Manchester Illejnoirs, Vol. liv. (1910), No. 14. 3 



consecutive numbers should be attached to an event ; but 

 we shall suppose that he has a consistent method of 

 avoiding the difficult)', as, for example, by always choosing 

 the larger number of the two. 



A satisfactory definition of simultaneity for two events 

 which happen in the immediate vicinity of the observer 

 can be given as soon as events are numbered, for we can 

 say that two events are simultaneous when their corre- 

 sponding numbers are equal. The actual enumeration 

 may depend upon the personal equation of the observer, 

 but discrepancies may be eliminated as soon as a method 

 of comparing the observations of different observers has 

 been adopted. 



We now require a method of comparison by means of 

 which we can decide whether the observations of time 

 made by two different observers are equivalent or not. 

 The criterion of equivalence must be such that if the 

 observations of A are equivalent to those of B, and also 

 to those of C, then the observations of B and C are 

 equivalent to one another. 



It is clear that if two observers are situated at different 

 points of space a comparison of observations can only be 

 made by means of something which travels from one to 

 the other, and for the sake of simplicit)' it is convenient 

 to choose something which can be supposed to travel in 

 a straight line with constant velocity. It should be 

 remarked, however, that these terms have no meaning 

 until time and distance have been defined. 



It is by no means obvious that a universal method of 

 comparing observations can be found which will lead to 

 consistent results, for this presupposes the existence of a 

 universal time, an entity which has sometimes been 

 regarded as the psychological time of an infinite mind 

 governing the whole of the universe. The latter point of 



