the Electrical Conductivity of Metals. 449 



The total resultant current density is thus 



?2£ 2 \X . . _ 2 ne 2 Xv& _ ne 2 \i?X # 

 mv o mv* ouU 



Giving for the conductivity o-, 



ne 2 \v 



(7 = 



which is the result found^on pages 441-445. 



Part IT. — Calculation of the electrical conductivity for the 

 case where the velocities of the electrons are distributed 

 according to Maxwell 9 s law in the absence of the electric 

 field, and where the number of electrons starting out in any 

 infinitesimal velocity range, from an element in which they 

 have suffered collisions, is the same when the field is 

 present as when it is absent. 



The number of electrons per c.c. having velocities between 

 c and c-hdc is, in the absence of the field, 



Ae- hmc2 c 2 dc, 



where * _ An 3m 



A 7= (km) 3 ' J , and hm = -, — -• 



V7T V ' 4«0 



If in (11) we replace v by c, n hjKe~ hmc2 c 2 dc, the resulting 

 expression will be the current density Sjj due to the flow from 

 left to right of that group of electrons which have velocities 

 between c and c-\-dc. The result is 



*. A . 2q fl 2Xe\\ 



dc. 



The corresponding current density 8j 2 due to the flow from 

 right to left is obtained by replacing X by —X in the above, 

 and the resultant current due to all the electrons whose 



* It is to be noted that the part , i.e. — — , represents the only 



mv 2ec9 



part of the current accounted for by Drude. The fact that he obtained 

 n ** 2 is simply due to the improper use of the quantity X already 



referred to. 



It is interesting to notice that if we were to imagine that all the 

 electrons for some reason or other travelled one and only one distance X, 



we should have <r= ^ ne v . 

 3 ccv 



