W., F.S.A., Dir. A.D. 28 Abingdon-street, West- minster, S.W. *Braby, Frederick, F.G.S., F.C.S. Cathcart House, Cathcart-road, London, 8.W. {Brace, Edmund. 3 Spring-gardens, Kelvinside, Glasgow. Bracebridge, Charles Holt, F.R.G.S. The Hall, Atherstone, War- wickshire. §Bradford, H. Stretton House, Walters-road, Swansea. *Bradshaw, William. Slade House, Green-walk, Bowdon, Cheshire. *Brapy, Sir Anronzo, J.P., F.G.S. Maryland Point, Stratford, Essex, E. *Brady, Cheyne, M.R.IL.A. Trinity Vicarage, West Bromwich. Brady, Daniel F, M.D. 5 Gardiner’s-row, Dublin. {Brapy, GEORGE ie M.D., F.L.S., Professor of Natural History in LIST OF MEMBERS, 15 Year of Election. the College of Physical Science, Newcastle-on-Tyne, 22 Faw- cett-street, Sunderland. 1862. 1880. ‘1875. 1864. 1870. 1864. §Brapy, Henry Bowman, F.R.S., F.L.S., F.G.S. Hillfield, Gates- head *Brady, Rey. Nicholas, M.A. Wennington, Essex. {Bragge, William, F.S.A., F.G.S. Shirle Hill, Birmingham. §Braham, Philip, F.0.S. 6 George-street, Bath. {Braidwood, Dr. Delemere-terrace, Birkenhead. §Braikenridge, Rev. George Weare, M.A., F.L.S. Clevedon, Somerset. 1879.§§Bramley, Herbert. Claremont-crescent, Sheffield. 1865. 1872. 1867. 1861. 1852. 1857. 1869. 1873. 1868. 1877. 1860. 1866. 1875.§ 1867. 1870. 1870. 1879, 1870. 1866. 1866. 1863. 1870. 1868. 1879. 1879. 1878. 1859. 1834. 1865. 1253. 1878. 1880. 1855. 1864. 1855. 1878. 1863. §BRAMWELL, Freperick J.. M.1C.E., F.R.S. 37 Great George- street, London, 8. W. {Bramwell, Wiliam J. 17 Prince Albert-street, Brighton, tBrand, William. Milnefield, Dundee. *Brandreth, Rev. Henry. Dickleburgh Rectory, Scole, Norfolk. {Brazrer, James §., F.C.S., Professor of Chemistry in Marischal Col- lege and University of Aberdeen. {Brazill, Thomas. 12 Holles-street, Dublin. *BREADALBANE, The Right Hon. the Earl of. Taymouth Castle, N.B.; and Carlton Club, Pall Mall, London, S.W. {Breffit, Edgar. Castleford, near Normanton. TBremridge, Elias. 17 Bloomsbury-square, London, W.C. {Brent, Francis. 19 Clarendon-place, Plymouth. {Brett,G. Salford. {Brettell, Thomas (Mine Agent). Dudley. §Briant, T. Hampton Wick, Kingston-on-Thames. TBrmeman, WILLIAM KENcELEY. 69 St. Giles’s-street, Norwich. *Bridson, Joseph R.- Belle Isle, Windermere. {Brierley, Joseph, C.E. New Market-street, Blackburn. §Brierley, Morgan. Denshaw House, Saddleworth. *Briee, JoHn. Broomfield, Keighley, Yorkshire. *Briggs, Arthur. Orage Royd, Rawdon, near Leeds. {Briggs, Joseph. Barrow-in-Furness. *Bricut, Sir Cuartes Tusron, C.E., F.G.S., F.R.G.S., F.R.A.S. 20 Bolton-gardens, London, S.W. tBright, H. A., M.A., F.R.G.S. Ashfield, Knotty Ash. Brieut, The Right Hon. Jonn, M.P. Rochdale, Lancashire. tBrine, Commander Lindesay. Army and Navy Club, Pall Mall, London, S.W. §Brittain, Frederick. Taptonville-crescent, Sheffield. *Britrain, W. H. Storth Oaks, Ranmoor, Sheffield. {Britten, James, F.L.S. Department of Botany, British Museum, London, W.C. *BropHuRsI!, BERNARD Epward, F.R.C.S., F.L.S. 20 Grosvenor- street, Grosvenor-square, London, W. {Broprig, Rey. Jamzs, F.G.S. Monimail, Fifeshire. {Bropre, Rey. Perer Brerrencer, M.A., F.G.S. Rowington Vicar- age, near Warwick. {Bromby, J. H., M.A. The Charter House, Hull. *Brook, George, F.L.S. Fernbrook, Huddersfield, Yorkshire, §Brook, G. B. Brynsyfi, Swansea, {Brooke, Edward. Marsden House, Stockport, Cheshire, “Brooke, Rev. J. Ingham. Thornhill Rectory, Dewsbury. {Brooke, Peter William. Marsden House, Stockport, Cheshire. {Brooke, Sir Victor, Bart., F.L.S. Colebrook, Brookeborough, Co. Fermanagh. tBrooks, John Crosse. Wallsend, Newcastle-on-Tyne. 16 LIST OF MEMBERS, Year of Election. 1846. *Brooks, Thomas. Cranshaw Hall, Rawtenstall, Manchester. Brooks, William, Ordfall Hill, East Retford, Nottinghamshire. 1874. t{Broom, William. 20 Woodlands-terrace, Glasgow. 1847. tBroome, C. Edward, F.L.S. Elmhurst, Batheaston, near Bath. 1863. *Brown, ALEXANDER Crum, M.D., F.R.S. L. & E., F.C.S., Professor of Chemistry in the University of Edinburgh. 8 Belgrave- crescent, Edinburgh. 1867. {Brown, Charles Gage, M.D. 88 Sloane-street, London, S.W. 1855. {Brown, Colin. 192 Hope-street, Glasgow. 1871.§§Brown, David. 93 Abbey-hill, Edinburgh. 1863. *Brown, Rey. Dixon. Unthank Hall, Haltwhistle, Carlisle. 1870. §Brown, Horace T. The Bank, Burton-on-Trent. Brown, Hugh. Broadstone, Ayrshire. 1870. *Brown, J. Campsett, D.Sc., F.0.S. Royal Infirmary School of Medicine, Liverpool. 1876. {Brown, John. Edenderry House, Belfast. : 1859. t{Brown, Rev. John Crombie, LL.D., F.L.S. Berwick-on-Tweed. 1874. {Brown, John S, Edenderry, Shaw’s Bridge, Belfast. 1863. {Brown, Ralph. Lambton’s Bank, Newcastle-on-Tyne. 1871. {Brown, Rosert, M.A., Ph.D., F.LS., F.R.G.S, 26 Guildford- road, Albert-square, London, 8.W. 1868, {Brown, Samuel. Grafton House, Swindon, Wilts. *Brown, Thomas. Evesham Lawn, Pittville, Cheltenham. *Brown, William. 11 Maiden-terrace, Dartmouth Park, London, N. 1855. {Brown, William. 33 Berkeley-terrace, Glasgow. 1850. {Brown, William, F.R.S.E. 25 Dublin-street, Edinburgh. 1865, {Brown, William. 414 New-street, Birmingham. 1879.§§Browne, J. Crichton, M.D., LL.D., F.R.S.E. 7 Cumberland-terrace, Regent’s Park, London, N.W. 1866. *Browne, Rev. J. H. Lowdham Vicarage, Nottingham. 1862. *Browne, Robert Clayton, jun., B.A. Browne's Hill, Carlow, Ive- land. 1872. LTS R. Mackley, F.G.S. Northside, St. John’s, Sevenoaks, ent, - 1875. t{Browne, Walter R. Bridgwater. 1865. *Browne, William, M.D. The Friary, Lichfield. 1865. {Browning, John, F.R.A.S. 111 Minories, London, E. 1855. {Brownlee, James, jun. 30 Burnbank-gardens, Glasgow. 1863. *Brunel, H. M. 23 Delahay-street, Westminster, S.W. 1863. {Brunel, J. 23 Delahay-street, Westminster, S.W. 1875. *Brunlees, James, C.K., F.G.S. 5 Victoria-street, Westminster, S.W. 1875. tBrunlees, John. 5 Victoria-street, Westminster, S.W. 1868. {Brunton, T. Lauper, M.D., F.R.S. 50 Welbeck-street, London, WwW 1878. §Brutton, Joseph. Yeovil. 1877. {Bryant, George. 82 Claverton-street, Pimlico, London, 8S. W. 1875. {Bryant, G. Squier. 15 White Ladies’-road, Clifton, Bristol. 1875. {Bryant, Miss 8. A. The Castle, Denbigh. 1861. {Bryce, James. York-place, Higher Broughton, Manchester. Bryce, Rey. R. J., LL.D., Principal of Belfast Academy. Belfast. 1859, {Bryson, William Gillespie. Cullen, Aberdeen. 1867, {BuccLEvcH AND QuEENSBERRY, His Grace the Duke of, K.G.,D.C.L., FE.RS. L. & E., F.L.S. Whitehall-gardens, London, S.W. ; and Dalkeith House, Edinburgh. 1871. §BucHan, ALEXANDER, M.A., F.R.S.E., Sec. Scottish Meteorological Society, 72 Northumberland-street, Edinburgh. LIST OF MEMBERS. pad Year of Election. 1867. tBuchan, Thomas. Strawberry Bank, Dundee. Bucwanan, ANDREW, M.D., Professor of the Institutes of Medicine in the University of Giasgow. 4 Ethol-place, Glasgow. Buchanan, Archibald. Catrine, Ayrshire. Buchanan, D. C. Poulton-cum-Seacombe, Cheshire. 1871. {Buchanan, John Young. 10 Moray-place, Edinburgh. 1864, §Buckir, Rev. Grorar, M.A. The Rectory, Weston-super- Mare. 1865. *Buckley, Henry. 27 Wheeley’s-road, Edgbaston, Birmingham. 1848. *Bucxman, Professor James, F.L.S., F.G.S. Bradford Abbas, Sher- borne, Dorsetshire. 1880. §Buckney, Thomas, F.R.A.S. Little Thurlow, Suffolk. 1869. {Bucknill, J.C., M. D., F.R.S. 39 Wimpole-street, London, W. 1851. *Buckron, GuorGE Bowbter, FE.R.S., F.L.S., F.C.S. Weycombe, Haslemere, Surrey. 1848. *Bupp, James Parmer. Ystalyfera Iron Works, Swansea. 1875. §Budgett, Samuel. Cotham House, Bristol. 1871. {Bulloch, Matthew. 11 Park-circus, Glasgow. 1845. *Bunzury, Sir Coarrtes James Fox, Bart., E.R.S., F.L.S., F.G.S., F.R.G.S. Barton Hall, Bury St. Edmunds. 1865. {Bunce, John Mackray. ‘ Journal’ Office, New-street, Birming- ham 1863. §Bunning, T. Wood. Institute of Mining and Mechanical Engineers, Neweastle-on-Tyne. 1842. *Burd, John. 5 Gower-street, London, W.C. 1875. {Burder, John, M.D. 7 South-parade, ’Bristol. 1869. {Burdett-Coutts, Baroness. Stratton-street, Piccadilly, London, W. 1874. {Burdon, Henry, M.D. Clandeboye, Belfast. 1876. {Burnet, John. 14 Victoria-crescent, Dowanhill, Glasgow. 1859. {Burnett, Newell. Belmont-street, Aberdeen. -1877. {Burns, David, C.E. Alston, Carlisle. 1860. {Burrows, Montague, M.A., Professor of Modern History, Oxford. 1877. {Burt, J. Kendall. Kendal. 1874. {Burt, Rev. J.T. Broadmoor, Berks. 1866. *Burtoy, FREDERICK M., F.G. 8. Highfield, Gainsborough. 1879.§§Bury, Percy B. Cambridge. 1864. {Bush, W. 7 Circus, Bath. Bushell, Christopher. Royal Assurance-buildings, Liverpool. 1855. *Busx, GEORGE, FE.R.S., F.LS8., F.G.8. 382 Harley-street, Caven- dish-square, London, W. 1878. {Burcusr, J. G., M.A. 22 Coilingham-place, London, 8. W. 1872. {Buxton, Charles Louis. Cromer, Norfolk. 1870. {Buxton, David, Ph.D. 1 Nottincham-place, London, W 1868. {Buxton, 8. Gurney. Catton Hall, Norwich. 1872. {Buxton, Sir T. Fowell, Bart. Warlies, Waltham Abbey, Essex. 1854. {Byertry, Isaac, F.L. 8. Seacombe, Liverpool. Byng, William Bateman. 2 Bank-street, Ipswich. 1852. {By rne, Very Rev. James. Ergenagh Rectory, Omagh. 1875. §Byrom, W. Ascroft, F.G.S. 31 King-street, Wigan, 1858.§§Cail, John. Stokesley, Yorkshire. 1863. {Cail, Richard. Beaconsfield, Gateshead. 1858. *Cuine, Rev. William, M.A. Christ Church Rectory, Denton, near Manchester. 1863. {Caird, Edward. Finnart, Dumbartonshire. 1876. {Caird, Edward B. 8 Scotland-street, Glasgow. 1861. *Caird, James Key. 8 Magdalene-road, Dundee. 18 Year of Election. 1855. 1875. 1877. 1868. 1868. 1857. 1855. 1876. 1857. 1870. 1857. 1874. 1876, 1872. 1859. 1871. 1876. 1862. 1868. 1880. 1873. 1877. 1876. 1861. 1867. 1867. 1876. 1871. 1871. 1854. 1845. 1872. 1842. 1867. 1861. 1857, LIST OF MEMBERS. *Caird, James Tennant. LBelleaire, Greenock. {Caldicott, Rev. J. W., D.D. The Grammar School, Bristol. {Caldwell, Miss. 2 Victoria-terrace, Portobello, Edinburgh. Caley, A. J. Norwich. Caley, W. Norwich. tCallan, Rev. N. J., Professor of Natural Philosophy in Maynooth College. tCalver, Captain E. K., R.N., F.R.S. The Grange, Redhill, Surrey. {Cameron, Charles, M.D., LL.D., M.P. 1 Huntly-gardens, Glasgow. {Cameron, CHartes A., M.D. 15 Pembroke-road, Dublin. {Cameron, John, M.D. 17 Rodney-street, Liverpool. *Camphell, Dugald, F.C.S. 7 Quality-court, Chancery-lane, London, W.C *CAMPBELL, Sir Grore®, K.C.8.1, M.P., D.C.L., F.R.G.S. 13 Corn- wall-gardens, South Kensington, London, S8.W.; and Eden- wood, Cupar, Fife. Campbell, Sir Hugh P. H., Bart. 10 Hill-street, Berkeley-square, London, W.; and Marchmont House, near Dunse, Berwick- shire. ; {Campbell, James A. 3 Claremont-terrace, Glasgow. Campbell, John Archibald, M.D., F.R.S.E. Albyn-place, Edinburgh. {CampseLt, Rev. J. R., D.D. 5 Eldon-place, Manningham-lane, Bradford, Yorkshire. {Campbell, William. Dunmore, Argyllshire. {tCampbell, William Hunter, LL.D. Georgetown, Demerara, British Guiana, (Messrs. Ridgway & Sons, 2 Waterloo-place, London, S.W.) CampBELL-JoHNston, ALEXANDER Ropert, F.R.S. 84 St.George’s- square, London, 8. W. §Campion, Frank, F.G.8., F.R.G.S. The Mount, Duffield-road, Derby. *Campron, Rev. Dr. Wint1AmM M. Queen’s College, Cambridge. *Cann, William. 9 Southernhay, Exeter. §Capper, Robert. Cwm Donkin, Swansea. *Carbutt, Edward Hamer, M.P., C.E. St. Ann’s, Burley, Leeds, Yorkshire. *Carew, William Henry Pole. Antony, Torpoint, Devonport. tCarkeet, John, C.E. 3 St. Andrew’s-place, Plymouth. {Carlile, Thomas. 5 St. James’s-terrace, Glasgow. CaRLIsLE, The Right Rev. Harvey Goopwin, D.D., Lord Bishop of. Carlisle. {Carlton, James. Mosley-street, Manchester. {Carmichael, David (Engineer). Dundee. {Carmichael, George. 11 Dudhope-terrace, Dundee. {Carmichael, Neil, M.D. 22 South Cumberland-street, Glasgow. {CARPENTER, CHARLES. Brunswick-square, Brighton. *Carpenter, P. Herbert, M.A. Eton College, Windsor. {Carpenter, Rev. R. Lant, B.A. Bridport. {Oarpenter, WILLIAM B., C.B., M.D., LL.D., F.RB.S., F.L.S., F.G.S. 56 Regent’s Park-road, London, N. W. §CARPENTER, WiLLIAM Lant, B.A., B.Sc., F.C.S. Winifred House, Pembroke-road, Clifton, Bristol. *Carr, William, M.D., F.LS., F.R.CS. Lee Grove, Blackheath, London, S.£. {CarrutHers, WitiiaM, F.R.S., F.L.S., F.G.8. British Museum, London, W.C. *Carson, Rev. Joseph, D.D., M.R.LA. 18 Fitzwilliam-place, Dublin. {tOarre, ALExanpER, M.D. Museum of Science and Art, Dublin. LIST OF MEMBERS, 19 “Year of “Election. 1868. {Oarteighe, Michael, F.C.S. 172 New Bond-street, London, W. 1866. {Carter, H. H. The Park, Nottingham. 1855, {Carter, Richard, C.E., F.G.S. Cockerham Hall, Barnsley, Yorkshire, 1870. {Carter, Dr. William. 