241 



outside the molecules, the density of the latter may be supposed to 

 be nearly constant. 



It was already remarked in § i (hat in this manner two great 

 difKiculties of the equipartition-theory are solved. In the first place" 

 as regards the contribution by the free electrons to the specific heat 

 of the metal, the heat necessary for the free electrons dissociating 

 away from the molecules being included, with the values of the 

 density of the electrons and of its change with temperature accepted 

 above, this is found, at ordinary temperatures, to be only a small 

 fraction of the whole specific heat (order of magnitude Viooo)- 



At the same time, as was also indicated, the considerations given 

 here show how the "WiEN-region" and the "RiCHARDsoN-region" 

 may be connected together. For this a closer consideration of the 

 dissociation equilibrium: free electrons ^ electrons within the mole- 

 cules is necessary. In any case it may be conjectured that the 

 curve which will represent the density of the free electrons as a 

 function of T will have, besides the part parallel to the T-axis 

 mentioned above for low temperatures, a similar part for high 

 temperatures \) (when all tjie available electrons have been disso- 

 ciated oflf'), and that between these two parts a region lies in which 

 the density of the electrons changes with temperature. When this 

 "boundary curve" or the corresponding "vapour pressure curve" 

 shall be known, the mean velocity of the electrons will follow by 

 the relations of the former paper. Inversely the fact that the velo- 

 city of the electrons is connected in that way directly with the 

 density, may be of advantage in deducing both from observations. 



We will suppose for a moment that for a metal such as the 

 one considered above') at 1800° K. F=4.10'. For the energy 

 of the free electrons a value is then found which is more than 

 5 times as large as the equipartition value. It will afterwards have 

 to be investigated whether this result, that the mean velocity of the 

 free electrons at these high temperatures, for densities of electrons 

 such as follow from the estimations indicated above from the 

 TnoMsoN-heat, appears to be considerably larger than would be the 

 case according to the equipartition-theory, is excluded by the obser- 



1) Probably this region (in so far as it should be realisable) lies for most of 

 the metals considerably higher than that over which the observations of Richardson 

 or those on thermoelectric powers extend. 



~) The number of electrons per cm"\: w= 1.7.10-21^ is then still below the 

 number admitted for platinum by Baedeker, Die elektrischen Erscheinungen in 

 metallischen Leitern, Braunschweig 1911, p. 12, in his discussion of the Richardson* 

 effect. 



16 



Proceedings Royal Acad, Amsterdam. Vol. XVI. 



