102 Dr. L. Silberstein on Molecular 



Since the forces F;, to be constructed on the type of (4), (5), 

 are all linear vector functions of the r's, we have in (9) 

 a system of k linear vector equations for as many vectors r t -. 

 On the other hand we have, by (7), 



(JT-l)E=gK«<5 (10) 



Introducing here the r's to be found from ^9) as linear 

 functions of (K+ 2)E, we shall obtain the ref ractivity 

 operator 



-= 3 ra' < n > 



which in the simplest case of isotropy reduces to the familiar 

 expression 3(>w. 2 — l)/(yLt 2 + 2). Our above JV, the molecular 

 refractivity-operafor, will be JV=^Mco/d. The operator co 

 will obviously contain, in the denominator, the determinant 

 of the equations (6) of the molecule under no external 

 forces, thus bringing into evidence the free frequencies and, 

 therefore, the absorption bands of the compound, and, in 

 fact, all Df its optical properties in terms of the attributes 

 of the atoms and of their configuration within the molecule. 

 This will be developed in detail on the particular examples 

 of two- and three-atomic molecules, which will pave the way 

 for the treatment of polyatomic ones. The operator co will 

 have, in general, three different principal values, and will, 

 in the case of a haphazard orientation of the molecules, 

 degenerate into an ordinary scalar magnitude. 



The equations (9) and (10), with the forces F; defined by 

 (4), (5), will be our fundamental system of equations, to be 

 developed in each particular case. 



Notice that with increasing mutual distances (i2 y -) of the 

 atoms all the interatomic forces F f tend to evanescence, and 

 (9) are at once reduced to the ordinary equations of the 

 Lorentz theory, as it should be. In that limiting case we 

 have from (9), calling xi the projection of r< upon any fixed 



i <?■ 



direction whatever, (yi — y) «i= ~ — (K + 2)E X , so that K, 



and therefore co, obviously becomes an ordinary scalar (the 

 substance becomes optically isotropic) and its value is, 



by (10), 



wh 



ere 



; =9?^-, (12) 



as in Lorentz's theory, and therefore also 



