23Ö 



^ 2. Ill order to make an estimate of tlie characteristic 

 temperatures of a detinite system of free electrons it is necessaiy 

 to have an estimation of the density of the electrons in the system, 

 or, which comes to the same, about the Nolume V of a gramme- 

 molecule of the electron gas. It is well known that the opinions 

 about the density of free electrons in metals diverge largely. To 

 obtain such an estimation we will start in this paper from the 

 following fact. The Thomson constant, which (cf. § 5) may be con- 

 sidered as the specific heat of the "saturated electron vapour", can 

 be written as the difference of two terms, of which the first re- 

 presents the specific heat at constant volume, whereas the second 

 depends on the change of the density of electrons with temperature. 

 If the first term is calculated according to the equipartition-tlieory 

 and compared with the value experimentally found, the latter appears 

 to be always (in absolute value) many times smaller than the first 

 term, on the average about 753 of if- The equipartition-theory was 

 therefore obliged to suppose the second term mentioned above to 

 be constantly and for all the metals nearly equal to the first. 

 According to J. J. Thomson^) this would be the case if the number 

 of free electrons is alvvciys nearly proportional to 7'V2. The theory 

 of LoRENTZ, to which the mode of calculation followed in § § 3 — 5 

 leads in the case of equipartition, would require n (the number of 

 electrons per cm'') to be nearly proportional to l^^l^-, Drude's theory 

 n to be nearly proportional to T'^'^. As far as I know for no one 

 of these modes of dependence on the temperature a reasonable 

 explanation has been given. Considered from the point of view of 

 the dissociation-theory they hardly can be accepted as generally 

 valid. 



It seems to me to be more reasonable to suppose, that for the 

 metals the specific heat at constant volume itself has a small value 

 compared with the equipartition value. If for a definite metal at 

 0° C. we put C,. = V'50 ^' «5 if follows from equation (22) with 

 {ISh) of the former paper o^ith 31 = iV X 0,8.10-'-^" for the elec- 

 trons) that for the free electrons in that metal at the temperature 



oscillator, would cause dilfereut difficulties of the equipartition-theory, which are 

 also mentioned in this section, to disappear. Cf. further the article of Herzfeld, 

 Ann. d. Phys. (4) 41 (1913), p. 27, which has just appeared ; a similar remark 

 was made by J. Koemgsberger, Verh. d. D. physik. Ges. 1911, p. 934. A, L. 

 Bernouilli, ZS. f. Eleklrochem. 17 (1911), p. 689, used also the Planck-Einstein's 

 formula for the energy in treating the thermo-electric phenomena, but in quite a 

 difïerent manner from the one in this paper (cf. in particular also the remarks 

 by Krüger, on p. 693 of the same volume). 



^) J. J. Thomson. Die Korpuskulartheorie der Materie, Braunschweig 1908, p. 77. 



