788 
MR. A. R. FORSYTH ON THE THETA-FUNCTIONS. 
that are used. The current-number notation adopted in this paper was chosen to 
coincide as closely as possible with that of Professor Cayley (with which it is almost 
identical as will be seen from the table) and with Poseyhain’s notation; that of 
Weierstrass is given as quoted by Konigsbebger. In the table i denotes ^/ — l. 
Asterisk 
denotes odd 
function. 
Herhite's 
characteristic. 
Current-number 
adopted in 
this paper. 
Eosenhaxn. 
Gopel. 
Cayley’s 
characteristic. 
Cayley’s 
current-number. 
Weierstbass. 
a>°>° 
0,0 
h) 
033 
p'/r 
o o' 
% 
hi 
0, 0 
0,1 
032 
Q"' 
0,1 
0,0 
^2 
h)l 
* 
0,1 
0,1 
"ho 
031 
iQ " 
KSi) 
h 
l io 
^ 02 
0,1 
0,0 
*8 
030 
p" 
0, 0 
0,1 
*8 
«9"l2 
0,0 
1,0 
*1 
023 
R'" 
1,0 
0,0 
"h 
^4 
0, 0 
1,1 
-h 
022 
S'" 
1,1 
0,0 
^3 
^23 
0,1 
1,1 
021 
iS " 
bQ 
is-,, 
% 11 
^13 
0,1 
1,0 
020 
R" 
1,0 
0,1 
h) 
h)3 
* 
1,0 
1,0 
4 
013 
'/R' 
bQ 
% 0 
3 
* 
1,0 
1,1 
'hr 
012 
iS' 
Ki:J) 
^24 
1,1 
1,1 
"h.5 
0n 
S 
-&) 
-hs 
1,1 
1,0 
hs 
0io 
m 
Km) 
ih 3 
*$04 
1 0 
0, 0 
003 
p' 
0,0 
1,0 
*4 
"$34 
1,0 
0,1 
^6 
002 
Q' 
0,1 
1,0 
* 
1,1 
0,1 
^14 
0oi 
»Q 
K 
1,1 
0,0 
0oo 
P 
0,0 
1,1 
h, 
