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GEORGE HOWARD DARWIN, Knight Commander of the Bath, was born at Down, Kent, on July 9, 1845. He was the second son of Charles Robert Darwin (author of The Origin of Species), and of Emma Wedgwood, granddaughter of the well-known potter of Etruria in Staffordshire. His own work was to be in spirit analogous to that of his illustrious father; but it is not impossible that the influence of his schoolmaster, the Rev. Charles Pritchard, is to be seen in the actual direction taken by his researches. Pritchard, before he became Savilian Professor at Oxford, was for 30 years a schoolmaster in Clapham, and there he had for his pupils the sons of many men distinguished in scientific and professional life. The names of Airy, Hamilton, and Herschel are sufficient to suggest the class of family to which the school especially appealed. Pritchard was a pioneer in scientific education, but this did not involve any neglect of the basic subjects of education, and Darwin in due course gained a mathematical scholarship at Trinity College, Cambridge. He graduated as Second Wrangler in 1868, won a Smith's Prize, and was elected a Fellow of Trinity in the same year. Lord Moulton was the Senior Wrangler of his year, and Sir William Christie was Fourth Wrangler in the same year. Darwin was called to the Bar in 1874, but he soon returned to Cambridge, and in 1875 began the series of mathematical papers, the flow of which was only to cease with his death.
The recent publication of Darwin's Scientific Papers has rendered comparatively simple the task of describing the side of his life which they represent. He himself had undertaken the task of classifying and codifying his work. What is of interest here is to discover from the chronological table of his papers the emergence of the germs of his subsequent work. In 1876 he produced the first of a long series of important discussions of the problems of geophysics. His paper "On the Influence of Geological Changes on the Earth's Axis of Rotation" was refereed for the Royal Society by Lord Kelvin. It was the occasion that brought the two into an intimate relationship which had most important effects on the line of research subsequently adopted by Darwin. The series of papers on "Tides in a Viscous Spheroid," published in 1879 and 1880, is to be largely attributed to the influence of Kelvin: this is made clear not only by the frequent reference to his name in these papers, but by Darwin's cordial acknowledgment of his debt to Kelvin in the prefaces to the first two volumes of his printed papers. But the development of the ideas was essentially Darwin's own. From cosmogony and theoretical tides in the solid earth, his practical instinct passed to the problem of detecting and measuring these tides. Experimental conditions required for the elimination of the many disturbing factors in this delicate research were not available, and the researches of Darwin and his brother Horace on this point remained inconclusive. But their papers contain an important historical account of the subject which remains of great interest now that the problem has been largely solved by others. Pressure from other work prevented Darwin from returning to these experiments, for he was already becoming closely concerned with the important but arduous "Harmonic Analysis of Tidal Observations." This work was carried out by Darwin in conjunction with Lord Kelvin, Professor Adams and Major Baird serving as committees to the British Association. In the midst of this work came the death of Professor Challis of Cambridge. Though Darwin's work had not been along orthodox astronomical lines, the value of his original research was already recognized, and in 1883 he became Plumian Professor of Astronomy and Experimental Philosophy: he was re-elected to a Trinity Fellowship in 1884.
Darwin's fresh responsibilities were happily not allowed to check his output of original work, and he shortly began to break fresh ground in a new direction. The heavy numerical work which he had to face in Tidal Analysis may have been to some extent responsible for the fact that in his work on "Rotating Masses of Fluid," he steadily cast his theoretical writings in such a form that numerical results could be derived from them. This interest in actual values underlying theoretical conclusions had always been present, but his later work was to involve him in enormous labour cheerfully undertaken and, to his own mind, well justified by the interest of his results Both in the theory of the "Figures of Equilibrium of Rotating Masses of Fluid" and in his "Periodic Orbits," Darwin was to make a straightforward frontal attack on problems which his competitor Poincaré was outflanking, so to speak, with brilliant, broad generalizations. As Darwin himself said in presenting the gold medal of this Society to Poincaré: "To one class of mind the easier process is the consideration of some simple concrete case and the subsequent ascent to the more general aspect of the problem [but Poincaré] finds it easier to consider first the wider issues, from then on to descend to the more special instances." Darwin's work places him clearly with the earlier class of thinkers, but the combination of Darwin and Poincaré working on the same problem was most fruitful in its results, and there is a sad fitness in the fact that obituary notices of both should be within the same binding of many a scientific journal. Before passing to a more detailed discussion of the results of Darwin's works which have a direct astronomical bearing, the fact should be again emphasized that it was the cosmical applications of his research that inspired him in the prodigious labour which his later work involved. This part of his work is far from exhausted. His original purpose in discussing periodic orbits arose from a "desire to discover how a Laplacian ring could coalesce into a planet." A family of orbits which throws light on this problem was discovered by him only last year and described in the Monthly Notices for June 1912. Other writers are still using and developing the ideas and methods which Darwin initiated.
