100 Dr. L. Silberstein on Molecular 



to the ;-th atom, playing simply tli8 part of a doublet, will 

 be directed along the line OiOj and its intensity will be 

 proportional to the projection of iy upon OiOj. 



In fact, let #,-, Xj be the components of the displacements 

 r^, Xj along OiOj (fig. 1) ; then, neglecting squares of n/E^, 

 rjfELij, the component of the force on — e% taken along that 

 direction will be 



Fig. 1. 



Z 1" 



Oi % Oj 



*-s[(i-'*r-(-vf] 





while the transversal component will be of higher order. 

 Thuis the whole force on the 2-th electron due to the 

 ^'-th atom will be 



™v = p~ir &j**iji W 



ixij 



where % is a unit vector from O t to Oj. And the resultant 

 force F t - on the i-th electron due to the remaining atoms of 

 the molecule will be the vector sum of all expressions of the 

 type of (4), 



Ft = SFt;, ........ (5) 



the summation to be extended over all jzfci. Thus F 2 will 

 be a linear function of the projections of r 2 , r 3 , etc., upon 

 0iO 2 , Oi0 3 , etc -> an( * similarly for F 2 , and so on. Thus, 

 taking account of the atomic interaction, we shall have, 

 instead of (3), for a molecule consisting of k atoms, k linear 

 differential equations : 



r* + w- -Ff=0, i=l,2,...*. . . (6) 



IKli 



The molecule as such will now have, generally speaking, 

 3/e new free frequencies, optically relevant, instead of the 



original ones, \Zyi> 



Finally, let us imagine a body composed of a large 

 number of such molecules. Let 9? be their number per unit 

 volume, and E an external electric field, e. g., the electric 

 force in an incident wave of light. Then, precisely as in the 



