﻿THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



I. The Unsteady Motion 'produced in a Uniformly Rotating 

 Cylinder of Water by a Sudden Change in the Angular 

 Velocity of the Boundary. By A. R. McLeod, M.A., 

 Fellow of Gonville and Caius College , Cambridge *. 



IN the following paper a comparison is made between 

 the observed angular velocities in a rotating circular 

 cylinder of water, and those calculated by two-dimensional 

 theory in which the effects of the base and the free surface 

 are neglected, and each particle of water is assumed to move 

 in a circle about the axis of rotation. The two cases dealt 

 with are those of unsteady motion in which the cylindrical 

 containing-wall is suddenly started from rest, or suddenly 

 stopped when, with the water, it is rotating uniformly. The 

 measurements are all of surface velocities, because the use of 

 lycopodium particles floating on the surface was necessary, 

 as liquid globules of the same density as the water would 

 not remain at the same depth for any length of time. 

 Three cylinders of approximate diameters 5 cm., 15 cm., 

 and 25 cm. were used, and three angular velocities, viz. 

 36 r.p.m., 10 r.p.m., and 1^ r.p.m. The small cylinder 

 was four diameters, and the other two cylinders were two 

 diameters long. The observed velocities show a departure 

 from theory, which increases with angular velocity and 

 with the size of the cylinder, but which tends to vanish 

 at very low speeds. The discrepancy is much greater 



* Communicated by the Author. 

 Phil Mag. S. 6. Vol. 44. No. 259. July 1922. B 



