﻿the Electron Theory of Solids. 667 



velocity in the direction of the electric force equal to X^X/2/>/r, 

 where X is the mean free path of an electron and v the menu 

 velocity. This result is obtained as follows : in a collision 

 between an electron and an atom, since the mass of the electron 

 is infinitesimal in comparison with that of the atom, there will 

 be no "persistence" of the velocity of the electron. The 

 velocity communicated by the electric force to the electron 

 before it came into collision with an atom will, as it were, 

 be completely wiped out by the collision, and the electron 

 will make an entirely fresh start. Thus if t be the interval 

 between two collisions, the average velocity of the electron 

 in the direction of the electric force will be 



lXe lXeX 

 o -*> 01 * 5 • 



On the theory we are now discussing, the carriers of 

 electricity are not free electrons, but chains of electrons 

 rigidly connected moving along a line of the lattice ; since 

 the chain has only one degree of freedom, the average energy 

 of a chain at the temperature 6 is R0/2 ; hence 



inmv 2 =JiR6, ...... (3) 



where n is the number of electrons in the chain and v its 

 velocity. Thus the average energy of a single electron in 

 the chain is ~R6/2/i. On the old theory when each electron 

 was supposed to be free, its average energy was 3U0/2. The 

 energy and velocity of an electron on the new theory are 

 smaller than on the old. 



The "collisions'" between the electrons and atoms are also 

 different. On the new 7 theory an electron in a chain is 

 moving past a row of atoms arranged at equal intervals 2c 

 along a line parallel to the path of an electron ; the time it 

 takes for an electron to pass from closest proximity to one 

 atom to closest proximity to the next is 2cjv. If the inter- 

 change of energy between the electron and the atom were 

 limited to the time when the electron was closest to the atom, 

 the electron for a time 2c\v would not be losing any energy, 

 and so could, under the electric force, acquire a velocity 

 equal to X<? , 2c\mv. The loss of energy by the electrons 

 will not, however, be confined to the positions of closest 

 proximity, but will extend some way on either side. The 

 result of this will be that in part of the interval 2c/v the 

 electron will be losing velocity, so that the velocity it will 

 .icquire under the electric force will be less than X<? . 2c/mv, 

 and the average velocity will be less than half this value. 



