336 On a Rotating Mass of Fluid. 



or, with rougher approximation, 



[Nov. 25, ; 



of which the limit is infinite. 

 Again, <=Y"(Z~) 



Now the function -(log e -— C ) has a maximum, when log e -=l-fC 



ct> \ a / a 



= 1-35:73, that is when -=1-696. 



'Ob 



On comparison with our tables it is obvious that the approximation 

 is bad, and that the true solution for a maximum is considerably dif- 

 ferent from the above. Nevertheless this investigation shows that 

 there is actually a maximum of kinetic energy. 



Since F= log.cot i 7 ) =f [log|+§ ]og e 2j , 



we have 



sin 



If we like we may express these several results in terms of the 



i ■ 3 



minor and major axes of the ellipsoid, for &=c= — , and therefore 



Thus 



^ c2r a ar T\ " 

 — =- 2 log e fC . 



