480 MR. W. M. HICKS OK THE MOTIOK OF TWO SPHERES IK A FLUID. 
IV 
2 . 1m~ r 2V 
arc- . V 
lea- C 1 log x 
Wherefore the whole amount of the second image in A, is (writing /3 =^ 
fiT*\l-a*J b + c*){l-a*J +4 V V l-« 2 
ft 2 . u 
a 2 C 1 log a? 
■an i 
I 2 ' ^ 
(18) 
Substituting for — and — in (7) we get the part of T depending on iq 2 correct to 
P'0 P>o 
the second image in A. Interchanging a and b, the part depending on a 3 2 is found. 
In the case of equal spheres 
Pa 
fh_i 
P-o S 
c'~—a‘ 
a 2 (c 2 —2a 2 ) 
IV 
P o 
2 ( c 2 —« 2 ) 2 
_ip3 i a 4 c~ + (c- — ft ') 3 p. : j / __i_ 9 \p 
2 4 ‘ b~c 2 (c~—cr) 
(c 2 -a 2 ) 2 
a 6 , a 4 , 0 . , C 1 log x , 
(c 2 — a 2 ) 2 c 2_ 2(c 2 — a 2 ) 2 °® ( : “ a ') ~4 k J ~ dx 
I 2 7 
J o a ~ 
16. To find the value of the coefficient of the term in a 1 v. : we need to find the 
amounts of the images in B due to the motion of A, and vice versa. 
b \3 
The first image in B of 1c in A at a distance p { is \ j7y~j ^ at Qi and a negative line 
doublet thence to B, whose line density is — 7 .^ 7 . 
J b BP, 
The whole amount is therefore 
BP,/ 
BP, 
c — 
Pi 
b\ 8 , 
For the first pi = 0 and —=l(-j k 
P'0 \ C J 
To find the amount of the second image in B we start from the first image in A 
/ ctb 
already found. This is, as has been shown, a doublet at p 2 = ( 2 _^ 2 J k and a line 
doublet thence to A, whose line density is 
