316 
A THIRD MEMOIR UPON QUANTICS. 
[144 
No. 37. 
a 2 h 2 
1 
bdVi 
_ 
40 
abgh 
+ 
14 
bdeg 
- 
50 
acjli 
- 
18 
bdf 2 
- 
360 
acg 2 
- 
24 
be 2 f 
+ 
240 
adeh 
+ 
10 
c 2 eg 
— 
360 
adfg 
+ 
60 
e 2 f 2 
- 
81 
ae?g 
- 
40 
cd 2 g 
+ 
240 
b 2 fh 
— 
24 
cdef 
+ 
990 
by 
— 
25 
ce 3 
- 
600 
Wg 
+ 
234 
d 3 f 
— 
600 
bceh 
+ 
60 
d-e~ 
+ 
375 
±2223 
The tables Nos. 38 to 45 relate to the octavic. No. 38 is the octavic itself; 
No. 39 the quadrinvariant; Nos. 40, 41 and 42 are the quadricovariants, the last of 
them being the Hessian; No. 43 is the cubinvariant; No. 44 the quartinvariant, and 
No. 45 the quin tin variant, which is also the catalecticant. 
No. 38. 
No. 39. No. 40. 
ai 
+ 
1 
ag 
+ 
1 
ah 
+ 
2 
ai 
+ 
1 
bi 
+ 
2 
ci 
+ 
1 
bh 
— 
8 
( 
bf 
— 
6 
bg 
— 
10 
bh 
- 
2 
ch 
— 
10 
dh 
- 
6 
w 
+ 
28 
ce 
+ 
15 
y 
+ 
18 
eg 
— 
8 
dg 
+ 
18 
eg 
+ 
15 
df 
— 
56 
d 2 
— 
10 
de 
— 
10 
df 
+ 
34 
e f 
— 
10 
r 
— 
10 
e- 2 
+ 
35 
e 2 
- 
25 
±64 
±16 
±20 
±35 
±20 
±16 
No. 41. 
ae + 1 
of + 4 
ag + 6 
ah + 4 
ai + 1 
bi + 4 
ci + 6 
4: 
ei + 1 
bd - 4 
be - 12 
bf - 8 
bg + 8 
bh + 12 
ch + 8 
dh — 8 
eh - 12 
fh- 4 
c 2 + 3 
cd + 8 
ce — 22 
d 2 + 24 
ef -48 
de + 36 
eg - 22 
df - 36 
e 2 + 45 
dg — 48 
ef + 36 
eg — 22 
f 2 + 24 
fg+ 8 
g 2 + 3 
±4 ±12 ±30 ±48 ±58 ±48 ±30 ±12 ±4 
No. 42. 
ac + 1 
b 2 -1 
ad+ 6 
be — 6 
ae + 15 
bd+ 6 
c 2 - 21 
af + 20 
be +50 
cd - 70 
ag + 15 
bf+ 90 
d 2 - 105 
ah + 6 
bg + 78 
cf + 126 
de — 210 
ai + 1 
bh+ 34 
eg + 154 
df- 14 
e 2 - 175 
bi + 6 
ch + 78 
dg + 126 
ef - 210 
ci + 15 
dh + 90 
f 2 - 105 
1 + + 
Ol to 
o o o 
ei +15 
fh+ 6 
g 2 -21 
f i + 6 
gh- 6 
gi + 1 
h 2 - 1 
±1 
±6 
±21 
±70 
±105 
±210 
±189 
±210 
±105 
±70 
±21 
±6 
±1