the Electrical Conductivity of Metals. 4,Yl 



distances between r and r-t-dr, the value of 2R(&i) 3 for this 

 •set is 



s^*r 



RdR=^e- r *-dr; . . . (15) 



and if I is the average distance which all the electrons to be 

 found at E have travelled 



nl=\ £ 2 e- r *jdr = n\; .... (16) 

 *• o 

 «o that 



Z=X, 



We may notice that if all the electrons had travelled one 



and only one distance A. the right-hand sides of equations 



(15) and (16) would have both been modified to the same 



n X 2 

 -expression, viz. -• — , so that I would have been equal to X/2, 



A, L 



which is the assumption made in the deduction of (1). In fact, 

 though X is the mean free path, we must not say that the 

 average distance which the electrons at E have travelled 

 is X/2. It is really \. If neglect of this consideration were 

 the only error in the usual calculation of (1), the true result 



would be o"= — 3-; but there is another source of error to 



which I will now refer. 



It is legitimate to argue that since X is the average distance 

 which all the electrons to be found at E have travelled, the 



average velocitv created bv the field is - — - (which is the 



j j mv \ 



argument made in the deduction of (1) after allowance has 

 been made for the fact that the X/2 of that argument should 

 be replaced by X), but it is not legitimate to say that the 



resultant current is therefore . ne. the point being- that 



mv l rt 



the field has, as it were, sorted out the electrons differently 



from the two sides of the plane PM. In fact, if each of the 



electrons at present at E were suddenly robbed of the velocity 



which the field has given it, there would still be a resultant 



current there. We can readily see this; for on glancing at 



fig. 1 we remember that the electrons which have come from 



to E have been bent in their path on the way. They 



•originally started out at an inclination 6 to the normal, 



i. e. at a greater inclination than the angle yjr. On the other 



hand, the electrons which have come from the element at Q 



2K2 



