Page:An Enquiry Concerning the Principles of Natural Knowledge.djvu/129

 DURATIONS, MOMENTS AND TIME-SYSTEMS 115 when B inheres in the duration which A and C bound : (iv) This relation of lying between has the following properties which generate continuous serial order in each time-system, namely, (α) Of any three moments of the same time-system, one of them lies between the other two: (β) If the moment B lies between the moments A and C, and the moment C lies between the moments B and D, then B lies between A and D: (γ) There are not four moments in the same time- system such that one of them lies between each pair of the remaining three: (δ) The serial-order among moments of the same time-system has the Cantor-Dedekind type of con tinuity. Nothing has yet been said about the measurement of the lapse of time. This topic will be considered as part of the general theory of congruence. . Levels, Rects, and Puncts. 35-1 The electro magnetic theory of relativity is obviously the more general of the two. It has also the merit of providing definitions of flatness, of straightness, of punctual position, of parallelism, of time-order and spatial order as interconnected phenomena, and (with the help of cogredience) of perpendicularity and of congruence. The theory of extension has also provided the definition of a duration. It is a remarkable fact that the charac teristic concepts of time and of geometry should thus be exhibited as arising out of the nature of things as expressed by the two fundamental relations of extension and cogredience. It has already been explained that a moment is the route of approximation towards an