318
A THIRD MEMOIR UPON QUANTICS.
[144
is equal to
L + 2\K + 3\ 2 J + ISA 3 / - 259 2\ s .
Nos. 46 to 48 relate to the nonic. No. 46 is the nonic itself; Nos. 47 and 48
are the two quartinvariants, each of them in its best form, viz. No. 48 does not
contain a 2 , and No. 47 does not contain aci 2 , the leading term of No. 48. The
nonic is the lowest quantic with two quartinvariants.
No. 46.
a + 1
6 + 9
c + 36
<7 + 84
e + 126
/+ 126
9 + 84
A+ 36
i + 9
j + 1
No. 47.
No. 48.
ay
_
i
bf 2 h
abij
+
18
bfg 2
—
720
aci 2
<?fj
+
432
achj
-
72
c 2 gi
-
1728
adgj
+
168
c 2 h 2
adhi
edej
-
720
ae fj
—
108
cd/i
+
2160
aegi
—
576
edgh
+
4608
aeh 2
+
432
ceH
afH
+
540
cefh
—
2592
afgh
-
720
ceg 2
—
5760
ag z
+
320
*p9
+
4320
bVij
d*j
+
320
b 2 i 2
—
81
d 2 ei
—
720
begj
d 2 fh
—
5760
bchi
+
648
d?g 2
—
1536
bdfj
-
576
defg
+
14688
bdgi
+
792
de 2 h
+
4320
bdh 2
—
1728
df 2
—
8640
begh
+
2160
e 3 g
—
8640
be 2 j
4-
540
e 2 / 2
+
5184
befi
—
972
a 2 f
bf 2 h
+
70
abij
W
-
45
aci 2
+
2
d-fj
+
27
achj
-
2
c 2 gi
-
52
adgj
+
7
c 2 h 2
+
25
adhi
-
7
edej
—
45
ae fj
-
5
cdfi
+
23
aegi
—
22
edgh
+
22
aeh 2
+
27
ce 3 i
+
70
af 2 i
+
25
cefh
—
127
afgh
-
45
ceg 2
+
32
ag 3
+
20
c Pg
+
25
b 2 hj
+
2
d 3 j
+
20
b 2 i 2
—
2
d 2 ei
—
45
begj
—
7
d 2 fh
+
32
bchi
+
7
d?g 2
+
47
bdfj
-
22
defg
+
85
bdai
+
74
de 2 h
+
25
bdh 2
—
52
df 3
—
50
begh
+
23
e s g
—
50
be 2 j
+
25
e 2 f 2
+
30
befi
—
73
±41650
±698
Nos 49, [49a] and 50 relate to the dodecadic. No. 49 is the dodecadic itself;
[No. 49 A, inserted in this place, but originally printed in the Fifth Memoir on Quantics,
is the dodecadic quadricovariant], No. 50 is the cubinvariant. [The numerical coefficients
in this last table as originally printed in the Third Memoir were altogether erroneous,
and the table as here printed is in fact the table No. 50 bis, of the Fifth Memoir on
Qualities.]
No. 49.
Qj +1
6 + 12
c + 66
<7+220
e + 495
/+792
g + 924
/¿ + 792
¿+495 N'+220
k + 66
¿+12
m + 1 \ *$x, y) 1
