﻿Approach to the Theory of Relativity. 509 



observers could by this experiment determine whether or not 

 their system is in motion. 



If, on the other hand, we assume with Lorentz that the 

 absolute length of the rod when moving lengthwise is less 

 than it is when moving sidewise (and by the proper amount), 

 then a rod which fits A'B' would also fit B'C, and in this 

 case the experiment would give no information as to whether 

 the platform is in motion through the sether or not. 



21. If we desire, therefore, that our system S' shall 

 conform to the Principle of Relativity, we must make the 

 following assumption, which was first suggested by Lorentz 

 in 1895 : 



Assumption A. The u absolute length " of a material rod 

 (see § 26) moving through the aether with velocity v, is less when 

 the rod is moving lengthwise than it is when the rod is moving 

 sidewise, the ratio of the lengths being 



1 



\/l-(v/c) 2 ' 



where c is the observed velocity of light. 



28. If this assumption is true, we can then deduce the 

 following remarkable theorem, in which S' is any platform, 

 moving with constant velocity through the sether, on which a 

 system of coordinates has been laid out by the method of 

 light-signals : 



Theoebm 8. If Assumption A is true, the " observed length " 

 of a material rod moving with an observed velocity u with 

 respect to platform S ; is less when the rod is moving lengthwise 

 than it is when the rod is moving sidewise — the ratio of the 

 lengths being 



1 



y/l-(u'/cy ; 



and this result is entirely independent of the constant velocity v 

 with which the platform S' is moving through the cether. 



This is one of the characteristic propositions of the Theory 

 of Relativity. 



Experiments with a portable clock : second physical 

 assumption involved in the Theory of Relativity. 



29. Finally, we suppose that the observers on S' have 

 acquired a portable clock P, which they can "send by express " 

 from one station A to another station B ; and we inquire 

 whether the use of this portable clock will enable the observers 

 to detect the mot ion of their platform S' through the cether, 