62 Elizabeth-street, Liverpool. *CARTMELL, Rev. Jams, D.D., F.G.S., Master of Christ’s College. Christ College Lodge, Cambridge. 1878.§§Cartwright, H. S., LL.B. Magherafelt Manor, Co. Derry. 2870. §Cartwricht, Joshua, A.I.C.E., Borough Surveyor. Bury, Lancashire. 1862. {Carulla, Facundo, F.A.S.L. Care of Messrs. Daglish and Oo., 8 Harrington-street, Liverpool. 1868. {Cary, Joseph Henry. Newmurket-road, Norwich. 1866, {Casella, L. P., F.R.A.S. 147 Holborn Bars, London, E.C. 1878. {Casey, John, LL.D., F.R.S., M.R.I.A., Professor of Higher Mathe- matics in the Catholic University of Ireland. 2 Iona-terrace, South Circular-road, Dublin. 1871. {Cash, Joseph. Bird-grove, Coventry. 1873. *Cash, William, F.G.S. 38 Elmfield-terrace, Saville Park, Halifax. Castle, Charles. Clifton, Bristol. 1874. {Caton, Richard, M.D., Lecturer on Physiology at the Liverpool j Medical School. 184 Abercromby-square, Liverpool. 1853. tCator, John B., Commander R.N. 1 Adelaide-street, Hull. 1859, {Catto, Robert. 44 King-street, Aberdeen. 1873. *Cavendish, Lord Frederick, M.P. 21 Carlton House-terrace, London, S.W 1849, {Cawley, Charles Edward. The Heath, Kirsall, Manchester. 1860. §CayLey, Anruur, LL.D., F.R.S., V.P.R.A.S., Sadlerian Professor of Mathemathics in the University of Cambridge. Garden House, Cambridge. Cayley, Digby. Brompton, near Scarborough. Cayley, Edward Stillingfleet. Wydale, Malton, Yorkshire. ‘1871. *Cecil, Lord Sackville. Hayes Common, Beckenham, Kent. 1879. §Chadburn, Alfred. Brincliffe Rise, Sheffield. 1870. {Chadburn, C. H. Lord-street, Liverpool. 1858. *Chadwick, Charles, M.D, Lynncourt, Broadwater Down, Tunbridge Wells. 1860. {CHapwick, Davip, M.P. The Poplars, Herne Hill, London, S.E. 1842, Onapwicxr, Epwin, C.B. Richmond, Surrey. 1859. {Chadwick, Robert. Highbank, Manchester. 1861. {Chadwick, Thomas. Wilmslow Grange, Cheshire. *Cuattis, Rev. Jamus, M.A., F.R.S., F.R.A.S., Plumian Professor of - Astronomy in the University of Cambridge. 2 Trumpington- street, Cambridge. 1859. {Chalmers, John Inglis. Aldbar, Aberdeen. 4865. {CHAMBERLAIN, J.H. Christ Church-buildings, Birmingham, 1868. t Chamberlain, Robert. Catton, Norwich. 1842. Chambers, George. High Green, Sheffield. 1868. {Chambers, W. O. Lowestoft, Suffolk. 1877. *Champernowne, Arthur, M.A., F.G.S. Dartington Hall, Totnes, Devon. *Champney, Henry Nelson. 4 New-street, York. 1865. {Chance, A. M. Edgbaston, Birmingham. 1865. *Chance, James T. 51 Prince’s-gate, London, 8. W. 1865. {Chance, Robert Lucas. Chad Hill, Edgbaston, Birmingham. 1861. *Chapman, Edward, M.A., F.L.S., F.C.S.__Frewen Hall, Oxford. 1877. §Chapman, T. Algernon, M.D. Burghill, Hereford. 4866, {Chapman, William. The Park, Nottingham. B 2 20 LIST OF MEMBERS. Year of Election. 1871:§§Chappell, William, F.S.A. Strafford Lodge, Oatlands Park, Wey= 1874. 1871. 1836. 1874. 1865. 1866. 1867. 1864. 1874, 1879. ridge Station. {Charles, John James, M.A., M.D. 11 Fisherwick-place, Belfast. tCharles, T. C., M.D. Queen's College, Belfast. OHARLESWORTH, EpwarD, F.G.S. 277 Strand, London, W.C. {Charley, William. Seymour Hill, Dunmurry, Ireland. {Charlton, Edward, M.D. 7 Eldon-square, Newcastle-on-Tyne. {Cuarnock, Richarp SrepHeN, Ph.D., F.S.A., F.R.G.S. Junior Garrick Club, Adelphi-terrace, London, W.C. Chatto, W. J. P. Union Club, Trafalgar-square, London, 8.W. *Chatwood, Samuel. 5 Wentworth-place, Bolton. {Cueapiz, W.B., M.A., M.D., F.R.G.S. 2 Hyde Park-place, Cum= berland-gate, London, S.W. *Chermside, Lieutenant H.C., R.E. Care of Messrs. Cox & Co., Craig’s-court, Charing Cross, London, 8.W. *Chesterman, W. Broomsgrove-road, Sheffield. 1879.§§Cheyne, Commander J. P., R.N. 1 Westgate-terrace, West Bromp-. 1860. 1857. 1868. 1863. ton, London, 8.W. . §CuicHEstTER, The Right Hon. the Earl of _Stanmer House, Lewes. Cuicurstrr, The Right Rev. Rrcwarp Durnrorp, D.D., Lord Bishop of. Chichester. . *Child, Gilbert W., M.A., M.D., F.L.S. Cowley House, Oxford. . *Chiswell, Thomas. 17 Lincoln-grove, Plymouth-grove, Manchester. . {Cholmeley, Rey. C. H. Dinton Rectory, Salisbury. . tChristie, John, M.D. 46 School-hill, Aberdeen. . {Christie, Professor R. C., M.A. 7 St. James’s-square, Manchester. Curistison, Sir Rosert, Bart., M.D., D.C.L., F.R.S.E., Professor: of Dietetics, Materia Medica, and Pharmacy in the University of Edinburgh. Edinburgh. : Besar a George, F.C.S. 8 Rectory-grove, Clapham, London, . *Curystat, G., B.A., Professor of Mathematics. 15 Chalmers- street, Edinburgh. . §CaurcH, A. H., M.A., F.C.S., Professor of Chemistry to the Royal Academy of Arts, London. Royston House, Kew, Surrey. tChurch, William Selby, M.A. St. Bartholomew's Hospital, London, E.C. Churchill, F.,M.D. Ardtrea Rectory, Stewartstown, Co, Tyrone. TClabburn, W. H. Thorpe, Norwich. tClapham, Henry. 5 Summerhill-grove, Newcastle-on-Tyne. 1855.§§CLapHAm, Ropert Catvert. Earsdon House, Earsdon, Newcastle 1869. 1857. 1859. 1877. 1876. 1876. 1861. 1855. 1865. 1875. 1872. on-Tyne. tClapp, Frederick. 44 Magdalen-street, Exeter. ‘-{Clarendon, Frederick Villiers. 1 Belvidere-place, Mountjoy-square,. Dublin. {Clark, David. Coupar Angus, Fifeshire. *Clark, F. J. 20 Bootham, York. Clark, G.T. 44 Berkeley-square, London, W. tClark, George W. Glasgow. tClark, Dr. John. 138 Bath-street, Glasgow. ua Sess 5 Westminster-chambers, Victoria-street, London, Ae tClark, Rev. William, M.A. Barrhead, near Glasgow. {Clarke, Rev. Charles. Charlotte-road, Edgbaston, Birmingham. tClarke, Charles S. 4 Worcester-terrace, Clifton, Bristol. Clarke, George. Mosley-street, Manchester. *CLARKE, Hypr. 32 St. George’s-square, Pimlico, London, S.W. LIST OF MEMBERS. 2) ‘Year of ‘Election. 1875. {Cruarkz, Jonn Henry, 4 Worcester-terrace, Clifton, Bristol. 1861. *Clarke, John Hope. Lark Hill House, Edgeley, Stockport. 1877. {Clarke, Professor John W. University of Chicago, Illinois. 1851. {Ciarxs, JosHua, F.L.S. Fairycroft, Saffron Walden. Clarke, Thomas, M.A. Knedlington Manor, Howden, Yorkshire, 1861. {Clay, Charles, M.D. 101 Piccadilly, Manchester. *Clay, Joseph Travis, F.G.S. Rastrick, near Brighouse, Yorkshire. 1856. *Clay, Colonel William, The Slopes, Wallasea, Cheshire. 1866. {Clayden, P. W. 13 Tavistock-square, London, W.C. 1850. {CrecHorN, Huen,M.D.,F.L.S. Stravithie, St. Andrews, Scotland. 1859. {Cleghorn, John. Wick. 1875. {Clegram, T. W. B. Saul Lodge, near Stonehouse, Gloucester- shire. 1861. §CieLanp, Jonny, M.D., F.R.S., Professor of Anatomy in the Univer- sity of Glasgow. 2 College, Glasgow. 1857. tClements, Henry. Dromin, Listowel, Ireland. tClerk, Rev. D. M. Deverill, Warminster, Wiltshire. 1873. §Cliff, John, F.G.S. Limeburn, Ilkley, near Leeds. 1861. *OCxirron, R. Bettany, M.A., F.R.S., F.R.A.S., Professor of Experi- mental Philosophy in the University of Oxford. Tortland Lodge, Park Town, Oxford. Clonbrock, Lord Robert. Clonbrock, Galway. 1854. tClose, The Very Rev. Francis, M.A. Carlisle. 1878. §§Close, Rev. Meese H., F.G. 8. 40 Lower Raggot-street, Dublin. 1866. §CLosr, THomas, F.S.A. St. James’s-street, Nottingham. 1873. {Clough, John. Bracken Bank, Keighley, Yorkshire. 1859. {Clouston, Rey. Charles. Sandwick, Orkney. 1861. *Clouston, Peter. 1 Park Terrace, Glasgow. 1863. *Clutterbuck, Thomas. Warkworth, Acklington. 1868. {Coaks, J. B. Thorpe, Norwich. 1855. *Coats, Sir Peter. Woodside, Paisley. 1855. *Coats, Thomas. Fergeslie Ilouse, Paisley. Cobb, Edward. 13 Great Bedford-street, Bath. 1851. *Cossotp, Jonn CuEvaLiier. Holywells, Ipswich ; and Atheneum Club, London, 8.W. 1864. {Copzpotp, T. Spencer, M.D., F.R.S., F.L.S., Professor of Botany and Helminthology in the Royal Veterinary College, London. 74 Portsdown-road, Maida Hill, London, W. 1864, *Cochrane, James Henry. Monmouth House, Wellington-terrace, Clevedon, Somersetshire. 1861. *Coe, Rey. Charles C,, F.R.G.S. Highfield, Manchester-road, Bolton. 1865. {Coghill, H. Newcastle-under-Lyme. 1876. {Colbourn, E. Rushton. 5 Marchmont-terrace, Hillhead, Glasgow. 1853. {Colchester, William, F.G.S. Springfield House, Ipswich. 1868. {Colchester, W. P. Bassingbourn, Royston. 1879.§§Cole, Skelton. 387 Glossop-road, Shettield. ‘1876. {Colebrooke, Sir T. E., Bart., M.P., F.R.G.S. 14 South-street, Park- lane, London, W.; and Abington House, Abington, N.B. .1860. {Coleman, J. J., F.C.S. 69 St. George’s-place, Glasgow. 1878.§§Coles, John, Curator of the Map Collection R.G.S. 1 Savile-row, London, W. 1854. *Colfox, William, B.A. Westmead, Bridport, Dorsetshire. 1857. {Colles, William, M.D. 21 Stephen’s-green, Dublin. 1869. {Collier, W. F. Woodtown, Horrabridge, South Devon. 1854. {CoLtinewoop, Curnpert, M.A., M.B., F.L.S. 4 Grove-terrace, Belvedere-road, Upper Norwood, Surrey, 8.E. 22 Year of Election. 1861. 1865. 1876. 1876. 1868. 1870. 1874. 1846. 1852. 1871. 1876. 1876. 1868. 1868. 1878. 1859, 1865. 1863. 1869. 1850. 1879. 1875. 1868. 1846. 1878. 1868. 1863. 1842. 1855. 1870. 1857. 1855. 1874. 1864. 1869. 1879. 1876. 1876. 1874. LIST OF MEMBERS. *Collingwood, J. Frederick, F.G.S. Anthropological Institute, 4 St. Martin’s-place, London, W.C. *Collins, James Tertius. Churchfield, Edgbaston, Birmingham. §Cotzins, J. H., F.G.S. 57 Lemon-street, Truro, Cornwall. {Collins, William. 3 Park-terrace East, Glasgow. *Corman, J. J..M.P. Carrow House, Norwich; and 108 Cannon-. street, London, E.C. {Coltart, Robert. The Hollies, Aigburth-road, Liverpool. tCombe, James. Ormiston House, Belfast. *Compron, The Ven. Lord Atwrn, Dean of Worcester. The Deanery,. Worcester. *Compton, Lord William. 145 Piccadilly, London, W. t{Connal, Michael. 16 Lynedock-terrace, Glasgow. *Connor, Charles C. Hope House, College Park East, Belfast. tCook, James. 162 North-street, Glasgow. *Cooxr, ConraD W.,C.E. 5 Westminster Chambers, London, 8.W. tCooke, Rev. George H. Wanstead Vicarage, near Norwich. Cooke, James R., M.A. 73 Blessington-street, Dublin. Cooke, J. B. Cavendish-road, Birkenhead. {Cooxn, M. C., M.A. 2 Grosvenor-villas, Upper Holloway, London, N. {Cooke, Samuel, M.A., F.G.S. Poona, Bombay. Cooke, Rev. T. L., M.A. Magdalen College, Oxford. *Cooke, William Henry, M.A., Q.C., F.S.A. 42 Wimpole-street,. London, W.; and Rainthorpe Hall, Long Stratton. tCooksey, Joseph. West Bromwich, Birmingham. tCookson, N. C. Benwell Tower, Newcastle-on-Tyne. §Cooling, Edwin, F.R.G.S. Mile Ash, Derby. f{Coorrr, Sir Henry, M.D. 7 Charlotte-street, Hull. Cooper, James. 58 Pembridge-villas, Bayswater, London, W. §Cooper, Thomas. Rose Hill, Rotherham, Yorkshire. tCooper, T. T., F.R.G.S. Care of Messrs. King & Co., Cornhill, London, E.C. tCooper, W. J. The Old Palace, Richmond, Surrey. tCooper, William White, F.R.C.S. 19 Berkeley-square, London, W. {Cope, Rev. 8. W. Bramley, Leeds. {Copeman, Edward, M.D. Upper King-street, Norwich. {Coppin, John. North Shields. Corbett, Edward. Ravenoak, Cheadle-hulme, Cheshire. {Corbett, Joseph Henry, M.D., Professor of Anatomy and Physiology in Queen’s College, Cork. *CorFIELD, W. H., M.A., M.D., F.C.S., F.G.8., Professor of Hygiéne and Public Health in University College. 10 Bolton-row, Mayfair, London, W. Cory, Rev. Robert, B.D., F.C.P.S. Stanground, Peterborough. Cottam, George. 2 Winsley-street, London, W. {Cottam, Samuel. Brazenose-street, Manchester. {Cotterill, Rev. Henry, Bishop of Edinburgh. Edinburgh. *Cotterill, J. H., M.A., F.R.S., Professor of Applied Mechanics. Royal Naval College, Greenwich, S.E. {tOorron, General Freprrick C., R.E., C.S.I. 13 Longridge-road, Earl’s Court-road, London, 8. W. {Corron, Wittram. Pennsylvania, Exeter. §Cottrill, Gilbert I. Shepton Mallett, Somerset. tCouper, James. City Glass Works, Glasgow. {Couper, James, jun. City Glass Works, Glasgow. {Courtauld, John M. Bocking Bridge, Braintree, Essex. LIST OF MEMBERS. 25 Year of Election. 1865. (Courtauld, Samuel, F.R.A.S. 76 Lancaster-gate, London, W.; and Gosfield Hall, Essex. 1834. tCowan, Charles. 38 West Register-street, Edinburgh. 1876. {Cowan, J. B. 159 Bath-sireet, Glasgow. Oowan, John. Valleyfield, Pennycuick, Edinburgh. 1863. {Cowan, John A. Blaydon Burn, Durham. 1863. {Cowan, Joseph, jun. Blaydon, Durham. 1872. *Cowan, Thomas William. Comptons Lea, Horsham. 1873. *Cowans, John. Cranford, Middlesex. Cowie, The Very Rev. Benjamin Morgan, M.A., B.D., Dean of Man- chester. The Deanery, Manchester. 1871. {Cowper, C. E. 3 Great George-street, Westminster, 8. W. 1860. {Cowper, Edward Alfred, M.I.C.E. 6 Great George-street, West- minster, 8S. W. 1867. *Cox, Edward. 18 Windsor-street, Dundee. 1867. *Cox, George Addison. Beechwood, Dundee. 1867. {Cox, James. Clement Park, Lochee, Dundee. 1870. *Cox, James. 8 Falkner-square, Liverpool. 1867. *Cox, Thomas Hunter. Duncarse, Dundee. 