Optical Activity of Solutions. 821 



molecular group, is, however, only appreciable in the neigh- 

 bourhood of the optically active molecules : for simplicity it 

 will be assumed to act only on the electrons actually 

 contained within these molecules. 



The typical equation of motion of a contained electron 

 thus assumes the more general form 



m(x + iiq 2 x) = e(E x + a?^ + eb Curls P. 



If plane homogeneous waves of light of frequency n are 

 propagated through the medium, we find in the usual manner 

 that the above equations lead to a general relation connecting 

 the electric force E with the electric polarization intensity P 

 of the form 



P=( S „-g,)(E + a P) + (s^)c„ r lP ;! 



wherein X denotes a sum taken over all the electrons, but 

 2' only over those contained in the optically active 

 molecules. 



Lorentz writes this relation in the form 



E = aP + /3CurlP, 



without giving any account of the constants a and ft. 



Starting from this relation, it can be easily verified that 

 the velocities of the two kinds of circularly polarized waves 

 are respectively the roots of the two cubic equations in fx : 



(fi 2 -l){*±ftnft) = l. 



The combination of these two oppositely circularly 

 polarized beams leads as usual to a pencil of linearly 

 polarized light whose plane of polarization is being rotated 

 at a rate per unit length 



6) 



= i(fj, + -fj,-)n. 



In any case we know that the coefficient ft is so small that 

 we can approximate to the values of fju by expanding in 

 powers of ft. This gives 



1 Sn . _„ 

 ti ± =fio±- 2 ^-+Aft*+.... 



so that very approximately 



CO 



Phil Mag. S. 6. Vol. 25. No. 150. June 19.13. 3 K 



In 2 ft 



