the Electrical Conductivity of Metals. 451 



these two quantities. The conductivity k is obtained by 

 dividing this by -=-. We thus have 



&= 3 a j 6-^^=— r (k)H e-^ c VM«. (21) 



For the present case, where we take X c as constant, we 

 find 



:i V a- 



and using (20) 



3 V 3^'*, 



^1= ^ =3-6 x 10 10 at 0° C, 

 <t 3 <r 



which is very far from the experimental value. 



If the mean free path were a function of the velocity, as 

 might conceivably happen if the centres inside the atoms with 

 which the collisions occur were in motion, the expressions 

 for& and g would require modification. \ c would have to be 

 retained inside the integral in equation (21), and if X c were a 

 function only of the initial velocity with which the electron 

 started out after collision, the only modification which would 

 be necessary in the calculation of cr would be to retain 

 X c inside the integral in (19), so that we should have 



f 



7-0 



k __ umjo 

 a~Je 2 



J. 



If, for example, \ were proportional to c n , we should have 



* 2eVl ' T ( n + l)~~ 3 «*\2 /' 

 so that if Xc were proportional to c% we should have 

 -=6-3 xlO 10 , 



a 



which is just the correct value. 



Unfortunately, when we form a physical picture of the 

 phenomenon it does not seem reasonable to try in the problem 



