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Bulletin 240: Contributions from the Museum of History and Technology Contributions from The Museum of History and Technology: Paper 44 Development of Gravity Pendulums in the 19th Century Victor F. Lenten and Robert P. Multbauj GALILEO, HUYCENS, AM) NEWTON ^>1 1 K.I RE OF THE EARTH 306 EARLY TYPES OF PENDULUMS ?09 kater's CONVERTIBLE AND INVARIABLE PENDULI Ms JI4 REPSOLD-BESSEL REVERSIBLE PENDULUM 320 PEIRCE AND DEFFORGES INVARIABLE REVERSIBL] PENDULI Ms J27 VON STERNECK AND MENDENHALL PENDULI Ms J3I ABSOLUTE VALUE OF GRAVITY AT POTSDAM Ms APPLICATION OF GRAVITY SURVEYS J42 SUMMARY 346 Victor F. Lenzen and Robert P. Multhauf DEVELOPMENT OF Paris, France Latitude 49° N Cayenne, South America Latitude 5° N Figure i. —A study of the figure of the earth was one of the earliest projects of the French Academy of Sciences. In order to test the effect of the earth's rotation on its gravitational force, the Academy in 1672 sent Jean Richer to the equatorial island of Cayenne to compare the rale of a clock which was known to have kept accurate time in Paris. Richer found that the clock lost 2 minutes and 28 seconds at Cayenne, indicating a substantial decrease in the force of gravity on the pendulum. Subsequent pendulum experiments revealed that the period of a pendulum varied not only with the latitude but also regionally, under the inlluence ol topographical features such as mountains. It became clear that the measurement of gravity should be made a part of the work of the geodetic surveyor. GRAVITY PENDULUMS IN THE 19th CENTURY The history of gravity pendulums dates back to the time of Galileo. After the discovery of the variation of the force of gravity over the surface of the earth, gravity measurement became a major concern of physics and geodesy. This article traces the history of the develop- ment of instruments for this purpose. the authors: Victor F. Lenten is Professor of Physics, Emeritus, at the University of California at Berke- ley and Robert P. Mjilthauf is Chairman of the Depart- ment of Science and Technology in the Smithsonian Institution s Museum of History and Technology. Tin intensity of gravity, or the acceleration of a law of gravitation and the laws of motion. Predic- (reel) falling body, is an important physical quan- tion of the motion of an artificial satellite requires an tn\ for the several physical sciences. The intensity of accurate knowledge of gravity for this astronomical gravity determines the weight of a standard pound problem. or kilogram as a standard or unit of force. In physical The gravity held of the earth also provides data for experiments, the force on a body may be measured a determination of the figure of the earth, or geoid, b) determining the weight of a known mass which but for this problem of geodesy relative values of serves to establish equilibrium against it. Thus, in gravity are sufficient. \i g is the intensity of gravity the absolute determination of the ampere with a cur- at some reference station, and A,? is the difference rent balance, the force between two coils carrying between intensities at two stations, the values of current is balanced by the earth's gravitational force gravity in geodetic calculations enter as ratios upon a body of determinable mass. The intensity of g gravity enters into determinations of the size of the over the surface of the earth. Gravimetric investiga- earth from the angular velocity of the moon, its tions in conjunction with other forms of geophysical distance from the earth, and Newton's inverse square investigation, such as seismology, furnish data to test PAPER 44: DEVELOPMENT OF GRAVITY PENDULUMS IN THE 19TH CENTURY 303 hypotheses concerning the internal structure of the during the years 1817-1818 was the first to design, earth. construct, and use a compound pendulum for the Whether the intensity of gravity is sought in absolute absolute determination of gravity. He constructed or relative measure, the most widely used instrument a convertible pendulum with two knife edges and for its determination since the creation of classical with it determined the absolute value of gravity at mechanics has been the pendulum. In recent dec- the house of Henry Browne, F.R.S., in Portland ades, there have been invented gravity meters based Place, London. He then constructed a similar upon the principle of the spring, and these instru- compound pendulum with only one knife edge, and ments have made possible the rapid determination of swung it to determine relative values of gravity at a relative values of gravity to a high degree of accuracy. number of stations in the British Isles. The 1 9th The gravity meter, however, must be calibrated at century witnessed the development of the theory and stations where the absolute value of gravity has been practice