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

metre
Seal of the International Bureau of Weights and Measures (BIPM) – Use measure (Greek: ΜΕΤΡΩ ΧΡΩ)
General information
Unit systemSI
Unit oflength
Symbolm[1]
Conversions
1 m[1] in ...... is equal to ...
   SI units   
   Imperial/US units   
  • ≈ 1.0936 yd
  • ≈ 3.2808 ft
  • ≈ 39.37 in
   Nautical units   ≈ 0.00053996 nmi

The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit mètre, from the Greek noun μέτρον, "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its prefixed forms are also used relatively frequently.

The metre was originally defined in 1793 as one ten-millionth of the distance from the equator 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; 299792458 m/s.

Spelling

Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States[2][3][4][5] and the Philippines,[6] which use meter. Other West Germanic languages, such as German and Dutch, and North Germanic languages, such as Danish, Norwegian, and Swedish,[7] likewise spell the word Meter or meter.

Measuring devices (such as ammeter, 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

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.[11]

History of definition

Main article: History of the metre
Meridian room of the Paris Observatory (or Cassini room): the Paris meridian is drawn on the ground.

Pendulum or meridian

In 1671, Jean Picard measured the length of a "seconds pendulum" and proposed a unit of measurement twice that length to be called the universal toise (French: Toise universelle).[12][13] In 1675, Tito Livio Burattini suggested the term metre for a unit of length based on a pendulum length, but then it was discovered that the length of a seconds pendulum varies from place to place.[14][15][16][17][18][19][20][21][22]

Since Eratosthenes, geographers had used meridian arcs to assess the size of the Earth, which in 1669, Jean Picard determined to have a radius of 3269000 toises, treated as a simple sphere. In the 18th century, 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 mathematical work,[23] and because the radius of the Earth was the unit to which all celestial distances were to be referred.[24][25][26]

Meridional definition

Paris Panthéon

As a result of the Lumières and during the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. On 7 October 1790 that commission advised the adoption of a decimal system, and on 19 March 1791 advised the adoption of the term mètre ("measure"), a basic unit of length, which they defined as equal to one ten-millionth of the quarter meridian, the distance between the North Pole and the Equator along the meridian through Paris.[27][28][29][30][31] On 26 March 1791, the French National Constituent Assembly adopted the proposal.[11][32]

The French Academy of Sciences commissioned an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from 1792 to 1799, which attempted to accurately measure the distance between a belfry in Dunkerque and Montjuïc castle in Barcelona at the longitude of the Paris Panthéon (see meridian arc of Delambre and Méchain).[33] The expedition was fictionalised in Denis Guedj, Le Mètre du Monde.[34] Ken Alder wrote factually about the expedition in The Measure of All Things: the seven year odyssey and hidden error that transformed the world.[35] This portion of the Paris meridian was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator. From 1801 to 1812 France adopted this definition of the metre as its official unit of length based on results from this expedition combined with those of the Geodesic Mission to Peru.[36][37] The latter was related by Larrie D. Ferreiro in Measure of the Earth: The Enlightenment Expedition that Reshaped Our World.[38][39]

In the 19th century, geodesy underwent a revolution through advances in mathematics as well as improvements in the instruments and methods of observation, for instance accounting for individual bias in terms of the personal equation. The application of the least squares method to meridian arc measurements demonstrated the importance of the scientific method in geodesy. On the other hand, the invention of the telegraph made it possible to measure parallel arcs, and the improvement of the reversible pendulum gave rise to the study of the Earth's gravitational field. A more accurate determination of the Figure of the Earth would soon result from the measurement of the Struve Geodetic Arc (1816–1855) and would have given another value for the definition of this standard of length. This did not invalidate the metre but highlighted that progress in science would allow better measurement of Earth's size and shape.[40][41][42][43]

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 second president, the Swiss meteorologist and physicist, Heinrich von Wild would represent Russia at the International Committee for Weights and Measures (CIPM).[44][45][46][47][48][49]

International prototype metre bar

The influence of the intellect transcends mountains and leaps across oceans. At the time when George Washington warned his fellow countrymen against entangling political alliances with European countries, there was started a movement of far reaching importance in a small country in the heart of the Alps which (as we shall see) exerted a silent, yet potent scientific influence upon the young republic on the eastern shores of North America.

— Florian Cajori[50]
Triangulation near New York City, 1817.

In 1816, Ferdinand Rudolph Hassler was appointed first Superintendent of the Survey of the Coast. Trained in geodesy in Switzerland, France and Germany, Hassler had brought a standard metre made in Paris to the United States in 1805. He designed a baseline apparatus which instead of bringing different bars in actual contact during measurements, used only one bar calibrated on the metre and optical contact. Thus the metre became the unit of length for geodesy in the United States.[51][52][53][54]

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.[55]

In 1841, Friedrich Wilhelm Bessel, taking into account errors which had been recognized by Louis Puissant in the French meridian arc comprising the arc measurement of Delambre and Méchain which had been extended southward by François Arago and Jean-Baptiste Biot, recalculated the flattening of the Earth ellipsoid making use of nine more arc measurements, namely Peruan, Prussian, first East-Indian, second East-Indian, English, Hannover, Danish, Russian and Swedish covering almost 50 degrees of latitude, and stated that the Earth quadrant used for determining the length of the metre was nothing more than a rather imprecise conversion factor between the toise and the metre.[56][57][58]

