PROFESSOR CAYLEY’S TENTH MEMOIR ON QUANTICS. 
607 
Deg-order. 
1.5 
a 
Tab. Mem 
2.2 
b 
13 2 
,,.6 
G 
14 „ 
3.3 
d 
15 „ 
,,.5 
e 
16 „ 
,,9 
f 
17 „ 
4.0 
9 
18 „ 
,,.4 
h 
19 „ 
,,.6 
i 
20 „ 
5.1 
] 
21 „ 
,,.3 
l 
22 „ 
„-7 
l 
23 „ 
6.2 
m 
83 8 
,,.4 
n 
84 „ 
7.1 
o 
90 9 
,,.5 
P 
91 „ 
8.0 
<1 
25 „ 
jj-2 
r 
92 „ 
9.3 
s 
* 
11.1 
t 
94 9 
12.0 
u 
29 3 
13.1 
V 
95 9 
18.0 
w 
29a 5 
Starting from the foregoing expression of the N.G.F. of the quin tic, we can, 
instead of each term a 9 otf, introduce a covariant or product of covariants of the proper 
deg-order O.fx : the mode of doing this depends of course on the different admissible 
partitions of 6, p, and it is for some of the terms very indeterminate : for instance, 
a 5 x 11 is ai, bf, or ce. I found it possible to perform the whole process so as to satisfy 
a condition which will be presently referred to ; and I found 
* See end of Memoir. The S of Table 93 has the value — 96(D, M) + 16 BO — 7GK, but it is better 
to use the simple value — (D, M) ; and the S of the present Memoir has this value, say S = — (cZ, rn ). 
4 i 
MDCCCLXXVIil. 
