MR. A. CAYLEY’S THIRD MEMOIR UPON QUANTICS. 
G41 
wliich is equal to — 
— 1 ayk 
— 1 bhi 
— 1 cij 
— 1 bch 
-1 acf 
— 1 abg 
— 1 bcj 
— i ach 
— 1 abi 
— 1 abc 
4* 1 fif/" 
+ 1 hV- 
4“ 1 cl" 
+ 2 bgl 
+ 1 ai^ 
+ 2 afl 
+ 1 6/ 
-1 afg 
+ 1 af 
+ 1 afi 
+ 1 gK- 
+ 1/=^ 
— 1 bij 
4~ 2 chi 
— 1 aik 
— 1 cfh 
4“ ^ (lil 
— 1 bgfi 
+ 1 % 
— 2 Jijl 
-2 fkl 
—2 fkl 
+ 1 cB 
— 1 cjk 
+ 1 bf 
+ 2 ckl 
+ 1 ch? 
+ 2 bjl 
+ 1 chk 
+ 1 j-k 
+ 1 ik" 
+ 1 
+ 1 fj 
+ !/<?/ 
+ ^fv 
+^ff 
-3fgk 
i 
A 
+ 1 g'^k 
+ 1 glik 
— 2 gik 
+ 1 yjk 
+ lg/P 
4“ 1 fhi 
— 2 ghi 
+ 1 hH 
+ 1 hP 
— 2 hij 
+ 1 hki 
+ 2 gkl 
+\fp 
-1 gP 
-1 hP 
- 1 iP 
-IjP 
-1 kP 
4“ ^ hil 
— 3 ijk 
-2 P 
The quartinvai'iant is S = 
No. 62. 
— 1 
abcl 
+ !>/ 
+ 1 
abgi 
+ 3 fghl 
+ 1 
acfk 
-1 
— 1 
+ 1 
ofy 
afil 
— 1 fhij 
-^fjP 
— 1 
aPk 
+ 1 g"k~ 
+ 1 
— 1 
bchj 
bg-h 
— 1 ghki 
-2 gkP 
+ 1 
+ 1 
— 1 
bif 
— 2 hiP 
— 1 
cf-h 
+ 3 ijkl 
+ 1 
chkl 
+ 1 P 
— 1 
cjlc 
No. 63. 
The sextin variant is T= 
+ 1 cPb’^c" 
—24 acf'-'hl 
-12 bcfhf 
< 
— 12 cfhH 
— 12 fgjkP 
— 6 d^bcfi 
— 12 acf-jk 
— 24 bcglPl 
+ 12 cfhPP 
-\2fhYi 
+ 4 (pbp 
-12 acfglP 
+ 18 bcghjk 
— 60 cfhjkl 
-12 fhijp 
+ 4 flV' 
+ 18 acf hki 
— 12 bcJPij 
+ 24 effk^ 
+ 36 fifkl 
— 3 df '^P 
+ 36 acfkP 
+ 36 bchjP 
+ 12 cghIPl 
+ 24 fjP 
— 6 ab'cgj 
— 24 acilPl 
— 24 be fkl 
— 1 2 cgjJP 
+ 8 fP 
+ 4 ab‘‘f 
-12 afgj 
+ 6 bfgY 
+ 12 cKHkl 
— 12 g~hJci 
— 6 abdhk 
+ 24 af 'Yk 
+ 12 bfgfl 
+ 6 chijIP 
-24 gVPP 
+ 6 abcfgh 
+ 6 afghi 
-12 bfif 
-12 chkP 
-12 gIPkP 
+ 12 abcfjl 
+ 12 afgP 
— 12 bfhk 
+ 12 cj/PP 
— 12 ghkiP 
+ 12 abcgkl 
+ 12 afHjl 
+ 24 bg-JPi 
+ 8 /!f 
+ 36 gijJPl 
+ 12 abchil 
— 60 afgkil 
+ 12 bg^hP 
-27 fYh^ 
+ 24 gkP 
+ t) abcijk 
+ 12 afhPl 
+ 12 bg^jkl 
-\2fgfk 
+ 8 
— 20 abcP 
+ 6 afrjk 
— 60 bghijl 
+ 36 fghjl 
-24 KH-P 
+ 18 abfgij 
-12 afiP 
+ 6 bgifk 
-\2fhif 
+ 24 hip 
-24 ahfgH 
+ 24 agJPP 
-12 bgjP 
-24 ffP 
+ 36 higkl 
— 12 abg~ki 
— 12 ahPk 
+ 24 bhPf 
+ 36 ffhkl 
—27 Pflc 
— 12 abghp 
+ 12 aPkP 
+ 12 bifP 
-\2fgiJP 
-36 ijkP 
+ 36 abgiP 
+ 4 b'^cf 
— 3 c~h~]r 
+ 36 fghHl 
— % P 
— 24 abpjl 
- 3 bYf 
+ 24 cYlPj 
— 6 fghijk 
+ 4 ac-k"^ 
K 
+ 4 bd^JP 
+ 6 cfgIPk 
— 36 fghP 
The discovery of the invariants S and T is due to Aronhold, the developed ex 
pressions were first obtained by Mr. Salmon. 