Regarding the precision of the conversion from the toise to the metre, both units of measurement were then defined by primary standards, and unique artifacts made of different alloys with distinct coefficients of expansion were the legal basis of units of length. A wrought iron ruler, the Toise of Peru, also called Toise de l'Académie, was the French primary standard of the toise, and the metre was officially defined by the Mètre des Archives made of platinum. Besides the latter, another platinum and twelve iron standards of the metre were made in 1799. One of them became known as the Committee Meter in the United States and served as standard of length in the Coast Survey until 1890. According to geodesists, these standards were secondary standards deduced from the Toise of Peru. In Europe, surveyors continued to use measuring instruments calibrated on the Toise of Peru. Among these, the toise of Bessel and the apparatus of Borda were respectively the main references for geodesy in Prussia and in France. A French scientific instrument maker, Jean Nicolas Fortin, had made two direct copies of the Toise of Peru, the first for Friedrich Georg Wilhelm von Struve in 1821 and a second for Friedrich Bessel in 1823.[59][54][49][60][61]

On the subject of the theoretical definition of the metre, it had been inaccessible and misleading at the time of Delambre and Mechain arc measurement, as the geoid is a ball, which on the whole can be assimilated to an oblate spheroid, but which in detail differs from it so as to prohibit any generalization and any extrapolation. As early as 1861, after Friedrich von Schubert showed that the different meridians were not of equal length, Elie Ritter, a mathematician from Geneva, deduced from a computation based on eleven meridian arcs covering 86 degrees that the meridian equation differed from that of the ellipse: the meridian was swelled about the 45th degree of latitude by a layer whose thickness was difficult to estimate because of the uncertainty of the latitude of some stations, in particular that of Montjuïc in the French meridian arc. By measuring the latitude of two stations in Barcelona, Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation. We know now that, in addition to other errors in the survey of Delambre and Méchain, an unfavourable vertical deflection gave an inaccurate determination of Barcelona's latitude, a metre "too short" compared to a more general definition taken from the average of a large number of arcs.[62][63][58][64][65]

Nevertheless Ferdinand Rudolph Hassler's use of the metre in coastal survey contributed to the introduction of the Metric Act of 1866 allowing the use of the metre in the United States, and also played an important role in the choice of the metre as international scientific unit of length and the proposal by the European Arc Measurement (German: Europäische Gradmessung) to “establish a European international bureau for weights and measures”. However, in 1866, the most important concern was that the Toise of Peru, the standard of the toise constructed in 1735 for the French Geodesic Mission to the Equator, might be so much damaged that comparison with it would be worthless, while Bessel had questioned the accuracy of copies of this standard belonging to Altona and Koenigsberg Observatories, which he had compared to each other about 1840. Indeed when the primary Imperial yard standard was partially destroyed in 1834, a new standard of reference had been constructed using copies of the "Standard Yard, 1760" instead of the pendulum's length as provided for in the Weights and Measures Act of 1824.[66][67][68][60][69][70][71]

In 1864, Urbain Le Verrier refused to join the first general conference of the Central European Arc Measurement because the French geodetic works had to be verified.[72]

Swiss baseline measurement with Ibáñez apparatus in 1880.

In 1866, at the meeting of the Permanent Commission of the association in Neuchâtel, Antoine Yvon Villarceau announced that he had checked eight points of the French arc. He confirmed that the metre was too short. It then became urgent to undertake a complete revision of the meridian arc. Moreover, while the extension of the French meridian arc to the Balearic Islands (1803–1807) had seemed to confirm the length of the metre, this survey had not been secured by any baseline in Spain. For that reason, Carlos Ibáñez e Ibáñez de Ibero's announcement, at this conference, of his 1858 measurement of a baseline in Madridejos was of particular importance. Indeed surveyors determined the size of triangulation networks by measuring baselines which concordance granted the accuracy of the whole survey.[73][58][74][75][62]

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.[76][77][78] The conference recommended the adoption of the metre in replacement of the toise and the creation of an international metre commission, according to the proposal of Johann Jacob Baeyer, Adolphe Hirsch and Carlos Ibáñez e Ibáñez de Ibero who had devised two geodetic standards calibrated on the metre for the map of Spain.[79][76][78][80]

Ibáñez adopted the system which Ferdinand Rudolph Hassler used for the United States Survey of the Coast, consisting of a single standard with lines marked on the bar and microscopic measurements. Regarding the two methods by which the effect of temperature was taken into account, Ibáñez used both the bimetallic rulers, in platinum and brass, which he first employed for the central baseline of Spain, and the simple iron ruler with inlaid mercury thermometers which was utilized in Switzerland. These devices, the first of which is referred to as either Brunner apparatus or Spanish Standard, were constructed in France by Jean Brunner, then his sons. Measurement traceability between the toise and the metre was ensured by comparison of the Spanish Standard with the standard devised by Borda and Lavoisier for the survey of the meridian arc connecting Dunkirk with Barcelona.[81][80][82][76][83][84][24][85][86]

Hassler's metrological and geodetic work also had a favourable response in Russia.[55] 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.[71]

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

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.[87][88][49][89]

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.[87]

