Electron Theory of the Metallic State. 75)1 



that of the atom. But according to the quantum theory 

 such great frequencies rarely occur at ordinary tempe- 

 ratures, so that the supposition or! equipartiiion of energy 

 would lead to discrepancy with the quantum theory. 



As the theory of Born and von Karman, which we have 

 made use of, is deduced for a simple cubic space-lattice, 

 it is not full}* clear what is meant by 8. We will, however, 

 for our approximate calculation simply put it equal to the 

 smallest atomic distance, or R \J2. 



§ 7. Electric Conduction at High Temperatures. 



The first effect of an electric field of force in the metal 

 will be a displacement of the free electrons in a direction 

 opposite the electric force; and this polarization in con- 

 nexion with the thermal motions of the electrons will call" 

 forth the electric current. To calculate the polarization, 

 we may in any definite way connect every election with 

 one of its neighbouring atoms and inversely every atom 

 with one electron. The state of the cubic centimetre of 

 the metal will be equivalent to n dipoles of a mean moment 

 nearly equal to eR. The motions of the electrons will be 

 equivalent to a rotation of these dipoles with an energy 

 of rotation equal to the kinetic energy (u) of the electrons 

 in the equipotential surfaces, corresponding to two degrees 

 of freedom. 



It is, moreover, possible that this way of description of 

 the state of a metal will have not only a mathematical but 

 also a physical meaning. In the statical state, dealt with 

 in § 4, the electrons are, because of the third term in (2'') r 

 always repelled by the neighbouring atoms. But where 

 the atoms, by their oscillations, are removed from each 

 other, the electrons will be attracted to them ; and as 

 the electrons will seek out such places, a great number of 

 them at least will move under the influence of a resulting 

 attracting force from one of the neighbouring atoms. 



The polarization as a function of the electric force X can 

 be calculated in conformity with the theory of magnetism 

 given by Langevin *. and is found to be 



p = p '»¥> • (") 



where l\„ = >*eR is the maximal moment conceivable as due 

 to polarization, and /' is given by (10). To the maximal 



• P. Langevin, Journ. de Fhy.s. iv. p. 078 (1905). 



