﻿deduced from the Electrical Theory of Matter. 75 



the time of occurrence of any electronic motion at x, y, z 

 in the system at rest, the necessary requirements are satisfied 

 if the corresponding electronic motion occurs in the moving 



system at the point x\ y, 2, at the time e 1/2 T-t- -t4~. Now 



we have already seen that if an electronic motion occurring 

 at produces its effect at the point P at the time t in the 

 system at rest, the effect due to the corresponding motion at 



0' will occur at P' at the time t'-e l ' 2 t+ ~. We are not 



C 2 



yet at liberty to say that, measuring time from the same 



origin, if an electronic motion occurring at the point A 

 produces its effect at P at the time t a , the corresponding- 

 electronic motion occurring at A' will produce its effect at the 



time e 1/2 C+ ~rw ^ e can readily see that this is so, how- 

 ever, for let us take and O r as our origins of coordinates in 

 the two systems, suppose the motion at A to take place at time 

 T a and suppose the effect to be felt at P at the time t a . Then, 

 as we have already seen, if x is the x coordinate of P' and 



€vS' 



/3' that of A', the motion occurs at A' at the time e l / 2 T a + ~^-, 

 and the disturbance produced by it at P' occurs later than 



€V 



the motion at A' by an amount e 1/2 (t a —T a ) + tt 2 (#'—£')• 

 Hence the disturbance at P' occurs at the time 



[«v»T.+ € [f] + |>(«.-T.) + ^O'-/ 3 ')] = £l/2 '° 



€VX 



Thus we see that the requirement stated on page 70 is satisfied 

 provided that, if any electron in the system at rest describes 

 an instantaneous motion at the point f, 97, f at the time T, 

 the corresponding electron in the system in motion shall 

 describe its corresponding instantaneous motion at the corre- 

 spondiug point £', tj^ £, at the time e 1/2 T + —J ; and we have 



further shown, that if the effect of a certain set of instan- 

 taneous motions is felt simultaneously at the time t at any 

 point x, y, z in the system at rest, the effect due to the 

 corresponding motions in the moving system will be felt at 



the corresponding point x' 3 y, z at the time ^ = e r -V -f - VJ . 



The origins of the spacial coordinate? in the above are. 



