Metre

metre
The historical standard metre in Paris
General information
Unit system	SI
Unit of	length
Symbol	m
Conversions
1 m in ...	... is equal to ...
SI units
Imperial/US units	≈  ≈  ≈
Nautical units	≈

The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019 the metre has been defined as the length of the path travelled by light in vacuum during a time interval of 1/ of a second, where the second is defined by a hyperfine transition frequency of caesium.

The metre was originally defined in 1791 by the French National Assembly as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's polar circumference is approximately .

In 1799, the metre was redefined in terms of a prototype metre bar, the bar used was changed in 1889, and 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 vacuum in 1/ of a second. After the 2019 redefinition of the SI base units, this definition was rephrased to include the definition of a second in terms of the caesium frequency Δν_Cs. This series of amendments did not alter the size of the metre significantly – today Earth's polar circumference measures , a change of 0.022% from the original value of exactly , which also includes improvements in the accuracy of measuring the circumference.

Spelling

Seal of the International Bureau of Weights and Measures (BIPM) – Use measure (Greek: )

Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations, the exceptions being the United States and the Philippines which use meter.

Measuring devices (such as ammeter, speedometer) 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 () ((I) 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.

History of definition

Main article: History of the metre

Universal measure: the metre linked to the figure of the Earth

The Meridian room of the Paris Observatory (or Cassini room): the Paris meridian is drawn on the ground.

Galileo discovered gravitational acceleration to explain the fall of bodies at the surface of the Earth. He also observed the regularity of the period of swing of the pendulum and that this period depended on the length of the pendulum.

Kepler's laws of planetary motion served both to the discovery of Newton's law of universal gravitation and to the determination of the distance from Earth to the Sun by Giovanni Domenico Cassini. They both also used a determination of the size of the Earth, then considered as a sphere, by Jean Picard through triangulation of Paris meridian. In 1671, Jean Picard also measured the length of a seconds pendulum at Paris Observatory and proposed this unit of measurement to be called the astronomical radius (French: Rayon Astronomique). In 1675, Tito Livio Burattini suggested the term ' meaning universal measure for this unit of length, but then it was discovered that the length of a seconds pendulum varies from place to place.

Gravimeter with variant of Repsold–Bessel pendulum

Christiaan Huygens found out the centrifugal force which explained variations of gravitational acceleration depending on latitude. He also mathematically formulated the link between the length of the simple pendulum and gravitational acceleration. According to Alexis Clairaut, the study of variations in gravitational acceleration was a way to determine the figure of the Earth, whose crucial parameter was the flattening of the Earth ellipsoid. In the 18th century, in addition of its significance for cartography, geodesy grew in importance as a means of empirically demonstrating the theory of gravity, which Émilie du Châtelet promoted in France in combination with Leibniz's mathematical work and because the radius of the Earth was the unit to which all celestial distances were to be referred. Indeed, Earth proved to be an oblate spheroid through geodetic surveys in Ecuador and Lapland and this new data called into question the value of Earth radius as Picard had calculated it.

After the Anglo-French Survey, the French Academy of Sciences commissioned an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from 1792 to 1798, which measured the distance between a belfry in Dunkirk and Montjuïc castle in Barcelona at the longitude of the Paris Panthéon. When the length of the metre was defined as one ten-millionth of the distance from the North Pole to the Equator, the flattening of the Earth ellipsoid was assumed to be 1/334.

In 1841, Friedrich Wilhelm Bessel using the method of least squares calculated from several arc measurements a new value for the flattening of the Earth, which he determinated as 1/299.15. He also devised a new instrument for measuring gravitational acceleration which was first used in Switzerland by Emile Plantamour, Charles Sanders Peirce and Isaac-Charles Élisée Cellérier (8.01.1818 – 2.10.1889), a Genevan mathematician soon independently discovered a mathematical formula to correct systematic errors of this device which had been noticed by Plantamour and Adolphe Hirsch. This allowed Friedrich Robert Helmert to determine a remarkably accurate value of 1/298.3 for the flattening of the Earth when he proposed his ellipsoid of reference in 1901. This was also the result of the Metre Convention of 1875, when the metre was adopted as an international scientific unit of length for the convenience of continental European geodesists following the example of Ferdinand Rudolph Hassler.

Meridional definition

In 1790, one year before it was ultimately decided that the metre would be based on the Earth quadrant (a quarter of the Earth's circumference through its poles), Talleyrand proposed that the metre be the length of the seconds pendulum at a latitude of 45°. This option, with one-third of this length defining the foot, was also considered by Thomas Jefferson and others for redefining the yard in the United States shortly after gaining independence from the British Crown.

