MR. W. M. HICKS OK THE MOTION OP TWO SPHERES IN A FLUID. 
471 
which differs from the equation for external spheres in having — p for p for all values 
of n. We may therefore use the same solution and writing here 
OA=vA 3 +« 3 
fW+W— v / X^+t?=c 
¥-a--c~ 
2c 
- / 
b 2 + c 2 — a 2 
2c 
— 
= r 2 — 
—X 
a 
a 
-f- X 
r 2 —X 
b 
b r 0 + A. 
1—qZ* 
which is the same form as before, only q is the inverse of its former value. 
And, as before, 
2T=JM 1 #{ l+3(1 
=-|M 1 w 2 { 1 + BQ(q.q } ) } 
A table for Q when b — 2a is given at the end of the paper. 
10. It will be well here, before passing on to the consideration of the motion, to 
make a short digression on the properties of the functions Q and Q'. In the first place 
it is easily seen that the series for the Q and Q' functions are both convergent, even 
up to the case when the spheres touch, or q— 1; for the ratio of the n th term to the 
n— 1 th is 
Li -grV "- 2 
\ q i-gr¥‘ 
3 
and this is always less than f, which is less than unity, except in the case when the 
spheres touch. In this particular case the A h term tends to the limit 
3 p 2 
