pendulums were swinging in synchronism. He measured the distance between the pivot blades with a microscope comparator, to an accuracy of 10−4 in. (2.5 μm). As with other pendulum gravity measurements, he had to apply small corrections to the result for a number of variable factors: the finite width of the pendulum's swing, which increased the period temperature, which caused the length of the rod to vary due to thermal expansion atmospheric pressure, which reduced the effective mass of the pendulum by the buoyancy of the displaced air, increasing the period altitude, which reduced the gravitational force with distance from the center of the Earth. Gravity measurements are always referenced to sea level. He gave his result as the length of the seconds pendulum. After corrections, he found that the mean length of the solar seconds pendulum at London, at sea level, at , swinging in vacuum, was 39.1386 inches. This is equivalent to a gravitational acceleration of 9.81158 m/s2. The largest variation of his results from the mean was . This represented a precision of gravity measurement of 0.7×10−5 (7 milligals). In 1824, the British Parliament made Kater's measurement of the seconds pendulum the official backup standard of length for defining the yard if the yard prototype was destroyed. Use The large increase in gravity measurement accuracy made possible by Kater's pendulum established gravimetry as a regular part of geodesy. To be useful, it was necessary to find the exact location (latitude and longitude) of the 'station' where a gravity measurement was taken, so pendulum measurements became part of surveying. Kater's pendulums were taken on the great historic geodetic surveys of much of the world that were being done during the 19th century. In particular, Kater's pendulums were used in the Great Trigonometric Survey of India. Reversible pendulums remained the standard method used for absolute gravity measurements until they were superseded by free-fall gravimeters in the 1950s. Repsold–Bessel pendulum Repeatedly timing each period of a Kater pendulum, and adjusting the weights until they were equal, was time-consuming and error-prone. Friedrich Bessel showed in 1826 that this was unnecessary. As long as the periods measured from each pivot, T1 and T2, are close in value, the period T of the equivalent simple pendulum can be calculated from them: Here and are the distances of the two pivots from the pendulum's center of gravity. The distance between the pivots, , can