Instead of the seconds pendulum method, the commission of the French Academy of Sciences – whose members included Borda, Lagrange, Laplace, Monge and Condorcet – decided that the new measure should be equal to one ten-millionth of the distance from the North Pole to the Equator, determined through measurements along the meridian passing through Paris. Apart from the obvious consideration of safe access for French surveyors, the Paris meridian was also a sound choice for scientific reasons: a portion of the quadrant from Dunkirk to Barcelona (about 1000 km, or one-tenth of the total) could be surveyed with start- and end-points at sea level, and that portion was roughly in the middle of the quadrant, where the effects of the Earth's oblateness were expected not to have to be accounted for. Improvements in the measuring devices designed by Borda and used for this survey also raised hopes for a more accurate determination of the length of this meridian arc.

The task of surveying the Paris meridian arc took more than six years (1792–1798). The technical difficulties were not the only problems the surveyors had to face in the convulsed period of the aftermath of the French Revolution: Méchain and Delambre, and later Arago, were imprisoned several times during their surveys, and Méchain died in 1804 of yellow fever, which he contracted while trying to improve his original results in northern Spain. In the meantime, the commission of the French Academy of Sciences calculated a provisional value from older surveys of 443.44 lignes. This value was set by legislation on 7 April 1795.

In 1799, a commission including Johan Georg Tralles, Jean Henri van Swinden, Adrien-Marie Legendre and Jean-Baptiste Delambre calculated the distance from Dunkirk to Barcelona using the data of the triangulation between these two towns and determined the portion of the distance from the North Pole to the Equator it represented. Pierre Méchain's and Jean-Baptiste Delambre's measurements were combined with the results of the Spanish-French geodetic mission and a value of 1/334 was found for the Earth's flattening. However, French astronomers knew from earlier estimates of the Earth's flattening that different meridian arcs could have different lengths and that their curvature could be irregular. The distance from the North Pole to the Equator was then extrapolated from the measurement of the Paris meridian arc between Dunkirk and Barcelona and was determined as 5 130 740 toises. As the metre had to be equal to one ten-millionth of this distance, it was defined as 0.513074 toise or 3 feet and 11.296 lines of the Toise of Peru, which had been constructed in 1735 for the French Geodesic Mission to the Equator. When the final result was known, a bar whose length was closest to the meridional definition of the metre was selected and placed in the National Archives on 22 June 1799 (4 messidor An VII in the Republican calendar) as a permanent record of the result.

Early adoption of the metre as a scientific unit of length: the forerunners

Triangulation near New York City, 1817

In 1816, Ferdinand Rudolph Hassler was appointed first Superintendent of the Survey of the Coast. 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 geodesy in the United States.

In 1830, Hassler became head of the Office of Weights and Measures, which became a part of the Survey of the Coast. He compared various units of length used in the United States at that time and measured coefficients of expansion to assess temperature effects on the measurements.

In 1832, Carl Friedrich Gauss studied the Earth's magnetic field and proposed adding the second to the basic units of the metre and the kilogram 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 in 1863, and by that of the International Meteorological Organisation whose president, the Swiss meteorologist and physicist, Heinrich von Wild would represent Russia at the International Committee for Weights and Measures (CIPM).

In 1834, Hassler, measured at Fire Island the first baseline of the Survey of the Coast, shortly before Louis Puissant declared to the French Academy of Sciences in 1836 that Jean Baptiste Joseph Delambre and Pierre Méchain had made errors in the meridian arc measurement, which had been used to determine the length of the metre. Errors in the method of calculating the length of the Paris meridian were taken into account by Bessel when he proposed his reference ellipsoid in 1841.

Ibáñez apparatus calibrated on the metric Spanish Standard and used at Aarberg, in canton of Bern, Switzerland

Egyptian astronomy has ancient roots which were revived in the 19th century by the modernist impetus of Muhammad Ali who founded in Sabtieh, Boulaq district, in Cairo an Observatory which he was keen to keep in harmony with the progress of this science still in progress. In 1858, a Technical Commission was set up to continue, by adopting the procedures instituted in Europe, the cadastre work inaugurated under Muhammad Ali. This Commission suggested to Viceroy Mohammed Sa'id Pasha the idea of buying geodetic devices which were ordered in France. While Mahmud Ahmad Hamdi al-Falaki was in charge, in Egypt, of the direction of the work of the general map, the viceroy entrusted to Ismail Mustafa al-Falaki the study, in Europe, of the precision apparatus calibrated against the metre intended to measure the geodesic bases and already built by Jean Brunner in Paris. Ismail Mustafa had the task to carry out the experiments necessary for determining the expansion coefficients of the two platinum and brass bars, and to compare the Egyptian standard with a known standard. The Spanish standard designed by Carlos Ibáñez e Ibáñez de Ibero and Frutos Saavedra Meneses was chosen for this purpose, as it had served as a model for the construction of the Egyptian standard. In addition, the Spanish standard had been compared with Borda's double-toise N° 1, which served as a comparison module for the measurement of all geodesic bases in France, and was also to be compared to the Ibáñez apparatus. In 1954, the connection of the southerly extension of the Struve Geodetic Arc with an arc running northwards from South Africa through Egypt would bring the course of a major meridian arc back to land where Eratosthenes had founded geodesy.

