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# Metre

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### Metre

Metre
Historical International Prototype Metre bar, made of an alloy of platinum and iridium, that was the standard from 1889 to 1960.
Unit information
Unit system SI base unit
Unit of Length
Symbol m
Unit conversions
1 m in ... ... is equal to ...
dm    10
cm    100
mm    1000
km    0.001
ft    3.28084
in    39.3701

The metre (BIPM spelling), or meter (American spelling), (SI unit symbol: m), is the fundamental unit of length (SI dimension symbol: L) in the International System of Units (SI).[1] 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 has been defined as "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second."[2]

## Contents

• History 1
• Meridional definition 1.1
• Prototype metre bar 1.2
• Standard wavelength of krypton-86 emission 1.3
• Speed of light 1.4
• Length measurement in metres 1.4.1
• Timeline of definition 1.5
• SI prefixed forms of metre 2
• Spelling 3
• Equivalents in other units 4
• Notes 6
• References 7

## History

A decimal-based unit of length, the universal measure or standard was proposed in an essay of 1668 by the English cleric and philosopher French Academy of Sciences and charged with determining a single scale for all measures, advised the adoption of a decimal system (27 October 1790) and suggested a basic unit of length equal to one ten-millionth of the distance between the North Pole and the Equator,[5] to be called mètre ("measure") (19 March 1791).[6][7][8] The National Convention adopted the proposal in 1793. The first occurrence of metre in this sense in English dates to 1797.[9]

Belfry, Dunkirk—the northern end of the meridian arc
Fortress of Montjuïc—the southerly end of the meridian arc
Creating the metre-alloy in 1874 at the Conservatoire des Arts et Métiers. Present Henri Tresca, George Matthey, Saint-Claire Deville and Debray

### 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 Rijnland inches or 39 14 English inches (997 mm) in length.[3] 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.

To establish a universally accepted foundation for the definition of the metre, more accurate measurements of this meridian would have to be made. 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 a belfry in Dunkerque and Montjuïc castle in Barcelona to estimate the length of the meridian arc through Dunkerque. This portion of the meridian, assumed to be the same length as the Paris 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". Despite this fact, and based on provisional results from the expedition, France adopted the metre as its official unit of length in 1793. 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 m).[10]

### Prototype metre bar

In the 1870s and in light of modern precision, a series of international conferences was held to devise new metric standards. The 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.[11]

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.[12]

### 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 International System of Units (SI) 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.[13]

### Speed of light

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

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.[2]

This definition fixed the speed of light in vacuum at exactly 299,792,458 metres per second. An intended by-product of the 17th CGPM's definition was that it enabled scientists to compare their 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.[14] 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.[14][15][16] 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).[17] Consequently, a realisation of the metre is usually delineated (not defined) today in labs as 1,579,800.800000(33) wavelengths of helium-neon laser light in a vacuum, the error stated being only that of frequency determination.[14] 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.[18] A commonly used medium is air, and the National Institute of Standards and Technology has set up an online calculator to convert wavelengths in vacuum to wavelengths in air.[19] 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.[20] 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 1,579,800.800000(33) wavelengths of helium-neon laser light in vacuum, and converting the wavelengths in a vacuum to wavelengths in air. Of course, 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.[21]

#### Length measurement in metres

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,[23] and converting the selected unit of wavelength to metres. Three major factors limit the accuracy attainable with laser interferometers for a length measurement:[18][24]

• Uncertainty in vacuum wavelength of the source
• Uncertainty in the refractive index of the medium
• Least count resolution of the interferometer

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

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

which converts the unit of wavelength λ to metres using c, the speed of light in a 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.[24]

### Timeline of definition

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
• 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. Based on Bessel's ellipsoid and legally equal to 443.44 lines on the toise du Pérou (a standard French unit of length from 1747).
• 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. Legally equal to 443.296 lines on the toise du Pérou.
• 1889 September 28 – The 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.
• 1927 October 6 – The 7th CGPM redefines the metre as the distance, at 0 °C (32 °F), 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 1 cm (0.39 in) diameter, symmetrically placed in the same horizontal plane at a distance of 571 millimetres (22.5 in) from each other.
• 1960 October 14 – The 11th CGPM defines the metre as 1,650,763.73 wavelengths in a vacuum of the radiation corresponding to the transition between the 2p10 and 5d5 quantum levels of the krypton-86 atom.[25]
• 1983 October 21 – The 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.[26]
• 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".[27]
Definitions of the metre since 1795[28]
Basis of definition Date Absolute
uncertainty
Relative
uncertainty
1/10,000,000 part of the quarter of a meridian, astronomical measure by Bessel (443.44 lines) 1792 0.5–0.1 mm 10−4
1/10,000,000 part of the quarter of a meridian, measurement by Delambre and Mechain (443.296 lines) 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; 1,650,763.73 wavelengths of light from a specified transition in krypton-86 (11th CGPM) 1960 4 nm 4x10−9[29]
Length of the path travelled by light in a vacuum in 1/299,792,458 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 (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 term micron is often used instead of micrometre, but this practice is officially discouraged.[30]

 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.