Closeup of National Prototype Metre Bar No. 27, made in 1889 by the International Bureau of Weights and Measures (BIPM) and given to the United States, which served as the standard for defining all units of length in the US from 1893 to 1960

The comparison of the new prototypes of the metre with each other and with the Committee metre (French: 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, for which its director, the Swiss physicist Charles-Edouard Guillaume, was granted the Nobel Prize for physics in 1920.[90]

Gravimeter with variant of Repsold-Bessel pendulum

As Carlos Ibáñez e Ibáñez de Ibero stated, the progress of metrology combined with those of gravimetry through improvement of Kater's pendulum 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 force of gravity by the mean of pendulum. Metrology had to create a common unit, adopted and respected by all civilized nations.[41]

Moreover, at that time, statisticians knew that scientific observations are marred by two distinct types of errors, constant errors on the one hand, and fortuitous errors, on the other hand. The effects of the latters can be mitigated by the least-squares method. Constant or regular errors on the contrary must be carefully avoided, because they arise from one or more causes that constantly act in the same way and have the effect of always altering the result of the experiment in the same direction. They therefore deprive of any value the observations that they impinge. However, the distinction between systematic and random errors is far from being as sharp as one might think at first assessment. In reality, there are no or very few random errors. As science progresses, the causes of certain errors are sought out, studied, their laws discovered. These errors pass from the class of random errors into that of systematic errors. The ability of the observer consists in discovering the greatest possible number of systematic errors in order to be able, once he has become acquainted with their laws, to free his results from them using a method or appropriate corrections.[91][92]

For metrology the matter of expansibility was fundamental; as a matter of fact the temperature measuring error related to the length measurement in proportion to the expansibility of the standard and the constantly renewed efforts of metrologists to protect their measuring instruments against the interfering influence of temperature revealed clearly the importance they attached to the expansion-induced errors. It was thus crucial to compare at controlled temperatures with great precision and to the same unit all the standards for measuring geodetic baselines and all the pendulum rods. Only when this series of metrological comparisons would be finished with a probable error of a thousandth of a millimetre would geodesy be able to link the works of the different nations with one another, and then proclaim the result of the measurement of the Globe.[93][41]

As the figure of the Earth could be inferred from variations of the seconds pendulum length with latitude, the United States Coast Survey instructed Charles Sanders Peirce in the spring of 1875 to proceed to Europe for the purpose of making pendulum experiments to chief initial stations for operations of this sort, in order to bring the determinations of the forces of gravity in America into communication with those of other parts of the world; and also for the purpose of making a careful study of the methods of pursuing these researches in the different countries of Europe. In 1886 the association of geodesy changed name for the International Geodetic Association, which Carlos Ibáñez e Ibáñez de Ibero presided up to his death in 1891. During this period the International Geodetic Association (German: Internationale Erdmessung) gained worldwide importance with the joining of United States, Mexico, Chile, Argentina and Japan.[81][94][95][96][97]

Artist's impression of a GPS-IIR satellite in orbit.

Efforts to supplement the various national surveying systems, which began in the 19th century with the foundation of the Mitteleuropäische Gradmessung, resulted in a series of global ellipsoids of the Earth (e.g., Helmert 1906, Hayford 1910 and 1924) which would later lead to develop the World Geodetic System. Nowadays the practical realisation of the metre is possible everywhere thanks to the atomic clocks embedded in GPS satellites.[98][99]

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.[100]

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.[101]

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:[102][103]

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[102] (≈300000 km/s or ≈1.079 billion km/hour[104]). 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.[105] 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 2.1×10−11.[105][106][107] 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 = 5×10−16).[108] 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.[105] 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.[109] 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.[110] 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.[111] 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.[112]

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,[115] and converting the selected unit of wavelength to metres. Three major factors limit the accuracy attainable with laser interferometers for a length measurement:[109][116]

  • 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.[116]

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 1016 per metre). In this case, the effects to be taken into account are those of special relativity only.

