Oil the Motion of a Sphere in a Viscous Fluid. 323 



perhaps never completely, oxidized by air at the ordinary 

 temperature, and therefore when old coal-bearing strata are 

 washed away, the bulk of the old carbonaceous matter may still 

 help to increase the percentage in the new deposits. However, 

 even if we should have to make a liberal allowance for the 

 destruction of old carbonaceous matter by oxidation in some 

 way or other, the results obtained by this line of inquiry are 

 not unfavourable to the credibility of a high estimate of the 

 world's supply of fuel, for all the elements in the above 

 calculation, required to give us 500,000,000,000,000 tons 

 of coal, viz. (1) the amount of rock annually denuded and 

 again deposited (85,000,000,000 tons), (2) the length of time 

 that this denudation has been going on (is0,000,000 years), 

 and (3) the proportion of organic matter present (0*03 per 

 cent.), are more likely, taken as a whole, to err on the side of 

 beiuo- estimated too low than of being estimated too high. 

 [To be continued.] 



XXXI. The Motion of a Sphere in a Viscous Fluid. 

 By H. S. Allen, M.A., B.Sc* 

 I. 

 1. Theoretical Formula of Stokes, 



y _ 2 a—p . g cr_ 

 9 p v\ 

 " 2. Steady FLow in a Uniform Tube. 



3. Law of Resistance to the Movement of a Sphere in Sinuous Motion. 



II. 



4. Motion of a Fluid Sphere. 



5. Observations of the Terminal Velocities of Small Bubbles. 



0. Observations of the Terminal Velocities of Small Solid Spheres. 



7. Conclusions from these Observations, 



V = /t ( <y ~P • ff\* a ~ . 



y p * v\ 

 in. 



8. Photographic Method of Determining Velocities. 



9. Accelerated Motion of the Falling Sphere. 



10. Terminal Velocity of the Falling Sphere. 



11. Law of Resistance, 



T, = kpa 2 Y 2 . 



12. Fall of an Oiled Sphere. 



13. Summary and Conclusion. 



I. 



1 . Theoretical. 



THE motion of a solid sphere falling freely under gravity 

 in a viscous fluid has been investigated theoretically by 

 Stokes f. The sphere will attain a constant terminal velocity 

 * Communicaied by P/of. J. J. Thomson, F.R.S. 

 t Camb. Phil. Trans, vol. ix. 1850. 



