506 
A MEMOIR ON THE SINGLE AND DOUBLE THETA-FUNCTIONS. [704 
that is, 
c 2 
c 2 
c 2 
c 2 
c 2 
c 2 
9 
2 
+ 4 
15 
- 3 
8 
2 
12 
- 15 
1 
- 8 
6 
12 
9 
- 1 
4 
+ 6 
3 
1 
6 
- 4 
3 
+ 15 
8 
6 
12 
+ 3 
9 
- 8 
2 
12 
1 
- 9 
4 
- 2 
15 
- 0 
12 
+ 4 
8 
+ 3 
15 
- 0 
1 
+ 3 
2 
+ 8 
9 
- 0 
6 
- 9 
15 
+ 2 
4 
- 0 
9 
- 15 
6 
+ 8 
1 
+ 0 
4 
- 8 
12 
- 6 
2 
- 0 
3 
- 12 
15 * 
- 1 
2 
- 0 
2 
+ 1 
3 
+ 4 
6 
+ 0 
15 
+ 6 
9 
- 3 
12 
+ 0 
8 
- 12 
4 
- 9 
1 
each of the lirst set of 15 giving a homogeneous linear relation between four terms 
c 4 ; and each of the second set giving a homogeneous linear relation between three 
terms c 2 . c 2 , formed with the 10 constants c. Thus the first equation is 
c a2 4 + c a 4 + c (j 4 - c 0 4 = 0 ; 
and so for the other lines of the two diagrams. 
79. I form in the two notations the following tables:— 
Table of the 16 Kummer hex ads. 
A 
A 
A 
A 
A 
B 
B 
B 
B 
C 
C 
C 
D 
D 
E 
A 
B 
C 
D 
E 
F 
C 
D 
E 
F 
D 
E 
F 
E 
F 
F 
B 
AB 
AC 
AD 
AE 
AB 
BC 
BD 
BE 
AB 
CD 
CE 
AC 
DE 
AD 
AE 
C 
CD 
BD 
BC 
BC 
AC 
AD 
AC 
AC 
BC 
AB 
AB 
BC 
AB 
BD 
BE 
D 
CE 
BE 
BE 
BD 
AD 
AE 
AE 
AD 
BD 
AE 
AD 
CD 
AC 
CD 
CE 
E 
DE 
DE 
CE 
CD 
AE 
DE 
CE 
CD 
BE 
BE 
BD 
CE 
BC 
DE 
DE 
F 
11 
11 
11 
11 
11 
7 
7 
7 
7 
5 
5 
5 
13 
13 
14 
11 
7 
5 
13 
14 
10 
5 
13 
14 
10 
13 
14 
10 
14 
10 
10 
7 i 
6 
4 
14 
12 
6 
8 
0 
3 
6 
2 
1 
4 
9 
12 
15 
5 1 
2 
0 
8 
8 
4 
12 
4 
4 
8 
6 
6 
8 
6 
0 
3 
13 
1 
3 
3 
3 
12 
15 
15 
12 
0 
15 
12 
2 
4 
2 
1 
14 ' 
9 
9 
1 
2 
15 
9 
1 
2 
3 
3 
0 
1 
8 
9 
9 
10