West Europe–Africa Meridian-arc: a meridian arc extending from the Shetland Islands, through Great Britain, France and Spain to El Aghuat in Algeria, whose parameters were calculated from surveys carried out in the mid to late 19th century. It yielded a value for the equatorial radius of the earth a = 6 377 935 metres, the ellipticity being assumed as 1/299.15. The radius of curvature of this arc is not uniform, being, in the mean, about 600 metres greater in the northern than in the southern part. Greenwich meridian is depicted rather than Paris meridian.

Seventeen years after Bessel calculated his ellipsoid of reference, some of the meridian arcs the German astronomer had used for his calculation had been enlarged. This was a very important circumstance because the influence of errors due to vertical deflections was minimized in proportion to the length of the meridian arcs: the longer the meridian arcs, the more precise the image of the Earth ellipsoid would be. After Struve Geodetic Arc measurement, it was resolved in the 1860s, at the initiative of Carlos Ibáñez e Ibáñez de Ibero who would become the first president of both the International Geodetic Association and the International Committee for Weights and Measure, to remeasure the arc of meridian from Dunkirk to Formentera and to extend it from Shetland to the Sahara. This did not pave the way to a new definition of the metre because it was known that the theoretical definition of the metre 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 from the measurement of a single meridian arc. In 1859, Friedrich von Schubert demonstrated that several meridians had not the same length, confirming an hypothesis of Jean Le Rond d’Alembert. He also proposed an ellipsoid with three unequal axes. In 1860, Elie Ritter, a mathematician from Geneva, using Schubert's data computed that the Earth ellipsoid could rather be a spheroid of revolution accordingly to Adrien-Marie Legendre’s model. However, the following year, resuming his calculation on the basis of all the data available at the time, Ritter came to the conclusion that the problem was only resolved in an approximate manner, the data appearing too scant, and for some affected by vertical deflections, in particular the latitude of Montjuïc in the French meridian arc which determination had also been affected in a lesser proportion by systematic errors of the repeating circle.

The definition of the length of a metre in the 1790s was founded upon Arc measurements in France and Peru with a definition that it was to be 1/40 millionth of the circumference of the earth measured through the poles. Such were the inaccuracies of that period that within a matter of just a few years more reliable measurements would have given a different value for the definition of this international standard. That does not invalidate the metre in any way but highlights the fact that continuing improvements in instrumentation made better measurements of the earth’s size possible.

— Nomination of the STRUVE GEODETIC ARC for inscription on the WORLD HERITAGE LIST, p. 40

Struve Geodetic Arc

It was well known that by measuring the latitude of two stations in Barcelona, Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation and that he didn't dare to admit this inaccuracy. This was later explained by clearance in the central axis of the repeating circle causing wear and consequently the zenith measurements contained significant systematic errors. Polar motion predicted by Leonard Euler and later discovered by Seth Carlo Chandler also had an impact on accuracy of latitudes' determinations. Among all these sources of error, it was mainly an unfavourable vertical deflection that gave an inaccurate determination of Barcelona's latitude and a metre "too short" compared to a more general definition taken from the average of a large number of arcs.

As early as 1861, Johann Jacob Baeyer sent a memorandum to the King of Prussia recommending international collaboration in Central Europe with the aim of determining the shape and dimensions of the Earth. At the time of its creation, the association had sixteen member countries: Austrian Empire, Kingdom of Belgium, Denmark, seven German states (Grand Duchy of Baden, Kingdom of Bavaria, Kingdom of Hanover, Mecklenburg, Kingdom of Prussia, Kingdom of Saxony, Saxe-Coburg and Gotha), Kingdom of Italy, Netherlands, Russian Empire (for Poland), United Kingdoms of Sweden and Norway, as well as Switzerland. The Central European Arc Measurement created a Central Office, located at the Prussian Geodetic Institute, whose management was entrusted to Johann Jacob Baeyer.

