﻿74 Dr. W. F. G. Swarm on the Effects of Uniform Motion 



at the times T Y and T 2 , instantaneous motions which give rise 

 to simultaneous effects at the point P at the time t, time 

 being measured, to fix our ideas, from the instant when one 

 of the electrons (say ei) crossed some point in its orbit in 

 the system at rest, and at the same time the corresponding 

 electron in the moving system passed the corresponding point 

 0'. We then have in the moving system 



Time taken by disturbance originated by e 1 to reach P' 



Time taken by disturbance originated by e 2 to reach P' 

 =ST 2 =6^(t 1 _T 2 ) + g(«'-y3') 1 



where a! and /3' are the differences of the x coordinates of 

 A' and P ; , and of A' and B' respectively, t x and T 2 being 

 measured from the same origin as t and T. t 1 is of course the 

 time of occurrence at P' of the disturbance produced by e 2 . 

 If the disturbances due to e± and e 2 are to be simultaneous at 

 the point P' in the moving system, we must have t x =t and 

 consequently 



ST. - oT s = e 1 ' 2 (T 2 - TJ + ^. 



Since this is the amount by which the time for the passage 



of the disturbance originated by e 1 exceeds the time for the 



passage of the disturbance originated by e 2 , we see that the 



instantaneous motion of e 2 must, in the moving system, occur 



ev8 f 

 later than that of e 1 by e 12 (T 2 — Tj) + —t^-. This condition 



is satisfied if the motion at A' occurs at the time € 1/ ' 2 T 1 + 





and the motion at B' at the time e 1/2 T 2 -f — ~- , where #/ and 



%</ are the coordinates of A' and B' measured from any 

 origin we choose. Thus we may say that if a series of 

 electronic motions occur at the points # 1? y u c l5 .r 2 , ?/ 2 , z 2 , 

 sr 3 , 7/ 3 , z 3l &c. at the times T,, T 2 , T 3 , &c. in the system at 

 rest, and give rise to a simultaneous set of effects at some 

 point P, the condition that the corresponding motions 

 occurring at the corresponding points .r/, y l5 z u ,v 2 , y 2 , z 2i 

 «fec. shall give rise to simultaneous effects at P 7 in the moving 



svstem is, that they shall occur at times e 1/2 T 1 -f A 2 ? 



e 1 2 T 2 -\ — —?■ . . . &c.j which is equivalent to saying that if T is 



