﻿Approach to the Theory of Relativity. 505 



Theorem 5. 



If u — observed velocity of the aviator with respect to S, 



u = » ?? ■>■> )■> y> v ^ j 



R = observed rate of the aviator's clock with respect to S, 

 and R' = ,. ,, „ „ ? ? „ >, £> , 



then R' R . r 



Vi-(«7cj a= vr^/c) 2 "^ vi-wc) 2 ' 



where v = observed velocity of O' and r — observed rate of the clock at 0', 

 with respect to S. 



All these theorems, strange as they may seem at first sight, 

 are readily proved from the transformation equations in 

 Theorem 1. 



III. The Principle of Relativity. 



19. We have now shown how observers on our moving 

 platform S' can regulate their clocks and lay out a permanent 

 system of coordinates, by the method of light-signals, and we 

 have shown how this system will appear to observers on a 

 stationary platform. 



We now 'proceed to inquire to what extent this system S' con- 

 forms to the Principle of Relativity. 



20. The guiding principle of the Theory of Relativity may 

 be stated as follows : 



Observers on a system which is moving with uniform velocity 

 through the ozther can never detect that motion by any observa- 

 tions which they can make. 



In order to ascertain to what extent our system S' con- 

 forms to this principle, toe now inquire wliether there are any 

 kinematical experiments that the observers on S' can make, the 

 results of which will be distinguishable from the residts of 

 similar experiments performed by observers on S. 



We shall consider first the experiments which can be made 

 without any observer's leaving his own station ; secondly, the 

 experiments which can be made by the aid of a portable 

 measuring-rod; and thirdly, the experiments which can be 

 made by the aid of a portable clock *. 



We begin by obtaining the inverse transformation equa- 

 tions, by which we may determine how the stationary system 

 S will appear to observers on the moving system S'. 



* Dynamical experiments, involving - the notion of moss, can be treated 

 in a similar way, but are not considered in the present paper, on account 

 of lack of space. 



