Now 
of Edinburgh, Session 1885-86. 
ds = adO , ds—ad& r = /yAe 2 + 4a 2 sin 2 J0 
653 
M = 
ry a 2 ! 
*J 0 o >s/ 
cos OdOdO' 
s/x 2 + 4a 2 sin 2 J0 
= 2™ 2 A" cosftW 
o 
/"* 2tt 
= 7ra/^ I 
J o 
*/ 4a 2 + # 2 - 4a 2 cos 2 ^0 
cos 
if 
* 2 = i^^ =sin2y(say) 
n 
= ‘I'jrak 
r 0 
/ (2 cos 2 |0- 1) . d . g 
= 4tt<xA; 
^(1 - 2 sin 2 |p)c£ . | 
r *(i - 2 j 
c / 2 — — 
0 VI- 
As 2 sin 2 -^ 
Ij 
+ ^ = 7T 
= kirak 
/ 
fj 1 + |( 1 -* 2sin2 || 1 )}^ 
^1 - A: 2 sin 2 
z 
iirak 
f n ' ,.*p 
\_Jo ^1 -/fc 2 sin 2 | */. Vl - * 2 sin 2 -| f/ 0 
V 1 -* 2 sin 2 -| • * 
-tai{R-lr + lE } 
{(' 
= im ■! ( * - ?-V + | E | 
k 
When F and E are the first and second complete elliptic integrals 
to modulus k. 
