﻿532 Mr. W. Ellis Williams on the 



Tin-* arrangement of the illumination ami exposure was 



somewhat different for the two troughs. The small trough 

 being used chiefly for low velocities, the exposures required 

 were long enough to be made by hand, and the beam of light 

 was strong enough to illuminate the whole field of motion. 

 Considerations of symmetry show that the motion must he 

 the same in any plane passing through the axis defined by 

 the path of the centre of the sphere, and hence it is sufficient 

 to investigate the motion in one such plane. A beam of 

 light from the condenser placed in front of the arc-lamp E 

 is focussed on a slit G and then rendered approximately 

 parallel by passing through a cylindrical lens formed by a 

 tall narrow beaker full of water ; it is then narrowed down 

 by a vertical slit placed on the end of the trough, and 

 passes through the trough as a thin vertical sheet of light 

 illuminating the central plane of the liquid in the trough. 

 The camera is placed directly in front of the trough and is 

 focussed on the sphere and the illuminated plane. If a plate 

 is exposed for a short time while the sphere is in motion, 

 each little aluminium particle will trace out a curve on the- 

 plate. This curve will be practically a short straight line, 

 and the ratio of its length to that of the trace of the sphere 

 itself will give the velocity of the particle, which, owing to 

 the lightness of the particle, is also that of the surrounding- 

 fluid. The photographs A-C reproduced in Plate IX. give an 

 idea of the results obtained by this method. 



The larger trough was used for the higher velocities, and the 

 above method could not be adopted with it as the beam of light 

 had to be made much more intense to get good photographs, 

 and hence only a small portion of the field could be illumi- 

 nated, and it was necessary to take several photographs of 

 different parts of the field and then combine them together to 

 give a stream-line diagram. The beam of light in this case 

 passes through both a cylindrical and a convex lens and enters 

 the trough as a convergent beam with a vertical-line focus 

 near the centre of the trough. In the neighbourhood of this 

 focus the beam gives a very strong illumination over a field 

 about 2 cm. each way, the average thickness of the illuminated 

 plane being about 2 mm. By suitably inclining the beam and 

 altering its focus by moving the lenses, the illuminated 

 portion could be brought to any desired part of the trough, 

 and thus, by taking a number of photographs, the whole of 

 the central plane can be covered. The camera is placed in 

 front of the trough as before, but the exposure is made by a 

 shutter attached to the lens which is automatically released 