of observations with pendulums for the determined by other means if absolute values are determination of absolute and relative values of sought. For absolute determinations of gravity,' the gravity. pendulum historically has been the principal instru- ment employed. Although alternative methods of Galileo, Huygens, and Newton determining absolute values of gravity are now in use, the pendulum retains its value for absolute determina- The pendulum has been both an objective and an tions, and even retains it for relative determinations, instrument of physical investigation since the founda- as is exemplified by the Cambridge Pendulum Ap- tions of classical mechanics were fashioned in the paratus and that of the Dominion Observatory at 17th century. 1 It is tradition that the youthful Ottawa, Ontario. Galileo discovered that the period of oscillation of a The pendulums employed for absolute or relative pendulum is constant by observations of the swings determinations of gravity have been of two basic of the great lamp suspended from the ceiling in the types. The first form of pendulum used as a physical cathedral of Pisa. 2 The lamp was only a rough instrument consisted of a weight suspended by a fiber, approximation to a simple pendulum, but Galileo cord, or fine wire, the upper end of which was attached later performed more accurate experiments with a to a fixed support. Such a pendulum may be called "simple" pendulum which consisted of a heavy ball a "simple" pendulum; the enclosure of the word suspended by a cord. In an experiment designed to simple by quotation marks is to indicate that such a confirm his laws of falling bodies, Galileo lifted the pendulum is an approximation to a simple, or mathe- ball to the level of a given altitude and released it. matical pendulum, a conceptual object which con- The ball ascended to the same level on the other side sists of a mass-point suspended by a weightless of the vertical equilibrium position and thereby inextensible cord. If / is the length of the simple confirmed a prediction from the laws. Galileo also pendulum, the time of swing (half-period in the sense discovered that the period of vibration of a "simple" of physics) for vibrations of infinitely small amplitude, pendulum varies as the square root of its length, a as derived from Newton's laws of motion and the hypothesis that weight is proportional to mass, is 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 mimoires relalifs a la physique, The second form of pendulum is the compound, or publiis par la Societe Francaise de Physique [hereinafter referred physical, pendulum. It consists of an extended to as Collection de mimoires]: vol. 4. Mi-moires sur le ptndule, precedes solid body which vibrates about a fixed axis under and vol. 5, d'une bibliographie I Paris: Gauthier-Villars, 1889); the action of the weight of the body. A compound Mimoires sur le pendule, part 2 (Paris: Gauthier-Villars, 1891). sources are: Wolf, "Introduction pendulum may be constituted to oscillate about one Important secondary C. historique," pp. 1-42 in vol. 4, above; and George Biddell axis only, in which case it is nonreversible and Airy, "Figure of the Earth," pp. 165-240 in vol. 5 of Encyclo- applicable only for relative measurements. Or a paedia metropolitana (London, 1845). pen- compound pendulum may be constituted to oscillate llileo Galilei's principal statements concerning the dulum occur in his Discourses Concerning Two Ketv Sciences, about two axes, in which case it is reversible (or transl. from Italian and Latin into English by Henry Crew and "convertible") and may be used to determine absolute Alfonso de Salvio (Evanston: Northwestern University Press, values of gravity. Capt. Henry Kater, F.R.S., 1939), pp. 95-97, 170-172. 304 BULLETIN 240: CONTRIBUTIONS FROM THE MUSEUM OF HISTORY AND TECHNOLOGY . result which is expressed by the formula for the time of swing of the ideal simple pendulum. He also Glossary oi Gravity Iermino used a pendulum to measure lapse of time, and he absoliii (.R.wii'i : the value of the designed a pendulum clock. Galileo's experimental acceleration of gravity, alsi expressed 1>\ the length of die sei onds pendulum. results are important historically, but have required correction in the light of subsequent measurements RELATTVi gravity: the value of the acceleration of gravity of greater precision. relative t" the valui i idard point. Mersenne in 1644 made the first determination of siMii i pendulum: see theoretical pendulum. 3 the length of the seconds pendulum, that is. the length \i a h'\i\ [-HEORETII pendulum: j bob (point-mass) at the of simple that seconds a pendulum beats (half- end of a weightless rod. period in the sense of physics). Subsequently, lie 1 : .1 1 in, ,il seconds pendi 1 m 1 on.
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