EINSTEIN'S LAW OF GRAVITATION 233 



Following this method Einstein developed a system of 

 measuring both space and time intervals. As a matter 

 of fact his system is identically that which we use in daily 

 life with reference to events here on the earth. He further 

 showed that if a man were to measure the length of a 

 rod, for instance, on the earth and then were able to carry 

 the rod and his measuring apparatus to Mars, the sun, or 

 to Arcturus he would obtain the same numerical value 

 for the length in all places and at all times. This doesn't 

 mean that any statement is implied as to whether the 

 length of the rod has remained unchanged or not; such 

 words do not have any meaning remember that we can- 

 not speak of true length. It is thus clear that an observer 

 living on the earth would have a definite system of units 

 in terms of which to express space and time intervals, i.e., 

 he would have a definite system of space coordinates 

 (^ y> #) and a definite time coordinate () ; and simi- 

 larly an observer living on Mars would have his system 

 of coordinates (V, y, z , t'). Provided that one observer 

 has a definite uniform velocity with reference to the other, 

 it is a comparatively simple matter to deduce the mathe- 

 matical relations between the two sets of coordinates. 

 When Einstein did this, he arrived at the same transfor- 

 mation formulae as those used by Lorentz in his develop- 

 ment of Maxwell's equations. The latter had shown that, 

 using this formulae, the form of the laws for all electro- 

 magnetic phenomena maintained the same form ; so Ein- 

 stein's method proves that using his system of measure- 

 ment an observer, anywhere in the universe, would as the 

 result of his own investigation of electromagnetic phenom- 

 ena arrive at the same mathematical statement of them as 

 any other observer, provided only that the relative veloc- 

 ity of the two observers was uniform. 



Einstein discussed many other most important questions 

 at this time; but it is not necessary to refer to them in 

 connection with the present subject. So far as this is 

 concerned, the next important step to note is that taken in 



