There is an exact correlation between the time-less space of a time-system and any momentary space of the same time-system. For any point of the momentary space is an event-particle which occupies one and only one point of the time-less space; and any straight line of the momentary space is a rect which lies in one associated matrix including one straight line of the time-less space, or (in other words) each straight line of the momentary space occupies a straight line of the time-less space. A time-system corresponds to a consentient set of the Newtonian group, and the time-less space of the time-system is the space of the corresponding consentient group. CHAPTER XII NORMALITY AND CONGRUENCE 47. Normality. 47.1 A point-track will be said to be 'normal' to the moments of the time-system in the space of which it is a point. A matrix is said to be 'normal' to the moments which are normal to any of the point-tracks which it contains. Consider an event-particle and a matrix which contains . Let , ... be the collinear set of time-systems whose points lie in or are parallel to the matrix . Let , ... be the moments of the time-systems ... which contain . Then the levels , ... in which respectively and , and , etc., intersect are identical, and the event-particle is the sole event-particle forming the intersection of and . Also intersects each of these moments , and , and , etc., in rects , etc., respectively. The level and the matrix are said to be mutually 'normal.' It will be noted that any two time-systems, and , determine one level and one matrix which are mutually normal and each contain a given event-particle. Corresponding to any level containing there is one matrix normal to it at ; and corresponding to any matrix containing there is one level normal to it at . If and be a level and a matrix normal to each other, then the rects in will be called normal to the rects and point-tracks in . A pair of rects which are normal to each other will also be called 'perpendicular' or 'at right-angles.' Two point-tracks can never be normal to each other since no point-track lies on a level. Parallels to normals are themselves normal. 47.2 Continuing the notation of 47.1 we note that the matrix includes straight lines , etc., of the spaces of , etc., and intersects the moments , etc., in rects , etc., which respectively occupy , etc. The rect contains and is normal to every rect lying in . Let ′ be any rect containing and lying in . Then ′ and are mutually normal and both lie in the moment .