﻿of Radiation in any Material System. 515 



the velocities-^-, &c, and also depends upon the coordinates 



g r , &c. e is a time taken large enough to ensure that all 

 elements in the integral with respect to e are included 

 which are coordinated with (j> t - The average values of the 

 functions at time t are of course to be taken on both sides 



o£ ( 5 ),-. 



If /is a function of II only say f(H) then (5) reduces to 



271 



= -S7r\- i i(fct> t \ ^(t-e)Cos( 2 ^e)dedY 2n . (7) 



And if /varies as e~ no as kinetic theory requires 



£a = 8ttR<9a,- 4 (8) 



The method by which (5) is reached does not give that 

 direct information as to the behaviour of a simple wave- train 

 which is required if the results reached are to be tested by 

 their accord with experimental evidence. I show that a plane 

 wave can advance in any medium with the electric intensity 

 in the wave-front. Let the electric intensity E be given by 



E = (E l9 E 2 , 0) ***-*•*-**. 



So that the wave advances in the direction of the axis of z. 

 Then 



E 1 /p_^ + 2^- r ^ + ^nE 1 -f$ 12 E 2 = . . (9) 



E/P-n* + 2tifen+ O + <E>aiEi + <S> 22 E 2 = 0. . (10) 



And the functions <J> U , 0, 2 , <l> 21 , <X> 22 are determinate in 

 terms of f and the wave-length. They are of form similar 

 to that which stands on the left of (5). Where there is no 

 rotation of the plane of polarization 



<&(12) = $>(21) = 0. 



From (9) and (10) the refractive index and the coefficient 

 of absorption are determinate when the distribution / is 

 known. 



The method used throughout is to treat the radiation a* 

 a small perturbing influence in the motion of the material 

 system. This is made possible by the absorption into that 

 system of the whole intermolecular field which arises fro 

 charge in the immediate neighbourhood of any point. 



2 M 2 



m 



