A 'family of parallel durations' is formed by all the durations parallel to a given duration, including that duration itself. Evidently any two members of such a family are parallel, and no duration out of the family is parallel to any duration of the family.
Analogously to such families of parallel durations, there are families of parallel moments, with the property that no two moments of the same family intersect and that any moment out of a given family intersects every moment belonging to the family.
The durations which are the members of the various moments of a given family of moments themselves form a family of parallel durations. Thus corresponding to a family of parallel durations there is one and only one family of parallel moments; and corresponding to a family of parallel moments there is one and only one family of parallel durations. A pair of such corresponding families, one of durations and the other of moments, form the 'time-system' associated with either of the two families.
Evidently each duration belongs to one and only one family of parallel durations; and thus each duration belongs to one and only one time-system. Also each moment belongs to one and only one family of parallel moments; and thus each moment belongs to one and only one time-system. Thus two distinct time-systems have no durations in common and no moments in common. But every event not a duration is contained in some durations of any given time-system. Furthermore there will be a minimum duration in a given time-system which is the duration 'when' the event happened in that time-system; namely, the minimum duration has the properties (i) that it extends over the event and (ii) that every duration which is part of it intersects the event.
[34.3] The moments of a time-system are arranged in serial order in this way:
(i) A duration belonging to a time-system is 'bounded' by a moment of the same time-system when each duration in which that moment inheres intersects the given duration and also intersects events separated from the given duration:
(ii) Every duration has two such bounding moments, and every pair of parallel moments bound one duration of that time-system:
(iii) A moment
of a time-system 'lies between' two moments