484 DR G. PLARR ON THE DETERMINATION OF 



Owing to 



Sj<j>j + Sk<pk _ S i<pi + m 2 

 m m 



the term in M, in the first line will be 



a 2 fc 4 -<w, 2 6 2 (a 2 +u 2 )+u 6 



= u 4 (u 2 -6 2 )-a 2 6 2 (u 2 -& 2 ) 

 = (u 4 — aW)na^ . 



We need not transform the other terms of M l5 except by changing the factors z x , y u y u z u 



respectively into 



na x a 2 , na^ , n 2 a^a 2 a z ; 



thus 



1 = (u 4 — a 2 ft 2 )na 1 



\ m ) v \ m / w 



vw 

 Proceeding to transform w 4 M/, and considering its first term, we remark 



Also 



Sj^-HSk^k-Skcfi-HSjcp-ik , 



namely, 



Zl w* - y^ = SVjkY<p -ik$-H = ^ = b% , 

 we get for the term in question, 



1 1_ on J 



But 



m 



Hence the term becomes 



^[y-a 2 ^]. 

 The second term in w 4 M/ is 



The factor between [ 



= na^\b 2 na^ — u^.na^] 

 = na 2 [b\w 2 - 6 2 ) - u\u 2 - b 2 )] 

 = na*[b\{w 2 + u*) - V] - u 4 ] 

 = na£\b\a? + b*-v i )-u i ] 



% J 



= —na 9 2 \ u i + -^ 

 ' |_ or, 



The third and fourth terms in M/ are respectively 



— na 2 a 3 



\ on /' 



w\ on 



