34 REFLEXION AND REFRACTION. 



It is plain that if the revolving mirror were for a moment 

 to rest in this position, the ray, after a second reflexion by it, 

 would return precisely by the path by which it came. But, 

 owing to the progressive movement of light, the mirror de- 

 scribes a certain small angle round its axis, in the interval 

 between the two appulses of the ray ; and the ray, after the 

 second reflexion, will deviate from its first position, by an 

 angle which is double of that described by the mirror in the 

 interval. Hence, if this angle can be observed, the velocity 

 of light is known. 



For, if t be the time taken by the light to traverse the 

 interval of the two mirrors, forwards and backwards, the 

 angle described by the mirror in that time will be = w, w de- 

 noting the angle described by the mirror in the unit of time. 

 Hence, the angle described by the reflected ray in the time t, 

 or the deviation, is 2wt. Let this angle be denoted by a, and 

 there is 



But the corresponding space is double the distance between 

 the two mirrors, or 2a. Consequently, the velocity of the 

 light is 



M. Foucault has been enabled to observe an appreciable 

 deviation of the reflected ray, when the distance of the two 

 mirrors was 4 metres, and the revolving mirror made only 

 25 turns in a second. And as such a mirror can be made 

 to revolve 1000 times in a second, it is obvious that the 

 time taken by light to traverse even this short distance is 

 capable of being measured with precision. 



(42) To apply this to the question at issue, we have only 



