Figure 28.—Apparatus which was developed in 1929 by the Gulf Research and Development Company, Harmarville, Pennsylvania. It was designed to achieve an accuracy within one ten-millionth of the true value of gravity, and represents the extreme development of pendulum apparatus for relative gravity measurement. The pendulum was designed so that the period would be a minimum. The case (the top is missing in this photograph) is dehumidified and its temperature and electrostatic condition are controlled. Specially designed pendulum-lifting and -starting mechanisms are used. The problem of flexure of the case is overcome by the Faye-Peirce method (see text) in which two dynamically matched pendulums are swung simultaneously, 180° apart in phase.
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.
Figure 29.—The Gulf pendulum is about 10.7 inches long, and has a period of .89 second. It is made of fused quartz which is resistant to the influence of temperature change and to the earth’s magnetism. Quartz pendulums are subject to the influence of electrostatic charge, and provision is made to counteract this through the presence of a radium salt in the case. The bearings are made of Pyrex glass.
In 1902, Dr. P. Furtwängler[89] 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.
Figure 30.—The accumulated data of gravity observations over the earth’s surface have indicated that irregularities such as mountains do not have the effect which would be expected in modifying gravity, but are somehow compensated for. The most satisfactory solution to this still unanswered question has been the theory of isostasy, according to which variations in the density of the material in the earth’s crust produce a kind of hydrostatic equilibrium between its higher and lower parts, as they “float” on the earth’s fluid core. The metals of different density floating in mercury in this diagram illustrate isostasy according to the theory of Pratt and Hayford.