Editing Pendulum (section)

== Standard of length ==
Because the [[Gravity of Earth|acceleration of gravity]] is constant at a given point on Earth, the period of a simple pendulum at a given location depends only on its length. Additionally, gravity varies only slightly at different locations. Almost from the pendulum's discovery until the early 19th century, this property led scientists to suggest using a pendulum of a given [[Frequency|period]] as a [[Unit of length|standard of length]].

Until the 19th century, countries based their systems of length measurement on prototypes, metal bar [[primary standard]]s, such as the standard [[yard]] in Britain kept at the Houses of Parliament, and the standard ''[[toise]]'' in France, kept at Paris. These were vulnerable to damage or destruction over the years, and because of the difficulty of comparing prototypes, the same unit often had different lengths in distant towns, creating opportunities for fraud.<ref name="Matthews2001">{{cite conference
  | first = Matthews
  | last = Michael R.
  | title = Methodology and Politics in Science: The fate of Huygens 1673 proposal of the pendulum as an international standard of length and some educational suggestions
  | book-title = Science, Education, and Culture: The contribution of history and philosophy of science
  | pages = 296
  | publisher = Springer
  | year = 2001
  | isbn = 0-7923-6972-6
  | url = https://books.google.com/books?id=6Mk3YwBe5L4C&pg=PA296
  }}</ref>  During the [[Age of Enlightenment|Enlightenment]] scientists argued for a length standard that was based on some property of nature that could be determined by measurement, creating an indestructible, universal standard. The period of pendulums could be measured very precisely by timing them with clocks that were set by the stars. A pendulum standard amounted to defining the unit of length by the gravitational force of the Earth, for all intents constant, and the second, which was defined by the [[Rotation of the Earth|rotation rate of the Earth]], also constant. The idea was that anyone, anywhere on Earth, could recreate the standard by constructing a pendulum that swung with the defined period and measuring its length.

Virtually all proposals were based on the [[seconds pendulum]], in which each swing (a half [[Frequency|period]]) takes one second, which is about a meter (39&nbsp;inches) long, because by the late 17th century it had become a standard for measuring gravity (see previous section). By the 18th century its length had been measured with sub-millimeter accuracy at a number of cities in Europe and around the world.

The initial attraction of the pendulum length standard was that it was believed (by early scientists such as Huygens and Wren) that gravity was constant over the Earth's surface, so a given pendulum had the same period at any point on Earth.<ref name="Matthews2001" />  So the length of the standard pendulum could be measured at any location, and would not be tied to any given nation or region; it would be a truly democratic, worldwide standard. Although Richer found in 1672 that gravity varies at different points on the globe, the idea of a pendulum length standard remained popular, because it was found that gravity only varies with [[latitude]]. Gravitational acceleration increases smoothly from the [[equator]] to the [[Geographical pole|poles]], due to the [[Oblate spheroid|oblate]] shape of the Earth, so at any given latitude (east–west line), gravity was constant enough that the length of a seconds pendulum was the same within the measurement capability of the 18th century. Thus the unit of length could be defined at a given latitude and measured at any point along that latitude. For example, a pendulum standard defined at 45° north latitude, a popular choice, could be measured in parts of France, Italy, Croatia, Serbia, Romania, Russia, Kazakhstan, China, Mongolia, the United States and Canada. In addition, it could be recreated at any location at which the gravitational acceleration had been accurately measured.

By the mid 19th century, increasingly accurate pendulum measurements by [[Edward Sabine]] and [[Thomas Young (scientist)|Thomas Young]] revealed that gravity, and thus the length of any pendulum standard, varied measurably with local geologic features such as mountains and dense subsurface rocks.<ref>{{cite book
  | last = Renwick
  | first = James
  | title = The Elements of Mechanics
  | publisher = Carey & Lea
  | year = 1832
  | location = Philadelphia
  | pages = [https://archive.org/details/elementsmechani00renwgoog/page/n322 286]–287
  | url = https://archive.org/details/elementsmechani00renwgoog
  }}</ref>  So a pendulum length standard had to be defined at a single point on Earth and could only be measured there. This took much of the appeal from the concept, and efforts to adopt pendulum standards were abandoned.

