'9II-] AGGREGATES OF ELECTRONS. 351 



be calculated from the properties of gases. This assertion is the 

 mathematical statement of the relation (4) enumerated above. 

 Making this substitution we find that the specific electrical conduc- 



/ /irX7' 

 tivitv of the material is cr = -y = - ^ . In this formula c- and a 



A 4^6/ 



have the same value for all substances, u and A are constants charac- 

 teristic of each substance, z' is independent of the nature of the 

 material but is proportional to the square root of the absolute 

 temperature. 



It is a well-known result of experiment that the specific conduc- 

 tivity of all substances is inversely proportional to the absolute tem- 

 perature. We therefore conclude that the product ;/A for all metals 

 must be inversely proportional to the square root of the absolute 

 temperature. 



It is a well-known result of the kinetic theory of gases that the 



thermal conductivitv of a gas is equal to iiiXz'a. Hence — = —6. 



Thus this ratio should have the same value for all metals at the 

 same temperature and the temperature variation should be the same 

 as that of the volume of a gas at constant pressure. These are the 

 relations which are exhibited by the experimental results of Jaeger 

 and Diesselherst. 



The electron theory of metallic conduction has enabled us to 

 understand a number of curious effects which occur when a con- 

 ductor is placed in a magnetic field. One of these, the Hall effect, 

 consists in a deflection of the line of flow of a current which is 

 caused by the magnetic field. Another effect, which is especially 

 marked in the case of Bismuth, is an alteration of the specific resist- 

 ance of the material caused by a magnetic field. These eifects are 

 intimately connected together and have a simple explanation on the 

 electron theory. It is well known that any electrified particle moving 

 in a magnetic field is acted on by a force which is perpendicular to 

 the plane containing the magnetic force and the direction of motion. 

 The superposition of this force upon the other forces acting on the 

 electrons in a metal carrying a current will cause all the electrons to 

 curve round in the same general direction, giving rise to the Hall 

 eifect. It will also increase the average curvature of the paths of the 



