connected with the Motion of Charged Spheres. 915 



results which agree well with those obtained by Lorentz on 

 more general grounds. 



The mean rate of radiation calculated from the Poynting 

 vector is easily seen to be 



3 . 





which agrees with Larmor's general result when — is small. 



Walker works out the case of the sphere under the action 

 of a given periodic force. The results can easily be deduced 

 from those given above. Thus if we use 



P=\ cos nt, 



then usino- the same m and k as before the solution for P is 



/, a ! a 2 aW 

 P = r — COS (nt + e), 



e 

 3 a? 











an 







where 







tan e 



c 







9 95 



a-n- 

 c 





and the 



mean r 



ite 



of radiation is 













le 2 

 3 c A 



X 2 



3 

 4 



a 2 X 2 





Ydac 2 ) 





and Is independent of /i. 



II. The Slow Hotation of Charged Spheres. 



Walker works out first the case of the rotation of a 

 perfectly conducting sphere rotating about a diameter. It 

 is, however, difficult to imagine what the motion of the 

 sphere has got to do with any motion of the electricity. 

 The conductor, being perfect, is such that any charge on it 

 is freely movable. A charge on a perfect conductor ex- 

 periences no resistance to its motion due to the conductor. 

 Thus for a slow rotation the motion of the conductor and the 

 motion of the charge are independent of each other, and 



