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The form of a single level surface that envelops all attracting matter and the value of the potential or of the gravitational attraction at a definite point on or outside the surface determine uniquely the field of force on and outside of the surface.This statement holds good even when we add to the gravitational attraction the centrifugal "force" due to uniform rotation. Hence, if we assume that the surface of the earth is an exact ellipsoid of rotation under its own attraction combined with the centrifugal force of uniform rotation about the minor axis, the field of force on and outside this ellipsoid is uniquely determined, if we assume, for instance, the value of gravity at the equator.This determination is carried out by means of a rather special set of curvilinear coordinates.

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