MR. A. CAYLEY'S SEVENTH MEMOIE ON QUANTICS. 
280 
BONUOLD. 
Caa'ley. 
f 
u 
A/' 
-GHU 
s 
4S 
riA 
1 
K 
1 
-R 
S/ 
6PU 
T 
V 
-2QU 
J 
648=* -pT 
P/ 
-2YU 
2ZU 
CU 
DU 
0 
H 
F 
-FU 
• 4 . 2(0^^U-TU^+4SU . HU), 
Avhere the notations YU, ZU (to correspond to M. Aronhold’s Py, Qy) and the notations 
CU, DU are first employed in the present memoir, I remark in regard to Py( = ~2YU), 
Avhere. as already mentioned, 
YU=r(l + 8P)^{Z(f+,^+^^)-3g;jO. 
that in my Memoir on Curves of the Third Order*, I Avas led incidentally to the curve 
and that I there gave the equation 
3T.PU-4S.QU=(l + 8/7{/(r+^^+^^)-3|^D- 
But the cui’A^e 
Avhich corresponds to (Qy=2ZU), does not occur in that memoir. 
236. I remark, further, in regard to M. Aronhold’s 0, H, that these are what he calls 
“ ZAA'ischenformen,” viz. they are co variants of the cubic and of the adjoint linear form 
or as they might be termed ContracovarianU. For the canonical form 
the value of ^0 is 
{yz—Vi^, zx—V'if, xy—Vz^, Ihyz — lx^^ l^zx — ly'^^ Vxy~~lz^\l,yi-,^f-> 
which is a form Avhich occurs incidentally in my memoir last referred to (see p. 427). 
The value of H in the same case is 
(-2/(1+2/>^-6/3/^, . , . , -(l + 4ZV+2/(l+2n3/2, . , .If, p;, 
AA'hich does not occur in that memoir. In my Third Memoir on Qualities I purposely 
abstained from the consideration of any such forms. 
237. My coA ariants 0U and 0^U involA ed unsymmetrically the cubic and its Hessian, 
* PLiilasoj)bical Transactions, t. cxlvii. (1857) see p. 427. 