1867. {Cox, William. Foggley, Lochee, by Dundee. 1866. *Cox, William H. 50 Newhall-street, Birmingham. 1871. {Cox, Wiliam J. 2 Vanburgh-place, Leith. Craig, J. T. Gibson, F.R.S.E. 24 York-place, Edinburgh. 1876. {Cramb, John. Larch Villa, Helensburgh, N.B. 1857. {Crampton, Rev. Josiah. Nettlebeds, near Oxford. 1879.§§Crampton, Thomas Russell. _ 13 Victoria-street, London, S.W. 1858. {Cranage, Edward, Ph.D. The Old Hall, Wellington, Shropshire. 1876. {Crawford, Chalmond, M.P. Ridemon, Crosscar. 1871. *Crawford, William Caldwell, M.A. Hobart House, Eskbank, near Edinburgh. 1871. {Crawshaw, Edward. Burnley, Lancashire. 1870. *Crawshay, Mrs. Robert. Cathedine, Bwlch, Breconshire. 1879.§§Creswick, Nathaniel. Handsworth Grange, near Sheffield. 1876. *Crewdson, Rev. George. St. George’s Vicarage, Kendal. Creyke, The Venerable Archdeacon. Bolton Percy Rectory, Tad- caster. 1880. *Crisp, Frank, B.A., LL.B. 5 Lansdowne-road, Notting Hill, Lon- don, W. 1858. {Crofts, John. Hillary-place, Leeds. 1878. §Croke, John O’Byrne, M.A. The French College, Blackrock; and 79 Strand-road, Sandymount, Dublin. 1859. {Croll, A. A. 10 Coleman-street, London, E.C. 1857. {Crolly, Rev. George. Maynooth College, Ireland. 1866, {Cronin, William. 4 Brunel-terrace, Nottingham. 1870. {Crookes, Joseph. Marlborough House, Brook Green, Hammersmith, London, W. 1865. §Crooxrs, Wittram, F-.R.S., F.C.S. 7 Kensington Park-gardens, London, W. 1879.§§Crookes, Mrs. 7 Kensington Park-gardens, London, W. 1855. {Cropper, Rev. John. Wareham, Dorsetshire. 1870. {Crosfield, C. J. 16 Alexandra-drive, Prince’s Park, Liverpool. 1870. {Crosfield, William, sen. Annesley, Aigburth, Liverpool. 1870. *Crosfield, William, jun. 16 Alexandra-drive, Prince’s Park, Liver- pool. 1861. {Cross, Rev. John Edward, M.A. Appleby Vicarage, near Brigg. 1868. {Crosse, Thomas William. St. Giles’s-street, Norwich. 24 LIST OF MEMBERS. Year of Election. 1867. §CRossKEY, Rev. H. W., F.G.S. 28 George-road, Edgbaston, Bir mingham. 1853. {Crosskill, William, C.E. . Beverley, Yorkshire. 1870. *Crossley, Edward, F.R.A.S. Bemerside, Halifax, 1871. {Crossley, Herbert. Broomfield, Halifax. 1866, *Crossley, Louis J., F.M.S. Moorside Observatory, near Halifax. 1861. §Crowley, Henry. Trafalgar-road, Birkdale Park, Southport. 1863. {Cruddas, George. Elswick Engine Works, Newcastle-on-Tyne. 1860. {Cruickshank, John. City of Glasgow Bank, Aberdeen. 1859. {Cruickshank, Provost. Macduff, Aberdeen. 1873. {Crust, Walter. Hiall-street, Spalding. Culley, Robert. Bank of Ireland, Dublin. 1878. §Culverwell, Joseph Pope. St. Lawrence Lodge, Sutton, Dublin. 1859. {Cumming, Sir A. P. Gordon, Bart. Altyre. 1874. {Cumming, Professor. 33 Wellington-place, Belfast. 1861. *Cunliffe, Edward Thomas. The Elms, Handforth, Manchester. 1861. *Cunliffe, Peter Gibson. The Elms, Handforth, Manchester. 1877. {Cunningham, D. J., M.D. University of Edinburgh. 1852. {Cunningham, John. Macedon, near Belfast. 1869. {CunnineHamM, Ropert O., M.D., F.L.S., Professor of Natural His- tory in Queen’s College, Belfast. 1855, {Cunningham, William A. 2 Broadwalk, Buxton. 1850, {Cunningham, Rey. William Bruce. Prestonpans, Scotland. 1866. {Cunnington, John, 68 Oakley-square, Bedford New Town, London, N.W 1867. *Cursetjee, Manockjee, F.R.G.S., Judge of Bombay. Villa-Byculla, Bombay. 1857. {Curtis, Professor ArtHur Hitt, LL.D. Queen’s College, Galway. 1878. §Curtis, William. Caramore, Sutton, Co. Dublin. 1863, {Daglish, John. Hetton, Durham. 1854, {Daglish, Robert, C.E. Orrell Cottage, near Wigan. 1863. TDale, J.B. South Shields. -1853. {Dale, Rev. P. Steele, M.A. Hbllingfare, Warrington. 1865. {Dale, Rev. R. W. 12 Calthorpe-street, Birmingham. 1867. {Dalgleish, W. Dundee. 1870. {Dallinger, Rey. W. H., F.R.S. The Parsonage, Woolton, Liverpool, Dalmahoy, James, F.R.S.E. 9 Forres-street, Edinburgh. 1859. {Dalrymple, Charles Elphinstone. West Hall, Aberdeenshire. 1859. {Dalrymple, Colonel. Troup, Scotland. Dalton, Edward, LL.D., F.S.A. Dunkirk House, Nailsworth. *Dalton, Rev. J. E., B.D. Seagrave, Loughborough. Dalziel, John, M.D. Holm of Drumlanrig, Thornhill, Dumfries- shire. 1862. {Dansy, T. W. Downing College, Cambridge. 1859. {Dancer, J. B., F.R.A.S. Old Manor House, Ardwick, Manchester. 1876, {Dansken, John. 4 Eldon-terrace, Partickhill, Glasgow. 1849, *Danson, Joseph, F.C.S. Montreal, Canada. 1861, *DarBIsHIRE, RopERT DUKINFIELD, B.A.,F.G.S. 26 George-street, Manchester. 1876, {Darling, G. Erskine. 247 West George-street, Glasgow. Darwin, Cartes R., M.A., F.R.S., F.L.S., F.G.S., Hon. F.R.S.E. and M.R.I.A. Down, near Bromley, Kent. 1878. §Darwin, Horace. Down, near Bromley, Kent. 1848, aaa? Johnson. Burntwood, Wandsworth Common, London, LIST OF MEMBERS. 25 ‘Year of lection. 1878. 1872. {D’Aulmay, G. 22 Upper Leeson-street, Dublin. tDavenport, John T, 64 Marine Parade, Brighton. 1870, {Davidson, Alexander, M.D. 8 Peel-street, Toxteth Park, Liverpool. 1859. {Davidson, Charles. Grove House, Auchmull, Aberdeen. 1871. {Davidson, James. Newbattle, Dalkeith, N.B. 1859. {Davidson, Patrick. Inchmarlo, near Aberdeen. 1872. {Davipson, THomas, F.R.S., F.G.S. 3 Leopold-road, Brighton. 1875. {Davies, David. 2 Queen’s-square, Bristol. ; 1870. {Davies, Edward, F.C.S. Royal Institution, Liverpool. 1842. Davies-Colley, Dr. Thomas. Newton, near Chester. 1873. *Davis, Alfred. 5 Westminster Chambers, London, S.W. 1870. *Davis, A.S. 12 Suffolk-square, Cheltenham. 1864, {Davis, Cuartzs E., F.S.A. 55 Pulteney-street, Bath. 1873 Davis, Rey. David, B.A. Lancaster. . “Davis, James W., F.G.S., F.S.A. Chevinedge, near Halifax, 1856. *Davis, Sir Jouw Francis, Bart., K.O.B., F.R.S., F.R.G.S. Holly- wood, near Compton, Bristol. 1859. {Davis, J. Barnarp, M.D., F.R.S., F.S.A. Shelton, Hanley, Staf- fordshire. 1859. *Davis, Richard, F.L.S. 9 St. Helen’s-place, London, E.C. 1873. 1864. 1857. 1869, 1869. 1854. 1860. 1864. 1855. 1859. 1879. 1871. 1870. 1861. 1859. 1861. 1870. 1866. 1878. 1854, 1879. 1870 18765 {Davis, William Samuel. 1 Cambridge Villas, Derby. *Davison, Richard, Beverley-road, Great Driffield, Yorkshire. {Davy, Epmunp W., M.D. Kimmage Lodge, Roundtown, near Dublin. tDaw, John. Mount Radford, Exeter, tDaw, R. M. Bedford-circus, Exeter. *Dawbarn, William. Elmswood, Aigburth, Liverpool. Dawes, John Samuel, F.G.S. Lappel Lodge, Quinton, near Bir- mingham. *Dawes, John T., jun. Lilanferris, Mold, North Wales. Dawkins, W. Boyp, M.A., F.R.S., F.G.S., F.S.A., Professor of Geology in Owens College, Manchester. Birchview, Norman- road, Rusholme, Manchester. Dawson, John. Barley House, Exeter. {Dawson, Joun W., M.A., LL.D., F.R.S., F.G.S., Principal-of M‘Gill College, Montreal, Canada. See Captain William G. Plumstead Common-road, Kent, E §Day, Francis. Kenilworth House, Cheltenham. fDay, Sr. Jomn Vincent, G.E., F.R.S.E. 166 Buchanan-street, Glasgow. §Dracon, G. F., M.LC.E. Rock Ferry, Liverpool. {Deacon, Henry. Appleton House, near Warrington. Dean, David. Banchory, Aberdeen. }{Dean, Henry. Colne, Lancashire. *Deane, Rev. George, B.A., D.Sc., F.G.S. Spring Hill College, Moseley, near Birmingham. {Desvus, Hetyricu, Ph.D., F.R.S., F.C.S., Lecturer on Chemistry at Guy’s Hospital, London, 8.E. §Delany, Rev. William. St. Stanislaus College, Tullamore. “DE La Run, Warren, M.A., D.O.L., Ph.D., F.RS., F.CS, F.R.A.S. 73 Portland-place, London, W. -§§De la Sala, Colonel. Sevilla House, Navarino-road, London, N.W. . }De Sar Thomas, M.A., LL.D. 4 Hare-court, Temple, London, Denchar, John. Morningside, Edinburgh. . {Denny, William. Seven Ship-yard, Dumbarton. 26 LIST OF MEMBERS. Year of Election. 1870. 1874. 1856. 1874. 1878. 1868. 1869. 1868. 1872. 1873. 1852. 1864. 1863. 1867. 1862. 1877. 1848. 1872. 1869. 1859. 1876. 1868, 1874. 1858. 1879. 1851. 1860. 1878. 1864, 1875. 1870. 1876. Dent, William Yerbury. Royal Arsenal, Woolwich. *Denton, J. Bailey, 22 Whitehall-place, London, S.W. §DeE Rance, Cuartes E., F.G.8S. 28 Jermyn-street, London, S.W. *Drrsy, The Right Hon. the Earl of, M.A., LL.D., F.R.S., F.R.G.S.. 23 St. James’s-square, London, S.W.; and Knowsley, near- Liverpool. *Derham, Walter, M.A., LL.M., F.G.S. Henleaze Park, Westbury- on-Trym, Bristol. tDe Rinzy, James Harward. Khelat Survey, Sukkur, India. }Dessé, Etheldred, M.B., F.R.C.S. 43 Kensington Gardens-square,. Bayswater, London, W. De TasrEy, GreoreE, Lord, F.Z.S. Tabley House, Knutsford, Cheshire. {Devon, The Right Hon. the Earl of, D.C.L. Powderham Castle, near Exeter. *DrvonsHirE, His Grace the Duke of, K.G., M.A., LL.D., F.R.S., F.G.S., F.R.G.S., Chancellor of the University of Cambridge. Devonshire House, Piccadilly, London, W.; and Chatsworth, Derbyshire. {Drewar, James, M.A., F.R.S., F.R.S.E., Fullerian Professor of Chemistry in the Royal Institution, London, and Jacksonian Professor of Natural Experimental Philosophy in the University of Cambridge. Brookside, Cambridge. {Dewick, Rey. E.S. 2 Southwick-place, Hyde Park, London, W. *Dew-Suiru, A.G. 7a Eaton-square, London, 8.W. }Dicxim, Grorez, M.A., M.D., F.L.S., Professor of Botany in the University of Aberdeen. *Dickinson, F. H., F.G.S. Kingweston, Somerton, Taunton; and 12} St. George’s-square, London, 8. W. {Dickinson, G. T. Claremont-place, Newcastle-on-Tyne. }Dicxson, ALEXANDER, M.D., Professor of Botany in the University of Glasgow. 11 Royal-circus, Edinburgh. *Ditxe, Sir Cuartes Wentworrs, Bart, M.P., F.R.G.S. 76 Sloane-street, London, 8. W. §Dillon, James, C.E. 2 Belgrave-road, Monkstown, Co. Dublin. {Diiitwyn, Lewis Lizwetyn, M.P., F.L.S., F.G.S. Parkwerne, near Swansea. §Divzs, GrorGE. Woodside, Hersham, Walton-on-Thames. {Dingle, Edward. 19 King-street, Tavistock. *Dingle, Rey. J. Lanchester Vicarage, Durham. }Ditchfield, Arthur. 12 Taviton-street, Gordon-square, London, W.C {Dittmar, W. Andersonian University, Glasgow. *Dixon, A. E. Dunowen, Cliftonville, Belfast. {Dixon, Edward, M.L.C.E. Wilton House, Southampton. *Dixon, Harold B., M.A., F.C.S. Trinity College, Oxford. *Dobbin, Leonard, M.R.I.A. 27 Gardiner’s-place, Dublin. {Dobbin, Orlando T., LL.D., M.R.LA. Ballivor, Kells, Co. Meath. *Dobbs, Archibald Edward, M.A. 34 Westbourne Park, London, Ww. *Dozson, G. E., M.A., M.B.,F.L.S. Royal Victoria Hospital, Netley, Southampton. *Dobson, William. Oakwood, Bathwick Hill, Bath. *Docewra, George, jun. Grosvenor-road, Handsworth, Birmingham. *Dodd, John. 6 Thomas-street, Liverpool. Dodds, J. M. 15 Sandyford-place, Glasgow. LIST OF MEMBERS. 27 Year of Election. *Dodsworth, Benjamin. Burton House, Scarborough. *Dodsworth, George. The Mount, York. Dolphin, John. Delves House, Berry Edge, near Gateshead. 1851. {Domvile, William C., F.Z.S. Thorn Hill, Bray, Dublin. 1867. {Don, John. The Lodge, Broughty Ferry, by Dundee. 1867. {Don, William G. St. Margaret’s, Broughty Ferry, by Dundee. 1873. {Donham, Thomas. Huddersfield. 1869. {Donisthorpe,G. T. St. David’s Hill, Exeter. 1877. *Donkin, Bryan, jun. May’s Hill, Shortlands, Kent. 1874. {Donnell, Professor, M.A. 76 Stephen’s-green South, Dublin. 1861. {Donnelly, Colonel, R.E. South Kensington Museum, London, W. 1867. {Dougall, Andrew Maitland, R.N. Scotscraig, Tayport, Fifeshire. 1871. {Dougall, John, M.D. 2 Cecil-place, Paisley-road, Glasgow. 1863. *Doughty, Charles Montagu. Theberton Hall, Saxmundham, Suffolk:. 1876. *Douglas, Rev. G. C. M. 10 Fitzroy-place, Glasgow. 1877. *Douglass, James N., C.E. Trinity House, London, E.C. 1878. {Douglass, William. 104 Baggot-street, Dublin. 1855. {Dove, Hector. Rose Cottage, Trinity, near Edinburgh. 1870. {Dowie, J. Muir. Wetstones, West Kirby, Cheshire. 1876. §Dowie, Mrs. Muir. Wetstones, West Kirby, Cheshire. 1878. t{Dowling, Thomas. Claireville House, Terenure, Dublin. 1857. {Downtne, S., C.E., LL.D., Professor of Civil Engineering in the- University of Dublin. 4 The Hill, Monkstown, Co. Dublin. 1878. {Dowse, The Right Hon. Baron. 38 Mountjoy-square, Dublin. 1872. *Dowson, Edward, M.D. 117 Park-street, London, W. 1865. *Dowson, E. Theodore. Geldeston, near Beccles, Suffolk. 1868, {DrussER, Henry E., F.Z.S. 6 Tenterden-street, Hanover-square,. London, W. 1878. §Drew, Frederic, F.G.S., F.R.G.S. Eton College, Windsor. 1869. §Drew, Joseph, LL.D., F.R.A.S., F.G.8. Weymouth. 1879.§§Drew, Joseph, M.B. Foxgrove-road, Beckenham, Kent. 1865. {Drew, Robert A. 6 Stanley-place, Duke-street, Broughton, Man- chester. 1879.§§Drew, Samuel, M.D., D.Sc., F.R.S.E. Chapeltown, Edinburgh. 1872. *Druce, Frederick, 27 Oriental-place, Brighton. 1874. {Druitt, Charles. Hampden-terrace, Rugby-road, Belfast. 1866. *Dry, Thomas. 