But in general it is inferred by a process of measurement depending on our direct sense-awareness of selected cases and a logical inference from the transitive character of congruence.
Congruence depends on motion, and thereby is generated the connexion between spatial congruence and temporal congruence.

Motion along a straight line has a symmetry round that line.

This symmetry is expressed by the symmetrical geometrical relations of the line to the family of planes normal to it.
Also another symmetry in the theory of motion arises from the fact that rest in the points of {beta} corresponds to uniform motion along a definite family of parallel straight lines in the space of {alpha}.

We must note the three characteristics, (i) of the uniformity of the motion corresponding to any point of {beta} along its correlated straight line in {alpha}, and (ii) of the equality in magnitude of the velocities along the various lines of {alpha} correlated to rest in the various points of {beta}, and (iii) of the parallelism of the lines of this family.
We are now in possession of a theory of parallels and a theory of perpendiculars and a theory of motion, and from these theories the theory of congruence can be constructed.

It will be remembered that a family of parallel levels in any moment is the family of levels in which that moment is intersected by the family of moments of some other time-system.