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XL VIII. The Expression for the Electrical Conductivity of 

 Metals as deduced from the Electron Theory. By W. F.. 

 G. SwAKN", D.Sc, A M.C.S., Assistant Lecturer in Physics 

 at the University of Sheffield *. 



Introduction. 



HE theory of the electrical conductivity of metals has 

 been worked out on many assumptions. One of the 

 simplest and best known of these methods is that employed 

 by Drude, in which the assumption is made that in the 

 absence of the electric field all the electrons move with the 

 same velocity, and that the velocity produced by the field in 

 an electron is the velocity which is produced in it while it is 

 travelling between two points of collision, the essential 

 assumption being that at each collision the effect of all 

 previous actions of the field on the electron are wiped out. 

 The value of the conductivity a which has been deduced from 

 these assumptions is 



ne 2 Xv , ^ N 



where n is the number of electrons per c.c. ? X is the mean 

 free path, v is the velocity, and a0 is the kinetic energy of a 

 gas molecule at a temperature 0. 



The object of Part I. of the present paper is to show that 

 the above assumptions do not lead to (1), but to the formula 



<r= n -^ (2) 



The difference between (1) and (2) is partly due to what is,, 

 in the opinion of the author, an improper use of the quantity 

 known as the mean free path, and partly due to another 

 cause which will be better understood at a later stage of the 

 paper. 



The thermal conductivity k calculated with the proper use 

 of the mean free path gives, for the above case, the ordinarily 

 accepted value k — hiiXvot ; and the interesting point is, that 

 while at 0° 0. (1) gives k/<r=G'3 x 10 10 , (2) results in 

 /j/<7 = 4*7 x 10 10 . The experimentally found value of k/<r for 

 most pure metals is about 6*3 X 10 10 at 0° 0.; so that the 

 conclusion to be drawn is, that the assumptions on which (1) 

 and (2) are based are nothing like as representative of th^ 



* Communicated by the Author (now of the Carnegie Institution of 

 Washington). 



f J.J. Thomson, ' Corpuscular Theory of Matter/ p. 56. 



