AND THE NEBULAR HYPOTHBBB. 



giving, on substitution from equation (43), 



471 



whence, for the ratio of p to o-, we have the general formula 



a- J (*a)\ 2wr/ 



For the particular con%uration which occurs at a point of bifurcation, 



<ta 



so that 



whence we obtain 



In the following table I have calculated the values of u^/2ir<r and of */2irj5 for 

 which cylinders of different radii (a) and compressibility (*) first become elliptical 111 

 cross section : 



It will be seen that the general result is fully confirmed, that incompressible 

 masses are the first to become uustable, and that the more compressible the mass is, 

 the greater is the rotation required for it to depart from a symmetrical configuration. 



Rotating nearly Spherical Mass n-ith High Internal Temperature. 



15. We now leave the artificial two-dimensional problem and return to the real 

 problem in three dimensions discussed in 13. 



The coefficient K was there assumed to have the same value throughout the mass, 

 as of course it would if the matter were homogeneous and of uniform temperature 



