1904.] 



Ions ty Electromagnetic Disturbances, etc. 



415 



If we take a moving origin so that V - z = , then will be the 

 distance of the ion from a plane moving with the disturbance, and 

 reckoned positive in the direction from which the waves come. The 

 equations then take the form 



Thus in general 



_ const. 



is an integral ; it indicates that the energy of the ion relative to the 

 moving origin is constant. 

 We also get 



. e Xn ft 



where a is a constant, 



We may note that if the disturbance is such that 



=o, 



then the original value of x is restored, when f = f lf and hence also the 

 original values of f or s on account of the equation of energy. 

 Let us now take a simple case so that 



/(f) = 1 from to d, 

 /(O = d 

 /(f) - -I'* 



-and thereafter let the form of disturbance recur. 

 From f = to = d, we have 



_ o A 

 " ~mV 



Hence 



m 



where a and c are the initial values of x and . 

 We also get 



Thus during the first pulse the ion describes a circle centre 



