Development of Gravity Pendulums in the 19th Century

Von Sterneck and Mendenhall Pendulums

While scientists who had used the Repsold-Bessel pendulum apparatus discussed its defects and limitations for gravity surveys, Maj. Robert von Sterneck of Austria-Hungary began to develop an excellent apparatus for the rapid determination of relative values of gravity.82 Maj. von Sterneck’s apparatus contained a nonreversible pendulum 1/4-meter in length, and 1/2-second time of swing. The pendulum was hung by a single knife edge, which rested on a plate that was supported by a tripod. The pendulum was swung in a chamber from which air was exhausted and which could be maintained at any desired temperature. Times of swing were determined by the observation of coincidences of the pendulum with chronometer signals. In the final form a small mirror was attached to the knife edge perpendicular to the plane of vibration of the pendulum and a second fixed mirror was placed close to it so that the two mirrors were parallel when the pendulum was at rest. The chronometer signals worked a relay that gave a horizontal spark which was reflected into the telescope from the mirrors. When the pendulum was at rest, the image of the spark in both mirrors appeared on the horizontal cross wire in the telescope, and during oscillation of the pendulum the two images appeared in that position upon coincidence. In view of the reduced size of the pendulum, the chamber in which it was swung was readily portable, and with an improved method of observing coincidences, relative determinations of gravity could be made with rapidity and accuracy.

By 1887 Maj. von Sterneck had perfected his apparatus, and it was widely adopted in Europe for relative determinations of gravity. He used his apparatus in extensive gravity surveys and also applied it in the silver mines in Saxony and Bohemia, by the previously described methods of Airy, for investigations into the internal constitution of the earth.

On July 1, 1889, Thomas Corwin Mendenhall became superintendent of the U.S. Coast and Geodetic Survey. Earlier, he had been professor of physics at the University of Tokyo and had directed observations of pendulums for the determination of gravity on Fujiyama and at Tokyo. Supt. Mendenhall, with the cooperation of members of his staff in Washington, designed a new pendulum apparatus of the von Sterneck type, and in October 1890 he ordered construction of the first model.83

Like the Von Sterneck apparatus, the Mendenhall pendulum apparatus employed a nonreversible, invariable pendulum 1/4-meter in length and of slightly more than 1/2-second in time of swing. Initially, the knife edge was placed in the head of the pendulum and hung on a fixed plane support, but after some experimentation Mendenhall attached the plane surface to the pendulum and hung it on a fixed knife edge. An apparatus was provided with a set of three pendulums, so that if discrepancies appeared in the results, the pendulum at fault could be detected. There was also a dummy pendulum which carried a thermometer. A pendulum was swung in a receiver in which the pressure and temperature of the air were controlled. The time of swing was measured by coincidences with the beat of a chronometer. The coincidences were determined by an optical method with the aid of a flash apparatus.

The flash apparatus was contained in a light metal box which supported an observing telescope and which was mounted on a stand. Within the box was an electromagnet whose coils were connected with a chronometer circuit and whose armature carried a long arm that moved two shutters, in both of which were horizontal slits of the same size. The shutters were behind the front face of the box, which also had a horizontal slit. A flash of light from an oil lamp or an electric spark was emitted from the box when the circuit was broken, but not when it was closed. When the circuit was broken a spring caused the arm to rise, and the shutters were actuated so that the three slits came into line and a flash of light was emitted. A small circular mirror was set in each side of the pendulum head, so that from either face of the pendulum the image of the illuminated slit could be reflected into the field of the observing telescope. A similar mirror was placed parallel to these two mirrors and rigidly attached to the support. The chronometer signals broke the circuit, causing the three slits momentarily to be in line, and when the images of the slit in the two mirrors coincided, a coincidence was observed. A coincidence occurred whenever the pendulum gained or lost one oscillation on the beat of the chronometer. The relative intensity of gravity was determined by observations with the first Mendenhall apparatus at Washington, D.C., at stations on the Pacific Coast and in Alaska, and at the Stevens Institute, Hoboken, New Jersey, between March and October 1891.

Under Supt. Mendenhall’s direction a smaller, 1/4-second, pendulum apparatus was also constructed and tested, but did not offer advantages over the 1/2-second apparatus, which therefore continued in use.

In accordance with Peirce’s theory of the flexure of the stand under oscillations of the pendulum, determinations of the displacement of the receiver of the Mendenhall apparatus were part of a relative determination of gravity by members of the Coast and Geodetic Survey. Initially, a statical method was used, but during 1908-1909 members of the Survey adapted the Michelson interferometer for the determinations of flexure during oscillations from the shift of fringes.84 The first Mendenhall pendulums were made of bronze, but about 1920 invar was chosen because of its small coefficient of expansion. About 1930, Lt. E. J. Brown of the Coast and Geodetic Survey made significant improvements in the Mendenhall apparatus, and the new form came to be known as the Brown Pendulum Apparatus.85

The original Von Sterneck apparatus and that of Mendenhall provided for the oscillation of one pendulum at a time. After the adoption of the Von Sterneck pendulum in Europe, there were developed stands on which two or four pendulums hung at the same time. This procedure provided a convenient way to observe more than one invariable pendulum at a station for the purpose of detecting changes in length. Prof. M. Haid of Karlsruhe in 1896 described a four-pendulum apparatus,86 and Dr. Schumann of Potsdam subsequently described a two-pendulum apparatus.87

The multiple-pendulum apparatus then provided a method of determining the flexure of the stand from the action of one pendulum upon a second pendulum hung on the same stand. This method of determining the correction for flexure was a development from a “Wippverfahren” invented at the Geodetic Institute in Potsdam. A dynamometer was used to impart periodic impulses to the stand, and the effect was observed upon a pendulum initially at rest. Refinements of this method led to the development of a method used by Lorenzoni in 1885-1886 to determine the flexure of the stand by action of an auxiliary pendulum upon the principal pendulum. Dr. Schumann, in 1899, gave a mathematical theory of such determinations,88 and in his paper cited the mathematical methods of Peirce and Cellérier for the theory of Faye’s proposal at Stuttgart in 1877 to swing two similar pendulums on the same support with equal amplitudes and in opposite phases.

In 1902, Dr. P. Furtwängler89 presented the mathematical theory of coupled pendulums in a paper in which he referred to Faye’s proposal of 1877 and reported that the difficulties predicted upon its application had been found not to occur. Finally, during the gravity survey of Holland in the years 1913-1921, in view of instability of supports caused by the mobility of the soil, F. A. Vening Meinesz adopted Faye’s proposed method of swinging two pendulums on the same support.90 The observations were made with the ordinary Stückrath apparatus, in which four Von Sterneck pendulums swung two by two in planes perpendicular to each other. This successful application of the method—which had been proposed by Faye and had been demonstrated theoretically to be sound by Peirce, who also published a design for its application—was rapidly followed for pendulum apparatus for relative determinations by Potsdam,91 Cambridge (England),92 Gulf Oil and Development Company,93 and the Dominion Observatory at Ottawa.94 Heiskanen and Vening Meinesz state:

The best way to eliminate the effect of flexure is to use two synchronized pendulums of the same length swinging on the same apparatus in the same plane and with the same amplitudes but in opposite phases; it is clear then the flexure is zero.95

In view of the fact that the symmetrical reversible pendulum is named for Bessel, who created the theory and a design for its application by Repsold, it appears appropriate to call the method of eliminating flexure by swinging two pendulums on the same support the Faye-Peirce method. Its successful application was made possible by Maj. von Sterneck’s invention of the short, 1/4-meter pendulum.