﻿Electron in the Neighbourhood of an Atom. 779 



current, specified by the angular velocity 0=—' , so that 



the absorbed energy and the angular velocity are connected 

 by the equation 



u=*Mn. 



Whittaker has further shown that the disturbance in the 

 atom after the collision consists in the displacement of a 

 single electron, and that the radiation emitted by the elec- 

 tron in its oscillatory subsidence to its normal state must 

 satisfy the equation Xj = Jiv. 



2. In his paper Whittaker has assumed that the electron 

 is projected towards the magnetic wheel * in a line per- 

 pendicular to its plane and directly towards its centre. If 

 we suppose the atoms to contain such structures as have 

 been described, we must suppose the magnetic wheels in the 

 substance to be bombarded to have all possible orientations, 

 and the electrons to be projected from any direction. It is 

 therefore of interest and importance to discuss the general 

 case, when the electron is projected in any direction and 

 passes in the neighbourhood of one of these magnetic 

 wheels. 



We will suppose, as before, that the magnetic wheel has 

 a radius a, and that if fia is the magnetic moment of one of 

 the elementary magnets, the sum of the quantities fi for 

 all the magnets forming the wheel is M. Further suppose 

 that the plane of the wheel is the plane of yz and that the 

 wheel is free to rotate about its axis, which is the axis of x ; 

 the wheel is therefore restricted to have only one degree of 

 freedom. Let the amount of rotation of the wheel at any 

 particular instant be specified by the angle i/r between the 

 axis of y and a definite fixed radius in the plane of the wheel, 

 the angle being considered positive when it is such as would 

 turn the axis of y towards the axis of z, the rectangular axes 

 of ocyz forming a right-handed system. Let the moment of 

 inertia of the wheel about its axis be A, so that when the 

 wheel is rotating with angular velocity yjr its kinetic energy 

 is iA-v//- 2 . Let the mass of the electron be m, its charge e, 

 and let its position at any instant be specified by spherical 

 polar coordinates (r, #, </>) connected with the rectangular 



* Note. — When referring here or elsewhere to a magnetic wheel, it is 

 to be understood that it is not suggested that an atom actually contains 

 a mechanism similar to that here described, but merely that the atom 

 behaves as if it contained such a structure. 