The application of tidal friction to a wide range of cosmogonical problems led in Darwin's hands to a number of interesting and novel results, the most important of which will be stated in summary form below. The mathematical analysis required in the investigation was necessarily somewhat heavy and need not be discussed here, but reference must be made to the extremely illuminating graphical method developed by Darwin. By comparing the equation of conservation of moment of momentum with the energy of the system for various configurations, he was able to trace for actual problems the direction in which individual elements would alter as the energy diminished by tidal friction.
The earliest of Darwin's papers, which calls for detailed notice here, is his paper "On the Precession of a Viscous Spheroid and on the Remote History of the Earth," published in 1879. Investigation showed that the period of diurnal rotation of the Earth, the obliquity of the ecliptic, and the Moon's distance were all in a state of flux under the influence of the action of the Moon and the Sun on the Earth's tides. Looking backward through the ages, we can see all three elements steadily decreasing. Under certain assumptions, it was calculated that at some period, not less than 54 million years ago, the Earth was rotating in about hours and the Moon revolving about it in the same time. This was a condition of dynamical instability, and Darwin was led to the conclusion that it had arisen through the breaking up of one rotating mass of fluid into two. This view that the Moon originated by fission from the Earth has been the subject of much controversy The later work on the figures of equilibrium of rotating fluids was undertaken largely for its bearing on the problem. Darwin discovered, simultaneously with Poincaré, that as the velocity of rotation of the fluid was increased, a new type of equilibrium figure was found, the so-called pear-shaped figure. Carrying his study of the question further, he reached a stage where the development of the pear into a kind of egg-glass form suggested that separation into two bodies was imminent; the tides lead backward to a similar crisis where two bodies appear close together in a very unstable and therefore transitional state. The further deduction that through some kind of gravitational instability, whose modus operandi defies the methods of exact analysis, the change indicated took place and a pear-shaped single body broke up into two, was made by Darwin; it does not seem that sub-sequent work ever led him to abandon the view, although he never insisted on it as a demonstrable fact. Darwin also traced the future development of the system in the way of a lengthening day and month and changing obliquity, but he pointed out other disturbing causes and refrained from making any numerical estimate of the present rate of tidal friction.
Darwin's next step was to make good the position he had gained by introducing into his analysis some of the factors of the case which, for the sake of mathematical simplicity, he had omitted in his earlier work. In his paper "On the Secular Changes in the Elements of the Orbit of a Satellite Revolving about a Tidally Distorted Planet," he took into account the effects of eccentricity and inclination in the satellite's orbit. His more precise and detailed discussion of the problem led to an alteration in his estimate of the time of Earth's rotation at about the period of instability; this he now places at between 2 hours and 4 hours. The gradual opening out and tilting of the lunar orbit, also its distortion from a circular form, was followed out step by step to the present day. Applications to the other satellite systems known to us were made in a tentative manner. This application of the tides, so important in the evolution of the Earth-Moon system to the other planets, was made in a subsequent paper The general conclusions to which Darwin came on this question were two: firstly, that the relative smallness of the other satellites compared with their primaries would make tidal friction a much less effective factor in modifying their orbits than in the case of the Moon; and secondly, that many data of our system, such as the progressive increase in the number of satellites as we recede from the Sun, are in agreement with the suggestion that tidal friction has been an effective agent in the evolution of the inner planetary sub-systems at least.
