The initial determinations of the variations in the lunar gravitational field are appreciably milder than those of the Earth in the sense of stress-implication, indicating a state closer to hydrostatic equilibrium. The variations determined also have a considerable correlation with the lunar topography, indicating a shallower origin than the Earth's variations. The data are still insufficient to determine firmly the lunar oblateness, and thus help resolve the problem of the Moon's moment of inertia. This paper is being issued as Publication No. 559 of the Institute of Geophysics and Planetary Physics, University of California, Los Angeles.