330 
A THIRD MEMOIR UPON QUANTICS. 
[144 
P (olU+6PHU)= (1, 0, 128, №\a, pyPU 
+ (0, 1, 0,-4S\a, /9) 3 QU. 
Q(olU + 6/3HU) = (0, 60S, 30T, 0, - 120TS, - 24T 2 + 576S 3 %+ /3) 5 PU 
+ (1, 0, 0, 10T, 240S 2 , . 24TS\a, /3) 5 QU. 
S(aU + 6/3HU) = (S, T, 24S 2 , ITS, T 2 -18S 3 \a, /9)4 
T {aU+OpHU) ={T, 96S 2 , 60TST, 20T\ 240TS 2 , - ISPS + 4608S 4 , - 8T ! + 576TS 3 $a, /9)4 
R(olU+6/3HU) = [(1, 0, — 24S, — 8T, -48S 2 %+ /9) 4 ]4R. 
F (olU + Q/3HU) = (1,0, -24S, -8T, - 48>ST 2 5«, /9) 4 TV 
+ (0, 24, 0, 0, -48T%a, Sy{PUf 
+ (0, 0, 24, 0, 90S\z, S) 4 PU.QU 
+ (0, o, 0, 8, o^a, /3) 4 .(QU) 2 . 
We have, in like manner, for the covariants and contravariants of the cubic 
OaPU +/3QU, the following Table: 
No. 69. 
6aPU+/3QU = 6uPU+/3QU. 
H(6ocPU+/3QU) = (-2T, 48S 2 , 18TS, T 2 +16S 3 \z, /9) 3 PU 
+ (8S, T, - 8S 2 , - TS 5«, /9) 3 Q U. 
P (OaPU4- SQTJ) = (32S 2 , 12TS, T 2 + 32S 3 , 4TS 2 %a, /9) 3 U 
+ (4T, 90S 2 , 12TS, T 2 - 32S 3 \a, /9) 3 HU. 
Q(6aPU + /3QU) = 
'+384T S 2 , 
+ 120T 2 S + 7680 S 4 , 
+ 10T 3 + 3200TS 3 , 
< + 480T 2 $ 2 , 
+ 30T 3 S, 
<[«, /3) 5 u 
{ + IT 4 - 24T 2 S 3 + 512S 6 
+ 
{- 24T 2 +4608 S 3 , ^ 
+ 1920TS 2 , 
+ 480T 2 S, 
+ 30T 3 + 1920TS 3 , 
+ 12QT 2 S 2 + 7680 S 5 , 
6T 3 S + 768TS 4 
0 a, /9) 5 HU. 
J 
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