[144 
144] 
A THIRD MEMOIR UPON QUANTICS. 
327 
fe n if 
No. 66. 
The quintic contravariant is QU = 
)n of 
S C) 3 . 
ab 2 c 2 
J- 
1 
a 2 bc 2 
+ 
i 
a 2 b 2 c + 
1 
adbei 
3 
abefi 
- 
6 
a 2 cfi 
— 
3 
a 2 bfi -- 
3 
adcf 2 
6 
obi 3 
+ 
4 
a 2 i 3 
+ 
2 
a 2 / 3 + 
2 
a 2 fi 2 
— 
3 
acf 3 
+ 
4 
abegj 
- 
6 
ab 2 gj - 
3 
abcgh + 
3 
a/H 2 
— 
3 
abg 3 
+ 
4 
abchk— 
6 
abcjl 
+ 
6 
b 2 cgj 
— 
3 
ac 2 hk 
— 
3 
ab/gh + 
3 
abgij 
+ 
9 
by 
+ 
2 
acfgh + 
3 
abfjl + 
6 
abg 2 l 
- 
12 
bedik 
— 
3 
acfjl 
+ 
6 
abgki + 
6 
acf hi 
- 
24 
bcfgh 
+ 
3 
acgkl 
+ 
6 
abhil + 
6 
acfjk 
- 
12 
bcfjl 
+ 
6 
achil 
+ 
6 
abijk + 
3 
aegk 2 
- 
6 
bcgkl 
+ 
6 
acvfli 
+ 
3 
abl 3 — 
10 
achki + 
9 
bchil 
+ 
6 
act 3 
— 
10 
acl? + 
4 
ackl 2 
+ 
18 
beijk 
+ 
3 
a fgb? 
+ 
9 
af 2 hl — 
12 
a .pg.i 
- 
18 
bcl 3 
- 
10 
afgd 
- 
12 
a/ 2 jk - 
6 
afg 2 k 
+ 
24 
¥s?v 
+ 
9 
ag 2 ki 
— 
6 
afgk 2 - 
6 
afghi 
+ 
6 
¥P 
— 
12 
aghi 2 
— 
6 
afliki + 
9 
afgt 2 
+ 
12 
bg 2 ki 
- 
6 
agil 2 
+ 
18 
ajkl 2 + 
18 
afijl 
+ 
12 
bghi 2 
— 
6 
ai 2 jl 
— 
12 
aikH — 
12 
agkil 
- 
30 
bgil 2 
+ 
18 
beg 3 
+ 
4 
b 2 j 3 + 
2 
aliiH 
+ 
6 
bi 2 jl 
- 
12 
iyf 
- 
3 
bell 3 + 
4 
ai 2 jk 
+ 
3 
c 2 k? 
+ 
2 
c 2 h 3 
2 
w - 
6 
ail 3 
— 
6 
cf 2 hl 
— 
12 
¥ h r 
— 
6 
bghH - 
12 
bchj 2 
— 
6 
cf 2 jk 
- 
6 
cgh 2 l 
- 
12 
bghjk + 
9 
bgdig 
+ 
3 
cfglc 2 
- 
6 
cghjk 
+ 
9 
bh 2 ij — 
6 
bgfl 
+ 
6 
cfhki + 
9 
chHj 
— 
6 
bhjl 2 + 
18 
big 3 
— 
6 
cfkl 2 
+ 
18 
chjl 2 
+ 
18 
bj 2 kl — 
12 
f'Pi 
+ 
24 
cik 2 l 
- 
12 
cg 2 kl 
- 
12 
ch 2 k 2 - 
3 
cg/dk 
+ 
3 
f s gj 
- 
6 
im 
+ 
3 
f¥i + 
12 
cliH 
- 
6 
fyk 
+ 
12 
fgfi 
+ 
6 
fg/dk + 
3 
del 2 
+ 
6 
f 2 ghi 
H* 
3 
fii 3 
— 
6 
fh 3 i - 
6 
chjkl 
- 
30 
fy: 1 
+ 
6 
g 3 hk 
- 
6 
fhH 2 + 
6 
cg 2 kd 
+ 
12 
pp 
+ 
6 
g~h 2 i 
+ 
12 
f hjkl — 
30 
f:r 
+ 
12 
fqkil 
— 
30 
g 2 hl 2 
+ 
6 
fj 2 k 2 + 
12 
fgdi 2 
- 
27 
fhiH 
+ 
6 
g 2 gkl 
+ 
6 
ghkH + 
6 
fg,r k 
- 
12 
fi 2 jk 
+ 
3 
ghijl 
— 
30 
gjk 3 - 
6 
fghji 
+ 
36 
fil 3 
— 
6 
gijdc 
+ 
3 
hHkl + 
6 
Mi 1 
— 
12 
gk 2 i 2 
+ 
12 
gjl 3 
- 
6 
hig Id + 
3 
m 
- 
24 
hi 3 k 
— 
6 
hi 2 j 2 
+ 
12 
hid 3 - 
6 
g 2 hkl 
+ 
18 
i 2 kl 2 
+ 
6 
ijh 2 
+ 
6 
jW 2 + 
6 
fgld 
- 
6 
ghHl 
18 
ghijk 
- 
3 
gill 3 
- 
18 
gjk? 