## 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.

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".[31]

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.[32]

Measuring devices (such as ammeter, speedometer) are spelt "-meter" in all countries.[33] The word "meter", signifying any such device, has the same derivation as the word "metre", denoting the unit of length.[34]

## 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 1×1010 ångström 1 ångström 1×10−10 metre
1 nanometre 10 ångström 1 ångström 100 picometres

Within this table, "inch" and "yard" mean "international inch" and "international yard",[35] respectively, though approximate conversions in the left-hand column hold for both international and survey units.

"≈" means "is approximately equal to";
"≡" means "equal by definition" or "is exactly equal to."

One metre is exactly equivalent to 10,000/254 inches and to 10,000/9,144 yards. A simple mnemonic aid exists to assist with conversion, as three "3"s:

1 metre is nearly equivalent to 3 feet–3 38 inches.[36] This gives an overestimate of 0.125 mm.

The ancient Egyptian cubit was about 12 m (surviving rods are 52.3–52.9 cm.) Scottish and English definitions of the ell (two cubits) were 0.941 m and 1.143 m, respectively. The ancient Parisian toise (fathom) was slightly shorter than 2 m, and was standardised at exactly 2 m in the mesures usuelles system, such that 1 m was exactly 12 toise. The Russian versta was 1.0668 km. The Swedish mil was 10.688 km, but was changed to 10 km when Sweden converted to metric units.

## Notes

1. ^ "Base unit definitions: Meter".
2. ^ a b "17th Conférence Générale des Poids et Mesures (CGPM) - Resolution 1 of the CGPM (1983): Definition of the metre".
3. ^ a b Wilkins c. 2007
4. ^ George Sarton (1935). "The First Explanation of Decimal Fractions and Measures (1585). Together with a History of the Decimal Idea and a Facsimile (No. XVII) of Stevin's Disme". Isis 23 (1): 153–244.
5. ^ ('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.
6. ^ Paolo Agnoli,Il senso della misura: la codifica della realtà tra filosofia, scienza ed esistenza umana, Armando Editore, 2004 pp.93-94,101.
7. ^ "Rapport sur le choix d'une unité de mesure, lu à l'Académie des sciences, le 19 mars 1791" (in French). Gallica.bnf.fr. 2007-10-15. Retrieved 2013-03-25.
8. ^ Paolo Agnoli and Giulio D’Agostini,'Why does the meter beat the second?,' December, 2004 pp.1-29.
9. ^ Oxford English Dictionary, Clarendon Press 2nd ed.1989, vol.IX p.697 col.3.
10. ^ Humerfelt 2010
11. ^ National Institute of Standards and Technology 2003; Historical context of the SI: Unit of length (meter)
12. ^ Beers & Penzes 1992
13. ^ Marion, Jerry B. (1982). Physics For Science and Engineering. CBS College Publishing. p. 3.
14. ^ a b c d "Iodine (λ≈633 nm)" (PDF). MEP (Mise en Pratique). BIPM. 2003. Retrieved 16 December 2011.
15. ^ 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.
16. ^ National Research Council 2010
17. ^ National Institute of Standards and Technology 2011.
18. ^ 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.
19. ^ The formulas used in the calculator and the documentation behind them are found at "Engineering metrology toolbox: Refractive index of air calculator". NIST. September 23, 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.
20. ^ "§VI: Uncertainty and range of validity". Engineering metrology toolbox: Refractive index of air calculator. NIST. September 23, 2010. Retrieved 16 December 2011.
21. ^ 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.
22. ^ National Physical Laboratory 2010
23. ^ The BIPM maintains a list of recommended radiations on their web site.[14][22]
24. ^ a b ffZagar, 1999, pp. 6–65
25. ^ Barbrow & Judson 1976, appendix 6.
26. ^ Taylor and Thompson (2008a), Appendix 1, p. 70.
27. ^ Taylor and Thompson (2008a), Appendix 1, p. 77.
28. ^ Cardarelli 2003
29. ^ Definition of the metre Resolution 1 of the 17th meeting of the CGPM (1983)
30. ^ Taylor & Thompson 2003, p. 11.
31. ^ BIPM, 2006, p. 130ff.
32. ^ 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).
33. ^ Cambridge Advanced Learner's Dictionary. , s.v. ammeter, meter, parking meter, speedometer.
34. ^ American Heritage Dictionary of the English Language (3rd ed.). Boston: , s.v. meter.
35. ^ Astin & Karo 1959.
36. ^ Well-known conversion, publicised at time of metrication.

