The arc measurement of Delambre and Méchain was a geodetic survey carried out by Jean-Baptiste Delambre and

Pierre Méchain Pierre François André Méchain (; 16 August 1744 – 20 September 1804) was a French astronomer and surveyor who, with Charles Messier, was a major contributor to the early study of deep-sky objects and comets. Life Pierre Méchain was born i ...

in 1792–1798 to measure an arc section of the Paris meridian between Dunkirk and

Barcelona Barcelona ( , , ) is a city on the coast of northeastern Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second most populous municipality of Spain. With a population of 1.6 million within ci ...

. This

arc measurement Arc measurement, sometimes degree measurement (german: Gradmessung), is the astrogeodetic technique of determining of the radius of Earth – more specifically, the local Earth radius of curvature of the figure of the Earth – by relating the la ...

served as the basis for the original definition of the

metre The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its prefi ...

. In 1791, the French Academy of Sciences chose to define the metre as one ten-millionth of the distance from the equator to the North or South Pole. This replaced the earlier definition based on the period of a pendulum, because the force of

Earth's gravity The gravity of Earth, denoted by , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quanti ...

varies slightly over the surface of the Earth, which affects the period of a pendulum. To establish a universally accepted foundation for the definition of the metre, more accurate measurements of a meridian were needed. The French Academy of Sciences commissioned an expedition led by

Jean Baptiste Joseph Delambre Jean Baptiste Joseph, chevalier Delambre (19 September 1749 – 19 August 1822) was a French mathematician, astronomer, historian of astronomy, and geodesist. He was also director of the Paris Observatory, and author of well-known books on t ...

and

, lasting from 1792 to 1799, which attempted to accurately measure the distance between a belfry in Dunkerque and

Montjuïc castle Montjuïc Castle ( ca, Castell de Montjuïc, es, Castillo de Montjuich) is an old military fortress, with roots dating back from 1640, built on top of Montjuïc hill in Barcelona, Catalonia, Spain. It currently serves as a Barcelona municipal faci ...

to estimate the length of the meridian arc through Dunkerque. This portion of the meridian, assumed to be the same length as the Paris meridian, was to serve as the basis for the length of the quarter meridian connecting the North Pole with the Equator. The problem with this approach is that the exact shape of the Earth is not a simple mathematical shape, such as a

sphere A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is th ...

or oblate spheroid, at the level of precision required for defining a standard of length. The irregular and particular shape of the Earth smoothed to sea level is represented by a mathematical model called a

geoid The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended ...

, which literally means "Earth-shaped". Despite these issues, in 1793 France adopted this definition of the metre as its official unit of length based on provisional results from this expedition. However, it was later determined that the first prototype metre bar was short by about 200 micrometres because of miscalculation of the

flattening Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution ( spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening i ...

of the Earth, making the prototype about 0.02% shorter than the original proposed definition of the metre. Regardless, this length became the French standard and was progressively adopted by other countries in Europe. This is why the polar circumference of the Earth is 40,008 km, instead of 40,000.

References

{{reflist Geodetic surveys

See also

References