24Ö 



mentioned F=4.10\ This corresponds to a number of electrons 

 per cm=' n = ^.7A0'\ &, then has the value 5500. 



Hence it appears that in this region of temperature the formulae 

 given in §§ 4c and 5c of the former communication for the low 

 temperatures, will be applicable. 



At decreasing temperature the density of the electrons, for a 

 metal like platinum, deci-eases, as follows froai the TnoMSON-constant 

 of this metal being negative. Later on in this section it will be 

 shown that for low temperatures a tinite limiting value has to be 

 assumed for n. We will for a moment suppose that for the tem- 

 peratures, which can be obtained with liquid helium, for the metal 

 considered above F= 10\ For this density of electrons ^„ = 139, 

 so that for these low temperatures also the same formulae are valid. 

 A fortiori this will be the case if the density of electrons is greater 

 than has been supposed. 



For such metals as the one considered above there will therefore 

 be a region of temperature larger or smaller according to the 

 density of electrons, in which the supposition of Wien : the velocity 

 of electrons = const., is nearly fultilled as regards the mean velocity, 

 if in that region the density of the electrons does not change appre- 

 ciably with temperature. 



It can easily be seen that this second supposition of Wien : the 

 number of electrons per cm^ = const., will also be nearly fulfilled 

 at sufficiently low temperatui-es. The number of free electrons is 

 determined by the dynamic equilibrium between the free electrons 

 in the intermolecular space and the electrons within the molecules. 

 Concerning the latter different suppositions may be made, e. g. that 

 they, or a number of them, are moving freely within the molecules. 

 In this case, as in general, at least at low temperatures, the density 

 of electrons will be greatei" within the molecule then outside it, the 

 velocity of the electrons within the molecule will in the region of 

 temperature considered be a fortiori constant if the density does not 

 change, it can also be supposed that the electrons inside (or on the 

 surface of) the molecule are more or less strongly bound to the 

 molecule ; the frequencies of those electrons will then depend on the 

 nature of this binding and perhaps also on the frequencies of the 

 molecules. Be that as it may, in follovv ing up the hypothesis regarding 

 the zero point energy (cf. the former paper) consistently we shall 

 have to admit that, when taking the temperature sufficiently low, 

 we shall come to a region in which the motions within the mole- 

 cule will be nearly independent of the temperature. In this region, 

 in so far as it lies in the corresponding region for the electrons 



