VELOCITY OF WHITE AND OF COLOURED LIGHT. 
235 
the condition is that in the same interval of time the following part of each tooth 
should pass beyond the advancing part of the r th tooth beyond it, but should not 
reach the following part of the r+1 | th tooth. 
It is seen then that with a wheel which is carefully cut the rate of change of 
intensity of the light with change of speed of the toothed wheel is quite constant at 
that part of a phase which is about half way between the maximum and minimum 
brightness. 
Our method of experimenting has reference to this part of a phase alone. 
Let us call the period,— 
From original brightness to the first extinction, the first phase; 
From first extinction to next full brightness, the second phase; 
From second full brightness to second extinction, the third phase ; 
and so on. 
Let N be the number of revolutions per second made by the wheel when the first 
central eclipse is attained. 
Let m be the number of teeth in the wheel. 
Let D be the distance from the toothed wheel to the distant reflector. 
Let I be the intensity of the star of light when the number of revolutions a second 
made by the toothed wheel is n. 
Let Y be the velocity of light. 
9J) 
Let r be the time taken by light to perform the double journey, r=^r. 
1. In the case of a wheel with teeth of the same width as the spaces (i.e., /c=|), 
~ is constant, then 
an 
I = CM2 + C 
an 
But if we be considering the first phase, then when n= 0, I=TE ; and when w=N, 
1=0. 
Therefore 
C=P, «=-*| 
and 
I= -i|«+P 
dl_ 2 E 
dn — sTyr 
2. In the case of a wheel with any width of teeth, the value of —, in the middle of 
dn 
an odd phase, is the same as in the last example, but the maximum intensity is 
E(l — k). Suppose that it is the p ih phase which we are considering, p being odd; 
then 
2 H 2 
