996 Mr. Gr. H. Livens on a Theory of the 



determining the extent of the effect of its asymmetric 

 structure on its optical behaviour. 



This simple statement, however, seems to require a little 

 more precision. Does the constant b depend on the relative 

 density of the chirally active molecules ? Or does this second 

 order force not act equally on all the electrons in the medium r 

 It seems difficult to realize that this force, originating in the 

 chiral structure of the active molecules, can be appreciable 

 equally well at any point of a medium throughout which the 

 actual chiral molecules are but sparsely distributed. This 

 leads to the view I have formerly adopted, that this chiral 

 part of the force is appreciable only in the immediate neigh- 

 bourhood of the optically active molecules. There is of 

 course the alternative and practically equivalent view that 

 the presence of so many active molecules imparts a slight 

 chiral structure to the whole medium, and to an extent 

 depending on the relative density of such molecules*. In 

 the actual analysis 1 shall adopt my former view, and for 

 simplicity will assume this force to be perceptible only for 

 those electrons contained within the active molecules. 



We have thus in isotropic media 



F = E + aP + &CurlP, 



and with this form the equations of motion of the typical 

 electron are of the form 



m (s r + n r ' s r + n r s r ) — e (E s + a~P s ) + b Curl s P. 



If now the light incident on the body is a simple harmonic 

 wa*ve-train of frequency n, the electrons are compelled by 

 the electric force in the incident beam, with more or less 



success, to vibrate with a period — . Thus the functions 



n 



may all be considered to depend on the time by the expo- 

 nential factor e int , so that we have 



m ( — 7i 2 + in n r ' + n r 2 ) s r = e (E s + aP s ) + b curl,,. P. 



By solving this equation for s r we determine the position 

 of the typical electron corresponding to the values E of the 

 electric force and P of the polarization. By forming the 

 vectorial sum %es r per unit volume, which we know is equal 

 to P s , we obtain a relation between the electric force and 



* On due consideration I think this alternative view untenable as 

 there would then be no distinction between chirally active electrons and 

 non-chirally active ones ; a distinction which is required by the results 

 of some of Cotton's experiments. 



