650 BELL SYSTEM TECHNICAL JOURNAL 



impeded by collision with the atoms (ions, really, since they are atoms 

 which have given up free electrons) according to some theories, and with 

 the spaces between atoms according to other theories, and this im- 

 peding process gave rise to electrical resistance. The free electrons 

 were capable of conducting thermal as well " as electrical currents. 

 Although the theory gave reasonable values for the electrical and 

 thermal conductivities of metals at room temperature, the predicted 

 dependence upon temperature was wrong: the resistance of a pure 

 metal is known from experiment to be very nearly proportional to 

 the absolute temperature; the classical theory, unless aided by very 

 unnatural assumptions, predicted proportionality to the square root 

 of the absolute temperature. Another difficulty, the greatest in fact 

 which beset the old theory of free electrons in metals, was concerned 

 with the specific heats of metals. According to the billiard ball 

 theory of gases, the specific heat arose from the kinetic energy of 

 motion of the gas atoms; thus the specific heat at constant volume of 

 one gram atom of a monatomic gas was (3/2)R, where R is the gas 

 constant. This was in good agreement with experiment. For solids 

 this specific heat was just doubled, giving {6/2)R because of the 

 addition of potential energy to the kinetic. For a metal the free 

 electrons were regarded as having kinetic energy. In order to explain 

 the observed electrical properties of a metal, the number of electrons 

 was taken as approximately equal to the number of atoms. Hence, 

 as for a monatomic gas, a specific heat of {S/2)R was expected for the 

 electron gas and, therefore, a specific heat of (9/2) i? was predicted for 

 a metal. Measurement shows that most crystals, metals included, fit 

 quite well the value of (6/2)i? and that (9/2)i? is incorrect. Thus 

 classical theory was left with the dilemma that to explain electrical 

 properties one free electron per atom was needed while to explain 

 specific heat one free electron per atom was far too many. This di- 

 lemma is very neatly resolved in the new theory; in this paper we 

 shall show why the free electrons are not free for specific heat and in 

 a later paper why they are free for conduction. We shall also show 

 that the new theory leads to quite proper values for the conductivity 

 and also explains facts concerning the resistance of alloys, which the 

 classical theory could not do. 



According to the classical theory there was one quantity that should 

 be the same for all metals and this was the ratio of the thermal to the 

 electrical conductivities. This ratio, known as the Wiedemann-Franz 

 ratio, was predicted to be equal to the absolute temperature times a 

 universal constant L called the Lorentz number. This prediction 

 was in reasonable agreement with experiment. The new wave me- 



