﻿Theory of the Metallic State. 139 



different directions. The few measurements available seem 

 to confirm this view, which would not seem to be readily 

 derivable from the old theory. On ohe other hand, the 

 elastic properties also vary in different axes, and the 

 variation of the atomic amplitudes occasioned thereby might 

 compensate the change in the distance which the electron 

 space-lattice would have to pass through, and thus sometimes 

 mask the phenomenon. This effect would of course not 

 be noticeable in an agglomeration of crystals oriented at 

 random, such as the specimens are which are used for 

 experiments. According to the proposed theory, an increase 

 of pressure would lead to an increase in the atomic frequency 

 and consequently to a decrease in the amplitude. This would 

 entail a decrease in the resistance, such as has been found 

 experimentally. It would seem difficult to explain this 

 phenomenon by the accepted theory. The thermodynamic 

 aspects of the space-lattice theory are particularly simple. 

 As the electrons form a crystal, Nernst's theorem may 

 certainly be applied to them, and all the consequences already 

 deduced by this method hold good. The admissibility of 

 applying this theorem, as has been done, to electrons con- 

 sidered as a perfect gas is much more doubtful *. 



It will be objected that the assumption of a force kf(r) 

 and of a number N and a dielectric constant D to satisfy 

 the condition $(N, &)~^r(N, D), are simply made to explain 

 the phenomena, without any regard for a priori probability. 

 On the other hand, once these assumptions are made, all the 

 essentially metallic phenomena may be explained without 

 any intrinsic contradictions, including some facts, such as the 

 electrical resistance of alloys and the photoelectric effect, on 

 which the accepted theory throws no light at all. 



The accepted theory, besides leading to the absolute contra- 

 dictions touched upon in the introduction, entails special 

 hypotheses for many of the secondary phenomena. Its one 

 triumph, the derivation of the constant of Wiedemann-Franz's 

 law, is based upon the theorem of the equipartition of energy, 

 whose applicability to electrons as they are supposed to exist, 

 is generally recognized as absolutely inadmissible. 



Conclusions, 



The free electrons in a metal may not be treated as a gas, 

 for a gas can only conduct heat well if its heat capacity is 

 large. Experiment proves that the free electrons conduct 

 heat well, but that their heat capacity is too small to be 



* E. Griineisen, Verh. d, <L Phys. G*s. xv. 0. p. 186 (1913). 



