182 L. Page— Relativity and the Ether. 



F, = eJE + ;,[vxH]) (it) 



and had a longitudinal mass — ^ and a transverse mass 



VI- P* 



The Mass of an Electron which has had a Constant 



Acceleration Relative to its own System 



for an Infinite Time. 



Let <|> be the constant acceleration of a point relative to 

 its own system. Orient axes so that the acceleration of the 

 point relative to system K is in the positive Z direction, and 

 fix time and space origins so that t= and z= when the 

 point is at rest relative to K. Let f be the acceleration and v 

 the velocity of the point relative to K at the time t. Then 



(1), (2), (3) give at once : 















/=<Mi-/3y 













(18) 



<$>t 















P- ° 



■ !- 



_ e 



i J 





-'} 



(19) 



'"•.♦*? 



—?{•» + *?- 



(20) 



1 Vi- 



■ff 



Instead of a point consider 



an 



infinitesimal str 



slight 



line 



OP parallel to the Z axis. The end has the acceleration 

 <(> ; we desire to find the acceleration and velocity of the end P 

 at any instant. Consider an infinite number of systems mov- 

 ing in the Z direction relative to K. Then, since OP has 

 had a constant acceleration relative to its own system for an 

 infinite time, the postulate of the relativity of all systems 

 moving with constant velocities demands that the length OP 

 as measured by an observer in iTwhen O is at rest in K shall 

 be the same as the length OP as measured by an observer in 

 any other system when is at rest in that system. Call this 

 constant length d\. Let dl be the length OP as measured in 

 K at any time. Then from (1) dl — d\ <\/\—f? to second 

 order of small quantities. 



Now when O is at rest in K, P may have a velocity dfi 

 and acceleration (j)-\-dcf) in the Z direction. dfJL will have to 



