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Summary:
This paper deals with the general derivation of Pizzetti-Somigliana's formula for the decomposition of gravity. The problem of derivation is solved formally geometrically on the equipotential surface $S$ that need not be the oblate ellipsoid of rotation. In individual cases of confocal systems of quadrics, the introduction of hyperbolic and circular functions in the equations of tri-orthogonal system is motivated. It is indicated that the validity of the formula may be formally generalized also to other quadrics of rotation.
References:
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