350 RICHARDSON— DYNAMICAL EFFECTS OF [April 22, 



These interesting relations were shown to be a consequence of the 

 electron theory of conductors by Drude. He proved that they fol- 

 low inevitably from the assumptions ( i ) that a metal contains 

 electrons which move about freely like the molecules of a gas, (2) 

 that they possess a certain average mean length of free path \ 

 during the traversing of which they are only acted on by the 

 external applied electric force, (3) that this path is terminated by 

 a collision and that the new motion which then ensues is, on the 

 average, independent of the previous motion ; and lastly (4) that 

 their average kinetic energy is the same as the average kinetic 

 energy of translation of a molecule of any gas at the same tempera- 

 tur as the metal. 



A simplified form of Drude's deduction may be given here. If 

 X is the electric intensity inside the metal, c the electric charge pos- 

 sessed by an electron and i;?. its mass, then the force acting on the 

 electron during its free path is Xc and its acceleration Xe/ni. If 

 the velocitv of the particle at the beginning of the path is n its 



velocitv at the end will be ?/ -|- — / where t is the average time be- 



tween two collisions. The average velocity in the direction of the 



I ^ 

 electric field is therefore -X—/ since the average value of n taken 



over a large number of electrons is zero. Now the free path A is 

 equal to vt where i' is the mean speed. Thus the average drift 

 velocity of the electrons in the direction of the electric field may be 



1 ^ ^' ^ 



written in the form X . If 11 is the number of electrons in 



2 jn V 



unit volume, the number of them which, in unit time, drift across a 

 unit area drawn perpendicular to the direction of the electric force 



1 ^ e \ 



X will be - nX . Each of these carries a charge c so that the 



2 m V 



quantity of electricity transported across unit area, or in other words, 

 the electric current densit\- will be 



2 ;// V 

 Now it is a necessar}' consequence of the principles which under- 

 lie the kinetic theory of matter that \mv- should be equal to nB where 

 B is the absolute temperature and ot is a universal constant which may 



