394 
A TENTH MEMOIR ON QUANTICS. 
[693 
Table No. 100 {concluded). 
6.8 
ok 
hi 
6 . 10 
a 2 g 
abd 
b 2 c 
ch 
al 2 
4 
2 1 
+ 
al 1 
0 
3 
~ T 
- 1 
+ 1 
ch 1 
+ \ 
+ 1 
ci 1 
0 
1 
2 
+ V 
i 
— IT 
ci 2 
+ 1 
+ -£z 
d/1 
0 
1 
9 
+ 1 
i 
~ s 
d/2 
1 1 
TTF8 
i 
54 
e /2 
+ aV 
+ i 
1 9 
4 5 
4 
5 
efZ 
, 3 2 
+ 3TT 
, 6 4 
+ 3lT 
//4 
+ TA2 
53 
TTif 
. 89 
+ T5T 
8 
6 . 12 
abe 
al ci 
6 . 14 
a 2 b 2 a 2 h acd 
be 2 
ef 1 
2 
¥ 
_ 2. —A 
5 5 
//2 
4 ,1 ,5 
8 T + ¥¥ + ¥ 
2 
9 
which is complete to the sixth degree. I had calculated the derivatives up to the 
tenth degree, but the results were not in the segregate form. 
On the form of the Numerical Generating Functions: the N.G.F. of a Sextic. 
Art. Nos. 385, 386. 
385. It is to be remarked that the R.G.F. is derived not from the fraction in 
its least terms, which is algebraically the most simple form of the N.G.F., but from 
a form which contains common factors in the numerator and denominator: thus for 
the quadric, the cubic, and the quartic, writing down the two forms (identical in the 
case of the quadric) these are— 
Quadric 
N.G.F. = 
Cubic 
N.G.F. = 
Quartic 
N.G.F. = 
1 — ax 2 .1 — a 2 
1 — ax + a 2 x 2 
1 — a 6 x e 
1 — a 4 .1 — aa?. 1 — ax 
1 — a 4 . 1 — aa? . 1 — a 2 a f. 1 — a 3 x 3 ’ 
1 — ax 2 + a 2 « 4 
1 — a 6 x 12 
1 — a 2 .1 — a 3 .1 — ax*. 1 — ax 2 1 - a 2 . 1 — a 3 .1 — aa? . 1 — a V. 1 — a 3 a?