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 Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Interna ...

in the

International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...

(SI), though its prefixed forms are also used relatively frequently. The metre was originally defined in 1793 as one ten-millionth of the distance from the

equator The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can als ...

to the North Pole along a

great circle In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geomet ...

, so the Earth's circumference is approximately km. In 1799, the metre was redefined in terms of a prototype metre bar (the actual bar used was changed in 1889). In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86. The current definition was adopted in 1983 and modified slightly in 2002 to clarify that the metre is a measure of proper length. From 1983 until 2019, the metre was formally defined as the length of the path travelled by light in a vacuum in of a

second The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ...

. After the

2019 redefinition of the SI base units In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144t ...

, this definition was rephrased to include the definition of a second in terms of the caesium frequency .

Spelling

''Metre'' is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States and the Philippines, which use ''meter.'' Other West Germanic languages, such as German and Dutch, and North Germanic languages, such as Danish, Norwegian, and Swedish, likewise spell the word ''Meter'' or ''meter''. Measuring devices (such as ammeter,

speedometer A speedometer or speed meter is a gauge that measures and displays the instantaneous speed of a vehicle. Now universally fitted to motor vehicles, they started to be available as options in the early 20th century, and as standard equipment f ...

) are spelled "-meter" in all variants of English. The suffix "-meter" has the same Greek origin as the unit of length.

Etymology

The etymological roots of ''metre'' can be traced to the Greek verb () (to measure, count or compare) and noun () (a measure), which were used for physical measurement, for poetic metre and by extension for moderation or avoiding extremism (as in "be measured in your response"). This range of uses is also found in Latin (), French (), English and other languages. The Greek word is derived from the Proto-Indo-European root '' *meh₁-'' 'to measure'. The motto () in the seal of the International Bureau of Weights and Measures (BIPM), which was a saying of the Greek statesman and philosopher Pittacus of Mytilene and may be translated as "Use measure!", thus calls for both measurement and moderation. The use of the word ''metre'' (for the French unit ) in English began at least as early as 1797. Oxford English Dictionary, Clarendon Press 2nd ed.1989, vol.IX p.697 col.3.

History of definition

Pendulum or meridian

In 1671,

Jean Picard Jean Picard (21 July 1620 – 12 July 1682) was a French astronomer and priest born in La Flèche, where he studied at the Jesuit Collège Royal Henry-Le-Grand. He is principally notable for his accurate measure of the size of the Earth, base ...

measured the length of a " seconds pendulum" and proposed a unit of measurement twice that length to be called the universal toise (French: ''Toise universelle''). In 1675,

Tito Livio Burattini Tito Livio Burattini ( pl, Tytus Liwiusz Burattini, 8 March 1617 – 17 November 1681) was an inventor, architect, Egyptologist, scientist, instrument-maker, traveller, engineer, and nobleman, who spent his working life in Poland and Lithu ...

suggested the term metre for a unit of length based on a pendulum length, but then it was discovered that the length of a seconds pendulum varies from place to place. Since

Eratosthenes Eratosthenes of Cyrene (; grc-gre, Ἐρατοσθένης ; – ) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandria ...

, geographers had used

meridian arc In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length. The purpose of measuring meridian arcs is to de ...

s to assess the size of the Earth, which in 1669,

determined to have a radius of toises, treated as a simple sphere. In the 18th century,

geodesy Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivale ...

grew in importance as a means of empirically demonstrating the theory of gravity, which

Émilie du Châtelet Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet (; 17 December 1706 – 10 September 1749) was a French natural philosopher and mathematician from the early 1730s until her death due to complications during childbirth in 1749. ...

promoted in France in combination with Leibniz mathematical work, and because the radius of the Earth was the unit to which all celestial distances were to be referred.

Meridional definition

As a result of the Lumières and during the French Revolution, the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...

charged a commission with determining a single scale for all measures. On 7 October 1790 that commission advised the adoption of a decimal system, and on 19 March 1791 advised the adoption of the term ''mètre'' ("measure"), a basic unit of length, which they defined as equal to one ten-millionth of the

quarter meridian In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length. The purpose of measuring meridian arcs is to d ...

, the distance between the North Pole and the

Equator The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can als ...

along the

meridian Meridian or a meridian line (from Latin ''meridies'' via Old French ''meridiane'', meaning “midday”) may refer to Science * Meridian (astronomy), imaginary circle in a plane perpendicular to the planes of the celestial equator and horizon * ...

through Paris. On 26 March 1791, the French National Constituent Assembly adopted the proposal. The

commissioned an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from 1792 to 1799, which attempted to accurately measure the distance between a belfry in

Dunkerque Dunkirk (french: Dunkerque ; vls, label=French Flemish, Duunkerke; nl, Duinkerke(n) ; , ;) is a commune in the department of Nord in northern France.Montjuïc castle in

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 ...

at the longitude of the Paris Panthéon (see

meridian arc of Delambre and Méchain Meridian or a meridian line (from Latin ''meridies'' via Old French ''meridiane'', meaning “midday”) may refer to Science * Meridian (astronomy), imaginary circle in a plane perpendicular to the planes of the celestial equator and horizon * ...

