704] 
A MEMOIR ON THE SINGLE AND DOUBLE THETA-FUNCTIONS. 
511 
Thus taking the tenth line of the upper half, and the fifth line of the lower half, 
we have 
10 
00 
01 
1 
1 1 
3 
3 
1 3 
3 
1 1 
3 1 
1 
3 
3 
3 
1 
2 2 
2 
2 2 
2 
1 2 
? 2 
2 
2 
2 
2 
10 
1 
r-H 
1 
o 
0 
1 
0-1 
0 
j 1 
0-1 
0 
1 
0 
-1 
0 
giving the value of 
viz. this is 
i i 
i i 
= ® l g (2«). 0 _ J J (2«') = ¿0 \ * (2«). 0 ” (2«') 
1 â 
3 1 
3 1 
+ ®I â ( ” ) - 0 -Î 0 ( ” ) o ( ” ) 0 l 0 ( ” } 
1 3 
3 1 
+ @| *(„) *(„).ef *(„), 
where the first column is the value given directly by the diagram: it is then reduced 
to that given by the second column. 
84. But instead of the @’s, we introduce single letters (X, Y, Z, W), (E, F, G, H), 
(I, J, K, L), (M, iV, P, Q), with the suffixes (0, 1, 2, 3), in all 64 symbols, thus 
@ 00 10 01 11 (2u)= X Y Z W 
00“ 
10 
01 
11 
that is, 
@J° = F, &c„ 
@“(2«) = X 1 „ 
that is, 
@ £0 il 
00 
10 
01 
11 
fl (2u) = E F G H 
0 “ 
1 
2 
3 
® 00 (2“) = E ' &0 "