386 Leigh Page, 



tween two points in a reference system, and synchronizing- time 

 at these points. In order to be of value in comparing coinci- 

 dences, this device must be subject to the following conditions, 

 though otherwise its nature is quite arbitrary : 



(a) Two points which are in synchronism with a third are 

 also in synchronism with each other. 



(b) The distance between two points is independent of the 

 time at which it is measured. 



Evidently the motion of a moving element may be described 

 relative to an infinite number of reference systems, which are 

 themselves in various states of motion relative to one another. 

 However, these systems are not, in general, of the same signifi- 

 cance. For let A, B and C be three systems from which the 

 motion of the moving element P may be observed. Suppose it 

 is found that the motion of P relative to A is conditioned by 

 that of B, but is independent of that of C. In such case the 

 motion of P is said to be related to B, which is known as a related 

 reference system. C, on the other hand, is an unrelated or ideal 

 reference system. Thus for the motion of a shot, the gun from 

 which it is fired constitutes a related reference system. The 

 velocity of a sound wave is determined, not by the motion of the 

 source, but by the characteristics of the medium through which it 

 passes. Hence in this case, the source determines an ideal 

 reference system, while the medium is a related one. 



In the case of propagation of a disturbance through empty 

 space it has been recognized for a long time that the source does 

 not constitute a related reference system. The Michelson-Morley 

 experiment has shown the same to be true of the "ether." Hence 

 it may be inferred that 



For the motion of an effect zvhicJi travels through empty space, 

 such as a light wave or one of the moving elements zvhich form 

 an electromagnetic or a gravitational field, there is no related 

 reference system. 



If this statement be granted, the question arises as to how the 

 law connecting a group of related physical phenomena may differ 

 when determined in terms of the space and time intervals of 

 different reference systems. Evidently, 



If a law governing physical phenomena whicJi are conditioned 

 solely by those effects which travel through empty space, is deter- 



