116 Dr. L. Silberstein on Molecular 



critical distance"*. It is that distance at which the restitu- 

 tive force is just balanced by the interatomic one. For 

 R<R C the higher powers of (n/R) are, of course, no more 

 negligible, and our linear equations cease to be applicable. 

 Therefore, having purposely retained only the first powers 

 of these ratios, we shall have to assume throughout that 

 R>R C . (The question as to what happens below R c may 

 occupy our attention at a future opportunity.) 



Using the critical distance as given above, we can 

 conveniently write 



'-[-(SB 



or in terms of wave-lengths, remembering that y = ( -^— ■ ) , 



and 



-p 3 _ BX _ A e jc (%9\ 



c — 9_2„2 — 9^2 • ™ > • . • W-v 



c being the velocity of light in empty space. The reader 

 will remember that, e being a charge in the electrost. 

 system, £ 2 /c 2 ra is a certain length. The critical distance 

 is, so to say, the natural unit of interatomic distance. If 

 R contains many of these units. A/ sensibly coincides with 

 \ Q , giving a close doublet. When R decreases, A/ is 

 lengthened, at first very slowly, but then, when R ap- 

 proaches the natural unit, very rapidly, so that in certain 

 cases the minutest approach of the atoms may suffice to 

 change entirely the " colour " of the resulting substance. 

 To illustrate the increasing rapidity of this process, let us 

 assume X in the remote ultraviolet, say, 



\ = 720 A.U., 

 a figure which would closely correspond to the free frequency 



* R c will not be confounded with the "singular distance" R'—R'{y). 

 The latter, a function of y, is that distance R for which the incident 

 7 becomes identical with y'. On the other hand, R c is a constant, whose 

 Talue depends only on B and y Q . 



