508 Mr. J. W. L. Glaisher on the Complete 
It can be shown that 
== 1 ae b-geg BH a3 
§ 6. Denoting by ea ee the same functions of 
k? that the unaccented letters are of £?, it can also be shown 
that, by the change of g into @?, 
k’ becomes e-”®, 
| eooamea aah a ICL ce 
Ve pest! aw): 
Vv! e~ 9 G +iG); 
and 
H’ becomes e~®{G/ +k K+i(G +kk’K’)}, 
GG, ees Oey —khK+iG  —kk’K)}, 
Wo, eG + WK + (G+ WKY}, 
Wi ge PEW AW +E K+iG4+W4kh'RK)}. 
2K’ 20 2v" 
§ 7. Starting with the series for —— | hel mae in powers 
of k”, and changing k’ into e—**, we find, by equating the real, 
and the i imaginary, pe in the ping formule, 
K 12 a3" 
roi 
= = sill cs sin 50+ 5 oF. a a8in 90+ 5 a. sin 130 + &e., 
K’ 12 Ne tae hae 
=. ces 6+ 92 CO8dE + 55 92 4208 90+ 52 42, 62 08 130 +&e. ") 
v= 5 sin 30+ = sin 70+ ee sin 110+ &e., 
