﻿Electron Theory of Thermoelectric Phenomena. 985 



surface of the metal cannot be determined in such a simple 

 manner. For the sake of brevity I shall consider here only 

 the simple case in which the piece of metal is of uniform 

 temperature and consists of two bars of different metals joined 

 together, the condensation of electricity taking place in one 

 and the evaporation in the other. 



If an electric current flows through a metal there will be 

 a transfer of energy through any surface in the interior of 

 the metal as a consequence of the flow of electrons through it. 

 The magnitude of energy transferred per unit of electric 

 current will depend not only on the potential energy of the 

 free electrons and on the temperature, but also on the con- 

 ditions of motion of the electrons in the metal. For, in 

 different metals according to the different conditions for the 

 motions of the free electrons, the electric current will be 

 distributed in a different way among the groups of electrons 

 with the various absolute velocities. — If, for instance, we 

 suppose that the electrons move freely between the metal 

 molecules and are only affected by them by separate collisions, 

 and if in these collisions the forces between the electrons 

 and the molecules vary inversely as the nth power of their 

 distance apart, the amount of kinetic energy transferred 

 through a surface in the interior of the metal when a unit 

 quantity of electricity is transferred through that surface 



will be -z . -T {cf. my paper, pp. 63 and G6), in which e 



is the charge on an electron, T the absolute temperature, 

 and k the universal gas-constant referred to a molecule 



The expression for the Peltier effect, calculated directly 

 from the difference in the transfer of energy in the two 

 metals, will therefore depend not only on (lj the difference 

 in potential energy of the free electrons, but also on (2) 

 the difference in kinetic energy transferred by the electric 

 current in the two metals. — If, for instance, we suppose that 

 the molecules in the one metal act upon the electrons as hard 

 elastic spheres (>i = co), and in the other as electric doublets 

 (w = 3, cf. my paper, p. 35), the part of the Peltier effect 



arising from (2) alone will be equal to - T, corresponding to 



a potential difference of c. O0235 volt, which is of the 

 same order of magnitude as the greatest Peltier effect 

 observed. 



Now returning to Prof. Piohardsons calculation, we 

 see that in the determination of the heat absorbed or 

 developed at the end of the piece of metal considered, 



