Front Matter

CONTENTS OF VOL. 154. I. Catalogue of Nebulae and Clusters of Stars. By Sir John Frederick William Herschel, Bart., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 1 II. On the Spectra of some of the Chemical Elements. By William Huggins, Esq., F.R.A.S. Communicated by Dr. W. A. Miller, Treas. R.S. . . . . . . . . . . . . . . . . . 139 III. Account of Magnetic Observations made in the years 1858–61 inclusive, in British Columbia, Washington Territory, and Vancouver Island. By Captain R. W. Haig, R.A. Communicated by General Sabine, P.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . 161 IV. On the Influence of Temperature on the Electric Conducting-Power of Alloys. By Augustus Matthiessen, F.R.S., Lecturer on Chemistry in St. Mary’s Hospital, and Carl Vogt, Ph.D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 V. On the Absorption and Radiation of Heat by Gaseous and Liquid Matter.—Fourth Memoir. By John Tyndall, F.R.S., Member of the Academies and Societies of Holland, Geneva, Göttingen, Zürich, Halle, Marburg, Breslau, Upsala, la Société Philomathique of Paris, Cam. Phil. Soc. &c.; Professor of Natural Philosophy in the Royal Institution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 VI. A Comparison of the most notable Disturbances of the Magnetic Declination in 1858 and 1859 at Kew and at Nertschinsk; preceded by a brief Retrospective View of the Progress of the Investigation into the Laws and Causes of the Magnetic Disturbances. By Major-General Edward Sabine, R.A., President of the Royal Society . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 VII. Theoretical Considerations on the Conditions under which the (Drift) Deposits containing the Remains of Extinct Mammalia and Flint Implements were accumulated, and on their Geological Age. By Joseph Prestwich, Esq., F.R.S., F.G.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 VIII. Experiments to determine the effect of Impact, Vibratory Action, and long-continued Changes of Load on Wrought-Iron Girders. By W. Fairbairn, LL.D., F.R.S. .......................................................... page 311 IX. The Bakerian Lecture.—Contributions to Molecular Physics.—Being the Fifth Memoir of Researches on Radiant Heat. By John Tyndall, F.R.S., Member of the Academies and Societies of Holland, of Geneva, Göttingen, Zürich, Halle, Marburg, Breslau, Upsala, la Société Philomathique, Paris, Cam. Phil. Soc. &c.; Professor of Natural Philosophy in the Royal Institution .................................................. 327 X. On Plane Water-Lines in two Dimensions. By William John Macquorn Rankine, C.E., LL.D., F.R.SS. L. & E., Associate of the Institution of Naval Architects, &c. ........................................................................................................... 369 XI. On the Joint-Systems of Ireland and Cornwall, and their Mechanical Origin. By the Rev. Samuel Haughton, M.D., Fellow of Trinity College, Dublin ......................................................... 393 XII. On the Spectra of some of the Fixed Stars. By William Huggins, F.R.A.S., and W. A. Miller, M.D., LL.D., Treas. & V.P.R.S., Professor of Chemistry, King’s College, London ...................................................................................... 413 XIII. On the Spectra of some of the Nebulae. By William Huggins, F.R.A.S. A Supplement to the Paper “On the Spectra of some of the Fixed Stars. By William Huggins, F.R.A.S., and W. A. Miller, M.D., LL.D., Treas. and V.P.R.S.” Communicated by Professor W. A. Miller, M.D., LL.D. ....................... 437 XIV. On the Arrangement of the Muscular Fibres in the Ventricles of the Vertebrate Heart, with Physiological Remarks. By James Bell Pettigrew, M.D. Edin.; Assistant in the Museum of the Royal College of Surgeons of England; Extra-ordinary Member and late President of the Royal Medical Society of Edinburgh, &c. &c. Communicated by John Goodsir, Esq., F.R.SS. L. and E., Professor of Anatomy in the University of Edinburgh ...................................................................................................... 