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The metre (or meter in American spelling; symbol: m) is the base unit of length in the International System of Units (SI).
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 circumference is approximately 40000 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 1/299792458 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 ΔνCs.
Spelling
Metre is the standard spelling of the metric unit for length in all English-speaking nations; the exceptions are 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) 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 μετρέω (metreo) (to measure, count or compare) and noun μέτρον (metron) (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 (metior, mensura), French (mètre, mesure), English and other languages. The Greek word is derived from the Proto-Indo-European root *meh₁- 'to measure'. The motto ΜΕΤΡΩ ΧΡΩ (metro chro) 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 mètre) in English began at least as early as 1797.
History of definition
Universal measure: the metre linked to the figure of the Earth
Scientific revolution began with Copernicus work. Galileo discovered gravitational acceleration explaining 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 metro cattolico 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.
Christiaan Huygens found out the centrifugal force which explained variations of gravitational acceleration depending on latitude. He also discovered that the seconds pendulum length was a means to measure gravitational acceleration. 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.
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. 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.
Early adoption of the metre as a scientific unit of length: the forerunners
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.
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 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.
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 rulers, and to compare 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 north from South Africa through Egypt would bring the course of a major meridian arc back to land where Eratosthenes had founded geodesy.
After Stuve 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 proposed a three-axis ellipsoid and demonstrated that several meridians had not the same length, confirming an hypothesis of Jean Le Rond d’Alembert. 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
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.
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 Association Géodesique réduite entre États neutre 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
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 the Mètre des Archives made of platinum. 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.
In the second half of the 19th century, the creation of the International Geodetic Association would mark the adoption of new scientific methods. The progress of metrology combined with those of gravimetry 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 the 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. 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 might also have 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".
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 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: Bureau International des Poids et Mesures) 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: Conférence Générale des Poids et Mesures), 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.
The comparison of the new prototypes of the metre with each other and with the Mètre des Archives 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 for physics in 1920.
Wavelength definition
In 1873, James Clerk Maxwell suggested that light emitted by an element be used as the standard both for the metre and for the second. These two quantities could then be used to define the unit of mass.
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 1650763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a 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 1/299792458 of a second.
This definition fixed the speed of light in vacuum at exactly 299792458 metres per second (≈300000 km/s 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, λHeNe, to be 632.99121258 nm with an estimated relative standard uncertainty (U) of 2.1×10.
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 = 5×10). Consequently, a realisation of the metre is usually delineated (not defined) today in labs as 1579800.762042(33) wavelengths of helium-neon laser light in a 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 1579800.762042(33) wavelengths of helium–neon laser light in a vacuum, and converting the wavelengths in a 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
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 10 per metre). In this case, the effects to be taken into account are those of special relativity only.
Timeline
Early adoptions of the metre internationally
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.
Metre 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,
- German Empire, Germany: 1872,
- Austria, 1875,
- Switzerland: 1877.
SI prefixed forms of metre
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.
Equivalents in other units
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.
"Three 3s" is a simple mnemonic to assist with conversion: 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
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