Metre

Metre
1 metre =
SI units
100 cm 1000 mm
US customary / Imperial units
3.2808 ft 39.370 in

The metre (or meter), symbol m, is the base unit of length in the International System of Units (SI). Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole (at sea level), its definition has been periodically refined to reflect growing knowledge of metrology. Since 1983, it is defined as the length of the path travelled by light in vacuum in of a second.[1]

History

Name

The first recorded proposal for a decimal-based unit of length was the universal measure unit proposed by the English philosopher John Wilkins in 1668.[2] In 1675, the Italian scientist Tito Livio Burattini, in his work Misura Universale, used the words metro cattolico (lit. "catholic [i.e. universal] metre"), which was derived from the Greek (métron katholikón), "a universal measure". This word gave rise to the French mètre which in 1797 was introduced into the English language.[3]

Belfry, Dunkirk - the northern end of the meridian arc
Fortress of Montjuïc - the southerly end of the meridian arc

Meridional definition

In 1668, Wilkins proposed using Christopher Wren's suggestion of a pendulum with a half-period of one second to measure a standard length that Christiaan Huygens had observed to be 38 Rhineland or 39¼ English inches (997 mm) in length.[2] In the 18th century, there were two favoured approaches to the definition of the standard unit of length. One approach followed Wilkins in defining the metre as the length of a pendulum with a half-period of one second, a 'seconds pendulum'. The other approach suggested defining the metre as one ten-millionth of the length of the Earth's meridian along a quadrant, that is the distance from the equator to the North Pole. In 1791, the French Academy of Sciences selected the meridional definition over the pendular definition because the force of gravity varies slightly over the surface of the Earth, which affects the period of a pendulum.

In order to establish a universally accepted foundation for the definition of the metre, measurements of this meridian more accurate than those available at that time were imperative. The French Academy of Sciences commissioned an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from 1792 to 1799, which measured the distance between the Dunkerque belfry and Montjuïc castle, Barcelona to estimate the length of the meridian arc through Dunkerque (assumed to be the same length as the Paris meridian). This portion of the meridian was to serve as the basis for the length of the half meridian, connecting the North Pole with the equator. The exact shape of the Earth is not a simple mathematical shape (sphere or oblate spheroid) at the level of precision required for defining a standard of length. The irregular and particular shape of the Earth (smoothed to sea level) is called a Geoid, which means "Earth-shaped".

However, in 1793, France adopted as its official unit of length a metre based on provisional results from the expedition. Although it was later determined that the first prototype metre bar was short by a fifth of a millimetre because of miscalculation of the flattening of the Earth, this length became the standard. The circumference of the Earth through the poles is therefore slightly more than forty million metres (40 007 863).[4]

Prototype metre bar

Historical International Prototype Metre bar, made of an alloy of platinum and iridium, that was the standard from 1889 to 1960.

In the 1870s and in light of modern precision, a series of international conferences was held to devise new metric standards. 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 would preserve the new prototype metre and kilogram standards when constructed, distribute national metric prototypes, and maintain comparisons between them and non-metric measurement standards. The organisation created a new prototype bar 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 ninety percent platinum and ten percent iridium, measured at the melting point of ice.[5]

The original international prototype of the metre is still kept at the BIPM under the conditions specified in 1889. A discussion of measurements of a standard metre bar and the errors encountered in making the measurements is found in a NIST document.[6]

Standard wavelength of krypton-86 emission

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 SI system as equal to 1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum.

Speed of light

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

The metre is the length of the path travelled by light in vacuum during a time interval of 1299 792 458 of a second.[1]

This definition fixed the speed of light in a vacuum at precisely 299,792,458 metres per second. Although the metre is now defined as the path length travelled by light in a given time, actual laboratory realisations of the metre are still delineated by measuring the wavelength of laser light of a standard type,[7] using interferometry to effectively count the number of wavelengths in a metre. Three major factors limit the accuracy attainable with laser interferometers:[8]

• Uncertainty in vacuum wavelength of the source,
• Uncertainty in the refractive index of the medium,
• Laser count resolution of the interferometer.

