472 MR, W. M. HICKS OK THE MOTION OF TWO SPHERES IN A FLUID. 
and the series is still convergent. 
The value of is the limit when \=0 of 
d h 
c/i —g 3 _ a + b 
1 Si b 
Hence when the spheres are in contact 
log r(l+x) .... (9) 
if x= - r. The values of this may be found from Legendre’s table of the 
a + b J 
log T-functions. 
If the spheres be equal x=\ and 
Q = 2j———=S' 3 —1 
^ ] (2?i+l) 3 3 
( 10 ) 
Now 
whence 
S 3 =l+y 3 +| 3 + .... =1-202056903159 . . 
= S / s +iS 3 
S' 3 =fS 3 = 1*051799790264 
When the spheres are equal If in this case q denote either or — 
<h ?i 
Q=(i 
■fi n \ 3 
yLi+2 
11. We may easily express the general term in terms of r, a, b. For writing it 
in the form 
qH 
2i- 
?i 
— ., 3 c 
£i_2 
.2" 2i 
% > = Uh suppose, 
we get at once from the relations (2), (3), (4) 
_ 2\a“b 11 
U,l ~~ (rj + ^)' i+ 1 (r 2 + \)» - (r x -X) >i+ 1 (r 2 -\)» 
which, since r. 2 —r — r 1 and r 2 — \ 2 =a 2 
__ 2 \a n b u __ 
( r i + ^) { r ( r i + ^) — cd }" — O’i — { r ( r i — — « 2 } “ 
