It has been known for some years that a C-field, generated by a certain source equation, leads to interesting changes in the cosmological solutions of Einstein's equations. The steady-state cosmology appears as an asymptotic case. The source equation has so far only been given in the macroscopic case of a smooth fluid. In the present paper we derive the source equation in terms of discrete particles. The method adopted is similar to that we have recently given for the generalization to Riemannian space of the Fokker action principle in the electromagnetic theory. In the latter, a 4-vector is defined in terms of the world lines of particles. The definition is such that the four-dimensional curl of the vector satisfies Maxwell's equations, which are therefore identities. Similarly, C is a scalar defined in terms of the world-lines of particles, and the source equation used formerly then follows as an identity.