a Sphere in a Viscous Fluid. 533 



12. Fall of an Oiled Sphere. 



The photograph reproduced in Piate II. fig. 4 is of special 

 interest aince it shows the fall through water of a sphere oiled 

 with Rangoon oil. It will be noticed that the greater portion of 

 the oil has collected on the upper surface of the sphere, form- 

 ing as it were a " tail " that follows the sphere in its down- 

 ward motion. The velocity of the oiled sphere found from 

 this photograph was 114*5 centim. per sec, as compared 

 with 120*5 centim. per sec. for the same sphere unoiled. 

 The effect of oiling the sphere has therefore been to reduce 

 the velocity by 5 per cent. 



No sensible change has been produced in the diameter of 

 the image, so that practically all the oil must be collected 

 in the tail. The volume of the tail is roughly estimated at 

 '0034 cub. centim. : the total volume of oil descending with 

 the sphere must certainly be less than '005 cub. centim. 

 The approximate weight of the ball is *70 grm., and its 

 volume '090 cub. centim., the density being about 7*8. The 

 mean density of the oiled sphere, taking the upper limit for 

 the volume of the oil, would be 7*2. The change in density 

 would therefore be sufficient to account for the observed re- 

 duction in the velocity, so that it is not necessary to assume 

 any change in the general character of the fluid motion. 



13. Summary and Conclusion. 



The experiments described in this paper have had for their 

 object the measurement of the terminal velocity attained by 

 a spherical body falling freely in a viscous fluid. From 

 these measurements it was desired to deduce the law of re- 

 sistance, and also to obtain information as to the existence of 

 " slipping " at the boundary of a fluid mass moving in a fluid 

 of different density. 



With regard to the latter point, the experiments made on 

 the velocity of ascent of small air-bubbles in water and 

 aniline, show that the velocity acquired is the same as would 

 be attained by a solid sphere of corresponding density and 

 dimensions. No appreciable slipping has been detected in 

 the case of a solid in contact with a liquid. We may there- 

 fore extend this conclusion to the case of two different fluids 

 in contact. 



It has also been shown that the law of resistance to the 

 motion of a sphere moving with constant velocity in a viscous 

 fluid depends on the magnitude of that velocity. Three dis- 

 tinct stages have been recognized. 



(1) When the velocity is sufficiently small the motion 

 Phil. Mag. S. 5. Vol. 50. No. 306. Nov. 1900. 2 P 



