Following a study of the statistical properties of a random potential field, which is often encountered as a background noise in observed geophysical potential fields, and particularly a study of conditions under which the random process is homogeneous and gaussian, an approximate analytical method has been developed to evaluate the correlation functions and the power spectrum of the random process when the mass density is locally uniform but varies randomly over an entire semi-infinite space. The method is particularly convenient for it gives a unified approach to evaluating the statistical properties of gravity as well as magnetic fields. The relationship between the autocorrelation function of the random potential field and the random mass density is quite involved, but by assuming that the mass density in successive cells is completely uncorrelated the relationship can be simplified. It is a matter of considerable interest to estimate, from the autocorrelation function, the size of cell characteristic of the random medium which reflects the geological characteristics of the rocks.

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