Use of the interferometer to define the metre is based upon the relation:

$\lambda = \frac{c}{n f} \ ,$

where λ is the determined wavelength; c is the speed of light in ideal vacuum; n is the refractive index of the medium in which the measurement is made; and f is the frequency of the source. In this way the length is related to one of the most accurate measurements available: frequency.[8]

An intended byproduct of the 17th CGPM’s definition was that it enabled scientists to measure the wavelength of their lasers with one-fifth the uncertainty. To further facilitate reproducibility from lab to lab, the 17th CGPM also made the iodine-stabilised helium-neon laser “a recommended radiation” for realising the metre. For purposes of delineating the metre, the BIPM currently considers the HeNe laser wavelength to be as follows: λHeNe = 632.99139822 nm with an estimated relative standard uncertainty (U) of 2.5×10−11.[9] This uncertainty is currently the limiting factor in laboratory realisations of the metre as it is several orders of magnitude poorer than that of the second (U = 5×10−16).[10] Consequently, a practical realisation of the metre is usually delineated (not defined) today in labs as 1,579,800.298728(39) wavelengths of helium-neon laser light in a vacuum.

Timeline of definition

• 1790 May 8 – The French National Assembly decides that the length of the new metre would be equal to the length of a pendulum with a half-period of one second.
• 1791 March 30 – The 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 the Earth's meridian along a quadrant through Paris, that is the distance from the equator to the north pole.
• 1795 – Provisional metre bar constructed of brass.
• 1799 December 10 – The French National Assembly specifies the platinum metre bar, constructed on 23 June 1799 and deposited in the National Archives, as the final standard.
• 1889 September 28 – The first 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 ten percent iridium, measured at the melting point of ice.
• 1927 October 6 – The seventh CGPM adjusts the definition of the metre to be the distance, at 0 °C, 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 one centimetre diameter, symmetrically placed in the same horizontal plane at a distance of 571 millimetres from each other.
• 1960 October 14 – The 11th CGPM defines the metre to be equal to 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between the 2p10 and 5d5 quantum levels of the krypton-86 atom.[11]
• 1983 October 21 – The 17th CGPM defines the metre as equal to the length of the path travelled by light in vacuum during a time interval of 1299,792,458 of a second.[12]
• 2002  – The 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".[13]
Definitions of the metre since 1795 [14]
Basis of definition Date Absolute
uncertainty
Relative

uncertainty

1/10,000,000 part of the quarter of a meridian,

measurement by Delambre and Mechain

1795 0.5–0.1 mm 10−4
First prototype Metre des Archives

platinum bar standard

1799 0.05–0.01 mm 10−5
Platinum-iridium bar at

melting point of ice (1st CGPM)

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.
Hyperfine atomic transition; 1650763.73 wavelengths

of light from a specified transition in Krypton 86 (11th CGPM)

1960 0.01–0.005 µm 10−8
Length of the path travelled by light in a vacuum

in 1/299792458 of a second (17th CGPM)

1983 0.1 nm 10−10

SI prefixed forms of metre

SI prefixes are often employed to denote decimal multiples and submultiples of the metre, as shown in the table below. As indicated in the table, some are commonly used, while others are not. Long distances are usually expressed in km, astronomical units, light-years, or parsecs, 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.

Submultiples Multiples Value Symbol Name Value 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 Common prefixed units are in bold face.

The term micron is often used instead of micrometre, but this practice is officially discouraged.[15]

Spelling

Metre is used as the standard spelling of the metric unit for length in all English-speaking nations except the USA, which uses meter.[16]

The most recent official brochure, written in 2006, about the International System of Units (SI), Bureau international des poids et mesures, was written in French by the International Bureau of Weights and Measures. An English translation (using the spelling: metre) is included to make the SI standard "more widely accessible".[17]

In 2008, the U.S. English translation published by the U.S. National Institute of Standards and Technology chose to use meter in accordance with the United States Government Printing Office Style Manual.[18]

Equivalents in other units

Metric unit
expressed in non-SI units
Non-SI unit
expressed in metric units
1 metre 1.09361 yards 1 yard 0.9144 metres
1 metre 39.370 inches                1 inch 0.0254 metres
1 centimetre 0.39370 inch   1 inch 2.54 centimetres
1 millimetre 0.039370 inch   1 inch 25.4 millimetres
1 metre 1×1010 ångström   1 ångström 1×10−10 metre
1 nanometre 10 ångström   1 ångström 100 picometres

Within this table, "inch" (and "yard") means "international inch" (and yard).[21] though approximate conversions in the left-hand column hold for both international units and survey units.

"≈" means "is approximately equal to".
"≡" means "equals by definition" or equivalently, "is exactly equal to".

One metre is exactly equivalent to 10000254 inches and to 100009144 yards.

