THE FIGURES OF THE EARTH AND MOON (Third Paper)

Abstract

Summary The paper consists of a general adjustment of the data relevant to the radius and ellipticity of the Earth, the lunar parallax and the differences of the moments of inertia of the Moon. The anomalies of gravity recently found to persist over distances of 10° and 30° imply similar anomalies in the deflexion of the vertical and provide a means of estimating the additional uncertainty that they introduce. When this is taken into account it is found that the data are satisfactorily consistent. Attempts are made to find additional checks on the existence of the anomalies of gravity represented by harmonics of degrees 2 and 3 other than the main ellipticity term, but they are indecisive, and the final solution is a compromise between solutions with and without them. The chief changes from current values are a reduction of the Earth's equatorial radius from 6371.388 km. to 6371-099±0.116 km. (s. e.) and the value of g at Potsdam from 981.274 gals, to 981-2606±0-0010 gal.; owing to recent work by the Anglo-Iranian Oil Company the British stations are now strongly connected with the new determination of the absolute value of g at Teddington. The change in the equatorial radius is due to the use of free-air instead of isostatic reductions; reasons are given why the latter may have introduced a systematic error.