Timeline

Date Deciding body Decision
8 May 1790 French National Assembly The length of the new metre to be equal to the length of a pendulum with a half-period of one second.[36]
30 Mar 1791 French National Assembly Accepts the proposal by the French Academy of Sciences that the new definition for the metre be equal to one ten-millionth of the length of a great circle quadrant along the Earth's meridian through Paris, that is the distance from the equator to the north pole along that quadrant.[117]
1795 Provisional metre bar made of brass and based on Paris meridan arc (French: Méridienne de France) measured by Nicolas-Louis de Lacaillle and Cesar-François Cassini de Thury, legally equal to 443.44 lines of the toise du Pérou (a standard French unit of length from 1766).[36][37][82][99] [The line was 1/864 of a toise.]
10 Dec 1799 French National Assembly Specifies the platinum metre bar, presented on 22 June 1799 and deposited in the National Archives, as the final standard. Legally equal to 443.296 lines on the toise du Pérou.[99]
24–28 Sept 1889 1st General Conference on Weights and Measures (CGPM) Defines the metre as the distance between two lines on a standard bar of an alloy of platinum with 10% iridium, measured at the melting point of ice.[99][118]
27 Sept – 6 Oct 1927 7th CGPM Redefines the metre as the distance, at 0 °C (273 K), between the axes of the two central lines marked on the prototype bar of platinum-iridium, this bar being subject to one standard atmosphere of pressure and supported on two cylinders of at least 10 mm (1 cm) diameter, symmetrically placed in the same horizontal plane at a distance of 571 mm (57.1 cm) from each other.[119]
14 Oct 1960 11th CGPM Defines the metre as 1650763.73 wavelengths in a vacuum of the radiation corresponding to the transition between the 2p10 and 5d5 quantum levels of the krypton-86 atom.[120]
21 Oct 1983 17th CGPM Defines the metre as the length of the path travelled by light in a vacuum during a time interval of ⁠1/299 792 458⁠ of a second.[121][122]
2002 International Committee for Weights and Measures (CIPM) Considers the metre to be a unit of proper length and thus recommends this definition be restricted to "lengths ℓ which are sufficiently short for the effects predicted by general relativity to be negligible with respect to the uncertainties of realisation".[123]
Definitions of the metre since 1795[124]
Basis of definition Date Absolute
uncertainty 		Relative
uncertainty
⁠1/10 000 000⁠ part of the quadrant along the meridian, measurement by Delambre and Méchain (443.296 lines) 1795 500–100 μm 10−4
First prototype Mètre des Archives platinum bar standard 1799 50–10 μm 10−5
Platinum-iridium bar at melting point of ice (1st CGPM) 1889 0.2–0.1 μm (200–100 nm) 10−7
Platinum-iridium bar at melting point of ice, atmospheric pressure, supported by two rollers (7th CGPM) 1927 n.a. n.a.
Hyperfine atomic transition; 1650763.73 wavelengths of light from a specified transition in krypton-86 (11th CGPM) 1960 4 nm 4×10−9[125]
Length of the path travelled by light in a vacuum in ⁠1/299 792 458⁠ second (17th CGPM) 1983 0.1 nm 10−10

Early adoptions of the metre internationally

Main article: Metrication

In France, the metre was adopted as an exclusive measure in 1801 under the Consulate. This continued under the First French Empire until 1812, when Napoleon decreed the introduction of the non-decimal mesures usuelles, which remained in use in France up to 1840 in the reign of Louis Philippe.[36] Meanwhile, the metre was adopted by the Republic of Geneva.[126] 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.[127][128] Louis Napoléon Bonaparte, a Swiss–French binational officer, was present when a baseline was measured near Zürich for the Dufour map, which would win the gold medal for a national map at the Exposition Universelle of 1855.[129][130][131] Among the scientific instruments calibrated on the metre that were displayed at the Exposition Universelle, was Brunner's apparatus, a geodetic instrument devised for measuring the central baseline of Spain, whose designer, Carlos Ibáñez e Ibáñez de Ibero would represent Spain at the International Statistical Institute. In 1885, in addition to the Exposition Universelle and the second Statistical Congress held in Paris, an International Association for Obtaining a Uniform Decimal System of Measures, Weights, and Coins was created there.[49][132][133][134] Copies of the Spanish standard were made for Egypt, France and Germany.[135][136][137] These standards were compared to each other and with the Borda apparatus, which was the main reference for measuring all geodetic bases in France.[135][86][81] In 1869, Napoleon III convened the International Metre Commission, which was to meet in Paris in 1870. The Franco-Prussian War broke out, the Second French Empire collapsed, but the metre survived.[138][68]

Metre adoption dates by country

SI prefixed forms of metre

Main article: Orders of magnitude (length)

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

The terms micron and millimicron can be used instead of micrometre (μm) and nanometre (nm), but this practice may be discouraged.[140]


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

Equivalents in other units

Metric unit
expressed in non-SI units 		Non-SI unit
expressed in metric units
1 metre ≈ 1.0936 yard 1 yard = 0.9144 metre
1 metre ≈ 39.370 inches 1 inch = 0.0254 metre
1 centimetre ≈ 0.39370 inch 1 inch = 2.54 centimetres
1 millimetre ≈ 0.039370 inch 1 inch = 25.4 millimetres
1 metre = 1010 ångström 1 ångström = 10−10 metre
1 nanometre = 10 ångström 1 ångström = 100 picometres

Within this table, "inch" and "yard" mean "international inch" and "international yard"[141] respectively, though approximate conversions in the left column hold for both international and survey units.

"≈" means "is approximately equal to";
"=" means "is exactly equal to".

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

A simple mnemonic aid exists to assist with conversion, as three "3"s:

1 metre is nearly equivalent to 3 feet 3+3⁄8 inches. This gives an overestimate of 0.125 mm; however, the practice of memorising such conversion formulas has been discouraged in favour of practice and visualisation of metric units.

The ancient Egyptian cubit was about 0.5 m (surviving rods are 523–529 mm).[142] Scottish and English definitions of the ell (two cubits) were 941 mm (0.941 m) and 1143 mm (1.143 m) respectively.[143][144] 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.[145] The Russian verst was 1.0668 km.[146] The Swedish mil was 10.688 km, but was changed to 10 km when Sweden converted to metric units.[147]

See also

Wikimedia Commons has media related to Metre.
Look up metre in Wiktionary, the free dictionary.