Baeyer's goal was a new determination of anomalies in the shape of the Earth using precise triangulations, combined with gravity measurements. This involved determining the geoid by means of gravimetric and leveling measurements, in order to deduce the exact knowledge of the terrestrial spheroid while taking into account local variations. To resolve this problem, it was necessary to carefully study considerable areas of land in all directions. Baeyer developed a plan to coordinate geodetic surveys in the space between the parallels of Palermo and Freetown Christiana (Denmark) and the meridians of Bonn and Trunz (German name for Milejewo in Poland). This territory was covered by a triangle network and included more than thirty observatories or stations whose position was determined astronomically. Bayer proposed to remeasure ten arcs of meridians and a larger number of arcs of parallels, to compare the curvature of the meridian arcs on the two slopes of the Alps, in order to determine the influence of this mountain range on vertical deflection. Baeyer also planned to determine the curvature of the seas, the Mediterranean Sea and Adriatic Sea in the south, the North Sea and the Baltic Sea in the north. In his mind, the cooperation of all the States of Central Europe could open the field to scientific research of the highest interest, research that each State, taken in isolation, was not able to undertake.

Spain and Portugal joined the European Arc Measurement in 1866. French Empire hesitated for a long time before giving in to the demands of the Association, which asked the French geodesists to take part in its work. It was only after the Franco-Prussian War, that Charles-Eugène Delaunay represented France at the Congress of Vienna in 1871. In 1874, Hervé Faye was appointed member of the Permanent Commission which was presided by Carlos Ibáñez e Ibáñez de Ibero.

The International Geodetic Association gained global importance with the accession of Chile, Mexico and Japan in 1888; Argentina and United-States in 1889; and British Empire in 1898. The convention of the International Geodetic Association expired at the end of 1916. It was not renewed due to the First World War. However, the activities of the International Latitude Service were continued through an thanks to the efforts of H.G. van de Sande Bakhuyzen and Raoul Gautier (1854–1931), respectively directors of Leiden Observatory and Geneva Observatory.

International prototype metre bar

Closeup of National Prototype Metre Bar No. 27, made in 1889 by the International Bureau of Weights and Measures (BIPM) in collaboration with Johnson Mattey and given to the United States, which served as the standard for American cartography from 1890 replacing the Committee Meter, an authentic copy of the Mètre des Archives produced in 1799 in Paris, which Ferdinand Rudolph Hassler had brought to the United States in 1805

After the French Revolution, Napoleonic Wars led to the adoption of the metre in Latin America following independence of Brazil and Hispanic America, while the American Revolution prompted the foundation of the Survey of the Coast in 1807 and the creation of the Office of Standard Weights and Measures in 1830. In continental Europe, Napoleonic Wars fostered German nationalism which later led to unification of Germany in 1871. Meanwhile, most European countries had adopted the metre. In the 1870s, German Empire played a pivotal role in the unification of the metric system through the European Arc Measurement but its overwhelming influence was mitigated by that of neutral states. While the German astronomer Wilhelm Julius Foerster, director of the Berlin Observatory and director of the German Weights and Measures Service boycotted the Permanent Committee of the International Metre Commission, along with the Russian and Austrian representatives, in order to promote the foundation of a permanent International Bureau of Weights and Measures, the German born, Swiss astronomer, Adolphe Hirsch conformed to the opinion of Italy and Spain to create, in spite of French reluctance, the International Bureau of Weights and Measures in France as a permanent institution at the disadventage of the Conservatoire national des Arts et Métiers.

At that time, units of measurement were 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 an artifact made of platinum kept in the National Archives. Besides the latter, another platinum and twelve iron standards of the metre were made by Étienne Lenoir in 1799. One of them became known as the Committee Meter in the United States and served as standard of length in the United States Coast Survey until 1890. According to geodesists, these standards were secondary standards deduced from the Toise of Peru. In Europe, except Spain, 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. These measuring devices consisted of bimetallic rulers in platinum and brass or iron and zinc fixed together at one extremity to assess the variations in length produced by any change in temperature. The combination of two bars made of two different metals allowed to take thermal expansion into account without measuring the temperature. A French scientific instrument maker, Jean Nicolas Fortin, had made three direct copies of the Toise of Peru, one for Friedrich Georg Wilhelm von Struve, a second for Heinrich Christian Schumacher in 1821 and a third for Friedrich Bessel in 1823. In 1831, Henri-Prudence Gambey also realized a copy of the Toise of Peru which was kept at Altona Observatory.

