Refr activity and Atomic Interaction. 107 



atomic interaction. This is a sort of compensation for the 

 disappearance of the ordinary law of additivity. 



Subcase : Equal Atoms. — If the two atoms compounding 

 the molecule are equal, z. e. when e 1 2 /m 1 = e 2 2 /m 2 = B x — B 2 — B 

 and ^ = 72 = 705 so that?2 =\/7o is the frequency belonging 

 to each atom, then we have, by (16), (17), and (18), 



2B9? 2B9? 



(o s = ; co a = — , . 



Yo— 7 7 —J 



(21) 



where 



7=7o- g (22) 



Notice that in the present case B' = 2B and B'' = 0, so that 

 the second new free frequency given by y" = y -\-2B/R^, 

 does not enter at all into the refractivity of the compound. 

 The axial refractivity o) a has the same coefficient as the 

 transversal one, but its singularity (absorption band) 7' is 

 shitted away from 70 towards the red, since B and R are 

 essentially positive. The absorption band of both (equal) 

 constituents being, say, in the extreme ultraviolet, the new 

 band of the molecule may well fall into the visible region of 

 the spectrum. 



In order not to interrupt the general course of ideas, 

 illustrative numerical examples will be given separately, in 

 Section 4. Here it will be enough to note that a crystal 

 composed even of the simplest kind of molecules, namely 

 diatomic ones, would show, by the above formulae, the 

 remarkable phenomenon known under the name of dichroism. 

 And when we come to consider more complicated molecules 

 we shall perceive the possibility of accounting for pleocliroism 

 as well. Let us now pass on to the second of the two cases 

 mentioned above. 



Isotropic Body. — The kind of isotropy we have in mind is 

 optical isotropy, of course *. Let, therefore, the directions 

 of the axes of our diatomic molecules be haphazardly dis- 

 tributed, so that no particular direction is privileged. Then, 

 for each individual molecule, we have still the formulae 

 (13 5), (13 a) with K s , K a replaced by the macroscopically 



* The body may well be a crystal in the nrineralogical sense of the 

 word and yet, like rock-salt, show no traces of optical anisotropy. Such 

 will "be the case if the molecules are distributed, say, in three cubic space 

 lattices with the axes of the molecules mutually perpendicular, so that 

 the molecular anisotropy will be macroscopically obliterated. 



