522 Dr. L. Silberstein on Molecular 



therefore, by no means be neglected. Thus, all of our 

 previous formulae for axial oscillations, axial ref ractivity, etc., 

 remain valid, while those associated with transversal oscilla- 

 tions have to be corrected in accordance with formula (1). 



The resultant force ¥ i on the i-th electron due to the 

 remaining atoms of the molecule will be the sum of vectors 

 of the type of (1), 



Thus F x will be a linear vector function of p 2 , p 3 , . . . . p^, 

 the moments of the second, third, etc., and /e-th doublet of 

 the molecule, and so on. Let, again, y i be the squared free 

 frequency of the i-th. electron, and let us denote by G- 

 the force, per unit charge, due to the doublets contained in 

 the neighbouring molecules and due to the external field E 

 (incident light). Then, for monochromatic light of squared 

 frequency y, and writing again B—ef/m., the equation of 

 motion of the i-th electron reduces to 



(%-7)P-^ 1 |Vi[3u(up.)-p / ]=B i G . (2) 



There are k of such equations (t=l, 2, . . . k) for each 

 molecule. In the simplest case of a gas in normal conditions 

 the perturbation due to foreign molecules is negligible, and 

 then we have simply Gr=E. For other bodies the difference 

 of these two vectors will be a complicated function of the 

 data fixing the arrangement of the molecules, as will be seen 

 later on in some concrete examples. The refractive pro- 

 perties of the body considered as an aggregate of such 

 molecules will follow from (2) and from the usual relation 



(K-1)E = 3?%, (3) 



where 9? is the number of molecules per unit volume, 

 K=-/jl 2 , as before, and p^ the average of p e . taken over a 

 " physically small " volume, as in the current electron 

 theoiy of dispersion. 



2. Refractivity of Diatomic Gases. 



Taking up again the case of diatomic molecules, let us 

 apply the suffixes i=l, 2 to all the attributes of the two 

 atoms composing each molecule. Let the substance consist- 

 ing of these molecules be a gas in normal conditions. Then 