Notes

  1. ^ "Base unit definitions: Meter". National Institute of Standards and Technology. Retrieved 28 September 2010.
  2. ^ "The International System of Units (SI) – NIST". 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,"…rather than "metre,"...as in the original BIPM English text...
  3. ^ The most recent official brochure about the International System of Units (SI), written in French by the Bureau international des poids et mesures, International Bureau of Weights and Measures (BIPM) uses the spelling metre; an English translation, included to make the SI standard more widely accessible also uses the spelling metre (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 spelling meter in 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 publication Le 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 with Taylor and Thompson (2008b), as the "legal interpretation" of the SI for the United States (Turner). Thus, the spelling metre is referred to as the "international spelling"; the spelling meter, as the "American spelling".
  4. ^ Naughtin, Pat (2008). "Spelling metre or meter" (PDF). Metrication Matters. Retrieved 12 March 2017.
  5. ^ "Meter vs. metre". Grammarist. 21 February 2011. Retrieved 12 March 2017.
  6. ^ The Philippines uses English as 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 the metric system uses metre (Batas Pambansa Blg. 8) following the SI spelling, in actual practice, meter is 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).
  7. ^ "295–296 (Nordisk familjebok / Uggleupplagan. 18. Mekaniker – Mykale)" [295–296 (Nordic Family Book / Owl Edition. 18. Mechanic – Mycular)]. Stockholm. 1913.
  8. ^ Cambridge Advanced Learner's Dictionary. Cambridge University Press. 2008. Retrieved 19 September 2012., 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 from the original on 26 April 2017.
  11. ^ a b Oxford English Dictionary, Clarendon Press 2nd ed.1989, vol.IX p.697 col.3.
  12. ^ texte, Picard, Jean (1620–1682). Auteur du (1671). Mesure de la terre [par l'abbé Picard]. pp. 3–4. Retrieved 13 September 2018. {{cite book}}: |website= ignored (help)CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link) [verification needed]
  13. ^ Bigourdan 1901, pp. 8, 158–159.
  14. ^ Lucendo, Jorge (23 April 2020). Centuries of Inventions: Encyclopedia and History of Inventions. Jorge Lucendo. p. 246. Retrieved 2 August 2021.
  15. ^ Camerini, Valentina (1 December 2020). 365 Real-Life Superheroes. Black Inc. p. 292. ISBN 978-1-74382-138-1.
  16. ^ "Appendix B: Tito Livio Burattini's catholic meter". roma1.infn.it. Retrieved 3 August 2021.
  17. ^ "Science. 1791, l'adoption révolutionnaire du mètre". humanite.fr (in French). 25 March 2021. Retrieved 3 August 2021.
  18. ^ "The meter, an ingenious intuition from belluno | Italiani Come Noi". italianicomenoi.it. Retrieved 3 August 2021.
  19. ^ Holtebekk, Trygve (30 November 2020). "Meter". Store norske leksikon (in Norwegian Bokmål). Retrieved 3 August 2021.
  20. ^ Poynting, John Henry; Thomson, Joseph John (1907). A Textbook of Physics. C. Griffin. pp. 20. [verification needed]
  21. ^ 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)
  22. ^ Bond, Peter, (1948- ...). (2014). L'exploration du système solaire. Dupont-Bloch, Nicolas. ([Édition française revue et corrigée] ed.). Louvain-la-Neuve: De Boeck. pp. 5–6. ISBN 9782804184964. OCLC 894499177.{{cite book}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)
  23. ^ 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. ISSN 1298-9800.
  24. ^ a b Clarke, Alexander Ross; Helmert, Friedrich Robert (1911). "Geodesy" . In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 11 (11th ed.). Cambridge University Press. pp. 607–615.
  25. ^ Badinter, Élisabeth (2018). Les passions intellectuelles. Normandie roto impr.). Paris: Robert Laffont. ISBN 978-2-221-20345-3. OCLC 1061216207.
  26. ^ von Struve, Friedrich Georg Wilhelm (July 1857). "Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels". Gallica. p. 509. Retrieved 30 August 2021.
  27. ^ Tipler, Paul A.; Mosca, Gene (2004). Physics for Scientists and Engineers (5th ed.). W.H. Freeman. p. 3. ISBN 0716783398.
  28. ^ ('decimalization is not of the essence of the metric system; the real significance of this is that it was the first great attempt to define terrestrial units of measure in terms of an unvarying astronomical or geodetic constant.) The metre was in fact defined as one ten-millionth of one-quarter of the earth's circumference at sea-level.' Joseph Needham, Science and Civilisation in China, Cambridge University Press, 1962 vol.4, pt.1, p.42.
  29. ^ Agnoli, Paolo (2004). Il senso della misura: la codifica della realtà tra filosofia, scienza ed esistenza umana (in Italian). Armando Editore. pp. 93–94, 101. ISBN 9788883585326. Retrieved 13 October 2015.
