Metallic Conduction. 297 



order to account for the law o£ Wiedemann and Franz, it is 

 necessary to suppose that at the temperatures at which this 

 law is valid, the electrons possess the kinetic energy appro- 

 priate to the molecules of a monatomic gas at the same 

 temperature. This suggests that the velocities are distributed 

 amongst the electrons in accordance with Maxwell's law. 

 If we adopt this assumption as a working hypothesis we can 

 calculate the number of electrons emitted from unit area of 

 the surface in unit time in the following manner : — 



The number which start outwards from unit area of the 

 surface per second is 



n = %Npd (2) 



Of these, the proportion which have a velocity component u 

 normal to the surface between the limits u and u + du is 



2(— Vr-*""'*! (3) 



In order to escape it is necessary that 



v?>2w/m, (4) 



where m is the mass of an electron and w is the work done 

 at the surface in escaping. The number which escape in 

 unit time is therefore 



7/1 



Since 2hw is a fairly large number, the integral on the right- 

 hand side of (5) is very nearly equal to \(21iw)-\e-' 2hw , 

 and, after substituting from (1), the number which escape 

 becomes, since 27i=(&T)~ 1 , 



i 3 *T /W , lT 



e=2^M C V ^<- W . ' • ' W 



where i is the surface- density of the saturation thermionic 

 current at temperature T. Since cT. is constant, this makes 

 t of the form AT^~ 6/T , where A and b are independent of T, 

 if M is independent of T. As is well known, this form 

 of expression agrees with the experimental results. A form 

 which is in better accord with the thermodynamical require- 

 ments and agrees as well with ihe experiments is ? = AT 2 e~ b/T . 



