PROFESSOR CAYLEY’S TENTH MEMOIR ON QUANTICS. 
657 
and 
1 
+ re 15 ).t° 
+ ( 1 
+ a 2 
+ a 4 
+ a 5 
+ a‘ 
+ a 9 
)a 3 x 3 
+ ( 
+ a 2 
+ a 3 
+ a 4 
+ a b 
+ a 6 
+ a 7 
+ a s 
+ a 9 
+ a" 
)a-x 4 
+ ( 1 
+ a 
+ 2 a 3 
+ a 5 
+ a 6 
+ « s 
-a' 3 
) a 3 x 6 
+ ( +« 
•5 
+ a 
2*5 
+ a 
4-5 
— a 
10-5 
— a 
12-5 
— Cl 
H.5 ) a 2-5 a; 8 
+ ( 
+ a' 2 
-al 
-« 9 
— a'° 
-2a' 3 
-a' 4 
— a’ 5 ) a?x'° 
+ ( 
— a x 
- a 6 
— co 
-a 8 
-a 9 
-a 26 
— a 11 
- a 12 
— a' 3 
)a 3 x 12 
+ ( 
- a 6 
— a 8 
-a™ 
— a 11 
-a' 3 
— a 15 ) a?x u 
+ (-l 
- a 15 )aV 6 
divided by 
l—a 2 . 1 — a 4 . 1 — a 6 . 1 — a 10 . 1 — ax 6 . 1 — a~x 4 . 1 — a-x s 
where observe that in the middle term, although for symmetry a' 5 (= x /ci) has been 
introduced into the expression, the coefficient is really rational, viz., the term is 
(a? a 5 -\- a 7 — a 13 — a 15 — a 77 )x 8 . The second form or one equivalent to it is due to 
Sylvester : I do not know whether he divided out the common factors so as to 
obtain the first form. I assume that it would be possible from this second form to 
obtain a Pt.G.F., and thence to establish for the 26 covariants of the sextic a theory 
such as has been given for the 23 covariants of the quintic, but I have not entered 
upon this question. 
4 p 2 
