53a 



by the observations of Kamerlingh Onnes down lo the lowest 

 temperatures at which electric condiictixit}' has been investigated. 

 The application of the quantum-theory given here again allows us 

 to consider the equilibrium between the free electrons and the 

 electrons within the uiolecules as a dissociation equilibrium in the 

 way as lately brought to the front particularly by Koenigsbergek 

 for the purpose of the theory of electric conductivity. 



In the second place the difticulty disappears which in the 

 equipartition-theory follo\> ed from the small contribution made 

 by the free electrons to the specific heat of the metaP), a diffi- 

 culty which — Dr. Oosterhuis drew my attention to this fact — 

 even more sharply appeal's in the theory of the TnoMsoN-heat (§ 2). 



The solution of these difTiculties can at present be adduced in 

 favour of the application of the quantum-theory as considered here. 

 For a further confirmation it will be particularly required, that on 

 the theory it will be found possible to ascribe to the free electrons 

 in the metal at different teuiperatures definite densities, which on 

 the one side bring iuto pro[)er mutual connection the different 

 phenomena which depend on those densities, and which on the 

 other side also change with temperature in a way which seems 

 reasonable. 



This paper, which bears only an introductory and surveying 

 character, cannot go so far. We will, after having given some 

 general considerations, limit ourselves to the treatment of the thermo- 

 electric power, with which the PELTiER-effect and the TaoMSON-effect 

 are connected. 



As Hunting laws for the thermoelectric power between two metals 

 and for the TfiOMSON-effect in a metal a decrease to at T=0 

 proportional to T\ for the PELTiER-effect a decrease to proportional 

 to 7'' are found. These results e.g. as regards the decrease of the 

 thermoelectric power are confirmed by the present observations, and 

 may perhaps give a method for a direct experimental test of the 

 theory *). 



of accurate measurements at very low temperatures, Leiden 1904, Comm. Leiden 

 Suppl. N'^. 9 p. 25 sqq , cf. also J. Becquerel and H. Kamerlingh Onnes, Gomm. 

 NO. 103, Febr. J 908, § 7). 



1; These and the preceding considerations were for the greater part given by me 

 before in the discussion at the Wolfskehl congress April 25 and 26 last. 



2; Since these considerations were developed by me, the article of K. F. Herz- 

 FELD, Wien Silz. Ber. 121, Oct. 1912, p. 1449 on contributions to the statistical 

 theory of radiation came into ray hands, in which the suggestion occurs that the 

 supposition, according to which for the energy of the free electrons in a metal 

 a formula would hold corresponding to that which is valid for the Planck's 



