and Dispersion of Light. 831 



though for a gaseous medium it is general to disregard the 

 heating effect accompanying the absorption, and conse- 

 quently to make no marked distinction between the scat- 

 tering and the absorption or extinction. 



In order to deduce more rationally the coefficient of 

 scattering, therefore, we have to resort to another process of 

 calculation ; an answer to this request will be obtained 

 through identifying the scattered energy with the energy 

 of radiation itself from the electron which is set in motion 

 forced by the incident light. The amount of radiated 



e 2 - 

 energy, then, must be measured by -p, — ,£ a *. where e is the 



charge of the electron, and c the light velocity in vacuum ? 

 while f is the acceleration of the vibratory motion of the 

 electron. It will be noticed here that no term needs to be 

 added to the equation of motion of the electron corresponding 

 to a reaction to the radiation from it, as it is too small to 

 affect the general features of the problem when we attack 

 it from this side. Let us take, then, the Lorentz equation of 

 motion of an electron for the case of a plane polarized wave 

 incident on it, in which no term of damping appears, namely, 

 of the form f 



m|f = ,(E, + aP I )-/f, 



where f is the displacement of the electron from its position 

 of equilibrium, a a constant nearly equal to J (Heaviside- 

 Lorentz Units of electromagnetism are adopted here), 

 f another certain positive constant that characterizes the 

 elastic force of restitution of the electron, and P*, the polari- 

 zation within the medium caused by the electric vector E x 

 of the incident light. 



Denoting by N the number of polarized particles per unit 

 volume of the medium, 



Thus m = e(E x + aN«f ) -/ fc 



or m^ + (f-aNe 2 )Z = eK x . 



Supposing the light vector to be a periodic function of 

 the frequency n, say E x = ~K Q e inf at a point, and putting the 

 frequency of the free vibration of the electron, as usual, 



* O. W. Richardson, ' The Electron Theory of Matter/ p. 256. 

 t H. A. Lorentz, < The Theory of Electrons,' p. 309. 

 X Ibid., p. 136. 



