537 



gas with the same order of magnitude of tlie number of particles 

 per unit of volume, become very mucli higher than in the ordinary 

 material gases. Hence the limiting laws deduced for low tempera- 

 tures may be valid for a system of free electrons up to much higher 

 temperatures, possibly even in the region of temperature which can 

 be reached experimentally. The consideration of the dynamic equili- 

 brium between the free electrons and the electrons within the 

 molecules of the metal leads (§ 2) to the supposition, that at low 

 temperatures the number of free electrons per unit of volume 

 approaches to a constant finite value. The same is then the case for 

 the mean velocity of the free electrons. 



In this manner the application of the quantum-theory to the free 

 electrons in a metal leads for low temperatui-es to the suppositions 

 regarding velocity^) and density of electrons, on which Wien^) 

 recently based his theory of electi'ic conduction, in which theory 

 further, as was done previously by Kamerlingh Onnes^) and by 

 LiNDEMANN ^), the quantum-theory is applied to the molecular oscil- 

 lations which impede the motion of the free electrons. On the other 

 hand the application of the quantum-theory to the free electrons 

 leads for high temperatures, e.g. for the region of temperatures, 

 which is characterised by phenomena as those investigated by 

 Richardson fperhaps even for still higher temperatures only), to the 

 theory of free electrons in metals in the form in which it has been 

 developed by Riecke'), Drude"), I.orentz'), and which we can call 

 the equipartition-theory. Hence the quantum-theory appears to be 

 able to unite both the theories mentioned into one simple and coherent 

 whole. 



By it at the same time two great difticulties, which were inherent 

 to the equipartition-theory, are solved. 



In the first place it does not follow any more, as was to be 

 assume on the equipartition-theory, that on approaching to l'=0 the 

 electrons all "freeze down" ^), a phenomenon which is contradicted 



1) At least as regards the mean velocity. 



-) W. WiEN. Berlin. Sitz.-Ber. 16 Jan. 1913, p. 184. 



■^) H. Kamerlingh Onnes. Gomm. No. 119 {Fehv. 1911). 



4) F. A. LiNDEMANN. Berlin Sitz.-Ber. 1911, p. 316. 



5) E. Rtecke. Wied. Ann. 66 (1898', p. 353, 545. 

 c) P. Drude. Ann. d. Pliys. (4) 1 (1900), p. 566. 



7) H. A. LoRENTz. These Proceedings Dec. 1904, Jan. 1905. 



*^) A number of the images used here, borrowed from the comparison of 

 electrons with a substance, such as the idea of the equation of stale of the 

 electrons, saturated electron-vapour, equilibrium with precipitated electrons, and 

 frozen down electrons were developed by Kamerlingh Onnes (On the importance 