=== Early proposals ===
One of the first to suggest defining length with a pendulum was Flemish scientist [[Isaac Beeckman]]<ref name="Alder">{{cite book
  | last = Alder
  | first = Ken
  | title = The measure of all things: The seven-year odyssey and hidden error that transformed the world
  | publisher = Simon and Schuster
  | year = 2003
  | location = US
  | page = 88
  | url = https://books.google.com/books?id=jwsDERPMPhsC&q=marin+mersenne+second+pendulum&pg=RA1-PT27
  | isbn = 978-0-7432-1676-0}}</ref> who in 1631 recommended making the seconds pendulum "the invariable measure for all people at all times in all places".<ref>cited in {{cite mailing list
  | last = Jourdan
  | first = Louis
  | title = Re: SI and dictionaries
  | mailing-list = USMA
  | date = 22 October 2001 <!-- 06:59:02
 --> 
  | url = http://www.mail-archive.com/usma@colostate.edu/msg07023.html
  | access-date = 2009-01-27}}</ref>  [[Marin Mersenne]], who first measured the seconds pendulum in 1644, also suggested it. The first official proposal for a pendulum standard was made by the British [[Royal Society]] in 1660, advocated by [[Christiaan Huygens]] and [[Ole Rømer]], basing it on Mersenne's work,<ref>{{cite arXiv
  | last = Agnoli
  | first = Paolo
  |author2=Giulio D'Agostini
  | title = Why does the meter beat the second?
  | date = December 2004
 | eprint=physics/0412078}}</ref> and Huygens in ''[[Horologium Oscillatorium]]'' proposed a "horary foot" defined as 1/3 of the seconds pendulum.  [[Christopher Wren]] was another early supporter. The idea of a pendulum standard of length must have been familiar to people as early as 1663, because [[Samuel Butler (poet)|Samuel Butler]] satirizes it in ''[[Hudibras]]'':<ref>quoted in {{cite journal
  | last = LeConte
  | first = John
  | title = The Metric System
  | journal = The Overland Monthly
  | volume = 6
  | issue = 2
  | page = 178
  | date = August 1885
  | url = https://books.google.com/books?id=sFQ4AAAAIAAJ&pg=PA178
  | access-date = 2009-03-04}}</ref>
:Upon the bench I will so handle ‘em
:That the vibration of this pendulum
:Shall make all taylors’ yards of one
:Unanimous opinion
In 1671 [[Jean Picard]] proposed a pendulum-defined 'universal foot' in his influential ''Mesure de la Terre''.<ref>[https://archive.org/details/bub_gb_uYCNFkRgXCoC/page/n143 <!-- pg=131 --> Zupko, 1990, p.131]</ref>  [[Gabriel Mouton]] around 1670 suggested defining the ''[[toise]]'' either by a seconds pendulum or a minute of terrestrial degree. A plan for a complete system of units based on the pendulum was advanced in 1675 by Italian polymath Tito Livio Burratini. In France in 1747, geographer [[Charles Marie de la Condamine]] proposed defining length by a seconds pendulum at the equator; since at this location a pendulum's swing wouldn't be distorted by the Earth's rotation. [[James Steuart (economist)|James Steuart]] (1780) and [[George Skene Keith]] were also supporters.

