396 
A TENTH MEMOIR ON QUANTICS. 
[693 
386. For the sextic the forms are, N.G.F. = 
( 1 
+ a 
- a 3 
— a 4 
- 
a 5 
+ a 7 
+ a 8 ) x° 
(-1 
— a 
+ a 2 
+ 2 a 3 
+ 2 a 4 
+ 
a 5 
— a 7 
— a 8 ) ax 2 
(-1 
+ or 
+ a 3 
+ a 4. 
+ 
a 5 
- a 7 
— a 8 ) ax 4 
( 1 
+ a 
- a 3 
- a 4 
- 
a 5 
- a 6 
+ a 8 ) a?x 6 
( 1 
+ a 
- a 3 
- 2a 4 
- 
2 a 5 
-a 6 
4- a 7 
+ a 8 ) a 2 ® 8 
(-1 
- a 
4- a 3 
+ a 4 
4- 
a 5 
-a 7 
i 
€ 
o 
divided by 
1+a.l — a 2 .1 — a 3 .l — a 4 .1 — a 5 .1 — ax 6 .1 — aoc 4 .1 — ax 2 ; 
and 
( 1 
4- a 15 ) x° 
+ ( 1 
+ a 2 
+ a 4 
+ a 5 
+ a 7 
4-a 9 
) ahc 2 
+ ( 
+ a 2 
+ a 3 
+ a 4 
+ a 5 
+ a 6 
4- a, 7 
+ a 8 
+ a 9 
4- a 11 
) a 2 « 4 
+( 1 
+ Qj 
+ 2a 3 
+ a 5 
+ a 6 
+ a 8 
— a 13 
) a 3 x s 
+ ( + a 
.5 
+ a 
2.5 
+ a 
4.5 
- a 
10.5 
— a 
12.5 
— a 
44 *5 ) a 2 - 5 (x* 
+ ( 
+ a 2 
- a 7 
-a 9 
-« 10 
-2a 1 ' 2 
-a 14 
— a 15 ) aV° 
+ ( 
- a 4 
-a 6 
— a 7 
- a 8 
-a 8 
-a 10 
-a 11 
- a 12 
— a 13 
) a 3 ,« 12 
+ ( 
- a 6 
a 
-a 8 
-a 10 
-a 11 
-a 13 
— a 13 ) a?x u 
+ (-l 
- a 15 ) a s x 16 
divided by 
1 — a 2 . 1 — a 4 . 1 — a 6 . 1 — a 10 .1 — ax 6 .1 — a 2 # 4 .1 — a?x?, 
where observe that in the middle term, although for symmetry a ,5 (= Va) has been 
introduced into the expression, the coefficient is really rational, viz. the term is 
(a 3 + a 5 + a 7 — a 13 — a 15 — a 17 ) 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 R.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.