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 "