516 Sir G. Greenhill on the 



12. With ?i = 6, we have 



p=p cosyv % , M = J7r/) c a sin</r 3 , . . . (1) 

 and for i = 4, 

 q = Me = Afsin qr*-qr z cos ?r 3 ), e = ^l-g£— ^ (2) 



The subject has been investigated generally in the 

 Bakerian Lecture, May 17, 1917, "Configuration of a 

 rotating compressible mass," by J. H. Jeans ; but on the 

 adiabatic law of p = kpy, the only case so far, besides that of 

 Laplace's 7=2, is for y=T2, given by A. Schuster in the 

 Report to the British Association, 1883, and then 



p - ( c2 V p-^-( f \-(p\* 



tvt 4 s/ ** V 4*rr*dp 15 



47rr 4 rfp 15cV ^ 



and the corresponding differential equation for 77 = Me, 

 with rj = r i+1 y, 



ld 2 v i(tfl) 15c 2 



^r 2 ~ r 2 (c 2 + r 2 ) ; 



^ 2 .V . O/V : ^.-^ lOcVj/ 



^ +2 ^ +i >^-^h#;=°= w 



■(»'+j 



or with r—ce™, y = ze~ 



^, + 1 = 0, I = /i(n + l)sech 2 ^-(i + i) 2 , n=|, (5) 



a Lame equation. 



This D.E. (4) becomes, with the new variable 



.2 • 22 



•'■= ( 4V • ,,(1 - i ' ) = c?+V' • • • < 6 > 



.,(l-,)g+(;+|-2.,)| + 3 J 5 y = 0, ..... (7) 



a H.G. D.E. (hyper-geometric-differential equation), having 

 an algebraical solution. 



Thus, when the disturbing harmonic is due to rotation, 



