[Illustration: Figure 12.--THE KATER CONVERTIBLE PENDULUM in use is placed before a clock, whose pendulum bob is directly behind the extended "tail" of the Kater pendulum. A white spot is painted on the center of the bob of the clock pendulum. The observing telescope, left, has a diaphragm with a vertical slit of such width that its view is just filled by the tail of the Kater pendulum when it is at rest. When the two pendulums are swinging, the white spot on the clock pendulum can be seen on each swing except that in which the two pendulums are in coincidence; thus, the coincidences are determined. (Portion of plate 5, _Mémoires publiés par la Société française de Physique_, vol. 4.)] [Illustration: Figure 13.--THIS DRAWING ACCOMPANIED John Goldingham's report on the work done in India with Kater's invariable pendulum. The value of gravity obtained, directly or indirectly, in terms of the simple pendulum, is called "absolute." Once absolute values of gravity were established at a number of stations, it became possible to use the much simpler "relative" method for the measurement of gravity at new stations. Because it has only one knife edge, and does not involve the adjustments of the convertible pendulum, this one is called "invariable." In use, it is first swung at a station where the absolute value of gravity has been established, and this period is then compared with its period at one or more new stations. Kater developed an invariable pendulum in 1819, which was used in England and in Madras, India, in 1821.] While the British were engaged in swinging the Kater invariable pendulums to determine relative values of the length of the seconds pendulum, or of gravity, the French also sent out expeditions. Capt. de Freycinet made initial observations at Paris with three invariable brass pendulums and one wooden one, and then carried out observations at Rio de Janeiro, Cape of Good Hope, Île de France, Rawak (near New Guinea), Guam, Maui, and various other places.[33] A similar expedition was conducted in 1822-1825 by Captain Duperry.[34] During the years from 1827 to 1840, various types of pendulum were constructed and swung by Francis Baily, a member of the Royal Astronomical Society, who reported in 1832 on experiments in which no less than 41 different pendulums were swung in vacuo, and their characteristics determined.[35] In 1836, Baily undertook to advise the American Lt. Charles Wilkes, who was to head the United States Exploring Expedition of 1838-1842, on the procurement of pendulums for this voyage. Wilkes ordered from the London instrument maker, Thomas Jones, two unusual pendulums, which Wilkes described as "those considered the best form by Mr. Baily for traveling pendulums," and which Baily, himself, described as "precisely the same as the two invariable pendulums belonging to this [Royal Astronomical] Society," except for the location of the knife edges.