﻿Electron in the Neighbourhood of an Atom. 783 



from the magnetic wheel the kinetic energy it had previously 

 given up to it. 



If, however, the direction and velocity of projection of the 

 electron are such as to allow it to pass through the magnetic 

 wheel, and, moreover, its energy is sufficient to allow it to 

 pass away to infinity without returning through the mag- 

 netic structure, then the total increment in the solid angle 

 will be 4tt, and the magnetic wheel will be left in rotation 

 with an angular velocity Q, given by the equation 



0=^ (15) 



If u denotes the final velocity of the electron when it has 

 passed again out of the influence of the magnetic wheel, we 

 obtain from equation (8) 



iA(l 2 = im(« 2 -M 2 ) (1G) 



In this case the electron has given up to the magnetic 

 structure an amount of kinetic energy U given by 



U = |A0 2 , 



or, using the value of H given by equation (15), 



U=^ (17, 



From equations (15) and (16) we see that, in order that this 

 should be possible, the initial velocity of projection of the 



electron must be at least as great as —. , and, moreover 



\ZAin 

 the direction of projection must be suitably adjusted. 



5. The remaining possibility is that the electron should 

 penetrate the magnetic structure but should not have suffi- 

 cient energy to pass out of its influence. In this case the 

 greatest value of ^r that can be attained by the wheel is 

 given by 



i 2 m 2 



and therefore, from equation (14) the greatest value of Aw 

 is given by the equation 



A 27r V Am /-, Q \ 



A<» = ^ w (18) 



Me 



After attaining this value, the electron will return towards 

 the magnetic wheel and must pass through it again in the 



