﻿Motion of a Sphere in a Viscous Fluid. 547 



For the case of an outer sphere of radius 5*7 we get on 

 substituting- for A, B, C, and D, and solving the boundary 

 equations for I, m, n, p, 



Z=--0171, p=-SU, m = '0224:, « = -000166. 



To compare with the experimental result of fig. 4 the values 

 of -^ have been calculated for Va/v = 2, and the resulting 

 A^alues of -y\r are plotted in fig. 10. It will be seen on com- 

 paring the two diagrams that the theoretical solution is a 



Fig. 10. 



Sphere in sphere, Va/v = 2 (Theoretical). 



very fair representation of the observed result. The second 

 term containing sin 2 cos 6 is unsymmetrical with respect 

 to the median plane, and accounts for the backward trend 

 of the stream-lines. A quantitative measure of the agree- 

 ment between the two diagrams may be obtained by mea- 

 suring the displacement of the point of zero velocity from 

 the median line. In the theoretical diagram this is *8 cm. 

 and in the experimental '9 cm. The approximate solution 



Va 

 is not applicable to values of — much higher than 2, on 



attempting to apply it for a value of 3 it was found that 

 the stream function became negative in portions of the field. 

 As has been already explained, the above solutions are 

 only applicable to motion in elongated vessels, as steady 

 motion is impossible in other cnses. The equations of motion 

 may, however, be solved in certain cases without the re- 

 striction to steady motion, and we may thus get a solution 

 applicable to a sphere moving in an infinitely extended thud. 

 This can be done if we apply the method of approximation 



2N2 



