EINSTEIN'S LAW OF GRAVITATION 231 



narily stated and used. He analyzed clearly the definitions 

 and postulates which were necessary before one could 

 speak with exactness of a length or of an interval of 

 time. He disposed forever of the propriety of speaking 

 of the "true" length of a rod or of the "true" duration ot 

 time, showing, in fact, that the numerical values which we 

 attach to lengths or intervals of time depend upon the 

 definitions and postulates which we adopt. The words 

 "absolute" space or time intervals are devoid of meaning. 

 As an illustration of what is meant Einstein discussed two 

 possible ways of measuring the length of a rod when it is 

 moving in the direction of its own length with a uniform 

 velocity, that is, after having adopted a scale of length, 

 two ways of assigning a number to the length of the rod 

 concerned. One method is to imagine the observer mov- 

 ing with the rod, applying along its length the measuring 

 scale, and reading off the positions of the ends of the rod. 

 Another method would be to have two observers at rest 

 on the body with reference to which the rod has the uni- 

 form velocity, so stationed along the line of motion of the 

 rod that as the rod moves past them they can note simul- 

 taneously on a stationary measuring scale the positions of 

 the two ends of the rod. Einstein showed that, accepting 

 two postulates which need no defense at this time, the two 

 methods of measurements would lead to different numeri- 

 cal values, and, further, that the divergence of the two 

 results would increase as the velocity of the rod was in' 

 creased. 



In assigning a number, therefore, to the length of a 

 moving rod, one must make a choice of the method to be 

 used in measuring it. Obviously the preferable method 

 is to agree that the observer shall move with the rod, 

 carrying his measuring instrument with him. This dis- 

 poses of the problem of measuring space relations. The 

 observed fact that, if we measure the length of the rod on 

 different days, or when the rod is lying in different posi- 

 tions, we always obtain the same value offers no informa- 



