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torsion balance,instrument used to measure small forces. It is based on the principle that a wire or thread resists twisting with a force that is proportional to the stress. The torsion balance consists essentially of a wire or thread attached at one end and arranged in such a way that a force applied at the other, or free, end tends to twist it out of shape. The force is measured by the extent to which the wire or thread is so twisted. Torsion balances are used to measure small electric, magnetic, and gravitational forces. One type is used to measure small weights. The invention of the torsion balance is commonly credited to the English geologist John Michell, who made his instrument c.1750, and to the French physicist Charles A. de Coulomb, who independently devised such a balance c.1777.
an instrument for measuring second derivatives of gravitational potential, which characterize the curvature of the equipotential gravitational surface and the horizontal change (gradient) of the force of gravity. Torsion balances that measure only gravity gradients are called gradiometers.
The torsion balance was invented at the end of the 19th century by the Hungarian physicist L. Eötvös. It consists of a light horizontal or inclined balance beam with masses suspended from or fastened to its ends at different heights. The beam is supported by a fine elastic torsion thread. In a nonhomogeneous gravitational field a gravitational force moment arises and acts on the beam’s masses. The beam rotates until the moment of attractive force equals the torsion moment of the thread. The derivatives of the gravitational potential are determined by the beam’s angle of rotation as the body of the balance is successively placed at various angles to the meridian (at different azimuths). Photographic recording or visual observation is used.
The construction of the balance eliminates the effects of temperature and of magnetic and electrostatic fields. Second derivatives of gravitational potential are measured with an accuracy of ±(1–2) × 10−9 sec−2. Torsion balances are used to study the distrivution of density inhomogeneities of the upper layers of the earth’s crust for purposes of geological prospecting and analysis. Since the readings of a torsion balance also depend on the actions of masses that make up the earth’s surface terrain, it is necessary to have detailed information about the terrain in the immediate vicinity of the place where measurements are made.
M. U. SAGITOV
a sensitive physical instrument for measuring small forces (force moments). The torsion balance was invented in 1784 by C. Coulomb (seeCOULOMB TORSION BALANCE).
The simplest type of torsion balance consists of a vertical thread from which a light balanced arm is suspended. The forces being measured act on the ends of the arm and rotate it in the horizontal plane until they are balanced by the elastic forces of the twisted thread. The torque Mt may be measured from the angle of rotation ϕ of the arm, since ϕ ~ Mtl/GI, where l is the length of the thread, G is the shear modulus of the thread material, and i is the total moment of inertia of the arm and thread. The readout scale of a torsion balance is usually calibrated directly in units of force or force moment. High sensitivity is attained in torsion balances through the use of a sufficiently long thread with a low shear modulus.
Balances with a moving system consisting of a horizontal axle attached by its ends to spiral springs, with an arm for placing the load, are also called torsion balances.
Torsion balances are used to measure mechanical, electrical, magnetic, and gravitational forces and their variations.
REFERENCESShokin, P. F. Gravimetriia. Moscow, 1964. Chapter 4.
Chechernikov, V. I. Magnitnye izmereniia, 2nd ed. Moscow, 1969. Chapter 7.
Braginskii, V. B., and V. I. Panov. “Proverka ekvivalentnosti inertnoi i gravitatsionnoi mass.” Zhurnal’ eksperimental’noi i teoreticheskoi fiziki, 1971, vol. 61, fase. 9, p. 873.
IU. N. DROZHZHIN