488 DR G. PLARR ON THE DETERMINATION OF 



As 2a 2 a 3 = 0, the term in a 2 + b* + c 2 disappears, and as a^ + b^+cf^l, we 

 get 



X = 2aM 2 x c^~ - 1) + 2« 2 « 3Cl 2 x 5 2 (^ - 1) • 

 The first term may be written 



=2a 2 a 3 &v(— — gjj&^j 

 the second term 



By circular permutation of a, ft, c, a v &c, we move the letters one step 

 forward in the 2 of the first term (a into b, b into c, &c), and one step back- 

 ward in the 2 of the second term (a into c, b into a, &c), the terms become 

 respectively, 



and 



Thus we get : 



Thus far as to X. For the other term in Y=u 2 &j(f^(f>- 1 i+X we have 

 Applying /3y = a, y /3=- a , &c, we get 



/ r 2 i 2 \ 



fa* c 2 \ 



/Z/ 2 a 2 \ 



Treating by S ../, and applying Sa/= -« 2 , S^/= -b 2 , S 7 j= -c 2 , 



--^b.f. 2 a l +—a.J>.f l 



v tJL 



h 2 a 2 



-— c 2 a 2 \ + ~ b 2 c 2 a x 



