MR. W. M. HICKS OK THE MOTION OF TWO SPHERES IN A FLUID. 
48.9 
where 2 is of the order Id at least. Substituting for 2 and neglecting cubes and 
higher powers of L, 
. • • dA 2 7 BLu, ,— dB 7 T — 
A oZ -—“ dr. — --cos y/ ix l t-\--^drLji l cos 
-iLV 1 (g-2£)f s sin- + sm* ^t=0 
and 
dr—x 1 —x. 2 = 
\/ Pi fJ r 
BL 
A 3 
Whence the equation takes the form 
A., 2 '■=/+{! cos v 7 frt+h cos 2 .y/fij 
when 
J/ 
LVi' 
c ^-—\ ' \dA 2 
aJIa, dr dr/ ‘ 2 A,\A, 1 dr' 
1 d/A x A 3 - B 2 
2 dr\ A, 
in which last form we may neglect in A 1 the as it disappears in the differen¬ 
tiation. Hence the mean action of («) on ( b ) is an acceleration towards (a) 
LVi d /A x A 2 —B 3 \ 
4A, dr\ A 2 ) 
/ttL\ 3 1 d AAj-Bh 
\ T / A 2 dr \ A 2 ) 
d 3 d /AjA^-BA 
A, dr \ A 2 ) 
if v is the “ velocity of mean square ” of (a). 
If the distance of the spheres is so large that we may neglect twelfth and higher 
inverse powers of the distance, we need only consider the first images or the first 
terms in A and B. In this case it will be found that the acceleration to (a) is 
18v 2 /aV l d 3 1] 
2p + l\r) { (r~ — b-)*"2p + lr\ 
To find when there is repulsion 
< 
(fi-b*)* 2p + i 
(23) 
