758 Dr. G. Borelius on the 



thermal dilatation. We will discuss them separately in the 

 three following sections. 



1. The part of o~, we may call it <r u due to the kinetic 

 energy of the electrons is 



when u is got from (10). It is for many metals but a few 

 tenths of a microvolt per degree, for none of them greater 

 than two microvolts ; and it is but a small part of the 

 observed Thomson effects. 



2. Of the atomic heat c v at constant volume, one half 

 is thought to increase the kinetic, the other half the 

 potential energy. If this increase of the potential energy 

 were equally distributed to atoms and electrons, we should 

 get the corresponding part of the Thomson heat to be 



c AO c v microvolt 



<7 2 = — pr^r- = — 4o — ; . 



4:N€ c vcrj degree 



However, such an equipartition of potential energy is not at 

 all probable, for the light moving electrons will be better 

 able than the atoms to avoid places where this potential is 

 increased. o- 2 is therefore probably but a little part (z) of 

 the value above, and we may put 



t^ microvolt 

 o- 2 = — £.43 - 1 (23) 



c c oo degree v J 



The calculation of z will not be possible without an intimate 

 knowledge about the external structure of the atoms. 



3. From the equations of § 4 we can calculate the 

 variations cr 3 of the mean potential \§ e of the electrons 

 due to the thermal dilatation. It is 



_ ld± e dR 



<73 - 2 si a • * (24) 



The nmltipler 1/2 appears because, by summing up all 

 the </> e) every electron is counted twice. From equations 

 (2) and (5) we find 



d(f> e _ fib' 

 dU ~ 2R^+ 1 ' 



