444 Lord Rayleigh on the Light emitted from a 



in which the effect is to be estimated. The n 2 term corre- 

 sponds to what would be due to a continuous uniform 

 distribution over the volume of the same total source, and 

 it may be regarded as due to the discontinuity at the surface. 

 In addition there is a term in n, due to the lack of complete 

 uniformity of distribution and issuing from every part of 

 the interior. 



Thus far we have been considering the operation of given 

 unit sources, by which in the case of sound is meant centres 

 where a given periodic introduction (and abstraction) of fluid 

 is imposed. We now pass to the problem of equal small 

 obstacles distributed at random and under the influence of 

 primary plane waves. It is easy to recognize that these 

 obstacles act as secondary sources, but it is not so obvious 

 that the strength of each source may be treated as given, 

 without regard to the action of neighbours. I apprehend, 

 however, that this assumption is legitimate ; in the case of 

 aerial waves it may be justified by a calculation upon the 

 lines of ' Theory of Sound,' § 335. For this purpose we may 

 suppose the density a of the gas to be unchanged at the ob- 

 stacles, while the compressibility is altered from m to m\ so 

 that the secondary disturbance issuing from each obstacle is 

 symmetrical, of zero order in spherical harmonics. The 

 expressions for the primary waves and of the disturbance 

 inside the spherical obstacle under consideration remain as 

 if the obstacle were isolated. But for the secondary dis- 

 turbance external to the obstacle we must include also that 

 due to neighbours. On forming the conditions to be satisfied 

 at the surface of the sphere, expressing the equality on the 

 two sides of pressure (or potential) and of radial velocity, 

 we find that when the radii are small enough, the ob- 

 stacle acts as a source whose strength is independent of 

 neighbours. 



The operation of a cloud of similar particles may now be 

 deduced without much difficulty from what has already been 

 proved. We suppose that the individual particles are so 

 small that the cloud has no sensible effect upon the progress 

 of the primary waves. Each particle then acts as a source of 

 given strength. But the initial phase for the various par- 

 ticles is not constant, being dependent upon the situation 

 along the primary rays. This is, in fact, the only new feature 

 of which we have to take account. 



Perhaps the most important difference thence arising is 

 that there is no longer equality of radiation in various direc- 

 tions, even from a spherical cloud, and that, whatever may 



