F. 



470 Mr. G. H. Livens on the Intrinsic 



charge on it: mn r 2 is the parameter o£ the quasi-elastic force,, 

 and JF the force on the contained electron due to the electric 

 field in the incident wave. 



We treat always the standard case of the propagation of 

 plane waves of light of frequency n along the axis of z, so 

 that all the functions depend on t and z by the factor 



e \ c J where /* is the index of refraction of the medium 

 for the light used, and c the velocity of radiation in vacuo. In 

 such cases each electron will vibrate more or less freely with 

 a period n, so that 7c = —n 2 .v, and therefore also 



,_ e l m w . 



,C = g 2 2 x , 



n r - — n 



and if P is the polarization intensity in the medium we 

 know that P r = 2 e%, and we therefore deduce that, 

 vectoriallv. 



the sum being taken per unit volume over all contained 

 electrons. This is the fundamental relation from which all 

 the circumstances of the propagation of the plane wave 

 above specified are deduced. 



What is the interpretation of F? This is where the 

 theories differ, and we cannot do better than examine them 

 in turn, taking each on its merits. 



1. Drude's Theory. — In the simple dispersion theory for 

 isotropic media Drude simply takes 



F = E, 



so that when he desires to extend the theory and to introduce 

 terms representing the effect of the asymmetric constitution 

 of a naturally active medium, he can admit in F only terms 

 depending simply on the differentials of the electric force 

 components. He takes, in fact, in this general case, 



F = E + &curlE, 



the second term on the right being of course merely a second 

 order term whose form is determined and justified by the 

 fundamental characteristics of the phenomena under review. 

 As I understand such a theory, it represents the optically 

 active substance as modifying by its presence the ordinary 

 structure of the sether, thereby imparting to it a slight 

 secondare chiral structure. 



