of the Hall Effect and Allied Phenomena. 529 



by R. Gans *, and some of the results for the more general 

 case have been given by Bohr f in his very general treatment 

 of the subject of the general electronic motions in a metal. 

 The method adopted by Bohr is essentially different from that 

 adopted in the following pages, depending on the establish- 

 ment of equations to determine the changes in the components 

 of the aggregate momentum of the electronic motions, and 

 is to a certain extent more general. It is possible, however, 

 to generalise the present mode of treatment to the extent 

 assumed by Bohr, but as the results are really only workable 

 in the particular type of problem here examined, it was 

 decided to confine the analysis to this type. 



2. General basis of the Jheory. 



The general ba^is of the present theory is the one now 

 usually adopted to explain the electrical and thermal pro- 

 perties of metals ; its physical bearing is elaborately discussed 

 in Dr. Bohr's dissertation, whilst certain aspects of the 

 analytical side have been discussed in several recent com- 

 munications of the present author. In this theory it is 

 usually assumed that the whole of the electrical and thermal 

 properties of the metals arise entirely in the average motion 

 impressed by the external circumstances on the swarm of 

 electrons which are otherwise moving about quite irregularly 

 and freely in the space between the atoms or atomic com- 

 plexes. In the absence of actions from any external agency 

 the electrons are presumed 1,0 be moving about in such a 

 manner that the distribution of velocities among them at any 

 instant is precisely that specified by Maxwell's law, so that 

 if N is the total number of free electrons per unit volume 

 the number in the same volume with their velocity com- 

 ponents between (f, ?;, f) and (f + tff, v + ^Vf ?+^?) is given 

 as usual by the formula 



//>3 -qn- 



wherein 



tfap-tV + P 



and q is a constant connected with the mean value u m * of w 3 

 for all the electrons by the relation 



__3 



* Ann. d. Physik, xx. (1906). 



t ' Studier over Metallerues Elektrontheori ' (Dissertation ; Copen- 

 hagen, 1911). I am greatly indebted to Dr. Bohr for the loan of a 

 translation of this paper. It contains a wonderfully lucid exposition of the 

 underlying assumptions and restrictions involved in the general theory. 



Phil. Mag. S. 6. Vol. 30. No. 178. Oct. 1915. 2 M 



