756 Dr. G. Borelius on the 



double energy of that in a gas we can write 



pc = 2un ! r (17) 



a = 2'06 . 10~ 10 being the gas constant for a single molecule. 

 As is shown by Born and von Karman, most of the 

 energy in a space-lattice is transported with velocities 

 nearly equal to the maximal velocity 2v m $ ; so that we 

 have approximately 



w = 2v8, (18) 



v being as before a mean frequency nearly equal to the 

 maximal one v m . 



The mean range L may be calculated from (16') as 

 follows. Every time a wave, embracing a number of 

 atoms, advances a distance d$ — 8, this wave gets into an 

 energy exchange with a like number of electrons. Now 

 this exchange must be effected in such a way that the ratio 

 of menu energies of the electrons (3u corresponding to 

 equipartition of energy in three kinetical and three potential 

 degrees of freedom) and the atoms (2aT) is kept unaltered. 

 The mathematically simplest way in which this can be done 

 is to assume that the mean relative loss of energy of the 



wave -jr- is every time in this ratio. As the electrons are 



not able to transport the energy a long distance, the energy 

 given off to them is lost for the regular transporting waves. 

 We thus get 



dK_ 3u 8 

 K ~ 2*T ~ U 



and from the last equation 



2aT 



Inserting (17), (18), and (19) in (16), we get the heat 

 conductivity for high temperatures, 



x = i ^im (20) 



T) O U 



As u, is, proportional to T, and all other quantities are 

 constant, we find \ constant for high temperatures, in good 

 agreement with experimental facts. The calculated value of \ 

 is also of the light order of magnitude. We need not, how- 

 ever, show r this separately, as the electric conduction is already 

 discussed, and the ratio of conductivities will be the subject 

 of the next paragraph. 



