﻿Approach to the Theory of Relativity. 503 



14. By this Theorem 1, the possibility of laying out a 

 permanent set ot coordinates on the moving system S' by the 

 method of light-signals is established : the definitions of 

 distance and velocity given for the stationary system S can 

 then be applied directly to the moving system S', and the 

 theory of analytical geometry and kinematics developed by the 

 residents on S' will be identical with the theory developed by 

 the residents on S. 



In particular, the velocity of a light- signal, as computed by 

 two observers on S', will be found to be constant and the same 

 in all directions, in spite of the fact that the platform is 

 moving through the aether. This proposition, which here 

 follows quite naturally from the way in which the coordinates 

 were laid out on the moving system, appears in Einstein's 

 treatment as a fundamental hypothesis, and is known as the 

 famous " second postulate of relativity ,' v 



features of the moving system. 



15. In order to show in detail how the coordinate system 

 thus laid out on the moving platform will appear to ob- 

 servers on the stationary platform, we state the two following 

 theorems, both of which can be deduced by a simple calcula- 

 tion from the transformation equations in § 13. 



Definition. Suppose a number of observers, A, B, C,... 

 on S agree to observe the points opposite them " at a speci- 

 fied time " — that is, each one is to make his observation when 

 his own clock reads, say, t . Let A' be the point opposite A 

 when A's clock reads t , W the point opposite B when B's 

 clock reads £ , &c. Then the figure formed by A, B, C,... in 

 S is called the image in S of the figure formed by A', B', 

 C/,...inS'. 



Theorem 2. Consider one of the " townships " A' B' C D' 

 into which the platform S' is divided, by its coordinate network ; 

 and let A B C D be the " image in S " of this township. Then 

 A' W C D', zuhen computed by the coordinates in S\isa square ; 

 but A B C D, when computed by the coordinates in S, is a 

 rectangle, with its short side lying in the direction of the motion 

 of S'. The ratio of the sides is given by 



longitudinal side / v 2 1 



transverse side ~~ v c 2 ~k' 



It should be noticed that this ratio depends only on the 

 velocity v, and not on the relative rates of the clocks at 

 and 0'. 



