S7/sf<')}i,t of CorpiL^rlcs (Ii\<!(')'ih\no C/rcHhi)' Orhits. (581 



"We see that these expression? represent, elliptically pohirized 

 light, the ratio of the axes being, as in the case when there is 

 only one particle, cos 6 ; in this case, however, since L and M 

 vanish when ^ = 0, the intensity of the light vanishes along 

 the normal to the plane o£ the orbit ; thus a system of two or 

 more particles rotating uniformly in a circular orbit does not 

 give out any light along the axis of that orbit, a point which 

 has to be kept in mind when considering the interpretation 

 of the Zeeman eftect. We see that as p increases the vibra- 

 tions tend to become confined to the plane of the orbit. 



t). The rate at which energy is streaming through unit 

 area of the surface at P is by Foynting's theorem equal to 



^^(L= + M=). 



Substituting for L and M the values given above w-e find 

 that the average rate at which energy is streaming through 

 the surface of a sphere with its centre at is 



V/ 2eoyp YY^M^P [•2^4... (2/9-2) _ 2.4.. .2/9 



_ Y / 2ecop Y / apcoYp 2 .A. . .2p-2 . 2p + 2 



~~ 4:\l.2.'d...p-l) \2VJ 1.3. .2/9 + 1 



7. From this expression we see that when aw tlie velocity 

 of the particle is small compared with Y the velocity of lights, 

 the rate at which energy radiates diminishes very rapidly as 

 the number of particles increases. This is brought out by the 

 following table, which gives the average radiation per jxtrticle 

 for various groups of particles in terms of the radiation from 

 a single particle moving wdth the same velocity in the same 

 orbit ; the table gives the results for two cases, in the first case 

 the velocity of the particle is 1/10 that of light, in the second 

 it is 1/100 of the s:une velocity. The radiation from a single 

 particle is in each case taken as unity. 



Radiation from each particle. 



Number of P< 



irticles. 



auj=W/10. 



«a; = V/10\ 



1 





1 



1 



2 





0-6 X 10-2 



9-6x10-^ 



a 





4-6 X 10-' 



4-6x10-7 



4 





1-7x10-1 



1-7 X 10-10 



5 





rn) X 10-^ 



5-6 xlO--^^ 



6 





1-Gx 10-' 



1-6x10-17 



