﻿by Change in Angular Velocity. 13 



the centre regularly. The effect of these eddies was observed 

 to cause a shifting of the curve for <j>/£l in the direction of 

 a greater <£ for the same value of vtjc 2 . In the same case, 

 secondary eddies were observed about the "4 circle when the 

 motion had reached the centre. Although mean velocities 

 were recorded (median Hue of the band of points), the effect 

 is shown in fig. 17 by the wavy appearance of tie two upper 

 curves. 



When the cylinder is stopped, the water continues to 

 rotate until the irregular motions, generated near the cylinder 

 wall, have had time to extend inwards. Small eddies then 

 travel about, and the central axis of rotation wanders con- 

 siderably and often seems to disappear temporarily amid 

 cross-currents. The motion is very irregular except at the 

 low speed, and even in this case some irregularity al\\ ays 

 remains. The lycopodium particles do not follow the circles 

 for very long, and are usually moving at an angle to them. 



With the large cylinder at the high speed, the velocity 

 immediately after stopping the cylinder seemed to give 

 stability and to aid in preserving the circular character 

 of the motion ; but when the kinetic energy had somewhat 

 diminished, eddying became more noticeable. 



On the curves mentioned in § 3 in which <£/H is plotted 

 against vtjc 2 , the bands of points are much narrower in the 

 " starting " experiments than in the others, and determine 

 the position of the median line easily to *001 in the value of 

 vtjc 2 in most cases. For the " stopping" curves, the limit 

 of error may be two or three times this occasionally. One 

 noticeable effect is that the band is narrow when the velocity- 

 gradient has a considerable value, i. e. when the curves in the 

 figures slope steeply. In these cases considerable momentum 

 is being transferred through the water, and there will be 

 considerable shearing stress and vorticity, and the stability 

 might therefore also be considerable. As soon as the 

 velocity-gradient becomes small, the band of points broadens. 

 For example, in the " starting " curves the bands are some- 

 times very narrow until the value of <j>/fl has risen to 0*9, 

 when they broaden out. Conditions seem to favour irre- 

 gularity at the centre (axis) of the cylinder where the 

 velocity-gradient vanishes. On the axis the stability is a 

 minimum. In the "stopping" curves the bands are nar- 

 rower the greater the angular velocity O, i. e. the greater 

 the vorticity of the water, especially near the cylinder wall 

 where the instability originates. 



The observational curves show that viscosity alone is not 



