Rotational Optical Activity in Isotropic Media. 1007 



inherent in the simpler formula, obtained by neglecting the 

 absorptioD, which did not admit a minimum rotation for 

 changing concentration of the substance * until a change in 

 the sign of the rotation had taken place. In fact changing 

 the concentration of the solution may conceivably bring into 

 closer proximity an absorption band, and complications are 

 at once introduced which may very well explain the results 

 actually obtained. I have not sufficient details to hand to 

 tell whether this explanation is a valid one in the few cases 

 involved, but the matter could easily be tested. A similar 

 explanation applies to the other difficulty (I. c.) mentioned, 

 viz. that the minimum rotation of a substance in solution, 

 for changing concentration, is independent of the solvent. 



Several other deductions could be made immediately from 

 the above formula, but no advantage is thereby gained 

 owing to the lack of experimental results on this subject, 

 with which they can be compared. Several obvious tests of 

 the theory, however, at once present themselves, and could 

 be submitted to examination. For the present we may be 

 content with the above explanations, and may therefore 

 proceed to an examination of the more general formula in 

 the remaining case of any importance, viz. when the absorp- 

 tion which is taken into account arises from a group of 

 rotationally active electrons. This formula in this case can 

 be written, in the same notation, 



(b 1+ **f£ , Ya 1+ ^J™. ,) 



oa-c .rtr , y 



\Wi — nr-\-inri x J 



The calculations and discussions for this formula can be 

 made to depend on those already given in the simpler case 

 above. In fact if we define ©j and co L ' by the relation 



2c 2 



\ n i — n A + inn x -/ 



(l-aA,- ^fJ^Q f 



» 2 -, _.a «n^/ 



then they are susceptible of the same treatment as co and <o f 

 above ; but then 



. , /- , N^e 2 . 1 v . 



so that co and co ! are easily determined. We need not enter 

 * See Phil. Mao-. June 1913. 



