MR. W. M. HICKS ON THE MOTION OF TWO SPHERES IN A FLUID. 
473 
Now 
O I 0 70 O 070 O 
. a ~—b~ 0 r~ — o- ar 
rr i cr= 
■a-— 
=— suppose, 
also 
\V 2 =(,v--<r) 
, N o (r 3 + « 3 -& 2 ) 3 -4a 2 r 3 #-4a 2 & 2 
4 
We shall further write 4a 2 & 2 —a 4 
Then 
2\a n b u 
u„— 
r ii (o'~h 
.2 
2 
2 ll a“b“ 
2rr x t 
2p + 1 k — 2g> — 1 
-2(2WYa1_l v c. k 2 «~^(2\r) 2 
J 1 |2p p — 2p 
2 u a u b" 
2 H a u b n 
{[n -(-1 )x 2 -f- 2(n—2p)a 2 }cc 2 " -4 ^ 2 (x 4 —a 4 )^ 
|2p + l |?i— 2p 
and 
v. — tt- - 7 y -{w+1« 2 + 2(n- 2p)a 2 }x 2 '‘- 4 *-Wi 
|2j? + l k —2p g \p—q L v j- / > 
Denote 
by S M 
Then 
Let 
■7J=?I 
In 
y= 
| 2g>+ 1 |jt— 2p —l 'jg | j? —g 
W={ S, (+1/r cc 2 "- 4 ? + 2S,, ? a 2 x 2 "-^- 2 } a 4 ? 
(1 + y/x) n — (1 — \/x) n n(n — l)(n—2) 
2 s/x 
£C —|— . . . 
|2p + l j?i— 2p — 1 
.... 
Then 
and in general 
S„. 0 =value of y when x is 1 = 2" 1 
S ;/il = value of ( ~ when x is l = (n—1)2"' 
^ 1 dfly 
S„» = value of p t - when aj=l 
|? ax'i 
(ii) 
jfr(j_ -vy)" =0wheE3;=1 
cfe a; 
Now q<n. Hence 
