34. Parallelism and Time-Systems. 34.1 If the Newtonian theory of relativity were true, no pair of durations would lack durations extending over both of them, namely larger durations including both the given durations. But on the electromagnetic theory of relativity this is not necessarily the case, namely some pairs of durations are extended over by a family of durations and some are not. We shall adopt the electromagnetic theory of relativity. A pair of durations both of which are parts of the same duration are called 'parallel'; and also a pair of moments such that there are durations in which both inhere are called 'parallel.' Parallelism has the usual properties of transitiveness, symmetry and reflexiveness. Also two durations which do not intersect are parallel; and parallel moments which are not identical never intersect. If two parallel durations intersect there is a duration which is their complete intersection, but there are no durations among the common parts of two durations which are not parallel. Two moments which are not parallel necessarily intersect. 34.2 Two durations which are parallel to the same duration are parallel to each other; thus it is evident that each absolute antiprime and each moment must be composed of parallel durations. 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.