[704 
T, the 
704] 
that is, 
A MEMOIR ON THE SINGLE AND DOUBLE THETA-FUNCTIONS. 
505 
mected 
angular 
tem of 
c 4 
c 4 
c 4 
c 4 
12 
+ 
1 
+ 6 
- 0 
9 
+ 
4 
+ 3 
- 0 
2 
+ 15 
+ 8 
- 0 
12 
“1“ 
9 
+ 2 
- 0 
1 
+ 
4 
+ 15 
- 0 
6 
+ 
3 
+ 8 
- 0 
1 
+ 
6 
- 9 
- 2 
6 
+ 12 
- 4 
- 15 
12 
+ 
1 
- 3 
- 8 
4 
+ 
3 
- 2 
- 12 
3 
+ 
9 
- 15 
- 1 
9 
+ 
4 
- 8 
- 6 
15 
+ 
8 
- 12 
- 9 
8 
+ 
2 
- 1 
- 4 
2 
+ 
15 
- 6 
- 3 
and we have, between their products, a system of 6 + 9 equations 
a'a" + b'b" + c'c" =0, 
a'a + b"b + c"c = 0, 
aa' + bb' + cc' = 0, 
be + b'c' 4- b"c" = 0, 
ca + c a' + c" a” = 0, 
ab + a'b' + a"b" = 0, 
a , 
b , 
o 
II 
cT 
— b"c', 
c'a" 
— c"a, 
a'b" 
— a'b', 
a', 
b', 
c' 
b"c 
-be", 
c"a 
— ca", 
ab" 
— a"b, 
a", 
b", 
c" 
be' 
-b'c , 
ca' 
— c'a , 
ah' 
-a'b : 
C. X. 
64