﻿786 Path of an Electron in Neighbourhood of an Atom. 



x is negative and r>a the curvature of the path is towards 

 the axis of x. 



Now suppose that the electron has penetrated the mag- 

 netic structure and reached a point for which r>a (if it 

 only reaches a point for which r<a it will obviously return 

 through the magnetic structure); then in order that equa- 

 tion (19) should be satisfied we must have 



IT '. 



therefore, when - <0<tt, r and r6 must have the same 



37T 



sign and when it <0< -~ } r and rd must have opposite 



signs ; thus on the outward path, in both cases, the electron 

 must at such a point be moving towards the axis of x, and 

 so long as r>a its motion, will be such as to bring it to an 

 even more favourable position for passing through the 

 magnetic structure on the return journey. 



6. It has therefore been shown that the electron can 

 permanently transfer an amount of energy to the magnetic 

 wheel only if its velocity and direction of projection are 

 such that it penetrates the magnetic structure and passes 

 away out of the influence of the wheel without returning on 

 its path. In such a case the wheel is finally left in rotation 



with an angular velocity 11 = -4— , and the amount of 



kinetic energy U transferred from the electron to the struc- 



2MV 

 ture is given by U=— j— ; in order to attain this result 



the initial velocity of the electron must be at least as great 

 2Mg 



V 7 Am 

 These results are precisely the same as those obtained by 

 Whittaker in the particular case which he considered, and 

 his further discussion of the way in which this absorbed 

 energy is converted by the atom into radiant energy and 

 the deduction of Planck's relation connecting the energy 

 and the frequency of the emitted radiation may equally be 

 applied in this more general case. 



