Since the creation of classical mechanics in the 17th century, the pendulum has been a basic instrument for the determination of the intensity of gravity, which is expressed as the acceleration of a freely falling body. Basis of theory is the simple pendulum, whose time of swing under gravity is proportional to the square root of the length divided by the acceleration due to gravity. Since the length of a simple pendulum divided by the square of its time of swing is equal to the length of a pendulum that beats seconds, the intensity of gravity also has been expressed in terms of the length of the seconds pendulum. The reversible compound pendulum has served for the absolute determination of gravity by means of a theory developed by Huygens. Invariable compound pendulums with single axes also have been used to determine relative values of gravity by comparative times of swing.
The history of gravity pendulums begins with the ball or “simple” pendulum of Galileo as an approximation to the ideal simple pendulum. Determinations of the length of the seconds pendulum by French scientists culminated in a historic determination at Paris by Borda and Cassini, from the corrected observations with a long ball pendulum. In the 19th century, Bessel found the length of the seconds pendulum at Königsberg and Berlin by observations with a ball pendulum and by original theoretical considerations. During the century, however, the compound pendulum came to be preferred for absolute and relative determinations.
Capt. Henry Kater, at London, constructed the first convertible compound for an absolute determination of gravity, and then he designed an invariable compound pendulum, examples of which were used for relative determinations at various stations in Europe and elsewhere. Bessel demonstrated theoretically the advantages of a reversible compound pendulum which is symmetrical in form and is hung by interchangeable knives. The firm of A. Repsold and Sons in Hamburg constructed pendulums from the specifications of Bessel for European gravity surveys.
Charles S. Peirce in 1875 received delivery in Hamburg of a Repsold-Bessel pendulum for the U.S. Coast Survey and observed with it in Geneva, Paris, Berlin, and London. Upon an initial stimulation from Baeyer, founder of Die Europäische Gradmessung, Peirce demonstrated by experiment and theory that results previously obtained with the Repsold apparatus required correction, because of the flexure of the stand under oscillations of the pendulum. At the Stuttgart conference of the geodetic association in 1877, Hervé Faye proposed to solve the problem of flexure by swinging two similar pendulums from the same support with equal amplitudes and in opposite phases. Peirce, in 1879, demonstrated theoretically the soundness of the method and presented a design for its application, but the “double pendulum” was rejected at that time. Peirce also designed and had constructed four examples of a new type of invariable, reversible pendulum of cylindrical form which made possible the experimental study of Stokes’ theory of the resistance to motion of a pendulum in a viscous fluid. Commandant Defforges, of France, also designed and used cylindrical reversible pendulums, but of different length so that the effect of flexure was eliminated in the reduction of observations. Maj. Robert von Sterneck, of Austria-Hungary, initiated a new era in gravity research by the invention of an apparatus with a short pendulum for relative determinations of gravity. Stands were then constructed in Europe on which two or four pendulums were hung at the same time. Finally, early in the present century, Vening Meinesz found that the Faye-Peirce method of swinging pendulums hung on a Stückrath four-pendulum stand solved the problem of instability due to the mobility of the soil in Holland.
The 20th century has witnessed increasing activity in the determination of absolute and relative values of gravity. Gravimeters have been perfected and have been widely used for rapid relative determinations, but the compound pendulums remain as indispensable instruments. Mendenhall’s replacement of knives by planes attached to nonreversible pendulums has been used also for reversible ones. The Geodetic Institute at Potsdam is presently applying the Faye-Peirce method to the reversible pendulum.[115] Pendulums have been constructed of new materials, such as invar, fused silica, and fused quartz. Minimum pendulums for precise relative determinations have been constructed and used. Reversible pendulums have been made with “I” cross sections for better stiffness. With all these modifications, however, the foundations of the present designs of compound pendulum apparatus were created in the 19th century.
FOOTNOTES:
[1] The basic historical documents have been collected, with a bibliography of works and memoirs published from 1629 to the end of 1885, in Collection de mémoires relatifs a la physique, publiés par la Société française de Physique [hereinafter referred to as Collection de mémoires]: vol. 4, Mémoires sur le pendule, précédés d’une bibliographie (Paris: Gauthier-Villars, 1889); and vol. 5, Mémoires sur le pendule, part 2 (Paris: Gauthier-Villars, 1891). Important secondary sources are: C. Wolf, “Introduction historique,” pp. 1-42 in vol. 4, above; and George Biddell Airy, “Figure of the Earth,” pp. 165-240 in vol. 5 of Encyclopaedia metropolitana (London, 1845).
[2] Galileo Galilei’s principal statements concerning the pendulum occur in his Discourses Concerning Two New Sciences, transl. from Italian and Latin into English by Henry Crew and Alfonso de Salvio (Evanston: Northwestern University Press, 1939), pp. 95-97, 170-172.
[3] P. Marin Mersenne, Cogitata physico-mathematica (Paris, 1644), p. 44.
[4] Christiaan Huygens, Horologium oscillatorium, sive de motu pendulorum ad horologia adaptato demonstrationes geometricae (Paris, 1673), proposition 20.