Historic Dutch replicas of metric standards in the collection of Rijksmuseum, Amsterdam: iron metre with case constructed by Étienne Lenoir in 1799, copper grave kilogram with case (1798), copper volume measures (1829)

In the second half of the 19th century, the creation of the International Geodetic Association would mark the adoption of new scientific methods. It then became possible to accurately measure parallel arcs, since the difference in longitude between their ends could be determined thanks to the invention of the electrical telegraph. Furthermore, advances in metrology combined with those of gravimetry have led to a new era of geodesy. If precision metrology had needed the help of geodesy, the latter could not continue to prosper without the help of metrology. It was then necessary to define a single unit to express all the measurements of terrestrial arcs and all determinations of the gravitational acceleration by means of pendulum.

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. This assertion was particularly worrying, because when the primary Imperial yard standard had partially been destroyed in 1834, a new standard of reference was 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, because the pendulum method proved unreliable. Nevertheless Ferdinand Rudolph Hassler's use of the metre and the creation of the Office of Standard Weights and Measures as an office within the Coast Survey contributed to the introduction of the Metric Act of 1866 allowing the use of the metre in the United States, and preceded 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".

Creating the metre-alloy in 1874 at the Conservatoire des Arts et Métiers. Present Henri Tresca, George Matthey, Saint-Claire Deville, and Debray.

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. According to a preliminary proposal made in Neuchâtel the precedent year, the General Conference recommended the adoption of the metre in replacement of the toise of Bessel, the creation of an International Metre Commission, and the foundation of a World institute for the comparison of geodetic standards, the first step towards the creation of the International Bureau of Weights and Measures.

Hassler's metrological and geodetic work also had a favourable response in Russia. In 1869, the Saint Petersburg Academy of Sciences sent to the French Academy of Sciences a report drafted by Otto Wilhelm von Struve, Heinrich von Wild and Moritz von Jacobi, whose theorem has long supported the assumption of an ellipsoid with three unequal axes for the figure of the Earth, inviting his French counterpart to undertake joint action to ensure the universal use of the metric system in all scientific work.

In the 1870s and in light of modern precision, a series of international conferences was held to devise new metric standards. When a conflict broke out regarding the presence of impurities in the metre-alloy of 1874, a member of the Preparatory Committee since 1870 and Spanish representative at the Paris Conference in 1875, Carlos Ibáñez e Ibáñez de Ibero intervened with the French Academy of Sciences to rally France to the project to create an International Bureau of Weights and Measures equipped with the scientific means necessary to redefine the units of the metric system according to the progress of sciences.

The Metre Convention (Convention du Mètre) of 1875 mandated the establishment of a permanent International Bureau of Weights and Measures (BIPM: ') to be located in Sèvres, France. This new organisation was to construct and preserve a prototype metre bar, distribute national metric prototypes, and maintain comparisons between them and non-metric measurement standards. The organisation distributed such bars in 1889 at the first General Conference on Weights and Measures (CGPM: '), establishing the International Prototype Metre as the distance between two lines on a standard bar composed of an alloy of 90% platinum and 10% iridium, measured at the melting point of ice.

Metrology and paradigm shift in physics

Invar wire baseline apparatus

The comparison of the new prototypes of the metre with each other involved the development of special measuring equipment and the definition of a reproducible temperature scale. The BIPM's thermometry work led to the discovery of special alloys of iron–nickel, in particular invar, whose practically negligible coefficient of expansion made it possible to develop simpler baseline measurement methods, and for which its director, the Swiss physicist Charles-Edouard Guillaume, was granted the Nobel Prize in Physics in 1920. Guillaume's Nobel Prize marked the end of an era in which metrology was leaving the field of geodesy to become a technological application of physics.

In 1921, the Nobel Prize in Physics was awarded to another Swiss scientist, Albert Einstein, who following Michelson–Morley experiment had questioned the luminiferous aether in 1905, just as Newton had questioned Descartes' Vortex theory in 1687 after Jean Richer's pendulum experiment in Cayenne, French Guiana.

Furthermore, special relativity changed conceptions of time and mass, while general relativity changed that of space. According to Newton, space was Euclidean, infinite and without boundaries and bodies gravitated around each other without changing the structure of space. Einstein's theory of gravity states, on the contrary, that the mass of a body has an effect on all other bodies while modifying the structure of space. A massive body induces a curvature of the space around it in which the path of light is inflected, as was demonstrated by the displacement of the position of a star observed near the Sun during an eclipse in 1919.

