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Metre

This article is about the unit of length. For other uses of "metre" or "meter", seeMeter (disambiguation).

Themetre(ormeterinUS spelling;symbol:m) is thebase unitoflengthin theInternational 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 of⁠1/299792458⁠of asecond,where the second is defined by ahyperfine transition frequency of caesium.[2]

metre
Historical public metre standard in Paris
General information
Unit systemSI
Unit oflength
Symbolm[1]
Conversions
1 m[1]in...... is equal to...
SI units
Imperial/USunits
  • ≈ 1.0936yd
  • ≈ 3.2808ft
  • ≈ 39.37in
Nautical units≈ 0.00053996nmi

The metre was originally defined in 1791 by theFrench National Assemblyas one ten-millionth of the distance from theequatorto theNorth Polealong agreat circle,so theEarth's polar circumferenceis approximately40000km.

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 ofkrypton-86.The current definition was adopted in 1983 and modified slightly in 2002 to clarify that the metre is a measure ofproper length.From 1983 until 2019, the metre was formally defined as the length of the path travelled bylightin vacuum in⁠1/299792458⁠of asecond.After the2019 redefinition of the SI base units,this definition was rephrased to include the definition of a second in terms of the caesium frequencyΔνCs.This series of amendments did not alter the size of the metre significantly – today Earth's polar circumference measures40007.863 km,a change of 0.022% from the original value of exactly40000km,which also includes improvements in the accuracy of measuring the circumference.

Spelling

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

Metreis the standard spelling of the metric unit for length in nearly all English-speaking nations, the exceptions being the United States[3][4][5][6]and the Philippines[7]which usemeter.

Measuring devices (such asammeter,speedometer) are spelled "-meter" in all variants of English.[8]The suffix "-meter" has the same Greek origin as the unit of length.[9][10]

Etymology

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The etymological roots ofmetrecan be traced to the Greek verbμετρέω(metreo) ((I) measure, count or compare)[11]and nounμέτρον(metron) (a measure),[12]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 mottoΜΕΤΡΩ ΧΡΩ(metro chro) in the seal of theInternational Bureau of Weights and Measures(BIPM), which was a saying of the Greek statesman and philosopherPittacus of Mytileneand may be translated as "Use measure!", thus calls for both measurement and moderation[citation needed].The use of the wordmetre(for the French unitmètre) in English began at least as early as 1797.[13]

History of definition

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Main article:History of the metre

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

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The Meridian room of theParis Observatory(or Cassini room): theParis meridianis drawn on the ground.

Galileodiscoveredgravitational accelerationto explain the fall of bodies at the surface of the Earth.[14]He also observed the regularity of the period of swing of thependulumand that this period depended on the length of the pendulum.[15]

Kepler's laws of planetary motionserved both to the discovery ofNewton's law of universal gravitationand to the determination of the distance from Earth to the Sun byGiovanni Domenico Cassini.[16][17]They both also used a determination of the size of the Earth, then considered as a sphere, byJean PicardthroughtriangulationofParis meridian.[18][19]In 1671, Jean Picard also measured the length of aseconds pendulumatParis Observatoryand proposed this unit of measurement to be called the astronomical radius (French:Rayon Astronomique).[20][21]In 1675,Tito Livio Burattinisuggested the termmetro cattolicomeaning universal measure for this unit of length, but then it was discovered that the length of a seconds pendulum varies from place to place.[22][23][24][25]

Gravimeterwith variant ofRepsold–Bessel pendulum

Christiaan Huygensfound out thecentrifugal forcewhich explained variations of gravitational acceleration depending on latitude.[26][27]He also mathematically formulated the link between the length of thesimple pendulumand gravitational acceleration.[28]According toAlexis Clairaut,the study of variations in gravitational acceleration was a way to determine thefigure of the Earth,whose crucial parameter was theflatteningof theEarth ellipsoid.In the 18th century, in addition of its significance forcartography,geodesygrew in importance as a means of empirically demonstrating thetheory of gravity,whichÉmilie du Châteletpromoted in France in combination withLeibniz'smathematical work and because theradius of the Earthwas the unit to which all celestial distances were to be referred. Indeed, Earth proved to be anoblate spheroidthrough geodetic surveys inEcuadorandLaplandand this new data called into question the value ofEarth radiusas Picard had calculated it.[28][29][30][22][19]

After theAnglo-French Survey,theFrench Academy of Sciencescommissioned an expedition led byJean Baptiste Joseph DelambreandPierre Méchain,lasting from 1792 to 1798, which measured the distance between a belfry inDunkirkandMontjuïc castleinBarcelonaat thelongitudeof theParis Panthéon.When the length of the metre was defined as one ten-millionth of the distance from theNorth Poleto theEquator,the flattening of the Earth ellipsoid was assumed to be⁠1/334⁠.[31][32][19][33][34][35]

In 1841,Friedrich Wilhelm Besselusing themethod of least squarescalculated from severalarc measurementsa new value for the flattening of the Earth, which he determinated as⁠1/299.15⁠.[36][37][38]He also devised a new instrument for measuring gravitational acceleration which was first used inSwitzerlandbyEmile Plantamour,Charles Sanders Peirce,and Isaac-Charles Élisée Cellérier (8.01.1818 – 2.10.1889), aGenevanmathematician soon independently discovered a mathematical formula to correctsystematic errorsof this device which had been noticed by Plantamour andAdolphe Hirsch.[39][40]This allowedFriedrich Robert Helmertto determine a remarkably accurate value of⁠1/298.3⁠for the flattening of the Earth when he proposed hisellipsoid of referencein 1901.[41]This was also the result of theMetre Conventionof 1875, when the metre was adopted as an international scientific unit of length for the convenience of continental European geodesists following the example ofFerdinand Rudolph Hassler.[42][43][44][45][46][47]

Meridional definition

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In 1790, one year before it was ultimately decided that the metre would be based on theEarth quadrant(a quarter of theEarth's circumferencethrough its poles),Talleyrandproposed that the metre be the length of the seconds pendulum at alatitudeof 45°. This option, with one-third of this length defining thefoot,was also considered byThomas Jeffersonand others forredefining the yard in the United Statesshortly after gaining independence from theBritish Crown.[48][49]

Instead of the seconds pendulum method, the commission of the French Academy of Sciences – whose members includedBorda,Lagrange,Laplace,Monge,andCondorcet– decided that the new measure should be equal to one ten-millionth of the distance from theNorth Poleto theEquator,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.[50][51][52][53][35]

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 laterArago,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.[50][51][53][54][55]

In 1799, a commission includingJohan Georg Tralles,Jean Henri van Swinden,Adrien-Marie Legendreand Jean-Baptiste Delambre calculated the distance from Dunkirk to Barcelona using the data of thetriangulationbetween 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 theSpanish-French geodetic missionand a value of⁠1/334⁠was 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 theFrench 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.[56][19][50][53][57][58][59]

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

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Triangulation nearNew York City,1817

In 1816,Ferdinand Rudolph Hasslerwas appointed first Superintendent of theSurvey of the Coast.Trained in geodesy in Switzerland, France andGermany,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.[60][61][46]

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 theUnited Statesat that time and measuredcoefficients of expansionto assess temperature effects on the measurements.[62]