## References

• 17th General Conference on Weights and Measures. (1983). Resolution 1. International Bureau of Weights and Measures.
• Astin, A. V. & Karo, H. Arnold, (1959), Refinement of values for the yard and the pound, Washington DC: National Bureau of Standards, republished on National Geodetic Survey web site and the Federal Register (Doc. 59-5442, Filed, 30 June 1959, 8:45 a.m.)
• Barbrow, Louis E. & Judson, Lewis V. (1976). Weights and Measures Standards of the United States: A brief history (Special Publication 447).. National Institute of Standards and Technology.
• Beers, J.S. & Penzes, W. B. (1992). NIST Length Scale Interferometer Measurement Assurance. (NISTIR 4998). National Institute of Standards and Technology.
• "The International System of Units (SI)" (PDF) (in French). Bureau International des Poids et Mesures. 2006. Retrieved 18 August 2008.
• HTML version. Retrieved 24 August 2008.
• Bureau International des Poids et Mesures. (n.d.). Resolutions of the CGPM (search facility). Retrieved 3 June 2006.
• Bureau International des Poids et Mesures. (n.d.). The BIPM and the evolution of the definition of the metre. Retrieved 3 June 2006.
• Cardarelli, Francois (2003). Encydopaedia of scientific units, weights, and measures: their SI equivalences and origins, Springer-Verlag London Limited, ISBN 1-85233-682-X, page 5, table 2.1, data from Giacomo, P., Du platine a la lumiere, Bull. Bur. Nat. Metrologie, 102 (1995) 5–14.
• Humerfelt, Sigurd. (26 October 2010). How WGS 84 defines Earth. Retrieved 29 April 2011.
• Layer, H.P. (2008). Length—Evolution from Measurement Standard to a Fundamental Constant. Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 18 August 2008.
• Mohr, P., Taylor, B.N., and David B. Newell, D. (28 December 2007). CODATA Recommended Values of the Fundamental Physical Constants: 2006. Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 18 August 2008.
• National Institute of Standards and Technology. (December 2003). The NIST Reference on Constants, Units, and Uncertainty: International System of Units (SI) (web site):
• SI base units. Retrieved 18 August 2008.
• Definitions of the SI base units. Retrieved 18 August 2008.
• Historical context of the SI: Meter. Retrieved 26 May 2010.
• National Institute of Standards and Technology. (27 June 2011). NIST-F1 Cesium Fountain Atomic Clock. Author.
• National Physical Laboratory. (25 March 2010). Iodine-Stabilised Lasers. Author.
• National Research Council Canada. (5 February 2010). Maintaining the SI unit of length. Retrieved 4 December 2010.
• Penzes, W. (29 December 2005). Time Line for the Definition of the Meter. Gaithersburg, MD: National Institute of Standards and Technology – Precision Engineering Division. Retrieved 4 December 2010.
• Taylor, B.N. and Thompson, A. (Eds.). (2008a). The International System of Units (SI). United States version of the English text of the eighth edition (2006) of the International Bureau of Weights and Measures publication Le Système International d’ Unités (SI) (Special Publication 330). Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 18 August 2008.
• Taylor, B.N. and Thompson, A. (2008b). Guide for the Use of the International System of Units (Special Publication 811). Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 23 August 2008.
• Tibo Qorl. (2005) The History of the Meter (Translated by Sibille Rouzaud). Retrieved 18 August 2008.
• Turner, J. (Deputy Director of the National Institute of Standards and Technology). (16 May 2008)."Interpretation of the International System of Units (the Metric System of Measurement) for the United States". Federal Register Vol. 73, No. 96, p. 28432-3.
• Wilkins, J. (c. 2007). An essay towards a real character, and a philosophical language.[Also available without images of original.] Metrication Matters. (Reprinted from title page and pp. 190–194 of original, 1668, London: Royal Society)
• Zagar, B.G. (1999). Laser interferometer displacement sensors in J.G. Webster (ed.). The Measurement, Instrumentation, and Sensors Handbook. CRC Press. isbn=0-8493-8347-1.

• 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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