Abstract
IN the problem of locating subterranean anomalies of density, the Eötvös balance measures two quantities, the horizontal gravity gradient and the difference between the principal curvatures of the level surface at the point of observation. In the two-dimensional case these reduce to Uxz and − Uxx denoted by G(x) and K(x) respectively. In all treatments of the subject, which I have seen G(x) and K(x) appear to be considered independent of one another. It can be shown, however, that there is a one-to-one relation between the two functions, namely, that they are conjugate trigonometrical integrals of one another;1 in fact :where P denotes the principal part of the subsequent integral.
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References
E. C. Titchmarsh, Proc. L.M. Soc., II., 24 p. 109.
“Geophysical Prospecting” Imperial Geophysical Experimental Survey, p. 173.
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ROBERTS, O. The Connexion between the Eotvos Magnitudes. Nature 130, 94 (1932). https://doi.org/10.1038/130094a0
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DOI: https://doi.org/10.1038/130094a0
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