Development of Gravity Pendulums in the 19th Century / Contributions from the Museum of History and Technology, Papers 34-44 On Science and Technology, Smithsonian Institution, 1966

by Victor F. Lenzen; Robert P. Multhauf

SECONDS PENDULUM: a theoretical or simple pendulum of such length that its time of swing (half-period) is one second. (This length is about one meter.)

GRAVITY PENDULUM: a precisely made pendulum used for the measurement of gravity.

COMPOUND PENDULUM: a pendulum in which the supporting rod is not weightless; in other words, any actual pendulum.

CONVERTIBLE PENDULUM: a compound pendulum having knife edges at different distances from the center of gravity. Huygens demonstrated (1673) that if such a pendulum were to swing with equal periods from either knife edge, the distance between those knife edges would be equal to the length of a theoretical or simple pendulum of the same period.

REVERSIBLE PENDULUM: a convertible pendulum which is also symmetrical in form.

INVARIABLE PENDULUM: a compound pendulum with only one knife edge, used for relative measurement of gravity.

From Newton’s laws of motion and the hypothesis that weight is proportional to mass, the formula for the half-period of a simple pendulum is given by T = π√(l/g). If a simple pendulum beats seconds, 1 = π√(λ/g), where λ is the length of the seconds pendulum. From T = π√(l/g) and 1 = π√(λ/g), it follows that λ = l/T². Then g = π²λ. Thus, the intensity of gravity can be expressed in terms of the length of the seconds pendulum, as well as by the acceleration of a freely falling body. During the 19th century, gravity usually was expressed in terms of the length of the seconds pendulum, but present practice is to express gravity in terms of g, for which the unit is the gal, or one centimeter per second per second.

Figure 2.—This drawing, from Richer’s Observations astronomiques et physiques faites en l’isle de Caïenne (Paris, 1679), shows most of the astronomical instruments used by Richer, namely, one of the two pendulum clocks made by Thuret, the 20-foot and the 5-foot telescopes and the large quadrant. The figure may be intended as a portrait of Richer. This drawing was done by Sebastian Le Clerc, a young illustrator who made many illustrations of the early work of the Paris Academy.