﻿Approach to the Theory of Relativity. 511 



motion through the aether ; and any experimental evidence 

 which may be obtained for the truth of the Principle of 

 Relativity (or for the truth of Theorems 8 and 9) may be 

 accepted as indirect evidence for the truth of Assumptions 

 A and B. 



Appendix. 



In this appendix we give an elementary method for 

 obtaining the transformation equations of Theorem 1. As 

 already stated, the correctness of Theorem 1 may be readily 

 verified when once the transformation equations have been 

 written down. The question naturally arises, however : 

 How could anyone hit upon these equations in the first 

 place ? The purpose of this appendix is to answer this 

 question. 



We consider four positions of the moving platform S', 

 namely : (1) when 0' is opposite ; (2) when a light- 

 signal starts from O f toward any station A' ; (3) when this 

 signal arrives at A' and is immediately started back toward 

 (y ; and (4) when the return signal has arrived at 0'. We 

 shall suppose for simplicity that A' lies on the axis O'X', 

 since the extension to the general case presents no new 

 difficulty and may well be left to the reader ; and we let the 

 abscissa of A', as determined by the method of light-signals, 

 be a/. 



In position 1, as shown in fig. 1, the clocks at and 0' 

 both read zero. 



Fig. 1. 



U \t' = 



O r*=o 



In position 2, at the instant when the signal starts from 

 0', let the clock at 0' read t \ and let the station which 

 happens to be opposite 0' at that instant have an abscissa # 

 and a clock-reading t . Then, since the observed rate of the 



Fig. 2. 



o ,(V = 



t = t a 



clock at 0' (see § 10) is r, we must have t ' = rt Q . Also, 



