Front Matter

CONTENTS OF VOL. 158. I. THE BAKERIAN LECTURE.—Researches on Vanadium. By Henry E. Roscoe, B.A., F.R.S. .................................................. page 1 II. Computation of the Lengths of the Waves of Light corresponding to the Lines in the Dispersion Spectrum measured by Kirchhoff. By George Biddell Airy, Astronomer Royal, F.R.S. ........................................... 29 III. An Account of the Observations on the Great Nebula in Orion, made at Birr Castle, with the 3-feet and 6-feet Telescopes, between 1848 and 1867. With a drawing of the Nebula. By Lord Oxmantown. Communicated by the Earl of Rosse, K.P., F.R.S. ................................................................................................................................. 57 IV. On the Curves which satisfy given Conditions. By Professor Cayley, F.R.S. .................................................................................................................................................. 75 V. Second Memoir on the Curves which satisfy given Conditions; the Principle of Correspondence. By Professor Cayley, F.R.S. .................................................................................................................................................. 145 VI. Addition to Memoir on the Resultant of a System of two Equations. By Professor Cayley, F.R.S. .................................................................................................................................................. 173 VII. On the Theory of Local Probability, applied to Straight Lines drawn at random in a plane; the methods used being also extended to the proof of certain new Theorems in the Integral Calculus. By Morgan W. Crofton, B.A., of the Royal Military Academy, Woolwich; late Professor of Natural Philosophy in the Queen’s University, Ireland. Communicated by Professor J. J. Sylvester, F.R.S. .................................................................................................................................................. 181 VIII. On the Anatomy of Balænoptera rostrata. By Alexander Carte, A.M., M.D. Univ. Dubl., F.R.C.S.I., M.R.I.A., F.L.S. Lond., Hon. Mem. Imp. Zool. and Bot. Soc. Vienna, &c., and Alexander Macalister, M.D., L.R.C.S.I., Demonstrator of Anatomy R.C.S.I. Communicated by W. H. Flower, F.R.S. .................................................................................................................................................. 201 IX. Researches on the Intimate Structure of the Brain.—Second Series. By J. Lockhart Clarke, F.R.S., &c. .................................................................................................................................................. 263 X. Notices of some Parts of the Surface of the Moon. By John Phillips, M.A., D.C.L., F.R.S., F.G.S., Professor of Geology in the University of Oxford .................................................................................................................................................. 333 XI. Results of Observations of Atmospheric Electricity at Kew Observatory, and at King's College, Windsor, Nova Scotia. By Joseph David Everett, D.C.L., F.R.S.E. Communicated by Sir William Thomson, F.R.S. . . . page 347 XII. Account of Experiments on Torsion and Flexure for the Determination of Rigidities.—Third Paper. By Joseph David Everett, D.C.L., Professor of Natural Philosophy in Queen's College, Belfast. Communicated by Sir William Thomson, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 XIII. Contributions to Terrestrial Magnetism.—No. XI. By Lieut.-General Edward Sabine, R.A., President of the Royal Society . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 XIV. On the Resistance of the Air to the Motion of Elongated Projectiles having variously formed Heads. By F. Bashforth, B.D., Professor of Applied Mathematics to the Advanced Class of Artillery Officers, Woolwich, and late Fellow of St. John's College, Cambridge. Communicated by Professor Stokes, Sec. R.S. . . . . . . . . . . 