524 Dr. L. Silberstein on Molecular 



given in I., and so are (3'). Thus we have for the axial 

 molecular refractivity of the orientated aggregate, 



M * 

 precisely as in I. (with 47rR 3 instead of R 3 ), 



where iV— — — ! — are the atomic refractivities of the 



constituents and « = 3w H /l'008 = 4*88 . 10" 24 gr. The 

 correct transversal equations (4 t), however, differ from the 

 original ones (in which the terms BfJ^irR? have been 

 absent). Thus the transversal molecular refractivity 



M 



JW t =i{fi* — 1) -rwill be different from that given in I. Its- 

 correct value, however, can be derived without much 

 additional trouble. In fact, the left hand members of (4 £) 

 differ from those of (4 a) only so far as —2ttR 3 is replaced by 

 H-47ri2 3 . In order, therefore, to obtain JS r t from N a we have 

 only to write, in (5 a), — \s instead of s. Consequently, the 

 transversal molecular refractivity will be 



v r _N 1 + N 2 -^N 1 N 8 r - A 



1 — 46 XNJIN2 



Thus, neither the axial nor the transversal refractivity of 

 the compound obeys the additive law. The real departure 

 from additivity is, therefore, even more radical than has 

 been asserted in the first paper, p. 104. At (he same time 

 all the free frequencies belonging to the molecule, those 

 corresponding to axial as well as to transversal oscillations^ 

 differ from the atomic ones. The new axial frequencies are 

 as in I , and the transversal ones will be given presently. 



Isotropic Gas. — Let now the directions of the molecular 

 axes be haphazardly distributed, as is the case in a real 



* The irrelevant constant factor |, a degeneration of (ju a 2 +2) -1 , is 

 inserted only to make the expression uniform with the " molecular refrac- 

 tivity " as usually defined ; M stands for the molecular weight and d 

 for the density of the substance, as before. 



