Refractivity and Atomic Interaction. 123 



three electrical, i. e. with two optical axes ; of its three prin- 

 cipal molecular refractivities, N n , N pi , W P2 , the first only will 

 obey the additive law and show the original absorption bands 

 7i> 72? 73 as i n (37), while the remaining two, showing six new 

 absorption bands, will contain products of the atomic refr ac- 

 tivities and will depend upon the size and the shape of the 

 molecule, i. e. upon the Rs and 0's. Each o£ these latter 

 refractivities will, in general, be of the form J' 5 (y)/Det., 

 where / 5 is of the 5th degree in y and Det. the determinant 

 of (41) ; that is, 



A' A iY 



7 —7 7—7 



and similarly for N P2 , where the coefficients A', etc., will 

 depend upon the intrinsic attributes, as well as upon the 

 configuration, of the three atoms. 



And in the case of haphazardly distributed orientations of 

 the molecules we shall have an isotropic substance whose 

 molecular refractivity, 



N = i(N, l + N pl + N P2 ), .... (42) 



will differ from the sum of the atomic refractivities in a 

 manner depending upon the size and the shape of the mole- 

 cules. Its dispersion formula will, in general, consist of 

 nine terms, corresponding to as many free frequencies or 

 absorption bands, three due to the atoms themselves, and six 

 due to their interaction. The formula for AT as a function 

 of 7, similar to (16), with w/9tf=aN, will be, in the general 

 case of unequal roots of Det -=0, 



M 1 i B, 14 B<o ,.,,, 



where y^ are the six new frequencies, Bi = e?jmi, and B (i) , 

 i. e. B', B", etc., are six coefficients depending upon the 

 attributes of the three atoms and upon their configuration 

 within the molecule. The new (squared) frequencies y( { \ 

 that is y' , y", etc., will also be functions of the configura- 

 tion, and of the old frequencies. If two roots coincide, 

 say 7' = 7", then we shall have, in the dispersion formula, 



„ ,, r const. , . , const. , 

 a term or the form ,- . -^ besides — : , and so on. 



(7 -vr 7 -7 



For the present it will be enough to develop our general 

 formulae, and especially to find the new frequencies, in the 



