HR. W. M. HICKS OK THE MOTION OF TWO SPHERES IK A FLUID. 
4G3 
Similarly when p—cr H <r„ > a and it becomes 
and 
d 2 a 4 a 
dp 3 p~ 3 p’ 
2T= — frr.uto Hu+^irahiti 
a'u 
Also p the original doublet = — , and if Mj be the mass of fluid displaced by the 
sphere A 
2T=p> 2 j i+sr^}+Mp( 2 sr ( Vn(£ '" 
p^ll 
But from what has been shown before 
P,i — - lV n 
Hence 
2T=AM>^ 1 + 32; 
( 1 ) 
By § 4 we have, if c is the distance between the centres, 
Also 
Hence 
Again 
p„ =- 
O' n 
b V 
cr 
+ =. 
ab 
c ~P"-i 
C — cr,= 
" P»-i = 
P I 
' P"-i 
bp,i 
V<r„(c—/»„_!)/ ' \a(c-p lt _{) 
3 
p »-1 
p,ip,l—l ■■■■ Pi 
bv>‘ 
a I 1 (.«—/»#_!)- 
cr cr 
P« = 
<T« V 
c- 
c — 
P»-l 
o 72 . o 
c b ft i 2 n 
P«P«-\ -— />*“ P„-l+« — 0 
3 0 2 
whence 
