578] A MEMOIR ON THE TRANSFORMATION OF ELLIPTIC FUNCTIONS. 167 
whence A = 0, A' — 6 ; or we have the equations 
giving as before 
^ M Sm~ ® u3 ’ ^ 8jjr-6 u , 
(2v 3 + 3v 2 u — u) ^ = 3 (vhi 2 + 2itfv + 1) u, 
1 2 
reducible by means of the modular equation to — = I + —. 
70. n = 5. Corresponding to /= 
0, 1, 2, 3, 4, 5, we have /i = 0. 
we find 
4= J ' 
V* 
S lvin g = ^4 
5s 
fell« 
ii 
o 
5s 
fe'l =2 
^1 W 
11 
© 
v 2 
if 
„ Sy -4V, 
if 
But for u = 1 the corresponding values 
of v, Jy are 
« = 1, - 
1, -1, -1, -1, -1, 
1 - 
if -0 ’ 
l, l, i, l, i; 
whence A = A' — 10, A" + B" — 0, or say the value of is — A u( 1 u s ). 
The value of A" is found very easily by the ^-formulae, viz. neglecting higher 
powers of q, we have 
= V2, ^2, i = 5 ; V2, ¿ g = 11 
hence 
S » = » +S 'fr =52 i (' / 2)« = 4'' 3 iV2; 
that is, = 20, and the equations are 
M~* W} ~if~ v ’ ~if 
si. = 10, S L = 0, 4=1«. 4=°' 4= 10 “‘ 
Fv 'M = 
20« (1 - it 8 ) 
- lOli 4 (&><> - v ) 
- 10« 2 (%»! - + «*^0 ” «*) 
- 10 (SvoVMVi - vSv<mv a v, + v*Sv 0 ViV 2 - v 3 Sv 0 v 1 + v 4 Sv 0 - v 5 ), 
whence