﻿526 Mr. W. Ellis Williams on the 



2. The ions do not exist in dust-free air, so the picture 

 most readil}' formed is that of a collection of water molecules 

 surrounding a dust particle, the whole being electrified by 

 the attachment of a small ion. The ion thus affords an 

 interesting example of the adsorption of water vapour at a 

 rigid surface. 



3. A thermodynamic argument, based on the relation 

 between mobility and relative humidity, leads to the con- 

 clusion that the adsorbed moisture is in the liquid state 

 with a latent heat and density little different from those of 

 water. 



4. The order of magnitude of the diameter of the ion, as 

 calculated on usual kinetic theory lines, varies from 3 to 

 •ix 10~ 7 centimetre according to the atmospheric conditions. 



The Physical Laboratory, 

 The University of Sydney, 

 November 25, 1914. 



LV. On the Motion of a Sphere in a Viscous Fluid. By 

 W. Ellis Williams, B.Sc, A.F.Ae.S., University College, 

 Bangor *. 



[Plate IX.] 



Notation : — 



jji coefficient of viscosity. 



y = fx/o . . kinematic coefficient of viscosity. 



V velocity of sphere. 



a radius of sphere. 



E, © . . . . velocities along the polar coordinates r, 8. 



u, w .... velocities along the cylindrical coordinates w, z. 



xp Stokes's current function. 



2) pressure at a point in the fluid. 



THE mathematical solution of the problem presented by 

 the motion of a solid body moving with finite velocity 

 through a viscous fluid has hitherto presented insuperable 

 difficulties, and no solution has been obtained even for the 

 apparently simple cases of a sphere or cylinder moving with 

 uniform velocity along a straight line. The complicated 

 nature of the equations of motion together with the difficulties 

 presented by the boundary conditions, which require that 

 both the normal and tangential velocities should have specified 

 values at the surface of the moving body, seem to place the 

 direct solution of the problem far above the reach of any 

 known method. The actual solutions of the problem which 

 are given in the current text-books of hydrodynamics are 

 * Communicated by Prof. E. Taylor Jones, D.Sc. 



