i 



THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[SIXTH SERIES.] 



JUNE 1911. 



LXXXII. On the Motion of Solid Bodies through Viscous 

 Liquid. By Lord Rayleigh, OJL, F.R.S.* 



§ 1. npHE problem of the uniform and infinitely slow 

 JL motion of a sphere, or cylinder, through an un- 

 limited mass of incompressible viscous liquid otherwise at 

 rest was fully treated by Stokes in his celebrated memoir on 

 Pendulumsj. The two cases mentioned stand in sharp 

 contrast. In the first a relative steady motion of the fluid 

 is easily determined, satisfying all the conditions both at the 

 surface of the sphere and at infinity; and the force required 

 to propel the sphere is found to be finite, being given by the 

 formula (126) 



-F^GiTfiaY, (I) 



where jju is the viscosity, a the radius, and V the velocity of 

 the sphere. On the other hand in the case of the cylinder, 

 moving transversely, no such steady motion is possible. If 

 we suppose the cylinder originally at rest to be started and 

 afterwards maintained in uniform motion, finite effects are 

 propagated to ever greater and greater distances, and the 

 motion of the fluid approaches no limit. Stokes .shows that 

 more and more of the fluid tends to accompany the travelling 

 cylinder, which thus experiences a continually decreasing 

 resistance. 



* Communicated by the Author. 



t Camb. Phil. Trans, ix. 1850 ; Math. & Phys. Papers, vol. ii : . p. 1. 



Phil. Mag. S. 6. Vol. 21. No. 126. June 1911. 2 Z 



