particles the matrix of the straight line r. A matrix intersects
any moment in a rect. Thus the matrix of r intersects the moment M in a
rect {rho}. Thus {rho} is the instantaneous rect in M which occupies at
the moment M the straight line r in the space of {alpha}. Accordingly
when one sees instantaneously a moving being and its path ahead of it,
what one really sees is the being at some event-particle A lying in the
rect {rho} which is the apparent path on the assumption of uniform
motion. But the actual rect {rho} which is a locus of event-particles is
never traversed by the being. These event-particles are the
instantaneous facts which pass with the instantaneous moment. What is
really traversed are other event-particles which at succeeding instants
occupy the same points of space {alpha} as those occupied by the
event-particles of the rect {rho}. For example, we see a stretch of road
and a lorry moving along it. The instantaneously seen road is a portion
of the rect {rho}--of course only an approximation to it. The lorry is
the moving object. But the road as seen is never traversed. It is
thought of as being traversed because the intrinsic characters of the
later events are in general so similar to those of the instantaneous
road that we do not trouble to discriminate. But suppose a land mine
under the road has been exploded before the lorry gets there. Then it is
fairly obvious that the lorry does not traverse what we saw at first.
Suppose the lorry is at rest in space {beta}. Then the straight line r
of space {alpha} is in the direction of {beta} in space {alpha}, and the
rect {rho} is the representative in the moment M of the line r of space
{alpha}. The direction of {rho} in the instantaneous space of the moment
M is the direction of {beta} in M, where M is a moment of time-system
{alpha}. Again the matrix of the line r of space {alpha} will also be
the matrix of some line s of space {beta} which will be in the direction
of {alpha} in space {beta}. Thus if the lorry halts at some point P of
space {alpha} which lies on the line r, it is now moving along the line
s of space {beta}. This is the theory of relative motion; the common
matrix is the bond which connects the motion of {beta} in space {alpha}
with the motions of {alpha} in space {beta}.

Motion is essentially a relation between some object of nature and the
one timeless space of a time-system. An instantaneous space is static,
being related to the static