Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/481

 an examination of the circumstances of a collision, in the manner of the kinetic theory of gases, shows that must have the form, where  denotes a constant which is closely related to the mean free path of the electrons. In the terms on the right-hand side of the equation, on the other hand, Maxwell's term gives a result different from zero; and in comparison with this we may neglect the terms which arisefrom. Thus we have

or

and thus the law of distribution of velocities is determined.

The electric current is determined by the equation

where the integration is extended over all possible values of the components of velocity of the electrons. The Maxwellian term in furnishes no contribution to this integral, so we have

When the integration is performed, this formula becomes

or

The coefficient of in this equation must evidently represent the ohmic specific resistance of the metal; so if  denote the specific conductivity, we have

Let the equation be next applied to the case of two metals. and in contact at the same temperature, forming an