114 Mr, G. H. Livens on the Electron 



to the group, is made to enter it. Writing adVdvdt and 



bdVdvdt for these two numbers, we have, after division by 



dVdv=dV'dv', 



fig+Xdt, V + Ydt, %+Zdt, x + %dt, y+ydt, z + %dt, t + dt) 



=/(?> V, & *> V, z > t)+(b-a)dt, 



or, since the function on the left-hand side may be re- 

 placed by 



this equation is the same as 



B£ d*? o? s o« oy oz ^t 



This is the general equation of which we have spoken. We 

 have now to calculate a and b, or at least their difference 

 (b-a). 



Thus far the argument is precisely the same as that given 

 by Lorentz ; it is, in fact, verbally transcribed from his own 

 account, which I am not inclined to attempt to improve 

 upon. We can, however, now proceed by a slightly different 

 line of argument whicli has the advantage of exhibiting the 

 beautiful generality of Lorentz's form of the theory. 



The present view of metallic conduction is that it takes 

 place by the free electrons whose velocities are prescribed 

 by collisions with the molecules, and so are taken as deter- 

 mined in the initial instants after collision by the law of 

 equality of mean energies in gas theory. This view, as 

 Drude states, seems to require tacitly that the average 

 velocity is in most instances restored by collision at the end 

 of each free path, although it might appear that such a 

 statement is not necessarily to be taken as literally true for 

 each individual electron, but merely collectively for the 

 whole swarm. 



Now in calculating bdtdVdv, which is the number of 

 electrons which enter the specified group by collision during 

 the time dt, we may notice that all the electrons which 

 collide with an atom during the small interval dt will, when 

 taken after collision, have the velocities assigned to them by 

 Maxwell's law, since the whole effect of the external fields 

 has been on the average obliterated by the collisions. The 

 number bdYdvdt would then be exactly the same as the 

 number adVdvdt, which is the number of electrons leaving 

 the aforesaid group in the same small interval, if there was 



