474 MR. W. M. HICKS ON THE MOTION OF TWO SPHERES IN A FLUID. 
Therefore 
2l q 
'dfl (1 + y/x) u ~ 
clx2 \fx 
X=\ 
Also we see that v a is a rational integral function of (r~ ct b ) 
When one sphere is inside the other the series for Q is still convergent. 
12. When the spheres are concentric 
r x =r 2 = co \=co 
2 i =0 q °=0 
1 Qa o 
and 
whence 
Q=U 
3 1 
1 — 
a\ 3 ¥ — o? 
2T=i^Af M i“ 2 
a ¥—a 
( 12 ) 
which agrees with the result found by Stokes in his paper of 1843 before referred to. 
When the inner touches the outer \=0 and 
Q=^(^=-i^ 1 ^ r < 1+a: ) 
= — l-15129a^log 10 r(l+*) 
• ■ • (13) 
where 
X = : 
)—a 
If x is an integer = m say 
Q=m 3 |s 3 —2fP} = »r 3 1*2020569 — 2/4*} 
a finite expression, and in this case 
in — 1 7 
a— - b 
in 
a — \b 
ci=%b 
In the particular cases 
Q = '61645 
Q=1'08054 
