ESSAY-REVIEWS 65 



have, by his own decision, not been included. Opportunity 

 has been taken to include two biographical memoirs, the one 

 by his brother Sir Francis Darwin, giving an account of his 

 life and activities ; the other by his friend and pupil, Prof. 

 E. W. Brown, of Yale University, giving a valuable account 

 of his scientific work. These memoirs are of considerable 

 interest, more especially to the many who knew Darwin at 

 Cambridge as a friend and a teacher. 



It is impossible in this brief article to give even a resume of 

 Darwin's work. The long series of papers on viscous spheroids, 

 on the effects of tidal friction, and on rotating masses of fluids 

 were directed to the important aim of developing a consistent 

 theory concerning the past history of planetary and satellite 

 systems. Darwin's theory was, briefly put, that the Earth and 

 the Moon had originally formed one body and that the origin 

 of the Moon was to be sought in the rupture of the parent 

 body into two parts. Darwin came to this conclusion by 

 working backward in time from a consideration of the present 

 state of the Earth and Moon. This theory, whilst Darwin 

 was at work upon it, received remarkable confirmation from 

 the brilliant work of Poincare, who traced the process of 

 evolution forwards by considering the process of change in a 

 rotating liquid planet as it gradually condensed through cool- 

 ing. He found that stability was ultimately transferred to 

 a pear-shaped figure resembling that to which Darwin had 

 been led in his researches, as the form of the parent body 

 before the rupture had taken place. To place the whole theory 

 on a firm basis it remained to prove that Poincare 's pear-shaped 

 figures would remain stable through the changes necessary to 

 fill the gap between these and Darwin's figures. Darwin was 

 never able quite to complete this . He discussed the equilibrium 

 of Poincare 's pear-shaped figure and thought he had estab- 

 lished its stability ; a concurrent investigation by Liapounoff 

 pointed to the opposite conclusion. It has been left to Mr. 

 J. H. Jeans, a pupil of Darwin, recently to settle the dispute 

 by proving that both Darwin and Liapounoff were wrong, as 

 their approximations were only carried to the second order, 

 and this, he finds, leaves the question of stability indetermi- 

 nate ; a third order approximation, however, shows that the 

 figure is unstable. The process of evolution then, traced 

 forwards as by Poincare, leads to the pear-shaped figure ; there 

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