In 1832,Carl Friedrich Gaussstudied theEarth's magnetic fieldand proposed adding thesecondto the basic units of the metre and thekilogramin the form of theCGS system(centimetre,gram,second). In 1836, he founded the Magnetischer Verein, the first international scientific association, in collaboration withAlexander von HumboldtandWilhelm Edouard Weber.The coordination of the observation of geophysical phenomena such as the Earth's magnetic field,lightningand 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 ofJohann Jacob Baeyerin 1863, and by that of theInternational Meteorological Organisationwhose president, the Swiss meteorologist and physicist,Heinrich von Wildwould representRussiaat theInternational Committee for Weights and Measures(CIPM).[58][41][63][64][65][66]

In 1834, Hassler, measured atFire Islandthe firstbaselineof the Survey of the Coast, shortly beforeLouis Puissantdeclared to the French Academy of Sciences in 1836 that Jean Baptiste Joseph Delambre and Pierre Méchain had made errors in themeridian arc measurement,which had been used to determine the length of the metre. Errors in the method of calculating the length of theParis meridianwere taken into account by Bessel when he proposed hisreference ellipsoidin 1841.[67][68][69][37][38]

Ibáñez apparatus calibrated on the metric Spanish Standard and used atAarberg,incanton of Bern,Switzerland

Egyptian astronomyhas ancient roots which were revived in the 19th century by the modernist impetus ofMuhammad Aliwho founded in Sabtieh,Boulaqdistrict, inCairoan 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, thecadastrework inaugurated under Muhammad Ali. This Commission suggested to ViceroyMohammed Sa'id Pashathe idea of buying geodetic devices which were ordered in France. WhileMahmud Ahmad Hamdi al-Falakiwas in charge, in Egypt, of the direction of the work of the general map, the viceroy entrusted toIsmail Mustafa al-Falakithe study, in Europe, of the precision apparatus calibrated against the metre intended to measure the geodesic bases and already built byJean Brunnerin 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 byCarlos Ibáñez e Ibáñez de IberoandFrutos Saavedra Meneseswas 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 withBorda'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 theStruve Geodetic Arcwith an arc running northwards fromSouth AfricathroughEgyptwould bring the course of a majormeridian arcback to land whereEratostheneshad foundedgeodesy.[70][71][72][73][74]

West Europe–Africa Meridian-arc:a meridian arc extending from theShetland 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 eartha= 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 meridianis depicted rather thanParis meridian.

Seventeen years after Bessel calculated hisellipsoid 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 tovertical deflectionswas minimized in proportion to the length of the meridian arcs: the longer the meridian arcs, the more precise the image of theEarth ellipsoidwould be.[36]AfterStruve Geodetic Arcmeasurement, it was resolved in the 1860s, at the initiative ofCarlos Ibáñez e Ibáñez de Iberowho would become the first president of both theInternational Geodetic Associationand theInternational Committee for Weights and Measure,to remeasure the arc of meridian fromDunkirktoFormenteraand to extend it fromShetlandto theSahara.[75][76][77][74]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 thegeoidis a ball, which on the whole can be assimilated to an oblatespheroid,but which in detail differs from it so as to prohibit any generalization and any extrapolation from the measurement of a single meridian arc.[34]In 1859,Friedrich von Schubertdemonstrated that several meridians had not the same length, confirming an hypothesis ofJean Le Rond d'Alembert.He also proposed an ellipsoid with three unequal axes.[78][79]In 1860, Elie Ritter, a mathematician fromGeneva,using Schubert's data computed that the Earth ellipsoid could rather be a spheroid of revolution accordingly toAdrien-Marie Legendre's model.[80]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 byvertical deflections,in particular the latitude ofMontjuïcin the French meridian arc which determination had also been affected in a lesser proportion by systematic errors of therepeating circle.[81][82][34]

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 inBarcelona,Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation and that he did not dare to admit this inaccuracy.[83][84][54]This was later explained by clearance in the central axis of therepeating circlecausing wear and consequently thezenithmeasurements contained significant systematic errors.[82]Polar motionpredicted byLeonhard Eulerand later discovered bySeth Carlo Chandleralso had an impact on accuracy of latitudes' determinations.[85][28][86][87]Among all these sources of error, it was mainly an unfavourablevertical deflectionthat gave an inaccurate determination of Barcelona'slatitudeand a metre "too short" compared to a more general definition taken from the average of a large number of arcs.[34]

As early as 1861,Johann Jacob Baeyersent a memorandum to the King ofPrussiarecommending international collaboration inCentral Europewith 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(forPoland),United Kingdoms of Sweden and Norway,as well asSwitzerland.TheCentral European Arc Measurementcreated a Central Office, located at the Prussian Geodetic Institute, whose management was entrusted to Johann Jacob Baeyer.[88][87]

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 thegeoidby 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 ofPalermoandFreetown Christiana(Denmark) and the meridians ofBonnand Trunz (German name forMilejewoinPoland). 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 theAlps,in order to determine the influence of this mountain range onvertical deflection.Baeyer also planned to determine the curvature of the seas, theMediterranean SeaandAdriatic Seain the south, theNorth Seaand theBaltic Seain the north. In his mind, the cooperation of all the States ofCentral Europecould open the field to scientific research of the highest interest, research that each State, taken in isolation, was not able to undertake.[89][90]

SpainandPortugaljoined theEuropean Arc Measurementin 1866.French Empirehesitated 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 theFranco-Prussian War,thatCharles-Eugène DelaunayrepresentedFranceat the Congress ofViennain 1871. In 1874,Hervé Fayewas appointed member of the Permanent Commission which was presided by Carlos Ibáñez e Ibáñez de Ibero.[68][91][77][47]

The International Geodetic Association gained global importance with the accession ofChile,MexicoandJapanin 1888;ArgentinaandUnited-Statesin 1889; andBritish Empirein 1898. The convention of the International Geodetic Association expired at the end of 1916. It was not renewed due to theFirst World War.However, the activities of theInternational Latitude Servicewere continued through anAssociation Géodesique réduite entre États neutrethanks to the efforts ofH.G. van de Sande Bakhuyzenand Raoul Gautier (1854–1931), respectively directors ofLeiden ObservatoryandGeneva Observatory.[74][87]

International prototype metre bar

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Closeup of National Prototype Metre Bar No. 27, made in 1889 by the International Bureau of Weights and Measures (BIPM) in collaboration withJohnson Matteyand given to the United States, which served as the standard for American cartography from 1890 replacing the Committee Meter, an authentic copy of theMètre des Archivesproduced in 1799 in Paris, whichFerdinand Rudolph Hasslerhad brought to the United States in 1805

After theFrench Revolution,Napoleonic Warsled to the adoption of the metre inLatin AmericafollowingindependenceofBrazilandHispanic America,while theAmerican Revolutionprompted the foundation of theSurvey of the Coastin 1807 and the creation of theOffice of Standard Weights and Measuresin 1830. Incontinental Europe,Napoleonic Wars fostered German nationalism which later led tounification of Germanyin 1871. Meanwhile, most European countries had adopted the metre. In the 1870s,German Empireplayed a pivotal role in the unification of the metric system through theEuropean Arc Measurementbut its overwhelming influence was mitigated by that of neutral states. While the German astronomerWilhelm Julius Foerster,director of theBerlin Observatoryand 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 permanentInternational Bureau of Weights and Measures,the German born, Swiss astronomer,Adolphe Hirschconformed 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 theConservatoire national des Arts et Métiers.[90][65][92]

