141]
A SECOND MEMOIR UPON QUANTICS.
273
[The Tables Nos. 13 to 24 which follow, and also Nos. 25 and 26 which are given
in 143 relate to the binary quintic. I have inserted in the headings the capital letters
A, B, ... L and also Q and Q' by which I refer to these covariants of the quintic. A is
the quintic itself, C is the Hessian, G is the quartinvariant, J a linear covariant: Q is
the simplest octinvariant, and Q' is the discriminant. As noticed in the original memoir
we have AI + BF-CE = 0; and Q' = G 2 -128Q, only the coefficient 128 was by mistake
given as 1152.]
A. No. 13.
a + 1
b + 5
c + 10
d + 10
e + 5
/+1
B.
No. 14.
yf
ae + 1
af+ 1
bf+ 1
Id-4
be - 3
ce — 4
c 2 + 3
cd + 2
æ + 3
yf
± 4
±3 ±4
C. No. 15.
ac + 1
b 2 - 1
ctd + 3
be - 3
ae + 3
bd+ 3
c 2 — 6
af + 1
be +7
cd — 8
bf + 3
ce + 3
d 2 - 6
cf + 3
de — 3
df + 1
e 2 - 1
± 1
i 3
± 6
± 8
± 6
± 3
± 1
D. No.
16.
5®. y f
(
a&/ ...
ace + 1
ad 2 - 1
6 2 e - 1
6cd + 2
c 3 - 1
acf + 1
ade — 1
b 2 f - 1
bee + 1
bd 2 + 1
c 2 d - 1
adf + 1
ae 2 - 1
bef- 1
ôde + 1
c 2 e + 1
cd 2 - 1
ay ...
6#+ 1
be 2 - 1
c 2 /-l
ede + 2
d 3 - 1
$*> d) 3
± 3
± 3
± 3
± 3
E.
No. 17.
a 2 / + 1
a&e — 5
acd + 2
6 2 d + 8
be 2 - 6
ay + 5
ace - 16
ad 2 + 6
b 2 e - 9
bed + 38
c 3 - 24
acf + 2
ade — 12
6 2 / + 8
bee — 38
6d 2 + 72
c 2 d - 32
adf — 2
ae 2 — 8
&c/ + 12
bde + 38
c 2 e -72
cd 2 + 32
aef — 5
6d/+ 16
be 2 + 9
c 2 /- 6
ede - 38
d 3 + 24
a/ 2 - 1
bef +h
cdf -2
ce 2 - 8
d 2 e + 6
± 11
± 49
± 82
± 82
rfc 49
± 11
\x, yf
F. No. 18.
a 2 d + 1
a 2 e +
2
af+ 1
abf +
7
acf + 5
adf — 5
aef -
7
a/ 2 - 1
bf 2 - 2
y 2 - 1
a6c — 3
abd +
1
abe + 11
ace —
8
ade — 40
ae 2 - 16
bdf +
8
bef — 11
cef - 1
def + 3
6 3 + 2
ac 2 -
12
acd— 34
ad 2 —
34
b 2 f + 16
bef + 40
be 2 -
29
cd/+ 34
dy + 12
e 3 - 2
b 2 c +
9
b 2 d + 16
b 2 e +
29
bee + 47
bde - 47
c 2 f +
34
ce 2 — 16
de 2 - 9
be 2 + 6
bed —
2
bd 2 - 44
c 2 e + 44
ede +
2
d 2 e - 6
c 3 +
8
c 2 d + 16
cd 2 - 16
d 3 -
8
a- 1 O
WIT 1
yf
i 3
C. II.
35
