770] 
ON THE 34 CONCOMITANTS OF THE TEBNABY CUBIC. 
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Table of the 34 Covariants of the Canonical Cubic ax 3 + by 3 + cz 3 + Qlxyz and 
the linear form %x + yy + Çz. 
First Part, 10 Forms. Class = Order. 
Current No. 
1 $ = 400 = — abcl + P. 
2 T = 600 = a 2 b 2 c 2 — 20 abcl 3 — 81 6 . 
3 A = 011 = %x + rjy + Çz. 
4 © = 222 = a; 2 [- PÇ 2 - 2alyÇ]... 
+ V z [bc^' 2 + 2p7jÇ].... 
5 ©'= 422 = x 2 [l (abc + 2l s ) f 2 + a (abc — 4;P)t]£]... 
+ yz [Gbcl 2 g 2 — 21 (abc + 2Z 3 ) .. 
6 ©"= 622 = x 2 [— (abc + 2l 3 ) 2 f 2 + 12aZ 2 (abc + 2P) yÇ]... 
+ y z [3 6bcP% 2 + 2 (abc + 21 3 ) 2 rjÇ].... 
7 B = 333 = a? [a 2 (c v 3 - bÇ 3 )]... 
+ y 2 z [(abc + 8P) rfÇ +12bl 2 Ç 2 % 4- Gbcl^rj]... 
+ yz 2 [— (abc + 8P) rjÇ 2 — ebcl& — 12c? 2 ffy 2 ].... 
8 F = 533 = æ 3 [Sa 2 l 2 (af - bÇ 3 )}... 
+ y 2 z [— P (abc + 81 3 ) rf-P, + 4bl (— abc + l 3 ) £ 2 f — bc (abc — 10P) Iprj]... 
+ yz 2 [P (abc + 8P) rjÇ 2 + bc (abc — 10£ 3 ) Çf 2 — 4cl (— abc + P) i-if].... 
9 B" = 733 = a? [9a 2 Z 4 (c V 3 - &Ç 8 )]... 
+ y 2 z [l (abc + 8P) (2abc + P) rfÇ 
+ b (abc + 2P) (abc — 10i 3 ) £ 2 £ + 66cZ 2 (— abc + l 3 ) f 2 ^]... 
+ V z2 [ — l ( a ^ c + 8£ 3 ) (Zubc + P) 
— 6bcl 2 (— abc + P) 2 — c (abc + 2P) (abc —10£ 3 ) Çr) 2 ].... 
10 F" = 933 = x 3 [21a 2 P (c v 3 - bÇ 3 )]... 
+ y 2 z [— (abc + 8P) (abc — l 3 ) 2 rfÇ + 9bP (abc + 2£ 3 ) 2 £ 2 £ 
— 27bcP (abc + 2 P) i- 2 rf\... 
4- yz 2 [(abc + SP) (abc — l 3 ) 2 rjÇ 2 4- 27bcP (abc + 2P) ÇÇ 2 
— 9cl 2 (abc + 2P) 2 Çy 2 ]. ... 
Second Part, (4 + 4 =) 8 forms. Class = 0, and Order = 0. 
Class=0. 
11 TJ = 103 = ax 3 + by 3 + cz 3 + Glxyz. 
12 H = 303 = P (ax 3 + by 3 + cz 3 ) - (abc 4- 2Z 3 ) xyz. 
13 \j/ = 806 = (abc + SP) 2 (a 2 x e + b 2 y 6 + c 2 z 3 — 10 (bcy 3 z 3 + caz 3 x? + abafy 3 )}. 
14 il = 1209 = (abc + SI 3 ) 3 (by 3 - cz 3 . cz 3 — ax 3 . ax 3 — by 3 }. 
C. XI. 
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