tion of vagrant routes in general. There are
however two simple sets of routes which are of vital importance. One is
a set of momental routes and the other of vagrant routes. Both sets can
be classed together as straight routes. We proceed to define them
without any reference to the definitions of volumes and surfaces.

The two types of straight routes will be called rectilinear routes and
stations. Rectilinear routes are momental routes and stations are
vagrant routes. Rectilinear routes are routes which in a sense lie in
rects. Any two event-particles on a rect define the set of
event-particles which lie between them on that rect. Let the
satisfaction of the condition {sigma} by an abstractive set mean that
the two given event-particles and the event-particles lying between them
on the rect all lie in every event belonging to the abstractive set. The
group of {sigma}-primes, where {sigma} has this meaning, form an
abstractive element. Such abstractive elements are rectilinear routes.
They are the segments of instantaneous straight lines which are the
ideals of exact perception. Our actual perception, however exact, will
be the perception of a small event sufficiently far down one of the
abstractive sets of the abstractive element.

A station is a vagrant route and no moment can intersect any station in
more than one event-particle. Thus a station carries with it a
comparison of the positions in their respective moments of the
event-particles covered by it. Rects arise from the intersection of
moments. But as yet no properties of events have been mentioned by which
any analogous vagrant loci can be found out.

The general problem for our investigation is to determine a method of
comparison of position in one instantaneous space with positions in
other instantaneous spaces. We may limit ourselves to the spaces of the
parallel moments of one time-system. How are positions in these various
spaces to be compared? In other words, What do we mean by motion? It is
the fundamental question to be asked of any theory of relative space,
and like many other fundamental questions it is apt to be left
unanswered. It is not an answer to reply, that we all know what we mean
by motion. Of course we do, so far as sense-awareness is concerned. I am
asking that your theory of space should provide nature with something to
be observed. You have not settled the question by bringing forward a
theory according to which there is nothing to be