346 
ON THE 34 CONCOMITANTS OF THE TERNARY CUBIC. 
[770 
Current No. Order=0. 
15 P = 330 = — l (6c£ 3 + car] 3 + ab£ 3 ) + (— abc + 4Z 3 ) %y%. 
16 Q = 530 = (abc — 10£ 3 ) (bef 3 + carf + abt, 3 ) — QP {babe + 41 3 ) %y(. 
17 F = 460 = 5 2 c 2 f + cW + a 2 b 2 £ 6 - 2 (abc + 16£ 3 ) {ay 3 £ 3 + &£ 3 £ 3 + c£V) 
— 24£ 2 (5c£ 3 + carf + ab'Cf) &ft — 24Z {abc + 2l 3 ) % 2 y 2 ?. 
18 II = 1290 = {abc + SI 3 ) 3 [cy 3 - b?. a? - c?. b? - arf}. 
Third Part, (8 + 8 =) 16 forms. Class less or greater than Order. 
Class less than Order. 
19 J = 414 = {abc + 81 3 ) [gx {by 3 — cz 3 ) + yy {cz 3 — ax 3 ) + £z {ax 3 — by 3 )}. 
20 K = 514 = {abc + 81 3 ) [alx 3 — 2blxy 3 — 2clxz 3 + Sbcy 2 z 2 \..}. 
21 K' = 714 = {abc + 81 3 ) [{abc + 2Z 3 ) {aP — 2bxy 3 — 2cxz 3 ) — 18bcPy 2 z 2 ~\...}. 
22 E = 625 = {abc + 81 3 ) {£ 2 (by 3 — cz 3 ) [2l 2 aP + bcyz\... 
+ vZ(% 3 — C2 ?) [4aloP + 2Pyz\...}. 
23 E' = 825 = {abc + 8Z 3 ) {£ 2 (by 3 — cz 3 ) [7 {abc + 21 3 ) x 2 — 3bcPyz]... 
+ y%(by 3 — cz 3 ) [a {abc — 4Z 3 ) x 2 + l {abc + 21 3 ) yz]...}. 
24 E" = 1025 = (abc + 81 3 ) {| 2 (by 3 — cz 3 ) [{abc + 21 3 ) 2 x 2 + ISbcPyz]... 
+ ’?£’{by 3 — cz 3 ) [— 12al 2 {abc + 21 3 ) x 2 + (abc + 2l 3 ) 2 yz]...}. 
25 M = 917 = {abc + 81 3 ) 2 {£(by 3 — cz 3 ) [balx^ — blxy 3 — clxz 3 — 3beyfz 2 ].. 
26 M' =1117 = {abc + 81 3 ) 2 {f (by 3 — cz 3 ) [{abc + 21 3 ) {oax 3 — bxy 3 — cxz 3 ) 
+ 18 bcl 2 y 2 z 2 ]...}. 
Order less than Class. 
27 J = 841 = {abc + 81 3 ) 2 [x%a {erf — b?) + yyb {a? — cf 3 ) + z? (b? — arf)}. 
28 K = 541 = {abc + 81 3 ) [x[bc? — 2ca%rf — 2ab%? — Qaly 2 ?-]...}. 
29 K' = 741 = {abc + 81 3 ) [x [l 2 (be? — 2ca%rf — 2ab%?) + a {abc + 21 3 ) y 2 ?]...}. 
30 . E = 652 = {abc + 81 3 ) [x 2 {erf — b?) [2all; 2 + a 2 y?\... 
+ yz {erf — b?) [4il 2 ? + 2 aly?...}. 
31 E' = 852 = (abc + 81 3 ) [x 2 {cy 3 — b?) [a {abc — 41 3 ) ? — 6a 2 l 2 y£],.. 
+ yz {cy 3 — btf) [4il {abc + 2i 3 ) ? + a {abc — 4 l 3 )y£]...}. 
32 E" = 1052 = (abc + 81 3 ) [x 2 {cy 3 — b?) [— Sal 2 {abc + 21 3 ) ? + 9a 2 Py£]... 
+ yz {cy 3 — b?) [{abc + 21 3 ) 2 ? — Sal 2 {abc — 41 3 ) y£]...}. 
33 M = 771 = {abc + 81 3 ) {x {cy 3 — 6£ 3 ) [{abc — 81 3 ) £ 4 — a 2 c%y 3 — a 2 b%£ 3 
— \2aP% 2 y(, — Ga 2 ly 2 ip]...}. 
34 M' = 971 = {abc 4- 81 3 ) [x {erf - b?) [P {7abc + 81 3 ) ? - 3a 2 cl 2 %y 3 - 3a 2 bl 2 ^ 3 
+ 4<al {abc — l 3 ) % 2 y( + a 2 {abc — 101 3 ) y 2 £ 2 ]...}-