646 
MR. A. CAYLEY’S THIRD MEMOIR UPON QUANTICS. 
(a, f3)=HU 
S(6aPU+|3QU) = 
Q(6aPU+(3QU)= f +384T ^ 
+ 120T"S+7680 
+ lOT^ +3200TS^ 
+ 480W, 
+ 30T^S, 
+ IT" — 24T"S"+512S® 
+ f - 24T" + 4608S^ ^ 
+ 1920TS^ 
+ 480T"S, 
+ 30T® 4-1920TS^ 
+ 120’PS"+7680 S®, 
— 6PS + 768TS" 
+ IP +192 
+ 128TS^ 
+ 18PS+384 S%(a,(3) 
+ IP + 64TS^ 
+ 5PS^- 64 
- 8P + 4608TS^ ’’ 
+ 1920PS"+ 73728 S®, 
+ 360PS +38400TS", 
i+ 20P + 8960PS^ tcc,(^y 
+ 840PS"+ 7680TS^ | 
+ 36PS + 384PS"+24576 S^ j 
+ IP - 40PS"+ 2560TS® J 
R(6«PU+/3QU)=[(48S, 8T, -96S^ -24TS, -P- i3)"]^R^ 
F(6aPU+/3QU=( 192 S, 32T ,—384 S" 96T S 
+ ( 0 ,512 192TS" , 24PS 
+ (13448^ 352TS, 24P— 1152S^ -288TS' 
T(6aPU+(3QU) = 
•64S^5;a, (3)"0U 
/3)".U 
20PS +64S"Xa, ^)"U 
- 4P 
rp3 
P ij 
.HUil 
+ ( 48T, 
288TS 
24P+1536S^ 144TS" 
I«, ^)"(HU)t 
The tables for the ternary cubic become much more simple if we suppose that the 
cubic is expressed in Hesse’s canonical form ; we have then the following table : — 
No. 70. 
U=x^ + 3 /^ + + 6 Ivi/z . 
s = _/+p. 
!v 
