Refractivity and Atomic Interaction. 115 



can also be expressed by saying that the expression 



1ST — £N 

 1 ° N-N ' ^ } 



(quite apart from its meaning as the cube of Rj2a) is very 

 nearly free from dispersion. For the present we shall con- 

 tent ourselves with the above examples, as an illustration of 

 formula (29), which is an inversion of (24 b) or of (2S). 



Free Frequencies and Interatomic Distance. Limit of 

 Stability. — Turning now to the form (25 b) of the molec. 

 refractivity, for the case of equal atoms, let us consider the 

 dependence of the new free frequency \/ y on the intrin- 

 sically atomic one, ^/y^ and on the interatomic distance, 



y>=y -2B/W, 



where B = e 2 /m is a constant attribute of the dispersive 

 particles. When R decreases, y becomes smaller and 

 smaller, that is to say, the " new " absorption band, due to 

 interaction, moves farther and farther away from the old 

 one towards the red or the infra-red end of the spectrum. 

 When R becomes so small that 2B/R* = y , we have y'^0,. 

 i. e. the corresponding free period T' and the wave-length 

 \ / = cT l become infinite. When R becomes still smaller, 

 then y'<0, that is, n'—^/y' becomes imaginary and the 

 oscillatory function e in '* degenerates into an aperiodic one. 

 The electric particles cease to oscillate round their atomic 

 centres. In other words, the system becomes unstable, 

 namel3 T , as regards axial displacements of the electric 

 particles *. 



Thus, to the particular distance 



2B\ 1/3 



MS 



corresponds the limit of optical stability of the molecule, — 

 " optical," i. e. so far as the dispersive particles are con- 

 cerned t- In view of this property we shall call R e the 



* The frequency of transversal oscillations is always *Jy , independent 

 of jR, under the express condition that higher powers of (rJH), (r 2 /JR) 

 are negligible. The second new frequency 



VyWy + 2B/R 3 



is always real. 



t This may well be accompanied by other profound modifications of 

 the molecule as a system of atoms, but, as has been said in Section 1, all 

 such questions are beyond the scope of the present investigation. 



I 2 



