Rotational Optical Activity in Isotropic Media. 1001 



for the rotative power of a mixture containing different 

 active substances at partial densities pi,p 2 ,... and inactive 

 substances at partial densities o- 1? a 2 , ... which is of the form 



wherein r/, r 2 ', ... ; r l9 r 2 , ... ; s 1? s 2 , .... are all physical 

 constants of the respective substances to which they refer, 

 depending on the nature of these substances and the frequency 

 ■of the light. 



A more fundamental interpretation of the formula, which 

 would avoid any irregularity in the probable truth of the 

 above assumption, makes it depend on the mean index of 

 refraction of the medium (e) which we know is determined 

 by the relation 



e 2 — 1 -^ e 2 /m 



T+a(€ 2 -l) = 2 *n^-n 2i 

 and thus 



It would appear that the main cause of the variation of a> 

 is identical with that which causes the variation of e, a fact 

 on which it is necessary to insist. 



One or two fundamental difficulties occur, however, even 

 in the applications of this formula. Some of these have 

 already been mentioned in a previous connexion (I. c.) ; 

 another one is that it would indicate no change in the sign 

 of the rotation on passage across an absorbing region, a 

 phenomenon observed by Cotton. Closer investigation to 

 which we shall now proceed will, however, remove even 

 these discrepancies. 



In the neighbourhood of the spectrum near an absorption 

 band, the absorption determined by the imaginary parts of 

 q 1 and q 2 is no longer negligible ; but even in these cases it 

 is only the absorption due to the electrons giving rise to the 

 one near band that is appreciable and needs to be reckoned 

 with. Two cases may, however, present themselves, the 

 band may arise from a set of the rotationally active electrons 

 or from a group of the others. The latter case being the 

 simpler is treated first. If we write 



then co determines the relative velocities of the two beams 



