﻿538 Mr. W. Ellis Williams on the 



is altogether more like that given by the ; ' irrotational " 

 solution ; in fact, at a distance from the sphere it is very 

 similar to that which would be produced by the motion 

 of a pear-shaped figure formed by the sphere and the fluid 

 which is moving along with it. This is the highest velocity 

 for which stream-lines could be mapped : photographs were 

 indeed taken with velocities up to twice this value, but the 

 lines were too faint to be measured. They do not indicate 

 any important change in the form of the stream-lines. 



The motion shown in Photo F (PL IX.) is altogether different 

 from the others and was obtained with a sphere moving in 

 water at the rate of *074 cm. per sec. giving Ya/v = 7'l. 

 This is the lowest velocity for which photographs could be 

 obtained in w^ater ; at lower velocities the motion is masked 

 by irregular currents in the water due to temperature and 

 other effects. The peculiar form of the stream-lines in this 

 diagram may be due to some such effect, but the regularity 

 with which the spreading out of the stream-lines behind the 

 sphere appeared in a large number of different photographs* 

 seemed to suggest that it may be due to some kind of 

 instability appearing at this velocity. 



It will be noticed that even at the highest velocity of 

 fig. 8 we do not get the irregular eddying motion which 

 has been observed in experiments in air and water channels. 

 This may be due to the comparatively small values of the 

 velocity employed in the present experiments, the eddies 

 being due to an instability of the motion which only appears 

 at values of the velocity beyond the highest used in these 

 experiments ; it is also possible that the turbulence of the 

 stream of air or water in the channel may affect the 

 motion . 



If, however, instead of a sphere we take a flat plate with 

 its plane perpendicular to the direction of motion, eddies are 

 formed and are shown very distinctly in the photographs, of 

 which two are reproduced in Gr & H (PI. IX.). In glycerine* 

 the motion is very similar to that produced by the sphere 

 under the s;ime circumstances: in fact, the motion at low 

 velocities is, except in the immediate neighbourhood of a 

 moving body, practically independent of its shape. As the 

 velocity changes beyond the critical value, the stream -lines 

 change in very much the same way as for the sphere. 

 Photo G for a velocity '2 cm per sec. is of the same type 

 as C, but beyond this Value the development of the motion 

 is very different. Photo H shows the motion for a velocity 

 of "59 cm. per sec, and it will be seen that we have here 

 a full development of eddying motion. The "wake*' is 