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

1 metre is nearly equivalent to 3 feet, 3 and 3/8 inches.[22] This gives an over-estimate of 0.125 mm.

Notes

1. ^ a b 17th General Conference on Weights and Measures (1983), Resolution 1.
2. ^ a b Wilkins c. 2007
3. ^ meter 2009.
4. ^ Humerfelt 2010
5. ^ National Institute of Standards and Technology 2003; Historical context of the SI: Unit of length (meter)
6. ^ Beers & Penzes 1992
7. ^ National Physical Laboratory 2010
8. ^ a b Zagar, 1999, pp. 6–67ff
9. ^ Penzes 2005, National Research Council 2010
10. ^ National Institute of Standards and Technology 2011.
11. ^ Barbrow & Judson 1976, appendix 6.
12. ^ Taylor and Thompson (2008a), Appendix 1, p. 70.
13. ^ Taylor and Thompson (2008a), Appendix 1, p. 77.
14. ^ Cardarelli 2003
15. ^ Taylor & Thompson 2003, p. 11.
16. ^ Naughtin 2008
17. ^ BIPM, 2006, p. 130ff.
18. ^ 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 (NIST) (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).
19. ^ Cambridge Advanced Learner's Dictionary 2008, s.v. parking meter, meter, speedometer.
20. ^ American Heritage Dictionary 1992, s.v. meter.
21. ^ Astin & Karo 1959.
22. ^ Well-known conversion, publicised at time of metrication.[where?]

References

• Alder, Ken. (2002). The Measure of All Things : The Seven-Year Odyssey and Hidden Error That Transformed the World. Free Press, New York ISBN 0-7432-1675-X

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• mètre — [ mɛtr ] n. m. • v. 1220; lat. metrum, gr. metron « mesure » I ♦ 1 ♦ Dans la prosodie grecque et latine, Nature du vers déterminée par le nombre et la suite des pieds qui le composent. 2 ♦ Élément de mesure du vers; chaque groupe de deux pieds… …   Encyclopédie Universelle

• métré — mètre [ mɛtr ] n. m. • v. 1220; lat. metrum, gr. metron « mesure » I ♦ 1 ♦ Dans la prosodie grecque et latine, Nature du vers déterminée par le nombre et la suite des pieds qui le composent. 2 ♦ Élément de mesure du vers; chaque groupe de deux… …   Encyclopédie Universelle

• Metre — Mètre Pour les articles homonymes, voir Mètre (homonymie) …   Wikipédia en Français

• -mètre — ♦ Élément, du gr. metrês, metros, metron, de metron « mesure » : géomètre, périmètre, baromètre, thermomètre. mètre, métrie, métrique, métro . éléments, du gr. metron, mesure, évaluation . I. ⇒ MÈTRE1, élém. formant Élém. entrant dans la constr.… …   Encyclopédie Universelle

• metre — me‧tre [ˈmiːtə ǁ ər] , meter written abbreviation m noun [countable] the basic unit for measuring length in the metric system: • This material is sold by the metre. * * * …   Financial and business terms

• metre — Adaptación gráfica propuesta para la voz francesa maître, ‘jefe de comedor de un restaurante’: «Le ocurre como al metre del gran restaurante, que parece siempre más distinguido que el más aseñorado de los comensales» (Época [Esp.] 11.8.97). Es… …   Diccionario panhispánico de dudas

• -metre — BrE meter AmE [mi:tə, mıtə US tər] suffix [in nouns] part of a metre, or a number of metres ▪ a millimetre ▪ a kilometer …   Dictionary of contemporary English

• metre — mettre; poser; placer ; admettre. Metre taula : mettre le couvert, mettre la table. Metem que li ague degun : admettons qu il n y ait personne. voir admetre …   Diccionari Personau e Evolutiu

• metre — Ⅰ. metre [1] (US meter) ► NOUN ▪ the fundamental unit of length in the metric system, equal to 100 centimetres (approx. 39.37 inches). ORIGIN French, from Greek metron measure . Ⅱ. metre [2] (US meter) …   English terms dictionary

• Metre — Me tre (m[=e] t[ e]r), n. See {Meter}. [1913 Webster] …   The Collaborative International Dictionary of English

• Mètre — (Meter), die Einheit des in der Revolutionsperiode eingeführten gesammten neuen französischen Längen , Flächen u. Hohlmaßes u. in Folge davon die Grundlage des französischen Gewichts. Der M. ist nach dem Gesetz vom 10. Dec. 1799 der… …   Pierer's Universal-Lexikon