Refractivity and Atomic Interaction. 103 



Thus the additive law of refractivities appears, of course, as 

 the limiting case for evanescent atomic interaction. 



Our supplementary terms concentrated in F» bring in 

 optical anisotropy (when not destroyed by haphazard 

 orientations of the molecules) and non-additivity, modifying 

 at the same time the free frequencies and, therefore, also the 

 position of the absorption bands. The quantitative aspect 

 of this departure from additivity will be discussed and 

 illustrated in the following sections. 



3. Diatomic Molecules, 



Let a? 1? x 2 be the axial components of r l5 x 2 > i. e. their 

 projections on 0\0 2 , and y±,y 2 their transversal components. 

 The forces F l5 F 2 being purely axial, the latter components are 

 not modified by the atomic interaction. Thus the transversal 

 component of (9) gives 



and the axial component, by (4), 



2e 2 » 1 --> 



f 



,(13 a) 



o 3 ei*i+(72-7>2«3= q — (K„+2)B„ . 



where R is the mutual distance of the centres O x , 2 , and 

 the suffixes a, 5 are used to distinguish between the axial 

 and the transversal directions. Oi0 2 will shortly be called 

 the axis of the molecule. The above equations have to be 

 combined with (10). In doing so we shall consider 

 separately the two important cases : 1) when the axes of 

 all the molecules are parallel to one another, and 2) when 

 their orientation is haphazardly distributed throughout the 

 substance. The first case will correspond to an optically 

 anisotropic, and the second to an isotropic substance. From 

 our present point of view the first case is the more important 

 one, since it reproduces the properties of the molecule as 

 such, while in the second case these properties are partly 

 obliterated by averaging through the crowd of molecules. 



Anisotropic Body. — All the axes being parallel to one 

 another we have simply ri=r^ i. e. Xi = x?i, yi=yi, and 



