﻿$2 Dr. A. D. Fokker : A Summary of 



and time, x, y, z, t, of the moving system must now be indi- 

 cated more exactly. In deducing them use is made of the 

 postulate, that the velocity of light at each point of the 

 moving system should be independent of the direction of 

 the light-beam, and therefore a function of the coordinates 

 only. In our case, where we shall suppose the system 

 (#, y, z, t) accelerated along the axis of Z, the velocity is a 

 function of z only. Lorentz * gave the equations in the 

 exact form 



(a) 



(l>) 



where c is a constant, the velocity of light in the resting 

 system, and 



The constant k is connected with the (variable) velocity of 

 light, c\ in the points of the moving system by the relation 



\c' = k (z — z Q ). 



The approximate equations given by Einstein f and valid 

 for very small values of t, so that i 3 may be neglected, are 

 easily deduced from these. They are 



CT=C f t, ^ 



1 c'H 2 i ' 



From the last equation we see 



f _ - . , -1 A* 



-,z—* 



that at t = the starting acceleration of the different points 



c 2 

 of the system is given by g = . Speaking exactly, the 



Z Zq 



acceleration is not the same for the different points of the 

 system. Nor is it the same throughout the time. A per- 

 fectly constant acceleration, by the way, would lead to a 

 contradiction with the old relativity theory, because it would 

 lead to an infinite velocity. We can see more distinctly 



* H. A. Lorentz, Het Relativiteitsbeginsel. Drie voordrachten, 

 bewerkt door Dr. W. H. Keesom, 1913 (De Erven Loosjes, Haarlem), 

 t A. Einstein, Annalen der Physik, xxxviii. pp. 359, 444 (1912). 



