﻿the Electron Theory of Solids. 669 



that the average number of electrons in a chain varies 

 inversely as the absolute temperature. 



If cn = Pjd, where ft is a constant, then by equation (3) 





Thus ncv is independent of the temperature except for the 

 variation in c, due to the alteration in the volume of the 

 metal caused by a change of temperature, p, the number of 

 electrons per unit volume, will only change with the temper- 

 ature through thermal expansion. Hence we see from the 

 expression (5) for the conductivity that if the number of 

 electrons concerned in carrying the current does not vary 

 with the temperature, the specific conductivity will vary 

 inversely as the absolute temperature, which is very approxi- 

 mately true for pure metals. 



Resistance under rapidly Alternating Forces. 



We can get an estimate of the average velocity of the 

 chains in the following way : — In the preceding investigation 

 we have supposed that the electric force acting on the metal 

 was steady. The argument will evidently not hold when 

 the force is alternating so rapidly that while the electron is 

 passing through the distance 2gc the force changes its 

 direction ; for in that case the effect of the electric field in 

 altering the motion of the chains will be much less than that 

 expressed by equation (4). When the force is reversed 

 many times during this period there will be very little 

 alteration, and therefore very little conductivity. Thus the 

 resistance of metals under alternating forces should begin to 

 increase when the period of alternation becomes comparable 

 with the time taken by an electron in a chain to travel over 

 a distance equal to g times that between two electrons in the 

 chain. When the period of alternation is considerably 

 greater than this time we should not expect the resistance to- 

 vary with the period. 



Kubens and Hagen determined the conductivity of metals 

 under alternating forces by measuring the amount of light 

 of very long wave-length reflected from the surface of the 

 metals. They found that the electrical conductivity of 

 certain metals at room temperature under electrical waves 

 whose wave-length was 2*5 X 10~ 3 cm. was the same as the 

 conductivity under steady electrical forces, and that even 

 when the wave-length was as short as 4 x 10 ~ 4 cm. the 

 electrical conductivity was within about 20 per cent, of that 



