﻿782 Mr. B. B. Baker on the Path of an 



the constant on the right-hand side of equation (9) is infinite, 

 and since, from equation (8), </> cannot become infinite, the 

 value of r must remain infinite, or, in other words, the elec- 

 tron can never approach the neighbourhood of the magnetic 

 wheel. To investigate the cases of interest we must there- 

 fore suppose <b to have a constant value which we can take 

 to be zero without loss of generality, so that the motion of 

 the electron is always in the plane of xy. 



The equations of motion of the system then reduce to 



A +- m (W- r+ w J ) =Q > ■ '.;. • (10) 



m(r-# 2 )+M^H-=:(), (11) 



■m(r0 + 2rr0)+Me1r~=O (12) 



4. Equation (10) may be integrated immediately, giving 



A^ — M*F(r, 0) = constant. . . . (13) 



Remembering that the wheel is initially at rest and replacing 

 F (r, 6) by its value in terms of the solid angle subtended at 

 the electron by the magnetic wheel, the value of ty, when the 

 electron has reached any point P, is given by the equation 



A^= —^ . /\co, . . . . . . (14) 



where Aw denotes the increase in the solid angle subtended 

 by the magnetic wheel at the electron, in its motion to P. 



From equations (8) and (14) we see that when the elec- 

 tron moving with its initial velocity u from a point at 

 infinity, comes into the neighbourhood of the magnetic 

 wheel, its velocity begins to diminish, whereas the wheel is 

 set into rotation ; the kinetic energy of the electron, in fact, 

 is being expended in setting the wheel into rotation. 



It may happen that the velocity and direction of pro- 

 jection of the electron are such that in its path it does not 

 pass through the magnetic structure, i. e., at no point of its 



path do we have d— — or 6— — and r<a simultaneously ; 



then in that case, when the electron has completed its path 

 and passed again to an infinite distance, the total increment 

 in the solid angle is zero and therefore, from equation (14), 

 the magnetic wheel will come finally to rest : from equation 

 (8) we see that the electron, in its later path, receives back 



