434 The Theory of Aether and Electrons in the 



Budde and Fitz Gerald* had advanced in a similar case ; a 

 conductor carrying a constant electric current and moving with 

 the earth would exert a force on electric charges at relative 

 rest in its vicinity, were it not that this force induces on the 

 surface of the conductor itself a compensating electrostatic 

 charge, whose action annuls the expected effect. 



The most satisfactory method of discussing the influence of 

 the terrestrial motion on electrical phenomena is to transform 

 the fundamental equations of the aether and electrons to axes 

 moving with the earth. Taking the axis of x parallel to the 

 direction of the earth's motion, and denoting the velocity of the 

 earth by w, we write 



x = #1 + wt t y = 2/1, z = Zi, 



so that (x-i, yi t Zj) denote coordinates referred to axes moving 

 with the earth. Lorentz completed the change of coordinates 

 by introducing in place of the variable t a "local time" t l} 

 defined by the equation 



t = t l + m^/c 2 . 



It is also necessary to introduce, in place of d and h, the electric 

 and magnetic forces relative to the moving axes : these aret 



d 1 = d + [w.h] 

 h 1 = h + (l/c 2 ) [d.w]; 



and in place of the velocity v of an electron referred to^the 

 original fixed axes, we must introduce its velocity Vi relative to 

 the moving axes, which is given by the equation 



V, = V - W. 



The fundamental equations of the aether and electrons, 

 referred to the original axes, are 



div d = 47re 2 , curl d = - h, 



div h = 0, curl h = (1/c 2 ) d + 



F = d + [v . h], 



where F denotes the ponderomotive force on a particle carrying 

 a unit charge. 



* Cf . p. 263. t Cf. pp. 365, 366. 



