﻿'llieory of the Optical Properties of Metals. 659 



which is the generalized form of a result already given for 

 two special cases of limited applicability. 



If E is constant for a time large compared with the mean 

 time between two collisions, this reduces at once to 



I'm 



wherein, if we write, what is approximately true, 



T m = 



we recognize Lorentz's well-known general law of distribu- 

 tion of velocities of the electrons under the action of a steadv 

 field. J 



If we put again, in a simple harmonic field, 



we get 



V 7T 3 L m ll-2pT w J b ' b ' 



which agrees with a result obtained directly in another 

 paper. 



It appears, however, on due consideration that this last 

 result is restricted for application to problems in which the 

 field is represented by a simple harmonic train of stationary 

 waves in which the wave-length is very long compared with 

 the mean free path of an electron. To remove this restriction 

 we must take account of the change of phase in the vibrations 

 of the field from point to point in the metal, and to do this 

 we must introduce a more general type of field. We may 

 assume quite generally that the field is propagated in the 

 direction of the s-axis as a plane simple harmonic wave-train 



with the velocity *, so that the electric force E, which is 



n 

 * c is the velocity of radiation iu vacuo. 



2U2 



