112 Mr. G. H. Livens on the Electron 



estimate o£ the number of free electrons taking part in 

 the conduction phenomena. As is well known, the various 

 coefficients occurring in connexion with the Hall effect and 

 allied phenomena contain this number as the only unknown 

 constant in their expression in terms of the electron constants 

 of the metal. It is, however, very significant that just in 

 this one particular part of the subject, where a good estimate 

 of the number could be expected, the results obtained on 

 the basis of the present theory are hopelessly inadequate 

 to express the actual experimental results determined. This 

 fact suggests and strongly emphasizes the view that the 

 simple theory is by no means consistent with the actual 

 state of affairs. 



It is therefore held that it is useless at present to make 

 any attempt to obtain the accuracy which Nicholson claims 

 for his calculations, and also, therefore, these calculations 

 cannot be said to result in favour of any theory, and more 

 particularly of the incomplete theory due to H. A. Wilson. 



The University, Sheffield, 

 December 4, 1914. 



VII. On the Electron Theory of Metallic Conduction. — III. 

 By G. H. Livens * . 



THE researches of Riecke, N '?<}?• Thomson, Lorentz, and 

 others have shown that in ductivity of metals for 



electricity and heat may be satisfactorily explained on the 

 hypothesis that a metal contains a very large number of free 

 electrons, and that these electrons, taking part in the heat 

 motion of the body, move to and fro with a speed depending 

 on the temperature. 



Problems f relating to the motion of enumerable electrons 

 in a piece of metal are best treated by the statistical method 

 which Maxwell introduced into the kinetic theory of gases, 

 and which may be represented in a simple geometrical form 

 so long as we are concerned only with the motion of trans- 

 lation of the electrons. Indeed, it is clear that, if we 

 construct a diagram in which the velocity of each electron 

 is represented in direction and magnitude by a vector OP 

 drawn from a fixed point 0, the distribution of the ends P 

 of these vectors, the velocity points, will give us an image- 

 of the state of the motion of the electrons. 



* Communicated by the Author. 



t Vide Lorentz, ' The Theory of Electrons' (pp. 266-271), from which 

 the first few paragraphs of this paper are taken. 



