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The field of dynamical astronomy is a wide one and it is obvious that it will be impossible to consider even in the most elementary manner all branches of it; for it embraces all those effects in the heavens which may be attributed to the effects of gravitation. In the most extended sense of the term it may be held to include theories of gravitation itself. Whether or not gravitation is an ultimate fact beyond which we shall never penetrate is as yet unknown, but Newton, whose insight into physical causation was almost preternatural, regarded it as certain that some further explanation was ultimately attainable. At any rate from the time of Newton down to to-day men have always been striving towards such explanation—it must be admitted without much success. The earliest theory of the kind was that of Lesage, promulgated some 170 years ago. He conceived all space to be filled with what he called ultramundane corpuscles, moving with very great velocities in all directions. They were so minute and so sparsely distributed that their mutual collisions were of extreme rarity, whilst they bombarded the grosser molecules of ordinary matter. Each molecule formed a partial shield to its neighbours, and this shielding action was held to furnish an explanation of the mutual attraction according to the law of the inverse square of the distance, and the product of the areas of the sections of the two molecules.
An account of Hill's Lunar Theory can best be prefaced by a few quotations from Hill's original papers. These will indicate the peculiarities which mark off his treatment from that of earlier writers and also, to some extent, the reasons for the changes he introduced. Referring to the well-known expressions which give, for undisturbed elliptic motion, the rectangular coordinates as explicit functions of the time—expressions involving nothing more complicated than Bessel's functions of integral order—Hill writes:
“Here the law of series is manifest, and the approximation can easily be carried as far as we wish. But the longitude and latitude, variables employed by nearly all lunar theorists, are far from having such simple expressions; in fact their coefficients cannot be finitely expressed in terms of Besselian functions. And if this is true in the elliptic theory how much more likely is a similar thing to be true when the complexity of the problem is increased by the consideration of disturbing forces?…There is also another advantage in employing coordinates of the former kind (rectangular): the differential equations are expressed in purely algebraic functions, while with the latter (polar) circular functions immediately present themselves.”
I propose to take advantage of the circumstance that this is the first of the lectures which I am to give, to say a few words on the Mathematical School of this University, and especially of the position of a professor in regard to teaching at the present time.
There are here a number of branches of scientific study to which there are attached laboratories, directed by professors, or by men who occupy the position and do the duties of professors, but do not receive their pay from, nor full recognition by, the University. Of these branches of science I have comparatively little to say.
You are of course aware of the enormous impulse which has been given to experimental science in Cambridge during the last ten years. It would indeed have been strange if the presence of such men as now stand at the head of those departments had not created important Schools of Science. And yet when we consider the strange constitution of our University, it may be wondered that they have been able to accomplish this. I suspect that there may be a considerable number of men who go through their University course, whose acquaintance with the scientific activity of the place is limited by the knowledge that there is a large building erected for some obscure purpose in the neighbourhood of the Corn Exchange.
George Howard, the fifth child of Charles and Emma Darwin, was born at Down July 9th, 1845. Why he was christened 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 genealogist 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 Professor Pearson's Life of Francis Galton. 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 it.”
Sir George Darwin (1845–1912) was the second son of Charles Darwin. After studying mathematics at Cambridge he read for the Bar, but soon returned to science and to Cambridge, where in 1883 he was appointed Plumian Professor of Astronomy and Experimental Philosophy. His work was concerned primarily with the effect of the sun and moon on tidal forces on Earth, and with the theoretical cosmogony which evolved from practical observation: he formulated the fission theory of the formation of the moon (that the moon was formed from still-molten matter pulled away from the Earth by solar tides). He also developed a theory of evolution for the Sun–Earth–Moon system based on mathematical analysis in geophysical theory. This volume, published in 1916 after the author's death, includes a biographical memoir by his brother Sir Francis Darwin, his inaugural lecture and his lectures on George W. Hill's lunar theory.
The scientific work of Darwin possesses two characteristics which cannot fail to strike the reader who glances over the titles of the eighty odd papers which are gathered together in the four volumes which contain most of his publications. The first of these characteristics is the homogeneous nature of his investigations. After some early brief notes, on a variety of subjects, he seems to have set himself definitely to the task of applying the tests of mathematics to theories of cosmogony, and to have only departed from it when pressed to undertake the solution of practical problems for which there was an immediate need. His various papers on viscous spheroids concluding with the effects of tidal friction, the series on rotating masses of fluids, even those on periodic orbits, all have the idea, generally in the foreground, of developing the consequences of old and new assumptions concerning the past history of planetary and satellite systems. That he achieved so much, in spite of indifferent health which did not permit long hours of work at his desk, must have been largely due to this single aim.
The second characteristic is the absence of investigations undertaken for their mathematical interest alone; he was an applied mathematician in the strict and older sense of the word. In the last few decades another school of applied mathematicians, founded mainly by Poincaré, has arisen, but it differs essentially from the older school. Its votaries have less interest in the phenomena than in the mathematical processes which are used by the student of the phenomena.
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