﻿Regular Reflexion of Light by Gas Molecules. 629 



regularly reflected waves, and the ratio of their energy to 

 that of the incident train. Now in a medium such as we 

 consider, plane waves retain their simple character as we 

 trace them back, even up to the plane of vibrators in which 

 they originated. At points close to, or in, that plane, there 

 will naturally be immense inequalities of disturbance, but all 

 these inequalities belong to the irregular motion, and have 

 nothing to do with the regular waves. A recognition of 

 this fact leads to great simplification in the problems which 

 here concern us : for example, a three-dimensional swarm of 

 vibrators can be divided up into laminae, each of which, in 

 regard to normally incident plane waves, behaves in a very 

 simple manner. 



10. Suppose, now, that there is a completely irregular 

 distribution of secondary vibrators over the plane of yz, the 

 number per unit of area being a ; and for the moment 

 suppose a to be small enough to justify the assumption that 

 all the vibrators send out disturbances of the same amplitude 

 and phase when excited by the primary waves (1). In § 24 

 it will be shown that this restriction can be removed. 



11. Let the secondary disturbance due to the vibrators be 



C 

 ^r' = % — cos (pt — vr n — y) ; . . . . (6) 



then it is the plane waves comprised in (6) that have to be 

 determined. In the diagram is the origin , P a point (#, 0, 0) , 



?— * // 0/ 2 + * 2 ) ^ ne distance from to any point Q in the 

 plane of yz, and PQ = s. As in the figure, draw two circles 

 with as centre and radii p, p + Jp : the annulus between 