Only brief reference can be made to Sir George Darwin's other mathematical work. His practical bent was demonstrated in his study of ripple marks and thrusts in sand. In his treatment of Ellipsoidal Harmonic Analysis, the claims of arithmetical work were borne in mind, with subsequent results in investigations of difficult problems of stability. His work on the "Theory of the Earth's Figure" contributed to his becoming the foremost English geodesist of his day. He bore the brunt of the practical application of Kelvin's analytical methods in the discussion of the Tides and contributed articles on the Tides to the Enzyklopädie der mathematischen Wissenschaften (with the collaboration of Mr. S. S. Hough) and to the Encyclopædia Britannica. He also published a popular book on Tides and Kindred Phenomena in the Solar System, which has been translated into many languages and has run into several editions. This book arose from a course of lectures delivered at the Lowell Institute in Boston, and it naturally leads to a mention of the addresses which Darwin gave before the learned societies of which at one time or another he was president. His address on "Cosmical Evolution," which he gave when President of the British Association in South Africa in 1905, gives a complete account of his later views on the evolution of the solar system and some suggestions in the wider field of the stellar universe,
Darwin in natural course came to hold many important scientific positions. Elected a Fellow of the Royal Society in 1879, he served on the Council for three terms and was a Vice-President for the year 1908-9 Due recognition of his work was shown by the Royal Medal, awarded in 1884, followed by the Society's highest honour, the Copley Medal in 1911. As a member of the Meteorological Council and Solar Physics Committee, he added to the valuable work he did for the practical science of the state his connection with the British Association has been referred to; he was President of Section A in 1886. He served on the Council of the Royal Astronomical Society in 1881-85 and 1895-1902; he was President in 1899-1900, when the Society's gold medal was presented to Poincaré. He himself had received the medal eight years earlier. He was Vice-President of the International Geodetic Association, represented Great Britain at its gatherings, and was largely responsible for the success of the meeting in London and Cambridge in 1909. As President of the Cambridge Philosophical Society, he welcomed the Fifth International Congress of Mathematicians to Cambridge in August last year and was elected President of the Congress. We cannot forbear to quote from his address of welcome to the Congress. It is perhaps his last published speech, and it truly reflects the modesty and honesty of the man. Speaking of the Problem of Three Bodies, he says:
One other aspect of Darwin's life calls for treatment here: his career as a professor of astronomy. Judged by the crude test of numbers, he would seem to have failed in this portion of his life's work. But this judgment would be wrong; it must be borne in mind that for advanced mathematical astronomy, with its small field of satisfactory careers, only a select few can be expected to find the necessary incentive to face the difficulty of the work. The names of a few of Darwin's pupils are sufficient to show the wide range of his influence and the stimulus that his teaching and personality have supplied: Professor Ernest Brown and Dr. Cowell have been awarded the Gold Medal of the Royal Astronomical Society; Mr. Hough and Mr. Jeans have, among much other work, made important additions to Darwin's own research. Of great value to astronomy was the work that Darwin did for over 20 years as Secretary of the Board of Electors for the Isaac Newton Studentships. He carefully followed the work of the students, many of whom owed much to his friendly interest.
To Darwin is largely due the revival of the teaching of practical astronomy in Cambridge; Professor H. H. Turner was his first demonstrator; the Geographical School at Cambridge also owes much to the friendly support which Darwin steadily gave to the teaching of geography in the university. Darwin served for a while on the Council of the Senate and on the Financial Board of the university, and he also rendered valuable service from the start to the Appointments Board, a body which seeks to facilitate the placement of university graduates in many non-academic walks of life. But it cannot be said that in work on committees, concerned with the details of academic life and reform, he was most happily employed. To a great extent he was able to avoid the loss of time involved in such work and to remain where he was far happier, in his study: there he was always to be found seated in an armchair, with a writing board in front of him and with papers covered with computations strewn all around. It was there that he lived his real professorial life, and there he was always ready to help the young student who sought his presence.
He married in 1884 Maud, daughter of Charles du Puy, of Philadelphia, USA. He leaves behind him two sons and two daughters. The eldest son, Charles G. Darwin, was Fourth Wrangler in 1909 and is now Reader in Mathematical Physics at the Victoria University, Manchester.
Sir George Darwin was elected a Fellow of the Society on November 14, 1879.
