Page:An Enquiry Concerning the Principles of Natural Knowledge.djvu/186



56.3 It is by means of the properties of material objects that the atomic properties of objects are com bined in mathematical calculations with the extensive continuity of events. Apart from material objects mathematical physics as at present developed would be impossible. For example where the physicist sees the electron as an atomic whole, the mathematician sees a distribution of electricity continuous in time and in space and capable of division into component objects which are also analogous distributions.

57. Stationary Events. 57.1 In order to understand the theory of the motion of material objects, it is first necessary to define the concept of a ‘stationary’ event. Consider some given time-system π, and let V denote a volume lying in a certain moment M of this time-system. Let d be a duration of π bounded by moments M1 and M2, and inhered in by M; so that M1, M2, M are three parallel moments of the time-system π, and M lies between M1 and M2. The volume V is the locus of a set of event-particles and each of these event-particles lies in one and only one station of the duration d. Also each station of d either does not intersect V or intersects it in one event-particle only. The assemblage of event-particles lying on stations of d which intersect V [namely, each event-particle lying on one of these stations] is the complete set of event-particles analysing an event. Such an event is called stationary in the time-system π and stretches throughout the duration d. It can also be called ‘stationary in d’, since d defines the time-system π. Every event-particle within the event lies on a station of d and a station of d either has all its event-particles lying within the event or none of