At that time,units of measurementwere defined by primarystandards,and unique artifacts made of differentalloyswith distinct coefficients ofexpansionwere the legal basis of units of length. A wrought iron ruler, the Toise of Peru, also calledToise 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 byÉtienne Lenoirin 1799. One of them became known as theCommittee Meterin the United States and served as standard of length in theUnited States Coast Surveyuntil 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 inPrussiaand inFrance.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 takethermal expansioninto account without measuring the temperature. A French scientific instrument maker,Jean Nicolas Fortin,had made three direct copies of the Toise of Peru, one forFriedrich Georg Wilhelm von Struve,a second forHeinrich Christian Schumacherin 1821 and a third for Friedrich Bessel in 1823. In 1831,Henri-Prudence Gambeyalso realized a copy of the Toise of Peru which was kept atAltona Observatory.[93][94][66][56][95][96][37][46][42]

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 theInternational Geodetic Associationwould mark the adoption of new scientific methods.[97]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 theelectrical telegraph.Furthermore, advances inmetrologycombined with those ofgravimetryhave led to a new era ofgeodesy.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 thegravitational accelerationby means of pendulum.[98][56]

In 1866, the most important concern was that the Toise of Peru, the standard of the toise constructed in 1735 for theFrench 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 toAltonaandKoenigsbergObservatories, which he had compared to each other about 1840. This assertion was particularly worrying, because when the primary Imperialyardstandard 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. NeverthelessFerdinand 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 theMetric Act of 1866allowing 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 theEuropean Arc Measurement(German:Europäische Gradmessung) to establish a "European international bureau for weights and measures".[93][99][47][90][56][100][101][102][103]

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.[104][105][106]According to a preliminary proposal made inNeuchâtelthe 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 theInternational Bureau of Weights and Measures.[107][104][106][108][109]

Hassler's metrological and geodetic work also had a favourable response in Russia.[62][61]In 1869, theSaint Petersburg Academy of Sciencessent to the French Academy of Sciences a report drafted byOtto Wilhelm von Struve,Heinrich von WildandMoritz 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 themetric systemin all scientific work.[102][22]

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 theParis Conferencein 1875,Carlos Ibáñez e Ibáñez de Iberointervened with theFrench Academy of Sciencesto 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 themetric systemaccording to the progress of sciences.[110][43][66][111]

TheMetre 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 inSèvres,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 firstGeneral Conference on Weights and Measures(CGPM:Conférence Générale des Poids et Mesures), establishing theInternational Prototype Metreas the distance between two lines on a standard bar composed of an alloy of 90%platinumand 10%iridium,measured at the melting point of ice.[110]

Metrology and paradigm shift in physics

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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'sthermometrywork led to the discovery of special alloys of iron–nickel, in particularinvar,whose practically negligible coefficient of expansion made it possible to develop simpler baseline measurement methods, and for which its director, the Swiss physicistCharles-Edouard Guillaume,was granted theNobel Prize in Physicsin 1920. Guillaume's Nobel Prize marked the end of an era in whichmetrologywas leaving the field ofgeodesyto become atechnologicalapplication ofphysics.[112][113][114]

In 1921, the Nobel Prize in Physics was awarded to another Swiss scientist,Albert Einstein,who followingMichelson–Morley experimenthad questioned theluminiferous aetherin 1905, just asNewtonhad questionedDescartes' Vortex theoryin 1687 afterJean Richer's pendulum experiment inCayenne,French Guiana.[115][116][18][22]

Furthermore,special relativitychanged conceptions oftimeandmass,whilegeneral relativitychanged that ofspace.According to Newton, space wasEuclidean,infinite and without boundaries and bodies gravitated around each other without changing the structure of space.Einstein's theory of gravitystates, 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.[117]

Wavelength definition

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In 1873,James Clerk Maxwellsuggested 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.[118]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 thesolar spectrum.Albert Michelson soon took up the idea and improved it.[103][119]

In 1893, the standard metre was first measured with aninterferometerbyAlbert A. Michelson,the inventor of the device and an advocate of using some particularwavelengthoflightas a standard of length. By 1925,interferometrywas 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 newInternational System of Units(SI) as equal to1650763.73wavelengthsof theorange-redemission linein theelectromagnetic spectrumof thekrypton-86atominvacuum.[120]

Speed of light definition

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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 thesecondand thespeed of light:[121][122]

The metre is the length of the path travelled by light in vacuum during a time interval of1/299792458of a second.

This definition fixed the speed of light invacuumat exactly299792458metres per second[121](≈300000km/sor ≈1.079 billion km/hour[123]). 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-stabilisedhelium–neon laser"a recommended radiation" for realising the metre.[124]For the purpose of delineating the metre, the BIPM currently considers the HeNe laser wavelength,λHeNe,to be632.99121258nmwith an estimated relative standard uncertainty (U) of2.1×10−11.[124][125][126]

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 fountainatomic clock(U=5×10−16).[127]Consequently, a realisation of the metre is usually delineated (not defined) today in labs as1579800.762042(33)wavelengths of helium–neon laser light in vacuum, the error stated being only that of frequency determination.[124]This bracket notation expressing the error is explained in the article onmeasurement 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.[128]A commonly used medium is air, and theNational Institute of Standards and Technology(NIST) has set up an online calculator to convert wavelengths in vacuum to wavelengths in air.[129]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.[130]

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 as1579800.762042(33)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 anypartial vacuumcan be used, or some inert atmosphere like helium gas, provided the appropriate corrections for refractive index are implemented.[131]

The metre isdefinedas 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,[134]and converting the selected unit of wavelength to metres. Three major factors limit the accuracy attainable with laserinterferometersfor a length measurement:[128][135]

  • uncertainty in vacuum wavelength of the source,
  • uncertainty in the refractive index of the medium,
  • least countresolution 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 wavelengthλto metres usingc,the speed of light in vacuum in m/s. Herenis therefractive indexof the medium in which the measurement is made, andfis 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.[135]

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 in1016per metre). In this case, the effects to be taken into account are those of special relativity only.

Timeline

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Date Deciding body Decision
8 May 1790 French National Assembly The length of the new metre to be equal to the length of apendulumwith a half-periodof 1second.[50]
30 Mar 1791 French National Assembly Accepts the proposal by theFrench Academy of Sciencesthat the new definition for the metre be equal to one ten-millionth of the length of a great circlequadrantalong the Earth'smeridianthrough Paris, that is the distance from the equator to the north pole along that quadrant.[136]
1795 Provisional metre bar made of brass and based onParis meridanarc (French:Méridienne de France) measured byNicolas-Louis de LacaillleandCesar-François Cassini de Thury,legally equal to 443.44linesof thetoise du Pérou(a standardFrench unit of lengthfrom 1766).[50][19][137][138][The line was 1/864 of atoise.]
10 Dec 1799 French National Assembly Specifies the platinum metre bar, presented on 22 June 1799 and deposited in theNational Archives,as the final standard. Legally equal to 443.296 lines on thetoise du Pérou.[138]
24–28 Sept 1889 1stGeneral Conference on Weights and Measures(CGPM) Defines the metre as the distance between two lines on a standard bar of an alloy ofplatinumwith 10%iridium,measured at the melting point of ice.[138][139]
27 Sept – 6 Oct 1927 7th CGPM Redefines the metre as the distance, at 0°C(273K), between the axes of the two central lines marked on the prototype bar of platinum–iridium, this bar being subject to one standardatmosphere of pressureand 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.[140]
14 Oct 1960 11th CGPM Defines the metre as1650763.73wavelengthsinvacuumof theradiationcorresponding to the transition between the 2p10and 5d5quantum levels of thekrypton-86atom.[141]
21 Oct 1983 17th CGPM Defines the metre as the length of the path travelled bylightin vacuum during a time interval of⁠1/299 792 458⁠of asecond.[142][143]
2002 International Committee for Weights and Measures(CIPM) Considers the metre to be a unit ofproper lengthand thus recommends this definition be restricted to "lengths ℓ which are sufficiently short for the effects predicted bygeneral relativityto be negligible with respect to the uncertainties of realisation ".[144]
Definitions of the metre since 1795[145]
Basis of definition Date Absolute
uncertainty 		Relative
uncertainty
⁠1/10000000⁠part of thequadrantalong themeridian,measurement byDelambreandMéchain(443.296 lines) 1795 500–100 μm 10−4
First prototypeMètre des Archivesplatinum bar standard 1799 50–10 μm 10−5
Platinum–iridium bar at melting point of ice (1stCGPM) 1889 0.2–0.1 μm 10−7
Platinum–iridium bar at melting point of ice, atmospheric pressure, supported by two rollers (7th CGPM) 1927 n.a. n.a.
Hyperfineatomic transition;1650763.73wavelengths of light from a specified transition inkrypton-86(11th CGPM) 1960 4 nm 4×10−9[146]
Length of the path travelled by light in vacuum in⁠1/299792458⁠second (17th CGPM) 1983 0.1 nm 10−10

