944 
PROFESSOR A. CAYLEY OR THE SINGLE 
81. Table of the 60 Gopel tetrads. 
A 
B 
. AE 
. BE 
C 
D 
CE 
. DE 
E 
F 
AB 
. CD 
AC 
BD 
. AD 
BC 
A 
B 
.AD 
. BD 
C 
E 
. CD 
. DE 
D 
F 
AB 
. CE 
AC 
BE 
AE 
BC 
A 
B 
AC 
BC 
c 
F 
AB 
. DE 
D 
E 
CD 
CE 
AD 
BE 
AE 
BD 
A 
C 
AE 
CE 
B 
D 
BE 
DE 
E 
F 
AC 
BD 
AB 
CD 
.AD 
BC 
A 
C 
AD 
CD 
B 
E 
BD 
DE 
D 
F 
AC 
BE 
AB 
CE 
AE 
BC 
A 
C 
AB 
BC 
B 
F 
.AC 
DE 
D 
E 
BD 
BE 
AD 
CE 
AE 
CD 
A 
D 
AE 
DE 
B 
C 
BE 
CE 
E 
F 
AD 
BC 
AB 
CD 
AC 
BD 
A 
D 
.AC 
CD 
B 
E 
BC 
CE 
C 
F 
AD 
BE 
AB 
DE 
AE 
BD 
A 
D 
AB 
BD 
B 
F 
AD 
CE 
C 
E 
CD 
DE 
AC 
DE 
AE 
CD 
A 
E 
AD 
DE 
B 
C 
BD 
CD 
D 
F 
AE 
BC 
AB 
CE 
.AC 
BE 
A 
E 
AC 
CE 
B 
D 
BC 
CD 
C 
F 
AE 
. BD 
AB 
DE 
AD 
BE 
A. 
E 
AB 
BE 
B 
F 
AE 
CD 
c 
D 
BC 
. BD 
AC 
DE 
AD 
CE 
A. 
F 
BC 
DE 
B 
C 
AB 
AC 
D 
E 
AD 
AE 
BD 
CE 
BE 
CD 
A 
F 
BD 
CE 
B 
D 
AB 
AD 
C 
E 
AC 
AE 
BC 
DE 
BE 
CD 
A 
F 
BE 
CD 
B 
E 
AB 
AE 
c 
D 
AC 
AD 
BC 
DE 
BD 
CE 
11 
7 
15 
3 
5 
13 
1 
9 
14 
10 
6 
2 
4 
0 
12 
8 
11 
7 
12 
0 
5 
14 
2 
9 
13 
10 
6 
1 
4 
3 
15 
8 
11 
7 
4 
8 
5 
10 
6 
9 
13 
14 
2 
1 
12 
3 
15 
0 
11 
5 
15 
1 
7 
13 
3 
9 
14 
10 
4 
0 
6 
2 
12 
8 
11 
5 
12 
2 
7 
14 
0 
9 
13 
10 
4 
3 
6 
1 
15 
8 
11 
5 
6 
8 
7 
10 
4 
9 
13 
14 
0 
3 
12 
1 
15 
2 
11 
13 
15 
9 
7 
5 
3 
1 
14 
10 
12 
8 
6 
2 
4 
0 
11 
13 
4 
2 
7 
14 
8 
1 
5 
10 
12 
3 
6 
9 
15 
0 
11 
13 
6 
0 
7 
10 
12 
1 
5 
14 
2 
9 
4 
9 
15 
2 
11 
14 
12 
9 
7 
5 
0 
2 
13 
10 
15 
8 
6 
1 
4 
3 
11 
14 
4 
1 
7 
13 
8 
2 
5 
10 
15 
0 
6 
9 
12 
3 
11 
14 
6 
3 
7 
10 
15 
2 
5 
13 
8 
0 
4 
9 
12 
1 
11 
10 
8 
9 
7 
5 
6 
4 
13 
14 
12 
15 
0 
1 
3 
2 
11 
10 
0 
1 
7 
13 
6 
12 
5 
14 
4 
15 
8 
9 
3 
2 
11 
10 
3 
2 
7 
14 
6 
15 
5 
13 
4 
12 
8 
9 
0 
1 
The product-theorem, and its results. 
82. The product-theorem was 
- L '' / 0 + 0 x ' 7 — 7 , o — o v ' 
7 + 7 
where only one argument is exhibited, viz. : u-\-u’, u—u', 2u, 2 it' are written in place 
of ( u-\-u !', v-\-v'), (u — u', v—v'), (2 u, 2v), (2 u! } 2v') respectively. The expression on 
the right hand side is always a sum of four terms, corresponding to the values (0, 0), 
(1, 0), (0, 1), and (l, 1) of (p, q). For the development of the results it was found 
convenient to use the following auxiliary diagram. 
