Kater's pendulum

A Kater's pendulum is a reversible free swinging pendulum invented by British physicist and army captain Henry Kater in 1817 (made public on 29 January 1818),[1] for use as a gravimeter instrument to measure the local acceleration of gravity.

For about a century, until the 1930s, Kater's pendulum and its various refinements remained the standard method for measuring the strength of the Earth's gravity during geodetic surveys.

From the period and the measured distance L between the pivots, the acceleration of gravity can be calculated with great precision from the equation (1) above.

After that discovery was made, freeswinging pendulums started 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.

It can be seen from equation (1) that for a seconds pendulum, the length is simply proportional to g: In Kater's time, the period T of pendulums could be measured very precisely by timing them with precision clocks set by the passage of stars overhead.

L in equation (1) above was the length of an ideal mathematical 'simple pendulum' consisting of a point mass swinging on the end of a massless cord.

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.

However, in Horologium Oscillatorium, Huygens had also proved that the pivot point and the center of oscillation were interchangeable.

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.

[6] He realized Huygens' principle could be used to find the center of oscillation, and so the length L, of a rigid (compound) pendulum.

[7][8] French mathematician Gaspard de Prony first proposed a reversible pendulum in 1800, but his work was not published until 1889.

[1][9] For a low friction pivot he used a pair of short triangular 'knife' blades attached to the rod.

In use the pendulum was hung from a bracket on the wall, supported by the edges of the knife blades resting on flat agate plates.

After corrections, he found that the mean length of the solar seconds pendulum at London, at sea level, at 62 °F (17 °C), swinging in vacuum, was 39.1386 inches.

[10][11][12][13] The large increase in gravity measurement accuracy made possible by Kater's pendulum established gravimetry as a regular part of geodesy.

Reversible pendulums remained the standard method used for absolute gravity measurements until they were superseded by free-fall gravimeters in the 1950s.

[14] Repeatedly timing each period of a Kater pendulum, and adjusting the weights until they were equal, was time-consuming and error-prone.

doesn't have to be determined with high accuracy, and the balancing procedure described above is sufficient to give accurate results.

In addition, Bessel showed that if the pendulum was made with a symmetrical shape, but internally weighted on one end, the error caused by effects of air resistance would cancel out.

Bessel didn't construct such a pendulum, but in 1864 Adolf Repsold, under contract to the Swiss Geodetic Commission, developed a symmetric pendulum 56 cm long with interchangeable pivot blades, with a period of about 3⁄4 second.

The Repsold pendulum was used extensively by the Swiss and Russian Geodetic agencies, and in the Survey of India.

The association decided in favor of the reversion pendulum and it was resolved to redo in Berlin, in the station where Friedrich Wilhelm Bessel made his famous measurements, the determination of gravity by means of devices of various kinds employed in different countries, in order to compare them and thus to have the equation of their scales, after an in-depth discussion in which an American scholar, Charles Sanders Peirce, took part.

[16] Indeed, as the figure of the Earth could be inferred from variations of the seconds pendulum length, the United States Coast Survey's direction instructed Charles Sanders Peirce in the spring of 1875 to proceed to Europe for the purpose of making pendulum experiments to chief initial stations for operations of this sort, in order to bring the determinations of the forces of gravity in America into communication with those of other parts of the world; and also for the purpose of making a careful study of the methods of pursuing these researches in the different countries of Europe.

These movements were particularly important with the apparatus designed by the Repsold brothers on the indications of Bessel, because the pendulum had a large mass in order to counteract the effect of the viscosity of the air.

While Emile Plantamour was carrying out a series of experiments with this device, Adolph Hirsch found a way to demonstrate the movements of the pendulum's suspension plane by an ingenious process of optical amplification.

Isaac-Charles Élisée Cellérier, a mathematician from Geneva and Charles Sanders Peirce would independently develop a correction formula that allowed the use of the observations made with this type of gravimeter.

Under Ibáñez's presidency, the International Geodetic Association acquired a global dimension with the accession of the United States, Mexico, Chile, Argentina and Japan.

As a result of the work of the International Geodetic Association, in 1901, Friedrich Robert Helmert found, mainly by gravimetry, parameters of the ellipsoid remarkably close to reality.