Early adoptions of the metre internationally

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Main article:Metrication

In France, the metre was adopted as an exclusive measure in 1801 under theConsulate.This continued under theFirst French Empireuntil 1812, whenNapoleondecreed the introduction of the non-decimalmesures usuelles,which remained in use in France up to 1840 in the reign ofLouis Philippe.[50]Meanwhile, the metre was adopted by the Republic of Geneva.[147]After the joining of thecanton of GenevatoSwitzerlandin 1815,Guillaume Henri Dufourpublished the first official Swiss map, for which the metre was adopted as the unit of length.[148][149]

Adoption dates by country

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SI prefixed forms of metre

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Main article:Orders of magnitude (length)

SI prefixescan 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), orparsecs(31 Pm), rather than in Mm or larger multiples; "30 cm", "30 m", and "300 m" are more common than "3 dm", "3 dam", and "3 hm", respectively.

The termsmicronandmillimicronhave been used instead ofmicrometre(μm) andnanometre(nm), respectively, but this practice is discouraged.[151]


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

Equivalents in other units

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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
1centimetre ≈ 0.39370 inch 1 inch = 2.54 centimetres
1millimetre ≈ 0.039370 inch 1 inch = 25.4 millimetres
1 metre = 1010 ångström 1 ångström = 10−10 metre
1nanometre = 10 ångström 1 ångström = 100 picometres

Within this table, "inch" and "yard" mean "international inch" and "international yard"[152]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 to⁠5 000/127⁠inches and to⁠1 250/1 143⁠yards.

A simplemnemonicto assist with conversion is "three 3s": 1 metre is nearly equivalent to 3feet3+3⁄8inches. This gives an overestimate of 0.125 mm.

The ancient Egyptiancubitwas about 0.5 m (surviving rods are 523–529 mm).[153]Scottish and English definitions of theell(2 cubits) were 941 mm (0.941 m) and 1143 mm (1.143 m) respectively.[154][155]The ancient Parisiantoise(fathom) was slightly shorter than 2 m and was standardised at exactly 2 m in themesures usuellessystem, such that 1 m was exactly1⁄2toise.[156]The Russianverstwas 1.0668 km.[157]TheSwedish milwas 10.688 km, but was changed to 10 km when Sweden converted to metric units.[158]

See also

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Wikimedia Commons has media related toMetre.
Look upmetrein Wiktionary, the free dictionary.

Notes

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  1. ^ "Base unit definitions: Meter".National Institute of Standards and Technology.Retrieved28 September2010.
  2. ^ International Bureau of Weights and Measures(20 May 2019),The International System of Units (SI)(PDF)(9th ed.),ISBN978-92-822-2272-0,archivedfrom the original on 18 October 2021
  3. ^ "The International System of Units (SI) – NIST"(PDF).US:National Institute of Standards and Technology.26 March 2008.The spelling of English words is in accordance with the United States Government Printing Office Style Manual, which follows Webster's Third New International Dictionary rather than the Oxford Dictionary. Thus the spellings 'meter', 'liter', 'deka', and 'cesium' are used rather than 'metre', 'litre', 'deca', and 'caesium' as in the original BIPM English text.
  4. ^The most recent official brochure about the International System of Units (SI), written in French by theBureau international des poids et mesures,International Bureau of Weights and Measures(BIPM) uses the spellingmetre;an English translation, included to make the SI standard more widely accessible also uses the spellingmetre(BIPM, 2006,p. 130ff). However, in 2008 the U.S. English translation published by the U.S.National Institute of Standards and Technology(NIST) chose to use the spellingmeterin accordance with the United States Government Printing Office Style Manual. The Metric Conversion Act of 1975 gives the Secretary of Commerce of the US the responsibility of interpreting or modifying the SI for use in the US. The Secretary of Commerce delegated this authority to the Director of the National Institute of Standards and Technology (Turner). In 2008, NIST published the US version (Taylor and Thompson, 2008a) of the English text of the eighth edition of the BIPM publicationLe Système international d'unités(SI)(BIPM, 2006). In the NIST publication, the spellings "meter", "liter" and "deka" are used rather than "metre", "litre" and "deca" as in the original BIPM English text (Taylor and Thompson (2008a), p. iii). The Director of the NIST officially recognised this publication, together withTaylor and Thompson (2008b),as the "legal interpretation" of the SI for the United States (Turner). Thus, the spellingmetreis referred to as the "international spelling"; the spellingmeter,as the "American spelling".
  5. ^ Naughtin, Pat (2008)."Spelling metre or meter"(PDF).Metrication Matters.Archived from the original on 11 October 2016.Retrieved12 March2017.{{cite web}}:CS1 maint: unfit URL (link)
  6. ^"Meter vs. metre".Grammarist.21 February 2011.Retrieved12 March2017.
  7. ^The Philippines usesEnglishas an official language and this largely follows American English since the country became a colony of the United States. While the law that converted the country to use themetric systemusesmetre(Batas Pambansa Blg. 8) following the SI spelling, in actual practice,meteris used in government and everyday commerce, as evidenced by laws (kilometer,Republic Act No. 7160), Supreme Court decisions (meter,G.R. No. 185240), and national standards (centimeter,PNS/BAFS 181:2016).
  8. ^Cambridge Advanced Learner's Dictionary.Cambridge University Press.2008.Retrieved19 September2012.[permanent dead link],s.v. ammeter, meter, parking meter, speedometer.
  9. ^ American Heritage Dictionary of the English Language(3rd ed.). Boston:Houghton Mifflin.1992.,s.v. meter.
  10. ^ "-meter – definition of -meter in English".Oxford Dictionaries. Archived fromthe originalon 26 April 2017.
  11. ^μετρέω.Liddell, Henry George;Scott, Robert;A Greek–English Lexiconat thePerseus Project.
  12. ^μέτρονinLiddellandScott.
  13. ^Oxford English Dictionary,Clarendon Press 2nd ed. 1989, vol. IX p. 697 col. 3.
  14. ^"Museo Galileo - In depth - Gravitational acceleration".catalogue.museogalileo.it.Retrieved29 December2023.
  15. ^"Museo Galileo - In depth - Pendulum".catalogue.museogalileo.it.Retrieved29 December2023.
  16. ^"M13. From Kepler's Laws To Universal Gravitation – Basic Physics".Archived fromthe originalon 30 December 2023.Retrieved30 December2023.
  17. ^ Bond, Peter (2014).L'exploration du système solaire.Dupont-Bloch, Nicolas. ([Édition française revue et corrigée] ed.). Louvain-la-Neuve: De Boeck. pp. 5–6.ISBN9782804184964.OCLC894499177.
  18. ^ab"Lettres philosophiques/Lettre 15 - Wikisource".fr.wikisource.org(in French).Retrieved7 October2023.
  19. ^abcdeLevallois, Jean-Jacques (1986)."La Vie des sciences".Gallica(in French). pp. 262, 285, 288–290, 269, 276–277, 283.Retrieved13 May2019.
  20. ^Picard, Jean (1620–1682) Auteur du texte (1671).Mesure de la terre [par l'abbé Picard].pp. 3–5.{{cite book}}:CS1 maint: numeric names: authors list (link)
  21. ^Bigourdan 1901,pp. 8, 158–159.
  22. ^abcd "Earth, Figure of the".Encyclopædia Britannica.Vol. 8 (11th ed.). 1911. pp. 801–813.
  23. ^Poynting, John Henry; Thomson, Joseph John (1907).A Textbook of Physics.C. Griffin. pp.20.
  24. ^"Science. 1791, l'adoption révolutionnaire du mètre".humanite.fr(in French). 25 March 2021.Retrieved3 August2021.
  25. ^Lucendo, Jorge (23 April 2020).Centuries of Inventions: Encyclopedia and History of Inventions.Jorge Lucendo. p. 246.Retrieved2 August2021.
  26. ^Silas, Walter (30 October 2022)."Centrifugal force Vs centripetal force".Probing the Universe.Retrieved30 December2023.[permanent dead link]
  27. ^"Gravity: Notes: Latitude Dependent Changes in Gravitational Acceleration".pburnley.faculty.unlv.edu.Retrieved30 December2023.
  28. ^abc Perrier, Général (1935)."Historique Sommaire De La Geodesie".Thalès.2:117–129, p. 128.ISSN0398-7817.JSTOR43861533.
  29. ^ Badinter, Élisabeth (2018).Les passions intellectuelles.Normandie roto impr. Paris: Robert Laffont.ISBN978-2-221-20345-3.OCLC1061216207.
  30. ^ Touzery, Mireille (3 July 2008)."Émilie Du Châtelet, un passeur scientifique au XVIIIe siècle".La revue pour l'histoire du CNRS(in French) (21).doi:10.4000/histoire-cnrs.7752.ISSN1298-9800.
  31. ^Capderou, Michel (31 October 2011).Satellites: de Kepler au GPS(in French). Springer Science & Business Media. p. 46.ISBN978-2-287-99049-6.
  32. ^Ramani, Madhvi."How France created the metric system".www.bbc.com.Retrieved21 May2019.
  33. ^Jean-Jacques Levallois, La méridienne de Dunkerque à Barcelone et la détermination du mètre (1792 – 1799), Vermessung, Photogrammetrie, Kulturtechnik, 89 (1991), 375-380.
  34. ^abcdZuerich, ETH-Bibliothek (1991)."La méridienne de Dunkerque à Barcelone et la déterminiation du mètre (1972-1799)".Vermessung, Photogrammetrie, Kulturtechnik: VPK = Mensuration, Photogrammétrie, Génie Rural(in French).89(7): 377–378.doi:10.5169/seals-234595.Retrieved12 October2021.
  35. ^abMartin, Jean-Pierre; McConnell, Anita (20 December 2008)."Joining the observatories of Paris and Greenwich".Notes and Records of the Royal Society.62(4): 355–372.doi:10.1098/rsnr.2008.0029.ISSN0035-9149.S2CID143514819.
  36. ^abvon Struve, Friedrich Georg Wilhelm (July 1857)."Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels".Gallica.pp. 509, 510.Retrieved30 August2021.
  37. ^abcViik, T (2006). "F. W. Bessel and geodesy".Struve Geodetic Arc, 2006 International Conference, The Struve Arc and Extensions in Space and Time, Haparanda and Pajala, Sweden, 13–15 August 2006.pp. 10, 6.CiteSeerX10.1.1.517.9501.
