45. Null-Tracks. 45.1 The relations between rects and point-tracks are best understood by taking a rect and a particle which is not co-level with . In this way a matrix is obtained as explained in 44.2. Fig. 9. Then in respect to the rect is divided into three (logical) parts by two event-particles and . The segment between and has the property that any event-particle on it is joined to by a point-track [e.g. in the figure]; and either of the two infinite segments, namely that beyond and that beyond , is such that any event-particle on it is joined to by a rect [e.g. ′ and ″ in the figure]. The above diagram and succeeding diagrams have the defect of representing matrices by levels, and thus of giving the conceptions an undeserved air of paradox. Again we may take an event-particle and a point-track not containing . In this way a matrix is obtained as explained in 44.3. Fig. 10. Then in respect to the point-track is divided by two event-particles and into three (logical) parts. The segment between and has the property that any event-particle on it is joined to by a rect [e.g. in the figure]; and either of the two infinite segments, respectively beyond and beyond , is such that any event-particle on it is joined to by a point-track [e.g. ′ and ″ in the figure]. 45.2 It is evident therefore that a matrix in respect to an event-particle P lying on it is separated into four regions by two loci and which may equally well be termed rects or point-tracks. Fig. 11. The event-particles in the vertically opposed regions and are joined to by rects; and the event-particles in the vertically opposed regions and are joined to by point-tracks. The loci which bound the regions separating point-tracks from rects will be called 'null-tracks.' Their special properties will be considered later when congruence has been introduced. In any matrix there are two families of parallel null-tracks; and there is one member of each family passing through each event-particle on the rectilinear track. The order of event-particles on a null-track is derived from its intersection with systems of parallel rects [not co-momental] or of parallel point-tracks or from the orders on routes lying on it. 46. Straight Lines. 46.1 There is evidently an important theory of parallelism for families of matrices analogous to the theory of parallels for families of levels. The detailed properties need not be elaborated here. Two matrices may either (i) be parallel, or (ii) intersect in one event-particle only, or (iii) intersect in a rect, or (iv) intersect in a point-track, or (v) intersect in a null-track. For the intersection of two levels only cases (i), (ii) and (iii) can occur; for the intersection of a level and a matrix only cases (ii) and (iii) can occur.