a Sphere in a Viscous Fluid. 327 



The theoretical result given by Stokes for the case of very 

 slow motion is obtained by putting w=l and the constant 

 k = Qir. Then the resistance is SirpvaV, and the terminal 



velocity = I £=£&* 

 J y p V 



If n were equal to §, the terminal velocity would be pro- 

 | ortional to the first power of the radius. 



If n were equal to 2, the square of the terminal velocity 

 would be proportional to the radius, and the resistance loould 

 he independent of the viscosity; while, if it were possible for n 

 to ba greater than 2, the resistance would increase as the 

 fluidity increased. 



II. 



4. Motion of a Fluid Sphere. 



The present investigation was commenced, at the suggestion 

 of Prof. J. J. Thomson, to see whether the velocity acquired 

 by small bubbles of gas ascending through a liquid would 

 conform to the theoretical result for a solid sphere, and, if 

 possible, to derive some information as to the existence of 

 sliding friction in this case. 



The question of the applicability of the formula to the 

 motion of a liquid sphere has already been discussed in a 

 paper read before the Physical Society by 0. G. Jones "*, who 

 made a series of experiments in which globules of mercury 

 were dropped through highly viscous fluids, and their velo- 

 cities determined. He assumed that the globule might be 

 treated as spherical, and that the coefficient /3 was infinite. 

 Lord Rayleigh observed that there might be circulation within 

 the globule; and Dr. Burton pointed out that with perfectly 

 liquid spheres there would be infinite slip, and /3 would there- 

 fore be zero. Later experiments based on the same assump- 

 tions were made by A. W. Duff t, who employed the measuie- 

 ments of the velocities of mercury globules and small shot in 

 glycerin or paraffin to detect any change in viscosity due to 

 an electrostatic field. 



If the fluid in the interior of a globule ascending or de- 

 scending in a liquid is in circulation, the viscosity of the fluid 

 of which the globule is composed must affect its velocitv. 

 But when the globule is a bubble of air, the internal friction 

 is so small that its effect on the velocity may be safely 

 neglected. 



We have also to assume that when the bubble is sufficiently 



* Phil. Mag. (5) xxxvii. pp. 452-462 (1894;. 

 t Pliys. Review, iv. pp. 23-38 (1896). 