  38. ^abBessel, Friedrich Wilhelm (1 December 1841)."Über einen Fehler in der Berechnung der französischen Gradmessung und seineh Einfluß auf die Bestimmung der Figur der Erde. Von Herrn Geh. Rath und Ritter Bessel".Astronomische Nachrichten.19(7): 97.Bibcode:1841AN.....19...97B.doi:10.1002/asna.18420190702.ISSN0004-6337.
  39. ^This article incorporates text from this source, which is in thepublic domain:Ibáñez e Ibáñez de Ibero, Carlos (1881).Discursos leidos ante la Real Academia de Ciencias Exactas Fisicas y Naturales en la recepcion pública de Don Joaquin Barraquer y Rovira(PDF).Madrid: Imprenta de la Viuda e Hijo de D.E. Aguado. pp. 70–78.
  40. ^"Rapport de M. Faye sur un Mémoire de M. Peirce concernant la constance de la pesanteur à Paris et les corrections exigées par les anciennes déterminations de Borda et de Biot".Comptes rendus hebdomadaires des séances de l'Académie des sciences.90:1463–1466. 1880.Retrieved10 October2018– viaGallica.
  41. ^abEncyclopedia Universalis.Encyclopedia Universalis. 1996. pp. 320, 370. Vol 10.ISBN978-2-85229-290-1.OCLC36747385.
  42. ^abBrunner, Jean (1 January 1857)."Appareil construit pour les opérations au moyen desquelles on prolongera dans toute l'étendue de l'Espagne le réseau trigonométrique qui couvre la France in Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels".Gallica(in French). pp. 150–153.Retrieved31 August2023.
  43. ^abPérard, Albert (1957)."Carlos Ibáñez e Ibáñez de Ibero (14 avril 1825 – 29 janvier 1891), par Albert Pérard (inauguration d'un monument élevé à sa mémoire)"(PDF).Institut de France – Académie des sciences.pp. 26–28.
  44. ^Adolphe Hirsch,Le général Ibáñez notice nécrologique lue au comité international des poids et mesures, le 12 septembre et dans la conférence géodésique de Florence, le 8 octobre 1891,Neuchâtel, imprimerie Attinger frères.
  45. ^Wolf, Rudolf (1 January 1891)."Histoire de l'appareil Ibañez-Brunner in Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels".Gallica(in French). pp. 370–371.Retrieved31 August2023.
  46. ^abcClarke, Alexander Ross (1873), "XIII. Results of the comparisons of the standards of length of England, Austria, Spain, United States, Cape of Good Hope, and of a second Russian standard, made at the Ordnance Survey Office, Southampton. With a preface and notes on the Greek and Egyptian measures of length by Sir Henry James",Philosophical Transactions,vol. 163, London, p. 463,doi:10.1098/rstl.1873.0014
  47. ^abcBericht über die Verhandlungen der vom 30. September bis 7. October 1867 zu BERLIN abgehaltenen allgemeinen Conferenz der Europäischen Gradmessung(PDF)(in German). Berlin: Central-Bureau der Europäischen Gradmessung. 1868. pp. 123–134.
  48. ^"The seconds pendulum".www.roma1.infn.it.Retrieved6 October2023.
  49. ^Cochrane, Rexmond (1966)."Appendix B: The metric system in the United States".Measures for progress: a history of the National Bureau of Standards.U.S. Department of Commerce.p. 532. Archived fromthe originalon 27 April 2011.Retrieved5 March2011.
  50. ^abcdefgLarousse, Pierre (1866–1877).Grand dictionnaire universel du XIXe siècle: français, historique, géographique, mythologique, bibliographique.... T. 11 MEMO-O / par M. Pierre Larousse.p. 163.
  51. ^ab"L'histoire des unités | Réseau National de la Métrologie Française".metrologie-francaise.lne.fr.Retrieved6 October2023.
  52. ^Biot, Jean-Baptiste (1774–1862) Auteur du texte; Arago, François (1786-1853) Auteur du texte (1821).Recueil d'observations géodésiques, astronomiques et physiques, exécutées par ordre du Bureau des longitudes de France en Espagne, en France, en Angleterre et en Écosse, pour déterminer la variation de la pesanteur et des degrés terrestres sur le prolongement du méridien de Paris... rédigé par MM. Biot et Arago,...pp. viii–ix.{{cite book}}:CS1 maint: numeric names: authors list (link)
  53. ^abcSuzanne, Débarbat."Fixation de la longueur définitive du mètre".FranceArchives(in French).Retrieved6 October2023.
  54. ^abDelambre, Jean-Baptiste (1749–1822) Auteur du texte (1912).Grandeur et figure de la terre / J.-B.-J. Delambre; ouvrage augmenté de notes, de cartes et publié par les soins de G. Bigourdan,...pp. 202–203, 2015, 141–142, 178.{{cite book}}:CS1 maint: numeric names: authors list (link)
  55. ^"Comprendre – Histoire de l'observatoire de Paris - Pierre-François-André Méchain".promenade.imcce.fr.Retrieved15 October2023.
  56. ^abcdClarke, Alexander Ross; James, Henry (1 January 1867)."X. Abstract of the results of the comparisons of the standards of length of England, France, Belgium, Prussia, Russia, India, Australia, made at the ordnance Survey Office, Southampton".Philosophical Transactions of the Royal Society of London.157:174.doi:10.1098/rstl.1867.0010.S2CID109333769.
  57. ^"Histoire du mètre | Métrologie".metrologie.entreprises.gouv.fr.Retrieved6 October2023.
  58. ^abDébarbat, Suzanne; Quinn, Terry (1 January 2019)."Les origines du système métrique en France et la Convention du mètre de 1875, qui a ouvert la voie au Système international d'unités et à sa révision de 2018".Comptes Rendus Physique.The new International System of Units / Le nouveau Système international d’unités.20(1): 6–21.Bibcode:2019CRPhy..20....6D.doi:10.1016/j.crhy.2018.12.002.ISSN1631-0705.S2CID126724939.
  59. ^Delambre, Jean-Baptiste (1749–1822) Auteur du texte; Méchain, Pierre (1744–1804) Auteur du texte (1806–1810).Base du système métrique décimal, ou Mesure de l'arc du méridien compris entre les parallèles de Dunkerque et Barcelone. T. 1 /, exécutée en 1792 et années suivantes, par MM. Méchain et Delambre, rédigée par M. Delambre,...pp. 93–94, 10.{{cite book}}:CS1 maint: numeric names: authors list (link)
  60. ^American Philosophical Society.; Society, American Philosophical; Poupard, James (1825).Transactions of the American Philosophical Society.Vol. new ser.:v.2 (1825). Philadelphia [etc.] pp. 234–278.
  61. ^abCajori, Florian (1921)."Swiss Geodesy and the United States Coast Survey".The Scientific Monthly.13(2): 117–129.Bibcode:1921SciMo..13..117C.ISSN0096-3771.
  62. ^abParr, Albert C. (1 April 2006)."A Tale About the First Weights and Measures Intercomparison in the United States in 1832".Journal of Research of the National Institute of Standards and Technology.111(1): 31–32, 36.doi:10.6028/jres.111.003.PMC4654608.PMID27274915– via NIST.
  63. ^"History of IMO".public.wmo.int.8 December 2015. Archived fromthe originalon 18 December 2023.Retrieved7 October2023.
  64. ^"Wild, Heinrich".hls-dhs-dss.ch(in German).Retrieved7 October2023.
  65. ^abHeinrich VON WILD (1833–1902)in COMlTÉ INTERNATIONAL DES POIDS ET MESURES. PROCÈS-VERBAUX DES SÉANCES. DEUXIÈME SÉRIE. TOME II. SESSION DE 1903. pp. 5–7.
  66. ^abcQuinn, T. J. (2012).From artefacts to atoms: the BIPM and the search for ultimate measurement standards.Oxford. pp. 20, 37–38, 91–92, 70–72, 114–117, 144–147, 8.ISBN978-0-19-990991-9.OCLC861693071.{{cite book}}:CS1 maint: location missing publisher (link)
  67. ^Hassler, Harriet; Burroughs, Charles A. (2007).Ferdinand Rudolph Hassler (1770–1843).NIST Research Library. pp. 51–52.
  68. ^abLebon, Ernest (1846–1922) Auteur du texte (1899).Histoire abrégée de l'astronomie / par Ernest Lebon,...pp. 168–171.{{cite book}}:CS1 maint: numeric names: authors list (link)
