144] 
A THIRD MEMOIR UPON QUANTICS. 
315 
No. 34. No. 35. 
aceg + 1 
a 2 d 2 g 2 + 1 
aedéf — 42 
bc 2 df 2 
+ 60 
acf 2 - 1 
a?defg — 6 
ace 4 +12 
bc 2 e 2 f 
-30 
ad?g — 1 
ahlf 3 + 4 
ad 4 g — 20 
bcd 3 g 
+ 24 
adef + 2 
a~e‘g + 4 
ad 3 ef +24 
bcd?ef 
- 84 
ae 3 — 1 
d?e 2 f 2 - 3 
ad 2 e 3 — 8 
bede 3 
+ 66 
b 2 eq -1 
abedg 2 — 6 
bhlg 2 + 4 
bdf 
+ 24 
bj 2 +i 
abcefg +18 
6V<7 -12 
bd 3 e 2 
-24 
bcdg + 2 
a6c/ 3 -12 
b 3 / 3 + 8 
c 4 eg 
+ 12 
beef — 2 
abd 2 fg +12 
b 2 c 2 g 2 - 3 
cf 2 
-27 
bdf - 2 
abde 2 g — 18 
b 2 ee 2 g +30 
c 3 d 2 g 
- 8 
bde 2 +2 
a6e/ + 6 
b 2 cef 2 - 24 
c 3 def 
+ 66 
c 3 g -1 
ac 3 (/ 2 + 4 
b 2 d?eg - 12 
c 3 e 3 
- 8 
c 2 df + 2 
ac?e?g — 24 
b 2 df 2 - 24 
c 2 +Z 
-24 
cV + 1 
ac 2 dfg — 18 
b 2 def + 60 
cW 
-39 
cd 2 e — 3 
ac 2 ef 2 +30 
6V - 27 
cd 4 e 
+ 36 
d 4 + 1 
acd?eg + 54 
aedf 2 — 12 
6c^ + 6 
bc 2 deg — 42 
d 6 
- 8 
±12 
±565 
The sextinvariant may be thus represented by means of a determinant of the 
sixth order and of the quadrinvariant 
and 
quartin variant. 
5 x No. 35 = 
a, 
26, 
3c, 
4 d, 
e 
b, 
2c, 
3d, 
4c, 
f 
c, 
2d, 
3c, 
4/ 
g 
a, 
46, 
3c, 
2d, 
e 
b, 
4c, 
U, 
2e, 
f 
c, 
4 d, 
3c, 
2/, 
g 
+ 4 (ag — 66/+ 15ce — 10c7 2 ) 
а, 
б, 
c, 
d, 
6, c, d 
c, d, e 
d, e, f 
f, g 
The tables Nos. 36 and 37 relate to a septimic. No. 36 is the septimic itself ; 
No. 37 the quartinvariant. 
No. 36. 
a + 1 
6 + 7 
c + 21 
e + 35 
/+21 
g + 7 
A + 1 
\ x > y) r 
( 
(7+35