30 



at in a recently M i)ublished paper lends itself readily to the invest- 

 i^-ation of the problem here considered, from equation (14) in 

 Art. 4 of the paper quoted a theorem can easily be deduced which 

 amounts to an extension ol Babinet's Rule; this corrected or gen- 

 eralised form of the rule we shall find to be consonant with the 

 result of all experiments. In the ))aper alluded to. the following 

 formula was established on the assumption that the substance con- 

 sidered contains onlv o)ip category of movable electrons: 



(l) ^1 - V; ^n^' — n'- 



Here v^. V2 are the values (for the right-handed and the left-handed 

 eircularlv polarized wave respectively) of the refractive index. 

 Xy and X., those of the coefficient of extinction of the medium; Hq 

 represents the frequency of the free or natural vibration of the 

 electron. // the frequency of vibrations in the incident beam of 

 light and k a constant coeffici(int connected with the intensity of 

 the damping which is known t(j operate in electro-molecular vibr- 

 ations. 



Two cases have to be considered; we shall take them in order. 



1st. Suppose /I > -^vo or 11 <i n^. 

 From equation (1) of the present Article it follows that in this 

 case — 



(2) 



v^ > t'o or r, < Co \ ,. ( x, > Xo I 



according as | 



v^ < v., or Ci > 0.2 \ I Xi < Xo I 



However, b}* formula (2) in Art. 1 above it is evident that 



(3) implies 



v^ <Vo \ I V < I 



and in Art. 3 it was shown that the revolution in tlie ellipse is 



left-handed I ,. f x, > x, | 



(4) [ according as " . 

 right-handed J [ ^1 < ^^2 I 



Hence, in this case, the revolution in the ellipse is 



left-handed | ,. \ ip > \ 



(D) according as { 



right-handed | | t^ < | 



1) Bulletin Int. for October 1908, page 764. 



