:MR. a. CAYLEY’S SEYEiYTH MEMOIE ON QUANTICS. 
285 
245. It will be convenient, before giving the Tables for the co variants of 
aU+6(3HU, 2aCU-2/3DU, 6aPU+|3QU, 2aYU-2,3ZU, 
which replace Tables 68 and 69 of my Third Memoir, to give the following separate 
Table of the quantics in (a, j3) which enter into the expressions of the invariants in 
Tables 68 and 69, and in these new Tables. 
Table No. 73. 
(1, 0, -24S, -8T, -48S^Ia, (3)^ 
(S, T, 24S% 4TS, P-48S^X«. |3)h 
(T, 96S^ 60TS, 20P, 240TS^ -48PS+4608Sh -SP+STbTS^^^a, (3)^ 
(48S, 8T, -96S^ -24TS, -T-ieS^Ja, (3)*, 
< 
P +192 S^ 
128 TS% 
18 PS +384 Sh 
P + 64TS^ 
5PS^- 64 SS 
< 
-8P + 4608 TS*, 
1920 PS^+ 73728 8*, 
360 PS +38400 TSh 
20 P + 8960 PS^ 
840PS^+ 7680 TS*, 
36 PS + 384 PS^+24576 Sq 
IP - 40PS*+ 2560 TS«, 
| 3 )«, 
where the first part of the Table contains the quantics in (a, (3) which relate to the 
forms aU+6/3IIU and 2aYU — 2|3ZU, and the second part of the Table contains the 
quantics in (a, (3) which relate to the forms 6aPU+|3QU and — 2o5CU+2/3DU. 
The quantics in (a, (3) contained in the foregoing Table are in the sequel indicated by 
means of their leading coefficients ; as thus, 
(1, 0, -24S, . .X«, (3)\ (S, T, . .X«, f3)\ (P+192S^ . /3)^ &c. 
246. It is easy to see what transformations must be performed on the results in 
Tables 68 and 69, in order to obtain the new Tables. Thus, in the formation of Table 
74, Table 68 gives «U + 6/3HU and H(aU+6/3HU), and from these C(aU + 6/3HU), 
D(aU + 6/3HU) have to be found: the same Table gives also P(aU + 6/3HU), 
Q(aU+6/3IIU), but the expressions of these quantities YU, ZU have to be intro- 