  69. ^Puissant, Louis (1769–1843) Auteur du texte.Nouvelle détermination de la distance méridienne de Montjouy à Formentera, dévoilant l'inexactitude de celle dont il est fait mention dans la base du système métrique décimal, par M. Puissant,... lu à l'Académie des sciences, le 2 mai 1836.{{cite book}}:CS1 maint: numeric names: authors list (link)
  70. ^Jamʻīyah al-Jughrāfīyah al-Miṣrīyah (1876).Bulletin de la Société de géographie d'Égypte.University of Michigan. [Le Caire]. pp. 6–16.
  71. ^texte, Ismāʿīl-Afandī Muṣṭafá (1825–1901) Auteur du (1886).Notes biographiques de S. E. Mahmoud Pacha el Falaki (l'astronome), par Ismail-Bey Moustapha et le colonel Moktar-Bey.pp. 10–11.{{cite book}}:CS1 maint: numeric names: authors list (link)
  72. ^texte, Ismāʿīl-Afandī Muṣṭafá (1825-1901) Auteur du (1864).Recherche des coefficients de dilatation et étalonnage de l'appareil à mesurer les bases géodésiques appartenant au gouvernement égyptien / par Ismaïl-Effendi-Moustapha,...{{cite book}}:CS1 maint: numeric names: authors list (link)
  73. ^"Nomination of the STRUVE GEODETIC ARC for inscription on the WORLD HERITAGE LIST"(PDF).pp. 40, 143–144.
  74. ^abcSoler, T. (1 February 1997)."A profile of General Carlos Ibáñez e Ibáñez de Ibero: first president of the International Geodetic Association".Journal of Geodesy.71(3): 176–188.Bibcode:1997JGeod..71..176S.CiteSeerX10.1.1.492.3967.doi:10.1007/s001900050086.ISSN1432-1394.S2CID119447198.
  75. ^J. M. López de Azcona, "Ibáñez e Ibáñez de Ibero, Carlos",Dictionary of Scientific Biography,vol. VII, 1–2, Scribner's, New York, 1981.
  76. ^commission, Internationale Erdmessung Permanente (1892).Comptes-rendus des séances de la Commission permanente de l'Association géodésique internationale réunie à Florence du 8 au 17 octobre 1891(in French). De Gruyter, Incorporated. pp. 23–25, 100–109.ISBN978-3-11-128691-4.
  77. ^ab"El General Ibáñez e Ibáñez de Ibero, Marqués de Mulhacén".
  78. ^Historische Commission bei der königl. Akademie der Wissenschaften (1908),"Schubert, Theodor von",Allgemeine Deutsche Biographie, Bd. 54,Allgemeine Deutsche Biographie (1. ed.), München/Leipzig: Duncker & Humblot, p. 231,retrieved1 October2023
  79. ^D'Alembert, Jean Le Rond."Figure de la Terre, in Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, par une Société de Gens de lettres".artflsrv04.uchicago.edu.Retrieved1 October2023.
  80. ^Société de physique et d'histoire naturelle de Genève.; Genève, Société de physique et d'histoire naturelle de (1859).Memoires de la Société de physique et d'histoire naturelle de Genève.Vol. 15. Geneve: Georg [etc.] pp. 441–444, 484–485.
  81. ^Société de physique et d'histoire naturelle de Genève.; Genève, Société de physique et d'histoire naturelle de (1861).Memoires de la Société de physique et d'histoire naturelle de Genève.Vol. 16. Geneve: Georg [etc.] pp. 165–196.
  82. ^abMartina Schiavon. La geodesia y la investigación científica en la Francia del siglo XIX: la medida del arco de meridiano franco-argelino (1870–1895).Revista Colombiana de Sociología,2004, Estudios sociales de la ciencia y la tecnologia, 23, pp. 11–30.
  83. ^"c à Paris; vitesse de la lumière..."expositions.obspm.fr.Retrieved12 October2021.
  84. ^Jouffroy, Achille de (1785-1859) Auteur du texte (1852–1853).Dictionnaire des inventions et découvertes anciennes et modernes, dans les sciences, les arts et l'industrie.... 2. H–Z / recueillis et mis en ordre par M. le marquis de Jouffroy; publié par l'abbé Migne,...p. 419.{{cite book}}:CS1 maint: numeric names: authors list (link)
  85. ^Yokoyama, Koichi; Manabe, Seiji; Sakai, Satoshi (2000)."History of the International Polar Motion Service/International Latitude Service".International Astronomical Union Colloquium.178:147–162.doi:10.1017/S0252921100061285.ISSN0252-9211.
  86. ^"Polar motion | Earth's axis, wobble, precession | Britannica".www.britannica.com.Retrieved27 August2023.
  87. ^abcTorge, Wolfgang (2016). Rizos, Chris; Willis, Pascal (eds.)."From a Regional Project to an International Organization: The" Baeyer-Helmert-Era "of the International Association of Geodesy 1862–1916".IAG 150 Years.International Association of Geodesy Symposia.143.Cham: Springer International Publishing: 3–18.doi:10.1007/1345_2015_42.ISBN978-3-319-30895-1.
  88. ^Levallois, J. J. (1 September 1980)."Notice historique".Bulletin géodésique(in French).54(3): 248–313.Bibcode:1980BGeod..54..248L.doi:10.1007/BF02521470.ISSN1432-1394.S2CID198204435.
  89. ^Zuerich, ETH-Bibliothek (1892)."Exposé historique des travaux de la commission géodésique suisse de 1862 à 1892".Bulletin de la Société des Sciences Naturelles de Neuchâtel(in French).21:33.doi:10.5169/seals-88335.Retrieved11 October2023.
  90. ^abcQuinn, Terry (2019)."Wilhelm Foerster's Role in the Metre Convention of 1875 and in the Early Years of the International Committee for Weights and Measures".Annalen der Physik.531(5): 2.Bibcode:2019AnP...53100355Q.doi:10.1002/andp.201800355.ISSN1521-3889.S2CID125240402.
  91. ^Drewes, Hermann; Kuglitsch, Franz; Adám, József; Rózsa, Szabolcs (2016)."The Geodesist's Handbook 2016".Journal of Geodesy.90(10): 914.Bibcode:2016JGeod..90..907D.doi:10.1007/s00190-016-0948-z.ISSN0949-7714.S2CID125925505.
  92. ^"Bericht der schweizerischen Delegierten an der internationalen Meterkonferenz an den Bundespräsidenten und Vorsteher des Politischen Departements, J. J. Scherer in Erwin Bucher, Peter Stalder (ed.), Diplomatic Documents of Switzerland, vol. 3, doc. 66, dodis.ch/42045, Bern 1986".Dodis.30 March 1875.
  93. ^abWolf, M. C (1882).Recherches historiques sur les étalons de poids et mesures de l'observatoire et les appareils qui ont servi a les construire(in French). Paris: Gauthier-Villars. pp. 7–8, 20, 32.OCLC16069502.
  94. ^Bigourdan 1901,pp. 8, 158–159, 176–177.
  95. ^NIST Special Publication.U.S. Government Printing Office. 1966. p. 529.
  96. ^"Borda et le système métrique".Association Mesure Lab(in French). Archived fromthe originalon 29 August 2023.Retrieved29 August2023.
  97. ^Zuerich, ETH-Bibliothek (1892)."Exposé historique des travaux de la commission géodésique suisse de 1862 à 1892".Bulletin de la Société des Sciences Naturelles de Neuchâtel(in German).21:33.doi:10.5169/seals-88335.Retrieved29 August2023.
  98. ^Carlos Ibáñez e Ibáñez de Ibero,Discursos leidos ante la Real Academia de Ciencias Exactas Fisicas y Naturales en la recepcion pública de Don Joaquin Barraquer y Rovira,Madrid, Imprenta de la Viuda e Hijo de D.E. Aguado, 1881, p. 78
  99. ^ab"Metric Act of 1866 – US Metric Association".usma.org.Retrieved15 March2021.
  100. ^Bessel, Friedrich Wilhelm (1 April 1840)."Über das preufs. Längenmaaß und die zu seiner Verbreitung durch Copien ergriffenen Maaßregeln".Astronomische Nachrichten.17(13): 193.Bibcode:1840AN.....17..193B.doi:10.1002/asna.18400171302.ISSN0004-6337.
  101. ^Britain, Great (1824).The Statutes of the United Kingdom of Great Britain and Ireland.
  102. ^abGuillaume, Ed. (1 January 1916)."Le Systeme Metrique est-il en Peril?".L'Astronomie.30:244–245.Bibcode:1916LAstr..30..242G.ISSN0004-6302.
  103. ^abCrease, Robert P. (1 December 2009)."Charles Sanders Peirce and the first absolute measurement standard".Physics Today.62(12): 39–44.Bibcode:2009PhT....62l..39C.doi:10.1063/1.3273015.ISSN0031-9228.S2CID121338356.
