page_title: Kater's pendulum
section_title: Kater's solution
hierarchical_section_title: Kater's pendulum / History / Kater's solution
caption_attribution_description: English: Drawing of a Kater pendulum from a 1920 physics textbook. Invented in 1817 by British physicist Henry Kater, it was used to measure the local acceleration of gravity in geophysical surveys. The labeled parts are identified in the text as: (a) opposing knife edges on either end from which pendulum is suspended, (b) fine adjustment weight operated by adjustment screw, (c) coarse adjustment weight, (d) bob, (e) pointers for reading. Alterations to image: removed part labels and replaced with different labels in color, converted from JPG to 32 color PNG.
context_page_description: A Kater's pendulum is a reversible free swinging pendulum invented by British physicist and army captain Henry Kater in 1817 for use as a gravimeter instrument to measure the local acceleration of gravity. Its advantage is that, unlike previous pendulum gravimeters, the pendulum's centre of gravity and center of oscillation do not have to be determined, allowing a greater accuracy. 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. It is now used only for demonstrating pendulum principles.
context_section_description: 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 till 1889. In 1811 Friedrich Bohnenberger again discovered it, but Kater independently invented it and was first to put it in practice.
caption: Drawing of Kater's pendulum 
  (a) opposing knife edge pivots from which pendulum is suspended 
  (b) fine adjustment weight moved by adjusting screw 
  (c) coarse adjustment weight clamped to rod by setscrew
  (d) bob 
  (e) pointers for reading
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