﻿of Radiation in any Material System. 533 



H 

 or if/ varies as e m , 



E x = 8wUe\- 4 ...... (76) 



§8. Absorption and Refraction of a Simple 

 Harmonic Wave-Train. 



The method of normal functions so far used gives no 

 information as to the behaviour of a simple harmonic wave- 

 train advancing into the medium. The defect must be 

 supplied before any theory of the distribution of energy can 

 be brought to the test of experiment. I shall show how the 

 refractive index, absorption, and rotation of the plane of 

 polarization can be expressed in terms of functions involving 

 / the distribution-function. 



The equation for Fj is as before 



(V 2 -JJ)^=?J^^. ■ . (28) 



where ( V 2 -* 2 ) F + 4tt^ = v(^) . (24) 



Div.F^O (18) 



Suppose a simple harmonic wave-train moves along the 

 axis of z so that ¥ 1 is a function of z and t only. Then (18) 

 shows that the component of Fj normal to the wave-front is 

 zero, 



Fj= (F,, G 1? 0) &*-***-** .... (77) 



This value must finally be supplemented by a conjugate 

 imaginary. 



(28) and (24) give 



/* \(<P l*\ '/ 1^\4^U 



The term in V(""j7J depends merely on the atomic 



structure of the medium. For a plane wave propagated 

 regularly its average value over the wave-front vanishes. 

 Neglecting scattering, therefore, we may replace (78) by 



Id 1 \i& 1 d*\ / 1 d*\±1rp\X , 7Q . 



