14 SCIENCE PROGRESS 



been awarded the Adams Prize of the University of Cambridge. 

 Some of the results obtained have appeared in papers published 

 recently in the Phil. Trans, dealing mainly with the equilibrium 

 of rotating fluids, and the chief astronomical applications are 

 given in a paper to appear in the Memoirs R.A.S. entitled, 

 " The Part played by Rotation in Cosmic Evolution." The 

 treatment of the subject necessarily involves much compli- 

 cated mathematics and this fact may deter the average reader 

 from giving to these papers the consideration which they merit. 

 The excellent summary of the chief results obtained, freed from 

 the analytical complications, which is given by Mr. Jeans in 

 the Observatory, vol. xl. pp. 196-203, May 191 7, is therefore 

 the more welcome. The method of treating the subject is 

 based on Poincare's elegant theory of linear series and points 

 of bifurcation, and this is briefly explained. As the physical 

 conditions of a rotating mass change, the whole system of 

 possible configurations of equilibrium fall into a " linear series ".; 

 on passing through such a series, with conditions gradually 

 changing, stability can only be lost either (1) at a " point of 

 bifurcation," where two series intersect in a configuration which 

 is common to both, or (2) on passing through a " turning point " 

 at which the variable parameter, which expresses the change 

 in the physical conditions, becomes stationary and then 

 decreases. Also at a point of bifurcation, at which the main 

 series loses its stability, the branch series will be stable if its 

 arms turn up (the parameter increasing) and unstable if they 

 turn down (the parameter decreasing). 



The simplest case of a homogeneous incompressible rotating 

 mass is first considered, the density being assumed constant 

 and the angular momentum being made to increase and being 

 taken as the variable parameter. Starting from the 

 spherical configuration, the sequence of configurations is traced 

 through the well-known Maclaurin spheroids, through a point 

 of bifurcation to the Jacobean ellipsoids which are initially 

 stable, and then through another point of bifurcation to the pear- 

 shaped figures of Darwin. Darwin thought he had proved 

 these to be stable ; Liapounoff, on the other hand, thought that 

 they were unstable. The detailed investigations of Mr. Jeans 

 prove that the branch series through the point of bifurcation 

 turns down, indicating instability. The only possibility when 

 this stage is reached is dynamical motion, and a violent dis- 