  30. ^ Rapport sur le choix d'une unité de mesure, lu à l'Académie des sciences, le 19 mars 1791 (in French). Gallica.bnf.fr. 15 October 2007. Retrieved 25 March 2013.: "Nous proposerons donc de mesurer immédiatement un arc du méridien, depuis Dunkerque jusqu'a Bracelone: ce qui comprend un peu plus de neuf degrés & demi." [We propose then to measure directly an arc of the meridian between Dunkirk and Barcelona: this spans a little more than nine-and-a-half degrees."] p. 8
  31. ^ Paolo Agnoli and Giulio D’Agostini,'Why does the meter beat the second?,' December, 2004 pp.1–29.
  32. ^ "Archives Parlementaires". sul-philologic.stanford.edu. p. 379. Retrieved 4 November 2021.
  33. ^ Ramani, Madhvi. "How France created the metric system". www.bbc.com. Retrieved 21 May 2019.
  34. ^ Guedj 2001.
  35. ^ Alder 2002.
  36. ^ a b c d e Larousse, Pierre (1817–1875) (1866–1877). Grand dictionnaire universel du XIXe siècle : français, historique, géographique, mythologique, bibliographique.... T. 11 MEMO-O / par M. Pierre Larousse. p. 163.{{cite book}}: CS1 maint: numeric names: authors list (link)
  37. ^ a b Levallois, Jean-Jacques (1986). "La Vie des sciences". Gallica (in French). pp. 288–290, 269, 276–277, 283. Retrieved 13 May 2019.
  38. ^ Robinson, Andrew (10 August 2011). "History: How Earth shaped up". Nature. 476 (7359): 149–150. Bibcode:2011Natur.476..149R. doi:10.1038/476149a. ISSN 1476-4687.
  39. ^ Ferreiro, Larrie D. (25 June 2013). Measure of the Earth: The Enlightenment Expedition That Reshaped Our World. Basic Books. ISBN 978-0-465-06381-9.
  40. ^ Clarke & Helmert 1911b, pp. 803–804.
  41. ^ a b c Public Domain This article incorporates text from this source, which is in the public 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.
  42. ^ "Nomination of the Struve geodetic arc for inscription on the World Heritage List" (PDF). Retrieved 13 May 2019.
  43. ^ Hirsch, Adolphe (1861). "Expériences chronoscopiques sur la vitesse des différentes sensations et de la transmission nerveuse". E-Periodica (in French). doi:10.5169/seals-87978. Retrieved 18 April 2021.
  44. ^ Débarbat, 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. 20 (1–2): 6–21. Bibcode:2019CRPhy..20....6D. doi:10.1016/j.crhy.2018.12.002. ISSN 1631-0705.
  45. ^ Géophysique in Encyclopedia Universalis. Encyclopedia Universalis. 1996. pp. Vol 10, p. 370. ISBN 978-2-85229-290-1. OCLC 36747385.
  46. ^ "History of IMO". World Meteorological Organization. 8 December 2015. Retrieved 16 March 2021.
  47. ^ "Wild, Heinrich". hls-dhs-dss.ch (in German). Retrieved 16 March 2021.
  48. ^ "Heinrich VON WILD (1833-1902) in COMlTÉ INTERNATIONAL DES POIDS ET MESURES. PROCÈS-VERBAUX DES SÉANCES. DEUXIÈME SÉRIE. TOME II. SESSION DE 1903" (PDF). BIPM. 1903.
  49. ^ a b c d Quinn, T. J. (2012). From artefacts to atoms : the BIPM and the search for ultimate measurement standards. Oxford. pp. 91–92, 70–72, 114–117, 144–147, 8. ISBN 978-0-19-990991-9. OCLC 861693071.{{cite book}}: CS1 maint: location missing publisher (link)
  50. ^ Cajori, Florian (1921). "Swiss Geodesy and the United States Coast Survey". The Scientific Monthly. Vol. 13, no. 2. American Association for the Advancement of Science. pp. 117–129.
  51. ^ Poupard, James (1825). Transactions of the American Philosophical Society. Vol. 2. Philadelphia: Abraham Small. pp. 234–240, 252–253, 274, 278.
  52. ^ Cajori, Florian (1921). "Swiss Geodesy and the United States Coast Survey". The Scientific Monthly. 13 (2): 117–129. Bibcode:1921SciMo..13..117C. ISSN 0096-3771.
  53. ^ Clarke, 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
  54. ^ a b Bigourdan 1901, pp. 8, 158–159, 176–177.
  55. ^ a b Parr, 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. PMC 4654608. PMID 27274915 – via NIST.
  56. ^ Viik, 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. p. 10. CiteSeerX 10.1.1.517.9501.
  57. ^ Bessel, 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. ISSN 0004-6337.
  58. ^ a b c "c à Paris ; vitesse de la lumière ..." expositions.obspm.fr. Retrieved 12 October 2021.
  59. ^ Wolf, 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. 20, 32. OCLC 16069502.
  60. ^ a b Clarke, 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. S2CID 109333769.
  61. ^ NIST Special Publication. U.S. Government Printing Office. 1966. p. 529.
  62. ^ a b Lebon, Ernest (1899). Histoire abrégée de l'astronomie / par Ernest Lebon,... Paris. p. 168.{{cite book}}: CS1 maint: location missing publisher (link)
  63. ^ Zuerich, ETH-Bibliothek (1991). "La méridienne de Dunkerque à Barcelone et la déterminiation du mètre (1972-1799)". E-Periodica (in French): 377–378. doi:10.5169/seals-234595. Retrieved 12 October 2021.
  64. ^ 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.
  65. ^ 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.] p. 196.
  66. ^ "Metric Act of 1866 – US Metric Association". usma.org. Retrieved 15 March 2021.
  67. ^ Bericht 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.
