478 MR. W. M. HICKS ON THE MOTION OF TWO SPHERES IN A FLUID. 
and c—r=— 
li 
a \ 3 k r dr 
c — r) b BP-l c£R 
dr a 2 
rfR = R 2 
.density = — 
k cR — a? 
ab BPj 
k r 
(2) a line doublet image of each portion. The doublet —"j’Tp" c ^ r P r0( iuces a positive 
k rdr R 
line doublet from a distance Pv' = — to A, whose line density = 7 __ 
c—r J ab Blfi c — r 
Hence the density at a distance It, due to this part, from the whole line doublet 
in B 
/'*BQ 1 
( k R rclr 
a* ab BP, c — r 
c -iT 
k R 
: ^‘bp, 
clog 
R 
P 2 
Hence finally the density at a distance II from A of the resultant line doublet 
kfb\ 3 R k cR-cd k R f , p, J 1 1\1 
” a \BpJ ACfi «&’ B?! ab BP 1 [ C R °\B, pj j 
k R 
b \ 3 . k R 
a ACfi \BBJ ab BPj 
and the whole amount 
+V^filogf-BQ 
%1 
= - loe - 1 E< ® 
&.BPj & R j 
-_7.fi/' ab V , 1 E Ql- ftS » fl3c 
— -^t> 1 T 27, 
9 \AQ V BBJ ' 2 &.BP 1 .AQ 1 2 4 6.BP 1 .AQ 1 S 
So that the whole amount of the image is 
ab 
® , (aq 1 .bp 1 ) 8 ^"*" 4 &.bp 1 .aq 1 ^ c 
or substituting for ACfi, &e., in terms of p l 
ab 
W . cd(c~ —c Pl — 2 & 2 ) 7 
/ 2 _ 72 _ 
'—W—cpJ 1 4 b(c*-b*-c Pl ) 