445 XV. On the Brain of a Bushwoman; and on the Brains of two Idiots of European Descent. By John Marshall, F.R.S., Surgeon to University College Hospital ......................................................................................................................................... 501 XVI. A Second Memoir on Skew Surfaces, otherwise Scrolls. By A. Cayley, F.R.S. .. 559 XVII. Algebraical Researches, containing a disquisition on Newton’s Rule for the Discovery of Imaginary Roots, and an allied Rule applicable to a particular class of Equations, together with a complete invariantive determination of the character of the Roots of the General Equation of the fifth Degree, &c. By J. J. Sylvester, M.A., F.R.S., Correspondent of the Institute of France, Foreign Member of the Royal Society of Naples, etc. etc., Professor of Mathematics at the Royal Military Academy, Woolwich .......................................................................................................... 579 XVIII. On a New Series of Bodies in which Nitrogen is substituted for Hydrogen. By Peter Griess, Esq. Communicated by A. W. Hofmann . . . . . . . page 667 XIX. On the Differential Equations which determine the form of the Roots of Algebraic Equations. By George Boole, F.R.S., Professor of Mathematics in Queen's College, Cork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757 APPENDIX. Presents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [1] LIST OF ILLUSTRATIONS. Plates I., II.—Mr. W. Huggins on the Spectra of some of the Chemical Elements. Plate III.—Captain Haig on the Magnetic Elements in British Columbia, Washington Territory, and Vancouver Island. Plates IV., V.—Mr. Prestwich on the Geology of the Deposits containing Flint Implements, and on the Loess. Plates VI., VII.—Dr. Fairbairn on the Effect of Impact, Vibratory Action, and long-continued Changes of Load on Wrought-Iron Girders. Plates VIII., IX.—Dr. W. J. Macquorn Rankine on Plane Water-Lines. Plates X., XI.—Mr. W. Huggins and Dr. W. A. Miller on the Spectra of some of the Fixed Stars. Plates XII. to XVI.—Dr. Pettigrew on the Arrangement of the Muscular Fibres in the Ventricles of the Vertebrate Heart. Plates XVII. to XXIII.—Professor Marshall on the Brain of a Bushwoman; and on the Brains of two Idiots of European Descent. Plates XXIV., XXV.—Professor Sylvester on the Real and Imaginary Roots of Equations. 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 | Kew | |--------|-----| | Cape of Good Hope | Liverpool | | Dublin | Madras | | Edinburgh | Oxford (Radcliffe) | | Greenwich | | ### 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 | | College of Surgeons | | Entomological Society | | Geological Society | | Geological Survey of Great Britain | | Horticultural Society | | Institute of British Architects | | Institution of Civil Engineers | | Linnean Society | | London Institution | | Royal Asiatic Society | | Royal Astronomical Society | | Royal College of Physicians | | Royal Geographical Society | | 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 | | 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 | ### Belgium | Brussels | Académie Royale de Médecine | |----------|-----------------------------| | Royal Academy of Sciences | ### Denmark | Altona | Royal Observatory | |---------|-------------------| | Copenhagen | Royal Society of Sciences | ### France | Montpellier | Academy of Sciences | |--------------|--------------------| | Faculté de Médecine | | Paris | Academy of Sciences | | Dépot de la Marine | | Ecole des Mines | | Geographical Society | | Geological Society | | Jardin des Plantes | | Société d'Encouragement pour l'Industrie Nationale | | Toulouse | Academy of Sciences | ### Germany | Berlin | Royal Academy of Sciences | |--------|--------------------------| | Society of Experimental Philosophy | | Brünn | Naturforschender Verein | | Dresden | Cesarean Acad. of Naturalists | | Frankfort | Natural History Society | | Giessen | University | | Göttingen | University | | Hamburg | Naturwissenschaftlicher-Verein | | Königsberg | Königlichen Physikalisch Ökonomenischen Gesellschaft | | Leipzig | Royal Saxon Society of Sciences | | Mannheim | Observatory | | Munich | Royal Academy of Sciences | | Prague | Bohemian Society of Sciences | | Vienna | Imperial Academy of Sciences | | Geologische Reichsanstalt | | Würzburg | Physico-Medical Society | ### Hungary | Pesth | Hungarian Academy of Sciences | ### Italy | Bologna | Academy of Sciences | |---------|---------------------| | Catanea | Accademia Gioenia di Scienze Naturali | | Milan | Institute of Sciences, Letters and Arts | | Modena | Italian Society of Sciences | | Naples | Institute of Sciences | | Palermo | Academy of Sciences and Letters | | 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 | Kazan | Imperial University | |-------|--------------------| | Moscow | Imperial Society of Naturalists | | Public Museum | | Pulkowa | Observatory | | St. Petersburg | Imperial Academy of Sciences | ### Spain | Cadiz | Observatory | |-------|-------------| | Madrid | Royal Academy of Sciences | ### Sweden and Norway | Christiania | Royal University | |-------------|------------------| | Drontheim | Royal Society of Sciences | | Gottenburg | Kongl. 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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 | | Berlin | Bologna Academy of Sciences | | Breslau | Brussels American Academy of Sciences | | Cadiz | Cambridge Bowdoin College | | Cambridge | Cambridge Trinity College Library | | Cape of Good Hope | Cambridge Harvard University | | Coimbra | Dublin University | | Copenhagen | Edinburgh University | | Dorpat | Glasgow University | | Dublin | Göttingen University | | Edinburgh | Leyden University | | Helsingfors | London Board of Ordnance | | Königsberg | London Royal Institution | | Madras | London Royal Society | | Mannheim | London The Queen's Library | | Marseille | Oxford Savilian Library | | Milan | Paris Academy of Sciences | | Munich | Paris Board of Longitude | | Oxford | Pesth Hungarian Academy of Sciences | | Palermo | Philadelphia American Philosophical Society | | Paris | Seeberg University | | Tübingen | St. Andrews University | | Turin | St. Petersburg Imperial Academy | | Vienna | Stockholm Royal Academy of Sciences | | Wilna | Upsal Royal Society | | | Waterville, Maine (U.S.) College | | 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. | | Smyth, 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 Magnetic and Meteorological Observations made at the Royal Observatory, Greenwich. ### Observatories - **Bombay** .............. Lieut. P. W. Mitcheson. - **Cambridge, United States** .... Prof. J. Lovering. - **Christia** ............. C. Hansteen. - **Gotha** ............... P. A. Hansen. - **Heidelberg** .......... M. Tiedemann. - **Kew** .................. B. Stewart. - **Kremsmünster** ........ P. A. Reslhuber. - **Leipzig** .............. Professor Möbius. - **Lisbon** .............. Senhor da Silveira. - **Marburg** ............. Professor Gerling. - **Prague** .............. K. Jelinek. - **Stockholm** .......... Professor H. Selander. - **Toronto** ............. Professor Kingston. - **Upsal** ............... Professor Svanberg. - **Washington** .......... Capt. Gilliss. ### Institutions - **Bombay** .............. Geographical Society. - **Bonn** ................ University. - **Boston, U.S.** ........ The Public Library (late Bowditch). - **Cambridge** ........... Philosophical Society. - **Cherkow** ............ University. - **Falmouth** ........... Royal Cornwall Polytechnic Society. - **London** ............. House of Lords, Library. - **London** ............. House of Commons, Library. - **London** ............. King's College. - **London** ............. Royal Society. - **London** ............. 