Motion of particles in Einstein's relativistic field theory. VI. Conservation laws and motion

In several earlier papers the author developed an approximation method for finding the Lorentz-covariant equations of structure and motion of interacting particles represented by singularities in Einstein's theory of the nonsymmetric field and in Einstein's theory of the gravitational field. In this paper the author presents a second method for finding these equations of structure and motion. This second method is based on certain conservation laws which are found to follow from Einstein's field equations. The first part of the paper reviews the older method in preparation for the second part of the paper, where the new method is developed. In the last part of the paper the new method is applied to the case of neutral particles interacting with each other. The amount of labor involved in finding the equations of structure and motion of particles is considerably reduced through the use of the conservation laws. The conservation laws are also expected to aid in the investigation of electromagnetic and gravitational radiation.