PREFACE 



THE present essay is primarily an attempt to follow up a line of research 

 initiated by Laplace and Maclaurin, and extended in various directions 

 by Roche, Lord Kelvin, Jacobi, Poincare and Sir G. Darwin. Within two 

 years of the close of his life, Darwin remarked that the way to further 

 progress in cosmogony was blocked by our ignorance of the figures of 

 equilibrium of rotating gaseous masses. He wrote as follows (Darwin and 

 Modern Science, p. 563, and Tides, 3rd edition, p. 401) : 



" As we have seen, the study of the forms of equilibrium of rotating liquids 

 is almost complete, and a good beginning has been made in the investigation 

 of the equilibrium of gaseous stars, but much more remains to be discovered. 



" As a beginning we should like to know how a moderate degree of com- 

 pressibility would alter the results for liquid, and.., to understand more as to 

 the manner in which rotation affects the equilibrium and stability of rotating 

 gas. The field for the mathematician is a wide one, and in proportion as the 

 very arduous exploration of that field is attained, so will our knowledge of 

 the processes of cosmical evolution increase 



" Human life is too short to permit us to watch the leisurely procedure 

 of cosmical evolution, but the celestial museum contains so many exhibits 

 that it may become possible, by the aid of theory, to piece together bit by 

 bit the processes through which stars pass in the course of their evolution." 



Guided possibly by considerations such as these, the Adjudicators of the 

 Adams Prize announced as the subject for the 1917 Essay : 



The course of evolution of the configurations possible for a rotating and 

 gravitating fluid mass, including the discussion of the stabilities of the various 

 forms. 



At this time I had for some years been engaged in an attack on this 

 problem. The announcement offered an excuse not only for putting together 

 my own results in essay form but also for welding them on to the earlier 

 results obtained in the classical papers of Darwin, Poincare and other workers 

 at this problem. After the adjudication of the prize, the essay was enlarged 

 by the addition of some further results which had been obtained in the 

 interval, and the present volume is the result. 