23 Gloucester-road, Regent’s Park, London, N.W. 1870. §Drysdale, J. J., M.D. 364 Rodney-street, Liverpool. 1856. *Ducrz, The Right. Hon. Henry Joun Reynotps Moreton, Ear! of, F.R.S.,F.G.S. 16 Portman-square, London, W. ; and Tort- worth Court, Wotton-under-Edge. 1870. LF eesiaet Henry, F.L.S., F.G.S. Holmfield House, Grassendale, iverpool. 1867. *Durr, Mocaniiruiits ELpHinstone Grant-, LL.B., M.P. York House, Twickenham, Middlesex. 1852. {Dufferin and Clandeboye, The Right Hon. the Earl of, K.P., K.O.B., LL.D., F.R.S., F.R.G.S. Clandeboye, near Belfast, Ireland. 1877. {Duffey, George F., M.D. 30 Fitzwilliam-place, Dublin. 1875. {Duffin, W. E. L’Estrange, C.E. Waterford. 1859. *Duncan, Alexander. 7 Prince’s-gate, London, S.W. 1859. {Duncan, Charles, 52 Union-place, Aberdeen. 1866. *Duncan, James. 71 Cromwell-road, South Kensington, London, W. Duncan, J. F., M.D. 8 Upper Merrion-street, Dublin. 1871. {Duncan, James Matthew, M.D. 30 Charlotte-square, Edinburgh. 1867.§§Duncan, PETER Martin, M.B., F.R.S., F.G.S., Professor of Geology in King’s College, London. 4 St. George’s-terrace, Regent's Park-road, London, N.W. 28 LIST OF MEMBERS. Year of #lection. 1880. §Duncan, William 8. 79 Wolverhampton-road, Stafford. 1853. *Dunlop, William Henry. Annanhill, Kilmarnock, Ayrshire. 1865. {Dunn, David. Annet House, Skelmorlie, by Greenock, N.B. 1876, *Dunn, James. 64 Robertson-street, Glaszow. 1876. {Dunnachie, James. 2 West Regent-street, Glasgow. 1878. 1859. 1866. 1869, 1860. 1869. 1868. 1861, 1877, 1874, 1871, 1863, 1876, 1870. 1861. 1858. 1870. 1855. 1859, 1870, 1867. 1867. 1867. 1855. 1867, 1859. 1878. 1876. 1868. 1863. 1880. 1855. 1861. {Dunne, D. B., M.A., Ph.D., Protessor of Logic in the Catholic Uni-~ versity of Ireland. 4 Clanwilliam-place, Dublin. tDuns, Rey. John, D.D., F.R.S.E. New College, Edinburgh. {Duprey, Perry. Woodbury Down, Stoke Newington,-London, N. tD’Urban, W. 8. M., F.L.S. 4 Queen-terrace, Mount Radford, Exeter. }Durwam, ArtrHuR Epwarp, F.R.C.S., F.L.S., Demonstrator of Anatomy, Guy’s Hospital. 82 Brook-street, Grosvenor-square, London, W. Dykes, Robert. Kilmorie, Torquay, Devon. §Dymond, Edward E. Oaklands, Aspley Guise, Woburn. tEade, Peter, M.D. Upper St. Giles’s-street, Norwich. {Eadson, Richard. 13 Hyde-road, Manchester. tEarle, Ven. Archdeacon, M.A. West Alvington, Devon. *HaRNSHAW, Rev. SamvEL, M.A. 14 Broomfield, Sheffield. §Eason, Charles. 30 Kenilworth-square, Rathgar, Dublin. *Easton, Epwarp, C.E., F.G.S. 7 Delahay-street, Westminster, S.W. §Easton, James. Nest House, near Gateshead, Durham. {Easton, John,C.E. Durie House, Abercromby-street, Helenshurgh, N.B §Eaton, Richard. Nuttall House, Nuttall, Nottinghamshire. . Ebden, Rev. James Collett, M.A., F.R.A.S. Great Stukeley Vicarage, Huntingdonshire. tEcroyd, William Farrer. Spring Cottage, near Burnley. *Eddison, Francis. Martinstown, Dorchester. *Eddison, John Edwin, M.D., M.R.C.S. 29 Park-square, Leeds. *Eddy, James Ray, F.G.S. Carleton Grange, Skipton. Eden, Thomas. Talbot-road, Oxton. *Edgeworth, Michael P., F.LS., F.R.AS. Mastrim House, Anerley, London, SE. tEdmiston, Robert. Elmbank-crescent, Glasgow. {Edmond, James. Cardens Haugh, Aberdeen. *Edmonds, F.B. 72 Portsdown-road, London, W. *Edward, Allan. Farington Hall, Dundee. {Edward, Charles. Chambers, 8 Bank-street, Dundee. {Edward, James. Balruddery, Dundee. *Epwarps, Professor J. Baker, Ph.D., D.C.L. Montreal, Canada. {Edwards, William. 70 Princes-street, Dundee. , *EGERTON, Sir Purirp pE Mapas Grey, Bart., M.P., F.R.S., F.G.S. Oulton Park, Tarporley, Cheshire. *Eisdale, David A., M.A. 388 Dublin-street, Edinburgh. tEleock, Charles. 39 Lyme-street, Shakspere-street, Ardwick, Man- chester. tElder, Mrs. 6 Claremont-terrace, Glasgow. fElger, Thomas Gwyn Empy, F.R.A.S. St. Mary, Bedford. Ellacombe, Rev. H. T., F.S.A. Clyst St. George, Topsham, Devon. tEllenberger, J. L. Worksop. *Elliot, Colonel Charles, C.B. Wateringbury, Maidstone, Kent. §Elliot, Robert, F.B.S.E. Wolfelee, Hawick, N.B. *Exxior, Sir Watrer, K.C.S.1., F.R.S., F.L.S. Wolfelee, Hawick, N.B. LIST OF MEMBERS. 29) Year of Election. 1864. 1872. 1879. 1864. 1877. 1875. 1864. 1880. 1864. 1869. 1862. 1863. 1863. 1858. 1866. 1866, 1853. 1869. 1869, 1844, 1864. 1862. tElhott, E. B. Washington, United States. yEllott, Rev. E. B. 11 Sussex-square, Kemp Town, Brighton. Elliott, John Fogg. Elvet Hill, Durham. §Elliott, Joseph W. Knowsley-street, Preston. *ELLIs, ALEXANDER JouN, B.A., F.R.S., F.S.A. 25 Argyll-road, Kensington, London, W. fEllis, Arthur Devonshire. School of Mines, Jermyn-street, London, S.W.; and Thurnscoe Hall, Rotherham, Yorkshire. *Ellis, H. D. Fair Park House, Exeter. *Ellis, Joseph. Hampton Lodge, Brighton. §Ellis, J. H. Town Hall, Southport. tEllis, J. Walter. High House, Thornwaite, Ripley, Yorkshire. *Ellis, Rey. Robert, A.M. The Institute, St. Saviour’s Gate, York. fExxris, Witt1am Horton. Hartwell House, Exeter. Ellman, Rey. KE. B. Berwick Rectory, near Lewes, Sussex. tElphinstone, H. W., M.A., F.L.S. Cadogan-place, London, S.W. {Embleton, Dennis, M.D. Northumberland-street, Newcastle-on— Tyne. {Emery, Rey. W., B.D. Corpus Christi College, Cambridge. {Empson, Christopher. Bramhope Hall, Leeds. {Enfield, Richard. Low Pavement, Nottingham. tEnfield, William. Low Pavement, Nottingham. fEnglish, Edgar Wilkins. Yorkshire Banking Company, Lowgate, Hull. fEnglish, J.T. Stratton, Cornwall. ENNISKILLEN, The Right Hon. Witt1am Wutovensy, Earl of, LL.D., D.C.L., F.RS., F.G.S., M.R.LA. 65 Eaton-place, London, 8.W.; and Florence Court, Fermanagh, Ireland. *Enys, John Davis. Care of F. G. Enys, Esq., Enys, Penryn, Cornwall. fErichsen, John Eric, F.R.S., F.R.C.S., Professor of Clinical Surgerv in University College, London. 6 Cavendish-place, London, W. *Eskrigge, R. A., F.G.S. 18 Hackins-hey, Liverpool. *Esson, Witt1AM, M.A., F.R.S., F.C.S., F.R.A.S. Merton College ; and 1 Bradmore-road, Oxford. 1878.§§Estcourt, Charles, F.C.S. 8 St. James’s-square, John Dalton-street, 1869 1870. 1865. 1876. 1869. 1861. 1876. 1865. 1875. 1866. 1865. 1871. Manchester. Estcourt, Rev. W. J. B. Long Newton, Tetbury. . {Erneriper, Rosert, F.R.S. L. & E., F.G.S., Palzontologist to the Geological Survey of Great Britain. Museum of Practical Geology, Jermyn-street ; and 19 Halsey-street, Cadogan-place, London, 8S. W. *Evans, Arthur John, F.S.A. Nash Mills, Hemel Hempsted. *Evans, Rey. Cuartes, M.A. The Rectory, Solihull, Birmingham. tEvans, Captain Freprricx J. O., C.B., R.N., F.RS., F.R.AS., F.R.G.S., Hydrographer to the Admiralty. 116 Victoria-street, Westminster, S.W. ee H. Saville W. Wimbledon Park House, Wimbledon, W. *Evans, Joun, D.C.L., LL.D., V.P.R.S., F.S.A., F.G.S. 65 Old Bailey, London, E.C.; and Nash Mills, Hemel Hempsted. {Evans, Mortimer, C.E. 97 West Regent-street, Glasgow. {Evans, Supastran, M.A., LL.D. Highgate, near Birmingham. tEvans, Sparke. 3 Apsley-road, Clifton, Bristol. {Evans, Thomas, F.G.S. Belper, Derbyshire. *Evans, William. Ellerslie, Augustus-road, Edgbaston, Birmingham. §Eve, H. Weston, M.A. University College, London, W.C 30 LIST OF MEMBERS. Year of Election. 1868. 1880. 18653. 1874. 1874. 1859. 1876. 1871. 1846. 1866. 1849, 1865. 1876. 1870. 1878. 1864, 1877. 1879. 1859. *Everert, J. D., M.A., D.C.L., F.R.S. L. & E., Professor of Natural Philosophy in Queen’s College, Belfast. Rushmere, Malone- road, Belfast. §Everingham, Edward. St. Helen’s-road, Swansea. *Everitt, George Allen, F.R.G.S. Knowle Hall, Warwickshire. . tEwart, William. Gleumachan, Belfast. {Ewart, W. Quartus. Glenmachan, Belfast. *Ewing, Archibald Orr, M.P. Ballikinrain Castle, Killearn, Stirling- shire. *Ewing, James Alfred, B.Sc., F.R.S.E., Professor of Mechanical En- eineering in the University of Tokio, Japan. 12 Laurel Bank, Dundee. *Exley, John T., M.A. 1 Cotham-road, Bristol. *Hyre, George Edward, F.G.8., F.R.G.S. 59 Lowndes-square, London, 8.W.; and Warrens, near Lyndhurst, Hants. {Eyrz, Major-General Sir Vincent, K.C.S.L, F.R.G.S. Atheneum Club, Pall Mall, London, 8.W. Eyton, Charles. Hendred House, Abingdon. {Hyton, T. C. Eyton, near Wellington, Salop. tFairley, Thomas, F.R.S.E., F.C.S. 8 Newington-grove, Leeds. {Fairlie, James M. Charing Cross Corner, Glasgow. {Fairlie, Robert, C.E. Woodlands, Clapham ~ Common, London, S.W. “Fairlie, Robert F. Palace-chambers, Victoria-street, Westminster, 3. W. {Falkner, F. H. Lyncombe, Bath. §Faraday, F. J., F.S.8. College Chambers, 17 Brazenose-street, Man- chester. *Farnworth, Ernest. Swindon, near Dudley. tFarquharson, Robert O. Houghton, Aberdeen. 1861.§§Farr, WittraM, C.B., M.D., D.C.L., F.R.S. 78 Portsdown-road, 1866. 1857. 1869. 1869. 1859. 1863. 1873. 1845. 1864. 1852. 1876, 1876. 1859. USily 1867. 1857. Maida Hill, London, W. *Farrar, Rev. FREDERICK WILLIAM, M.A., D.D., F.R.S., Canon of Westminster. St. Margaret’s Rectory, Westminster, S.W. {Farrelly, Rev. Thomas. Royal College, Maynooth. *Faulding, Joseph. ‘The Grange, Greenhill Park, New Barnet, Herts. {Faulding, W. F. Didsbury College, Manchester. *Fawcert, The Right Hon. Henry, M. A., M.P., Professor of Political Economy i in the University of Cambridge. 51 The Lawn, South Lambeth-road, London, 8.W.; and 8 Trumpington-street, Cam- bridge. {Fawcus, George. Alma-place, North Shields. *Fazakerley, Miss. The Castle, Denbigh. {Felkin, William, F.L.S. The Park, Nottingham. Fell, John B. Spark’s Bridge, Ulverstone, Lancashire. *FEeLLows, Frank P., F.S.A., F.S.S. 8 The Green, Hampstead, London, N.W. tFenton,S.Greame. 9 College-square ; and Keswick, near Belfast. *Fergus, Andrew, M.D. 3 Elmbank-crescent, Glasgow. tFerguson, Alexander A. 11 Grosvenor-terrace, Glasgow. tFerguson, John. Cove, Nigg, Inverness. *Ferguson, John, M.A., Professor of Chemistry in the University of Glasgow. {Ferguson, “Robert M., Ph.D., F.R.S.E. 8 Queen-street, Edinburgh. ig sa Sir Samuel, LL. D. ,Q.C. 20 Great George’s-street North, Dublin. — LIST OF MEMBERS, 31 “Year of ‘Election. 1854. {Ferguson, William, F.L.S., F.G.S. Kinmundy, near Mintlaw, Aberdeenshire. 1867. *Fergusson, H. B. 13 Airlie-place, Dundee. 1863. *Frrnie, Jonny. Bonchurch, Isle of Wight. 1862. {FERRERSs, Rev. Norman MacLeop, M.A., F.R.S. Caius College, P Cambridge. 1873. {Ferrier, David, M.A., M.D., F.R.S., Professor of Forensic Medicine in King’s College. 16 Upper Berkeley-street, London, W. 1875. {Fiddes, Walter. Clapton Villa, Tyndall's Park, Clifton, Bristol. 1868. {Field, Edward. Norwich. 1869. *Frevp, RocErs, B.A., 0.E. 5 Cannon-row, Westminster, S.W. 1876. {Fielden, James. 2 Darnley-street, Pollokshields, near Glasgow. Finch, John, Bridge Work, Chepstow. Finch, John, jun. Bridge Work, Chepstow. 1878. *Findlater, William. 2 Fitzwilliam-square, Dublin. 1868. {Firth,@. W. W. St. Giles’s-street, Norwich. Firth, Thomas. Northwick. 1863. *Firth, William. Burley Wood, near Leeds. 1851. *Fiscuer, Wituam L. F., M.A., LL.D, FBS. St. Andrews, Scotland. 1858. {Fishbourne, Admiral E.G., R.N. 26 Hogarth-road, Earl’s Court- road, London, 8S. W. 1869. {FisHER, Rev. Osmonp, M.A., F.G.S. Harlston Rectory, near Cambridge. 1873. §Fisher, William. Maes Fron, near Welshpool, Montgomeryshire. 1879.§§Fisher, William. Norton Grange, near Sheffield. 1875. *Fisher, W. W., M.A., F.0.S8. 2 Park-crescent, Oxford. 1858. {Fishwick, Henry. Carr-hill, Rochdale. 1871. *Fison, Frederick W., F.C.S. Eastmoor, Ilkley, Yorkshire. e871. tive, J. G., MAs 5 Lancaster-terrace, Regent’s Park, London, N.W 1868. {Fitch, Robert, F.G.S., F.S.A. Norwich. 1878. {Fitzgerald, C. E., M.D. 27 Upper Merrion-street, Dublin. 1878. §FirzeEratp, Grorcr Francis. Trinity College, Dublin. 1857. ea The Right Hon. Lord Otho. 13 Dominick-street, Dublin. _ 1857. {Fitzpatrick, Thomas, M.D. 31 Lower Baggot-street, Dublin. 1865, {Fleetwood, D. J. 45 George-street, St. Paul’s, Birmingham. Fleetwood, Sir Peter Hesketh, Bart. Rossall Hall, Fleetwood, Lancashire. 1850. {Fleming, Professor Alexander, M.D. 121 Hagley-road, Birmingham. Fleming, Christopher, M.D. Merrion-square N. orth, Dublin. 1876. {Fleming, James Brown. Beaconsfield, Kelvinside, near Glasgow. 1876. {Fleming, Sandford. Ottawa, Canada. 1867. §FiercuEr, Atrrep E. 5 Edge-lane, Liverpool. 1870. {Fletcher, B. Edgington. Norwich. 1869, {FiercHer, Lavineron E., C.E. 41 Corporation-street, Manchester. Fletcher, T. B. E., M.D. 7 Waterloo-street, Birmingham. 1862. {FLowrr, Witr1am Henry, LL.D., F.R.S., E.LS., F.G.S., F.R.C.S., Hunterian Professor of Comparative Anatomy, and Conservator of the Museum of the Royal College of Surgeons. Royal College of Surgeons, Lincoln’s-Inn-fields, London, W.C. 1877. *Floyer, Ernest A., F.R.G.S. 7 The Terrace, Putney, S.W. 1879.