417 XV. On the Law of the Resistance of the Air to Rifled Projectiles. By Charles W. Merrifield, F.R.S., Principal of the Royal School of Naval Architecture. . . . . . . . . . 443 XVI. On the Communication of Vibration from a Vibrating Body to a surrounding Gas. By G. G. Stokes, M.A., D.C.L., Sec. R.S., Fellow of Pembroke College, and Lucasian Professor of Mathematics in the University of Cambridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 XVII. Comparison of Magnetic Disturbances recorded by the Self-registering Magnetometers at the Royal Observatory, Greenwich, with Magnetic Disturbances deduced from the corresponding Terrestrial Galvanic Currents recorded by the Self-registering Galvanometers of the Royal Observatory. By George Biddell Airy, Astronomer Royal, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 XVIII. On the Relation of Form and Dimensions to Weight of Material in the Construction of Iron-clad Ships. By E. J. Reed, Chief Constructor of the Navy. Communicated by Professor G. G. Stokes, Sec. R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 XIX. On the Amount and Changes of the Polar Magnetism at certain positions in Her Majesty’s Iron-built and Armour-plated Ship 'Northumberland.' By Frederick John Evans, Staff Captain, R.N., F.R.S., Chief Naval Assistant, Hydrographic Department, Admiralty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 XX. Contributions towards determining the Weight of the Brain in different Races of Man. By Joseph Barnard Davis, M.D., &c. Communicated by J. Marshall, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 XXI. Further Observations on the Spectra of some of the Stars and Nebulae, with an Attempt to determine therefrom whether these Bodies are moving towards or from the Earth, also Observations on the Spectra of the Sun and of Comet II., 1868. By William Huggins, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529 XXII. New Researches upon the Dispersion of the Optic Axes in Harmotome and Wöhlerite, proving these Minerals to belong to the Clinorhombic [Oblique] System. By A. L. O. Des Cloizeaux. Communicated by Professor W. H. Miller, For. Sec. R.S. XXIII. On the Conditions for the existence of Three Equal Roots, or of Two Pairs of Equal Roots, of a Binary Quartic or Quintic. By Professor A. Cayley, F.R.S. XXIV. Researches on the Blood.—On the Action of Nitrites on Blood. By Arthur Gamgee, M.D., F.R.S.E., Assistant to the Professor of Medical Jurisprudence in the University of Edinburgh. Communicated by Professor Frankland, F.R.S. XXV. On the Mysteries of Numbers alluded to by Fermat.—Second Communication. By the Right Hon. Sir Frederick Pollock, Bart., M.A., F.R.S., F.S.A., F.G.S., &c. XXVI. On a Method of making a Direct Comparison of Electrostatic with Electromagnetic Force; with a Note on the Electromagnetic Theory of Light. By J. Clerk Maxwell, F.R.S.S. L. & E. XXVII. On Supersaturated Saline Solutions. By Charles Tomlinson, F.R.S. XXVIII. The Caudal Heart of the Eel a Lymphatic Heart.—Effect of the force with which the lymph-stream is propelled therefrom on the flow of the blood in the Vein into which the heart opens.—Explanation of the appearance of blood propelled in successive drops, as if from the heart, along the Caudal Vein.—Influence which the force of the lymph-stream from the heart exerts in accelerating and promoting the flow of blood in the Caudal Vein. By Thomas Wharton Jones, F.R.S., Professor of Ophthalmic Medicine and Surgery in University College, London, Ophthalmic Surgeon to the University College Hospital, &c. XXIX. On the Tides of Bombay and Kurrachee. By William Parkes, M.Inst. C.E. Communicated by G. B. Airy, Astronomer Royal, F.R.S. Index APPENDIX. Presents ERRATUM. The — prefix has been accidentally omitted in the Values of the Magnetic Intensities in pages 407 and 408. LIST OF ILLUSTRATIONS. Plates I. to III.