640 
PROFESSOR CAYLEY’S TENTH MEMOIR ON QUANTICS. 
While it is very remarkable that (by general reasoning, as already mentioned, and 
with a very small amount of calculation) Gordan should have been able in effect 
to show this, the great excess of the number of derivatives over that of the covariants 
seems a reason why the derivations ought not to be made a basis of the theory. 
It is to be remarked that we may consider derivatives pq\, p<fi, &c., where p, q 
instead of being simple covariants are powers or products of co variants; but that 
these may be made to depend upon the derivatives formed with the simple covariants. 
(As to this see my paper “ On the Derivatives of Three Binary Qualities,” Quart. Math. 
Journal, t. xv. (1877) pp. 157-168.) 
Table No. 99 (Index Table of Derivatives). 
2 
3 
0 2 4 6 
1 3 5 7 9 
b c 
cl e ab f 
act, 4 2 
ab 2 1 
ac 5 4 3 2 1 
2 clerivs. 7 derivs. 
4 
5 
0 2 4 6 8 10 12 
1 3 5 7 9 11 13 
</ 5 3 i ad ae a 2 b 
h be c 2 
j 1c ag be ab 3 ai a?d 
bd l ah . . bf aba 
cd ce 
ad 3 2 1 
ae 5 4 3 2 1 
af 5 4 3 2 1 
bb 2 
be 2 1 
cc 6 4 2 
1 
ah 4 3 2 1 
cm 5 4 3 2 1 
bd 2 1 
be 2 1 
bf 2 1 
cd 3 2 1 
ce 5 4 3 2 1 
of 6 5 4 3 2 1 
19 derivs. 
29 derivs. 