§§Foote, Charles Newth, M.D. 3 Albion-place, Sunderland. -1879.§§Foote, Harry D’Oyley, M.D. Rotherham, Yorkshire. 1880. cd be Bruce. Linkwood, Central Hill, Upper Norwood, London, 32 LIST OF MEMBERS. Year of Election. 1873. 1855. 1877. 1866. 1875. 1867. 1858. 1854. 1877. 1870. 1875. 1865, 1865. 1857. 1845. 1877. 1859. 1873. 1863. 1859. 1873. 1870, 1866. 1868. 1876. 1870. 1876. 1860. 1866. 1846. 1859. 1865. 1871. 1859. *Forbes, Professor George, M.A., F.R.S.E. Andersonian University, Glasgow. tForbes, Rey. John. Symington Manse, Biggar, Scotland. §Forbes, W. A. West Wickham, Kent. Ford, H. R. Morecombe Lodge, Yealand Conyers, Lancashire. f¥ord, William. Hartsdown Villa, Kensingtun Park-gardens East, London, W. *Forpuam, H. Grorex, F.G.S. Odsey Grange, Royston, Herts. *Forrest, William Hutton. 1 Pitt-terrace, Stirling. {Forster, Anthony. Finlay House, St. Leonard’s-on-Sea. *ForsteR, The Right Hon. Wiit1am Epwarp, M.P., F.R.S. 80 Eccleston-square, London, 8.W.; and Wharfeside, Burley-in- Wharfedale, Leeds. *Fort, Richard. Read Hall, Whalley, Lancashire. {Forrrscur, The Right Hon. the Earl. Castle Hill, North Devon. {Forwood, William B. Hopeton House, Seaforth, Liverpool tFoster, A. Le Neve. East Hill, Wandsworth, Surrey, 8.W. TFoster, Balthazar, M.D., Professor of Medicine in Queen’s College, Birmingham. 16 Temple-row, Birmingham. *Fosrer, CremEent Lz Neve, B.A., D.Se., F.G.S. Llandudno. *FosreR, GrorcE Oarey, B.A., F.R.S., F.C.S., Professor of Physics in University College, London. 12 Hilldrop-road, London, N. © *Foster, Rev. John, M.A. The Oaks Vicarage, Loughborough, tFoster, John N. Sandy Place, Sandy, Bedfordshire. §Foster, Joseph B. 6 James-street, Plymouth. *Foster, Micnart, M.A., M.D., F.RS., F.LS., F.0.8. Trinity College, and Great Shelford, near Cambridge. { Foster, Peter Le Neve. {Foster, Robert. 30 Rye-hill, Newcastle-upon-Tyne. *Foster, 8. Lloyd. Brundall Lodge, Ealing, Middlesex, W. *Foster, William. Harrowins House, Queensbury, Yorkshire. {Poulger, Edward. 55 Kirkdale-rvad, Liverpool. {Fowler, George, M.I.C.E., F.G.S. Basford Hall, near Nottingham. tFowler, G. G. Gunton Hall, Lowestoft, Suffolk. *Fowler, John. 4 Kelvin Bank-terrace, Glasgow. *Fowler, Robert Nicholas, M.A., F.R.G.S. 50 Cornhill, London, E.C *Fox, Rev. Edward, M.A. Upper Heyford, Banbury. tFox, G.S. Lane. 9 Sussex-place, London, 8. W. *Fox, Joseph Hayland. The Cleve, Wellington, Somerset. {Fox, Joseph John. Church-row, Stoke Newington, London, N. *Francis, G. B. Inglesby House, Stole Newington-green, London, N.. Francis, WILLIAM, Ph.D., F.L.S., F.G.S., F-R.A.S. Red Lion-court, Fleet-street, London, E.C.; and Manor House, Richmond, Surrey. {Franxianp, Epwarp, D.C.L., Ph.D., F.R.S., F.C.S., Professor of Chemistry in the Royal School of Mines. 14 Lancaster-gate, London, W. *Frankland, Rey. Marmaduke Charles. Chowbent, near Manchester, {Fraser, George B. 3 Airlie-place, Dundee. Fraser, James. 25 Westland-row, Dublin. Fraser, James William. 84 Kensington Palace-gardens, London, W.. *Fraser, Jonn, M.A., M.D. Chapel Ash, Wolverhampton. tFrasrr, Toomas R., M.D., F.R.S.L. & E. 3 Grosyenor-street, Edinburgh. *Frazer, Daniel. 113 Buchanan-street, Glasgow. LIST OF MEMBERS. 33 Year of Election. 1871. 1860. 1847. 1877. 1865. 1880. 1869. 1869. 1857. 1869. 1847, 1875. 1875. 1872. 1873. 1859. 1869. 1864. 1857. 1863. 1876. 1850. 1861. 1876. 1863. 1861. 1861. 1875. 1860. 1860. 1869. 1870. 1870. 1872. 1877. 1868. {Frazer, Evan L. R. Brunswick-terrace, Spring Bank, Hull. tFreeborn, Richard Fernandez. 38 Broad-street, Oxford. *Freeland, Humphrey William, F.G.S. West-street, Chichester, Sussex. §Freeman, Francis Ford. Blackfriars House, Plymouth. tFreeman, James. 15 Francis-road, Edgbaston, Birmingham. §Freeman, Thomas. Brynhyfryd, Swansea. Frere, George Edward, F.R.S. Roydon Hall, Diss, Norfolk. }F rere, The Right Hon. Sir H. Barrie E., Bart., G.C.S.1., G.C.B., F.R.S., F.R.G.S. 34 Hyde Park-gardens, London, W. tFrere, Rev. William Edward. The Rectory, Bilton, near Bristol. *Frith, Richard Hastings, C.E,, M.R.LA., F.R.G.S.1. 48 Summer- hill, Dublin. {Frodsham, Charles. 26 Upper Bedford-place, Russell-square, Lon- don, W.C. tFrost, William. Wentworth Lodge, Upper Tulse Hill, London, S.W. tFry, F. J. 104 Pembroke-road, Clifton, Bristol. Fry, Francis. Cotham, Bristol. *Fry, Joseph Storrs. 2 Charlotte-street, Bristol. Fry, Richard. Cotham Lawn, Bristol. *Fuller, Rev. A. Pallant, Chichester. [Fuller, Claude S., R.N. 44 Holland-road, Kensington, London, W. {Furter, Frepericx, M.A., Professor of Mathematics in the Uni- versity and Kine’s College, Aberdeen. {Forrer, Gores, C.E., Professor of Engineering in Queen’s College, Belfast. 6 College-gardens, Belfast. *Furneaux, Rey. Alan. St. German’s Parsonage, Cornwall. *Gadesden, Augustus William, F.S.A. Ewell Castle, Surrey. TGaces, ALpHonsE, M.R.I.A. Museum of Irish Industry, Dublin. *Gainsford, W. D. Richmond Hill, Sheffield. tGairdner, Charles. Broom, Newton Mearns, Renfrewshire. tGairdner, Professor W. T., M.D. 225 St. Vincent-street, Glascow. tGalbraith, Andrew. Glasgow. GasraltH, Rey. J. A., M.A., M.R.LA, Trinity College, Dublin. tGale, James M. 23 Miller-street, Glasgow. tGale, Samuel, F.C.S. 338 Oxford-street, London, W. {Galloway, Charles John. Knott Mill Iron Works, Manchester. {Galloway, John, jun. Knott Mill Iron Works, Manchester. {Gattoway, W., H.M. Inspector of Mines. Cardiff. *Gatron, Captain Doveras, C.B., D.C.L., F.RS., F.LS., F.G.S., F.R.G.S. (Gunerat SECRETARY.) 12Chester-street, Grosvenor- place, London, 8S. W. *Gatton, Franots, M.A., F.R.S., F.G.S., F.R.G.S. 42 Rutland- gate, Knightsbridge, London, 8. W. tGatron, Jonn C., M.A., F.L.S. 13 Margaret-street, Cavendish- square, London, W. §Gamble, Lieut.-Colonel D. St. Helen’s, Lancashire. tGamble, J. C. St. Helen’s, Lancashire. *Gamble, John G., M.A. Civil Service Club, Capetown. (Care of Messrs. Ollivier and Brown, 37 Sackville-street, Piccadilly, London. W.) tGamble, William. St. Helen’s, Lancashire. tGamern, Arravr, M.D., F.R.S., F.R.S.E., Professor of Physiology in Owens College, Manchester. Fairview, Princes-road, Fal- lowfield, Manchester. 1862.§§GaRNER, Ropert, F.L.S, Stoke-upon-Trent. . Cc 34 LIST OF MEMBERS. Year of Election. 1865.§§Garner, Mrs. Robert. Stoke-upon-Trent. 1842. Garnett, Jeremiah. Warren-street, Manchester. 1873. {Garnham, John. 123 Bunhill-row, London, E.C. 1874. 1870. 1870. 1847. 1842. 1862. 1876. 1875. 1873. 1871. 1859, 1854, 1867. 1871. 1855. 1875. 1854. 1870. 1870. 1865. 1871. 1874, 1876. 1870. 1870. 1842, 1857. 1859. 1878. 1878. 1871. 1868, 1864, 1861. 1867. 1876. *Garstin, John Ribton, M.A., LL.B., M.R.LA., F.S.A. Bragans- town, Castlebellingham, Ireland. {Gaskell, Holbrook. Woolton Wood, Liverpool. *Gaskell, Holbrook, jun. Clayton Lodge, Aigburth, Liverpool. *Gaskell, Samuel. Windham Club, St. James’s-square, London, 8. W. Gaskell, Rev. William, M.A. Plymouth-grove, Manchester. *Gatty, Charles Henry, M.A., F.LS., F.G.S. Felbridge Park, East Grinstead, Sussex. §Gavey, J. 48 Stacey-road, Routh, Cardiff. {Gaye, Henry 8. Newton Abbott, Devon. tGeach, R. G. Cragg Wood, Rawdon, Yorkshire. tGeddes, John. 9 Melville-crescent, Edinburgh. tGeddes, William D., M.A., Professor of Greek in King’s College, Old Aberdeen. tGee, Robert, M.D. 5 Abercromby-square, Liverpool. tGerkie, ArcuiparD, LL.D., F.R.S. L. & E., F.G.S., Director of the Geological Survey of Scotland. Geological Survey Office, Vic- toria-street, Edinburgh ; and Boroughfield, Edinburgh. §Geikie, James, F.R.S. L. & E., F.G.S. Balbraith, Perth, tGemmell, Andrew. 88 Queen-street, Glasgow. *George, Rev. Hereford B., M.A., F.R.G.S. New College, Oxford. tGerard, Henry. 8A Rumford-place, Liverpool. {Gerstl, R., F.C.S. University College, London, W.C. *Gervis, Walter S., M.D., F.R.S. Ashburton, Devonshire. {Gibbins, William. Battery Works, Digbeth, Birmingham, {Gibson, Alexander. 10 Albany-street, Edinburgh. {Gibson, aay Right Hon. Edward, Q.0. 23 Fitzwilliam-square, Dublin. *Gibson, George Alexander, M.B., D.Sc., F.G.S. 1 Randolph Cliff, Edinburgh. *Gibson, George Stacey. Saffron Walden, Essex. {Gibson, Thomas. 51 Oxford-street, Liverpool. {Gibson, Thomas, jun. 10 Parkfield-road, Prince’s Park, Liverpool. GitpErRt, JoserpH Henry, Ph.D., F.R.S., F.C.S. Harpenden, near St. Albans. tGilbert, J.T., MRA. Villa Nova, Blackrock, Dublin, *Gilchrist, James, M.D. Crichton House, Dumfries. Gilderdale, Rev. John, M.A. Walthamstow, Essex. §Giles, Oliver. 16 Bellevue-crescent, Clifton, Bristol. Giles, Rev. William. Netherleigh House, near Chester. {Gill, Rev. A. W. H. 44 Eaton-square, London, 8. W. *Grit, Davip. The Observatory, Cape Town. {Gill, Joseph. Palermo, Sicily. (Care of W. H. Gill, Esq., General Post Office, St. Martin’s-le-Grand, E.C.) {Girt, Tuomas, 4 Sydney-place, Bath. *Gilroy, George. Hindley Hall, Wigan. tGilroy, Robert. Craigie, by Dundee. §Gimingham, Charles H. 45 St. Augustine’s-road, Camden-square, London, N.W 1867.§§GinsBure, Rev. GoD; D.C.L., LL.D. Wokingham, Berkshire. 1869, {Girdlestone, Rev. Canon E., M.A. Halberton Vicarage, Tiverton. 1874. 1850, *Girdwood, James Kennedy. Old Park, Belfast. *Gladstone, George, F.C.S., F.R.G.S, 31 Ventnor-villas, Cliftonville, Brighton. “Year of LIST OF MEMBERS, 35 Election. 1849, 1875. 1861, 1871, 1870. 1859. 1867. 1874, 1874. 1870. 1872. 1878. 1880, 1852, 1879. 1846, 1876. 1877. 1873. 1878. 1852. 1870. 1842, 1865. 1869, 1870. 1878. 1871. 1840, 18657. 1865. 1870. 1875. *GtapsTonE, JoHN Hatt, Ph.D., F.R.S., F.C.S. 17 Pembridge- square, Hyde Park, London, W. *Glaisher, Ernest Henry. 1 Dartmouth-place, Blackheath, London, S.E *GLAIsHER, JAMES, F.R.S., F.R.A.S, 1 Dartmouth-place, Black- heath, London, 8.E. *GuatsHeR, J. W. L., MA., F.RS., F.R.A.S. Trinity College, Cambridge. §Glen, David Corse, F.G.S. 14 Annfield-place, Glasgow. he S. Stuart. 6 Stone-buildings, Lincoln’s Inn, London, W. fGloag, John A. L. 10 Inverleith-place, Edinburgh. Glover, George. Ranelagh-road, Pimlico, London, S.W. tGlover, George T. 30 Donegall-place, Belfast. {Glover, Thomas. 77 Claverton-street, London, S.W. {Glynn, Thomas R. 1 Rodney-street, Liverpool. TGoppaRD, RicHaRD. 16 Booth-street, Bradford, Yorkshire. *Godlee, J. Lister. 3 New-square, Lincoln’s Inn, London, W.C. §Godman, F. D, 10 Chandos-street, Cavendish-square, London, W. {tGodwin, John. Wood House, Rostrevor, Belfast. §Godwin-Austen, Major H. H., F.R.S., F-Z.S. 17 Bessborough- gardens, London, 8.W. tGopwry-Avsren, Ropert A. C., B.A., F.R.S., F.G.S. Shalford House, Guildford. {Goff, Bruce, M.D. Bothwell, Lanarkshire. {Gorr, JAmes. 11 Northumberland-road, Dublin. {Goldthorp, Miss R. F. C, Cleckheaton, Bradford, Yorkshire. {tGood, Rey. Thomas, B.D. 51 Wellington-road, Dublin. tGoodbody, Jonathan. Clare, King’s County, Ireland. Goodison, George William, CLE. Gateacre, Liverpool. *GoopMAN, JoHn, M.D. 8 Leicester-street, Southport. tGoodman, J. D. Minories, Birmingham. {tGoodman, Neville. Peterhouse, Cambridge. *Goodwin, Rev. Henry Albert, M.A., F.R.A.S. Lambourne Rectory, . Romford. §Gorpon, J. E. H., B.A. (Assistant Secretary.) Holmwood Cottage, Dorking. *Gordon, Joseph Gordon, F.C.S. 20 King-street, St. James’s, London, S.W. {tGordon, Lewis D. B. Totteridge, Whetstone, London, N. {tGordon, Samuel, M.D. 11 Hume-street, Dublin. {Gore, George, LL.D., F.R.S. 50 Islington-row, Edgbaston, Bir- mingham. {Gossage, William. Winwood, Woolton, Liverpool. *Gotch, Francis. Stokes Croft, Bristol. *Gotch, Rey. Frederick William, LL.D. Stokes Croft, Bristol. *Gotch, Thomas Henry. Kettering. 1873.§§Gott, Charles, M.I.C.E. Parlkfield-road, Manningham, Bradford, 1849 1857 1868 1873 1867 Yorkshire. t{Gough, The Hon. Frederick. Perry Hall, Birmingham. tGough, The Right Hon. George 8., Viscount, M.A., F.L.S., F.G.S. St. Helen’s, Booterstown, Dublin. tGould, Rey. George. Unthank-road, Norwich. Gouxp, Jomn, F.R.S., F.L.S., F.R.G.S., F.Z.S. 26 Charlotte-street, Bedford-square, London, W.C. {Gourlay, J. McMillan. 21 St. Andrew’s-place, Bradford, Yorkshire. {Gourley, Henry (Engineer). Dundee, c2 36 LIST OF MEMBERS. Year of Election. 1876. §Gow, Robert. Oairndowan, Dowanhill, Glasgow. Gowland, James. London-wall, London, H.C. 1873.§§Goyder, Dr. D. Marley House, 88. Great Horton-road, Bradford, Yorkshire. 1861. {Grafton, Frederick W.. Park-road, Whalley Range, Manchester. 1867. *Granam, Crrit, F.L.S., F.R.G.S. Colonial Office, London, 8.W. 1875. {Grawame, JAmus. Auldhouse, Pollokshaws, near Glasgow. . 1852. *Grainger, Rev. Canon John, D.D., M.R.I.A. Skerry and Rathcavan Rectory, Broughshane, near Ballymena, Co. Antrim. 