Wavelength definition

In 1873, James Clerk Maxwell suggested that light emitted by an element be used as the standard both for the unit of length and for the second. These two quantities could then be used to define the unit of mass. About the unit of length he wrote:

In the present state of science the most universal standard of length which we could assume would be the wave length in vacuum of a particular kind of light, emitted by some widely diffused substance such as sodium, which has well-defined lines in its spectrum. Such a standard would be independent of any changes in the dimensions of the earth, and should be adopted by those who expect their writings to be more permanent than that body.

— James Clerk Maxwell, A Treatise on Electricity and Magnetism, 3rd edition, Vol. 1, p. 3

Charles Sanders Peirce’s work promoted the advent of American science at the forefront of global metrology. Alongside his intercomparisons of artifacts of the metre and contributions to gravimetry through improvement of reversible pendulum, Peirce was the first to tie experimentally the metre to the wave length of a spectral line. According to him the standard length might be compared with that of a wave of light identified by a line in the solar spectrum. Albert Michelson soon took up the idea and improved it.

In 1893, the standard metre was first measured with an interferometer by Albert A. Michelson, the inventor of the device and an advocate of using some particular wavelength of light as a standard of length. By 1925, interferometry was in regular use at the BIPM. However, the International Prototype Metre remained the standard until 1960, when the eleventh CGPM defined the metre in the new International System of Units (SI) as equal to wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in vacuum.

Speed of light definition

To further reduce uncertainty, the 17th CGPM in 1983 replaced the definition of the metre with its current definition, thus fixing the length of the metre in terms of the second and the speed of light:

The metre is the length of the path travelled by light in vacuum during a time interval of of a second.

This definition fixed the speed of light in vacuum at exactly metres per second (≈ or ≈1.079 billion km/hour). An intended by-product of the 17th CGPM's definition was that it enabled scientists to compare lasers accurately using frequency, resulting in wavelengths with one-fifth the uncertainty involved in the direct comparison of wavelengths, because interferometer errors were eliminated. To further facilitate reproducibility from lab to lab, the 17th CGPM also made the iodine-stabilised helium–neon laser "a recommended radiation" for realising the metre. For the purpose of delineating the metre, the BIPM currently considers the HeNe laser wavelength, λ_HeNe, to be with an estimated relative standard uncertainty (U) of .

This uncertainty is currently one limiting factor in laboratory realisations of the metre, and it is several orders of magnitude poorer than that of the second, based upon the caesium fountain atomic clock (U = ). Consequently, a realisation of the metre is usually delineated (not defined) today in labs as wavelengths of helium–neon laser light in vacuum, the error stated being only that of frequency determination. This bracket notation expressing the error is explained in the article on measurement uncertainty.

Practical realisation of the metre is subject to uncertainties in characterising the medium, to various uncertainties of interferometry, and to uncertainties in measuring the frequency of the source. A commonly used medium is air, and the National Institute of Standards and Technology (NIST) has set up an online calculator to convert wavelengths in vacuum to wavelengths in air. As described by NIST, in air, the uncertainties in characterising the medium are dominated by errors in measuring temperature and pressure. Errors in the theoretical formulas used are secondary.

By implementing a refractive index correction such as this, an approximate realisation of the metre can be implemented in air, for example, using the formulation of the metre as wavelengths of helium–neon laser light in vacuum, and converting the wavelengths in vacuum to wavelengths in air. Air is only one possible medium to use in a realisation of the metre, and any partial vacuum can be used, or some inert atmosphere like helium gas, provided the appropriate corrections for refractive index are implemented.

The metre is defined as the path length travelled by light in a given time, and practical laboratory length measurements in metres are determined by counting the number of wavelengths of laser light of one of the standard types that fit into the length, and converting the selected unit of wavelength to metres. Three major factors limit the accuracy attainable with laser interferometers for a length measurement:

• uncertainty in vacuum wavelength of the source,
• uncertainty in the refractive index of the medium,
• least count resolution of the interferometer.

Of these, the last is peculiar to the interferometer itself. The conversion of a length in wavelengths to a length in metres is based upon the relation

$\lambda ={\frac {c}{nf}},$

which converts the unit of wavelength λ to metres using c, the speed of light in vacuum in m/s. Here n is the refractive index of the medium in which the measurement is made, and f is the measured frequency of the source. Although conversion from wavelengths to metres introduces an additional error in the overall length due to measurement error in determining the refractive index and the frequency, the measurement of frequency is one of the most accurate measurements available.

The CIPM issued a clarification in 2002:

Its definition, therefore, applies only within a spatial extent sufficiently small that the effects of the non-uniformity of the gravitational field can be ignored (note that, at the surface of the Earth, this effect in the vertical direction is about 1 part in per metre). In this case, the effects to be taken into account are those of special relativity only.

