■S20 Mr. G. H. Livens on Rotational 



vectors by E and H respectively, and the corresponding 

 fluxes by D and B, these relations are expressed by the 

 following vector equations : 



--H = CurlE, il) = CurlH. 



c c 



The Herz-Heaviside units are adopted. 



The influence of the molecules of the medium expresses 

 itself only on the form of the relations, depending on the 

 constitution of the medium, connecting each flux with the 

 corresponding force. Since in light phenomena we can 

 always assume B = H, we need only to investigate further 

 the relation between D and E. This is obtained in Drude's 

 theory by a statistical analysis of the motions of the contained 

 electrons, to which the electric flux due to the presence of 

 the medium is directly reducible. These electrons are 

 supposed to be connected to the molecules of the medium 

 by quasi-elastic forces, and are resisted in their motion by 

 frictional forces proportional to the velocity. In the present 

 discussion we shall neglect these frictional forces, so that the 

 equations of motion of the electrons are of a type 



m 



(x + n Q 2 x) = eYjxy 



wherein (#, ?/, z) are the components of the displacement of 

 the electron from its position of rest ; m its mass and c the 

 charge on it ; mn 2 is the parameter of the quasi-elastic 

 force. 



Lorentz has, however, shown* that the force on a contained 

 electron due to the electric field is not completely represented 

 by <?E. We must, in fact, add a term ef(P), where /(P) 

 denotes an undetermined vector function of the polarization 

 P of the medium. To a first approximation it is shown that 

 /(P) = aP, where a is very nearly equal to J- ; but in second 

 order effects of the kind under discussion other terms may 

 occur, [n order to explain the broad general facts of the 

 phenomenon at present under review, it is, in fact, necessary 

 to assume, after Lorentz, that 



/(P)-aP-r-^CurlP. 



The constant b being another physical constant of the 

 medium. This second order term 6 Curl P, which has its 

 origin in an intrinsic chiral structure of the molecule or 



* Versuch einer Theorie der elekt., u. opt., Erscheinungen fyc, (Leipzig, 

 1906) pp. 78-81. 