1871. {Grant, Sir ALEXANDER, Bart., M.A., Principal of the University of Edinburgh, 21 Lansdowne-crescent, Edinburgh. 1859. {Grant, Hon. James. Cluny Cottage, Forres. 1870. {Grant, Colonel James A., C.B., C.S.L, F.R.S., F.LS8., F.R.G.S. 19 Upper Grosvenor-street, London, W. 1855. *Grant, Ropert, M.A., LL.D... F.R.S., F.R.A.S., Regius Professor of Astronomy in the University of Glasgow. The Observatory, Glasgow. 1854, {GranTHaM, Ricwarp B., C.E., F.G.S. 22 Whitehall-place, London, S.W. 1864. {Grantham, Richard F. 22 Whitehall-place, London, S.W. 1874, {Graves, Rey. James, B.A., M.R.L.A. Inisnag Glebe, Stonyford, Co, Kilkenny. 1864, *Gray, Rev. Charles. The Vicarage, Blyth, Worksop. 1865. tGray, Charles. Swan-bank, Bilston. 1870, tGray, C. B. 5 Rumford-place, Liverpool. 1876. {Gray, Dr. Newton-terrace, Glasgow. 1864. {Gray, Jonathan. Summerhill House, Bath. 1859. {Gray, Rev. J. H. Bolsover Castle, Derbyshire. 1870. {Gray, J. Macfarlane. 127 Queen’s-road, Peckham, London, S.E. 1878. §Gray, Matthew Hamilton. 14 St. John’s Park, Blackheath, London,. S.E 1878. §Gray, Robert Kaye. 14 St. John’s Park, Blackheath, London, S.E 1873.§§Gray, William, M.R.I.A. 6 Mount Charles, Belfast. *Gray, Colonel Witt1aM. Farley Hall, near Reading. 1854. *Grazebrook, Henry. Clent Grove, near Stourbridge, Worcester= shire. 1866. §Greaves, Charles Augustus, M.B., LL.B. 101 Friar-gate, Derby. 1873. {Greaves, Jomes H., C.E. Albert-buildings, Queen Victoria-street, London, E.C. 1869.§§Greaves, William. Station-street, Nottingham. 1872.§§Greaves, William. 3 South-square, Gray’s Inn, London, W.C. 1872. *Grece, Clair J., LL.D. Redhill, Surrey. 1879.§§Green, A. F. Leeds, 1858. *Greenhalgh, Thomas. Thornydikes, Sharples, near Bolton-le-Moors, 1863. {Greenwell, G@. E. Poynton, Cheshire. 1875, {Greenwood, Frederick. School of Medicine, Leeds. 1862. *Greenwood, Henry. 32 Castle-street, and the Woodlands, Anfield= road, Anfield, Liverpool. 1877. {Greenwood, Holmes. 78 King-street, Accrington. 1849, {Greenwood, William. Stones, Todmorden. 1861. *Gree, Ropert Puiries, F.G.S., F.R.A.S. Coles Park, Bunting- ford, Herts. 1833. Gregg, T. H. 22 Ironmonger-lane, Cheapside, London, E.C. 1860. {GRrGoR, Rev. Watrer, M.A. Pitsligo, Rosehearty, Aberdeenshire, 1868. +Gregory, Charles Hutton, C.E. 1 Delahay-street, Westminster, .W, : LIST OF MEMBERS. 37 Year of Election. 1861. 1875. 1869, 1875. 1871. 1859. 1875, 11870. 1878. 1859. 1870. 1868, 1870. 1847, §Gregson, Samuel Leigh. Aigburth-road, Liverpool, tGrenfell, J. Granville, B.A., F.G.8. 5 Albert-villas, Clifton, Bristol. *GRESWELL, Rey. RIcHARD, M. A., F.R.S., F.R.G.S. 39 St. Giles’s- street, Oxford. {Grey, Sir Georez, F.R.G.S. Belgrave-mansions, Grosvenor- gardens, London, &.W. tGrey, Mrs. Maria G. 18 Cadogan-place, London, 8. W. *Grierson, Samuel, Medical Superintendent of the District Asylum, Melrose, N. B. t{Grrerson, THomas Bortz, M.D. Thornhill, Dumfriesshire. §Grieve, David, F.R.S.E., F.G.S8. Hobart House, Dalkeith, Edin- burgh. tGrieve, John, M.D. 21 Tages eet, Glasgow. {Guiffin, Robert, M.A., LL.D. Trinity College, Dublin. Griffith, Rev. C. T., DD. Elm, near Frome, Somerset. *GRIFFITH, Grorer, M.A., F.C.8. Harrow. Griffith, George R. Fitzwilliam-place, Dublin. tGriflith, Rey. “Henry, F.G.S. Barnet, Herts. TGrigith, Rev. John, M.A., D.C.L. Findon Rectory, Worthing, Sussex. {Grifith, N. R. The Coppa, Mold, North Wales. tGriffith, Thomas. Bradford-street, Birmingham. Grirritus, Rev. Joun, M.A. Wadham College, Oxford. 1879.§§ Griffiths, Thomas, F.C.S., F.S.8. Silverdale, Oxton, Birkenhead. 1875. 1870. 1842, 1864, 1869, 1863. 1869. 1867. 1842. 1856. 1862. 1877. 1866. 1880. 1868, 1860, 1876, 1859. 1857. 1876. tGrignon, James, H.M. Consul at Riga. Riga. tGrimsdale, T. F.. M.D. 29 Rodney-street, Liverpool. Grimshaw, Samuel, M.A. Errwod, Buxton. tGroom-Narrer, CHartes Orrizy, F.G.S. 18 Elgin-road, St. Peter’s Park, London, N.W. §Grote, Arthur, F.L.S., F.G.S. 20 Cork-street, Burlington-gardens, London, W. GROVE, The Hon, Sir Wrnr1aM Rosert, Knt., M.A., D.C.L., F.RBS. 115 Harley-street, London, W. *Groves, THomas B., F.C.S. 80 St. Mary-street, Weymouth. tGruss, Howarp, F.R.A.S. 40 Leinster-square, Rathmines, Dublin. Guild, John. Bayfield, West Ferry, Dundee. Guinness, Henry. 17 College-green, Dublix. Guinness, Richard Seymour. 17 College-green, Dublin. *GuisE, Lieut.-Colonel Sir Wirttam Vernon, Bart., F.G.S., F.L.S. Elmore Court, near Gloucester. t@Gunn, John, M.A., F.G.S. Irstedd Rectory, Norwich. tGunn, William, F.G.S. Barnard Castle, Darlington. tGtnrner, ArBERTC. L.G., M.A., M.D., Ph.D., F.R.S., Keeper of the Zoological Collections in the British Museum. British Museum, London, W.C. §Guppy, John J. Ivy-place, High-street, Swansea. *Gurney, John. Sprouston Hall, Norwich. *GuURNEY, SAMUEL, F.L.S., F. RG.S. 20 Hanover-terrace, Begoal Park, London, N.W. *Gutch, John James. Holgate ee York. Guthrie, Francis. Cape Town, Cape ‘of Good Hope. {Gurueiz, Frepericr, B.A., F.R.S. L. & E., Professor of Physics in the Royal School of Mines. Science Schools, South Kensington, London, 8. W. tGwynne, Rev. John. Tullyagnish, Letterkenny, Strabane, Ireland. tGwyther, R. F. Owens College, Manchester. 38 LIST OF MEMBERS. Year of a Election. 1865. 1858. {Hackney, William. 9 Victoria~chambers, Victoria-street, London, S.W. : *Hadden, Frederick J. South Cliff, Scarborough. . [Haddon, Henry. Lenton Field, Nottingham. Haden,G. N. Trowbridge, Wiltshire. Hadfield, George. Victoria-park, Manchester. . THadivan, Isaac. 3 Huskisson-street, Liverpool. . {Hadland, William Jenkins. Banbury, Oxfordshire. . THaigh, George. Waterloo, Liverpool. *Hailstone, Edward, F.S.A. Walton Hall, Wakefield, Yorkshire. . §Hake, H. Wilson, Ph.D., F.C.S. Queenswood College, Hants. . THake, R. C. Grasmere Lodge, Addison-road, Kensington. Lon- don, W. . THale, Rev. Edward, M.A., F.G.S., F.R.G.S. Eton College, Windsor. . THalhead, W. B. 7 Parkfield-road, Liverpool. max, The Right Hon. Viscount. 10 Belgrave-square, London, S.W.; and Hickleston Hall, Doncaster. . THall, Dr. Alfred. 30 Old Steine, Brighton. . *Hall, Ebenezer. Abbeydale Park, near Sheffield. . “Hatx, Hue Ferrers, F.G.S. Greenheys, Wallasey, Birkenhead. . {Hall, John Frederic. Ellerker House, Richmond, Surrey. . *Hall, Captain Marshall. 13 Old-square, Lincoln’s Inn, London, W.C *Hall, Thomas B. Australia. (Care of J. P. Hall, Esq., Crane House, Great Yarmouth.) . “Hatz, TownsHend M.,F.G.S._ Pilton, Barnstaple. . THall, Walter. 11 Pier-road, Erith. . *Hatrert, T. G. P., M.A. Claverton Lodge, Bath. . “Hatrerr, Wiir1am Henry, F.L.S. Buckingham House, Marine Parade, Brighton. Halsall, Edward. 4 Somerset-street, Kingsdown, Bristol. *Hambly, Charles Hambly Burbridge, F.G.S. The Leys, Barrow-on- Soar, near Loughborough. 1866.§§Hammton, ARcHIBALD, F.G.S. South Barrow, Bromley, Kent. 1869. 1851. 1878. 1878. 1875. 1863. 1850. 1861. 1857. 1847, 1876. 1865. 1867. 1859. 1853, 1865. §Hamilton, Rowland. Oriental Club, Hanover-square, London, W. {Hammond, C. C. Lower Brook-street, Ipswich. {Hanagan, Anthony. Luckington, Dalkey. : §Hance, Edward M., LL.B. 103 Hartington-road, Sefton Park; Liverpool. tHancock, O. F., jun., M.A. 386 Blandford-square, London, N.W. tHancock, John. 4 St. Mary’s-terrace, Newcastle-on-Tyne. tHancock, John, J.P. The Manor House, Lurgan, Co. Armagh. ed aes Walker. 10 Upper Chadwell-street, Pentonville, London, tHancock, William J. 23 Synnot-place, Dublin. tHancock, W. Nemson, LL.D., M.R.I.A. 64 Upper Gardiner~ street, Dublin. tHancock, Mrs. W. Neilson. 64 Upper Gardiner-street, Dublin. fHands, M. Coventry Handyside, P. D., M.D., F.R.S.E. Edinburgh. tHannah, Rev. John, D.C.L. The Vicarage, Brighton. tHannay, John. Montcoffer House, Aberdeen. tHansell, Thomas T. 2 Charlotte-street, Sculcoates, Hull. *Harcourt, A. G. Vernon, M.A., F.R.S., F.0.S. Cowley Grange, Oxford. Harcourt, Egerton V. Vernon, M.A., F.G.S. Whitwell Hall, York- shire. {Harding, Charles. Harborne Heath, Birmingham. LIST OF MEMBERS. 89 Year of Election. 1869. tHarding, Joseph. Millbrooke House, Exeter. 1877. §Harding, Stephen. Bower Ashton, Clifton, Bristol. 1869. tHarding, William D. Islington Lodge, King’s Lynn, Norfolk. . 1874. t{Hardman, E. T., F.C.S. 14 Hume-street, Dublin. 1872. tHardwicke, Mrs. 192 Piccadilly, London, W. 1880. §Hardy, John. 118 Embden-street, Manchester. *Harp, Cuartes Joun, M.D., Professor of Clinical Medicine in Uni- versity College, London. 57 Brook-street, Grosvenor-square, London, 1858. {Hargrave, James. Burley, near Leeds. 1876. tHarker, Allen. 17 Southgate-street, Gloucester. 1878. *Harkness, H. W. Sacramento, California. 1871.§§Harkness, William. Laboratory, Somerset House, London, W.C. 1875, *Harland, Rev. Albert Augustus, M.A., F.G.S., F.LS., FSA. The Vicarage, Harefield, Middlesex. 1877. *Harland, Henry Seaton. Brompton, Wykeham Station, York. 1862. *Hartxy, Groren, M.D., F.R.S., F.C.S. 25 Harley-street, London, *Harley, John. Ross Hall, near Shrewsbury. . 1862. *Harrey, Rev. Roser, F.R.S., F.R.A.S. Mill Hill School, Mid- : dlesex ; and Burton Bank, Mill Hill, Middlesex, N.W. 1868. *Harmer, F. W., F.G.8. Oakland House, Cringleford, Norwich. 1872.§§Harpley, Rev. William, M.A., F.C.P.S. Clayhanger Rectory, Tiverton. *Harris, Alfred. Oxton Hall, Tadcaster. *Harris, Alfred, jun. Lunefield, Kirkby-Lonsdale, Westmoreland. 1871. tHarris, GzorGE, F.S.A. Iselipps Manor, Northolt, Southall, Mid- dlesex. 1863. tHarris, T. W. Grange, Middlesbrough-on-Tees. 1873. tHarris, W. W. Oak-villas, Bradford, Yorkshire. 1860, {Harrison, Rev. Francis, M.A. Oriel College, Oxford. 1864, {Harrison, George. Barnsley, Yorkshire. 1873. tHarrison, George, Ph.D., F.LS., F.C.S. 14 St. James’s-row, Sheffield. 1874, tHarrison, G. D. B. 8 Beaufort-road, Clifton, Bristol. 1858, *Harrison, James Parx, M.A. Junior Oxford and Cambridge Club, St. James’s-square, London, S. W. 1870. {Harrison, RecrnaLp. 51 Rodney-street, Liverpool. 1853. tHarrison, Robert. 36 George-street, Hull. 1863, roe T. E. Engineers’ Office, Central Station, Newcastle-on- ne. 1849. | ees The Right Hon, Duprny Rypzr, Karl of, K.G., D.C.L., F.R.S., F.R.G.S. 39 Grosvenor-square, London, W.; and Sandon Hall, Lichfield. 1876, *Hart, Thomas. Bank View, 33 Preston New-road, Blackburn. 1875.§$Hart, W. E. Kilderry, near Londonderry. Hartley, James. Sunderland. 1871. {Hartley, Walter Noel, F.C.S., Professor of Chemistry in the Royal College of Science, Dublin. 1854.§§Harrup, Joy, F.R.A.S. Liverpool Observatory, Bidston, Birkenhead. 1850. {Harvey, Alexander. 4 South Wellington-place, Glasgow. 1870. {Harvey, Enoch. Riversdale-road, Aigburth, Liverpool. *Harvey, Joseph Charles. Knockrea, Douglas-road, Cork. Harvey, J. R., M.D. St. Patrick’s-place, Cork. 1878. {Harvey, R. J., M.D. 7 Upper Merrion-street, Dublin. 1862. *Harwood, John, jun. Woodside Mills, Bolton-le-Moors. 40 LIST OF MEMBERS. Year of Election, 1875. 1837, 1857. ft 1874. 1872. 1864, 1868. 1863. 1859. 1877. 1861. 1858. 1867, 1857. 1873. 1869. 1858. 1879. 1851. 1869, 1869. 1863. 1871. 1861. 1877. 1865. 1877. 1866. 1863, 1861.§§HratHrretp, W. E., F.C.S., F.R.G.S., F.R.S.E, 20 King-street 1865. 1858, 1833. 1855, 1867. 1869. 1863. 1857. 1867. 1845. 1873. tHasrives, G. W., M.P. Barnard’s Green House, Malvern. Hastings, Rev. H.S. Martley Rectory, Worcester. { Hastings, W. Huddersfield. Haveuron, Rev. Samunt, M.A., M.D., D.C.L., F.R.S., M.R.LA, F.G.S., Professor of Geology in the University of Dublin. Trinity College, Dublin. {Hawkins, B. Waterhouse, F.G.S. Century Club, East Fifteenth- street, New York. *Hawkshaw, Henry Paul. 20 King-street, St. James's, London, WwW. *HAwKsHAW, Sir Jonny, O.E., F.R.S., F.G.S., F.R.G.S._ Hollyeombe, Liphook, Petersfield ; and 33 Great George-street, London, S.W. “Hawkshaw, John Clarke, M.A., F.G.S. 25 Cornwall-zardens, South Kensington, S.W.; and 33 Great George-street, London, S.W. {Hawxstzy, Tuomas, C.E.,F.R.S., F.G.8. 30 Great George-street, London, S.W. {Hawthorn, William. The Cottage, Benwell, Newcastle-upon-Tyne. tHay, Sir Andrew Leith, Bart. Rannes, Aberdeenshire. {Hay, Arthur J. Lerwick, Shetland. “Hay, Rear-Admiral the Right Hon. Sir Joun C. D., Bart., O.B., M.P., D.C.L., F.R.S. 108 St. George’s-square, London, 8. W. tHay, Samuel. Albion-place, Leeds. tHay, William. 21 Magdalen-yard-road, Dundee. {Hayden, Thomas, M.D. 30 Harcourt-street, Dublin. *Hayes, Rev. William A., M.A. 3 Mountjoy-place, Dublin. tHayward, J. High-street, Exeter, *HAYwarD, Rosert Batpwiy, M.A., F.R.S. The Park, Harrow. “Hazlehurst, George 8. The Elms, Runcorn, §Hxap, JnremMran, C.E., F.C.S8. Middlesbrough, Yorkshire, tHead, R. T. The Briars, Alphineton, Exeter, tHead, W. R. Bedford-circus, Exeter. {Heald, Joseph. 