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ON THE FIGURE ANI) STABILITY OF A LIQUID SATELLITE. 
cylinder to two revolving about one another, and if I am correct now, the two 
problems must part company at some undetermined stage. M. Liapounoff will no 
doubt contend that it is at the beginning of the pear-shaped series, but for the 
present I should disagree with such an opinion. 
I have no suggestion to make as to the stage at which the pear-shaped figure may 
become unstable, or as to the figure which must be coalescent with it when instability 
supervenes. These points must await the elucidation which they will no doubt 
receive from future investigations. 
One question remains : If my present conclusions are correct, do they entirely 
destroy the applicability of this group of ideas to the explanation of the birth of 
satellites or of double stars 'l I think not, for we see how a tendency to fission arises, 
and it is not impossible that a period of turbulence may naturally supervene in the 
process of separation. Finally, as Mr. Jeans points out, heterogeneity of density 
introduces new and important differences in the conditions. 
i. -—2-1 ■. -Ajfc) 
/JULIUS 
