there is no fixed method by which two sequences of events may be compared in the mind. The comparisons which actually occur give a qualitative description of events, inasmuch as the sequence of processes is generally unaltered in direct perception and in memory, but the lack of a standard set of units invariably connected with the method of comparison, prevents the description from being a true quantitative one.
This being the case, we are met with a fundamental difficulty when we try to analyse the idea of simultaneity as presented to us by the mind.
If we could represent an event by a point on a line, the idea of simultaneity would be quite simple, for two events could be regarded as simultaneous when their representative points were coincident. In reality such a representation is not valid, there is no sensation of such a simple nature that it can be represented by a point on a line. If we adopt a representation by means of an interval on a line, we obtain what is probably a truer representation of an event as regards its duration; but if we suppose that two events are simultaneous when their representative intervals have a common part, it is clear that two events which are simultaneous with the same event would not necessarily be simultaneous with one another.
It will be realised after a little thought that we can only obtain a satisfactory definition of simultaneity by introducing the idea of the measurement of time; we are thus obliged to consider the physical aspect of time in order to understand the idea of simultaneity.
An observer provided with an instrument for measuring time, such as a clock or a pendulum, can attach a definite number to each event that occurs. In some cases he may find it difficult to decide as to which of two
