﻿Motion of a Sphere in a Viscous Fluid. 549 



This equation together with 



KM-J<h(>)-v*,<>)=f(V) 



serve to determine X 1 and </>i(r), the arbitrary constants 

 being determined by the boundary conditions, and the 

 problem is thus reduced to that of the solution of the two 

 linear equations (14) and (15). 



To solve (14) we must evidently have X x = V^A,, and then 

 the equation becomes 



A particular solution of the left-hand equated to zero is 

 f(?')— Br 3 , and hence the complete solution is 



e=4°+DJ£+$J^*] 



(16) 



We have now to solve 



The equation 



*i"(»-)-^i(r)-2A^(r) = 



is solved by 



if this be written f(r) for brevity, then the solution of the 

 complete equation is 



Mr) = Rr) [E + fJ^ + j*JJL (>(,) f (,)*•] . . (17) 



The solution for ty may now be written 



yjr = ce X2vt (j> Q (r) sin 2 6 + <?<? xh * ^(r) sin 2 cos 



= V^ o (r)sin 2 (9 + V 2 1 (r)sin 2 0cos0. . . (18) 



In calculating this solution for particular cases the inte- 

 grals occurring in the expressions for (p { ()-) are best evaluated 

 by numerical methods. In order to reduce the labour of 

 calculation, it is necessary to use an interpolation formula 

 so as to be able to carry out the calculation with a small 