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. - **Buys Ballot**, Dr. .......... Utrecht. - **Dove**, Prof. H. W. .......... Berlin. - **Erman**, Dr. Adolph .......... Berlin. - **Fox**, R. W., Esq. .......... Falmouth. - **Harris**, Sir W. Snow .......... Plymouth. - **Hoskins**, Dr. S. E. .......... Guernsey. - **Kacemtz**, Prof. L. F. .......... Dorpat. - **Kreil**, Prof. K. ........ Vienna. - **Kupffer**, A. T. ........ St. Petersburg. (Twelve copies for distribution to the Russian Mag. and Met. Obs.) - **Lloyd**, Rev. Dr. .......... Dublin. - **Loomis**, Prof. E. .......... Yale College, Newhaven (Conn.). - **Phillips**, Prof. John .......... Oxford. - **Quetelet**, A. ........ Brussels. - **Sabine**, Major-General, R.A. .......... London. - **Senhor de Souza** .......... Coimbra. - **Vernon**, G. V., Esq. .......... Manchester. - **Wartmann**, Prof. Elie .......... Geneva. - **Younghusband**, Col., R.A. .......... Woolwich. CONTENTS. I. Catalogue of Nebulae and Clusters of Stars. By Sir John Frederick William Herschel, Bart., F.R.S. . . . . . . . . . . . . . . . . . . . . . . page 1 II. On the Spectra of some of the Chemical Elements. By William Huggins, Esq., F.R.A.S. Communicated by Dr. W. A. Miller, Treas. R.S. . . . . page 139 III. Account of Magnetic Observations made in the years 1858–61 inclusive, in British Columbia, Washington Territory, and Vancouver Island. By Captain R. W. Haig, R.A. Communicated by General Sabine, P.R.S. . . . . . . . . . . 161 IV. On the Influence of Temperature on the Electric Conducting-Power of Alloys. By Augustus Matthiessen, F.R.S., Lecturer on Chemistry in St. Mary's Hospital, and Carl Vogt, Ph.D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 V. On the Absorption and Radiation of Heat by Gaseous and Liquid Matter.—Fourth Memoir. By John Tyndall, F.R.S., Member of the Academies and Societies of Holland, Geneva, Göttingen, Zürich, Halle, Marburg, Breslau, Upsala, la Société Philomathique of Paris, Cam. Phil. Soc. &c.; Professor of Natural Philosophy in the Royal Institution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 VI. A Comparison of the most notable Disturbances of the Magnetic Declination in 1858 and 1859 at Kew and at Nertschinsk; preceded by a brief Retrospective View of the Progress of the Investigation into the Laws and Causes of the Magnetic Disturbances. By Major-General Edward Sabine, R.A., President of the Royal Society . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 VII. Theoretical Considerations on the Conditions under which the (Drift) Deposits containing the Remains of Extinct Mammalia and Flint Implements were accumulated, and on their Geological Age. By Joseph Prestwich, Esq., F.R.S., F.G.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 VIII. Experiments to determine the effect of Impact, Vibratory Action, and long-continued Changes of Load on Wrought-Iron Girders. By W. Fairbairn, LL.D., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 IX. The Bakerian Lecture.—Contributions to Molecular Physics.—Being the Fifth Memoir of Researches on Radiant Heat. By John Tyndall, F.R.S., Member of the Academies and Societies of Holland, of Geneva, Göttingen, Zürich, Halle, Marburg, Breslau, Upsala, la Société Philomathique, Paris, Cam. Phil. Soc. &c.; Professor of Natural Philosophy in the Royal Institution . . . . . . . . . . 327 X. On Plane Water-Lines in two Dimensions. By William John MacQuorn Rankine, C.E., LL.D., F.R.S.S. L. & E., Associate of the Institution of Naval Architects, &c. . . . . . . . . . . . . . . . . . . . . . . page 369 XI. On the Joint-Systems of Ireland and Cornwall, and their Mechanical Origin. By the Rev. Samuel Haughton, M.D., Fellow of Trinity College, Dublin . . 393 XII. On the Spectra of some of the Fixed Stars. By William Huggins, F.R.A.S., and W. A. Miller, M.D., LL.D., Treas. & V.P.R.S., Professor of Chemistry, King's College, London . . . . . . . . . . . . . . . . . . . . . . 413 XIII. On the Spectra of some of the Nebulae. By William Huggins, F.R.A.S. A Supplement to the Paper "On the Spectra of some of the Fixed Stars. By William Huggins, F.R.A.S., and W. A. Miller, M.D., LL.D., Treas. and V.P.R.S." Communicated by Professor W. A. Miller, M.D., LL.D. . . 