37.6 The theory of contact is based on the four-dimensionality of the geometry of event-particles. Some results of that datum are now to be noted. A 'simple' abstractive class is an abstractive class for which there is no one event-particle on the boundaries of all those members of the converging end, which succeed some given member of the class; namely, for a simple abstractive class there is no one event-particle at which all members of the converging end have contact. Absolute antiprimes and absolute primes are simple abstractive classes. The 'atomic' property of an absolute prime is expressed by the theorem, that an absolute prime is a simple abstractive class which is covered by every simple abstractive class which it covers. The property of 'instantaneous completeness' exhibited by an absolute antiprime is expressed by the theorem, that an absolute antiprime is an abstractive class which covers every abstractive class that covers it. 38. Routes. 38.1 Event-particles are abstractive elements of atomic simplicity. Routes are abstractive elements in which is found the first advance towards increasing complexity. A 'linear' abstractive class is a simple abstractive class () which (i) covers two event-particles and (called the end-points), and (ii) is such that no selection of the event-particles which it covers can be the complete set of event-particles covered by another simple abstractive class, provided that the selection comprises and and does not comprise all the event-particles covered by . The condition (i) secures that a linear abstractive class converges to an element of higher complexity than an event-particle; and the condition (ii) secures that it has the linear type of continuity. A 'linear prime' is an abstractive class which is prime in respect to the formative condition of (i) being covered by an assigned linear abstractive class covering two assigned end-points and (ii) being itself a linear abstractive class covering the same assigned end-points. This formative condition is evidently regular for primes. A 'route' is the abstractive element deduced from a linear prime. The two assigned event-particles which occur as end-points in the definition of the linear prime from which a route is deduced are called the 'end-points' of that route. A route is said to lie between its end-points. 38.2 A route is a linear segment, straight or curved, between two event-particles, co-momental or sequent. There are an indefinite number of routes between a given pair of event-particles as end-points. A route will cover an infinite number of event-particles in addition to its end-points. The continuity of events issues in a theory of the continuity of routes. If and be any two event-particles covered by a route , there is one and only one route with and as end-points which is covered by .