Timeline

Date	Deciding body	Decision
8 May 1790	French National Assembly	The length of the new metre to be equal to the length of a pendulum with a half-period of one second.
30 Mar 1791	French National Assembly	Accepts the proposal by the French Academy of Sciences that the new definition for the metre be equal to one ten-millionth of the length of a great circle quadrant along the Earth's meridian through Paris, that is the distance from the equator to the north pole along that quadrant.
1795	Provisional metre bar made of brass and based on Paris meridan arc (French: Méridienne de France) measured by Nicolas-Louis de Lacaillle and Cesar-François Cassini de Thury, legally equal to 443.44 lines of the toise du Pérou (a standard French unit of length from 1766). [The line was 1/864 of a toise.]
10 Dec 1799	French National Assembly	Specifies the platinum metre bar, presented on 22 June 1799 and deposited in the National Archives, as the final standard. Legally equal to 443.296 lines on the toise du Pérou.
24–28 Sept 1889	1st General Conference on Weights and Measures (CGPM)	Defines the metre as the distance between two lines on a standard bar of an alloy of platinum with 10% iridium, measured at the melting point of ice.
27 Sept – 6 Oct 1927	7th CGPM	Redefines the metre as the distance, at 0 °C (273 K), between the axes of the two central lines marked on the prototype bar of platinum–iridium, this bar being subject to one standard atmosphere of pressure and supported on two cylinders of at least 10 mm (1 cm) diameter, symmetrically placed in the same horizontal plane at a distance of 571 mm (57.1 cm) from each other.
14 Oct 1960	11th CGPM	Defines the metre as wavelengths in vacuum of the radiation corresponding to the transition between the 2p10 and 5d5 quantum levels of the krypton-86 atom.
21 Oct 1983	17th CGPM	Defines the metre as the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.
2002	International Committee for Weights and Measures (CIPM)	Considers the metre to be a unit of proper length and thus recommends this definition be restricted to "lengths ℓ which are sufficiently short for the effects predicted by general relativity to be negligible with respect to the uncertainties of realisation".

Definitions of the metre since 1795

Basis of definition	Date	Absolute uncertainty	Relative uncertainty
1/ part of the quadrant along the meridian, measurement by Delambre and Méchain (443.296 lines)	1795
First prototype ' platinum bar standard	1799
Platinum–iridium bar at melting point of ice (1st CGPM)	1889
Platinum–iridium bar at melting point of ice, atmospheric pressure, supported by two rollers (7th CGPM)	1927	n.a.	n.a.
Hyperfine atomic transition; wavelengths of light from a specified transition in krypton-86 (11th CGPM)	1960
Length of the path travelled by light in vacuum in 1/ second (17th CGPM)	1983

Early adoptions of the metre internationally

Main article: Metrication

In France, the metre was adopted as an exclusive measure in 1801 under the Consulate. This continued under the First French Empire until 1812, when Napoleon decreed the introduction of the non-decimal mesures usuelles, which remained in use in France up to 1840 in the reign of Louis Philippe. Meanwhile, the metre was adopted by the Republic of Geneva. After the joining of the canton of Geneva to Switzerland in 1815, Guillaume Henri Dufour published the first official Swiss map, for which the metre was adopted as the unit of length.

Adoption dates by country

• France: 1801–1812, then 1840
• Republic of Geneva, Switzerland: 1813
• Kingdom of the Netherlands: 1820
• Kingdom of Belgium: 1830
• Chile: 1848
• Kingdom of Sardinia, Italy: 1850
• Spain: 1852
• Portugal: 1852
• Colombia: 1853
• Ecuador: 1856
• Mexico: 1857
• Brazil: 1862
• Argentina: 1863
• Italy: 1863
• United States: 1866
• German Empire, Germany: 1872
• Austria, 1875
• Switzerland: 1877

SI prefixed forms of metre

Main article: Orders of magnitude (length)

SI prefixes can be used to denote decimal multiples and submultiples of the metre, as shown in the table below. Long distances are usually expressed in km, astronomical units (149.6 Gm), light-years (10 Pm), or parsecs (31 Pm), rather than in Mm, Gm, Tm, Pm, Em, Zm or Ym; "30 cm", "30 m", and "300 m" are more common than "3 dm", "3 dam", and "3 hm", respectively.

The terms micron and millimicron have been used instead of micrometre (μm) and nanometre (nm), respectively, but this practice is discouraged.