F. J. M. S
The recent publication of Darwin's Scientific Papers has rendered comparatively simple the task of describing the side of his life which they represent. He himself had undertaken the task of classifying and codifying his work. What is of interest here is to discover from the chronological table of his papers the emergence of the germs of his subsequent work. In 1876 he produced the first of a long series of important discussions of the problems of geophysics. His paper "On the Influence of Geological Changes on the Earth's Axis of Rotation" was refereed for the Royal Society by Lord Kelvin. It was the occasion that brought the two into an intimate relationship which had most important effects on the line of research subsequently adopted by Darwin. The series of papers on "Tides in a Viscous Spheroid," published in 1879 and 1880, is to be largely attributed to the influence of Kelvin: this is made clear not only by the frequent reference to his name in these papers, but by Darwin's cordial acknowledgment of his debt to Kelvin in the prefaces to the first two volumes of his printed papers. But the development of the ideas was essentially Darwin's own. From cosmogony and theoretical tides in the solid earth, his practical instinct passed to the problem of detecting and measuring these tides. Experimental conditions required for the elimination of the many disturbing factors in this delicate research were not available, and the researches of Darwin and his brother Horace on this point remained inconclusive. But their papers contain an important historical account of the subject which remains of great interest now that the problem has been largely solved by others. Pressure from other work prevented Darwin from returning to these experiments, for he was already becoming closely concerned with the important but arduous "Harmonic Analysis of Tidal Observations." This work was carried out by Darwin in conjunction with Lord Kelvin, Professor Adams and Major Baird serving as committees to the British Association. In the midst of this work came the death of Professor Challis of Cambridge. Though Darwin's work had not been along orthodox astronomical lines, the value of his original research was already recognized, and in 1883 he became Plumian Professor of Astronomy and Experimental Philosophy: he was re-elected to a Trinity Fellowship in 1884.
Darwin's fresh responsibilities were happily not allowed to check his output of original work, and he shortly began to break fresh ground in a new direction. The heavy numerical work which he had to face in Tidal Analysis may have been to some extent responsible for the fact that in his work on "Rotating Masses of Fluid," he steadily cast his theoretical writings in such a form that numerical results could be derived from them. This interest in actual values underlying theoretical conclusions had always been present, but his later work was to involve him in enormous labour cheerfully undertaken and, to his own mind, well justified by the interest of his results Both in the theory of the "Figures of Equilibrium of Rotating Masses of Fluid" and in his "Periodic Orbits," Darwin was to make a straightforward frontal attack on problems which his competitor Poincaré was outflanking, so to speak, with brilliant, broad generalizations. As Darwin himself said in presenting the gold medal of this Society to Poincaré: "To one class of mind the easier process is the consideration of some simple concrete case and the subsequent ascent to the more general aspect of the problem [but Poincaré] finds it easier to consider first the wider issues, from then on to descend to the more special instances." Darwin's work places him clearly with the earlier class of thinkers, but the combination of Darwin and Poincaré working on the same problem was most fruitful in its results, and there is a sad fitness in the fact that obituary notices of both should be within the same binding of many a scientific journal. Before passing to a more detailed discussion of the results of Darwin's works which have a direct astronomical bearing, the fact should be again emphasized that it was the cosmical applications of his research that inspired him in the prodigious labour which his later work involved. This part of his work is far from exhausted. His original purpose in discussing periodic orbits arose from a "desire to discover how a Laplacian ring could coalesce into a planet." A family of orbits which throws light on this problem was discovered by him only last year and described in the Monthly Notices for June 1912. Other writers are still using and developing the ideas and methods which Darwin initiated.
The application of tidal friction to a wide range of cosmogonical problems led in Darwin's hands to a number of interesting and novel results, the most important of which will be stated in summary form below. The mathematical analysis required in the investigation was necessarily somewhat heavy and need not be discussed here, but reference must be made to the extremely illuminating graphical method developed by Darwin. By comparing the equation of conservation of moment of momentum with the energy of the system for various configurations, he was able to trace for actual problems the direction in which individual elements would alter as the energy diminished by tidal friction.
