548 Electron Theory of Hall Effect and Allied Phenomena. 



field at any point in the interior of the metal will not simply 

 be the electric force in the external field, but will, as in the 

 case of the magnetic field, be increased by a local part which,, 

 if we assume again isotropy, may be written in the form 



aP, 



P defining the intensity of the polarization induced in the 

 metallic atoms around the point. The driving field for the- 

 current is therefore 



E + aP. 



If we assume that K is the specific inductive capacity of 

 the metal, 



P = D-E = (K-1)E, 



D denoting the total electric displacement in Maxwell's sense. 

 The driving field is thus 



E[l + a(K-l)], 

 so that the current is 



<7(l + aK^l)E, 



or the conductivity as ordinarily defined must be taken as 

 (r' = ff(l + aK^i). 



The application of the magnetic field will now have the* 

 additional effect of destroying the isotropy of the local 

 electric field, so that the constant a will become a function 

 of direction in the metal, again with the coefficients as even 

 functions of the magnetic force intensity. 



In conclusion, it would seem that there appears to be 

 ample scope for adapting the theory propounded in the 

 previous pages to provide an effective explanation of all the 

 regularities and irregularities observed in connexion with 

 the present phenomena, and although the precise mathe- 

 matical theory necessarily suffers from the essential incap- 

 ability of taking a full account of the constitutional irregu- 

 larities of the phenomena, it is nevertheless capable of 

 interpretation in a manner which provides for an explanation 

 of these irregularities. In this respect therefore the theory 

 must be regarded as complete as is possible in the present, 

 stage of our knowledge. 



The University, Sheffield, 

 January 28th,] 9] 5. 



