294 The Electron Theory of Metallic Conduction, 



p as here ; we have 



so that 





pdp = —^ad<x, 



and then 



1 — e _ Awn/A 



Tn/m 2 u T° 



cos 2 Q scda. 



The integral in this expression is a mere numerical factor 

 of which estimates may be found by quadrature as soon as s 

 is given. If we write 



— = AiTrnfj? I cos 2 Q ccdot, 

 tm Jo 



then the equation for the fundamental function is thus to be 

 interpreted with 



T =US t m . 



m 



The further developments of the theory now proceed along 

 the usual lines laid down by Lorentz, Bohr, Enskog, 

 Richardson *, and others. 



Before concluding this paper reference must be made to 

 the work of Enskog f and Bohr, who have given elaborate 

 discussions of the theoretical basis of the present theory, but 

 in a form which is hardly as simple or as direct as that 

 suggested above. Bohr reduces the problem of the deter- 

 mination of the distribution function to an integral equation 

 whose solution can be effected only in certain special cases, 

 but which is otherwise much too general to be of any real 

 service. In his paper, however, Enskog proceeds on a rather 

 more tentative method, and assumes a general solution for 

 the fundamental function which differs from that here given 

 by the presence of additional terms of the second order in 

 (?> Vt ?)• The presence of these additional terms is required 

 if, and only if , the theory is generalized to include the effect 

 of the collisions of the electrons with one another, a factor 

 which has been purposely neglected in the above discussion. 



* Phil. Mag. July 1911. 



t Ann. der Physik, xxxviii. p. 731 (1912). where the reference to 

 Bohrs dissertation will be found. 