—Lord OXMANTOWN on the Great Nebula in Orion. Plates IV. to VII.—Drs. A. CARTE and A. MACALISTER on the Anatomy of Balænoptera rostrata. Plates VIII. to XIV.—Mr. J. L. CLARKE on the Intimate Structure of the Brain. Plates XV. to XVII.—Professor PHILLIPS on some Parts of the Surface of the Moon. Plates XVIII. to XXI.—Dr. EVERETT on Atmospheric Electricity. Plates XXII. to XXIV.—Lieut.-General SABINE on Terrestrial Magnetism. Plates XXV. to XXX.—The Astronomer Royal on the Comparison of Magnetic Disturbances with Terrestrial Galvanic Currents. Plates XXXI. & XXXII.—Staff Captain EVANS, R.N., on the Changes of Polar Magnetism in the Iron and Armour-Plated Ship 'Northumberland.' Plate XXXIII.—Mr. W. HUGGINS on the Spectra of some of the Stars and Nebulæ. Plate XXXIV.—M. A. L. O. DES CLOIZEAUX on the Dispersion of the Optic Axes in Harmotome and Wöhlerite. Plate XXXV.—Professor T. WHARTON JONES on the Caudal Heart of the Eel. Plates XXXVI. & XXXVII.—Mr. WILLIAM PARKES on the Tides of Bombay and Kurrachee. N.B. Plate III. is issued in a separate pocket. 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. 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. - Cape Town . . . . South African Library. - Dublin . . . . . Royal Dublin Society. - Royal Irish Academy. - Edinburgh . . . . Royal Society. - London . . . . . Admiralty Library. - Chemical Society. - Entomological Society. - Geological Society. - Geological Survey of Great Britain. - Institution of Civil Engineers. - Linnean Society. - London Institution. - Royal Asiatic Society. - Royal Astronomical Society. - Royal College of Surgeons. - Royal College of Physicians. - Royal Geographical Society. - Royal Horticultural Society. - Royal Institute of British Architects. - Royal Institution of Great Britain. - Royal Medical and Chirurgical Society. - Royal Society of Literature. - Society of Antiquaries. - Society of Arts. - The Queen's Library. - The Treasury Library. - The War Office. - United Service Museum. - Zoological Society. - Malta . . . . . Public Library. - Manchester . . . Literary and Philosophical Society. - Melbourne . . . University Library. - Montreal . . . . McGill College. **Oxford . . . . . Ashmolean Society.** - Radcliffe Library. - Swansea . . . . . Royal Institution. - Sydney . . . . . University Library. - Woolwich . . . . Royal Artillery Library. **Argentine Republic.** - Buenos Ayres . . . Museo Publico. **Belgium.** - Brussels . . . . Académie Royale de Médecine. - Académie Royale des Sciences. **Denmark.** - Copenhagen . . . Kongelige Danske Videnskabernes Selskab. **France.** - Montpellier . . . Académie des Sciences et Lettres. - Faculté de Médecine. - Paris . . . . . Académie des Sciences de l'Institut. - Dépôt de la Marine. - Ecole des Mines. - Ecole Normale Supérieure. - Faculté des Sciences de la Sorbonne. - Jardin des Plantes. - Société Entomologique. - Société de Géographie. - Société Géologique. - Société d'Encouragement pour l'Industrie Nationale. - Toulouse . . . . Académie Impériale des Sciences. **Germany.** - Altona . . . . . Die Sternwarte. - Berlin . . . . . Königliche Akademie der Wissenschaften. - Physikalische Gesellschaft. - Brünn . . . . . Naturforschender Verein. - Danzig . . . . . Naturforschende Gesellschaft. - Dresden . . . . Kaiserliche Leopoldino-Carolinische deutsche Akademie der Naturforscher. - Frankfort . . . . Senckenbergische naturforschende Gesellschaft. - Giessen . . . . . Grossherzogliche Universität. - Göttingen . . . . Königliche Gesellschaft der Wissenschaften. - Gratz . . . . . Naturwissenschaftliche Verein für Steiermark. - Hamburg . . . . Naturwissenschaftlicher Verein. 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 (continued). Innsbruck ....... Das Ferdinandeum. Jena ........ Medicinisch-Naturwissenschaftliche Gesellschaft. Königsberg .... Königliche physikalisch-ökonomische Gesellschaft. Leipzig ......... Königlich Sächsische Gesellschaft der Wissenschaften. Astronomische Gesellschaft. Mannheim ...... Grossherzogliche Sternwarte. Munich ......... Königlich Bayerische Akademie der Wissenschaften. Prague .......... Königlich böhmische Gesellschaft der Wissenschaften. Vienna ......... Kaiserliche Akademie der Wissenschaften. Geologische Reichsanstalt. Würzburg ....... Physikalisch-medicinische Gesellschaft. Hungary. Pesth .......... Á Magyar Tudós Társaság—Die Ungarische Akademie der Wissenschaften. Italy. Bologna ....... Accademia delle Scienze dell’ Istituto. Catanea ....... Accademia Gioenia di Scienze Naturali. Florence ....... Reale Museo di Fisica. Milan .......... Reale Istituto Lombardo di Scienze, Lettere ed Arti. Modena ....... Società Italiana delle Scienze. Naples ....... Società Reale, Accademia delle Scienze. Palermo ....... Accademia di Scienze e Lettere. Rome .......... Accademia Pontificia de’ Nuovi Lincei. Osservatorio del Collegio Romano. Turin .......... Reale Accademia delle Scienze. Venice ......... I. R. Istituto Veneto di Scienze, Lettere ed Arti. Java. Batavia ....... Bataviaasch Genootschap van Kunsten en Wetenschappen. Netherlands. Amsterdam ..... Koninklijke Akademie van Wetenschappen. Haarlem ....... Hollandsche Maatschappij der Wetenschappen. Rotterdam ..... Bataafsch Genootschap der Proefondervindelijke Wijsbegeerte. Portugal. Coimbra ....... University. Lisbon .......... Academia Real das Sciencias. Russia. Kazan .......... Imperatorsky Kazansky Universitet. Moscow ....... Société Impériale des Naturalistes. Le Musée Publique. Pulkowa ....... Nikolai-Haupsternwarte. St. Petersburg .... Académie Impériale des Sciences. Spain. Cadiz .......... Observatorio de S. Fernando. Madrid ......... Real Academia de Ciencias. Sweden and Norway. Christiania .... Kongelige Norske Frederiks Universitet. Gottenburg .... Kongl. Vetenskaps och Vitterhets Samhälle. Lund .......... Universitet. Stockholm ....... Kongliga Svenska Vetenskaps-Akademie. Trondhjem ....... Kongelige Norske Videnskabers Selskab. Switzerland. Bern .......... Allg. Schweizerische Gesellschaft. Geneva ......... Société de Physique et d’Histoire Naturelle. Institut National Genevois. Zurich .......... Das Schweizerische Polytechnikum. Transylvania. Klausenburg .... Az Erdélyi Muzeum—Das siebenbürgisches Museum. United States. Albany ......... New York State Library. Boston ......... American Academy of Sciences. Cambridge ...... Harvard University. Newhaven (Conn.) The Editors of the American Journal. Philadelphia .... Academy of Natural Sciences. American Philosophical Society. Washington .... Smithsonian Institution. U. S. Naval 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 of Sciences | | 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 | Glasgow University | | Dorpat | Göttingen University | | Dublin | Leyden University | | Edinburgh | London Board of Ordnance | | Helsingfors | Königsberg Royal Institution | | Madras | Mannheim Royal Society | | Mannheim | Marseille The Queen’s Library | | Marseille | Oxford Savilian Library | | Milan | Paris Academy of Sciences | | Munich | Paris Bureau des Longitudes | | Oxford | Palermo Hungarian Academy of Sciences | | Palermo | Pesth Hungarian Academy of Sciences | | Paris | Philadelphia American Philosophical Society | | Seeberg | St. Andrews University | | Tübingen | St. Petersburg Imperial Academy | | Turin | Stockholm Royal Academy of Sciences | | Vienna | Upsal Royal Society | | Wilna | Waterville, Maine (U.S.) College | | Individuals | | |-----------------------|--------------------------------------------------| | Lowndes’ Professor of Astronomy | Cambridge | | Plumian Professor of Astronomy | Cambridge | | President of the Royal Society | London | | 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 - Christiania .............. C. Hansteen. - Gotha ..................... P. A. Hansen. - Heidelberg ............... M. Tiedemann. - Kew ....................... B. Stewart. - Kremsmünster ............ P. A. Reslhuber. - Leipzig ................... Dr. C. Bruhns. - Lisbon .................... Senhor da Silveira. - Marburg .................. Prof. C. L. Gerling. - Prague .................... K. Jelinek. - Stockholm ................. Professor H. Selander. - St. Petersburg ........... (Twelve copies for distribution to the Russian Mag. and Met. Obs.) - The Compass Observatory, Capt. Belavenetz. - Toronto ................... Professor Kingston. - Upsal ...................... Professor Svanberg. ### Institutions - Bombay ................... Geographical Society. - Bonn ...................... University. - Cherkow .................. University. - Falmouth ................. Royal Cornwall Polytechnic Society. - London ................... House of Lords, Library. - House of Commons, Library. - Royal Society. - University College, Library. - Meteorol. Office, Board of Trade. - Paris ..................... Meteorological Society. - St. Bernard .............. The Hospice. - Washington .............. Smithsonian Institution. - Woolwich ................. Office of Mag. and Met. Publication. ### Individuals - Buys Ballot, Dr. .......... Utrecht. - Dove, Prof. H. W. ......... Berlin. - Erman, Dr. Adolph ....... Berlin. - Fox, R. W., Esq. .......... Falmouth. - Hoskins, Dr. S. E. ........ Guernsey. - Kaemtz, Prof. L. F. ....... Dorpat. - Lloyd, Rev. Dr. .......... Dublin. - Loomis, Prof. E. .......... Yale College, Newhaven (Conn.). - Phillips, Prof. John ...... Oxford. - Quetelet, Mons. A. ....... Brussels. - Sabine, Lieut.-General, R.A. London. - Souza, Senhor da ......... Coimbra. - Wartmann, Prof. Elie ..... Geneva. - Younghusband, Col., R.A. Woolwich. CONTENTS. I. The Bakerian Lecture.—Researches on Vanadium. By Henry E. Roscoe, B.A., F.R.S. .................................................. page 1 II. Computation of the Lengths of the Waves of Light corresponding to the Lines in the Dispersion Spectrum measured by Kirchhoff. By George Biddell Airy, Astronomer Royal ................................................................. 29 III. An Account of the Observations on the Great Nebula in Orion, made at Birr Castle, with the 3-feet and 6-feet Telescopes, between 1848 and 1867. With a drawing of the Nebula. By Lord Oxmantown. Communicated by the Earl of Rosse, K.P., F.R.S. ............................................................................. 57 IV. On the Curves which satisfy given Conditions. By Professor Cayley, F.R.S. ............................................................... 75 V. Second Memoir on the Curves which satisfy given conditions; the Principle of Correspondence. By Professor Cayley, F.R.S. ........................................................................... 145 VI. Addition to Memoir on the Resultant of a System of two Equations. By Professor Cayley, F.R.S. ............................................................................. 173 VII. On the Theory of Local Probability, applied to Straight Lines drawn at random in a plane; the methods used being also extended to the proof of certain new Theorems in the Integral Calculus. By Morgan W. Crofton, B.A., of the Royal Military Academy, Woolwich; late Professor of Natural Philosophy in the Queen's University, Ireland. Communicated by J. J. Sylvester, F.R.S. ........................................................................... 181 VIII. On the Anatomy of Balænoptera rostrata. By Alexander Carte, A.M., M.D. Univ. Dubl., F.R.C.S.I., M.R.I.A., F.L.S. Lond., Hon. Mem. Imp. Zool. and Bot. Soc. Vienna, &c., and Alexander Macalister, M.D., L.R.C.S.I., Demonstrator of Anatomy R.C.S.I. Communicated by W. H. Flower, F.R.S. ............................................................................. 201 IX. Researches on the Intimate Structure of the Brain.—Second Series. By J. Lockhart Clarke, F.R.S., &c. ........................................................................... 