XVII. 



ON THE VELOCITY OF LIGHT AS DETERMINED BY 

 FOUCAULT'S REVOLVING MIRROR. 



[Nature, vol. xxxm. p. 582, April 22, 1886.] 



IT has been shown by Lord Rayleigh and others that the velocity 

 with which a group of waves is propagated in any medium may 

 be calculated by the formula 



dlogV^ 



dlog\ 



where V is the wave-velocity, and X the wave-length. It has also 

 been observed by Lord Rayleigh that the fronts of the waves reflected 

 by the revolving mirror in Foucault's experiment are inclined one to 

 another, and in consequence must rotate with an angular velocity 



dV 



d\ a > 



where a is the angle between two successive wave-planes of similar 

 phase. When dV/d\ is positive (the usual case), the direction of 

 rotation is such that the following wave-plane rotates towards the 

 position of the preceding (see Nature, vol. xxv. p. 52). 



But I am not aware that attention has been called to the important 

 fact, that while the individual wave rotates the wave-normal of the 

 group remains unchanged, or, in other words, that if we fix our 

 attention on a point moving with the group, therefore with the 

 velocity U, the successive wave-planes, as they pass through that 

 point, have all the same orientation. This follows immediately from 

 the two formulae quoted above. For the interval of time between 

 the arrival of two successive wave-planes of similar phase at the 

 moving point is evidently X/( V U), which reduces by the first for- 

 mula to d\/dV. In this time the second of the wave-planes, having 

 the angular velocity adV/d\, will rotate through an angle a towards 

 the position of the first wave-plane. But a is the angle between the 

 two planes. The second plane, therefore, in passing the moving point, 

 will have exactly the same orientation which the first had. To get a 

 picture of the phenomenon, we may imagine that we are able to see 

 a few inches of the top of a moving carriage- wheel. The individual 

 spokes rotate, while the group maintains a vertical direction. 



