The motion of a particle of finite mass in an external gravitational field

The analogy between the electromagnetic and the Einstein gravitational field theories raises the question as to whether the motion of a particle of finite mass moving in a gravitational field may be described in terms of an external gravitational field. There are many ways of defining the external field, and it is difficult to decide which to choose. It is shown that an inertial mass M can be defined in such a way that the EIH equations are derivable from the geodesic equation in the external field, this being defined as the field obtained from the whole field by putting M = 0. It turns out, however, that the analogy between the electromagnetic and the gravitational cases is not a close one-terms proportional to the square of the mass do not necessarily describe reaction forces; these appear even in the 6th order, in which the problem of gravitational radiation has not yet arisen. Moreover, certain terms defined as external field functions are reduced, on the basis of the equations of motion, to terms proportional to the square of the mass.