﻿Motion of a Sphere in a Viscous Fluid. 



535 



thus be accurately represented by a solution obtained by 

 neglecting the inertia terms. If, however, the lines of fig. 2' 

 be compared with the diagram of Stokes's solution given 

 on p. 532 of Lamb's ' Hydrodynamics ' it will be seen that the 

 observed motion differs widely from the theoretical diagram. 

 This is obviously due to the effect of the containing vessel 

 on the motion, Stokes's solution referring to a sphere moving 

 in a fluid extending to infinity. It may in fact be shown 

 that the effect of the boundary is appreciable even when the 

 sphere is small compared with the vessel. The velocity in 

 Stokes's solution is everywhere in the same direction as that 

 of the sphere, while if we consider the flux across the median 

 plane perpendicular to the motion, it is obvious that the 

 total amount of fluid crossing the plane must be zero at 

 every instant (the sphere itself being reckoned as though it 

 were fluid) ; hence the forward motion of the liquid near 

 the sphore must be compensated by a backward flow in the 

 outer portions of the vessel. As the velocity of the fluid 

 only diminishes with the first power of the distance, the effect 

 is very marked even when the vessel is very large compared 

 with the sphere. This in fact is what we see in the photo- 

 graph ; in the immediate neighbourhood of the sphere the 

 fluid moves along with it, but as w r e go away from the sphere 

 we see that the velocity diminishes to zero and in the outer 

 parts of the vessel is mainly in the opposite direction. 



Ficr. 4. 



Sphere iu glycerine, Va/V = 2 , l (Experimental). 



Passing on to the diagram of fig. 4 and the corresponding- 

 photograph B, PI. IX., these refer to a velocity of *217 cm. 

 per sec. in a mixture of glycerine and water of viscosity 

 ^ = '09. The value o£ Va/v is therefore 2*1 and the critical 



