58 ME. J. H. JEANS ON THE POTENTIAL OF ELLIPSOIDAL BODIES, AND 



The value of u a is now given by 



^te t) . . (124) 



whence, by equation (45), 



f x 

 = - V\,, f M a d\ 



Jo 



4 ic 



(125) 



where the K's are constants, to be chosen so as to make ^v vanish when A = 0. 



222 

 The value of V 2 tf ,, fi (4r) is derived from that of 4- by replacing ^ 3 , / 2 , f 2 by -T-J, ^5, ^ 2 



and omitting all other terms. Thus we have, again from equation (45), 



= -i [ V 8 j,, if (4w)c?X 



Jo 





__ __ 

 V " a A :t 2 AB 2 2 AC 3 A 8 B A 2 C ABC 



+ ++ (126) 



in which K 5 is a new constant, chosen so as to make w' vanish when X = 0. 

 On collecting terms, we obtain 



4( w +>') = P,f + P^ + P 3 i 2 + P 1 ....... (127) 



where 



3 . M'A . 3 N'A 'A m' 



" - 



, 03 . . 3 , i , I4 ^ 



8 " -^+^-^ ++lr TJ" *B 



(128) 



