Front Matter

ADVERTISEMENT. The Committee appointed by the Royal Society to direct the publication of the Philosophical Transactions, take this opportunity to acquaint the Public, that it fully appears, as well from the Council-books and Journals of the Society, as from repeated declarations which have been made in several former Transactions, that the printing of them was always, from time to time, the single act of the respective Secretaries till the Forty-seventh Volume; the Society, as a Body, never interesting themselves any further in their publication, than by occasionally recommending the revival of them to some of their Secretaries, when, from the particular circumstances of their affairs, the Transactions had happened for any length of time to be intermitted. And this seems principally to have been done with a view to satisfy the Public, that their usual meetings were then continued, for the improvement of knowledge, and benefit of mankind, the great ends of their first institution by the Royal Charters, and which they have ever since steadily pursued. But the Society being of late years greatly enlarged, and their communications more numerous, it was thought advisable that a Committee of their members should be appointed, to reconsider the papers read before them, and select out of them such as they should judge most proper for publication in the future Transactions; which was accordingly done upon the 26th of March 1752. And the grounds of their choice are, and will continue to be, the importance and singularity of the subjects, or the advantageous manner of treating them; without pretending to answer for the certainty of the facts, or propriety of the reasonings, contained in the several papers so published, which must still rest on the credit or judgement of their respective authors. It is likewise necessary on this occasion to remark, that it is an established rule of the Society, to which they will always adhere, never to give their opinion, as a Body, upon any subject, either of Nature or Art, that comes before them. And therefore the thanks, which are frequently proposed from the Chair, to be given to the authors of such papers as are read at their accustomed meetings, or to the persons through whose hands they received them, are to be considered in no other light than as a matter of civility, in return for the respect shown to the Society by those communications. The like also is to be said with regard to the several projects, inventions, and curiosities of various kinds, which are often exhibited to the Society; the authors whereof, or those who exhibit them, frequently take the liberty to report and even to certify in the public newspapers, that they have met with the highest applause and approbation. And therefore it is hoped that no regard will hereafter be paid to such reports and public notices; which in some instances have been too lightly credited, to the dishonour of the Society. The Meteorological Journal hitherto kept by the Assistant Secretary at the Apartments of the Royal Society, by order of the President and Council, and published in the Philosophical Transactions, has been discontinued. The Government, on the recommendation of the President and Council, has established at the Royal Observatory at Greenwich, under the superintendence of the Astronomer Royal, a Magnetical and Meteorological Observatory, where observations are made on an extended scale, which are regularly published. These, which correspond with the grand scheme of observations now carrying out in different parts of the globe, supersede the necessity of a continuance of the observations made at the Apartments of the Royal Society, which could not be rendered so perfect as was desirable, on account of the imperfections of the locality and the multiplied duties of the observer. A List of Public Institutions and Individuals, entitled to receive a copy of the Philosophical Transactions of each year, on making application for the same directly or through their respective agents, within five years of the date of publication. **Observatories.