693] 
A TENTH MEMOIR ON QUANTICS. 
395 
For the quintic the two forms are, N.G.F. = 
( 1 
- a 6 
+ a 12 ) x° 
+ (-1 
+ a 4 
+ 2a 6 
- a 12 ) ax? 
+ ( 
+ a- 
- a 8 
+ a 10 ) x 2 
+ (-1 
+ № 4 
+ a e 
+ a 8 
- a 10 
— a? 2 ) ax? 
+ (+ 1 
+ a 2 
— a 4 
- a 6 
- a 8 
+ a 12 ) a 2 x 4 
+ ( 
- a 2 
+ a 4 
- a 10 
) a?x° 
+ (+l 
-2a 6 
- a 8 
+ a 12 ) a¥ 
+ (-1 
+ a 6 
— a 12 ) a 2 x 7 
divided by 
and 
1 — a 4 .1 — a 6 .1 — a 8 . 1 — ax 5 .1 — act?. 1 — ax ; 
( 1 
+ a 18 ) x° 
( 
a 4 
+ a 6 
+ a 10 
+ a 12 
) ax 
( 
a 4 
+ a 6 
+ a 8 
+ a w 
+ a 14 
— a 18 ) a 2 x 2 
( 1 
+ a 2 
+ a 4 
+ a 8 
) a 3 x? 
( 1 
+ a 2 
+ a 4 
+ a 6 
+ a 10 
-a 14 
) a 4 x 4 
( 1 
+ a 4 
+ a 6 
-a 16 
) a 3 x? 
( 
a 2 
-a 12 
-a 14 
) a 2 x 6 
( 
a 4 
-a 8 
-a 12 
-a 14 
-a 16 
— a 18 ) ax 7 
( 
-a 10 
-a 12 
-a 14 
-a 16 
— a 18 ) a 2 x 8 
( 
— a 4 
-a 8 
-a 10 
-a 12 
— a 14 
) a 3 x 9 
( 
-a 6 
-a 8 
-a 12 
- a 14 
) a 4 x 10 
(-1 
— a 48 ) a 5 x u 
divided by 
1 — a*. 1 — a 8 .1 — a 12 .1 — ax?. 1 — a 2 oc 2 .1 — a 2 x 6 : 
this last being in fact equivalent to that used for the determination of the R.G.F.