MR. A. R. FORSYTH ON THE THETA-FUNCTIONS, 
03 +1 + +0 13 0iA + = 01201A + +01 02 + +o" 
03 08 +1+ + 05 01A A = 04 015+2+ + 02 09 + +0 > 
00 08 + 1 + +05 + 3 + + 4 = 04 012 + +5 + 01 0 9 + +0 . 
( 214 ) 
00 08 + 0 + +05 013 + + 5=04 012 + + 4+01 09 + +1 
02 08 + 0 + +07 013 + +5 = 06 012 + + 4 + 03 09 + +1 
0 O + + 0 + +05 07 + 3 + 5=04 00 + 2 + 4+01 03 + +1 
(215) 
02 06 + + +08 012+1+5 = 010014+ +3 + 00 04 + + 
01 06 + + +08 015 + 1+2 = 010013 + +4 + 03 04 + + r 
01 02 + + + 012015 + 1 + = 013014 + +0 + 00 03 + + J 
(216) 
04 06 + + +05 07 + + =01 03 + + +00 02 + + 
0j) 011+2+4+ 08 0.10+3+5 = 012014+ +1+013015+ +0 
0 3 04 + + +08 015 + 0 + 3=01 06 ++ + 010013 + +5 
02 05 + + +09 014+1+2= 00 07 + + +011012+ +4 
03 06 + + +09 012 + 1 + 4 = 01 04 + + + 011011 + +2 
02 07 + + +08 013 + 5 + 0=00 05 + + + 01 Q 015 + +3 
00 03 + 5+2 + 013014 + + = 015012 + + +01 02 + 3+4 
03 012 + 5 + +05 010 + + =01500 + + 2+09 06 + +0 
0 O 012 + 5 + + 0110 ? + + —04 08 + 1 + +01503 + +2 
02 014 + +3 + 09 05 + 0 + =01 013 + + 4+06 010 + + 
01104 + + +01302 + + 4 = 07 08 + +1 + 01 014 + +3 
08 011 + + +05 06 + + 0=04 07 + +1 + 09 010 + + 
r 
(218) 
09 04 + 4 + +02 015 + + —01 012 + +1 + 07 010 + +3 
03 09 + 4 + +02 08 + + 5=06 012 + +1 + 07 013 + +0 > 
03 04 + 4 + +08 015 + + —01 06 + 2+1 + 01 Q 013 + + _ 
(219) 
and others, as follow, which do not admit of being arranged symmetrically, the equa¬ 
tions necessary to complete systems such as (218) or (219) not having been used : 