). The expedition was fictionalised in Denis Guedj, ''Le Mètre du Monde''. Ken Alder wrote factually about the expedition in ''The Measure of All Things: the seven year odyssey and hidden error that transformed the world''. This portion of the

Paris meridian The Paris meridian is a meridian line running through the Paris Observatory in Paris, France – now longitude 2°20′14.02500″ East. It was a long-standing rival to the Greenwich meridian as the prime meridian of the world. The "Paris merid ...

was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator. From 1801 to 1812 France adopted this definition of the metre as its official unit of length based on results from this expedition combined with those of the Geodesic Mission to Peru. The latter was related by Larrie D. Ferreiro in ''Measure of the Earth: The Enlightenment Expedition that Reshaped Our World''. In the 19th century, geodesy underwent a revolution through advances in mathematics as well as improvements in the instruments and methods of observation, for instance accounting for individual bias in terms of the personal equation. The application of the

least squares The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...

method to

measurements demonstrated the importance of the scientific method in geodesy. On the other hand, the invention of the telegraph made it possible to measure parallel arcs, and the improvement of the

reversible pendulum 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 previo ...

gave rise to the study of the Earth's

gravitational field In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenome ...

. A more accurate determination of the

Figure of the Earth Figure of the Earth is a Jargon, term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A Spherical Earth, sphere is a well-k ...

would soon result from the measurement of the

Struve Geodetic Arc The Struve Geodetic Arc is a chain of survey triangulations stretching from Hammerfest in Norway to the Black Sea, through ten countries and over , which yielded the first accurate measurement of a meridian arc. The chain was established ...

(1816–1855) and would have given another value for the definition of this standard of length. This did not invalidate the metre but highlighted that progress in science would allow better measurement of Earth's size and shape. In 1832,

Carl Friedrich Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refe ...

studied the

Earth's magnetic field Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magneti ...

and proposed adding the

to the basic units of the metre and the

kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...

in the form of the CGS system ( centimetre, gram, second). In 1836, he founded the ''Magnetischer Verein'', the first international scientific association, in collaboration with Alexander von Humboldt and Wilhelm Edouard Weber. The coordination of the observation of geophysical phenomena such as the Earth's magnetic field, lightning and gravity in different points of the globe stimulated the creation of the first international scientific associations. The foundation of the ''Magnetischer Verein'' would be followed by that of the Central European Arc Measurement (German: ''Mitteleuropaïsche Gradmessung'') on the initiative of

Johann Jacob Baeyer Johann Jacob Baeyer (born 5 November 1794 in Berlin, died 10 September 1885 in Berlin) was a German geodesist and a lieutenant-general Lieutenant general (Lt Gen, LTG and similar) is a three-star military rank (NATO code OF-8) used in many ...

in 1863, and by that of the International Meteorological Organisation whose second president, the Swiss meteorologist and physicist, Heinrich von Wild would represent Russia at the International Committee for Weights and Measures (CIPM).

International prototype metre bar

In 1816, Ferdinand Rudolph Hassler was appointed first Superintendent of the

Survey of the Coast The United States Coast and Geodetic Survey (abbreviated USC&GS), known from 1807 to 1836 as the Survey of the Coast and from 1836 until 1878 as the United States Coast Survey, was the first scientific agency of the United States Government. It ...

. Trained in geodesy in Switzerland, France and Germany, Hassler had brought a standard metre made in Paris to the United States in 1805. He designed a baseline apparatus which instead of bringing different bars in actual contact during measurements, used only one bar calibrated on the metre and optical contact. Thus the metre became the unit of length for

in the United States. Since 1830, Hassler was also head of the Bureau of Weights and Measures which became a part of the Coast Survey. He compared various units of length used in the United States at that time and measured

coefficients of expansion Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions. Temperature is a monotonic function of the average molecular kinetic ...

to assess temperature effects on the measurements. In 1841, Friedrich Wilhelm Bessel, taking into account errors which had been recognized by Louis Puissant in the French meridian arc comprising the arc measurement of Delambre and Méchain which had been extended southward by

François Arago Dominique François Jean Arago ( ca, Domènec Francesc Joan Aragó), known simply as François Arago (; Catalan: ''Francesc Aragó'', ; 26 February 17862 October 1853), was a French mathematician, physicist, astronomer, freemason, supporter of t ...

and Jean-Baptiste Biot, recalculated the flattening of the Earth ellipsoid making use of nine more arc measurements, namely Peruan, Prussian, first East-Indian, second East-Indian, English, Hannover, Danish, Russian and Swedish covering almost 50 degrees of latitude, and stated that the Earth quadrant used for determining the length of the metre was nothing more than a rather imprecise

conversion factor Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects. Overview The process ...

between the toise and the metre. Regarding the precision of the conversion from the toise to the metre, both units of measurement were then defined by primary standards, and unique artifacts made of different alloys with distinct coefficients of expansion were the legal basis of units of length. A wrought iron ruler, the Toise of Peru, also called ''Toise de l'Académie'', was the French primary standard of the toise, and the metre was officially defined by the ''Mètre des Archives'' made of platinum. Besides the latter, another platinum and twelve iron standards of the metre were made in 1799. One of them became known as the ''Committee Meter'' in the United States and served as standard of length in the Coast Survey until 1890. According to geodesists, these standards were secondary standards deduced from the Toise of Peru. In Europe, surveyors continued to use measuring instruments calibrated on the Toise of Peru. Among these, the toise of Bessel and the apparatus of Borda were respectively the main references for geodesy in Prussia and in France. A French scientific instrument maker,

Jean Nicolas Fortin Jean Nicolas Fortin (1750–1831) was a French maker of scientific instruments, born on 9 August 1750 in Mouchy-la-Ville in Picardy. Among his customers were such noted scientists as Lavoisier, for whom he made a precision balance, Gay-Lussac, Fra ...

