no way to find the location of the center of oscillation in a real pendulum accurately. It could theoretically be calculated from the shape of the pendulum if the metal parts had uniform density, but the metallurgical quality and mathematical abilities of the time didn't allow the calculation to be made accurately. To get around this problem, most early gravity researchers, such as Jean Picard (1669), Charles Marie de la Condamine (1735), and Jean-Charles de Borda (1792) approximated a simple pendulum by using a metal sphere suspended by a light wire. If the wire had negligible mass, the center of oscillation was close to the center of gravity of the sphere. But even finding the center of gravity of the sphere accurately was difficult. In addition, this type of pendulum inherently wasn't very accurate. The sphere and wire didn't swing back and forth as a rigid unit, because the sphere acquired a slight angular momentum during each swing. Also the wire stretched elastically during the pendulum's swing, changing L slightly during the cycle. Kater's solution However, in Horologium Oscillatorium, Huygens had also proved that the pivot point and the center of oscillation were interchangeable. That is, if any pendulum is suspended upside down from its center of oscillation, it has the same period of swing, and the new center of oscillation is the old pivot point. The distance between these two conjugate points was equal to the length of a simple pendulum with the same period. As part of a committee appointed by the Royal Society in 1816 to reform British measures, Kater had been contracted by the House of Commons to determine accurately the length of the seconds pendulum in London. He realized Huygens' principle could be used to find the center of oscillation, and so the length L, of a rigid (compound) pendulum. If a pendulum were hung upside down from a second pivot point that could be adjusted up and down on the pendulum's rod, and the second pivot were adjusted until the pendulum had the same period as it did when swinging right side up from the first pivot, the second pivot would be at the center of oscillation, and the distance between the two pivot points would be L. Kater wasn't the first to have this idea. French mathematician Gaspard de Prony first proposed a reversible pendulum in 1800, but his work was not published