374 
TABLES FOB THE BINABY SEXTIC. 
[774 
But these two invariants W and Z have been already calculated; viz. as already 
mentioned, W is Salmon’s invariant D, and Z his invariant E, given each of them 
in the second edition of his Higher Algebra (but not reproduced in the third 
edition): on account of the great length of these expressions, it has been thought 
that it was not expedient to give them here. 
For the reason appealing above, I have added the expressions for the remaining 
coefficients of C, E, G. 
A, X s B, x° C, x i D, x H E, x 2 F, x 6 G, a? H, x vl 
Qj 4* 1 
<*g + 1 
a e +1 
a c + 1 
a eg +1 
ace +1 
df + 1 
a?d + 1 
a°bf — 6 
a°bd — 4 
a°b 2 - 1 
df -3 
cP - 1 
a be — 5 
abc — 3 
ce + 15 
c 2 + 3 
e 2 +2 
a°b 2 e — 1 
cd +2 
a°b :i + 2 
d 2 - 10 
a°b 2 g - 1 
bed + 2 
a°b 2 d + 8 
bef + 3 
c 3 - 1 
be 2 — 6 
bde — 1 
c 2 e — 3 
cd 2 + 2 
I, x° 
J, 
x 4 
K, 
x' 3 
L, x 10 
M, 
X 2 
JS r , x* 
0, 
K 8 
a ceg + 1 
af 2 
+ 1 
a 2 dg 
+ 
l 
edef + 1 
a 2 cg 2 + 
1 
a 2 cfg - 1 
a 2 cdg 
0 
cf 2 -1 
a bef 
- 10 
e f 
- 
l 
de — 1 
dfg - 
6 
deg + 1 
eef - 
1 
d 2 g -1 
cdf 
+ 4 
a beg 
- 
3 
a bf — 1 
e 2 g + 
8 
df 2 + 3 
df + 
3 
def + 2 
ce 2 
+ 16 
bdf 
— 
2 
bee — 2 
f' 2 ~ 
3 
ef - 3 
de 2 — 
2 
e 3 - 1 
dre 
- 12 
be 2 
4" 
5 
bd 2 + 4 
a b 2 g 2 - 
1 
a bfg + 1 
a l) 2 dg 
0 
a°b 2 eg — 1 
a°b 2 df + 16 
of 
+ 
9 
c 2 d — 1 
befg + 
6 
beeq + 2 
b 2 ef + 
1 
b 2 / 2 + 1 
b 2 e 2 
+ 9 
ede 
- 
17 
a°b s e + 3 
bdeg — 
34 
bef 2 - 3 
bc 2 g 
0 
bedg + 2 
bef 
- 12 
d 3 
8 
b 2 cd— 6 
bdf 2 + 
48 
bdf - 4 
bedf — 
14 
beef — 2 
bede 
- 76 
a°b 3 g 
+ 
2 
be 3 + 3 
bef - 
18 
bdef — 12 
bee 2 + 
11 
bdf - 2 
bd 3 
+ 48 
b 2 ef 
— 
6 
c 2 eg + 
18 
be 3 + 15 
bd 2 e + 
1 
bde 2 + 2 
c s e 
+ 48 
b 2 de 
+ 
2 
ef 2 - 
45 
c 2 dg + 1 
cf + 
9 
c 3 g - 1 
c 2 d 2 
- 32 
bc 2 e 
+ 
6 
cd 2 g + 
4 
c 2 ef + 9 
c 2 de — 
14 
c 2 df + 2 
bed 2 
- 
4 
edef + 
78 
cdf + 4 
cd 3 + 
6 
c 2 e 2 + 1 
ce 3 — 
36 
ede 1 - 21 
a°b 3 eg 
0 
cd 2 e — 3 
df - 
48 
d 3 e + 8 
b 3 df + 
8 
d 4 + 1 
d 2 e 2 + 
28 
a°b 3 eg — 3 
b 3 e 2 - 
9 
a°b 2 ceg 
0 
b 2 cdg+ 6 
b 2 cf - 
6 
b 2 d 2 g + 
64 
b 2 cef + 9 
b 2 cde + 
16 
b 2 def — 
144 
b 2 df+ 32 
b 2 d 3 - 
8 
b 2 e 3 + 
81 
b 2 de 2 — 39 
bc 3 j — 
3 
bc 2 dg - 
96 
bc 3 g - 3 
bc 2 d 2 + 
2 
bc 2 ef + 
108 
bc 2 df— 66 
■ 
bedf+ 
96 
bc 2 e 2 + 18 
bede 2 - 
126 
bcd 2 e +76 
bd 3 e + 
16 
bd 4 - 32 
cf + 
36 
ef +27 
e 3 df - 
72 
c s de — 45 
c 3 e 2 — 
27 
c 2 d 3 ' + 20 
c 2 d 2 e + 
96 
cd 4 — 
32