** - Armagh. - Cape of Good Hope. - Dublin. - Edinburgh. - Greenwich. - Kew. - Liverpool. - Madras. - Oxford (Radcliffe). **Institutions.** - Barbadoes Library and Museum. - Calcutta Asiatic Society. - Geological Museum. - Cambridge Philosophical Society. - Dublin Royal Dublin Society. - Royal Irish Academy. - Royal Society. - London Admiralty Library. - Chemical Society. - Entomological Society. - Geological Society. - Geological Survey of Great Britain. - Horticultural Society. - Institute of British Architects. - Institution of Civil Engineers. - Linnean Society. - London Institution. - Medical and Chirurgical Society. - Queen's Library. - Royal Asiatic Society. - Royal Astronomical Society. - Royal College of Physicians. - Royal Geographical Society. - Royal Institution of Great Britain. - Royal Society of Literature. - Society of Antiquaries. - Society of Arts. - The Treasury Library. - United Service Museum. - Zoological Society. - Malta Public Library. - Manchester Literary and Philosophical Society. - Oxford Ashmolean Society. - Radcliffe Library. - Swansea Royal Institution. - Sydney University Library. - Woolwich Royal Artillery Library. **Belgium.** - Brussels Royal Academy of Sciences. **Denmark.** - Altona Royal Observatory. - Copenhagen Royal Society of Sciences. **France.** - Paris Academy of Sciences. - Dépôt de la Marine. - Ecole des Mines. - Geographical Society. - Geological Society. - Jardin des Plantes. - Toulouse Academy of Sciences. **Germany.** - Berlin Royal Academy of Sciences. - Society of Experimental Philosophy. - Bonn Cesarean Acad. of Naturalists. - Frankfort Natural History Society. - Giessen University. - Göttingen University. - Hamburg Naturwissenschaftlicher-Verein. - Leipzig Royal Saxon Society of Sciences. - Mannheim Observatory. - Munich Royal Academy of Sciences. - Prague Bohemian Society of Sciences. - Vienna Imperial Academy of Sciences. - Würzburg Physico-Medical Society. **Hungary.** - Pesth Hungarian Academy of Sciences. **Italy.** - Milan Institute of Sciences, Letters and Arts. - Modena Italian Society of Sciences. - Naples Institute of Sciences. - Rome Academy de' Nuovi Lincei. - Collegio Romano. - Turin Royal Academy of Sciences. - Venice Institute of Sciences, Letters, and Arts. **Java.** - Batavia Batavian Society of Sciences. **Netherlands.** - Amsterdam Royal Institute. - Haarlem Dutch Society of Sciences. - Rotterdam Batavian Society of Experimental Philosophy. **Portugal.** - Lisbon Royal Academy of Sciences. **Russia.** - Moscow Imperial Society of Naturalists. - Pulkowa Observatory. - St. Petersburgh Imperial Academy of Sciences. **Spain.** - Cadiz Observatory. - Madrid Royal Academy of Sciences. **Sweden and Norway.** - Drontheim Royal Society of Sciences. - Stockholm Royal Academy of Sciences. **Switzerland.** - Bern Allg. Schweizerischen Gesellschaft. - Geneva Société de Phys. et d'Hist. Naturelle. **United States.** - Albany New York State Library. - Boston American Academy of Sciences. - The Editors of Silliman's Journal. - Cambridge Harvard University. - Philadelphia American Philosophical Society. - Washington Smithsonian Institution. - Observatory. The fifty Foreign Members of the Royal Society. A List of Public Institutions and Individuals, entitled to receive a copy of the Astronomical Observations (including Magnetism and Meteorology) made at the Royal Observatory at Greenwich, on making application for the same directly or through their respective agents, within two years of the date of publication. | Observatories | Institutions | |-----------------------|--------------------------------------------------| | Altona | Aberdeen University | | Armagh | Berlin Academy | | Berlin | Bologna Academy | | Breslau | Boston American Academy of Sciences | | Brussels | Brunswick U.S. Bowdoin College | | Cadiz | Cambridge Trinity College Library | | Cambridge | Cambridge U.S. Harvard University | | Cape of Good Hope | Dublin University | | Coimbra | Edinburgh University | | Copenhagen | Royal Society | | Dorpat | Glasgow University | | Dublin | Göttingen University | | Edinburgh | Leyden University | | Helsingfors | London Board of Ordnance | | Königsberg | Queen's Library | | Madras | Royal Institution | | Mannheim | Royal Society | | Marseille | Oxford Savilian Library | | Milan | Paris Academy of Sciences | | Munich | Board of Longitude | | Oxford | Dépôt de la Marine | | Palermo | Pesth Hungarian Academy | | Paris | Philadelphia American Philosophical Society | | Seeberg | St. Andrews University | | Trevandrum | St. Petersburgh Imperial Academy | | Tübingen | Stockholm Royal Academy of Sciences | | Turin | Upsal Royal Society | | Vienna | Waterville, Maine (U.S.) College | | Wilna | | | Individuals | | |-----------------------|--------------------------------------------------| | Christie, S. H., Esq. | Twickenham | | Lubbock, Sir John William, Bart. | London. | | Lowndes Professor of Astronomy | Cambridge. | | Plumian Professor of Astronomy | Cambridge. | | President of the Royal Society | London. | | Ross, Rear-Admiral Sir J. C. | Aylesbury. | | Smyth, Vice-Admiral W. H. | Aylesbury. | | South, Sir James | Kensington. | | The Earl of Rosse | Parsonstown. | A List of Observatories, Institutions and Individuals, entitled to receive a Copy of the Magnetical and Meteorological Observations made at the Royal Observatory, Greenwich. ### Observatories - **Bombay** - **Cairo** - **Cambridge, United States** Prof. J. Lovering. - **Christiania** C. Hansteen. - **Gotha** - **Heidelberg** M. Tiedemann. - **Kew** B. Stewart. - **Kremsmünster** P. A. Reslhuber. - **Leipsic** Professor Möbius. - **Marburg** Professor Gerling. - **Prague** K. Jelinek. - **Stockholm** Professor H. Selander. - **Toronto** Professor Kingston. - **Upsal** Professor Svanberg. - **Washington** Com. Maury, U.S. Navy. ### Institutions - **Bombay** Geographical Society. - **Bonn** University. - **The Public Library (late Bowditch)** Boston, U.S. - **Cambridge** Philosophical Society. - **Cherkow** University. - **Falmouth** Royal Cornwall Polytechnic Society. - **London** House of Lords, Library. House of Commons, Library. King's College. Royal Society. University College, Library. - **Oxford** Radcliffe Observatory. - **Paris** Meteorological Society. - **St. Bernard** Convent. - **Washington** Smithsonian Institution. - **Woolwich** Office of Mag. and Met. Publication. ### Individuals - **Bache**, Dr. A. D. Washington. - **Barlow**, P., Esq. Charlton. - **Ballot**, Dr. Buys Utrecht. - **Dove**, Prof. H. W. Berlin. - **Erman**, Dr. Adolph Berlin. - **Fox**, R. W., Esq. Falmouth. - **Gilliss**, Lt. J. M., U.S. Navy Washington. - **Harris**, Sir W. Snow Plymouth. - **Howard**, Luke, Esq. Tottenham. - **Kaemtz**, Prof. L. F. Dorpat. - **Kreil**, Prof. K. Vienna. - **Kupffer**, A. T. St. Petersburgh. (Twelve copies for distribution to the Russian Mag. and Met. Obs.) - **Lloyd**, Rev. Dr. Dublin. - **Loomis**, Prof. E. New York University. - **Lovering**, Prof. J. Cambridge, U.S. - **Pegado**, Dr. Lisbon. - **Phillips**, Prof. John Oxford. - **Quetelet**, A. Brussels. - **Sabine**, Major-General, R.A. London. - **Senftenberg**, Baron von Prague. - **Vernon**, G. V., Esq. Manchester. - **Wartmann**, Prof. Elie Geneva. - **Younghusband**, Lieut.-Col., R.A. Woolwich. CONTENTS. I. On the Analytical Theory of the Attraction of Solids bounded by surfaces of a hypothetical Class including the Ellipsoid. By W. F. Donkin, M.A., F.R.S., F.R.A.S., Savilian Professor of Astronomy in the University of Oxford .................................................. page 1 II. On an Extended Form of the Index Symbol in the Calculus of Operations. By William Spottiswoode, M.A., F.R.S. .......................................................... 13 III. On the Resin of Ficus rubiginosa, and a new Homologue of Benzylic Alcohol. By Warren De la Rue, Ph.D., F.R.S., Treasurer of the Chemical Society, Secretary of the Royal Astronomical Society, &c., and Hugo Müller, Ph.D., F.C.S. ......................................................................................... 