Correspondence between the equations of motion of a trial particle in the theory of direct gravitational interaction and the equations of geodesics in the general theory of relativity

For an arbitrary specified background space - time, an action of Fokker type to arbitrary order in the gravitational - interaction constant is constructed for a trial particle interacting with a certain material system characterized by a specified energy - momentum tensor. It is shown that the equations of motion of the trial particle following from this principle are quations of the geodesic line in some effective metric depending on the variables of the system.