ME, W. M. HICKS ON THE MOTION OF TWO SPHERES IN A FLUID. 481 
The amount in B from the former is 
«Z> 3 
and from the second is 
So also 
(c —p.f)(e 2 —Z> 2 ) 
€GY)Y lo =t- ,-*1. 
S ;1 —eZR 
. n , c ~p-2 _ &W 
~ 4 ae \c-pf 9 g c (c 2 - V) (c - pf 
kb 2 f cpo c 2 —& 3 —cp 0 , , , c — pc 
=IX +* °8 —' 
4«c [r-i 2 (e-p,) 2 
@ 2 r fl » ( C 2 -& 2 ) 2 -^ 2 , _ 
• 4ae [ c s _ h 2 _ a 2 _ & 2 )s w 2 °8 [ ■ r? _ 7)3 
Yo 
— i 
ctb 2 
c(c 2 —a 2 — 6 2 ) J 4ae 
3 7,2 
^ +7Zi • • • • ) 
p,\ n f « 2 & 1 3 a 2 f &2 ( c 2_ a 2)2_J2 c 2 C*-Cr-tf 
v 0 ~ 9 \c{f-a?-W)\ + 45ctc 3 -a 2 ’ (c 2 -« 2 -& 2 ) 2 + 2 1 °g‘ c s_ a s 
Whence from (8) 
L '=2^fA±£i') + 2TO3 ( , i±i5 
\ V 0 / \ Po 
=|M' 
W f « 2 6 2 l 3 a 2 Z> 2 (c 3 —« 2 —6 2 ) 2 
+ ] r .(r?-a?-l-W I 8r l0g (c 2 - a 2 ) (c 2 - 5 2 ) 
c(c 2 —a 2 —5 2 ) : 
cM 
4c(c 2 —a 2 —6 2 ) s 
c*(a a +6 8 )-2o»6 9 -c 8 VH-4 
6 4 
c 2 — ft 2 1 c 3 —& 2 
(19) 
Similarly can be found the coefficient of when one sphere moves inside another. 
Motion in the line of centres. 
17. When the two spheres are moving in the line of centres the kinetic energy is 
given by 
2T=Ap^ 2 +Apt/—2 Bw 1 w 2 
where 
A 1 =« 1 1 +-|m / 1 j 1 + 3Q^-.(? 
b=|M'Q'($) 