— 
6 
ldi 2 g 
- 
6 
high 2 
- 
6 
ij 2 kl 
+ 
18 
jl 4 
+ 
12 
ab 2 cj — 3 
aid/ + 6 
abcfh + 3 
abckl + 6 
abfij + 9 
abfgl — 24 
abgki— 12 
abhi 2 — 6 
abil 2 +18 
acfk 2 — 6 
af 3 j — 6 
a/ 2 gk+ 24 
afdii + 3 
af 2 l 2 + 6 
afkil — 30 
aldi 2 +12 
b 2 gj 2 - 3 
bch 2 l -12 
bchgk + 9 
¥ghi + 6 
bfjH + 6 
b/hk — 18 
bgh 2 i +24 
bgld 2 + 12 
bgjkl + 12 
bhijl — 30 
bij 2 k + 3 
bjl 3 - 6 
cfh 2 k + 3 
chkH + 6 
cjk? — 6 
2 _ 1-7 
1 + 18 
k - 3 
-18 
2 - 6 
g 2 k? +12 
ghkH - 12 
gk 2 t 2 -24 
h 2 ki 2 - 6 
hkil 2 — 6 
ijk 2 l 
kl* 
abc 2 k — 3 
abcfg + 3 
aboil + 6 
abgi 2 — 6 
ac/H - 12 
acf ki+ 9 
a/ 2 gi+ 3 
afi 2 l + 6 
ai 3 k — 6 
bc 2 h 2 + 6 
befj 2 — 6 
boghl - 24 
bcgjk + 9 
belli] — 12 
bcjl 2 + 18 
¥g : j + 3 
bfk — 6 
bg'ld +24 
bg 2 l 2 + 6 
bgijl — 30 
bi 2 j 2 + 12 
c 2 hk 2 - 3 
c/ 2 hj + 24 
cfghk + 6 
cfhH — 18 
of hi 2 + 12 
cfjkl — 30 
cgk 2 l + 6 
child +12 
cijk 2 + 3 
ckl 3 - 6 
f 2 gdi - 27 
Pdjl + 18 
fHj 2 - 6 
fg 2 kl + 18 
fghil +36 
fgiik - 3 
fgl 3 -18 
fhi 2 j - 12 
fijk - 6 
g-kH - 6 
ghki 2 - 12 
gkiP — 6 
h 2 i 3 +12 
hid 2 -24 
i 2 jkl +18 
il* +12 
cdbcf - 
3 
ab 2 cg — 
3 
abedi 
_ 
3 
a 2 bi 2 + 
6 
abefi + 
6 
abcgl 
4“ 
6 
adfH - 
3 
abeik + 
3 
abeij 
+ 
3 
abchi + 
6 
abfgi + 
9 
abgH 
- 
6 
abegk + 
3 
abi 2 l — 
12 
ac 2 ld 
+ 
6 
a ¥gj + 
9 
acf 2 k — 
6 
acf 2 .? 
- 
6 
abg 2 k — 
6 
a f 3 g - 
6 
acfgk 
- 
12 
abg hi — 
12 
af 2 il + 
6 
acf hi 
+ 
9 
abgl 2 + 
18 
afi 2 k + 
3 
acf l 2 
+ 
18 
abijl — 
24 
b 2 cj 2 + 
6 
acikl 
— 
24 
acfhk+ 
9 
byj - 
3 
a Pg 2 
+ 
12 
ackH - 
12 
bcfhj— 
12 
afgil 
- 
30 
af 2 gh + 
3 
beg hk + 
9 
a p 2 j 
+ 
3 
a Pjl + 
6 
bcldi — 
6 
agki 2 
+ 24 
afgki- 
30 
behl? + 
18 
alii? 