263 MDCCCLXVIII. X. Notices of some Parts of the Surface of the Moon. By John Phillips, M.A., D.C.L., F.R.S., F.G.S., Professor of Geology in the University of Oxford. . . page 333 XI. Results of Observations of Atmospheric Electricity at Kew Observatory, and at King's College, Windsor, Nova Scotia. By Joseph D. Everett, D.C.L., F.R.S.E. Communicated by Sir William Thomson, F.R.S. . . . . . . . . . . . . . . 347 XII. Account of Experiments on Torsion and Flexure for the Determination of Rigidities.—Third Paper. By Joseph David Everett, D.C.L., Professor of Natural Philosophy in Queen's College, Belfast. Communicated by Sir William Thomson, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 LIST OF ILLUSTRATIONS. Plates I. to III.—Lord Oxmantown on the Great Nebula in Orion. Plates IV. to VII.—Drs. A. Carte and A. Macalister on the Anatomy of Balaenoptera rostrata. Plates VIII. to XIV.—Mr. J. L. Clarke on the Intimate Structure of the Brain. Plates XV. to XVII.—Professor Phillips on some Parts of the Surface of the Moon. Plates XVIII. to XXI.—Dr. Everett on Atmospheric Electricity. N.B. Plate III. is issued in a separate pocket. CONTENTS. XIII. Contributions to Terrestrial Magnetism.—No. XI. By Lieut.-General Edward Sabine, R.A., President of the Royal Society .................................................. page 371 XIV. On the Resistance of the Air to the Motion of Elongated Projectiles having variously formed Heads. By F. Bashforth, B.D., Professor of Applied Mathematics to the Advanced Class of Artillery Officers, Woolwich, and late Fellow of St. John's College, Cambridge. Communicated by Professor Stokes, Sec. R.S. ........................................................................................................... 417 XV. On the Law of the Resistance of the Air to Rifled Projectiles. By Charles W. MERRIFIELD, F.R.S., Principal of the Royal School of Naval Architecture ................................................................. 443 XVI. On the Communication of Vibration from a Vibrating Body to a surrounding Gas. By G. G. Stokes, M.A., D.C.L., Sec. R.S., Fellow of Pembroke College, and Lucasian Professor of Mathematics in the University of Cambridge ............................................................... 447 XVII. Comparison of Magnetic Disturbances recorded by the Self-registering Magnetometers at the Royal Observatory, Greenwich, with Magnetic Disturbances deduced from the corresponding Terrestrial Galvanic Currents recorded by the Self-registering Galvanometers of the Royal Observatory. By George Biddell Airy, Astronomer Royal, F.R.S. ............................................................................. 465 XVIII. On the Relation of Form and Dimensions to Weight of Material in the Construction of Iron-clad Ships. By E. J. Reed, Chief Constructor of the Navy. Communicated by Professor G. G. Stokes, Sec. R.S. ................................................................. 473 XIX. On the Amount and Changes of the Polar Magnetism at certain positions in Her Majesty's Iron-built and Armour-plated Ship 'Northumberland.' By Frederick John Evans, Staff Captain, R.N., F.R.S., Chief Naval Assistant, Hydrographic Department, Admiralty ........................................................................ 487 XX. Contributions towards determining the Weight of the Brain in different Races of Man. By Joseph Barnard Davis, M.D., &c. Communicated by J. Marshall, F.R.S. ........................................................................................................................................ 505 XXI. Further Observations on the Spectra of some of the Stars and Nebulae, with an Attempt to determine therefrom whether these Bodies are moving towards or from the Earth, also Observations on the Spectra of the Sun and of Comet II., 1868. By William Huggins, F.R.S. ...................................................................... 