Rotational Optical Activity in Isotropic Media. 995 



B, these relations are expressed by the following vector 

 equations 



--B=CurlE, if) = CurlH, . . . (1) 



wherein the Hertz-Heaviside units are adopted and c = 3 . 10 1 * 

 is the velocity of light in vacuo. 



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 take B = H, we need only to investigate the relation 

 between D and E. This is obtained, as 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, as 

 usual, 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 their velocity. 

 The equations of motion of such electrons are therefore of a 



m(s r + n/s r + n r 2 Sr) = eF s , 



wherein s r is the vectorial displacement of the electron from 

 its position of equilibrium ; m is its mass and e the charge 

 on it ; mn r 2 is the parameter of the quasi-elastic force and 

 mn r ' that of the frictional resistance. The force F s is the 

 component force (parallel to direction of displacement) on 

 the contained electron due to the electric field in the incident 

 light wave. 



In the usual, Drude's, form of the theory one simply takes 

 F = E ; but Lorentz has shown* that the force on the con- 

 tained electron is not thereby completely represented ; we 

 must in fact add a term /(P), where /(P) denotes some un- 

 determined vector function of the polarization intensity P in 

 the medium. As a first approximation for isotropic media 

 it is shown that /(P) = aP, where a is very nearly equal to 

 1/3 ; but in second order effects of the kind under discussion 

 other terms may occur. In order to explain the broad 

 general facts of the phenomena at present under review it is 

 in fact necessary to assume, with Lorentz, that 



/(P)=aP + 6 0urlP, 



the constant b being some physical constant of the medium 



* 'Versuch. einer Theorie der elekt. u. opt. Erscheiiiimgen, &c/ 

 (Leipzig-, 1906) pp. 78-81. 



