2±6 Prof. E. P. Adams on some Electromagnetic 



acquires in this direction. Consider an electron which moves 

 away from a collision at the point r' 6', in a direction making 

 an angle a with the radius. At the beginning of its free 

 path its radial and tangential velocities are : 



dr 



= v cos « 



It " c ~"° "' 



tf<9 



r -=- = t 1 sin a. 

 at 



From (3) the constant k is determined : 



£=r' v sin a, 

 and using this in (4) the constant A is determined : 



lae , 



A = v 2 — - — log r . 



Therefore the radial velocity of the electron during its free 

 path is given by 



dr\ „ „ 2ae , r 

 cos^aH l°g^7* 



© - 



At the end of its free path the value of r will be ap- 

 proximately 



r' -fXcos a, 



where \ is the length of the free path of the electron. So 

 its radial velocity at the end of its free path is given by : 



/dr\ 2 «, 9 2 ae , /., \cosa\ 



^ =r . cos . a+ _ log | 1+ __j. 



f — , is very small compared with unity. This may then 



be replaced by : 



2 ae\ cos a 



(I)"- 



v 2 cos 2 a. + 



The average radial velocity acquired under the influence 

 of the electric force is one-half the difference of its radial 

 velocities at the end and beginning of its free path. This 

 gives for the radial velocity during the free path : 



dr 1 (( 2ae\ \i ? 



— = - ■ v cos « j I 1 + — —, /—If 



at J. (A mv r cosa/ ) 



