466 ME, W. M. HICKS ON THE MOTION OF TWO SPHERES TN A FLUID. 
Whence 
2 T=*M 1 «^ 1 + 3(1 -qr -) 3 ^(, 
. (5) 
We shall denote, in what follows, 
(i-grT*r! 
■Q\ 2 f n 
by the functional symbol Q^—, qj. 
6 . If the sphere B is also moving along the line AB, the kinetic energy of the 
fluid will be of the form 
2T=pi,w 1 3 j l + 3Q(^,<7j j + £M 2 % 2 { 1 + 3Q(2 2 .g)}+Lw 1 w 2 
It remains, then, to find the value of L. 
It is easily seen that L depends on the part of belonging to the images of B's 
motion taken over the sphere A, together with that belonging to the images of A’s 
motion taken over the sphere B. Let now dashed letters apply to the images, &c., 
of the B system, then using the results in § 5 , the part of L due to the integration 
over A is 
4 -O 00 / IS 3 1 
= — fflrWjSj p ,+%Tra 6 u ] 2 <0 — 
But as before, remembering that now the original doublet is in B, 
/ a \ 3 
>'-i 
"-1 
f a \ } ' 
fa\ 
- v'=\ 
- 
\r / 
A / 
and 
P 
A i=' 
^i= — iirit-\!I {%!*.'„) 
O .CQ /fA n 
— o Si ( , 
c Vi 
and 
/X 7 , - 
Wn 
p 
A 3 " -3 J p'u-p'n-! 
a) \(c-p'„_J.. 
Pa 
(c~P\) 
P 
Now as before 
p ,/—i i 
-,,+ A r” 
