456 



Mr. R. Hargreaves o;> 





. f dco 



4z7T p L* dco 



= —7= , or or course l ->- — r-j- = 



4tt 

 v'A 



. (136) 



In the middle integral of (124) write A for p in u P , it is then 

 ^dco/uji ; and in the third integral J, which is 



1 + \2 {pa + '2p'a') + A, 2 2(PA + 2P'A') + \ 3 A p A a , 

 becomes l+\(3A a )-f X 2 (3A A ) +\ 3 A A A fl or (1 + XA,) 3 . 

 Thus (124) yields in that case 



d\ 4tt 47r 



J("a)* Jo (1 



XA«)i A fl v'Aa' 



These expressions for L ... may be used in the formula 

 for S f (117). For principal axes v A /A a = ?Za 2 T 2 , and therefore 



p 2 r () abc f dw w „, ,„ v 



70V- ' 2tt 



which is essentially positive. Also, since for the motional 



case u p = l— (Zip) 2 , T x which is *Zp -j— shows the additional 



factor 2(2,lp) 2 /up under the sign of integration, and is 

 essentially positive. 



§ 35. The formula (134) may be shown to be a solution by 

 a direct method. For that we set out from 



J (^W^A^t ~ .yACX) ° J K + /^# V /A(/,) ' 



which is a case of (136). Differentiate both sides with 

 regard to A or A', using the formula in /*, with 



c 



^) = AWor ^) ; ^ = 2A'(,):the„ 



f Pdfft) 477^ j* ?»»f7a? 47ra' /Voox 



3A -JW+^# = {A(^}I' 3A "J (- + /.»,)* -{A(«)}*' (lab) 



and therefore 



47r i <i&> 



