﻿Cubic Crystals with Theoretical Atoms. 



771 



force, and substituting #=^ J, the equilibrium distance, 

 ^_* 2 / + i£A\ (58) 



omitting the term in x~* as being small. 



This expression gives the force acting per unit of distance 

 and per unit of mass. Equating to the mass times the acce- 

 leration per unit of distance, we derive the frequency ot 



oscillation 



= __^L_ (59) 



SiTTima- 



By a similar process we find from (40) the frequency of 

 vibration of the mass m perpendicular to the line joining the 

 atoms to be 



n _™along .... (GO) 



"perp. yy • • v / 



These were published as equations (13) and (15) in a recent 

 paper * t without the process of derivation. 



Comparison of Experimental and Theoretical Values^. 

 We are now in a position to use the experimental deter- 

 minations of the distances between atoms in cubic crystals, 

 and of the frequencies of vibration in the hydrogen atom as 

 determined by the light spectrum, to compare the results 

 of the theory with known experimental values. For many 

 points in the theory reference must be made to a recent 

 paperj. The fundamental constant b, the radius of the 



* Phil. Mag. vol. xxix. p. 326, Feb. 1915. 



t Since this paper was communicated the force of every atom in a 

 cube, of edge four times the length of the elementary cube, upon the 

 central atom has been calculated. There are 26 atoms surrounding" the 

 centre in the first cube, and 98 more in the next cube, making a total of 



124 atoms besides the central atom. "With the central atom there aie 



125 =5 3 atoms. The approximate result in equation (66) has been 

 modified a little by this work so that it comes into good agreement with 

 the atomic theory in (70). A study of monometric crystals of various 

 compounds has made it possible to find the values of 2m' 2 characteristic 

 of individual atoms. This is an additional property of the atom itself, 

 as characteristic as the atomic weight or the atomic number, and has 

 proved to be of importance in determining the compounds into which the 

 atom enters. It has in fact made it possible to predict the arrangement 

 of the atoms in some crystals in advance of the published investigation 

 by means of X-rays, and it will prove interesting if these predictions are 

 later confirmed by such a study. 



\ Loc. cit. 



3D2 



