Theory of the Optical Properties of Metals. 437 



that the potential energy o£ the particle at a distance r from 

 the centre of the force is 



m 



then 



wherein, if n denotes the number of atoms per unit volume 

 in the metal 



9 i_r T 

 ■nu~u l si 



where 



^2= f + ^t? 2 

 and 



I = 4 \ cos 2 # CI da. 

 c o 



The relation between O and a being defined by the equation? 



dv 



where v is the only real positive root of the equation 



i-*+0- L 



We have also used 



wherein N denotes the total uumber of electrons per unit 

 volume, and q a constant connected with the mean square of 

 their velocities (u 2 ) by the relation 



3 



7 = ^TT^. 



If: we now use 



1 



= JTUfl 2 !, 