, had made two direct copies of the Toise of Peru, the first for Friedrich Georg Wilhelm von Struve in 1821 and a second for Friedrich Bessel in 1823. On the subject of the theoretical definition of the metre, it had been inaccessible and misleading at the time of Delambre and Mechain arc measurement, as the geoid is a ball, which on the whole can be assimilated to an oblate spheroid, but which in detail differs from it so as to prohibit any generalization and any extrapolation. As early as 1861, after Friedrich von Schubert showed that the different meridians were not of equal length, Elie Ritter, a mathematician from Geneva, deduced from a computation based on eleven meridian arcs covering 86 degrees that the meridian equation differed from that of the ellipse: the meridian was swelled about the 45th degree of latitude by a layer whose thickness was difficult to estimate because of the uncertainty of the latitude of some stations, in particular that of Montjuïc in the French meridian arc. By measuring the latitude of two stations in

, Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation. We know now that, in addition to other errors in the survey of Delambre and Méchain, an unfavourable vertical deflection gave an inaccurate determination of Barcelona's latitude, a metre "too short" compared to a more general definition taken from the average of a large number of arcs. Nevertheless Ferdinand Rudolph Hassler's use of the metre in coastal survey contributed to the introduction of the Metric Act of 1866 allowing the use of the metre in the United States, and also played an important role in the choice of the metre as international scientific unit of length and the proposal by the European Arc Measurement (German: ''Europäische Gradmessung'') to “establish a European

international bureau for weights and measures The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation, through which its 59 member-states act together on measurement standards in four areas: chemistry ...

”. However, in 1866, the most important concern was that the Toise of Peru, the standard of the toise constructed in 1735 for the French Geodesic Mission to the Equator, might be so much damaged that comparison with it would be worthless, while Bessel had questioned the accuracy of copies of this standard belonging to Altona and Koenigsberg Observatories, which he had compared to each other about 1840. Indeed when the primary Imperial yard standard was partially destroyed in 1834, a new standard of reference had been constructed using copies of the "Standard Yard, 1760" instead of the pendulum's length as provided for in the Weights and Measures Act of 1824. In 1864, Urbain Le Verrier refused to join the first general conference of the Central European Arc Measurement because the French geodetic works had to be verified. Appareil Ibáñez

In 1866, at the meeting of the Permanent Commission of the association in

Neuchâtel , neighboring_municipalities= Auvernier, Boudry, Chabrey (VD), Colombier, Cressier, Cudrefin (VD), Delley-Portalban (FR), Enges, Fenin-Vilars-Saules, Hauterive, Saint-Blaise, Savagnier , twintowns = Aarau (Switzerland), Besançon (France), ...

, Antoine Yvon Villarceau announced that he had checked eight points of the French arc. He confirmed that the metre was too short. It then became urgent to undertake a complete revision of the meridian arc. Moreover, while the extension of the French meridian arc to the

Balearic Islands The Balearic Islands ( es, Islas Baleares ; or ca, Illes Balears ) are an archipelago in the Balearic Sea, near the eastern coast of the Iberian Peninsula. The archipelago is an autonomous community and a province of Spain; its capital is ...

(1803–1807) had seemed to confirm the length of the metre, this survey had not been secured by any baseline in Spain. For that reason,

Carlos Ibáñez e Ibáñez de Ibero Carlos Ibáñez e Ibáñez de Ibero, 1st Marquis of Mulhacén, (14 April 1825 – 28 or 29 January 1891) was a Spanish divisional general and geodesist. He represented Spain at the 1875 Conference of the Metre Convention and was the first presid ...

's announcement, at this conference, of his 1858 measurement of a baseline in Madridejos was of particular importance. Indeed surveyors determined the size of

triangulation In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle me ...

networks by measuring baselines which concordance granted the accuracy of the whole survey. In 1867 at the second general conference of the International Association of Geodesy held in Berlin, the question of an international standard unit of length was discussed in order to combine the measurements made in different countries to determine the size and shape of the Earth. The conference recommended the adoption of the metre in replacement of the toise and the creation of an international metre commission, according to the proposal of

Adolphe Hirsch Adolphe Hirsch (21 May 1830 - 16 April 1901) was a German born, Swiss astronomer and geodesist. Bibliography Adolph Hirsch was born in Halberstadt. He studied astronomy at the universities of Heidelberg and Vienna. He founded and directed the ...

and