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



in the plane PO^ at right-angles to OP, together with a force, 

 at right-angles to the plane VOz, equal to 



eaw 



COS ^ COS (o)^— tF""*^)- 



Here 6 is the angle OP makes with Oz, and ^ the angle 

 the plane VOz makes with the plane of xz. 



Using the language of the Electromagnetic Theory of 

 Light, we may say that the rotating particle produces a wave 

 of elliptically polarized light, the ratio of the axes of the 

 ellipse being cos 6 ; thus along the normal to the orbit we 

 have circular polarized light, while in the plane of the orbit 

 the light is plane polarized. 



Along wdth these magnetic forces we have in the plane 

 PO;: at right-angles to OP an electric force equal to 



cos 



^cosf G)i— ^ —<^\ 



and at right-angles to the plane VOz another electric force 

 equal to 



eaoy^ . / cor ,\ 



applying Poynting's theorem we see that the rate at which 

 energy is streaming through unit area at P is 



the mean value of this is 



integrating this over the sphere through P we find that the 

 mean rate at which the rotating corpuscle is emitting energy is 



2 2 e'^ 



-^r^e^o^oi^ = -15 -vT (acceleration of the particle)^. 

 oV o V 



4. Case of p particles separated by equal angular intervals 

 rotating with uniform velocity « round a circle. 



Suppose that the particle we call (1) makes at the time t an 

 angle wt with the axis of x, the particle (2) will make an angle 



a)i H , the particle (3) an angle cot + 2 . — , and so on ; 



hence if 71, 72, 73, . . . are the magnetic forces parallel to z 



