ormed by durations of the associated
family. Each such instantaneous space represents the ideal of nature at
an instant and is also a moment of time. Each time-system thus possesses
an aggregate of moments belonging to it alone. Each event-particle lies
in one and only one moment of a given time-system. An event-particle has
three characters[12]: (i) its extrinsic character which is its character
as a definite route of convergence among events, (ii) its intrinsic
character which is the peculiar quality of nature in its neighbourhood,
namely, the character of the physical field in the neighbourhood, and
(iii) its position.

[12] Cf. pp. 82 et seq.

The position of an event-particle arises from the aggregate of moments
(no two of the same family) in which it lies. We fix our attention on
one of these moments which is approximated to by the short duration of
our immediate experience, and we express position as the position in
this moment. But the event-particle receives its position in moment M
in virtue of the whole aggregate of other moments M{'}, M{''}, etc.,
in which it also lies. The differentiation of M into a geometry of
event-particles (instantaneous points) expresses the differentiation of
M by its intersections with moments of alien time-systems. In this way
planes and straight lines and event-particles themselves find their
being. Also the parallelism of planes and straight lines arises from the
parallelism of the moments of one and the same time-system intersecting
M. Similarly the order of parallel planes and of event-particles on
straight lines arises from the time-order of these intersecting moments.
The explanation is not given here[13]. It is sufficient now merely to
mention the sources from which the whole of geometry receives its
physical explanation.

[13] Cf. _Principles of Natural Knowledge_, and previous chapters of the
present work.

The correlation of the various momentary spaces of one time-system is
achieved by the relation of cogredience. Evidently motion in an
instantaneous space is unmeaning. Motion expresses a comparison between
position in one instantaneous space with positions in other
instantaneous spaces of the same time-system. Cogredience yields the
simplest outcome of such comparison, namely, rest.

Motion and rest are immediately observed facts. They are relative in the
sense that they depend on the time-system which is fundamental for the
observation. A string of event-particle