1904] Ions by Electromagnetic Disturbances, etc. 417 



Thus the ion will describe a circle of the same radius as before with 



the same angular velocity, but the curvature is now in the opposite 



direction and the centre is different. The ion leaves the second pulse 



with velocity (a, c), and proceeds in a straight line. The path is 



shown in the diagram (1). 



We now calculate the time taken to travel from =0 to =2l + 2d 



and also the displacement. The simple character of the path enables 



us to do this easily. 



If we denote eXo/wV by <*>, the time, T, is given by 



T=l 



ha 2 )U 



Now, {=Vt-z. Hence the displacement of the ion from its- 

 original position, in the direction of the waves, is 



The displacement in the direction of x is 



2 



Let us now consider two particular cases. 

 Case I. The ion was originally at rest. 

 Neglecting w 4 and higher terms, we get 



Hence a = and c. = V. 





Thus, if the impulses recur, the ion will appear to travel in space 

 with velocities which are approximately 



It will thus appear to drift on in the direction of the waves.* 



* These are also the mean values of the true velocities x and z during a com- 

 plete pulse. I wish to emphasize the fact that if we could observe the ion just as- 

 it leaves the pulse it will again be at rest if it was initially at rest, but its position 

 is altered. I shall therefore refer to these as apparent velocities. 



