The determination of the masses necessary to produce a given gravitational field

Abstract

Two methods are described for calculating the distribution of mass at a given depth that will produce a specified gravitational field. In one the observed field is extrapolated down­wards by a finite difference procedure; in the other a solution is obtained in the form of an integral which can be evaluated numerically. Tables of the quantities necessary for the practical use of the method are provided, and real and artificial examples are given. The limit to the possible depth of the masses producing an anomaly is also discussed.