  68. ^ a b Quinn, 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. ISSN 1521-3889. S2CID 125240402.
  69. ^ 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. ISSN 0004-6337.
  70. ^ Britain, Great (1824). The Statutes of the United Kingdom of Great Britain and Ireland.
  71. ^ a b Guillaume, Ed. (1 January 1916). "Le Systeme Metrique est-il en Peril?". L'Astronomie. 30: 244–245. Bibcode:1916LAstr..30..242G. ISSN 0004-6302.
  72. ^ Zuerich, ETH-Bibliothek (1864). "Rapport à la commission géodésique suisse sur la conférence géodésique internationale de Berlin". E-Periodica (in German). doi:10.5169/seals-88011. Retrieved 29 November 2021.
  73. ^ Zuerich, ETH-Bibliothek (1865). "Sur les progrès des travaux géodésiques en Europe". E-Periodica (in German). doi:10.5169/seals-88030. Retrieved 29 November 2021.
  74. ^ Clarke & Helmert 1911b, pp. 801–813.
  75. ^ texte, Académie des sciences (France) Auteur du (January 1836). "Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels". Gallica. pp. 428–433. Retrieved 29 November 2021.
  76. ^ a b c Hirsch, Adolphe (1891). "Don Carlos IBANEZ (1825–1891)" (PDF). Bureau International des Poids et Mesures. pp. 4, 8. Retrieved 22 May 2017.
  77. ^ "BIPM – International Metre Commission". www.bipm.org. Retrieved 26 May 2017.
  78. ^ a b "A Note on the History of the IAG". IAG Homepage. Retrieved 26 May 2017.
  79. ^ 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.
  80. ^ a b 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. Retrieved 15 May 2019.
  81. ^ a b c Soler, 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. doi:10.1007/s001900050086. ISSN 1432-1394. S2CID 119447198.
  82. ^ a b 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)
  83. ^ Wolf, Rudolf (January 1891). "Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels". Gallica. pp. 370–371. Retrieved 30 August 2021.
  84. ^ Brenni, Paolo (1996). "19th Century French Scientific Instrument Makers - XI: The Brunners and Paul Gautier" (PDF). Bulletin of the Scientific Instrument Society. 49: 3–5 – via Universidad de Navarra.
  85. ^ Schiavon, Martina (1 December 2006). "Les officiers géodésiens du Service géographique de l'armée et la mesure de l'arc de méridien de Quito (1901-1906)". Histoire & mesure (in French). XXI (XXI - 2): 55–94. doi:10.4000/histoiremesure.1746. ISSN 0982-1783.
  86. ^ a b Expériences faites avec l'appareil à mesurer les bases appertant à la commission de la carte d'Espagne /: ouvrage publié par ordre de la reine (in French). J. Dumaine. 1860.
  87. ^ a b National Institute of Standards and Technology 2003; Historical context of the SI: Unit of length (meter)
  88. ^ Pérard, Albert (1957). "Carlos IBAÑEZ 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.
  89. ^ 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, retrieved 20 September 2021
  90. ^ "BIPM – la définition du mètre". www.bipm.org. Retrieved 15 May 2019.
  91. ^ Public Domain This article incorporates text from this source, which is in the public domain: Ritter, Élie (1858). Manuel théorique et pratique de l'application de la méthode des moindres carrés: au calcul des observations (in French). Mallet-Bachelier.
  92. ^ Public Domain This article incorporates text from this source, which is in the public domain: Perrier, Georges (1872-1946) Auteur du texte (1933). Cours de géodésie et d'astronomie / par G. Perrier (in French). pp. 17–18.{{cite book}}: CS1 maint: numeric names: authors list (link)
  93. ^ Public Domain This article incorporates text from this source, which is in the public domain: "The Nobel Prize in Physics 1920". NobelPrize.org. Retrieved 13 March 2021.
  94. ^ Public Domain This article incorporates text from this source, which is in the public domain: "Report from Charles S. Peirce on his second European trip for the Anual Report of the Superintendent of the U. S. Coast Survey, New York, 18.05.1877". www.unav.es. Retrieved 22 May 2019.
  95. ^ Faye, Hervé (1880). "Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels". Gallica (in French). pp. 1463–1466. Retrieved 22 May 2019.
  96. ^ Torge, 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. Springer International Publishing: 3–18. doi:10.1007/1345_2015_42. ISBN 9783319308951.
  97. ^ Torge, W. (1 April 2005). "The International Association of Geodesy 1862 to 1922: from a regional project to an international organization". Journal of Geodesy. 78 (9): 558–568. Bibcode:2005JGeod..78..558T. doi:10.1007/s00190-004-0423-0. ISSN 1432-1394. S2CID 120943411.
  98. ^ Archived at Ghostarchive and the Wayback Machine: Laboratoire national de métrologie et d'essais (13 June 2018), Le mètre, l'aventure continue..., retrieved 16 May 2019
  99. ^ a b c d "Histoire du mètre". Direction Générale des Entreprises (DGE) (in French). Retrieved 16 May 2019.
  100. ^ Maxwell, James Clerk (1873). A Treatise On Electricity and Magnetism. Vol. 1. London: MacMillan and Co. p. 3.
