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The Scientific Papers of Sir George Darwin Supplementary Volume The Scientific Papers of Sir George Darwin Supplementary Volume Volume 5 George Howard Darwin Edited by F.J.M. Stratton and J. Jackson Downloaded from https://www.cambridge.org/core. National University of Singapore (NUS), on 08 Jul 2019 at 11:40:44, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511703515 CAMBRIDGE UNIVERSITY PRESS Cambridge New York Melbourne Madrid Cape Town Singapore São Paolo Delhi Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9781108004480 © in this compilation Cambridge University Press 2009 This edition first published 1916 This digitally printed version 2009 ISBN 978-1-108-00448-0 This book reproduces the text of the original edition. The content and language reflect the beliefs, practices and terminology of their time, and have not been updated. Downloaded from https://www.cambridge.org/core. National University of Singapore (NUS), on 08 Jul 2019 at 11:40:44, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511703515 SCIENTIFIC PAPERS Downloaded from https://www.cambridge.org/core. National University of Singapore (NUS), on 08 Jul 2019 at 11:40:44, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511703515 CAMBRIDGE UNIVERSITY PRESS C. F. CLAY, MANAGER Ionium: FETTER LANE, E.C. ioo PRINCES STREET £eto gorfe: G. P. PUTNAM'S SONS Bombag, Calcutta anti JEatom: MACMILLAN AND CO., LTD. Toronto: J. M. DENT AND SONS, LTD. Eofcgo: THE MARUZEN-KABUSHIKI-KAISHA All rights reserved Downloaded from https://www.cambridge.org/core. National University of Singapore (NUS), on 08 Jul 2019 at 11:40:44, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511703515 Downloaded from https://www.cambridge.org/core. National University of Singapore (NUS), on 08 Jul 2019 at 11:40:44, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511703515 SCIENTIFIC PAPERS BY SIR GEORGE HOWARD DARWIN K.C.B., F.R.S. FELLOW OF TRINITY COLLEGE PLUMIAN PROFESSOR IN THE UNIVERSITY OF CAMBRIDGE VOLUME V SUPPLEMENTARY VOLUME CONTAINING BIOGRAPHICAL MEMOIRS BY SIR FRANCIS DARWIN AND PROFESSOR E. W. BROWN, LECTURES ON HILL'S LUNAR THEORY, ETC. EDITED BY F. J. M. STRATTON, M.A., AND J. JACKSON, M.A., B.Sc. Cambridge : at the University Press 1916 Downloaded from https://www.cambridge.org/core. National University of Singapore (NUS), on 08 Jul 2019 at 11:40:44, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511703515 Cambrtoge: PRINTED BY JOHN CLAY, M.A. AT THE UNIVERSITY PRESS Downloaded from https://www.cambridge.org/core. National University of Singapore (NUS), on 08 Jul 2019 at 11:40:44, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511703515 PREFACE "DEFORE his death Sir George Darwin expressed the view that his lectures on Hill's Lunar Theory should be published. He made no claim to any originality in them, but he believed that a simple presentation of Hill's method, in which the analysis was cut short while the fundamental principles of the method were shewn, might be acceptable to students of astronomy. In this belief we heartily agree. The lectures might also with advantage engage the attention of other students of mathematics who have not the time to enter into a completely elaborated lunar theory. They explain the essential peculiarities of Hill's work and the method of approximation used by him in the discussion of an actual problem of nature of great interest. It is hoped that sufficient detail has been given to reveal completely the underlying principles, and at the same time not be too tedious for verification by the reader. During the later years of his life Sir George Darwin collected his principal works into four volumes. It has been considered desirable to publish these lectures together with a few miscellaneous articles in a fifth volume of his works. Only one series of lectures is here given, although he lectured on a great variety of subjects connected with Dynamics, Cos- mogony, Geodesy, Tides, Theories of Gravitation, etc. The substance of many of these is to be found in his scientific papers published in the four earlier volumes. The way in which in his lectures he attacked problems of great complexity by means of simple analytical methods is well illustrated in the series chosen for publication. Two addresses are included in this volume. The one gives a view of the mathematical school at Cambridge about 1880, the other deals with the mathematical outlook of 1912. Downloaded