842 
MB.. A. R. FORSYTH ON THE THETA-EUNCTIONS, 
55. Sixteenth Set, with ®' 15 . 
G 6 C 9 ©Q © 15 = 00 ^9 $0 $15 + 05 01O$12$3 04 ^1|$2 $13 — @8 $| $14 
C 6 G 8 ®! ®' 15 = 0 G 0 8 3* ^+0* Ma $18-00 01-A $9 -03 013$4 $10 
C 1 G 12©2 ® 15—012$2 $15 + 0'/ 01O$4 $9 ~~^Q 011$6 $8 — 0Q 013$3 $14 
G 0 C 12©3 © 15—00 012^3 $15+07 011$4 $8 @5 @9 $10$6 @2 014$l $13 
C 2 C 9 ©4 © 1502 09 $4 $15+05 014$3 $8 ^7 012$1 $10 00 011$6 $13 
C 2 C 8 ©5 ©15 02 08 $5 $15 + 05 015$2 $8 013$O $10 00 01O$7 $13 
C 0 C 0 © 6 © is =0 O 0 9 $o $15+07 0]4$i $8 —04 013$2 $11 — 03 01O$5 $12 
Cq Cg ©7 © 15 ==; 0 O 0 8 $7 $15 + 07 015$O $8 05 013$2 $10 — 02 01O$5 $13 
C 3 C 4 ©8 © r i5 = 03 04 $8 $15+01Q013$1 $(i “09 014$2 $5 “00 @7 $11$12 
G 0 C 6 ©9 © 15 — 00 06 $9 $15 + 011013$2 $4 —^8 014$1 $7 ^3 @5 $10$12 
G 1 G 4 ©10© 15 — 01 04 $10$15 + 01O015$1 $4 0110l4$O $5 ‘00 @5 $11$14 
C 0 C 4 ©11© 15~0O 04 $11$15 + 0J 1015$O $4 0K)014$1 $5 01 $10$14 
C 0 C 3 ©12© 15 = 0O 03 $12$15+013014$1 $2 ~^8 011$7 $4 “ 05 00 $9 $10 
C 0 C 2 ©13© 15 — 00 02 $1S$15 + 013015$O $2 05 @7 $8 $10 08 01O$5 $7 
C Q C x ©i4© 15=0 O 0i $14$15+014015$0 $0 01O011$4 $5 —04 05 $11$10 
G 15 G 15©]5© 15— 015015$15$15 + 01Q01O$1O$1O 011011$11$11 014014$14$14 
56. Any one equation giving cc© f ©' M where r, n are different, also gives cc© w ©',. by 
changing the sign of £ 77 : thus from 
C 2 C 3©1© 0—0 3 03$i$(j + 0 6 0 7 $4$' 01Q011$8$9 014015$12$13 
there follows in this manner 
°2 C 3©0© / 1 — 0203$O$1 0Q07$4$5 01Q0U$8$9 + 011015 $ 12 $ 13 * 
In addition to the equations given in formulae (205), (206), (207), the following 
include most of those used in order to obtain the above sixteen sets in the form in 
which they are presented. 
