﻿6 Mr. A. E. McLeod on Unsteady Motion produced 



of cylinder, all angular velocities X2, and all incompressible 

 fluids. The significance of vt/c 2 is of interest. According 

 to (6) and (7), the behaviour of a cylinder of liquid is 

 exactly similar to that of a cylinder of double the radius 

 in four times the time. Larger eddies should therefore 

 be of relatively longer duration than smaller eddies. If 

 in these same cylinders we have different liquids, the liquid 

 in the larger cylinder must have a viscosity four iimes that 

 of the liquid in the smaller cylinder, in order that (f> may 

 have the same value for the same values of X2, r/c, and t. 

 For air i> = 0*14, and for water ^ = 0'011 at ordinary tempe- 

 rature, the ratio being about 12. Ignoring the compres- 

 sibility of air, eddies of the assumed kind should die away 

 much faster in air than in water, the values of c and 12 being 

 the same. 



According to (6) and (7), the rates of growth and decay 

 of (£/X2 in the cylinders are independent of 12. We shall 

 see from the experiments that this is true only when 12 is 

 very small, or when the radius c is a small fraction of the 

 length of the cylinder. 



§ 3. Experiments. 



In the experiments which have been made, a brass 

 cylinder, bored as accurately as possible and at least 

 two diameters in length, was rotated about a vertical axis 

 at constant speed. The cylinder was filled to within 1 cm. 

 of: the top with ordinary tap-water ; and the observations 

 consisted in timing through a measured angle by stop- 

 watch, lycopodium particles floating on the surface, and 

 so deducing the angular velocity <jf> at the radius r/c 

 selected. The time of the stop-watch observation was also 

 noted on a watch, in order to get the value of t from the 

 instant of starting or stopping the cylinder. To time the 

 lycopodium particles with more accuracy, a horizontal plane 

 glass plate was mounted just over the cylinder. This was 

 marked with ink in circles centring on the axis of rotation. 

 The radii of the circles had the values r/c =0*3, 0*5, 0*7, and 

 0*9, and a fifth circle was added at r/c= l'O to aid in centring 

 the plate over the cylinder. Straight lines, 45° apart, through 

 the centre of the circles served to indicate the angles through 

 which the particles were timed. A large plane mirror, 

 inclined at 45°, was placed on the glass plate to enable 

 observations to be made from the side. 



To obtain freedom from vibration, the driving-motor and 