from https://www.cambridge.org/core. National University of Singapore (NUS), on 08 Jul 2019 at 11:40:43, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511703515.001 VI PREFACE The previous volumes contain all the scientific papers by Sir George Darwin published before 1910 which he wished to see reproduced. They do not include a large number of scientific reports on geodesy, the tides and other subjects which had involved a great deal of labour. Although the reports were of great value for the advancement and encouragement of science, he did not think it desirable to reprint them. We have not ventured to depart from his own considered decision; the collected lists at the beginning of these volumes give the necessary references for such papers as have been omitted. We are indebted to the Royal Astronomical Society for permission to complete Sir George Darwin's .work on Periodic Orbits by reproducing his last published paper. The opportunity has been taken of securing biographical memoirs of Darwin from two different points of view. His brother, Sir Francis Darwin, writes of his life apart from his scientific work, while Professor E. W. Brown, of Yale University, writes of Darwin the astronomer, mathematician and teacher. F. J. M. S. J. J. GREENWICH, 6 December 1915. Downloaded from https://www.cambridge.org/core. National University of Singapore (NUS), on 08 Jul 2019 at 11:40:43, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511703515.001 CONTENTS PORTRAIT OF SIR GEORGE DARWIN Frontispiece PAGE MEMOIR OF SIR GEORGE DARWIN BY HIS BROTHER SIR FRANCIS DARWIN ix THE SCIENTIFIC WORK OF SIR GEORGE DARWIN BY PROFESSOR E. W. BROWN ............ xxxiv INAUGURAL LECTURE (DELIVERED AT CAMBRIDGE, IN 1883, ON ELECTION TO THE PLUMIAN PROFESSORSHIP) 1 INTRODUCTION TO DYNAMICAL ASTRONOMY. ...... 9 LECTURES ON HILL'S LUNAR THEORY . 16 § 1. Introduction .......... 16 § 2. Differential Equations of Motion and Jacobi's Integral . 17 § 3. The Variational Curve . 22 § 4. Differential Equations for Small Displacements from the Variational Curve . 26 § 5. Transformation of the Equations in § 4 . 29 § 6. Integration of an important type of Differential Equation . 36 § 7. Integration of the Equation for 8p ..... 39 § 8. Introduction of the Third Coordinate 43 § 9. Results obtained ......... 45 § 10. General Equations of Motion and their solution ... 46 § 11. Compilation of Results 52 Note 1. On the Infinite Determinant of § 5 . 53 Note 2. On the periodicity of the integrals of the equation where © = ©0 + ©j cos 2T + ©2 cos 4T + ....- . 55 ON LIBRATING PLANETS AND ON A NEW FAMILY OF PERIODIC ORBITS . 59 [Monthly Notices of the Royal Astronomical Society, Vol. 72 (1912), pp. 642— 658.] ADDRESS TO THE INTERNATIONAL CONGRESS OF MATHEMATICIANS AT CAMBRIDGE IN 1912 76 INDEX 80 Downloaded from https://www.cambridge.org/core. National University of Singapore (NUS), on 08 Jul 2019 at 11:40:43, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511703515 MEMOIE OF SIR GEORGE DARWIN BY HIS BROTHER SIR FRANCIS DARWIN George Howard, the fifth1 child of Charles and Emma Darwin, was born at Down July 9th, 1845. Why he was christened2 George, I cannot say. It was one of the facts on which we founded a theory that our parents lost their presence of mind at the font and gave us names for which there was neither the excuse of tradition nor of preference on their own part. His second name, however, commemorates his great-grandmother, Mary Howard, the first wife of Erasmus Darwin. It seems possible that George's ill-health and that of his father were inherited from the Howards. This at any rate was Francis Galton's view, who held that his own excellent health was a heritage from Erasmus Darwin's second wife. George's second name, Howard, has a certain appropriateness in his case for he was the genea- logist and herald of our family, and it is through Mary Howard that the Darwins can, by an excessively devious route, claim descent from certain eminent people, e.g. John of Gaunt. This is shown in the pedigrees which George wrote out, and in the elaborate genealogical tree published in Pro- fessor Pearson's Life of Francis Oalton. George's parents had moved to Down in September 1842, and he was born to those quiet surroundings of which Charles Darwin wrote " My life goes on like clock-work and I am fixed on the spot where I shall end it3." It would have been difficult to find a more retired place so near London.
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