Theory of Metallic Conduction. 559 



/We have therefore 



a/ = /-a 



-[H- 2 « x+ .Ut-"k) 



4-t?(...)+ ...]A<r?" a . 



Now multiply both sides of this equation by f and then 

 integrate the resulting equation over all values of (f, 77, f) 

 subject to the condition 



u 2 < p+if + ?< {u+du)\ 



and using, after Bohr, 



,1 M + Jtt 



the integration being over the same extension, we get 

 JG (*) = _ G.00 WA/_ 1 |A 3j\ 



which is precisely the equation obtained by Bohr in this 

 special case of the more general principles. 



The theory given by Bohr is slightly more general than 

 that discussed above, but is apparently tractable only in the 

 restricted cases which are included in the present treatment. 

 In any case we may assert that most of the assumptions on 

 which this simpler form of the theory is based are sufficiently 

 verified in actual practice to render the theory as good an 

 approximation to the actual facts as it is possible to obtain 

 under the present circumstances. 



In conclusion we may thus state that under the usually 

 accepted restrictions on which the general theory of the 

 electronic motions in a metal is based, the apparently dif- 

 ferent modes of treatment which have been suggested for 

 dealing with the various problems under review are con- 

 sistent with each other, and are in fact reducible all to 

 method suggested by Lorentz, which is apparently the more 

 fundamental of the three. 



The University, Sheffield, 

 January 28, 1915. 