  101. ^ Marion, Jerry B. (1982). Physics For Science and Engineering. CBS College Publishing. p. 3. ISBN 978-4-8337-0098-6.
  102. ^ a b "17th General Conference on Weights and Measures (1983), Resolution 1". Retrieved 19 September 2012.
  103. ^ BIPM (20 May 2019). "Mise en pratique for the definition of the meter in the SI". BIPM.
  104. ^ The exact value is 299792458 m/s = 1079252848 + ⁠4/5⁠ km/h.
  105. ^ a b c "Iodine (λ ≈ 633 nm)" (PDF). Mise en Pratique. BIPM. 2003. Retrieved 16 December 2011.
  106. ^ 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. Retrieved 19 December 2011.
  107. ^ National Research Council 2010.
  108. ^ National Institute of Standards and Technology 2011.
  109. ^ a b A more detailed listing of errors can be found in Beers, 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. 9 ff. Retrieved 17 December 2011.
  110. ^ 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. Retrieved 16 December 2011. The choice is offered to use either the modified Edlén equation or the Ciddor equation. The documentation provides a discussion of how to choose between the two possibilities.
  111. ^ "§VI: Uncertainty and range of validity". Engineering metrology toolbox: Refractive index of air calculator. NIST. 23 September 2010. Retrieved 16 December 2011.
  112. ^ 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. ISBN 978-0-12-475977-0. The error [introduced by using air] can be reduced tenfold if the chamber is filled with an atmosphere of helium rather than air.
  113. ^ "Recommended values of standard frequencies". BIPM. 9 September 2010. Retrieved 22 January 2012.
  114. ^ National Physical Laboratory 2010.
  115. ^ The BIPM maintains a list of recommended radiations on their web site.[113][114]
  116. ^ a b Zagar, 1999, pp. 6–65ff.
  117. ^ Bigourdan1901, pp. 20–21.
  118. ^ "CGPM : Compte rendus de la 1ère réunion (1889)" (PDF). BIPM.
  119. ^ "CGPM : Comptes rendus de le 7e réunion (1927)" (PDF). p. 49.
  120. ^ Judson 1976.
  121. ^ Taylor and Thompson (2008a), Appendix 1, p. 70.
  122. ^ "Meter is Redefined". US: National Geographic Society. Retrieved 22 October 2019.
  123. ^ Taylor and Thompson (2008a), Appendix 1, p. 77.
  124. ^ Cardarelli 2003.
  125. ^ Definition of the metre Resolution 1 of the 17th meeting of the CGPM (1983)
  126. ^ "Metrisches System". hls-dhs-dss.ch (in German). Retrieved 15 December 2021.
  127. ^ "Kartografie". hls-dhs-dss.ch (in German). Retrieved 13 December 2021.
  128. ^ 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.
  129. ^ Durand, Roger (1991). Guillaume-Henri Dufour dans son Temps 1787-1875 (in French). Librairie Droz. p. 145. ISBN 978-2-600-05069-2.
  130. ^ "Napoleon III". hls-dhs-dss.ch (in German). Retrieved 14 December 2021.
  131. ^ "Henri Dufour et la carte de la Suisse". Musée national - Blog sur l'histoire suisse (in French). 14 July 2019. Retrieved 15 December 2021.
  132. ^ Yates, James (1856). Narrative of the Origin and Formation of the International Association for Obtaining a Uniform Decimal System of Measures, Weights and Coins. Bell and Daldy. pp. 2–6.
  133. ^ Brenni, Paolo (1996). "19th Century French Scientific Instrument Makers - XI: The Brunners and Paul Gautier" (PDF). Bulletin of the Scientific Instrument Society. 49: 3–5 – via UNAV.
  134. ^ Appell, Paul (1925). "Le centenaire du général Ibañez de Ibéro". Revue internationale de l'enseignement. 79 (1): 208–211.
  135. ^ a b 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)
  136. ^ Tardi, Pierre (1897-1972) Auteur du texte (1934). Traité de géodésie / par le capitaine P. Tardi ; préface par le général G. Perrier. p. 25.{{cite book}}: CS1 maint: numeric names: authors list (link)
  137. ^ Zuerich, ETH-Bibliothek. "Procès-verbaux des séances de la commission géodésique suisse". E-Periodica (in German). pp. 14, 18. Retrieved 18 December 2021.
  138. ^ Boucheron, Patrick; Delalande, Nicolas; Mazel, Florian; Potin, Yann; Singaravélou, Pierre (2018). Histoire mondiale de la France (Édition augmentée de quinze notices inédites ed.). Paris. p. 694. ISBN 978-2-7578-7442-4. OCLC 1057452808.{{cite book}}: CS1 maint: location missing publisher (link)
  139. ^ a b "Metrisches System". hls-dhs-dss.ch (in German). Retrieved 9 December 2021.
  140. ^ Taylor & Thompson 2003, p. 11.
  141. ^ Astin & Karo 1959.
  142. ^ Arnold Dieter (1991). Building in Egypt: pharaonic stone masonry. Oxford: Oxford University Press. ISBN 978-0-19-506350-9. p.251.
  143. ^ "Dictionary of the Scots Language". Archived from the original on 21 March 2012. Retrieved 6 August 2011.
  144. ^ The Penny Magazine of the Society for the Diffusion of Useful Knowledge. Charles Knight. 6 June 1840. pp. 221–22.
  145. ^ 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.
  146. ^ Cardarelli 2004.
  147. ^ Hofstad, Knut. "Mil". Store norske leksikon. Retrieved 18 October 2019.

References

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