43 IV. On the Theory of Compound Colours, and the Relations of the Colours of the Spectrum. By J. Clerk Maxwell, M.A., Professor of Natural Philosophy in Marischal College and University of Aberdeen. Communicated by Professor Stokes, Sec. R.S. .............................................................................. 57 V. On the Effect of the presence of Metals and Metalloids upon the Electric Conducting Power of Pure Copper. By A. Matthiessen, Ph.D., and M. Holzmann, Ph.D. Communicated by Professor Wheatstone, F.R.S. ......................................................................................... 85 VI. On the Equation of Differences for an Equation of any Order, and in particular for the Equations of the Orders Two, Three, Four, and Five. By Arthur Cayley, Esq., F.R.S. ..................................................................................... 93 VII. On the Volumetric Relations of Ozone, and the Action of the Electrical Discharge on Oxygen and other Gases. By Thomas Andrews, M.D., F.R.S., M.R.I.A., Vice-President of Queen’s College, Belfast; and Peter G. Tait, M.A., late Fellow of St. Peter’s College, Cambridge, Professor of Mathematics in Queen’s College, Belfast .................................................................................................................. 113 VIII. On the Mathematical Theory of Sound. By the Rev. S. Earnshaw, M.A., Sheffield. Communicated by Professor W. H. Miller, F.R.S. ......................................................................................... 133 IX. On the Lines of the Solar Spectrum. By Sir David Brewster, K.H., D.C.L., F.R.S. L. & E., and Dr. J. H. Gladstone, F.R.S. . . . . . . . . . . . . page 149 X. On the Electric Conducting Power of Alloys. By A. Matthiessen, Ph.D. Communicated by Professor Wheatstone, F.R.S. . . . . . . . . . . . . . . . . . . 161 XI. On the Specific Gravity of Alloys. By A. Matthiessen, Ph.D. Communicated by Professor Wheatstone, F.R.S. . . . . . . . . . . . . . . . . . . 177 LIST OF ILLUSTRATIONS. Plates I. II.—Professor J. Clerk Maxwell on the Theory of Compound Colours. Plate III.—Dr. Andrews and Professor Tait on the Volumetric Relations of Ozone. Plate IV.—Sir David Brewster and Dr. J. H. Gladstone on the Lines of the Solar Spectrum. Plates V. VI.—Dr. A. Matthiessen on the Electric Conducting Power of Alloys. XII. The Bakerian Lecture.—Experimental Researches to determine the Density of Steam at different Temperatures, and to determine the Law of Expansion of Superheated Steam. By William Fairbairn, Esq., F.R.S., and Thomas Tate, Esq. .................................................. page 185 XIII. On a new Method of Approximation applicable to Elliptic and Ultra-elliptic Functions. By Charles W. Merrifield. Communicated by the Rev. H. Moseley, F.R.S. ........................................................................................................... 223 XIV. On Quaternary Cubics. By the Rev. George Salmon, D.D., M.R.I.A. Communicated by A. Cayley, Esq., F.R.S. ........................................................................................................... 229 XV. On Isoprene and Caoutchine. By C. Greville Williams ................................................................................................................................................................................................. 241 XVI. On the Relation between Boiling-point and Composition in Organic Compounds. By Hermann Kopp, M.D., Ph.D., Professor of Theoretical Chemistry in the University of Giessen. Communicated by Dr. A. W. Hofmann, F.R.S. ........................................................................................................... 257 XVII. On the Occurrence of Flint-implements, associated with the Remains of Animals of Extinct Species in Beds of a late Geological Period, in France at Amiens and Abbeville, and in England at Hoxne. By Joseph Prestwich, F.R.S., F.G.S. &c. ................................................................................................................................................................................................. 