Motion of a Perfectly Conducting Electrified Sphere. G45 



In fact, i£ the motion of the sphere is along the axis of x, 

 and if (x 1 y 1 Zi t{) be the coordinates of space and time in the 

 moving axes, connected with (x, y, z, t) those in the fixed 

 axes by the relations 



#j = e*x f = 62 (# — vt), 



yi= y = y 



1 



/' V€ A 



6' 2 



then Maxwell's equations referred to moving axes assume 

 the form 



irJT dt (/i> 9u h) =Curli (a 1? 6 l9 c r ) 



— J^2 ^^ ^' C l) = Curl l (/l9 0i> ^i)j 



where (/i g x 7*i ; «i &i c x ) are related to the actual vectors in 

 the field by the equations 



(«ij &i> = e * ( e_la ' b-\-4r7rvh, c — ^Trvg). 



Thus if the values (/ b gr l5 /^ ; «: b l c x ) given as functions of 

 (x 1 iji Zi t\) express the course of change of the aethereul 

 vectors of any electrical system referred to the axes ix x y x z x t{) 

 at rest in the aether, then 



expressed by the same functions of the variables 



eKv',y\z ! , e-h'-~eKv', 

 c 



will represent the course of change of the aethereal vectors 

 (f,g,h; a, b, c) of a correlated system of moving charges 

 referred to axes (V, y', z') moving through the aether with 

 uniform translatory velocity (v, 0, 0). Moreover, in tin's 

 correlation between the courses of change, in the two systems, 

 elements of charge occupy corresponding positions in the 

 two systems and are of equal strengths. However, electro- 

 dynamic forces per unit charge are not the same in the two 

 systems. They are, however, related in an obvious manner. 



