682 Prof. J. J. Thomson on the Magnetic Properties of 



From this we see that the radiation from each of a group 

 of 6 particles moving with one tenth the velocity of light is 

 considerably less than one five-millionth part of the radiation 

 from a single particle describing the same orbit with the 

 same velocity, while when the particles are moving with only 

 1/100 of the velocity of light the radiation falls to 1*6 X 10"^^ 

 of that from the single particle. 



8. Action of an external magnetic field on a ring of rotating 

 particles. 



Since a ring of particles produces a magnetic field 

 similar to that due to a current flowing round the orbit of 

 the particles, it might seem at first sight as if a body whose 

 atoms contained systems of such rotating particles ought to 

 be strongly magnetic, the following investigation of the 

 action of an external field on such a system shows that this 

 is not the case. 



Let us suppose that the external magnetic force H is 

 uniform and parallel to the axis of X ; and let the moving 

 electrified particle be describing its orbit under a radial 

 attractive force proportional to its distance from a fixed 

 point. If 7n is the mass of the particle, e its electric charge, 

 fi the force at unit distance, the equations of motion are 



mj'" = -^^ ....... (1) 



"'d¥^-''i'-^'Tt • • • • (2) 



If 7) and f are the coordinates of the point referred to axes 

 in the plane of ^z rotating with the angular velocity 

 j9 = J He/m so that 



y = 7) cos pt—l^ sin pt, z = rj sin pt + ^ cos pty 

 equations (2) and (3) become, if we neglect terms in H^, 



The solutions of these equations are if uy^=^p.jm 



.^' = A cos ft)^ + B sin wt, 

 t; = C cos cot-\-D sin (ot, 

 f=Ecoscw^ + Fsina)^ 



Let the time be measured from the instant when the 



