If , and be any three event-particles covered by a route , then is said to 'lie between' and on the route if is covered by that route with and as end-points which is covered by . The particles on any route are arranged in a continuous serial order by his relation of 'lying between' holding for triads of points on it. The necessary and sufficient conditions which the relation must satisfy to produce this serial order are detailed in (iv) of 34.3. 38.3 A route may, or may not, be covered by a moment. If it is so covered it is called a 'co-momental route.' A 'rectilinear route' is a route such that all the event-particles which it covers lie on a rect. In a rectilinear route the order of the event-particles on the rect agrees with the order of the event-particles as defined by the relation of 'lying between' as defined for the route. Between any two event-particles on a rect there is one and only one rectilinear route. If and be two event-particles on a rect, the rectilinear route between them can also be defined as the element deduced from the prime with the formative condition of being a simple abstractive class which covers and and all the event-particles between and on the rect. 38.4 Among the routes which are not co-momental, the important type is that here named 'kinematic routes.' A 'kinematic route' is a route (i) whose end-points are sequent and (ii) such that each moment, which in any time-system lies between the two moments covering the end-points, covers one and only one event-particle on the route, and (iii) all the event-particles of the route are so covered. The event-particles covered by a kinematic route represent a possible path for a 'material particle.' But this anticipates later developments of the subject, since the concept of a 'material particle' has not yet been defined. 39. Solids. 39.1 A 'solid prime' is a prime with the formative condition of being a simple abstractive class which covers all the event-particles shared in common by both boundaries of two adjoined events. This formative condition is evidently regular for primes. A 'solid' is the abstractive element deduced from a solid prime. 39.2 If two event-particles are covered by a solid, there are an indefinite number of routes between them covered by the same solid. A solid may or may not be covered by a moment. If it is so covered, it is called 'co-momental.' A solid which is not co-momental is called 'vagrant.' The properties of vagrant solids are assuming importance in connection with Einstein's theory of gravitation; the consideration of these properties is not undertaken in this enquiry. Co-momental solids are also called 'volumes.' Volumes are capable of a simpler definition which is given in the next article.