414 Mr. G. W. Walker. On the Drift produced in [Dec. 16, 



" On the Drift produced in Ions by Electromagnetic Disturbances, 

 and a Theory of Radio-activity." By GEORGE W. WALKER, 

 M.A., A.RC.Sc., Fellow of Trinity College, Cambridge, 

 Lecturer on Physics in the University of Glasgow. Commu- 

 nicated by Professor A. GRAY, F.R.S. Received December 16, 

 1904, Read January 26, 1905. 



Some time ago I showed* how the equations of motion of a free ion 

 under the influence of a harmonic train of plane waves might be 

 completely integrated, subject to the restriction that the viscous effect 

 of radiation from the ion may be neglected. 



The equations are closely analogous to those for a simple pendulum, 

 and by following out the analogy in the case where the pendulum 

 makes complete revolutions, it is easy to show that while the passage 

 of a complete wave restores the initial velocities of the ion, its position 

 in space is altered. This change of position cannot be accounted for 

 entirely by the change due to velocity which the ion may be assumed 

 to possess before the wave reaches it. 



The continuance of the waves thus involves the result that the ion 

 must continue to change its position in space. It will thus appear to 

 move in a definite manner which can be determined in terms of the 

 initial circumstances of the ion and the constants of the train of waves. 

 The result is very remarkable, and is not confined to an infinite train 

 of harmonic waves. Similar results follow in the case of any form of 

 electro-magnetic disturbance propagated in a straight line. 



I propose here to discuss the case of a plane polarised disturbance 

 propagated in a straight line. Let the electric force be X = X f(Vt - z) 

 where V is the velocity and s the direction of propagation. Associated 

 with this we must have a magnetic force M = X /V f(Vt -z) in a 

 direction at right angles to that of X. If m be the inertia and e the 

 charge of the ion, the equations of motion may be written 



mx = e(X-zM), 

 my = 0, 



m = +exM. 



We may thus confine attention to the motion in the xz plane. We 

 have 







* ' Roy. Soc. Proc.,' vol. 69, p. 394; 'Phil. Mag.,' 1903, vol. 6, p. 537. 



