Geodesic
On the Somigliana's formula
Applications of Mathematics, Tome 16 (1971) no. 2, pp. 98-108.

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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. 
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Hora, Ladislav. On the Somigliana's formula. Applications of Mathematics, Tome 16 (1971) no. 2, pp. 98-108. doi : 10.21136/AM.1971.103334. https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1971.103334/

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