482 



DR G. PLARR ON THE DETERMINATION OF 



then 



and remembering r*u* = t, we have 



Thus 

 and also 



s = - r r 4 cos 2 2(J, 



Sr« = £^ (cos2(E)2 



2onr A' 4a 4 6 6 



(III") 

 (IV) 



The term independent of t and u 2 in (V") will be, 



~4>a?b*M v 3a 2 b 2 "1 x [a 4 6 4 ] 

 _-8a 2 2& 4 .6 2 .a 2 & 2 _ 

 + [ - 2b* x 1 x a 4 6 4 ] [9a 4 & 4 - 8a 2 6 2 . a^ 2 ] 

 12a 4 &%-16a 4 & 8 1a 4 & 4 xl 

 _-2a 4 6 8 J 



= a 8 6 10 [12(a 2 + 26 2 ) - 166 2 - 26 2 ] 

 = a 8 6 10 [12a 2 +66 2 ]. 



This shows that the equation (V") does not admit the factor t. 

 We have promised to establish the identity between 



M_i M\ W\ 



(Xj Q>2 ^3 



where a x , a 2 , a s are the scalar coefficients of 



a = ia 1 +ja 2 + ka 3> 



and where M_ u M/, M/', are the expressions which we have quoted at the beginning 

 We take R l5 R 2 under the form 



m \ wu/ 



\ nv) 



m 



Having 



Sj<f>jSk<j>Jc-S 2 j<j>k = 

 as was shown before, we shall have 



■u z 



m 



+ 



Wi-^Vi-^). 



\ uv/\ wu/ 



