Electron Theory of the Metallic State. 7G1 



where r=- is the specific resistance. Putting /> = 1, and 



A' OX" 



as n=—£- we get 



A <fr degree' 



(2(5 



Inserting numerical values, we find in two extreme cases 

 for Ag c' — 0*004, and for Bi c' = 00D calorie per degree. 

 As the atom-heat is for high temperatures almost equal 

 to () calories per degree, we see that the electrons give 

 but an imperceptible contribution to it, which is in good 

 agreement with the modern theory of specific heat and 

 experimental facts. 



§ 12. /^mission of Electrons from Hot Metals. 



Measurements on the density i of the electric current 

 from the surfaces of hot metals are satisfied by 



i =: ATV'i 



where A, X, and b are constants. The constancy of b is 

 well established. It is for some metals known with an 

 uncertainty of a few tenths per cent. A has a similar 

 uncertainty already in its logarithm. About X we only know 

 that it cannot be much greater than one. 



On the presumption that the kinetic energy of the 

 electrons is proportional to T, and that Maxwell's law 

 of distribution holds, this expression is deduced theoretically, 



wherebv X is found to be one-half. ^ is then interpreted as 



the ratio of the work necessary to remove an electron from 



the metal to two-thirds of the mean kinetic energy of the 



electrons. Assuming the electron energy to be equivalent 



to that of a gas molecule at t e same temperature, and the 



work done when an electron is removed to be of the order 



e 2 

 of magnitude of =r, the classical theory comes into good 



agreement with the experimental values for b. 



We can try to calculate i in a similar way from the point 

 of view of our theory. If the electrons are supposed to be 

 emitted from the interior of the hot metal, we should have 



— = -^-\ where $ e is calculated from (2), (4), and (5) to be 



1-742^-T L and u is given by (10) or (14). In this way 

 Phil. Mag. S. 6. Vol. 40. No. 240. Dec. 1920. 3 D- 



