Kater's Pendulum - Gravity Measurement With Pendulums

Gravity Measurement With Pendulums

A pendulum can be used to measure the acceleration of gravity g because its period of swing T depends only on g and its length L:

So by measuring the length L and period T of a pendulum, g can be calculated. The first person to discover that gravity varied over the Earth's surface was French scientist Jean Richer, who in 1671 was sent on an expedition to Cayenne, French Guiana by the French Académie des Sciences, assigned the task of making measurements with a pendulum clock. Through the observations he made in the following year, Richer determined that the clock was 2½ minutes per day slower than at Paris, or equivalently the length of a pendulum with a swing of one second there was 1¼ Paris lines, or 2.6 mm, shorter than at Paris. It was realized by the scientists of the day, and proven by Isaac Newton in 1687, that this was due to the fact that the Earth was not a perfect sphere but slightly oblate; it was thicker at the equator because of the Earth's rotation. Since the surface was farther from the Earth's center at Cayenne than at Paris, gravity was weaker there. Since that time pendulums began to be used as precision gravimeters, taken on voyages to different parts of the world to measure the local gravitational acceleration. The accumulation of geographical gravity data resulted in more and more accurate models of the overall shape of the Earth.

Pendulums were so universally used to measure gravity that, in Kater's time, the local strength of gravity was usually expressed not by the value of the acceleration g which is now used, but by the length at that location of the seconds pendulum, a pendulum with a period of two seconds, so each swing takes one second. It can be seen from equation (1) that for a seconds pendulum, the length is simply proportional to g: