Some simple methods for the unique assignment of a density distribution to a harmonic function

One to one relationships are established between functions harmonic outside a sphere and density functions (1) with support equal to the sphere and (2) having the property that the density functions rho, multiplied by a positive function of the distance from the center of the sphere, are harmonic. The derived relations may be used to assign a density distribution to the harmonic part of the potential of the Earth, and a covariance function of a density anomaly distribution to the covariance function of the anomalous potential of the Earth.