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XCIX. Note on the Electron Theory of Thermoelectric 

 Phenomena. 

 To the Editors of the PhilosopJiical Magazine. 

 Gentlemen, — 



IN the February number o£ the Philosophical Magazine 

 Prof. 0. W. Richardson has published a paper on " The 

 Electron Theory of Contact Electromotive Force and Thermo- 

 electricity." As his results with respect to the Peltier and 

 Thomson effects are in disagreement with results 1 have 

 obtained in a previous paper (N. Bohr, Studier over Metal- 

 lemes Elektrontheori, Diss., Copenhagen, 1911), I shall be 

 glad to be allowed to try to explain briefly the reasons for 

 this disagreement. 



Prof. Richardson uses a very interesting method to cal- 

 culate the Peltier and Thomson effects. By this method, 

 which is based upon deductions from the results of expe- 

 riments on the emission and absorption of free electrons by 

 hot metal-surfaces, electricity is imagined to be transferred 

 by a reversible cyclic process through a circuit partly 

 consisting of metals ; and the amount of work gained and 

 the heat absorbed by this process is discussed on thermo- 

 dynamic principles. [It may be remarked that the process 

 adopted for the calculation of the Thomson effect is not 

 strictly reversible, and that the influence of this fact, as 

 Boltzmann has shown (Sitzungsber. d. Wiener Acad. d. Wis&., 

 math.-nat. Kl., Bd. 96, Abt. ii. p. 1258,. 1887; cf. my paper, 

 p. 72), cannot be infinitely diminished by altering the dimen- 

 sions and the shape of the piece of metal which forms the 

 part of the circuit considered. We shall not, however, 

 discuss this point further here.] 



In the circuits considered by Prof. Richardson, the transfer 

 of electricity through a piece of metal is established in the 

 following way. Electricity in the form of free electrons is 

 " condensed " from the surrounding space into the metal 

 at one end of the piece of metal considered and allowed to 

 " evaporate " from the metal at the other end. The Peltier 

 and Thomson effects are then calculated from the difference 

 between the whole amount of heat developed in the metal 

 during the process considered and the amount of heat deve- 

 loped at the ends of the piece of metal by the condensation 

 and evaporation of the electrons. 



The latter quantity of heat is calculated from the difference 

 in potential energy of an electron inside and outside the metal 

 surface. This way of calculating is, however, in my opinion 

 not justifiable, as the amount of heat developed at the 



