[170] PROFESSOR STOKES, ON THE 



In order that two streams of scattered light may be capable of interfering, it is necessary 

 that they should be scattered, in passing and repassing, by the same set of particles. Two 

 streams which have been scattered by two different sets of particles, although they may 

 have come originally from the same source, behave with respect to each other like two streams 

 coming from different sources. 



According to this law, in all calculations relating to the colours of thick plates, we must 

 consider the elementary system of rings or bands corresponding to each element of the dimmed 

 surface of the mirror, and then conceive these elementary systems superposed. We must not 

 compound the vibrations corresponding to streams which have been scattered by different 

 elements, and then find the resulting illumination. 



28. The reason of this law will be apparent if it be considered that particles of dust, &c. 

 small as they may be, are usually large in comparison with waves of light, so that the light 

 scattered at entrance, taken as a whole, is most irregular ; and the only reason why regular 

 interference is possible at all is, that each particle of dust acts twice in a similar manner, once 

 when the general wave is going, and again when it is returning. 



To examine more particularly the mode of action, let P be any particle of dust, and 

 consider a wave of light which emanates from any particular element of the flame or source of 

 light whatever it be. When this wave reaches P and proceeds along it, a portion is reflected 

 externally in all directions, and with this we have nothing more to do. When the wave 

 has just passed P, we may conceive it as having in a certain sense a hole in its front, corre- 

 sponding in size to P, that is to say, there will be a certain portion of the surface forming the 

 general front of the wave where the ether is quiescent. As the wave proceeds, the disturbance 

 diverges from the neighbourhood of this hole by regular diffraction, and when the disturbance 

 reaches the quicksilvered surface the general wave suffers reflection, as well as the secondary 

 waves, which, having diverged from the neighbourhood of P, do not constitute a wave with an 

 unruffled front, in consequence of the absence of secondary waves diverging from the hole, 

 which would be necessary to complete a wave with a front similar to that of the original wave. 

 If we consider any particular diffracted ray, the chances are that on its return it will get 

 out by regular refraction, since the dust is supposed to cover a moderate portion only of the 

 first surface of the mirror. A portion of the original wave which entered the glass by regular 

 refraction at a certain distance from P, after regular reflexion is incident on P from within. 

 The chances are that the portion thus incident on P does not correspond to a spot where 

 the front of the wave is materially ruffled by diffraction at entrance, so that in considering 

 the wave incident on P we may neglect the previous diffraction. The wave, then, just 

 after refraction, is incident on P, by which a portion is reflected back again in various direc- 

 tions, with which we have nothing to do, a portion, it may be, is refracted or absorbed by P, 

 and the remainder passes on. The wave so passing on diverges from the neighbourhood of 

 P by ordinary diffraction, and the two diffracted streams, having been diffracted in a similar 

 manner by the same particle, are in a condition to interfere. The similarity of the two 

 diffractions will be considered in more detail in the next section. 



