Motio7i of a Perfectly Conducting Electrified Sphere. 647 



of the actual field vectors by relations already given, cor- 

 respond to the values already obtained for the electric and 

 magnetic vectors, when these are expressed as functions of 

 the coordinates (#,' ?/,' z,' t r ) referred to the moving axes. 



Thus if (X x Y 1 Z : ; a^ 0i 71) are the components of the 

 electrodynamic vectors referred to spherical polar coordinates 

 moving with the cartesian axes, but whose polar axis is 

 in the direction of the applied acceleration, which need 

 not necessarily be the direction of the uniform motion, 

 then the field referred to moving coordinates is determined 

 by relations similar to those already obtained. 



e 2 cos e x , m x>,f\ 



*i= rr + " r 3 fa/i +/d, 

 Y 1= !^|j(, 1 v 1 "+n/ 1 '+/i), 



7 1 



whe re 



Sin "1 / <> r " , _r '\ 



c 7i= "TT-fa/i + ? 'i/i)> 



' 1 



4A 1 a 8 -£isin.r lv /3 . - OA 



and tf . 1 = c j 1 _y i + aj A 1 =^- 2 . 



The density of the charge on the sphere is given by 

 . e 2A'' cos 6 



47TO-! = - '-+ , 



a z a 



and the force on the sphere in the direction of the accelera- 

 tion is 



Whence we deduce that the electromagnetic masses of the 

 sphere are 



They are all three 

 oscillating manner tc 

 stationary principles 



They are all three initially zero, but tend rapidly 1 

 oscillating manner to the values usually obtained from quasi- 



o ac 2K - }€ >* ) % 