- 
6 
afhil + 
12 
bcgkl — 
24 
ai 2 l 2 
+ 
6 
af ijk + 
6 
bfgdi + 
3 
beghj 
+ 
9 
aft 3 - 
6 
¥gji + 
12 
bcj 2 l 
- 
12 
agldi + 
24 
¥bf - 
18 
bg 3 li 
- 
6 
ahi 2 k — 
18 
bg 2 kl + 
6 
bg-jl 
+ 
6 
aikl 2 + 
12 
bghil — 
30 
bgij 2 
+ 
3 
be!eg — 
6 
bgigk + 
6 
c 2 h 2 k 
- 
3 
¥:f 
6 
bgl 3 - 
6 
efgh 2 
+ 
3 
bg 2 h 2 + 
12 
bhi 2 j + 
24 
cfhgl 
— 
30 
bcfhjl — 
30 
big? 2 + 
12 
cfg 2 k 
+ 
24 
bgg 2 k + 
3 
cf‘ 2 le + 
12 
cglikl 
+ 
12 
bldg 2 + 
24 
cfhki- 
30 
cgjk 2 
— 
18 
bj 2 lr + 
6 
cfjk 2 + 
24 
cldtl 
+ 
6 
cfh 3 - 
6 
cgk? - 
6 
chigk 
+ 
6 
cldkl + 
6 
child + 
3 
chi 3 
— 
6 
cligk 2 + 
3 
cldl 2 + 
6 
cjkl 2 
+ 
12 
/v - 
6 
Pr + 
12 
fV 
- 
6 
fgldl + 
18 
pgjk - 
12 
ffhl 
+ 
18 
fghjk - 
3 
pghl + 
18 
ftfjk 
- 
12 
im - 
12 
pkij - 
12 
fg¥) 
- 
3 
№ - 
6 
pp - 
24 
fgp 
— 
6 
m + 
18 
fg 2 k 2 - 
6 
fifi 
+ 
18 
gddd - 
6 
fghik - 
3 
<fld 
+ 
12 
gldki — 
12 
fgk? 2 - 
6 
g 2 hki 
— 
12 
ghki 2 — 
6 
fhH 2 - 
6 
fkl 2 
- 
24 
gjldl + 
18 
fhil 2 - 
6 
gliH 2 
— 
6 
hH 2 + 
12 
fijkl + 
36 
ghil 2 
— 
6 
hHl 2 - 
24 
ft 4 + 
12 
gijkl 
+ 
36 
hi 3 + 
12 
gildl + 
18 
gi 4 
+ 
12 
/tij/cl 4- 
36 
hi 2 kl + 
18 
hi 2 jl 
+ 
18 
ifld — 
27 
i?jk? - 
27 
i 2 j 2 k 
- 
27 
jkl 3 - 
18 
ikl 3 - 
18 
jkl 3 
18 
abefj + 6 
abegk+ 6 
abchi + 6 
abcl 2 — 30 
abfg 2 - 12 
abgil +36 
abi 2 j - 12 
acf 2 h — 12 
acfkl + 36 
acik 2 — 12 
afdgl + 12 
a/Hj + 6 
afgki — 30 
a/hi 2 + 6 
afil 2 — 18 
ai 2 kl +12 
begh 2 - 12 
bclijl +36 
bcj 2 k — 12 
bfgj 2 + 6 
bcfhl + 12 
bg 2 jk + 6 
bghij — 30 
bgjP -18 
bijd +12 
cfhH + 12 
<fhjk - 30 
cghk 2 + 6 
chHk + 6 
chid 2 - 18 
cjkH + 12 
f 2 ghj + 18 
f 2 fl -24 
fg 2 hk + 18 
fghH + 18 
fhijl — 12 
fi/k +18 
fjl 3 + 48 
g 2 k 2 l -24 
ghkil — 12 
gij/d +18 
gkP +48 
im -24 
hil 3 + 48 
hi 2 jk + 18 
igkl? — 54 
1 5 -24 
± 145 
±145 
±145 
±282 
±282 
±282 
±282 
±282 
:282 
±488