By the end of the 18th century, when many nations were reforming their [[Weights and measures|weight and measure systems]], the [[seconds pendulum]] was the leading choice for a new definition of length, advocated by prominent scientists in several major nations. In 1790, then US Secretary of State [[Thomas Jefferson]] proposed to Congress a comprehensive decimalized US 'metric system' based on the seconds pendulum at 38° North latitude, the mean latitude of the United States.<ref>[https://archive.org/details/bub_gb_uYCNFkRgXCoC/page/n143 <!-- pg=131 --> Zupko, 1990, p.140-141]</ref>  No action was taken on this proposal. In Britain the leading advocate of the pendulum was politician [[John Riggs Miller]].<ref>[https://archive.org/details/bub_gb_uYCNFkRgXCoC/page/n143 <!-- pg=131 --> Zupko, 1990, p.93]</ref>  When his efforts to promote a joint British–French–American metric system fell through in 1790, he proposed a British system based on the length of the seconds pendulum at London. This standard was adopted in 1824 (below).

=== The metre ===
In the discussions leading up to the French adoption of the [[metric system]] in 1791, the leading candidate for the definition of the new unit of length, the [[metre]], was the seconds pendulum at 45° North latitude. It was advocated by a group led by French politician [[Talleyrand]] and mathematician [[Marquis de Condorcet|Antoine Nicolas Caritat de Condorcet]]. This was one of the three final options considered by the [[French Academy of Sciences]] committee. However, on March 19, 1791, the committee instead chose to base the metre on the length of the [[meridian (geography)|meridian]] through Paris. A pendulum definition was rejected because of its variability at different locations, and because it defined length by a unit of time. (However, since 1983 the metre has been officially defined in terms of the length of the second and the speed of light.) A possible additional reason is that the radical French Academy didn't want to base their new system on the second, a traditional and nondecimal unit from the ''[[ancien regime]]''.

Although not defined by the pendulum, the final length chosen for the metre, 10<sup>−7</sup> of the pole-to-equator [[meridian arc]], was very close to the length of the seconds pendulum (0.9937 m), within 0.63%. Although no reason for this particular choice was given at the time, it was probably to facilitate the use of the seconds pendulum as a secondary standard, as was proposed in the official document. So the modern world's standard unit of length is certainly closely linked historically with the seconds pendulum.

=== Britain and Denmark ===
Britain and Denmark appear to be the only nations that (for a short time) based their units of length on the pendulum. In 1821 the Danish inch was defined as 1/38 of the length of the mean solar seconds pendulum at 45° latitude at the meridian of [[Skagen]], at sea level, in vacuum.<ref>{{cite journal
  | last = Schumacher
  | first = Heinrich
  | title = Danish standard of length
  | journal = The Quarterly Journal of Science, Literature and the Arts
  | volume = 11
  | issue = 21
  | pages = 184–185
  | year = 1821
  | url = https://books.google.com/books?id=KwEXAAAAYAAJ&pg=PA184
  | access-date = 2009-02-17}}</ref><ref>{{cite encyclopedia
  | title = Schumacher, Heinrich Christian
  | encyclopedia = [[The American Cyclopedia]]
  | volume = 14
  | pages = 686
  | publisher = D. Appleton & Co., London
  | url =https://books.google.com/books?id=OlJMAAAAMAAJ&pg=PA686
  | year = 1883
  | access-date = 2009-02-17}}</ref>  The British parliament passed the ''Imperial Weights and Measures Act'' in 1824, a reform of the British standard system which declared that if the prototype standard [[yard]] was destroyed, it would be recovered by defining the [[inch]] so that the length of the solar seconds pendulum at London, at [[sea level]], in a vacuum, at 62&nbsp;°F was 39.1393&nbsp;inches.<ref>{{cite book
  | last = Trautwine
  | first = John Cresson
  | title = The Civil Engineer's Pocket-Book, 18th Ed
  | publisher = John Wiley
  | year = 1907
  | location = New York
  | page = 216
  | url = https://books.google.com/books?id=qg41AAAAMAAJ&pg=PA216
  }}</ref>  This also became the US standard, since at the time the US used British measures. However, when the prototype yard was lost in the [[Burning of Parliament|1834 Houses of Parliament fire]], it proved impossible to recreate it accurately from the pendulum definition, and in 1855 Britain repealed the pendulum standard and returned to prototype standards.