Kater's Pendulum - Experimental Procedure

Experimental Procedure

To use, the pendulum was hung from a bracket on a wall, with the knife blade pivots supported on two small horizontal agate plates, in front of a precision pendulum clock to time the period. It was swung first from one pivot, and the oscillations timed, then turned upside down and swung from the other pivot, and the oscillations timed again. The small weight (c) was adjusted with the adjusting screw, and the process repeated until the pendulum had the same period when swung from each pivot. By putting the measured period T, and the measured distance between the pivot blades L, into the period equation (1), g could be calculated very accurately.

Kater performed 12 trials. He measured the period of his pendulum very accurately using the clock pendulum by the method of coincidences; timing the interval between the coincidences when the two 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 62°F, 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 0.00028 inches (7.1 µm). This represented a precision of gravity measurement of 7(10−6) (7 milligals).

In 1824, the British Parliament made Kater's measurement of the seconds pendulum the official standard of length for defining the yard.