438 Dr. H. Stanley Allen on Optical Rotation, 



If the arrangement represented in fig. 3 be adopted, the 

 asymmetry of pair a is due to groups c and d, and the 

 resulting contribution to the rotation will be equal to 

 the algebraic sum o£ two terms of the type given above. In 

 order to explain the absence of rotation in a symmetrical 

 molecule, it is necessary to assume that the sign is positive 

 for one electron and negative for the second electron of the 

 pair. Let us further assume, at least as a first approxima- 

 tion, that the natural free period is the same for each electron, 



/ T ,\2 



so that the denominator 1—1 'J is the same. The con- 

 tribution to the rotation made by the pair of electrons may 

 then be written 



£ _ h AN ,„, _ ,, . 



= A(/' a -/'« 2 ). 

 Hence the total result may be written 



P-A(K c -K,) + B(K,-K c ) + C(Iv a -K.) + I)(K 6 -K a ), 



since ihe difference between f' ai and f ao _ is due to the 

 presence of the unlike groups c and d. It follows that 



P = (A-B)(K C -K ( ,)+(C-D)(K -K 4 ). 



In the case in which the groups a and d become identical, 

 K c = K rf and C = D, so that there is no resultant activity. 



If, on the other hand, the alternative arrangement of 

 coaxial rings be adopted, the resultant effect would have to 

 be calculated by methods similar to those employed by Gray * 

 in the case of purely electrostatic forces. 



According to the principle of optical superposition formu- 

 lated by van't Hoff, the total rotatory power in a compound 

 containing several asymmetric carbon atoms is the algebraic 

 sum of the various radicles taken separately. This rule 

 seems to be valid at least to a first approximation f . The 

 work of C. S. Hudson % and his collaborators shows that the 

 principle holds fairly closely in the case of certain amides. 

 The approximate validity of the rule is to be expected on 

 such a theory of optical rotation as that here put forward. 



The variation of optical activity with temperature, 



* Loc, cit. 



f Tschngaeff, loe. cit. 



X C. S. Hudson, Journ. Amer. Cliem. Soc. vol. xli. pp. 1140, 1141 

 (1919). 



