preliminary explanations necessary will, I hope,
serve as a general explanation of the function of event-particles in the
analysis of nature.

We note that event-particles have 'position' in respect to each other.
In the last lecture I explained that 'position' was quality gained by a
spatial element in virtue of the intersecting moments which covered it.
Thus each event-particle has position in this sense. The simplest mode
of expressing the position in nature of an event-particle is by first
fixing on any definite time-system. Call it {alpha}. There will be one
moment of the temporal series of {alpha} which covers the given
event-particle. Thus the position of the event-particle in the temporal
series {alpha} is defined by this moment, which we will call M. The
position of the particle in the space of M is then fixed in the ordinary
way by three levels which intersect in it and in it only. This procedure
of fixing the position of an event-particle shows that the aggregate of
event-particles forms a four-dimensional manifold. A finite event
occupies a limited chunk of this manifold in a sense which I now proceed
to explain.

Let e be any given event. The manifold of event-particles falls into
three sets in reference to e. Each event-particle is a group of equal
abstractive sets and each abstractive set towards its small-end is
composed of smaller and smaller finite events. When we select from these
finite events which enter into the make-up of a given event-particle
those which are small enough, one of three cases must occur. Either (i)
all of these small events are entirely separate from the given event
e, or (ii) all of these small events are parts of the event e, or
(iii) all of these small events overlap the event e but are not parts
of it. In the first case the event-particle will be said to 'lie
outside' the event e, in the second case the event-particle will be
said to 'lie inside' the event e, and in the third case the
event-particle will be said to be a 'boundary-particle' of the event
e. Thus there are three sets of particles, namely the set of those
which lie outside the event e, the set of those which lie inside the
event e, and the boundary of the event e which is the set of
boundary-particles of e. Since an event is four-dimensional, the
boundary of an event is a three-dimensional manifold. For a finite event
there is a continuity of boundary; for a duration the boundary consists
of those event-particl