632 
MR. A. CAYLEY’S THIRD MEMOIR UPON QUANTICS. 
No. 31. 
+ 1 ag 
-6 6 / 
+ 15 ce 
-10 
No. 32. 
+ 1 «e 
+ 2 af 
+ 1 ag 
+ 2 bg 
+ 1 eg 
-4 M 
— 6 be 
—9 ce 
—6 cf 
-4 df 
+ 3 
+ 4 
+ 8 
+ 4 rfe 
+ 3 ^ 
No. 33. 
+ \ ac 
+ 4 
+ 6 ae 
+ 4 (?/ 
+ 1 ag 
+ 4 6^ 
+ 6 c^ 
+ 4 c?^ 
+ 1 eg 
-1 6= 
— 4 be 
+ 4 6c? 
— 10 c® 
+ l6 be 
— 20 cd 
+ 14 6/ 
+ 5 ce 
-20 d^ 
+ 16 cf 
— 20 de 
+ 4 df 
-10 e^ 
-4 ef 
No. 34. No. 35. 
+ 1 edd’^g’^ 
— 42 acd^f 
+ 60 bc^df^ 
— 6 eddefg 
+ 12 ace^ 
-30 6cV/ 
+ 4 a^df 
—20 ad^g 
+ 24 bed^g 
+ 4 a“e^g 
+ 24 ad^ef 
— 84 bed^ef 
- 3 a^ey^ 
— 8 ad~e^ 
+ 66 6cc?e® 
— 6 abedg"^ 
+ 4 b^dg^ 
+ 24 6c?y 
+ 18 abcefg 
— 12 b^efg 
— 24 6c?V 
— 12 abef^ 
+ 8 bY 
- 3 6"cy 
+ 12 c'^eg 
+ 12 abdfg 
-27 cy^ 
— 18 abde^g 
+ 30 b’^c^g 
— 8 c^d'^g 
+ 6 ab^f 
— 24 b-cef“ 
+ 66 (?def 
+ 4 ac^g“ 
— 12 b'^d'^eg 
— 8 c®e® 
— 24 a(?^g 
-24 b'^df^ 
-24 c^df 
— 18 ac“dfg 
+ 60 6W/ 
-39 e"c?V 
+ 30 acP'ef’^ 
-27 6V 
+ 36 cd'^e 
+ 54 acd^eg 
— 12 aedf" 
+ 6 befg 
— 42 bc^deg 
- 8 
+ 1 
aceg 
— 1 
acf 
— 1 
ad^g 
-j- 2 
adef 
— 1 
ae^ 
— 1 
b‘eg 
+ 1 
hT 
+ 2 
bedg 
-2 
beef 
-2 
bdf 
+ 2 
bde^ 
— 1 
&g 
+ 2 
c^df 
+ 1 
c^e^ 
-3 
cdPe 
+ 1 
d^ 
The sextinvariant may be thus represented by means of a determinant of the sixth 
order and of the quadrinvariant and quartinvariant. 
5xNo. 35 = 
a, 
2b, 
3c, 
4d, 
e 
b, 
2c, 
3d, 
4e, 
f 
c, 
2d, 
3e, 
4/, 
g 
a, 
4b, 
3c, 
2d, 
e 
b, 
4c, 
3d, 
2e, 
f 
c, 
4d, 
3c, 
2/, 
g 
I5ce- 
-lOd^) 
a, 
b, 
c, 
d 
b, 
c, 
d. 
e 
c, 
d, 
e. 
f 
d, 
e, 
1 
g 
