﻿128 Dr. F. A. Lindeinann on the 



The latest and most elaborate assume the electrons to have 

 certain definite velocities which are independent of the 

 temperature *. Like Planck's zero-point energy (Nullpunkts- 

 energie) this motion cannot be interchanged or observed. 

 The variation of the resistance with the temperature is attri- 

 buted to the change in the mean free path due to the change 

 in the amplitude of the atom's oscillations. These theories 

 do not account for the supra-conductivity at temperatures 

 below 3° absolute. 



Conduction of heat in metals is usually assumed to take 

 place analogously to in a gas, the electrons taking the place 



JN TfXCl 



of the gas molecules. The formula found is X = — « — 7, 



o 



I being the mean free path, c the velocity, and 7 the specific 



heat of 1 gram of electrons. Comparing this with the 



Ne 2 t N<?-7 

 expression for the electrical conductivity <r = -^ — = *-«— 



2m 2m c 

 ~\ 2 ,2 



one finds - = — r - r <y. This reduces to the Wiedemann- 

 c be- ' 



Franz law if one assumes the atomic heats (and therefore 

 also the speed of the electrons) to be independent of the 

 metal. If one supposes the law of the equi partition of 



M 3R 



energy to hold, 7 must be — where M is the mass of an 



atom of hydrogen, m the mass of an electron, and -3 



must be — ^ — where n is the number of atoms in a gram- 

 2n & 



atom, and T the absolute temperature. Thus - reduces to 



3MR 2 T 3 R 2 , T 1 rru . , . . „ . 



— : — 7, — or 7 -s-9 1 as IVI = - . Inis value is in very tair 

 ■kuw 4 e^n" n J 



agreement with the constant of the Wiedemann-Franz law, 

 and the variation of the constant with the absolute temperature 

 is in accordance with the facts. 



It is unnecessary to go into the various theories that have 

 been put forward to explain the various secondary phenomena, 

 such as the Peltier effect, the Hall effect, the Thomson effect, 

 the Richardson effect, and so on. Each has necessitated 

 secondary hypotheses_, and none of them is very convincing. 

 It is sufficient to point out that the main points enumerated 

 above are in absolute contradiction with one another or with 

 the facts. The most obvious difficulty, of course, is the 



* W. Wien, Berl Ber. 6. ii. 1913 ; W. II. Keesom, Phijs. ZS. xiv. 

 p. 670 (1913). 



