44 
PROFESSOR CAYLEY’S NINTH MEMOIR ON QUANTICS. 
It may be noticed in regard to the numerical coefficients that we have as follows : — 
x coefficient. y coefficient. 
a b b° 
+ 
36 
a 5 b° 
+ 
24 ' 
+ 
36 
+ 
24 
a 4 b 2 
+ 
20 
a 4 b 2 
+ 
4 
b 1 
284 
b 
144 
b° 
1094 
b° 
436 
+ 
1398 
b 
584 
a 3 b 4 
2 
a 3 b 3 
+ 
24 
b 3 
184 
b 2 
776 
b 2 
1656 
b 
2696 
b 
3624 
b° 
1264 
b a 
4898 
1- 
4760 
+ 
10364 
a 2 b b 
+ 
14 
a 2 b 5 
+ 
6 
b 4 
666 
b 4 
300 
b 3 
6608 
b 3 
2236 
b 2 
10512 
b 2 
8616 
b 
22042 
b 
15442 
b° 
9162 
b° 
33044 
4- 
59644 
1 
a b 7 — 4 
+ 
a // 
+ 
78 
b 6 + 
28 
48 
b s 
852 
b 5 - 84 
2956 
b 4 
8310 
b 4 + 
140 
11806 
b 3 
30200 
O 
1 
CO 
23924 
b 2 
56740 
b 2 + 
84 
25026 
b 
39956 
b - 28 
25 524 
b° 
17986 
b° + 
4 
8818 
+ 154122 
G* 
+1 
56 + 
98102 
+ 
98358 
a°b 9 + 
18 + 
a° b 8 - 
2 
V- 140 
184 
V 
+ 
16 + 
270 
b 6 + 
476 
3622 
b 5 - 
56 
2026 
6 5 — 924 
19350 
b 5 
+ 112 
9248 
b 4 +11 20 
41278 
b 4 ~ 
140 
19760 
i 3 — 868 
51872 
b 3 
+ 112 
36330 
b 2 + 
420 
43900 
b 2 - 
56 
30340 
i 1 — 116 
20624 
b 
+ 
16 
23410 
b° + 
14 
3856 
b°- 
2 
5120 
+ 2048 +184686 +256 +126504 
— +186734 +126760 
+ 345894 | +345894 
viz. in the x coefficient, the coefficients of a 5 b° are ±36, that is the sum of the positive 
coefficients is =±36, and the sum of the negative coefficients is = — 36. But in ab 6 
the coefficients are ±28±4S, that is, the sum of the positive coefficients is =±76, and 
the sum of the negative coefficients is = — 48 ; and so in other cases. The total sum 
is ±345894, viz. the sum of the positive coefficients and that of the negative coefficients 
(taken as a positive number) are each =345894, and so in the y coefficient there is the 
same total sum ±345894; which is as it should be, since there are in a different order 
the same numerical coefficients. 
