122 



whether the hypothesis that restistance is caused by vibrators (the 

 electrons otherwise moving freely through the metal with speeds in 

 accordance with the kinetic theory of' gases ^)) is well adapted to 

 deduce the change of resistance with temperature, I put the mean 

 free path of the free electrons inversely proportional to the mean 

 amplitnde of Planck's vibrators, which disturb them in their move- 

 ments, while this mean amplitude was calculated by the formula 

 which Planck at the time gave for the mean energy of the vibrators. 

 The way in which mean values were introduced by this (comp, the 

 reasonings in Wien's theory, which clearly show the deficiencies of 

 mine) could not allow us to expect more than a qualitative repre- 

 sentation. Yet, as is rather remarkable, a close agreement was 

 obtained with the observations between the ordinary temperature 

 and that of liquid hydrogen. It is more difficult to judge of the 

 suitability of the new hypothesis for reproducing the observations 

 Avith metals above the vanishing point. According to the note at 

 the end of Comm. N". 119 the energy of the vibrators would also 

 determine the increase of the volume of the metal fj-om 2^=0. 

 The mean distance of the surface of the atoms may thus perhaps 

 be taken proportional to the square of the mean amplitude calculated 

 according to Planck's just mentioned formula. We may perhaps 

 further conclude that the idea of the condition above the vanishing 

 point at which we arrived starting from the hypothesis concerning 

 the sviper-conducting state, will appear to be not unsuitable, and in 

 any case gives no ground for objecting to the last named hypothesis. 

 On both assumptions, however, the assumption that the free path 

 is continuously described by the same electron, and also the other 

 that it is broken by the movement being transferred from one 

 electron to another, a difficulty arises in the explanation of normal 

 resistance, because Planck's previous formula has been replaced by 

 a new one. In the discussions at the Conseil Solvay ^) (Oct. 1911) I 

 pointed out that according io the theory developed in Comm. N". 119, 

 if we introduce the new formula, and further calculate in the same 

 way, i.e. with only one frequency, the resistance could not fall 

 below a certain value determined by the "internal temperature" 



1) Keesom (Verslag Akademie XXII, p. 108, Suppl. No. 30b) not yet translated 

 in These Proceedings) has come to theimportant conclusion, by the application 

 of the quanta-theory to the free electrons in a metal (considered as a monatomic 

 gas) that at low temperatures the velocity of the free electrons becomes independent 

 of the temperature, and has called this field of temperature the "Wien field". 



~) La theorie du rayonnement et des quanta, Rapports et discussions de la 

 reunion a Bruxelles sous les auspices de M. Solvay. Paris 1912 p. 129. 



