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The Leading Edge; August 2001; v. 20; no. 8; p. 840-847; DOI: 10.1190/1.1487293
© 2001 Society of Exploration Geophysicists
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Surfaces of equal potential and the physics behind the torsion balance and gradiometers

Klaus Helbig

Hannover, Germany

Corresponding author: helbig@real-net.de

The first 20% of the full text of this article appears below.

The torsion balance as an exploration instrument was invented by the Hungarian baron Eötvös Lóránd. In the first third of the 20th century, the torsion balance was the standard instrument for gravity exploration (Figure 1) but by the early 1930s it was replaced by less cumbersome instruments.


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  		Figure 1. The small Eötvös-Suess torsion balance (from Haalck, 1953).

 
The history of the Eötvös torsion balance has been described in TLE by Domenico (1994). My article relates to the physics of a whole class of instruments of which the torsion balance is but one, albeit important, member. These instruments detect features of the gravity field by observing the behavior of a simple "mass quadrupole" free to rotate about its center. A mass quadrupole is a distribution of masses that deviates from spherical symmetry, i.e., from a "monopole." (Note that a mass dipole would require the combination of a positive and a negative mass. Mass dipoles can occur as "anomalies," as the combination of mass excess and mass deficit, but not outside the earth.)

A simple mass quadrupole is a linear mass distribution such that the moment of inertia about this line is (practically) zero, and the moments about axes through the center perpendicular to the line are about equal. The sensitivity of the instrument increases with these moments of inertia. The ideal embodiment is a stiff "massless" rod with two identical point masses at its ends. Another simple embodiment is the homogeneous cylindrical rod. It is less efficient as a detector, but more easily manufactured.

An early embodiment of the instruments discussed in this article is the torsion balance used by Cavendish (1797–98) in his famous determination of the Universal Gravitational Constant. At the end of the 18th century, the instrument was used by Coulomb to measure the curvature of the gravity . . . [Full Text of this Article]






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