This conception is diagrammatically illustrated [but not exactly represented] by the annexed diagram in which two dimensions have been lost. Thus the three-dimensional regions and are represented by two straight lines. These lines also represent [with full dimensions] two rects and in and respectively: the genesis of these rects will be explained below. The two-dimensional 'level' is represented by the single event-particle which lies in it: is the -point-track through , and the -point-track through ; these are represented by dotted lines. The plane of the paper is the two-dimensional matrix containing all the -point-tracks through event-particles on , and all the -point-tracks through event-particles on . This matrix intersects in the rect , and in the rect . Then the rect is perpendicular to the level, or instantaneous plane it , where both and lie in the three-dimensional instantaneous space ; also analogously for the rect and the level in . Thus the system of levels parallel to in is a system of instantaneous planes in perpendicular to the system of rects in parallel to . This pair of systems reflects in the relation between the system of -moments to the system of -point-tracks. Thus the geometry of an instantaneous moment expresses the relations of the event-particles of the moment to the whole bundle of alternative time-systems. In this connection it may be well to expand the substance of a paragraph [pp. 89, 90] in the Concept of Nature:—An instantaneous point is an event-particle. It has two aspects. In one aspect it is there, where it is, in relation to the moments of the various space-time systems of the whole bundle of such systems. This aspect is expressed by the definition of a punct, which is determined by the individual moments (one from each space-time system) which contain it. The indivisibility of a point is expressed by the fact that any moment either contains the whole punct or contains nothing of the punct: the three-dimensionality of space, with time as a fourth dimension, is expressed by the fact that a punct is defined by four moments [not exceptionally related]: the position of the punct is expressed by those moments which do contain it. In another aspect a point is got at as a limit by indefinitely diminishing the dimensions of circumambient space-time. This aspect of absence of dimensions is expressed by the definition of an event-particle by means of abstractive sets with a certain quality of primeness in relation to puncts. The intimate connection of geometry with the properties of the bundle of space-time systems is thus illustrated by the characters of instantaneous points, planes, and lines, and by the origin of parallelism and normality. Geometry expresses in three-dimensions these qualities of the four-dimensional space-time continuum. Note VI.The deductions in 50.3 and 51.1 are over condensed. They can be expanded as follows: