Editing Kater's pendulum (section)

===Gravity measurement with pendulums===
[[File:PenduloCaminos.jpg|thumb|A Kater's pendulum and stand]]

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 {{frac|2|1|2}} minutes per day slower than at Paris, or equivalently the length of a pendulum with a swing of one second there was {{frac|1|1|4}} Paris ''lines'', or 2.6&nbsp;mm, shorter than at Paris.<ref>{{cite book
  | last = Poynting
  | first = John Henry
  |author2=Joseph John Thompson
  | title = A Textbook of Physics, 4th Ed.
  | publisher = Charles Griffin & Co.
  | year = 1907
  | location = London
  | page = [https://archive.org/details/bub_gb_TL4KAAAAIAAJ/page/n30 20]
  | url = https://archive.org/details/bub_gb_TL4KAAAAIAAJ
  }}</ref><ref>{{cite conference
  | first = Lenzen 
  | last = Victor F.
  |author2=Robert P. Multauf
  | title = Paper 44: Development of gravity pendulums in the 19th century
  | book-title = United States National Museum Bulletin 240: Contributions from the Museum of History and Technology reprinted in Bulletin of the Smithsonian Institution
  | page = 307
  | publisher = Smithsonian Institution Press 
  | year = 1964
  | location = Washington
  | url = http://www.gutenberg.org/files/35024/35024-h/35024-h.htm
  | access-date = 2009-01-28}}</ref> 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 spheroid|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. After that discovery was made, freeswinging pendulums started to be used as precision [[gravimeter]]s, 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'' 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'':

:<math>g = \pi^2 L \,</math>