PROEESSOR CAYLEY’S EIGHTH MEMOIR ON QUANT TCS. 
533 
Table No. 86. 
a 4 cef 3 
aWf 
+ 9 
a 3 bef 3 
_ 
9 
d 2 b 3 df 
+ 
120 
ab 4 cf 3 

576 
i>T 
+ 
192 
+ 21 
a fbcdf* 
— 
162 
<fb 3 e 2 / 2 
— 
21 
aVdef 
+ 
672 
¥cef 
— 
1440 
a'def' 1 
-78 
a 3 bce 2 f 2 
+ 
99 
a-b 2 <?f 
+ 
486 
ab 4 ef 
— 
359 
b 3 d 4 f- 
— 
192 
«V/ 
+ 48 
a 3 bd 2 ef 2 
+ 
309 
a 2 b 2 cdef 2 
— 
2160 
ab 3 c 2 ef' 2 
+ 
3456 
Vde 2 f 
— 
1080 
a 3 bde 3 f 
+ 
12 
a 2 b 2 ce 3 f 
+ 
1023 
ab 3 cd' 2 f 2 
— 
864 
b 5 e 4 
+ 
2025 
a 3 be 5 
— 
240 
a 2 b 2 d 3 J 2 
+ 
120 
ab 3 ede 2 f 
+ 
2094 
b 4 c 2 df 
+ 
2592 
a 3 c 3 / 3 
- 
81 
drb 2 d 2 e 2 f 
— 
1053 
ab 3 ce 4 
— 
3915 
b 4 c 2 e 2 f 
+ 
3546 
a 3 (?def 2 
+ 1026 
a 2 b 2 de 4 
+ 
1314 
ab 3 d 3 ef 
+ 
528 
b 4 cd 2 ef 
+ 
5280 
a 3 c~e 3 f 
— 
768 
a 2 bc 2 ef- 
— 
1863 
abW 
— 
45 
b 4 cde 3 
— 
13500 | 
a 3 cd 3 f 2 
- 
738 
a 2 bc 2 d 2 f 2 
+ 
2538 
ab 2 c 3 df 2 
— 
2592 
b 4 d 4 f 
— 
4800 
aWV/ 
— 
564 
a 2 bc 2 de 2 f 
+ 
2340 
ab 2 c 3 e 2 f 
— 
9747 
b 4 d 3 e 2 
+ 
7800 
a 3 cde 4 
+ 
1056 
a 2 bc 2 e 4 
+ 
672 
ab 2 c 2 d' 2 ef 
— 
8496 
b 3 c 4 f 2 
— 
648 i 
cdd'ef 
+ 
756 
a 2 bcd 3 ef 
a 2 bcd 2 e 3 
+ 
2820 
ab 2 c 2 de 3 
+ 
26610 
b 3 c 3 def 
— 
14040 
a 3 d 3 e 3 
— 
696 
— 
7812 
ab 2 cdf 
+ 
8544 
b 3 c 3 e 3 
+ 
3075 
a 2 bd 3 f 
— 
3024 
ab 2 cd 4 e 
— 
16650 
bWf 
+ 
9120 
a 2 bd 4 e 2 
+ 
4572 
alrd^e 
+ 
720 
b 3 c 2 d 2 e 2 
+ 16350 
a 2 c 4 df 
— 
324 
abtff 2 
+ 
972 
b 3 cd 4 e 
— 
19200 
aW/ 
+ 
3888 
abc'def 
abc 4 e 3 
+ 
24048 
b 3 d 6 
+ 
4800 
aWef 
— 
8748 
— 
4464 
b‘c r 'ef 
+ 
4860 
a?c 3 de 3 
— 
4800 
abc 3 d 3 f 
— 
15984 
b 2 c 4 d 2 f 
b 2 c 4 de 2 
— 
3240 
crfd'f 
+ 
4248 
abc 3 d 2 e 2 
— 
30108 
— 
8100 
d 2 c 2 d 3 e 2 
+ 14520 
obc 2 d 4 e 
+ 
35088 
b 2 c 3 d 3 e 
+ 
9000 
a 2 cd 3 e 
— 
11448 
abed 6 
— 
8640 
bcW 
- 
2400 
a?cP 
+ 
2592 
ac 6 ef 
— 
7776 
ac'd 2 f 
+ 
5184 
ac 3 de 2 
+ 
12960 
ac 4 d 3 e 
— 
14400 
ac 3 d 5 
+ 
3840 
+ 78 +3258 +41253 + 124716 +68640 
289. The equation in z is of the form 
D z d~ U ’ 
where D is the discriminant of the quintic and 91, 35, C, 23 denote rational and integral 
functions of the coefficients ( a , b, c , d, e, f). And the covariants <£,(#, y), <p. 2 (#, y ), 
<p 3 (#, y), y) having the values given to them above, the actual value of Q is obtained 
as a quadric function of the indeterminates ( t . u , v, w), viz. this is 
= [D,f - 6BDft> — D(D, - 10AB> 2 ] + D[ - Bw 2 + 2D jrn + 9(BD - 1 0 ADJw 2 ], 
where D,=25AB+16C, these quantities, and the quantity 
N( = D 2 - 10 ABD, + 9B 2 D) 
afterwards spoken of, being in the notation of the present Memoir as follows : 
A = 
J 
(= 
No. 
19 ), 
B = 
-K 
(=- 
No. 
25), 
C = 
9L+JK 
(= — 
9 No. 
29+No. 19. No. 25; 
D = 
D 
(= 
No. 
26), 
D,= 
9(16L - 
JK), 
N = 
1152(18L 2 — 
JKL- 
- K 3 ). 