277 XVIII. On the Formulae investigated by Dr. Brinkley for the general Term in the Development of Lagrange's Expression for the Summation of Series and for successive Integrations. By Sir J. F. W. Herschel, Bart., F.R.S. &c. ................................................................................................................................................................................................. 319 XIX. On the Thermal Effects of Fluids in Motion.—Part III. On the Changes of Temperature experienced by bodies moving through Air. By Professor W. Thomson, A.M., LL.D., F.R.S. &c., and J. P. Joule, LL.D., F.R.S. &c. ................................................................................................................................................................................................. 325 XX. Reduction and Discussion of the Deviations of the Compass observed on board of all the Iron-built Ships, and a selection of the Wood-built Steam-ships in Her Majesty's Navy, and the Iron Steam-ship 'Great Eastern'; being a Report to the Hydrographer of the Admiralty. By Frederick J. Evans, Esq., Master R.N., Superintendent of the Compass Department of Her Majesty's Navy. Communicated by Captain Washington, R.N., F.R.S., by command of the Lords Commissioners of the Admiralty ................................................................................................................................................................................................. 337 XXI. On the Construction of a new Calorimeter for determining the Radiating Powers of Surfaces in Air; and its Application to the Surfaces of various Mineral Substances. By W. Hopkins, Esq., M.A., F.R.S. page 379 XXII. Contributions to the History of the Phosphorus-Bases.—First Memoir. By Augustus William Hofmann, F.R.S. 409 XXIII. Contributions to the History of the Phosphorus-Bases.—Second Memoir. By Augustus William Hofmann, F.R.S. 449 XXIV. Contributions to the History of the Phosphorus-Bases.—Third Memoir. By Augustus William Hofmann, F.R.S. 497 XXV. Researches on Foraminifera.—Fourth and concluding Series. By William B. Carpenter, M.D., F.R.S., F.G.S., F.L.S. 535 XXVI. Researches on Sugar Formation in the Liver. By Frederick William Pavy, M.D. Communicated by Dr. Sharpey, Sec. R.S. 595 XXVII. On the Distribution of Nerves to the Elementary Fibres of Striped Muscle. By Lionel S. Beale, M.B., F.R.S., Professor of Physiology and of General and Morbid Anatomy in King's College, London; Physician to King's College Hospital 611 Index ... 621 APPENDIX. Presents [1] ERRATA IN VOL. 149. Page 743, line 9, for 774 indicated horse-power read 744 indicated horse-power. —- 744, line 9, after the words marine boilers, insert the engine had been in some respects modified by the makers, Messrs. J. M. Rowan and Co.; and in particular, a surface condenser designed by them had been substituted for the former surface condenser. ERRATUM IN VOL. 150. Page 288, line 21, for Deliquiere read Lereillé. LIST OF ILLUSTRATIONS. Plates VII. VIII. IX.—Mr. W. Fairbairn and Mr. T. Tate on the Density of Steam at different Temperatures. Plates X. XI. XII. XIII. XIV.—Mr. Prestwich on the Occurrence of Flint Implements, associated with the Remains of Animals of Extinct Species in Beds of a late Geological Period, in France at Amiens and Abbeville, and in England at Hoxne. Plates XV. XVI.—Mr. Evans on the Deviation of the Compass in the Iron Ships of the Royal Navy. Plates XVII. XVIII. XIX. XX. XXI. XXII.—Dr. Carpenter’s Researches on the Foraminifera. Plate XXIII.—Mr. Beale on the Distribution of Nerves to the Elementary Fibres of Striped Muscle. ADJUDICATION of the Medals of the Royal Society for the year 1860 by the President and Council. The Copley Medal to Professor Robert Wilhelm Bunsen, of Heidelberg, Foreign Member of the Royal Society, for his Researches on Cacodyl, Gaseous Analysis, the Volcanic Phenomena of Iceland, and other Researches. A Royal Medal to Mr. William Fairbairn, F.R.S., for his various Experimental Inquiries on the Properties of the Materials employed in Mechanical Construction, contained in the Philosophical Transactions and in the Publications of various Scientific