Moving Electrified Particles passing through Matter. 15 



of the forces in question for collisions in which p is great in 

 comparison with \. This simplifies the calculation very 

 much, because then we can assume that the displacement 

 during the collision is negligibly small in proportion to p. 

 In the following calculation we shall consider separately the 

 motion of the electrons perpendicular and parallel to the 

 path of the particle ; the total energy transferred to the 

 electrons during the collisions will be the sum of the energy 

 corresponding to these two motions. 



In the figure the line AB represents the path of the 

 particle, which in the collisions considered here (i. e., p great 



Ss. 



X 



- v -c 



in proportion to \) will be very nearly a straight line. 

 Further, A is the position of the particle at the time t, and 

 C is the mean position of the electron. BC is perpendicular 

 to AB. According to the above notation, B(3 = p ; and 

 assuming that the particle will be at B when the time is 0, 

 we have AB = V . t. 



For the force acting on the electron in the direction CB, 

 we now get 



Fl=eE S=(V¥W =m -* (0, 



For the equation of motion of the electron perpendicular 

 to the path of the particle we get 



in which n is the frequency corresponding to the forces in 

 question. 