The earliest of Darwin's papers, which calls for detailed notice here, is his paper "On the Precession of a Viscous Spheroid and on the Remote History of the Earth," published in 1879. Investigation showed that the period of diurnal rotation of the Earth, the obliquity of the ecliptic, and the Moon's distance were all in a state of flux under the influence of the action of the Moon and the Sun on the Earth's tides. Looking backward through the ages, we can see all three elements steadily decreasing. Under certain assumptions, it was calculated that at some period, not less than 54 million years ago, the Earth was rotating in about hours and the Moon revolving about it in the same time. This was a condition of dynamical instability, and Darwin was led to the conclusion that it had arisen through the breaking up of one rotating mass of fluid into two. This view that the Moon originated by fission from the Earth has been the subject of much controversy The later work on the figures of equilibrium of rotating fluids was undertaken largely for its bearing on the problem. Darwin discovered, simultaneously with Poincaré, that as the velocity of rotation of the fluid was increased, a new type of equilibrium figure was found, the so-called pear-shaped figure. Carrying his study of the question further, he reached a stage where the development of the pear into a kind of egg-glass form suggested that separation into two bodies was imminent; the tides lead backward to a similar crisis where two bodies appear close together in a very unstable and therefore transitional state. The further deduction that through some kind of gravitational instability, whose modus operandi defies the methods of exact analysis, the change indicated took place and a pear-shaped single body broke up into two, was made by Darwin; it does not seem that sub-sequent work ever led him to abandon the view, although he never insisted on it as a demonstrable fact. Darwin also traced the future development of the system in the way of a lengthening day and month and changing obliquity, but he pointed out other disturbing causes and refrained from making any numerical estimate of the present rate of tidal friction.
Darwin's next step was to make good the position he had gained by introducing into his analysis some of the factors of the case which, for the sake of mathematical simplicity, he had omitted in his earlier work. In his paper "On the Secular Changes in the Elements of the Orbit of a Satellite Revolving about a Tidally Distorted Planet," he took into account the effects of eccentricity and inclination in the satellite's orbit. His more precise and detailed discussion of the problem led to an alteration in his estimate of the time of Earth's rotation at about the period of instability; this he now places at between 2 hours and 4 hours. The gradual opening out and tilting of the lunar orbit, also its distortion from a circular form, was followed out step by step to the present day. Applications to the other satellite systems known to us were made in a tentative manner. This application of the tides, so important in the evolution of the Earth-Moon system to the other planets, was made in a subsequent paper The general conclusions to which Darwin came on this question were two: firstly, that the relative smallness of the other satellites compared with their primaries would make tidal friction a much less effective factor in modifying their orbits than in the case of the Moon; and secondly, that many data of our system, such as the progressive increase in the number of satellites as we recede from the Sun, are in agreement with the suggestion that tidal friction has been an effective agent in the evolution of the inner planetary sub-systems at least.
Only brief reference can be made to Sir George Darwin's other mathematical work. His practical bent was demonstrated in his study of ripple marks and thrusts in sand. In his treatment of Ellipsoidal Harmonic Analysis, the claims of arithmetical work were borne in mind, with subsequent results in investigations of difficult problems of stability. His work on the "Theory of the Earth's Figure" contributed to his becoming the foremost English geodesist of his day. He bore the brunt of the practical application of Kelvin's analytical methods in the discussion of the Tides and contributed articles on the Tides to the Enzyklopädie der mathematischen Wissenschaften (with the collaboration of Mr. S. S. Hough) and to the Encyclopædia Britannica. He also published a popular book on Tides and Kindred Phenomena in the Solar System, which has been translated into many languages and has run into several editions. This book arose from a course of lectures delivered at the Lowell Institute in Boston, and it naturally leads to a mention of the addresses which Darwin gave before the learned societies of which at one time or another he was president. His address on "Cosmical Evolution," which he gave when President of the British Association in South Africa in 1905, gives a complete account of his later views on the evolution of the solar system and some suggestions in the wider field of the stellar universe,