22 Leazes-terrace, Newcastle-on-Tyne. §Healey, George. Matson’s, Windermere. *Heape, Benjamin. Northwood, Prestwich, near Manchester. tHearder, Henry Pollington. Westwell-street, Plymouth. {Hearder, William. Rocombe, Torquay. {Hearder, William Keep, F.S.A. 195 Union-street, Plymouth. {Heath, Rev. D. J. Esher, Surrey. }Heath, G. Y., M.D. Westgate-street, Neweastle-on-Tyne. ? St. Jumes’s, London, 8.W. tHeaton, Harry. Harborne House, Harborne, near Birmingham “Heaton, Joun Draxrn, M.D., F.R.G.P. Claremont, Leeds. {Hxavistpr, Rey. Canon J. W. L., M.A. The Close, Norwich. tHxcror, Jamns, M.D., F.R.S., F.G.S., F.R.G.S., Geological Survey of New Zealand. Wellington, New Zealand. {Heppre, M. Fosrrr, M.D., Professor of Chemistry in the University of St. Andrews, N.B. tHedgeland, Rev. W. J. 21 Mount Radford, Exeter. tHedley, Thomas, Cox Lodge, near Neweastle-on-Tyne. *Hemans, George William, C.E., M.R.LA., F.G.S. 1 Westminster- chambers, Victoria-street, London, S.W. tHenderson, Alexander. Dundee. tHenderson, Andrew. 120 Gloucester-place, Portman-square, Lon- don, W. “Henderson, A. L. 49 King William-street, London, E.C. LIST OF MEMBERS. 41 Year of Election, 1874, {Henderson, James Alexander. Norwood Tower, Belfast. 1876, *Henderson, William. Williamfield, Irvine, N.B. 1873. *Hunprrson, W. D. 9 University-square, Belfast. 1856, {Hennessy, Henry G., F.R.S., M.R.1A., Professor of Applied Mathematics and Mechanics in the Royal. College of Science for Ireland. 3 Idrone-terrace, Blackrock, Co. Dublin. 1857. {Hennessy, John Pope, C.M.G, Governor and Commander-in-Chief of Hong Kong. 1873. *Henrici, Olaus M. F. E., Ph.D., F.R.S., Professor of Applied Mathe- matics in University College, London. Meldorf Cottage, Green- hill Park, Harlesden, London, N.W. Henry, Franklin. Portland-street, Manchester. Henry, J. Snowdon. East Dene, Bonchurch, Isle of Wight. Henry, Mitchell, M.P. Stratheden House, Hyde Park, London, W. 1874. {Heyry, Rev. P. Suurpam, D.D.,M.R.LA. Belfast. “Henry, WILLIAM Cnarzes, M.D., F.R.S., F.G.S., F.R.G.S., F.C,S8. Haffield, near Ledbury, Herefordshire. 1870. {Henty, William. 12 Medina-villas, Brighton. 1855. *Hepburn, J. Gotch, LL.B., F.C.S. Baldwyns, Bexley, Kent. 1855. tHepburn, Robert. 9 Portland-place, London, W. Hepburn, Thomas. Clapham, London, 8.W. 1871. {Hepburn, Thomas H. St. Mary’s Cray, Kent. Hepworth, John Mason. Ackworth, Yorkshire. 1856. tHepworth, Rev. Robert. 2 St. James’s-square, Cheltenham. 1866, {Herrick, Perry. Bean Manor Park, Loughborough. 1871. *Hrrscoet, Professor ALEXANDER S., B.A., F.R.A.S. College of Science, Newcastle-on-Tyne. 1874.§§Herschel, Major John, R.E., F.R.S. Mussoorie, N. W. P. India. ( wis of Messrs. H. Robertson & Co., & Crosby-square, London, _ EC.) ; 1865. {Heslop, Dr. Birmingham. 1873. {Heugh, John. Gaunt’s House, Wimborne, Dorset. Hey, Rey. William, M.A., F.C.P.S. Clifton, York, 1866. *Heymann, Albert. West Bridgford, Nottinghamshire, 1866. {Heymann, L. West Bridgford, Nottinghamshire. 1879. §Heywood, A. Percival. Duffield Bank, Derby. 1861. *Heywood, Arthur Henry. Elleray, Windermere. ? *Hrrwoop, Jamus, F.R.S., F.G.S., F.S.A., F.R.GS., F.S.S. 26 Ken- sington Palace-gardens, London, W. : 1861. *Heywood, Oliver. Claremont, Manchester. Heywood, Thomas Percival. Claremont, Manchester. 1875. {Hicxs, Henry, M.D., F.G.S. Heriot House, Hendon, Middlesex, N.W 1877. §Hicks, W. M. St. John’s College, Cambridge. 1864, *Hrmrn, W. P., M.A. Castle House, Barnstaple. 1854, *Higgin, Edward. Troston Lodge, near Bury St. Edmunds. 1861. *Higgin, James. Lancaster-avenue, Fennel-street, Manchester. Higginbotham, Samuel. 4 Springfield-court, Queen-street, Glas- pow. . 1875. {Higgins, Charles Hayes, M.D., M.R.C.P., F.R.C.S., F.R.S.E. Alfred House, Birkenhead. 1871. {Hieers, Crement, B.A., F.C.S. 103 Holland-road, Kensington, London, W. 1854, {Hieerns, Rey. Henry H., M.A. The Asylum, Rainhill, Liver- ool. 1861, “Higgins, James. Holmwood, Turvey, near Bedford. 1870. tHigginson, Alfred. 135 Tulse Hill, London, S.W. 42 LIST OF MEMBERS. Year of Election. 5 Hildyard, Rey. James, B.D., F.C.P.S. Ingoldsby, near Grantham, Lincolnshire. Hill, Arthur. Bruce Castle, Tottenham, Middlesex. 1880. §Hill, Benjamin. Cwmdwr, near Clydach, Swansea. 1872. §Hill, Charles, F.S.A. Rockhurst, West Hoathley, East Grin- 1857. 1871. 1876. 1863. 1871. 1858. 1870. 1865. 1863. 1861. 1858. 1861. 1870, 1864. 1864, 1864. 1879. 1879. 1866. 1877. 1877. 1876. 1852. 1863. 1880. 1873. 1873. 1865. 1865. 1830. 1865. 1860. 1876. 1854. 1873. stead. *Hill, Rev. Edward, M.A., F.G.S. Sheering Rectory, Harlow. §Hill, John, C.K., M.R.LA., F.R.G.S.I. County Surveyor’s Office, Ennis, Ireland. THill, Lawrence. The Knowe, Greenock. Hill, William H. Barlanark, Shettleston, N.B. tHills, F.C. Chemical Works, Deptford, Kent, S.E. *Hills, Thomas Hyde. 358 Oxtord-street, London, W. tHincxs, Rev. Tuomas, B.A., F.R.S. Stancliff House, Clevedon, Somerset. tHinde, G. J. Buenos Ayres. *Hindmarsh, Luke. Alnbank House, Alnwick. tHinds, James, M.D. Queen’s College, Birmingham. t¢Hinds, William, M.D. Parade, Birmingham. *Hinmers, William. Cleveland House, Birkdale, Southport. tHirst, John, jun. Dobcross, near Manchester. *Hirst, T. Arcuer, Ph.D., F.R.S., F-R.A.S. Royal Naval College, Greenwich, 8.E.; and Athenzeum Club, Pall Mall, London, S.W. {Hitchman, William, M.D., LL.D., F.L.S. 29 Erskine-street, Liverpool. *Hoare, Rev. Canon. Godstone Rectory, Redhill. Hoare, J. Gurney. Hampstead, London, N.W. tHobhouse, Arthur Fane. 24 Cadogan-place, London, 8.W. t{Hobhouse, Charles Parry. 24 Cadogan-place, London, 8. W. tHobhouse, Henry William. 24 Cadogan-place, London, 8.W. §Hobkirk, Charles P., F.L.S. Huddersfield. §Hobson, John. Tapton Elms, Sheffield. tHocxry, Cuarites, M.D. 8 Avenue-road, St. John’s Wood, Lon- don, N.W. tHockin, Edward. Poughill, Stratton, Cornwall. tHodge, Rey. John Mackey, M.A. 38 Tavistock-place, Plymouth. tHodges, Frederick W. Queen’s College, Belfast. tHodges, John F., M.D., F.C.S., Professor of Agriculture in Queen's College, Belfast. *Hopexin, THomas. Benwell Dene, Newcastle-on-Tyne. §Hodgkinson, W. R. Eaton, Ph.D. Science Schools, South Kensing- ton Museum, London, 8. W. ; *Hodgson, George. Thornton-road, Bradford, Yorkshire. tHodgson, James. Oakfield, Manningham, Bradford, Yorkshire. tHodgson, Robert. Whitburn, Sunderland. tHodgson, R. W. North Dene, Gateshead. fHodgson, W. B., LL.D., F.R.A.S., Professor of Commercial and Political Economy in the University of Edinburgh. *Hormann, Aveust WitHELM, M.D., LL.D., Ph.D., F.R.S., F.C.S. 10 Dorotheen Strasse, Berlin. tHogan, Rev. A. R., M.A. Watlington Vicarage, Oxfordshire. {Hogg, Robert. 54 Jane-street, Glasgow. *Holcroft, George. Byron’s-court, St. Mary’s-gate, Manchester, *Holden, Isaac. Oakworth House, near Keighley, Yorkshire. 1879.§§Holland, Calvert Bernard. Ashdell, Broomhill, Sheffield. 1878. *Holland, Rev. F. W., M.A. Evesham. LIST OF MEMBERS. 43 ‘Year of Hlection. 1865. 1866. 1873. 1876. 1870. 1875. 1847. 1865. 1877. 1856. 1842. 1869, 1865. 1870. 1871. 1858, 1876. 1875. 1854. 1856, 1868. 1858, 1879. 1859. 1863. 1876, 1857, 1868. 1865. 1863. 1854. 1870. 1835. 1842. *Holland, Philip H. Home Office, London, S.W. tHolliday, William. New-street, Birmingham. *Holmes, Charles. 59 London-road, Derby. tHolmes, J. R. Southbrook Lodge, Bradford, Yorkshire. tHolms, Colonel William, M.P. 95 Cromwell-road, South Kensing- ton, London, 8. W. tHolt, William D. 23 Edge-lane, Liverpool. *Hood, John. The Elms, Cotham Hill, Bristol. tHooxer, Sir Josepn Darron, K.C.S.1., K.C.B., M.D., D.O.L., LL.D., F.R.S., V.P.L.S., F.G.S., F.R.G.S. Royal Gardens, Kew, Surrey. *Hooper, John P, Coventry Park, Streatham, London, S.W. *Hooper, Samuel F., B.A. Tamworth House, Mitcham Common, Surrey. {Hooton, Jonathan. 80 Great Ducie-street, Manchester. Hope, Thomas Arthur. Stanton, Bebington, Cheshire. {Hope, Wilkam, V.C. Parsloes, Barking, Essex. tHopkins, J. S. Jesmond Grove, Edgbaston, Birmingham. *Hopxinson, Joun, F.R.S. 78 Holland-road, Kensington, Lon- don, W. *Hopxrnson, Joun, F.L.S., F.G.S. 235 Regent-street, London, W.;. and Wansford House, Watford. Hopkinson, Joseph, jun. Britannia Works, Huddersfield. Hornby, Hugh. Sandown, Liverpool. *Horne, Robert R. 150 Hope-street, Glaszow. *Horniman, F. J. Surrey House, Forest Hill, London, S.E. }Horsfall, Thomas Berry. Bellamour Park, Rugeley. tHorsley, John H. 1 Ormond-terrace, Cheltenham. {Hotson, W. C. Upper King-street, Norwich. Hoveuton, The Right Hon. Lord, M.A., D.C.L., F.R.S., F.R.G.S.. Travellers’ Club, London, S. W. }Hounsfield, James. Hemsworth, Pontefract. Hovenden, W. F., M.A. Bath. *Howard, D, South Frith Lodge, Tonbridge. {tHoward, Captain John Henry, R.N. The Deanery, Lichfield. tHoward, Philip Henry. Corby Castle, Carlisle. tHowatt, James. 146 Buchanan-street, Glascow. tHowell, Henry H., F.G.S. Museum of Practical Geology, Jermyn-. street, London, 8. W. tHowex tt, Rev. Canon Hinps. Drayton Rectory, near Norwich. *How ert, Rey. Freperick, F.R.A.S. East Tisted Rectory, Alton, Hants. tHoworrn, H. H. Derby House, Eccles, Manchester. tHowson, The Very Rev. J. S., D.D., Dean of Chester. Chester. tHubback, Joseph. 1 Brunswick-street, Liverpool. *Hupson, Henry, M.D., M.R.I.A. Glenville, Fermoy, Co. Cork. §Hudson, Robert, F.R.S., F.G.S., F.L.S. Clapham Common, London, S.W. 1879.§§ Hudson, Robert S., M.D. Redruth, Cornwall. 1867. 1858. 1857. 1871. 1870. }Hudson, William H.H., M.A. 19 Bennet’s-hill, Doctors’ Commons, London, E.O. ; and St. John’s College, Cambridge. *Hueerns, Wit11aM, D.O.L. Oxon., LL.D. Camb., F.R.S., F.R.A.S. Upper Tulse Hill, Brixton, London, 8.W. tHuggon, William. 30 Park-row, Leeds. *Hughes, George Pringle, J.P. Middleton Hall, Wooler, Northum- berland. *Hughes, Lewis. Fenwick-court, Liverpool. 44 Year of Election. 1876. 1868. 1863. 1865. 1867. 1861. 1878. 1880. 1856. 1862. 1877. 1865. 1840. 1864, 1875. 1868. 1867. 1869. 1879. 1863. 1875. 1869, 1861. 1870, 1876. 1876. 1868. 1864. 1857. 1861. 1852. 1871. 1879. 1873.§ 1861. LIST OF MEMBERS. *Hughes, Rey. Thomas Edward. Wallfield House, Reigate. §Huaues, T. M‘K., M.A., F.G.S., Woodwardian Professor of Geology in the University of Cambridge. tHughes, T. W. 4 Hawthorn-terrace, Newcastle-on-Tyne. tHughes, W. R., F.L.S., Treasurer of the Borough of Birmingham. Birmingham. §Huit, Epwarp, M.A., F.R.S., F.G.S., Director of the Geological Survey of Ireland, and Professor of Geology in the Royal Callege of Science. 14 Hume-street, Dublin. *Hulse, Sir Edward, Bart., D.C.L. 47 Portland-place, London, W. ; and Breamore House, Salisbury. f{Hume, Rey. Canon Asranam, D.C.L., LL.D., F.S.A. All Souls’ Vicarage, Rupert-lane, Liverpool. tHumphreys, H. Castle-square, Carnarvon. §Humphreys, Noel A., F.S.S.. Ravenhurst, Hook, Kingston-on- Thames. tHumphries, David James. 1 Keynsham-parade, Cheltenham. *Humpury, GeorcE Murray, M.I)., F.R.S., Professor of Anatomy in the University of Cambridge. Grove Lodge, Cambridge. *Hont, Arraur Roopg, M.A., F.G.8. Southwood, Torquay. t{Hunt, J. P. Gospel Oak Works, Tipton. tHounr, Rozert, F.R.S., Keeper of the Mining Records. Museum of Practical Geology, Jermyn-street, London, S.W. : tHunt, W. 72 Pulteney-street, Bath. *Hunt, William. The Woodlands, Tyndall’s Park, Clifton, Bristol. Hunter, Andrew Galloway. Denholm, Hawick, N.B. {Hunter, Christopher. Alliance Insurance Office, North Shields. tHunter, David. Blackness, Dundee. *Hunter, Rev. Robert, F.G.S. 9 Mecklenburgh-street, London, W.C. §Huntington, A. K., Professor of Metallurgy in Kine’s College, London. Abbeville House, Arkwright-road, Hampstead, London, N. W. tHuntsman, Benjamin. West Retford Hall, Retford. tHurnard, James. Lexden, Colchester, Essex. {Hurst, George. Bedford. *Hurst, William John. Drumaness Mills, Ballynahinch, Lisburn, Ireland. tHurter, Dr. Ferdinand. Appleton, Widnes, near Warrington. Husband, William Dalla. May Bank, Bournemouth. tHutchinson, John. 22 Hamilton Park-terrace, Glasgow. [ Hutchison, Peter. 28 Berkeley-terrace, Glasgow. *Hutchison, Robert, F.R.S.E. 29 Chester-street, Edinburgh. Hutton, Crompton. Putney Park, Surrey, S.W. *Hutton, Darnton. (Care of Arthur Lupton, Esq., Headingley, near Leeds.) tHutton, Henry D. 10 Lower Mountjoy-street, Dublin. *Horron, T. Maxwett. Summerhill, Dublin. f{Huxtzy, Tuomas Henry, Ph.D., LL.D., Sec. R.S., F.L.S., F.G.S., Professor of Natural History in the Royal School of Mines. 