of Energy in the Spectra of Solids. 427 



Since the same value 8 corresponds to the values <f> and ?r— <£ 

 of the angle cp, the probability that an atom whose initial dis- 

 Ffe. 1. 



tance from the centre of the sphere lies between r and r + dr 

 shall strike the spherical surface at an angle lying between 8 

 and 8 -t- dS, is given by the expression 



. , ,. p 2 sin S cos 8^8 

 sm <fr#=^— 7 (2) 



We obtain the same probability for any atom whatever by 



dr 

 multiplying this expression by — , and extending the total to 



all possible values of r for a given 8 ; that is to say, by 

 integrating with reference to r between the limits p sin 8 and p, 

 C° p sin 8 cos 8 dS (ir A 



*H 7— T=T = ^ ) cos ■ ' (3) 



P 



S Sill u 



r 



It is evident that this probability has a maximum value when 

 8 = ; that is to say, that motions along diameters of the 

 spheres of displacement are the most probable. It will happen 

 most frequently that, between two neighbouring disturbances, 

 each atom will describe trajectories differing bat little from 

 the stellar form (fig. 2). 



Fisr. 2. 



If we suppose that each periodic change in the motion of 