Darwin in natural course came to hold many important scientific positions. Elected a Fellow of the Royal Society in 1879, he served on the Council for three terms and was a Vice-President for the year 1908-9 Due recognition of his work was shown by the Royal Medal, awarded in 1884, followed by the Society's highest honour, the Copley Medal in 1911. As a member of the Meteorological Council and Solar Physics Committee, he added to the valuable work he did for the practical science of the state his connection with the British Association has been referred to; he was President of Section A in 1886. He served on the Council of the Royal Astronomical Society in 1881-85 and 1895-1902; he was President in 1899-1900, when the Society's gold medal was presented to Poincaré. He himself had received the medal eight years earlier. He was Vice-President of the International Geodetic Association, represented Great Britain at its gatherings, and was largely responsible for the success of the meeting in London and Cambridge in 1909. As President of the Cambridge Philosophical Society, he welcomed the Fifth International Congress of Mathematicians to Cambridge in August last year and was elected President of the Congress. We cannot forbear to quote from his address of welcome to the Congress. It is perhaps his last published speech, and it truly reflects the modesty and honesty of the man. Speaking of the Problem of Three Bodies, he says:
My own work on the subject cannot be said to involve any such skill at all, unless indeed you describe as skill the procedure of a housebreaker who blows in a safe door with dynamite instead of picking the lock. It is thus by brute force that this tantalizing problem has been compelled to give up some of its secrets, and, great as has been the labour involved, I think it has been worth while. To put at their lowest the claims of this clumsy method, which may almost excite the derision of the pure mathematician, it has served to shed light on the celebrated generalizations of Hill and Poincaré.In the words which we have put into italics lies the motto of Darwin's life. Lived simply as he lived it, with his ability and persistence it brought him necessarily honored recognition from all parts of the world. Ten universities gave him their doctorate, twenty-five learned societies or academies elected him as a foreign or corresponding member. Berlin, Paris, Rome, St. Petersburg, Vienna, and Washington all recognized his worth, and he served as by natural right on the International Association of Academies Committee of the Royal Society. Societies as diverse as the Royal Geographical Society and the Institution of Civil Engineers awarded him their medals
I appeal, then, for mercy to the applied mathematician, and would ask you to consider in a kindly spirit the difficulties under which he labours. If our methods are often wanting in elegance and do but little to satisfy that aesthetic sense of which I spoke before, yet they are honest attempts to unravel the secrets of the universe in which we live.
One other aspect of Darwin's life calls for treatment here: his career as a professor of astronomy. Judged by the crude test of numbers, he would seem to have failed in this portion of his life's work. But this judgment would be wrong; it must be borne in mind that for advanced mathematical astronomy, with its small field of satisfactory careers, only a select few can be expected to find the necessary incentive to face the difficulty of the work. The names of a few of Darwin's pupils are sufficient to show the wide range of his influence and the stimulus that his teaching and personality have supplied: Professor Ernest Brown and Dr. Cowell have been awarded the Gold Medal of the Royal Astronomical Society; Mr. Hough and Mr. Jeans have, among much other work, made important additions to Darwin's own research. Of great value to astronomy was the work that Darwin did for over 20 years as Secretary of the Board of Electors for the Isaac Newton Studentships. He carefully followed the work of the students, many of whom owed much to his friendly interest.
To Darwin is largely due the revival of the teaching of practical astronomy in Cambridge; Professor H. H. Turner was his first demonstrator; the Geographical School at Cambridge also owes much to the friendly support which Darwin steadily gave to the teaching of geography in the university. Darwin served for a while on the Council of the Senate and on the Financial Board of the university, and he also rendered valuable service from the start to the Appointments Board, a body which seeks to facilitate the placement of university graduates in many non-academic walks of life. But it cannot be said that in work on committees, concerned with the details of academic life and reform, he was most happily employed. To a great extent he was able to avoid the loss of time involved in such work and to remain where he was far happier, in his study: there he was always to be found seated in an armchair, with a writing board in front of him and with papers covered with computations strewn all around. It was there that he lived his real professorial life, and there he was always ready to help the young student who sought his presence.
He married in 1884 Maud, daughter of Charles du Puy, of Philadelphia, USA. He leaves behind him two sons and two daughters. The eldest son, Charles G. Darwin, was Fourth Wrangler in 1909 and is now Reader in Mathematical Physics at the Victoria University, Manchester.
Sir George Darwin was elected a Fellow of the Society on November 14, 1879.
F. J. M. S
George Howard Darwin's obituary appeared in Journal of the Royal Astronomical Society 73:4 (1913), 204-210.