﻿530 Mr. W. Ellis Williams on the 



the moving sphere has been observed, and it has been found 

 possible to photograph the motion and to map out the stream- 

 lines for velocities up to 720 times the critical value. At 

 the same time certain mathematical solutions have been 

 obtained which serve to throw some light on the changes 

 which take place in the form of the motion as the velocity 

 increases beyond the critical value. We shall first describe 

 the methods by which the stream-lines were experimentally 

 observed and measured, and then proceed to describe the 

 results and to compare them with the solutions obtained. 

 The greater -part of the experiments was carried out with 

 a sphere moving in water, but in order to obtain measure- 

 ments over as wide a range as possible it was found desirable 

 to use liquids of different viscosities. The advantage of doing 

 this lies in the fact that irregular currents are set up in the 

 liquid by the inevitable slight differences of temperature of 

 different parts of the trough, and accurate measurements are 

 impossible if these currents have a velocity which is an 

 appreciable fraction of the velocity of the sphere. It was 

 found that the lowest practicable velocity in water was about 

 1 cm. per sec, which gave Va/v = 23, and it was thus im- 

 possible to work in the immediate neighbourhood ot the 

 critical velocity. After trying a number of different liquids, 

 it was found that good results could be obtained by using 

 mixtures of glycerine and water in different proportions 

 according to the viscosity desired. For pure glycerine the 

 value of v is about 15 and all values between this and 013, 

 the value for water, may be obtained by suitably adjusting 

 the proportions of water and glycerine in the mixture. The 

 viscosity of the mixture was determined in each case by 

 means of an Ostwald viscosimeter. 



The experiments were carried out with two rectangular 

 troughs of similar shapes but of different dimensions. The 

 smaller trough was of glass and measured 19x10x9 cm., 

 and was used for the glycerine experiments, while the larger 

 trough was of wood with glass face and ends and measured 

 46x18x17 cm. The radii of the spheres used were 1*25, 

 •88, and -40 cm. respectively. The experimental results 

 obtained with different spheres and liquids can be correlated 

 by means of the dimensional theorem : — The motion in any 

 two liquids with geometrically similar boundaries is similar 

 when the quantity Va/v is the same in the two cases. In 

 what follows, therefore, the value of this quantity is given 

 for each result. In the experiments Va/v varied from *01 

 to 720. 



