1 36 Mr. Ivory on the figure requisite to maintain the equilibrium 
Now, we have 
R' 3 = — 
P' 1 + C 1 — lO Sin. 1 ?' + (* “ P'^ Cos •* ?' 
or, which is the same thing, 
r>/ a _ h* h' x h"* 
+ e*y*> Sin* ?' + ■*'* (A* + e 14 !/*) Cos .*/’ 
h ' 2 — h 2 = e 2 , h ' 2 — h 2 -= e ' 2 ; 
wherefore 
//R ' <*/>' </ ?' =jf/‘ 4 - vk'v'.iti i 
'» (A*+ e^' a ) Sin . 1 + k' z (A 1 + e'^p' 1 ) Cos . 1 
This expression is now integrable with regard to : and we 
get, between the limits q' = 0 and q' = 2 ?r, 
//R ' 2 d p’dcf-= 2 v-.hH h”. f , idP \ , • 
The integral now found increases as much, while p' decreases 
from 1 to 0, as it does, while p' decreases from 0 to — 1 : 
wherefore the whole value will be the same, if we make p ' 
vary between the limits 1 and 0 ; and then double the result : 
thus, 
f/R 2 dp* dq = 4 v .hh! . (** + e 'v 2 ) * 
Finally put = — ; then we get, 
//R'W *< = 4 ir.AA' A"./ 
the limits of a: being, x =zh and x = co. 
Wherefore, by substitution, we get, 
- (-jf -) r3 = **■** V' JvWTWW + n • 
Now, multiply by — , and then integrate ; and, having 
multiplied by r 2 after the integration, we shall obtain, 
