General Relativity and Einstein's Theory. 387 



mined from observations made in two different reference systems, 

 the form of this law and the valnes of the constants entering into 

 it can differ in the two cases only in so far as the geometry and the 

 devices for measuring time and distance together with the units of 

 these quantities may differ in the tzvo systems. Their relative 

 motion can in no way affect either the form of the law or the 

 values of the constants involved. This is the principle of general 

 relativity. 



Consider two reference systems which have the same geometry, 

 devices of the same character for measuring time and distance, 

 and interchangeable units of these quantities. Such systems may 

 be called reciprocal. If follows that 



A law governing physical phenomena zvhich are conditioned 

 solely by those effects which travel through empty space, has the 

 same form and its constants have the saine values for tzvo 

 mutually reciprocal systems. This is the restricted principle of 

 relativity. 



Consider two reciprocal Euclidean systems 6" and S', such that 

 all points of S' have the same constant velocity v relative to 5". 

 Let light travel in straight lines in 5" with constant speed c. Then 

 the restricted principle .of relativity requires that light shall 

 travel in straight lines in S' with the same constant speed c. 

 Moreover, the laws governing physical phenomena must have the 

 same form in terms of the space and time intervals of S' as in 

 terms of those of 6^. Investigation shows that the coordinates 

 and time in S' are related to the corresponding quantities in 6" by 

 the familiar Lorentz-Einstein transformations. 



As systems ^ and S' are entirely equivalent, and the only 

 velocity of either which has any significance is that relative to 

 the other or to a third system, the question arises as to whether 

 acceleration is not also relative. Let S and S" be two reciprocal 

 Euclidean systems in which light travels in straight lines with 

 the constant speed c. Then investigation shows the only possible 

 state of motion of S" relative to 6" to be that in which every point 

 of S" moves with the same constant velocity relative to S. A 

 system accelerated relative to 6' would have a non-Euclidean 

 geometry jf the velocity of light were constant relative to it. 

 Hence the objectional terms "constant velocity system" and "un- 

 accelerated system" may be avoided by describing the systems 



