﻿162 Mr. G. H. Livens on Lorentzs 



or, on substitution of the value of cr , we get 



N6 2 L 



8 mu m 



377 . 32tTC»Z,, 



■*- I o^v O 



a formula reducing to the Lorentz-Drude formula for large 

 values of A,. 



We have therefore for the coefficient of absorption under 

 the conditions specified and for plane-polarized radiation of 

 wave-length A, 



mu 

 A = 



1+ 3 



3\ 2 u m 2 



Now let us consider the radiation from the plate, still 

 closely and often verbally following Lorentz. We need 

 only consider the radiation normally from the small volume 

 w/\ of the plate, as this is the only part of all the radiation 

 through w from the whole plate that gets through w' . Now 

 according to a well-known formula of electrodynamics, a 

 single electron moving with a velocity v (a vector with 

 components v x , v y> v z ) in the part of the plate under con- 

 sideration, will produce at the position of w' an electro- 

 magnetic field in which the ^-component of the electric 

 force is given by 



e dv x 

 ~~ ^7rc 2 VTt } 



if we take the value of the differential coefficient at the 

 proper instant. But on account of the assumption as to 

 the thickness of the plate, this instant may be represented 



for all the electrons in the portion wA by t , if t is the 



time for which we wish to determine the state of things at 

 the distant surface w . We may therefore write for the 

 .e-component of the electric force in the total field at w' 



c 



and then the flow of energy through id' per unit of time 

 will be 



GE X V 



as far as this one component is concerned. 



