MR. W. M. HICKS OK THE MOTION OF TWO SPHERES IK A FLUID. 479 
For the first image in A, p x =0 
Hence 
/U 
= i \( <*> V , c^-2V) } 
2 1 \c 2 —& 2 / ' 2&(c 2 —& 2 ) 2 J ^ 
• (17) 
The density at any point of the first image is 
m r i 
a |_ c 2 —5 2 & 2 ® R 
rAgtl® 
together with a doublet 
\ 3 
e 2 —6 2 
A: at a distance p 2 
The amount of that part of the second image in A which depends on the latter is 
11 / db \ 3 _| « 8 (e 3 — cpn — 2& 2 )] / ab . , 
2 1 \ c z^_ cp J ' 2&(c 3 —& 2 —cp 3 ) 2 J \c 2 —& 3 4 ' 
and the amount of the part due to the portion of the former at a distance R is 
Tel \( ab \s g»(c8—26 8 —cR) 1 [1 1 , p 2 l PTO 
'2a j\c 2 -5 2 -cR/ ^2Rc 2 -6 2 -cR) 2 j |e 2 -& 2 ft 2 ° g E J R ' R 
whence the whole amount due to the former 
kb pF « 3 &(c 3 + & 3 ) a 3 c 2 a : 
“ 2acJ o u (c 2 —b~ — cR) 3 2(c 2 -& 2 -cR) 2 + 2&(c 2 -& 2 -cR) 2&_ 
ka~b 
Rc 2 + & 2 ) cR c_ 2 , 3 72 -p xl 
4c 2 (c 2 — & 2 )L(c 2 —5 2 —cR) 2 c 2 — & 2 — cR & 6 ° g ^ ' cR )J 
c s -& 2 V 
>= 
o 
5-RogfRR 
£ 
logg 
7'A 
+ 4ft 2 Jo C c 2 -& 2 -cR 
dR 
+ 
hr 
MW 
4 c 2 (c 3 —& 2 —ep 2 ) 2 4(i 
hcd U 2 , p 2 d J’ 5 3 (e 2 —& 2 ) 5(c 2 + & 2 ) cR 
i&dJo ° g R dRl(c 3 -& 2 -cR) 2 “c 2 -& 2 -cR — l 1 r-& 2 
2& 2 -e 2 ^(& 2 _2 c 2 ) 
‘ Z> 2 .c c~(c~ — b~) 
d R 
7u 2 f 2b" 
r — & 2 ) { c 2 — 5 2 — c p % 
1 2 bo- c8 - 53 -^ g] _ r 1 _ lo sR_ c /, r 
+ Zl0 ^ c 2_ & 2 f 4 & 2\ c 2_ & 2 
do C P2 
Now cp 2 = 
ft 2 C 2 
(? — b v 
— acoL say. 
Then the above is 
3 Q 2 