  104. ^abHirsch, Adolphe (1891)."Don Carlos Ibanez (1825–1891)"(PDF).Bureau International des Poids et Mesures.pp. 4, 8.Retrieved22 May2017.
  105. ^"BIPM – International Metre Commission".www.bipm.org.Retrieved26 May2017.
  106. ^ab"A Note on the History of the IAG".IAG Homepage.Retrieved26 May2017.
  107. ^Ross, Clarke Alexander; James, Henry (1 January 1873)."XIII. Results of the comparisons of the standards of length of England, Austria, Spain, United States, Cape of Good Hope, and of a second Russian standard, made at the Ordnance Survey Office, Southampton. With a preface and notes on the Greek and Egyptian measures of length by Sir Henry James".Philosophical Transactions of the Royal Society of London.163:445–469.doi:10.1098/rstl.1873.0014.
  108. ^Brunner, Jean (1857)."Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels".Gallica(in French). pp. 150–153.Retrieved15 May2019.
  109. ^Guillaume, Charles-Édouard (1927).La Création du Bureau International des Poids et Mesures et son Œuvre[The creation of the International Bureau of Weights and Measures and its work]. Paris: Gauthier-Villars. p. 321.
  110. ^abNational Institute of Standards and Technology 2003; Historical context of the SI: Unit of length (meter)
  111. ^Dodis, Diplomatische Dokumente der Schweiz | Documents diplomatiques suisses | Documenti diplomatici svizzeri | Diplomatic Documents of Switzerland | (30 March 1875),Bericht der schweizerischen Delegierten an der internationalen Meterkonferenz an den Bundespräsidenten und Vorsteher des Politischen Departements, J. J. Scherer(in French), Diplomatische Dokumente der Schweiz | Documents diplomatiques suisses | Documenti diplomatici svizzeri | Diplomatic Documents of Switzerland | Dodis,retrieved20 September2021
  112. ^"BIPM – la définition du mètre".www.bipm.org.Archived fromthe originalon 30 April 2017.Retrieved15 May2019.
  113. ^"Dr. C. E. Guillaume".Nature.134(3397): 874. 1 December 1934.Bibcode:1934Natur.134R.874..doi:10.1038/134874b0.ISSN1476-4687.S2CID4140694.
  114. ^Guillaume, C.-H.-Ed (1 January 1906)."La mesure rapide des bases géodésiques".Journal de Physique Théorique et Appliquée.5:242–263.doi:10.1051/jphystap:019060050024200.
  115. ^Huet, Sylvestre."Einstein, le révolutionnaire de la lumière".Libération(in French).Retrieved7 October2023.
  116. ^Ferreiro, Larrie D. (31 May 2011).Measure of the Earth: The Enlightenment Expedition That Reshaped Our World.Basic Books. pp. 19–23.ISBN978-0-465-02345-5.
  117. ^Stephen Hawking, Paris, Dunod, 2003, 2014, 929p.,p. 816–817
  118. ^Maxwell, James Clerk(1873).A Treatise On Electricity and Magnetism.Vol. 1. London: MacMillan and Co. p. 3.
  119. ^Lenzen, Victor F. (1965)."The Contributions of Charles S. Peirce to Metrology".Proceedings of the American Philosophical Society.109(1): 29–46.ISSN0003-049X.JSTOR985776.
  120. ^Marion, Jerry B. (1982).Physics For Science and Engineering.CBS College Publishing. p. 3.ISBN978-4-8337-0098-6.
  121. ^ab"17th General Conference on Weights and Measures (1983), Resolution 1".Retrieved7 December2022.
  122. ^BIPM (20 May 2019)."Mise en pratique for the definition of the meter in the SI".BIPM.
  123. ^The exact value is299792458m/s=1079252848.8 km/h.
  124. ^abc"Iodine (λ ≈ 633 nm)"(PDF).Mise en Pratique.BIPM. 2003.Retrieved16 December2011.
  125. ^The term "relative standard uncertainty" is explained by NIST on their web site:"Standard Uncertainty and Relative Standard Uncertainty".The NIST Reference on constants, units, and uncertainties: Fundamental physical constants.NIST.Retrieved19 December2011.
  126. ^National Research Council 2010.
  127. ^National Institute of Standards and Technology 2011.
  128. ^ab A more detailed listing of errors can be found inBeers, John S; Penzes, William B (December 1992)."§4 Re-evaluation of measurement errors"(PDF).NIST length scale interferometer measurement assurance; NIST document NISTIR 4998.pp. 9ff.Retrieved17 December2011.
  129. ^The formulas used in the calculator and the documentation behind them are found at"Engineering metrology toolbox: Refractive index of air calculator".NIST. 23 September 2010.Retrieved16 December2011.The choice is offered to use either themodified Edlén equationor theCiddor equation.The documentation providesa discussion of how to choosebetween the two possibilities.
  130. ^"§VI: Uncertainty and range of validity".Engineering metrology toolbox: Refractive index of air calculator.NIST. 23 September 2010.Retrieved16 December2011.
  131. ^Dunning, F. B.; Hulet, Randall G. (1997)."Physical limits on accuracy and resolution: setting the scale".Atomic, molecular, and optical physics: electromagnetic radiation, Volume 29, Part 3.Academic Press. p. 316.ISBN978-0-12-475977-0.The error [introduced by using air] can be reduced tenfold if the chamber is filled with an atmosphere of helium rather than air.
  132. ^"Recommended values of standard frequencies".BIPM. 9 September 2010.Retrieved22 January2012.
  133. ^National Physical Laboratory 2010.
  134. ^The BIPM maintains a list of recommended radiations on their web site.[132][133]
  135. ^abZagar, 1999, pp. 6–65ff.
  136. ^Bigourdan1901,pp. 20–21.
  137. ^Wolf, Charles (1827–1918) Auteur du texte (1882).Recherches historiques sur les étalons de poids et mesures de l'Observatoire et les appareils qui ont servi à les construire / par M. C. Wolf...(in French). pp. C.38–39, C.2–4.{{cite book}}:CS1 maint: numeric names: authors list (link)
  138. ^abc"Histoire du mètre".Direction Générale des Entreprises (DGE)(in French).Retrieved16 May2019.
  139. ^"CGPM: Compte rendus de la 1ère réunion (1889)"(PDF).BIPM.
  140. ^"CGPM: Comptes rendus de le 7e réunion (1927)"(PDF).p. 49.
  141. ^Judson 1976.
  142. ^Taylor and Thompson (2008a), Appendix 1, p. 70.
  143. ^"Meter is Redefined".US: National Geographic Society.Retrieved22 October2019.[permanent dead link]
  144. ^Taylor and Thompson (2008a), Appendix 1, p. 77.
  145. ^Cardarelli 2003.
  146. ^Definition of the metreResolution 1 of the 17th meeting of the CGPM (1983)
  147. ^"Metrisches System".hls-dhs-dss.ch(in German).Retrieved15 December2021.
  148. ^"Kartografie".hls-dhs-dss.ch(in German).Retrieved13 December2021.
  149. ^Dufour, G.-H. (1861)."Notice sur la carte de la Suisse dressée par l'État Major Fédéral".Le Globe. Revue genevoise de géographie.2(1): 5–22.doi:10.3406/globe.1861.7582.
  150. ^ab"Metrisches System".hls-dhs-dss.ch(in German).Retrieved9 December2021.
  151. ^Taylor & Thompson 2003, p. 11.
  152. ^Astin & Karo 1959.
  153. ^Arnold Dieter (1991).Building in Egypt: pharaonic stone masonry.Oxford: Oxford University Press.ISBN978-0-19-506350-9.p.251.
  154. ^"Dictionary of the Scots Language".Archived fromthe originalon 21 March 2012.Retrieved6 August2011.
  155. ^The Penny Magazine of the Society for the Diffusion of Useful Knowledge.Charles Knight. 6 June 1840. pp. 221–22.
  156. ^Hallock, William; Wade, Herbert T (1906)."Outlines of the evolution of weights and measures and the metric system".London: The Macmillan Company. pp. 66–69.
  157. ^Cardarelli 2004.
  158. ^Hofstad, Knut."Mil".Store norske leksikon.Retrieved18 October2019.

References

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