529 XXII. New Researches upon the Dispersion of the Optic Axes in Harmotome and Wöhlerite, proving these Minerals to belong to the Clinorhombic [Oblique] System. By A. L. O. DES CLOIZEAUX. Communicated by Professor W. H. MILLER, For. Sec. R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565 XXIII. On the Conditions for the existence of Three Equal Roots, or of Two Pairs of Equal Roots, of a Binary Quartic or Quintic. By Professor A. CAYLEY, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577 XXIV. Researches on the Blood.—On the Action of Nitrites on Blood. By ARTHUR GAMGEE, M.D., F.R.S.E., Assistant to the Professor of Medical Jurisprudence in the University of Edinburgh. Communicated by Professor FRANKLAND, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589 XXV. On the Mysteries of Numbers alluded to by FERMAT.—Second Communication. By the Right Hon. Sir FREDERICK POLLOCK, Bart., M.A., F.R.S., F.S.A., F.G.S., &c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627 XXVI. On a Method of making a Direct Comparison of Electrostatic with Electromagnetic Force; with a Note on the Electromagnetic Theory of Light. By J. CLERK MAXWELL, F.R.S.S. L. & E. . . . . . . . . . . . . . . . . . . . . . . . . . . . 643 XXVII. On Supersaturated Saline Solutions. By CHARLES TOLMINSON, F.R.S. . . . 659 XXVIII. The Caudal Heart of the Eel & Lymphatic Heart.—Effect of the force with which the lymph-stream is propelled therefrom on the flow of the blood in the Vein into which the heart opens.—Explanation of the appearance of blood propelled in successive drops, as if from the heart, along the Caudal Vein.—Influence which the force of the lymph-stream from the heart exerts in accelerating and promoting the flow of blood in the Caudal Vein. By THOMAS WHARTON JONES, F.R.S., Professor of Ophthalmic Medicine and Surgery in University College, London, Ophthalmic Surgeon to the University College Hospital, &c. . . . . 675 XXIX. On the Tides of Bombay and Kurrachee. By WILLIAM PARKES, M.Inst. C.E. Communicated by G. B. AIRY, Astronomer Royal, F.R.S. . . . . . . . . . . . . . . . . . . . 685 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697 APPENDIX. Presents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [1] ERRATUM. The — prefix has been accidentally omitted in the Values of the Magnetic Intensities in pages 407 and 408. LIST OF ILLUSTRATIONS. Plates XXII. to XXIV.—Lieut.-General Sabine on Terrestrial Magnetism. Plates XXV. to XXX.—The Astronomer Royal on the Comparison of Magnetic Disturbances with Terrestrial Galvanic Currents. Plates XXXI. & XXXII.—Staff Captain Evans, R.N., on the Changes of Polar Magnetism in the Iron and Armour-Plated Ship 'Northumberland.' Plate XXXIII.—Mr. W. Huggins on the Spectra of some of the Stars and Nebulae. Plate XXXIV.—M. A. L. O. Des Cloizeaux on the Dispersion of the Optic Axes in Harmotome and Wöhlerite. Plate XXXV.—Professor T. Wharton Jones on the Caudal Heart of the Eel. Plates XXXVI. & XXXVII.—Mr. William Parkes on the Tides of Bombay and Kurrachee. ADJUDICATION of the Medals of the Royal Society for the year 1868 by the President and Council. The Copley Medal to Sir Charles Wheatstone, F.R.S., for his Researches in Acoustics, Optics, Electricity, and Magnetism. A Royal Medal to Mr. Alfred Russell Wallace, for his Labours in Practical and Theoretical Zoology. A Royal Medal to the Rev. George Salmon, D.D., F.R.S., for his Researches in Analytical Geometry and the Theory of Surfaces, published in the Philosophical Transactions, the Transactions of the Royal Irish Academy, and the Quarterly Journal of Mathematics. The Rumford Medal to Dr. Balfour Stewart, F.R.S., for his researches on the qualitative as well as quantitative relation between the emissive and absorptive powers of bodies for heat and light, published originally in the Transactions of the Royal Society of Edinburgh, and the Proceedings of the Royal Society of London, and now made more generally accessible by the publication in 1866 of his Treatise on Heat. The Bakerian Lecture was delivered by Professor Henry E. Roscoe, F.R.S.; it was entitled "Researches on Vanadium." The Croonian Lecture was not delivered.