626 
PROFESSOR CAYLEY’S TENTH MEMOIR ON QU ANTICS. 
— 6dt — 6mr + «g Sum 
d\f 
4- 
486 
+ 
486 
d?& 
+ 
36 
+ 54 
- 27 
+ 
63 
c 3 fZ 4 e 
— 
1296 
-486 
+ 324 
— 
1458 
cd^f 
— 
324 
-324 
+ 216 
— 
432 
ede 5 
+ 1 
+ 
1 
c s d 2 e s 
+ 
144 
+ 324 
-216 
+ 
252 
c^deff 
+ 
6 
+ 36 
— 24 
+ 
18 
c 4 e 5 
- 6 
+ 4 
— 
2 
where the last column is, in fact, what V, becomes on writing therein a= 1, b= 0. 
The verification would not of course apply to terms which contain b ; thus (13.3) a 
derived syzygy is jr=bt-\-mo ; and the foregoing values give, as they should do, 
jr—mo : we might for the verification of most of the terms in b use values a, b, c, d, 
e, f~ = 1, b, 0, d, e, —d: the only failure would be for terms containing be. 
Table No 97 (Covariants of A, in the of- or standard forms : W is not given). 
The several covariants are — 
A=( 
1 
0 
c + 10 
/+ 10 
a%+ 5 
a 2 e+ 1 
c 2 -15 
cf -2 
0.0 1.3 
2.6 
3.9 
4.12 
5.15 
B = <X 3 ( 
b +1 
e +1 
ad — 3 
be -1 
l x > yf 
l x > yf 
2.2 3.5 4.8 
c + l 
/+! 
a?b+ 3 
c 2 -15 
a 3 e+ 1 
cf -10 
a 3 d + 6 
a%c — 3 
c 3 +15 
a%f— 3 
„ ce + 3 
a°c/+ 3 
a 4 5 2 -1 
a s cd + 2 
a, 2 5c 3 +4 
» e f +1 
a¥ -1 
2.6 
3.9 
4.12 
5.15 
6.18 
7.21 
8.24 
ad + 1 
bf~ 1 
a 2 & 3 - 1 
ad.f + 1 
ce + 1 
acd + 3 
a°bcf+ 1 
a°5c 2 + 4 
,, c 2 e— 1 
„ ef + 1 
l x > yf 
4.8 
5.11 
6.14 
7.17 
