Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/482

 open circuit in which there is no conduction of heat or electricity (so that and  are zero). Integrating the equation

across the junction of the metals, we have

or since, which represents the average kinetic energy of an electron, is by Drude's assumption equal to , where denotes a universal constant, we have

This may be interpreted as the difference of potential connected with the Peltier effect at the junction of two metals; the product of the difference of potential and the current measures the evolution of heat at the junction. The Peltier discontinuity of potential is of the order of a thousandth of a volt, and must be distinguished from Volta's contact-difference of potential, which is generally much larger, and which, as it presumably depends on the relation of the metals to the medium in which they are immersed, is beyond the scope of the present investigation.

Returning to the general equations, we observe that the flux of energy is parallel to the axis of, and is given by the equation

where the integration is again extended over all possible values of the components of velocity; performing the integration, we have

or, substituting for from the equation already found,