4 Marlborough-place, London, N.W. Hyde, Edward. Dukinfield, near Manchester. *Hyett, Francis A. Painswick House, Stroud, Gloucestershire. §Ibbotson, H. J. 26 Collegiate-crescent, Sheffield. Ihne, William, Ph.D. Heidelberg. §Ikin, J. I. 19 Park-place, Leeds. fIles, Rey. J. H. Rectory, Wolverhampton. LIST OF MEMBERS. 45 Year of Election. 1858, {Ingham, Henry. Wortley, near Leeds. 1876. {Inglis, Anthony. Broomhill, Partick, Glasgow. 1871. {Inaxis, The Right Hon. Joun, D.C.L., LL.D., Lord Justice General of Scotland. Edinburgh. 1876. {Inglis, John, jun. Prince’s-terrace, Dowanhill, Glasgow. 1852. tIneram, J. K., LL.D., M.R.LA., Regius Professor of Greek in the University of Dublin. 2 Wellington-road, Dublin. 1870. *Inman, William. Upton Manor, Liverpool. 1857. {Irvine, Hans, M.A., M.B. 1 Rutland-square, Dublin. 1862. {Isenin, J. F., M.A., F.G.S. South Kensington Museum, London, S.W 1863. *Ivory, Thomas. 23 Walker-street, Edinburgh. 1865. {Jabet, George. Wellington-road, Handsworth, Birmingham. 1870. {Jack, James. 26 Abercromby-square, Liverpool. 1859. {Jack, John,M.A. Belhelvie-by-Whitecairns, Aberdeenshire. 1876. {Jack, William. 19 Lansdowne-road, Notting Hill, London, W. 1879. §Jackson, Arthur, F.R.0.S. Wilkinson-street, Sheffield. 1866. {Jackson, H. W., F.R.AS., F.G.S. 15 The Terrace, High-road, Lewisham, 8.E. 1869. §Jackson, Moses. The Vale, Ramsgate. 1863, *Jackson-Gwilt, Mrs. H. Moonbeam Villa, The Grove, New Wim- : bledon, London, 8. W. 1852. {Jacoss, Berne. 40 George-street, Hull. 1874. *Jaffe, John. Cambridge Villa, Strandtown, near Belfast. 1865. *Jaffray, John. Park-grove, Edgbaston, Birmingham. 1872. {James, Christopher. 8 Laurence Pountney Hill, London, E.C. 1860. {James, Edward H. Woodside, Plymouth. 1863. *Jamzs, Sir Watrer, Bart., F.G.S. 6 Whitehall-cardens, London, 5. W, 1858. {James, William C. Woodside, Plymouth. 1876. {Jamieson, J. L. K. The Mansion House, Govan, Glasgow. 1876. {Jamieson, Rev. Dr. R. 156 Randolph-terrace, Glasgow. 1859. *Jamieson, Thomas F., F.G.S. Ellon, Aberdeenshire. 1850. {Jardine, Alexander. Jardine Hall, Lockerby, Dumfriesshire. 1870. {Jardine, Edward. Beach Lawn, Waterloo, Liverpool. 1853. ea Rey. Canon J., M.A. North Cave, near Brough, York- shire. JARRETT, Rey. THomas, M.A., Professor of Arabic in the University of Cambridge. Trunch, Norfolk. 1870.§§Jarrold, John James. London-street, Norwich. 1862. {Jeakes, Rev. James, M.A. 54 Argyll-road, Kensington, London, W. Jebb, Rev. John. Peterstow Rectory, Ross, Herefordshire. 1868. {Jecks, Charles. 26 Langham-place, Northampton. 1856. {Jeffery, Henry M., M.A., F.R.S. 438 High-street, Cheltenham. 1855. *Jeffray, John. Cardowan House, Millerston, Glasgow. : 1867. ee Howel, M.A., F.R.A.S. 5 Brick-court, Temple, London, 1861. *Jerrreys, J. Gwyn, LL.D., F.R.S., F.L.S., Treas, G.S., F.R.G.S. Ware Priory, Herts. 1852. ey Rey. Joun H., B.D., M.R.LA. 64 Lower Leeson-street, ublin. 1862.§§JENKIN, H. ©. Freemine, F.R.S., M.LO0.E., Professor of Civil Engineering in the University of Edinburgh. 3 Great Stuart- street, Edinburgh. eta Major-General J. J. 14 St. James’s-square, London, 46 LIST OF MEMBERS. Year of Election. 1880, *JzEnKINs, JoHN JonEs. The Grange, Swansea. Jennette, Matthew. 106 Conway-street, Birkenhead. 1852, {Jennings, Francis M., F.G.S., M.R.LA. Brown-street, Cork. 1872, {Jennings, W. Grand Hotel, Brighton. 1878, {Jephson, Henry L. Chief Secretary’s Office, The Castle, Dublin. *Jerram, Rey. 8. John, M.A. Chobham Vicarage, Woking Station, Surrey. 1872. {Jesson, Thomas. 7 Upper Wimpole-street, Cavendish-square, London, W. Jessop, William, jun. Butterley Hall, Derbyshire. 1870, *Jevons, W. Sranztey, M.A., LL.D., F.R.S., Professor of Political Economy in University College, London. 2 The Chestnuts, Branch Hill, Hampstead Heath, London, N.W. 1872. *Joad, George C. Oaktield, Wimbledon, Surrey, S.W. 1871. *Johnson, David, F.C.S., F.G.S. Irvon Villa, Grosvenor-road, Wrexham. 1865. *Johnson, G. J. 36 Waterloo-street, Birmingham. 1875. §Johnson, James Henry, F.G.S., F.S.A. 73 Albert-road, Southport. 1866. {Johnson, John. Knighton Fields, Leicester. 1866. tJohnson, John G. 18a Basinghall-street, London, E.C. 1872. {Johnson, J.T. 27 Dale-street, Manchester. 1861. {Johnson, Richard. 27 Dale-street, Manchester. 1870.§§Johnson, Richard C., F.R.A.S. Higher Bebington Hall, Birken- head. 1863. {Johnson, R. S. Hanwell, Fence Houses, Durham. *Johnson, Thomas. Bache Hurst, Liverpool-road, Chester. 1861. {Johnson, William Beckett. Woodlands Bank, near Altrincham. 1864, {Johnston, David. 15 Marlborough-buildings, Bath. 1859. {Johnston, James, Newmill, Elgin, N.B. 1864. {Johnston, James. Manor House, Northend, Hampstead, London, N.W *Jobhnstone, James. Alva House, Alva, by Stirling, N.B. 1864. tJohnstone, John. 1 Barnard-villas, Bath. 1876. {Johnstone, William. 5 Woodside-terrace, Glasgow. 1864, {Jolly, Thomas. Park! View-villas, Bath. 1871.§§Jolly, William (H.M. Inspector of Schools). Inverness, N.B. 1849, {Jones, Baynham. Selkirk Villa, Cheltenham. 1856, {Jones, C. W. 7 Grosvenor-place, Cheltenham. 1877.§§ Jones, Henry C., F.C.S. 166 Blackstock-road, London, N, *Jones, Robert. 2 Castle-street, Liverpool. 1873. {Jones, Theodore B. 1 Finsbury-cireus, London, E.C. 1880. §Jones, Thomas. 15 Gower-street, Swansea. 1860. {Jonzs, Toomas Rupert, F.R.S., F.G.S., Professor of Geology at the Staff College, Sandhurst. Powis Villa, Camberley, Surrey. 1847. {Jonzs, THomas Rymer, F.R.S. 52 Cornwall-road, Westbourne Park, London, W. 1864.§§JonEs, Sir Wintovensy, Bart., F.R.G.S. Cranmer Hall, Fakenham, Norfolk. 1875, *Jose, J. E. 38 Queen-square, Bristol. *Joule, Benjamin St. John B., J.P. 28 Leicester-street, Southport, Lancashire. 1842. *JouLE, James Prescorr, LL.D., F.R.S., F.C.S. 12 Wardle-road, Sale, near Manchester. 1847. {Jowerr, Rev. B., M.A., Regius Professor of Greek in the University of Oxford. Balliol College, Oxford. 1858. {Jowett, John. Leeds. ; 1879.§§Jowitt, A. Hawthorn Lodge, Clarkehouse-road, Sheffield. LIST OF MEMBERS, 47 ‘Year of ‘Election. 1872, 1848. 1870. 1868. 1857. 1859. 1847. 1872. 1875. 1878. 1876, 1864, 1853. 1875. 1876. 1865. 1857. 1857. 1855. 1876. 1868. 1869. 1869. 1861. 1876. 1876. 1865. 1878. 1860. 1875. 1872. 1875. 1871. 1855. 1870. 1864, {Joy, Algernon, Junior United Service Club, St. James's, London, S.W *Joy, Rey. Charles Ashfield. Grove Parsonage, Wantage, Berkshire, Joy, Rev. John Holmes, M.A. 3 Coloney-terrace, Tunbridge Wells. *Jubb, Abraham. Halifax. fJudd, John Wesley, F.R.S.,F.G.S, 4 Auriol-road, West Kensington, London, W. *Kaines, Joseph, M.A.,D.Se. 401 Finsbury-pavement, London, E.C. Kang, Sir Roserr, M.D., LL.D., F.R.S., M.R.LA., F.0.8., Prin- cipal of the Royal College of Cork. Fortland, Killiney, Oo. Dublin. {Kavanagh, James W. Grenville, Rathgar, Ireland. {Kay, David, F.R.G.S. 19 Upper Phillimore-place, Kensington, London, W. Kay, John Cunliff. Fairfield Hall, near Skipton. Kay, Robert. Haugh Bank, Bolton-le-Moors. *Kay, Rey. William, D.D. Great Leghs Rectory, Chelmsford. {Keames, William M. 5 Lower Rock-gardens, Brighton. {Keeling, George William. Tuthill, Lydney. *Kelland, William Henry. 110 Jermyn-street, London, S.W.; and Grettans, Bow, North Devon. {Kelly, Andrew G. The Manse, Alloa, N.B. *Kelly, W. M., M.D. 11 The Crescent, Taunton, Somerset. {Kemp, Rey. Henry William, B.A. The Charter House, Hull. [Kunnepy, ALexanper B, W., C.E., Professor of Engineering in University College, London. 9 Bartholomew-road, London, N. W. {Kennedy, Hugh. Redclyffe, Partickhill, Glasgow. {Kenrick, William. Norfolk-road, Edgbaston, Birmingham. Kent, J.C. Levant Lodge, Earl’s Croome, Worcester. {Kent, William T., M.R.D.S. 51 Rutland-square, Dublin. *Ker, André Allen Murray. Newbliss House, Newbliss, Ireland. *Ker, Robert. Dougalston, Milngavie, N.B. {Ker, William. 1 Windsor-terrace West, Glasgow. {Kerrison, Roger. Crown Bank, Norwich. *Kesselmeyer, Charles A. 1 Peter-street, Manchester. *Kesselmeyer, William Johannes. 1 Peter-street, Manchester. *Keymer, John. Parker-street, Manchester. {Kidston, J. B. West Regent-street, Glasgow. {Kidston, William. Ferniegair, Helensburgh, N.B. pamabe Edward Hudson, M.R.LA. 11 Merrion-square North, Dublin. {Kinahan, Edward Hudson, jun. 11 Merrion-square North, Dublin. {Kuvanan, G. Huyry, M.R.LA., Geological Survey of Ireland. 14 Hume-street, Dublin. *Kinch, Edward, F.C.S. Agricultural College, Home Department, Tokio, Japan. (Care of C. J, Kinch, Esq., 8 West Kensington- terrace, London, W. “King, Mrs. E. M. 84 Cornwall-road, Westbourne Park, London, W. *King, F. Ambrose. Avonside, Clifton, Bristol. “King, Herbert Poole. Theological College, Salisbury. {King, James. Levernholme, Hurlet, Glasgow. §King, John Thomson, C.E. 4 Clayton-square, Liverpool. King, Joseph. Blundell Sands, Liverpool. § Kine, saline M.D. 27 George-street, and Royal Institution, Hull, 48 LIST OF MEMBERS. Year of Election. 1860, *King, Mervyn Kersteman. 1 Vittoria-square, Clifton, Bristol. - - 1875. *King, Perey L. Avonside, Clifton, Bristol. 1870. {King, William. 13 Adelaide-terrace, Waterloo, Liverpool. King, William Poole, F.G.S. Avonside, Clifton, Bristol. 1869. {Kinedon, K. Taddiford, Exeter. 1861. {Kingsley, John. Ashfield, Victoria Park, Manchester. 1876. §Kingston, Thomas. Strawberry House, Chiswick, Middlesex. 1835. Kingstone, A. John, M.A. Mosstown, Longford, Ireland. 1875. §Krnezerr, Cxartus T., F.C.S. 12 Auriol-road, The Cedars, West Kensington, London, W. 1867. {Kinloch, Colonel. Kirriemuir, Logie, Scotland. 1867. *Kinnatrp, The Right Hon. Lord. 2 Pall Mall East, London, S.W.; and Rossie Priory, Inchture, Perthshire. 1870. {Kinsman, William R. Branch Bank of England, Liverpool. 1863. { Kirkaldy, David. 28 Bartholomew-road North, London, N.W. 1860. {Krrxman, Rev. Tuomas P., M.A., F.R.S. Croft Rectory, near Warrington. Kirkpatrick, Rev. W. B., D.D. 48 North Great George-street, Dublin. 1876. *Kirkwood, Anderson, LL.D., F.R.S.E. 12 Windsor-terrace West, Hillhead, Glasgow. 1875. {Kirsop, John. 6 Queen’s-crescent, Glasgow. 1870. {Kitchener, Frank EK. Newcastle, Staffordshire. 1869. {Knapman, Edward. The Vineyard, Castle-street, Exeter. 1870. {Kneeshaw, Henry. 2 Gambier-terrace, Liverpool. 1836. Knipe, J. A. Botcherby, Carlisle. 1872. *Knott, George, LL.B., F.R.A.S. Knowles Lodge, Cuckfield, Hay- ward's Heath, Sussex. 1878. *Knowles, George. Moorhead, Shipley, Yorkshire. 1872. {Knowles, James. The Hollies, Clapham Common, S.W. 1842. Knowles, John. The Lawn, Rugby. 1870. {Knowles, Rev. J. L. 103 Earl’s Court-road, Kensington, London, W. 1874.§§Knowles, William James. Cullybackey, Belfast, Ireland. 1876. {Knox, David N., M.A., M.B. 8 Belgrave-terrace, Hillhead, Glasgow. *Knox, George James. 2 Coleshill-street, Eaton-square, London, S.W 1835. Knox, Thomas Perry. Union Club, Trafalgar-square, London, W.C. 1875. *Knubley, Rev. E. P. Staveley Rectory, Leeds. 1870. {Kynaston, Josiah W., F.C.S. St. Helen’s, Lancashire. 1865. tKynnersley, J.C.S. The Leveretts, Handsworth, Birmingham. 1858. §Lace, Francis John. Stone Gapp, Cross-hill, Leeds. 1859. §Ladd, William, F.R.A.S. 11 & 18 Beak-street, Regent-street, Lon- don, W. 1870. {Laird, H.H. Birkenhead. 1870. §Laird, John, jun. Grosvenor-road, Claughton, Birkenhead. 1880. *Lake, Samuel. Milford Docks, Milford Haven. 1877. §Lake, W.C., M.D. Teignmouth. 1859. {Lalor, John Joseph, M.R.I.A. 2 Longford-terrace, Monkstown, Co. Dublin. 1871. {Lancaster, Kdward. Karesforth Hall, Barnsley, Yorkshire. 1877. {Landon, Frederic George, M.A., F.R.A.S. 8 The Circus, Green- wich, London, S.E. 1859. {Zang, Rev. John Marshall. Bank House, Morningside, Edinburgh. 1864, tLang, Robert. Langford Lodge, College-road, Clifton, Bristol. 1870, {Langtou, Charles. Barkhill, Aigburth, Liverpool. LIST OF MEMBERS. 49° ‘Year of Election. 1865, 1880. 1878, 1861. 1870. 1870. 1875. 1870. 1878. 1857, 1862. 1870. 1875. 1857. 1876. 1868. 1863. 1853. 1865. 1857. 1870. 1847, 1844. 1858. 1863. 1872. 1858. 1861. 1853. 1859. 1872. 1869, *Langton, William. Docklands, Ingatestone, Essex. tLanxester, E. Ray, M.A., F.R.S., Professor of Comparative Ana- tomy and Zoology in University College, London. Exeter College, Oxford; and 11 Wellington Mansions, North Bank, London, N.W. “Lansdell, Rev. Henry. Eyre Cottage, Blackheath, London, S.E. Lanyon, Sir Charles. The Abbey, White Abbey, Belfast. tLapper, E., M.D. 61 Harcourt-street, Dublin. *Latham, Arthur G. Lower King-street, Manchester. *LatHaM, Barpwin, C.E., F.G.S. 7 Westminster-chambers, West- minster, 8. W. tLaughton, John Knox, M.A., F.R.A.S., F.R.G.S. Royal Naval College, Greenwich, S.E. tLavington, William F, 107 Pembroke-road, Clifton, Bristol.