280 Prof. L. Natanson on the Molecular Theory 



system. Bur from the point of view of the present paper 

 the question evidently is of secondary importance] 



It remains for us (with the view of investigating forced 

 vibrations) to evaluate the force E acting on the electron. 

 The component E z of this efficacious force is made up of (E x ), 

 "the electric field calculated in § 5 and a further additional 

 part whose importance was insisted upon, many years ago, 

 by H. A. Lorentz and Sir Joseph Larmor. In-order to 

 express this term in our notation, we must recur to (3), § 2. 

 With use of this relation we can write * 



E x =ae* n (*- teo+ ^— IttN . ? 'A (2) e"^-^+^, . (2) 



where a is a constant. When we bear in mind that the 

 expression (6), § 5, with z written instead of z, will exactly 

 represent what in the foregoing equation (2) is denoted by 

 ae«K'- te o+l»), we find 



4 7 rNA (2) = ?(^' 2 - 1 ) ae " ?( ^" ry) - • • • ( ; ^ 



We now require another equation connecting A (2) with a ; 

 for this purpose recourse must be had to the equation of 

 motion. From (1) and (2) we deduce 



{n 2 -n 2 + i$n*)e%= ^ Jaefrfr-d-^N . iAW)^ : *»o+?), 



; • • • « 



and substituting from (3), § 2, we have the result 



Uo 2 -H 2 -37rN^ +tan s U.«=*^ae*"fr--0. . (5) 



We come therefore to an important conclusion. If we 

 assume 



bc = v—i/c,' (6) 



v will represent the refractive index, k the coefficient of 

 extinction of the medium. Equations (3), (5), (6) now 

 give 



( n ,»-n»-|»N^+iSn«)((i-u t )«-l)=4wlir^. (7) 



This is in agreement with experimental evidence and has 

 been known to hold true ever since the Theory of Dispersion 

 in its contemporary form was elaborated. 



In the domain of Optical Dispersion, the basis of the usual 



* A slight change in the original calculation is introduced here ; 

 -cf. /. c. pp. 10 and 22. 



