Accordingly in the instantaneous space of a moment we should expect the fundamental properties to be marked by the intersections with moments of other families.

If M be a given moment, the intersection of M with another moment A is an instantaneous plane in the instantaneous space of M; and if B be a third moment intersecting both M and A, the intersection of M and B is another plane in the space M.Also the common intersection of A, B, and M is the intersection of the two planes in the space M, namely it is a straight line in the space M.An exceptional case arises if B and M intersect in the same plane as A and M.Furthermore if C be a fourth moment, then apart from special cases which we need not consider, it intersects M in a plane which the straight line (A, B, M) meets.

Thus there is in general a common intersection of four moments of different families.

This common intersection is an assemblage of abstractive elements which are each covered (or 'lie in') all four moments.

The three-dimensional property of instantaneous space comes to this, that (apart from special relations between the four moments) any fifth moment either contains the whole of their common intersection or none of it.