MR. A. CAYLEY’S THIRD MEMOIR UPON QUANTICS. 
f)35 
is equal to 
L+2XK+3X"J+18>."I — 2592?v^ 
Nos. 46 to 48 relate to the nonic. No. 46 is the nonic itself ; Nos. 47 and 48 are the 
two quart! n variants, each of them in its best form, viz. No. 48 does not contain r/, 
and No. 47 does not contain aci^, the leading’ term of No. 48. The nonic is the 
lowest quantic with two quartinvariants. 
No. 46. 
+ 1 a\ +9 b +36 c 
+ 84 d 
+ 126 e +126 / +84 g +36 h 
+ 9 
+ 1 j 
yf 
No. 47. 
No. 48. 
— 
1 
+ 
18 
abij 
acr 
— 
72 
achj 
+ 
168 
adgj 
adlii 
— 
108 
aefj 
— 
576 
aegi 
+ 
432 
aeh? 
+ 
540 
afi 
— 
720 
afgh 
+ 
320 
af 
¥hj 
— 
81 
bcgj 
+ 
648 
bchi 
— 
576 
bdfj 
+ 
792 
hdgi 
— 
1728 
bdld 
+ 2160 
begh 
+ 
540 
bdj 
— 
972 
befi 
0^ 
bfk 
— 
720 
bff 
+ 
432 
d\f.i 
— 
1728 
dgi 
— 
720 
cdej 
+ 
2160 
cdfi 
+ 
4608 
cdgh 
ceH 
— 
2592 
cefh 
— 
5760 
ceg^ 
+ 
4320 
afa 
+ 
320 
d-y 
— 
720 
d“ei 
— 
5760 
djh 
— 
1536 
d'Y 
+ 
14688 
dafg 
+ 
4320 
de~h 
8640 
dp 
— 
8640 
e^g 
+ 
5184 
ep 
af 
abij 
+ 
2 
acP 
— 
2 
achj 
+ 
7 
adgj 
— 
7 
adhi 
— 
5 
aefj 
— 
22 
aegi 
+ 
27 
aeh^ 
+ 
25 
afi 
— 
45 
afgh 
+ 
20 
af 
+ 
2 
b%j 
— 
2 
b^i? 
— 
7 
bcgj 
+ 
7 
bchi 
— 
22 
bdfj 
+ 
74 
bdgi 
— 
52 
bdJd 
+ 
23 
begh 
+ 
25 
bdj 
— 
73 
befi 
+ 
70 
bf-h 
— 
45 
bff 
+ 
27 
dfj 
— 
52 
crgi 
+ 
25 
— 
45 
cdej 
+ 
23 
cdfi 
+ 
22 
cdgh 
+ 
70 
ceH 
127 
cefh 
+ 
32 
cef 
+ 
25 
afa 
+ 
20 
dj 
— 
45 
d^ei 
+ 
32 
d-fh 
— 
47 
drf 
+ 
85 
defg 
+ 
25 
de^h 
— 
50 
df 
— 
50 
e^g 
+ 
30 
ef 
Nos. 49 and 50 relate to the dodecadic. No. 49 is the dodecadic itself; No. 50 is 
the cubinvariant. 
No. 49. 
a 
12 b 
66 c 
220 d 
495 e 
792/ 
924 g 
792 h 
495 
220 j 
66 k 
12 1 
m 
lix,y) 
12 
No. 50. 
+ 3 agm 
— 12 ahl 
+ 30 aik 
— 20 af 
— 24 hfm 
+ 90 bgl 
— 108 hhk 
+ 60 bij 
+ 60 cem 
— 2l6 cfl 
+ 72 cgk 
+ 300 chj 
— 270 ci^ 
— 40 d'm 
+ 120 del 
+ 600 dfk 
— 1290 dgj 
+ 540 dhi 
— 540 e^k 
+ 1080 efj 
+ 1485 egi 
— 1080 eh^ 
-2160 f 'H 
+ 2160 fgh 
— 840 / 
4 P 
MDCCCLVI. 
