﻿Theory of Long Wave Radiation, 161 



But in the conceptions we have adopted, the calculation 

 of both E and A under the assumptions specified can be 

 directly accomplished. 



If we consider that the thickness A of the metallic plate 

 is so small that the absorption may be considered as pro- 

 portional to it, we shall find by an obvious calculation, after 

 Lorentz, that 



A=-A*, 

 c 



e being the usual velocity constant and a the conductivity 

 of the metal. 



Now the interpretation of a in terms of the electron 

 constants of the metal, although a matter of some difficulty, 

 is nevertheless fairly certain f. If N denote the number 

 of free electrons per unit volume in the metal, each of 

 mass m and with a charge e, moving with velocities the 

 average square of which is u m 2 , then we know that in all 

 applications involving steady or slowly varying currents the 

 conductivity <r is given by 



o- = 



8 Ne 2 l 



37r mm 



wherein l m is a constant, a certain mean length of path, which 

 is determined by the formula 



i 



lm == 



R 2 ' 



in which n is the number of atoms per unit volume in the 

 metal and R the sum of the radii of an atom and an 

 electron. 



However, in applications involving more rapid alter- 

 nations in the current the above formula is found to be 

 insufficient and requires modification along lines already 

 laid down by various authors. According to Jeans J the 

 correct form to be used for alternating currents with a 

 c 



frequencv — is 



1 + 



4o- Wm 2 ' 

 " A 2 NV 



* ' The Theory of Electrons,' p. 280 (note 33). 



t ' The Theory of Electrons/ chapter I., and p. 266 (note 20V 



J Phil. Mag. June 1909. 



Phil. Mag. S. G. Vol. 29. No. 169. Jan. 1915. M 



