506 Mr. J. W. L. Glaisher on the Complete 
It can be shown that, by the change of q into q?, 
ee 
Lieder} * 
nd that, by the change of g into —q, 
Hy’ becomes 
k becomes _ 
” k’(K’—iK), 
H’—?K’ +7(h— —hPR) 
4) kf 
Thus, by the change of g into ig2, EH’ becomes 
e~ 4H! — 7K! + kK + i(H—kOK + kk’ K)}. 
It follows, therefore, that 
24H’ —h’?K/ +k K+1(B-k?OK +k’ Kt 
K/ 
Hy’ 
7 
1 1.3135) ese ee 
=e ea ee 
whence, equating imaginary parts, 
2(B—h?K +4 RK!) _ 
3 an 16-2 ke. 
vi 
2 42 
sin 0+ sin 30+ 5, 
The left-hand member of this equation 
_ 2H—K 3 K’ sin 20—K cos 20° 
T 1 
and therefore the equation itself may be written 
2H K is K cos 2€6—K’ sin 26 
ire ae T 
+sin 0+ Sin 30 + — sin 70+ &e. 
Now 
* =sind+5 sin Ron ele ee Bee 2 ae sin 130+ &e. 
TT 97, 42 ae A? G6? e 
/ 
2 
* 008 0+ 5: 5008 90+ 55 7008 904% Finny 008 130+ do, 
ae 
2?, 4”. 