Societies. A Royal Medal to Dr. Augustus V. Waller, F.R.S., for his Investigations into the Anatomy and Physiology of the Nervous System, and for the introduction of a valuable Method of conducting such investigations. The Rumford Medal to Professor J. Clerk Maxwell, for his Researches on the Composition of Colours, and other Optical Papers. The Bakerian Lecture was delivered by Mr. William Fairbairn, F.R.S., and entitled "Experimental Researches to determine the Density of Steam at all Temperatures, and to determine the Law of Expansion of Superheated Steam." The Croonian Lecture was delivered by Mr. James Pettigrew, and entitled "On the Arrangement of the Muscular Fibres of the Ventricular Portion of the Heart of the Mammal." I. On the Analytical Theory of the Attraction of Solids bounded by surfaces of a hypotethetical Class including the Ellipsoid. By W. F. Donkin, M.A., F.R.S., F.R.A.S., Savilian Professor of Astronomy in the University of Oxford . . . . page 1 II. On an Extended Form of the Index Symbol in the Calculus of Operations. By William Spottiswoode, M.A., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 III. On the Resin of Ficus rubiginosa, and a new Homologue of Benzylic Alcohol. By Warren De la Rue, Ph.D., F.R.S., Treasurer of the Chemical Society, Secretary of the Royal Astronomical Society, &c., and Hugo Müller, Ph.D., F.C.S. . . . 43 IV. On the Theory of Compound Colours, and the Relations of the Colours of the Spectrum. By J. Clerk Maxwell, M.A., Professor of Natural Philosophy in Marischal College and University of Aberdeen. Communicated by Professor Stokes, Sec. R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 V. On the Effect of the presence of Metals and Metalloids upon the Electric Conducting Power of Pure Copper. By A. Matthiessen, Ph.D., and M. Holzmann, Ph.D. Communicated by Professor Wheatstone, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 VI. On the Equation of Differences for an Equation of any Order, and in particular for the Equations of the Orders Two, Three, Four, and Five. By Arthur Cayley, Esq., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 VII. On the Volumetric Relations of Ozone, and the Action of the Electrical Discharge on Oxygen and other Gases. By Thomas Andrews, M.D., F.R.S., M.R.I.A., Vice-President of Queen's College, Belfast; and Peter G. Tait, M.A., late Fellow of St. Peter's College, Cambridge, Professor of Mathematics in Queen's College, Belfast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 VIII. On the Mathematical Theory of Sound. By the Rev. S. Earnshaw, M.A., Sheffield. Communicated by Professor W. H. Miller, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 IX. On the Lines of the Solar Spectrum. By Sir David Brewster, K.H., D.C.L., F.R.S. L. & E., and Dr. J. H. Gladstone, F.R.S. . . . . . . . . . . . . page 149 X. On the Electric Conducting Power of Alloys. By A. Matthiessen, Ph.D. Communicated by Professor Wheatstone, F.R.S. . . . . . . . . . . . 161 XI. On the Specific Gravity of Alloys. By A. Matthiessen, Ph.D. Communicated by Professor Wheatstone, F.R.S. . . . . . . . . . . . . . 177 XII. The Bakerian Lecture.—Experimental Researches to determine the Density of Steam at different Temperatures, and to determine the Law of Expansion of Superheated Steam. By William Fairbairn, Esq., F.R.S., and Thomas Tate, Esq. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 XIII. On a new Method of Approximation applicable to Elliptic and Ultra-elliptic Functions. By Charles W. Merrifield. Communicated by the Rev. H. Moseley, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 XIV. On Quaternary Cubics. By the Rev. George Salmon, D.D., M.R.I.A. Communicated by A. Cayley, Esq., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . 229 XV. On Isoprene and Caoutchine. By C. Greville Williams . . . . . . . . . . . 241 XVI. On the Relation between Boiling-point and Composition in Organic Compounds. By Hermann Kopp, M.D., Ph.D., Professor of Theoretical Chemistry in the University of Giessen. Communicated by Dr. A. W. Hofmann, F.R.S. . . 