1002 Mr. Gr. H. Livens on a Theory of the 



(and approximately the rate of ^"rotation of the polarization 

 plane), and to' their relative absorption, the two quantities 

 alone necessary to determine the nature of the emergent 

 light. We have now 



B ( Al + - ^Y^ X 

 2c 2 , . ,. V ni'—rf + inniJ 



(l-aA,- 2 aN f lm X 

 \ Ui—rJ + inni) 



wherein Nj is the number of electrons per unit volume with 

 free period n u which are responsible for the band under 

 consideration ; 



this sum being taken per unit volume over all the electrons 

 in the medium other than those reckoned in N : ; and finally, 



B=S 



' be 2 /m 



this sum being taken only over the rotationally active 

 electrons for none of which is ?i r =n 1 . 



We can again interpret this formula in terms of the mean 

 index of refraction e and mean absorption coefficient k 

 determined as usual by 



(e-ifc) 2 =A + V ^i e2 /' m 

 l + a(e— ik) 2 l ft,. 2 — n 2 + inrii' 



The result is that 



9r 2 



^(o)-zV)=B[{(e-^) 2 -l}{a(e-^) 2 + l-a[] 



= B[(e 2 - f c 2 -l-2i6K){a{e 2 -K 2 -l) + l-2iae f c}, 



so that 



2c 2 co 

 n 2 



2c 2 co' 



= B[(e 2 -A: 2 -l){a(6 2 -A: 2 -l)+l}-4a6V] 

 = 2B[(a+l)(e 2 -K 2 -l) + l]efc. 



To discuss these formulae it will be convenient to resolve 

 them by a method similar to that adopted by the author in a 

 recent communication * on absorption spectra. The formulae 



* ' Ueber die Veranderlichkeit von Absorptionsspektren/ Phys. ZeitscK 

 xiv. pp. 841-844 (1913). 



