Theory of Metallic Conduction. 291 



or introducing the new variable, 



and writing 



this equation becomes 

 d 



p*u 2 



so that 



_ r dv 



The apsidal distance is obtained directly from the fact 

 that 



there, and it therefore corresponds to the one positive root 

 of the equation 



"=©' 



+ 1. 



Denoting this root by v , we see that the angle between 

 the asymptote and apsidal radius is 6 where 



,_r *__ 



3o\A-»'+a 



The angle the direction of motion of the electron is turned 

 through, which is the angle between the asymptotes to its 

 path, is then 20 o . The important conclusion is that 6 is a 

 function of a only. 



Now let us examine the change in the velocity of the 

 electron which is brought about by this encounter : this is 

 easily obtained because the new values of the velocity may 

 be written down from the fact that the velocities after 

 collision parallel and perpendicular to the apsidal radius are 



— ?/cos2# and u sin 20 . 



U 2 



