﻿978 Mr. A. I. Steven on the Composition of Two Simple 



of phonic wheel controlled by a tuning-fork is recommended.) 

 If the wheel be running evenly at this rate, a person standing 

 a few feet away and looking at the string through the slits 

 as they pass will now see stationary a few waves of the com- 

 pounded vibrations. If one fork only is sounding, he will 

 see one of the components as a simple sine curve. Indeed, 

 he will see a replica of the motion of the string as a whole, 

 the effect being what would be produced by very greatly 

 diminishing the length of the string without affecting its 

 transverse motion. The explanation evidently is that all 

 points of the string at any instant are in the same phase, and 

 as the slit passes round, the part of the string viewed only 

 differs from that previously seen by the phase having 

 advanced a little in the time taken by the slit to pass round. 

 In the same way, if the wheel go either too slowly or too 

 quickly the motion will appear to progress in the backward 

 or forward direction. 



The figures 1 and 2 given on the plate (XVI.) are photo- 

 graphs through the stroboscope of the string in the case where 

 the two tuning-forks are in the ratio 1 : 3. The lower fork 

 had a frequency of 32 vibrations per second, and controlled 

 the stroboscope, and that of the higher fork was approximately 

 96. The slight difference from the exact ratio gave rise to a 

 continuous change of phase difference between the two 

 vibrations, which was readily seen, as the curves gradually 

 changed from the one form to the other. The photographs 

 show the curves diminished to about one third of their 

 apparent size. They represent : — 



(1) The case when a trough of the wave motion of 

 smaller period falls on a crest of that of larger period, and 

 (2) when crest falls on crest. Though these photographs 

 are exceedingly good they are more blurred than when the 

 phenomena are observed. This is due partly to the difficulty 

 of keeping the stroboscopic wheel in steady motion (for, 

 of course, if it went for a short time either too quickly or 

 too slowly, a displacement of the figure occurred), and 

 partly to the varying phase difference, which made it 

 necessary to expose the plate several times when the phase 

 was approximately correct. 



In order to make the phenomena visible to a large 

 audience, I find that the stroboscopic wheel must be 

 replaced by a rotating mirror. If a very narrow vertical 

 beam of light from a lantern be allowed to fall on the 

 string, and the image of the bright part of the string observed 

 in the mirror, which is rotated about a vertical axis, it 

 will trace out the time-displacement curve of a point on the 



