shall vanish, where o 
[A =] No. 13 = (a, b, c, d, e, y) 5 , the quintic itself. 
[B =] No. 14= ( 
ae 
af 
5/ 
bd-i 
be - 3 
ce — 4 
c 2 + 3 
cd + 2 
c? 2 + 3 
y) 2 - 
ac 
ac? 3 
ae 3 
af 
bf 3 
o/ 3 
df 
[(7 =] No. 15 = ( 
6 8 - 
be-3 
6c? + 3 
c 2 — 6 
be + 7 
cd - 8 
ce + 3 
c? 2 - 6 
de — 3 
e 2 - 
5«, yf 
11. The developed expression of the foregoing function is as follows: 
21 
23 
© 
2) 
© 
8 
© 
£ 
3 
3 
£ 
8 
a 3 e + 3 
a 3 / + 3 
a 2 // + 33 
a 2 c/+ 10 
a 2 c?/- 90 
a 2 ef — 114 
a 2 / 2 - 19 
abf 2 — 114 
ac/ 2 - 90 
adf 2 + 10 
aef 2 + 33 
a/ 3 + 3 
bf 3 + 3 
a 2 6c?-12 
a 2 6e + 21 
a 2 ce —102 
a 2 c?e — 390 
a 2 e 2 — 195 
abdf- 264 
a6e/" - 608 
acef- 264 
adef+ 360 
ae 2 /+ 155 
6c?/ 2 -102 
6c/ 2 + 21 
ce/ 3 - 12 
a 2 c 2 -16 
a 2 cd— 144 
a 2 cP -216 
a6 2 /+ 155 
abef + 360 
abe 2 — 990 
acdf+ 537 
ad 2 f+ 468 
ae 3 + 225 
6c/ 2 - 390 
6e 2 / +135 
cdf 2 - 144 
c? 2 / 2 - 16 
a6 2 c + 50 
ab 2 d+ 30 
a6 2 e +135 
a6ce + 100 
abde— 1500 
acf + 468 
ace 2 - 245 
ade 2 + 900 
b 2 / 2 - 195 
6c?e/+ 100 
c 2 / 2 — 216 
ce 2 / + 30 
def+ 50 
6 4 -25 
a6c 2 + 240 
abed+120 
a6c? 2 — 600 
ac 2 e + 900 
acde+ 1320 
acPe + 1740 
b 2 ef — 990 
beef — 1500 
6e 3 + 125 
cc?e/ +120 
c? 2 e/+ 240 
e 4 -25 
6 3 c -150 
ac 3 +480 
ac 2 d +1600 
acd 2 + 1800 
ad? +1080 
6 2 c?/- 245 
bedf + 1320 
bd 2 f+ 900 
c 2 e/ — 600 
ce 3 -150 
de 3 -150 
6 3 c? -150 
6 3 e + 125 
6 3 / + 225 
b 2 cf + 900 
b 2 e 2 -1700 
6ce 2 - 2700 
c 2 df +1800 
cc? 2 / + 1600 
c? 3 / + 480 
6 2 c 2 -300 
b 2 cd— 1000 
b 2 d 2 —1500 
b 2 de — 2700 
6c 2 /+ 1740 
bd 2 e+ 900 
c 2 e 2 -1500 
o 
o 
o 
t-H 
1 
TS 
d 2 e 2 - 300 
bc 2 e + 900 
bede — 2000 
c 3 / +1080 
bed 2 - 600 
bd 3 + 600 
c 2 c?e — 600 
c 3 e + 600 
c 2 d 2 - 400