538 Mr. G. H. Livens on the Electron Theory 



This is the result obtained by Bohr and agrees with that 

 obtained by Grans in the particular case he examines (which 

 corresponds to s = <x> in the present analysis). 



There is a second order effect which is directly associated 

 with the Hall effect and which can easily be discussed at the 

 present stage. In the absence of the magnetic field the 

 current parallel to the y-axis has a density 



O-Ey, 



if E y is the driving force. When the magnetic field is on 

 and the arrangement is that adopted by Hall, the current in 

 the same direction has a density 



r ( 1+ s) vnA ™uH r (2 + 7) , 



or using the form for E~ obtained above, it is 



o-E, 



■"(■+'> / Cg +7)) ' 



a result which is usually expressed by saying that the mag- 

 netic field decreases the conductivity of the metal for currents 

 flowing in the direction specified and in the ratio 



eV; 



Aa _ 

 a 





r( 2+ 





For 5 = go 



this reduces to 









v=-('- 



4 Jm 



en: 



Vg- 1 ' 



m 2 c 2 q * 



which is the result obtained by Gans in this particular case. 



In most of the cases investigated it appears that the con- 

 ductivity for transverse currents does decrease when the 

 magnetic field is put on, although for the ferromagnetic 

 metals in particular the reverse takes place. 



* Notice that Ao-=^Qfor s = 4, which corresponds to the case in which 

 the molecules of the metals act on the electrons like little magnetic 

 doublets (see Bohr, /. c). 



