page_title: History of the metre
section_title: Universal measure
hierarchical_section_title: History of the metre / Universal measure
context_page_description: The history of the metre starts with the scientific revolution that began with Nicolaus Copernicus's work in 1543. Increasingly accurate measurements were required, and scientists looked for measures that were universal and could be based on natural phenomena rather than royal decree or physical prototypes. Rather than the various complex systems of subdivision in use, they also preferred a decimal system to ease their calculations.
  With the French Revolution came a desire to replace many features of the Ancien Régime, including the traditional units of measure. As a base unit of length, many scientists had favoured the seconds pendulum one century earlier, but this was rejected as it had been discovered that it varied from place to place with local gravity and that it could complement meridian arc measurements in determining the figure of the Earth. A new unit of length, the metre was introduced – defined as one ten-millionth of the shortest distance from the North Pole to the equator passing through Paris, assuming an Earth's flattening of 1/334.
  For practical purposes however, the standard metre was made available in the form of a platinum bar held in Paris.
context_section_description: The standard measures of length in Europe diverged from one another after the fall of the Carolingian Empire (around 888): while measures could be standardised within a given jurisdiction (which was often little more than a single market town), there were numerous variations of measure between regions. Indeed, as the measures were often used as the basis for taxation (of cloth, for example), the use of a particular measure was associated with the sovereignty of a given ruler and often dictated by law.
  Nevertheless, with the increasing scientific activity of the 17th century came calls for the institution of a standard measure or "metro cattolico" (as Italian Tito Livio Burattini said ), which would be based on natural phenomena rather than royal decree, and would also be decimal rather than using the various systems of subdivision, often duodecimal, which coexisted at the time.
  In 1645 Giovanni Battista Riccioli had been the first to determine the length of a "seconds pendulum" (a pendulum with a half-period of one second). In 1671 Jean Picard measured the length of a "seconds pendulum" at the Paris Observatory. He found the value of 440.5 lines of the Toise of Châtelet which had been recently renewed. He proposed a universal toise (French: Toise universelle) which was twice the length of the seconds pendulum. However, it was soon discovered that the length of a seconds pendulum varies from place to place: French astronomer Jean Richer had measured the 0.3% difference in length between Cayenne (in French Guiana) and Paris.
  Jean Richer and Giovanni Domenico Cassini measured the parallax of Mars between Paris and Cayenne in French Guiana when Mars was at its closest to Earth in 1672. They arrived at a figure for the solar parallax of 9.5 arcseconds, equivalent to an Earth–Sun distance of about 22,000 Earth radii. They were also the first astronomers to have access to an accurate and reliable value for the radius of Earth, which had been measured by their colleague Jean Picard in 1669 as 3269 thousand toises. Isaac Newton used this measurement for establishing his law of universal gravitation. Picard's geodetic observations had been confined to the determination of the magnitude of the earth considered as a sphere, but the discovery made by Jean Richer turned the attention of mathematicians to its deviation from a spherical form. The determination of the figure of the earth became a problem of the highest importance in astronomy, inasmuch as the diameter of the earth was the unit to which all celestial distances had to be referred.
  The French main unit of length was the Toise of Paris whose standard was the Toise of Châtelet which was fixed outside the Grand Châtelet in Paris from 1668 to 1776. In 1735 two geodetic standards were calibrated against the Toise of Châtelet. One of them, the Toise of Peru was used for the Spanish-French Geodesic Mission. In 1766 the Toise of Peru became the official standard of the Toise in France and was renamed as the Toise of the Academy (French: Toise de l'Académie).
  In his famous work Theory of the Figure of the Earth, drawn from the Principles of Hydrostatics published in 1743, Alexis Claude Clairaut synthesized the relationships existing between gravity and the shape of the Earth. Clairaut exposed there his theorem which established a relationship between gravity measured at different latitudes and the flattening of the Earth considered as a spheroid composed of concentric layers of variable densities. Towards the end of the 18th century, the geodesists sought to reconcile the values of flattening drawn from the measurements of meridian arcs with that given by Clairaut's spheroid drawn from the measurement of gravity. In 1789, Pierre-Simon de Laplace obtained by a calculation taking into account the measures of meridian arcs known at the time a flattening of 1/279. Gravimetry gave him a flattening of 1/359. Adrien-Marie Legendre meanwhile found at the same time a flattening of 1/305. The Weights and Measures Commission would adopt in 1799 a flattening of 1/334 by combining the arc of Per
caption: Giovanni Domenico Cassini
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