752 Dr. G. Borelius on the 



will be in a " fluid " state far below the melting-point of the 

 metal. 



As an electron cannot escape from between the atoms- 

 without a way being opened for it by the elastic waves of 

 thermal agitation, and as the greatest velocities for these 

 waves are, by the theory of Born and von Karman *, 2vB, 

 we may as a limit for high temperatures write the transport 

 velocity 



v=p. 2vS, (9) 



where p is a constant of the order one. 



The kinetic energy of the electrons must be intimately 

 connected with the transport velocity v. It will probably 

 not tend to a limit in the same way, but increase pro- 

 portionally to the heat content of the metal, which is at 

 high temperatures proportional to the absolute temperature. 



The correspondence of the kinetic energy with —- will 



probably be best in the neighbourhood of the characteristic 

 temperature 6 ( = fiv, /3 = 4*87 . 10 _u ), where the thermal 

 oscillations become appreciable. We are therefore led to 

 write the two-thirds (u) of the kinetic energy corresponding 

 to the two degrees of freedom of the motions on the (variable) 

 equipotential surfaces as 



« = </-f (2 " s,2 -J' (10) 



where the constants q have to be at least approximately of 

 order one. 



The part of the electrons' kinetic energy that exceeds 



171V 



—~- must, as is seen from the foregoing, give rise to 



u 



oscillations with amplitudes smaller than S. We have 

 shown that it is probable that this surplus is at least com- 



parable with -^-, which is only about a hundredth or 



thousandth of the kinetic energy of a molecule at ordinary 

 temperatures. It is perhaps worth while giving a further 

 reason for this disproportion between the energy of oscil- 

 lation of the electrons and atoms. If their kinetic energies 

 were alike, the electron, which is many thousand times 

 lighter than the atom, would have velocities that were a 

 hundred times greater. Now as the amplitudes must be 

 of the same order of magnitude, or about B, the frequency of 

 the electron would be about a hundred times greater than 

 * M, Born and v. Karman, Phys. Zeiischr. xiii. p. 297 (1912). 



