8±S Prof. L. T. More on the Postulates and 



This is due to the fact that the observer of a moving body- 

 must depend on some signal such as light in determining its 

 length. But the following illustration seems to make it clear 

 that concordant results can always be obtained when two 

 observers are able to compare their standards directly or 

 statically either before or after the measurement. 



Let a long train (fig. 1) be moving in the direction of the 



Fi*. 1. 



► A J 



x J2 



arrow, then an observer A, on the train, would measure its 

 length by applying a standard length. If, however, B, 

 standing on the embankment, desires to measure the length 

 of the moving train, Einstein states that his result must be a 

 different one, involving the composition of the velocities of 

 the train and of the light signal. But suppose that B 

 marks off a distance XY along the embankment and either 

 before or after the observation he can compare this distance 

 with A's standard length, then he can obtain the length of 

 the train in static measure and concordantly with B's 

 measurement. For let him station himself half-way between 

 X and Y. Let him record the times when Q reaches X and 

 Y by either light or sound signals and also when P reaches 

 the same points ; although it may take time for the signals 

 to reach him from X and from Y, yet, the distances BX and 

 BY being equal, the differences in time will be correctly 

 given. 



Then, if t x and t y be the times noted when Q reaches X 

 and Y, and if tj and tj be the times for P, 



= the velocity of the train =v, 



ty t x 



and 



v(tJ-t x ) = XYj L ~ = I = length of the train. 



t?/ t x 



And this length will agree with the length measured by A 

 on the train, provided that XY is long enough to separate 



