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 consecutive numbers should be attached to an event; but we shall suppose that he has a consistent method of avoiding the difficulty, 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 corresponding 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 simplicity 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