4 ¿Hf h| HI 1 a, tz, ■ u
' w:.¡Hj
!
[144
A THIRD MEMOIR UPON QUANTICS
No. 62.
The quartinvariant i.s S =
abcl — 1
P? +1
abgi + 1
fghl + 3
acfk + 1
fgjk -1
«/V -1
fm -i
afil + 1
fp -2
ai 2 k — 1
g 2 k 2 +1
bchj + 1
ghki — 1
bg 2 h — 1
gkl 2 -2
bgjl + 1
li 2 i 2 +1
bij 2 — 1
hil 2 -2
cf 2 h - 1
ijkl + 3
chkl + 1
7 4 + 1
cjk 2 — 1
The sextinvariant is T =
No. 63
c, y, z f.
a 2 b 2 c 2
+
1
acf 2 hl
-24
bcfh?
- 12
cfh 3 i
- 12
fgjki 2
-12
d 2 bcfi
-
6
acf 2 jk
-12
bcgh 2 l
-24
cfh 2 l 2
+ 12
fh 2 i 2 j
-12
a 2 bi 3
+
4
acfgk 2
- 12
bcghjk
+ 18
cfhjkl
60
fhijl 2
- 12
a 2 cf 3
+
4
acfhki
+ 18
bchHj
-12
cfj 2 k 2
+ 24
fi?kl
+ 36
a 2 f 2 i 2
-
3
acfkl 2
+ 36
bchj l 2
+ 36
cghk 2 l
+ 12
fil 4
+ 24
ab 2 cgj
-
6
acikH
-24
bcj 2 kl
-24
cgjk 3
- 12
(fk 3
+ 8
aby
+
4
a P’W
-12
bffhj
+ 6
chHkl
+ 12
g 2 hk 2 i
- 12
abc 2 hk
-
6
af 2 g 2 k
+ 24
bfgj' 2 l
+ 12
chij Id
+ 6
g 2 k 2 l 2
- 24
abcfgh
+
6
afhghi
+ 6
bfif
- 12
chkP
- 12
gh 2 ki 2
- 12
abcfjl
+
12
af 2 gP
+ 12
bg 3 hk
-12
cj/dl 2
+ 12
ghkil 2
- 12
abcgkl
+
12
qf 2 ijl
+ 12
bg 2 h 2 i
+ 24
f S f
+ 8
gijkH
+ 36
abchil
+ 12
afgkil
-60
bg 2 ld 2
+ 12
fyh 2
-27
gkl 4
+ 24
abcijk
+
6
cfhi 2 l
+ 12
bg 2 jkl
+ 12
Pg?k
- 12
h 3 i 3
+ 8
abcl 3
—
20
afi 2 jk
+ 6
bghijl
- 60
Pghji
+ 36
h 2 i 2 l 2
- 24
ah Mi
+
18
afil 3
- 12
bgij 2 k
+ 6
Phi?
-12
hil 4
+ 24
abfg 2 l
-
24
agkH 2
+ 24
bgjl 3
-12
fW
-24
hidjkl
+ 36
abg 2 ki
-
12
ahi 3 k
- 12
bhi 2 j 2
+ 24
ffhkl
+ 36
i 2 j 2 k 2
-27
abghi 2
—
12
ai 2 kl 2
+ 12
bi?l 2
+ 12
fgW
-12
ijkl 3
- 36
abgiP
+
36
b 2 cj 3
+ 4
c 2 h 2 k 2
- 3
fghHl
+ 36
l 6
- 8
abi 2 jl
-
24
by?
- 3
cf 2 h 2 j
+ 24
fghijk
- 6
ac 2 k 3
+
4
bc 2 h 3
+ 4
cfgh 2 k
+ 6
fghP
-36
The discovery of the invariants S and
expressions were first obtained by Mr Salmon.
No. 64.
There is an octicovariant for which we may take
@77-
d x HU,
dyHU,
d z HU
d x HU,
R* U,
R dyU,
id x d z U
d y HU,
dy d x U,
s’ V U,
isd y d z U
d HU,
<y d z d x U,
h d y d z U,
R 2 u