257 XVII. On the Occurrence of Flint-implements, associated with the Remains of Animals of Extinct Species in Beds of a late Geological Period, in France at Amiens and Abbeville, and in England at Roxane. By Joseph Prestwich, F.R.S., F.G.S. &c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 XVIII. On the Formulae investigated by Dr. Brinkley for the general Term in the Development of Lagrange's Expression for the Summation of Series and for successive Integrations. By Sir J. F. W. Herschel, Bart., F.R.S. &c. . . . . . . . . . . 319 XIX. On the Thermal Effects of Fluids in Motion.—Part III. On the Changes of Temperature experienced by bodies moving through Air. By Professor W. Thomson, A.M., LL.D., F.R.S. &c., and J. P. Joule, LL.D., F.R.S. &c. . . . . . . . 325 XX. Reduction and Discussion of the Deviations of the Compass observed on Board of all the Iron-built Ships, and a selection of the Wood-built Steam-ships in Her Majesty's Navy, and the Iron Steam-ship 'Great Eastern'; being a Report to the Hydrographer of the Admiralty. By Frederick J. Evans, Esq., Master R.N., Superintendent of the Compass Department of Her Majesty's Navy. Communicated by Captain Washington, R.N., F.R.S., by command of the Lords Commissioners of the Admiralty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 XXI. On the Construction of a new Calorimeter for determining the Radiating Powers of Surfaces in Air; and its Application to the Surfaces of various Mineral Substances. By W. Hopkins, Esq., M.A., F.R.S. . . . . . . . . . . . . . . . . . . . . . page 379 XXII. Contributions to the History of the Phosphorus-Bases.—First Memoir. By Augustus William Hofmann, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . 409 XXIII. Contributions to the History of the Phosphorus-Bases.—Second Memoir. By Augustus William Hofmann, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . 449 XXIV. Contributions to the History of the Phosphorus-Bases.—Third Memoir. By Augustus William Hofmann, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . 497 XXV. Researches on Foraminifera.—Fourth and Concluding Series. By William B. Carpenter, M.D., F.R.S., F.G.S., F.L.S. . . . . . . . . . . . . . . . . . . . . . 535 XXVI. Researches on Sugar Formation in the Liver. By Frederick William Pavy, M.D. Communicated by Dr. Sharpey, Sec. R.S. . . . . . . . . . . . . . . . . . . . . . . 595 XXVII. On the Distribution of Nerves to the Elementary Fibres of Striped Muscle. By Lionel S. Beale, M.B., F.R.S., Professor of Physiology and of General and Morbid Anatomy in King's College, London; Physician to King's College Hospital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621 APPENDIX. Presents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [ 1 ] ERRATA IN VOL. 149. Page 743, line 9, for 774 indicated horse-power read 744 indicated horse-power. — 744, line 9, after the words marine boilers, insert the engine had been in some respects modified by the makers, Messrs. J. M. Rowan and Co.; and in particular, a surface condenser designed by them had been substituted for the former surface condenser. ERRATUM IN VOL. 150. Page 283, line 21, for Deliquiere read Lereillé. LIST OF ILLUSTRATIONS. Plates I. II.—Professor J. Clerk Maxwell on the Theory of Compound Colours. Plate III.—Dr. Andrews and Professor Tait on the Volumetric Relations of Ozone. Plate IV.—Sir David Brewster and Dr. J. H. Gladstone on the Lines of the Solar Spectrum. Plates V. VI.—Dr. A. Matthiessen on the Electric Conducting Power of Alloys. Plates VII. VIII. IX.—Mr. W. Fairbairn and Mr. T. Tate on the Density of Steam at different Temperatures. Plates X. XI. XII. XIII. XIV.—Mr. Prestwich on the Occurrence of Flint Implements, associated with the Remains of Animals of Extinct Species in Beds of a late Geological Period, in France at Amiens and Abbeville, and in England at Hoxne. Plates XV. XVI.—Mr. Evans on the Deviation of the Compass in the Iron Ships of the Royal Navy. Plates XVII. XVIII. XIX. XX. XXI. XXII.—Dr. Carpenter's Researches on the Foraminifera. Plate XXIII.—Mr. Beale on the Distribution of Nerves to the Elementary Fibres of Striped Muscle.