Electron Theory of Metallic Conduction. 12£ 



If we now remember that 



1 sin nr e m - 



Jo 



T m l+W 2 T m 2 ' 



1 



,-, -^-dr n 2 r m 2 

 (l — COS7lT)e '« — = - ^ — ^, 



then we find easily that 



_T 7ra f^.BA ^5;/ ^ d~ ht„, / BA BA\\ 



L*a# 1+nV l + n z T TO z \*d# 0-/J J 



Whence the expression for / is immediately obtained. By 

 this formula all details of the Hall effect and the allied 

 phenomena in metals may be effectively explained. A 

 particular case of this formula, deduced in rather a different 

 manner, and its application in these problems has been 

 discussed at length by Gans *. 



3. A final particular case of the general formula, which is 

 of some importance in the optical theory of metals, is the 

 one in which the acceleration R is a rapidly alternating 

 function of the time, such as, for example, would be the case 

 were the acceleration produced by the electric field associated 

 with radiation passing through the metal. We neglect the 

 effect of the magnetic field in this case, and thus 



x =^(„E)-l(«V.)A + ) r(„V)?. 



Now, as in the first example, we may neglect the variation 

 °f (f> Vi ?» u ) produced by the action of the electric force, so 

 that in this case the only part of ^ which varies with the 

 time is that containing the factor E. Also, if we use 





F=| e r »— \ Edt, 



Jo T mjt-r 



* Ami. der Physih, xx. (190(>). 



