234 
DR. J. YOUNG AND PROFESSOR G. FORBES ON THE 
when the toothed wheel is in position and revolving slowly, but fast enough to cause 
the persistence of visual impressions to prevent us from distinguishing the separate 
teeth, is E(1— k). 
When the speed is increased the intensity depends upon the time taken by light to 
go to the distant reflector and to return. As the speed of the toothed wheel is 
gradually increased the star of light diminishes and increases in regular phases. 
If the teeth be wider than the spaces the maximum light is less than -|E, and the 
light is eclipsed not only at certain critical speeds, but also during a change of speed 
of rotation, which may be considerable if h be much greater than J. 
If the spaces be wider than the teeth the maximum light is greater than |E, and 
the light is at no speed completely eclipsed, the minimum light being considerable if 
k be much less than jj. 
If the teeth of the wheel be not perfectly uniform, and if some teeth are wider than 
others, this will alter the law according to which the intensity varies with the speed 
of rotation. But, if the inequalities be not very great indeed, it is only in the neigh¬ 
bourhood. of the maxima and minima that its influence is shown. The general effect is 
to increase the intensity of light at the minimum and to diminish it at the maximum. 
If there be no very great irregularities in the width of the teeth, then (1) the 
diminution of intensity of the light with a definite increase of speed in the odd 
phases is perfectly constant, provided that in the interval of time taken by light to 
perform the double journey, the advancing part of each tooth of the wheel passes 
beyond the advancing part of the r th tooth in front of it, and does not reach the 
following part of the r+1 | th tooth nor its following part reach the advancing part of 
the r xh tooth in front, where r is any whole number from zero upwards. “ 
Similarly, if there be no very great irregularities in the width of the teeth, then 
(2) the increase of intensity of the light with a definite increase of speed in the even 
phases is perfectly constant, provided that in the interval of time taken by light to 
perform the double journey the advancing part of each tooth in the wheel passes 
beyond the following part of the r th tooth in front of it, and does not reach the 
advancing part of that tooth. This is in the condition where the width of a tooth is 
less than that of a space. If the width of a tooth be greater than that of a space 
* "We mean, by this notation, that if in the figure the arrow represents the direction of rotation of 
the toothed wheel a is the advancing and / the following part of that tooth, x, y, and z are the third, 
fourth, and fifth teeth in front of it. 
