Full text: The collected mathematical papers of Arthur Cayley, Sc.D., F.R.S., sadlerian professor of pure mathematics in the University of Cambridge (Vol. 2)

462 
ON THE SYMMETRIC FUNCTIONS OF THE ROOTS 
[149 
3af = S X x y x X 2 y 2 Z 3 X a , 
3hg=Sy l z 1 y a z0tf„ 
3ch = S z x x x z^c 2 y 3 z z , 
3bf = 8 y£y£y 3 z 3 , 
3cg = 8 z£z£z 3 x 3 , 
3ah == 8 x£x£x 3 y 3 y 
3cf = 8 y x z x y 2 z 2 z£, 
3ag = 8 z x x x z^c 2 x £, 
3bh = 8 x x y x x 2 y 2 y£, 
3ai = 8 x x y x z^c 2 z 3 x 3 , 
3bj = 8 y x z x x 2 y 2 x 3 y 3 , 
3ck = S z x x x y 2 z 2 y 3 z 3 , 
3bi = 8 y£y 2 z 2 y 3 z 3 , 
3cj = 8z£z 2 x 2 z 3 x 3 , 
3ak = 8 x x “x 2 y 2 x 3 y 3 , 
3ci = 8y x z x z£z£, 
3aj = 8 z x x x x 2 x£, 
3bk = 8 x x y x y£y£, 
6al —- 8 x x j x 2 y 2 z 3 x 3 j 
6bl = S y£y 2 z 2 x 3 y 3 , 
6 cl = 8 z£z^ic 2 y 3 z z , 
9f 2 - 6bi =8 y£y£z£, 
9 g 2 — 6cj = S z£z£x£, 
9h 2 — 6ak = 8 x x x 2 y 3 , 
9i 2 - 6cf = 8 y£z£z£, 
9j 2 — 6ag = 8 z£x£x£, 
9k 2 — 6bh = 8 x x 2 y£y£, 
9fg - 3ck = S x x y x y 2 z 2 z£, 
9gh — 3ai = S y x z x z 2 x 2 x£, 
9hf - 3bj = 8 z x x x x 2 y 2 y£,
	        
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