SI multiples of metre (m)

Submultiples			Multiples
Value	SI symbol	Name	Value	SI symbol	Name
10−1 m	dm	decimetre	101 m	dam	decametre
10−2 m	cm	centimetre	102 m	hm	hectometre
10−3 m	mm	millimetre	103 m	km	kilometre
10−6 m	μm	micrometre	106 m	Mm	megametre
10−9 m	nm	nanometre	109 m	Gm	gigametre
10−12 m	pm	picometre	1012 m	Tm	terametre
10−15 m	fm	femtometre	1015 m	Pm	petametre
10−18 m	am	attometre	1018 m	Em	exametre
10−21 m	zm	zeptometre	1021 m	Zm	zettametre
10−24 m	ym	yoctometre	1024 m	Ym	yottametre
10−27 m	rm	rontometre	1027 m	Rm	ronnametre
10−30 m	qm	quectometre	1030 m	Qm	quettametre

Equivalents in other units

Metric unit expressed in non-SI units					Non-SI unit expressed in metric units
1 metre	≈	1.0936	yard		1 yard	=	0.9144	metre
1 metre	≈	39.370	inches		1 inch	=	0.0254	metre
1 centimetre	≈		inch		1 inch	=	2.54	centimetres
1 millimetre	≈		inch		1 inch	=	25.4	millimetres
1 metre	=	1010	ångström		1 ångström	=	10−10	metre
1 nanometre	=	10	ångström		1 ångström	=	100	picometres

Within this table, "inch" and "yard" mean "international inch" and "international yard" respectively, though approximate conversions in the left column hold for both international and survey units.

"≈" means "is approximately equal to";

"=" means "is exactly equal to".

One metre is exactly equivalent to 5 000/127 inches and to 1 250/1 143 yards.

A simple mnemonic to assist with conversion is "three 3s": 1 metre is nearly equivalent to 3 feet 3+3⁄8 inches. This gives an overestimate of 0.125 mm.

The ancient Egyptian cubit was about 0.5 m (surviving rods are 523–529 mm). Scottish and English definitions of the ell (two cubits) were 941 mm (0.941 m) and 1143 mm (1.143 m) respectively. The ancient Parisian toise (fathom) was slightly shorter than 2 m and was standardised at exactly 2 m in the mesures usuelles system, such that 1 m was exactly 1⁄2 toise. The Russian verst was 1.0668 km. The Swedish mil was 10.688 km, but was changed to 10 km when Sweden converted to metric units.

See also

• ISO 1 – standard reference temperature for length measurements
• Metric prefix
• Vertical position

References

     Astin, A. V. & Karo, H. Arnold, (1959), Refinement of values for the yard and the pound, Washington DC: National Bureau of Standards, republished on  National Geodetic Survey web site and the Federal Register (Doc. 59–5442, Filed, 30 June 1959)

• Clarke, Alexander Ross; Helmert, Friedrich Robert (1911b). "Earth, Figure of the" . In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 8 (11th ed.). Cambridge University Press. pp. 801–813.

     Historical context of the SI: Meter. Retrieved 26 May 2010.

     National Institute of Standards and Technology. (27 June 2011). NIST-F1 Cesium Fountain Atomic Clock. Author.

     National Physical Laboratory. (25 March 2010). Iodine-Stabilised Lasers. Author.

     "Maintaining the SI unit of length". National Research Council Canada. 5 February 2010. Archived from the original on 4 December 2011.

     Republic of the Philippines. (2 December 1978). Batas Pambansa Blg. 8: An Act Defining the Metric System and its Units, Providing for its Implementation and for Other Purposes. Author.

     Republic of the Philippines. (10 October 1991). Republic Act No. 7160: The Local Government Code of the Philippines. Author.

      Supreme Court of the Philippines (Second Division). (20 January 2010). G.R. No. 185240. Author.

     Taylor, B.N. and Thompson, A. (Eds.). (2008a). The International System of Units (SI). United States version of the English text of the eighth edition (2006) of the International Bureau of Weights and Measures publication Le Système International d' Unités (SI) (Special Publication 330). Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 18 August 2008.

     Taylor, B.N. and Thompson, A. (2008b). Guide for the Use of the International System of Units (Special Publication 811). Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 23 August 2008.

     Turner, J. (deputy director of the National Institute of Standards and Technology). (16 May 2008). "Interpretation of the International System of Units (the Metric System of Measurement) for the United States". Federal Register Vol. 73, No. 96, p. 28432–28433.

     Zagar, B.G. (1999). Laser interferometer displacement sensors in J.G. Webster (ed.). The Measurement, Instrumentation, and Sensors Handbook. CRC Press. ISBN 0-8493-8347-1.

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