46.2 Each matrix contains various sets of parallel point-tracks. Any one such set is a locus of points in the space of some time-system. Such a locus of points is called a 'straight line' in the space of the time-system. A matrix which contains the points of a straight line in the space of any time-system will be called 'an associated matrix for ,' and it is called 'the matrix including' that straight line. A matrix is an associated matrix for many time-systems, but it is the matrix including only one straight line in each corresponding space. The family of time-systems for which a given matrix is an associated matrix is called a 'collinear' family. A whole family of parallel matrices are associated matrices for the same collinear family of time-systems, if any one matrix of the family is thus associated. In the space of any one time-system the straight lines included by a family of parallel associated matrices are said to be parallel. 46.3 A matrix intersects a moment in a rect. If the moment belong to a time-system with which the matrix is associated, this rect in the moment corresponds to the straight line included by the matrix in the sense that it has one particle occupying each of its points. A rect thus associated with a straight line will be said to 'occupy' it. Thus the event-particles on a matrix associated with a time-system can be exhaustively grouped into mutually exclusive subsets in two distinct ways: (i)They can be grouped into the points of which lie on ; this locus of points is the included straight line in the space of , which we will name : (ii) The event-particles on can be grouped into the sets of parallel rects which are the intersections of with the moments of , and thus each of these rects occupies . 46.4 There are three different types of meaning which can be given to the idea of 'space' in connection with external nature, (i) There is the four-dimensional space of which event-particles are the points and the rects and point-tracks and null-tracks are the straight lines. In the geometry of this space there is a lack of uniformity between the congruence theories for rects and for point-tracks, and no such theory for null-tracks, (ii) There are the three-dimensional momentary (instantaneous) spaces in the moments of any time-system , of which event-particles are the points and rects are the straight lines. The observed space of ordinary perception is an approximation to this exact concept, (iii) There is the time-less three-dimensional space of the time-system , of which point-tracks are the points and matrices include the straight lines. This is the space of physical science.