216 Dr. L. Silber stein on Dispersion and the Size of 



interatomic distance R is large enough for gNq to become 

 a negligible fraction, then N=2N Q , as in the usual theory 

 The expression for JSf itself is, in our previous symbols, 



7V7- B /" _ B . V (3) 



where \ is the incident, and X the free wave-length belong- 

 ing to each of the atoms, when undisturbed by its neighbours; 

 B = e 2 /m, m = mass, e charge of dispersive particle, in rational 

 units. 



In general, the atomic X w iU fall into the extreme ultra- 

 violet, and since, in all cases to be treated hereafter, we 

 shall limit ourselves to the visible region of the spectrum, 

 the fourth and the higher powers of \ j\ will be negligible, 

 so that 



N = &o + <7oA 2 . W 



where b 0) g , two constant attributes of the atom, are 

 denned by 



whence also 



BX 2 



4ttW 

 6 2 B 1*008 



g Q " IttV* 127r 2 c 2 \mAm H ;' ' ' ^ 



independent of the free wave-length. The latter formula 

 will be useful in the sequel. Introducing (4) into (2), 

 developing the denominator and rejecting the second and 

 the higher powers of # /X 2 , we have, for the molecular refrac- 

 tivity of the substance in question, 



N=b + glX\ . . (7) 



where 



= H 2 + TiJ> ] 



(8) 



Thus the refraction- and the dispersion-coefficient of the sub- 

 stance, as b, g may be called, appear as simple functions of 

 the atomic coefficients b , g and of the interatomic distance 

 involved in a. Notice in passing that, the denominator 

 1 — ab being a fraction (as in all concrete cases to be treated 

 in the following sections'), the dispersion will show a stronger 

 departure from additivity than the refraction, which is a 

 well-known feature of this class of phenomena. As to the 

 range of ab Q in connexion with the condition of stability, we 

 shall return to it a little later on. 



