The gravitational Equations and the Problem of Motion. (Part I). (Received June 16, 1937). (+) II. (Received May 29, 1939). 2 Papers (Paper II only Einstein and Infeld).

(Princeton, NJ.), Annals of Mathematics, 1938 a. 1940. Both papers in orig. printed wrappers. Offprints from "Annals of Mathematics", Vol. 39, No. 1, january, 1938 and Vol. 41, No. 2, April, 1940. Pp. 65-100 and pp. 455-464. Both clean and fine. This copy has belonged to Abraham Pais (1918-2000) - the famous Einstein scholar, theoretical physicist and Einsteins collegue at Princeton - and having his name on top of both frontwrappers "A Pais". First editions, in the scarce offprint versions, of Einstein's last and highly important contributions to General relativity, and in which is shown that the equation of motion follows directly from the field equation that defined the geometry."Einstein's last importent contribution to general relativity deals again with the problem of motion. It is the work done with Leopold Infeld and Banash Hoffmann on the N-body problem of motion. In these papers, the gravitational field is no longer treated as external. Instead, it and the motion of its (singular) sources are treated simultaneously. Anew approximationscheme is introduced in which the fields are no longer necessarily weak but in which the source velocities are small compared with the light velocity . The equations obtained have found use in situations where Newtonian interaction must be included. '(These equations) are widely used in analyses of planetary orbits in the solarsystem. For example, the Cal Tech Jet Propulsion Laboratory uses them, in modified form, to calculate ephmerides for high-precision tracking of planets and spacecraft."(Pais "Subtle is the Lord", p. 290-91)."The problem of the equation of motion of bodies is the following. The 1916 theory had a classical structure in the sense that there were both field equations (the curvature of space-time is determined by the mass and motion of bodies in space-time) and equations of motion of bodies (the world line of small mass is a geodesic). Are these two statements really separate? If the field equations were linear, they indeed would be. They are not linear, however, and Einstein showed (in the papers offered) that if matter is represented by a point singularity of the metric field, these singularities are located on world lines that are geodesics of space-time, provided its metric satisfies the equation of general relativity."(DSB).Weil: 202 a. 295 (both with an asterix denoting a major paper). - Boni: 236 a. 236.1.…