﻿Motion of a Sphere in a Viscous Fluid, 541 



that there is no very great difference between the values of 

 the velocities in the neighbourhood of the sphere, so that the 

 above solution may be regarded as an approximate repre- 

 sentation of the motion of a sphere in an elongated vessel, 

 the approximation being fairly close in the neighbourhood 

 of the sphere. 



Fio-. 9. 



Sphere in sphere, Ya/v=Q (Theoretical). 



Taking the solution obtained above as a base, we shall 

 now attempt to obtain a second approximation in which the 

 terms containing the second power of the velocity are partly 

 taken into account. 



Returning to the general equations of motion (1) and 

 writing them in terms of cylindrical coordinates z, vr (sym- 

 metry about axis of z), we get for steady motion and no 

 impressed forces the two equations 



u^ \-w^- = ^- + v\7-u\ 



Introducing the operator D defined above, these may be 

 written 



dp B*r . dw 1 d / n .n 