437 LIST OF ILLUSTRATIONS. Plates I. to II.—Mr. W. Huggins on the Spectra of some of the Chemical Elements. Plate III.—Captain Haig on the Magnetic Elements in British Columbia, Washington Territory, and Vancouver Island. Plates IV. to V.—Mr. Prestwich on the Geology of the Deposits containing Flint Implements, and on the Loess. Plates VI. to VII.—Dr. Fairbairn on the Effect of Impact, Vibratory Action, and long-continued Changes of Load on Wrought-Iron Girders. Plates VIII. to IX.—Dr. W. J. Macquorn Rankine on Plane Water-Lines. Plates X. to XI.—Mr. W. Huggins and Dr. W. A. Miller on the Spectra of some of the Fixed Stars. CONTENTS. XIV. On the Arrangement of the Muscular Fibres in the Ventricles of the Vertebrate Heart, with Physiological Remarks. By James Bell Pettigrew, M.D., Edin.; Assistant in the Museum of the Royal College of Surgeons of England; Extra-ordinary Member and late President of the Royal Medical Society of Edinburgh, &c. &c. Communicated by John Goodsir, Esq., F.R.SS. L. and E., Professor of Anatomy in the University of Edinburgh .......................................................... page 445 XV. On the Brain of a Bushwoman; and on the Brains of two Idiots of European Descent. By John Marshall, F.R.S., Surgeon to University College Hospital ..................... 501 XVI. A Second Memoir on Skew Surfaces, otherwise Scrolls. By A. Cayley, F.R.S. 559 XVII. Algebraical Researches, containing a disquisition on Newton's Rule for the Discovery of Imaginary Roots, and an allied Rule applicable to a particular class of Equations, together with a complete invariantive determination of the character of the Roots of the General Equation of the fifth Degree, &c. By J. J. Sylvester, M.A., F.R.S., Correspondent of the Institute of France, Foreign Member of the Royal Society of Naples, etc. etc., Professor of Mathematics at the Royal Military Academy, Woolwich ........................................ 579 XVIII. On a New Series of Bodies in which Nitrogen is substituted for Hydrogen. By Peter Griess, Esq. Communicated by A. W. Hofmann ........................................ 667 XIX. On the Differential Equations which determine the form of the Roots of Algebraic Equations. By George Boole, F.R.S., Professor of Mathematics in Queen's College, Cork ......................................................... 733 Index ................................................................................................................... 757 APPENDIX. Presents .......................................................................................................... [1] LIST OF ILLUSTRATIONS. Plates XII. to XVI.—Dr. Pettigrew on the Arrangement of the Muscular Fibres in the Ventricles of the Vertebrate Heart. Plates XVII. to XXIII.—Professor Marshall on the Brain of a Bushwoman; and on the Brains of two Idiots of European Descent. Plates XXIV., XXV.—Professor Sylvester on the Real and Imaginary Roots of Equations. ADJUDICATION of the Medals of the Royal Society for the year 1864 by the President and Council. The Copley Medal to Charles Darwin, Esq., F.R.S., for his important Researches in Geology, Zoology, and Botanical Physiology. The Rumford Medal to Professor John Tyndall, F.R.S., for his Researches on the Absorption and Radiation of Heat by Gases and Vapours. A Royal Medal to Jacob Lockhart Clarke, Esq., F.R.S., for his Researches on the Intimate Structure of the Spinal Cord and Brain, and on the Development of the Spinal Cord, published in five Memoirs in the Philosophical Transactions and in other writings. A Royal Medal to Warren De la Rue, Esq., F.R.S., for his Observations on the Total Eclipse of the Sun of 1860, and for his improvements in Astronomical Photography. Professor J. Tyndall's Paper, entitled "Researches on Radiant Heat,—Fifth Memoir," was appointed as the Bakerian Lecture. The Croonian Lecture was delivered by Professor Hermann Helmholtz, For. Mem. R.S.: it was entitled "On the Normal Motions of the Human Eye in relation to Binocular Vision."