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, its definition has been periodically refined to reflect growing knowledge of metrology. Since 1983, it is defined as the distance travelled by light in vacuum in 1⁄299,792,458 of a second.[1]

Contents

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][3] In 1675 the Italian scientist Tito Livio Burattini, in his work Misura Universale, used the words metro cattolico (metre catholic) which was derived from the Greek μέτρον καθολικόν (métron katholikón), "a universal measure". This word gave rise to the French mètre which in 1797 was introduced into the English language.[4]

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][3]

In the eighteenth 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 Delambre and Pierre Méchain, lasting from 1792 to 1799, which measured the length of the meridian arc between Dunkerque and Barcelona. This portion of the meridian, which also passes through Paris, 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 ellipse) 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.

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 distance. 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 1⁄299 792 458 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 distance travelled by light in a given time, actual laboratory realisations of the metre are still delineated by counting the required number of wavelengths of light along the distance. Three major factors limit the accuracy attainable with laser interferometers:[7]

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.[7]

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.[8] 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).[9] 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

Definitions of the metre since 1795 [13]
Basis of definition Date Absolute
uncertainty		 Relative

uncertainty
1/10000000 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 specfied transition in Krypton 86 (11th CGPM)

 1960 0.01–0.005 µm 10−8
Distance traversed in vacuum by light

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, 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.

SI multiples for metre (m)
Submultiples Multiples
Value Symbol Name Value 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
Common prefixed units are in bold face.

The term micron is often used instead of micrometre, but this practice is officially discouraged.[14]

Spelling

Two spellings of the name of the unit are common in English: metre and meter. The former is the standard spelling in Britain and most Commonwealth countries, while the latter is American English.[15]

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".[16]

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.[17]

Measuring devices (such as parking meter, speedometer) are traditionally spelt "...meter" in all countries.[18] The word "meter", signifying any such device, has the same derivation as the word "metre", denoting the unit of length this article is about.[19]

Equivalents in other units

Metric unit
expressed in non-SI units  		 Non-SI unit
expressed in metric units
1 metre ≈ 39.37 inches                1 inch ≡ 0.0254 metres           
1 centimetre ≈ 0.3937 inch   1 inch ≡ 2.54 centimetres  
1 millimetre ≈ 0.03937 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" means "international inch".[20]

"≈" means "is approximately equal to".

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

A simple mnemonic aid exists to assist with conversion;

1 metre is equivalent to 3 feet, 3 and 3/8 inches.[21] This gives an over-estimate of 0.125 mm.

See also

Orders of magnitude for length in E notation, shorter than one metre:
<−24 −24 −23 −22 −21 −20 −19 −18 −17 −16 −15 −14 −13 −12 −11 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0
longer than 1 metre:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Notes

  1. ↑ 1.0 1.1 17th General Conference on Weights and Measures (1983), Resolution 1.
  2. ↑ 2.0 2.1 An Essay towards a Real Character and a Philosophical Language (Reproduction)
  3. ↑ 3.0 3.1 An Essay towards a Real Character and a Philosophical Language (Transcription)
  4. ↑ meter. (2009). In Merriam-Webster Online Dictionary. Retrieved 8 December 2009.
  5. ↑ National Institute of Standards and Technology 2003; Historical context of the SI: Unit of length (meter)
  6. ↑ Beers & Penzes 1992
  7. ↑ 7.0 7.1 Zagar, 1999, pp. 6–67ff
  8. ↑ See Penzes 2005 and these papers from the BIPM database; particularly Optical Frequency - Maintaining the SI Metre (National Research Council of Canada, 2008)
  9. ↑ NIST: NIST-F1 Cesium Fountain Atomic Clock.
  10. ↑ National Institute of Standards and Technology
  11. ↑ Taylor and Thompson (2008a), Appendix 1, p. 70.
  12. ↑ Taylor and Thompson (2008a), Appendix 1, p. 77.
  13. ↑ Cardarelli, Francois Encydopaedia of scientific units, weights, and measures: their SI equivalences and origins, Springer-Verlag London Limited 2003, 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.
  14. ↑ NIST Guide to the SI: #5.2.3 Other Unacceptable Units - Retrieved 12 March 2010
  15. ↑ See American and British English spelling differences#-re, -er
  16. ↑ BIPM, 2006, p. 130ff.
  17. ↑ 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).
  18. ↑ Cambridge Advanced Learner's Dictionary (2008). Cambridge University Press. s.v. parking meter, meter, speedometer.
  19. ↑ American Heritage Dictionary of the English Language. 3rd ed. (1992). Boston: Houghton Mifflin. s.v. meter.
  20. ↑ A. V. Astin & H. Arnold Karo, (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.)
  21. ↑ Well-known conversion, publicised at time of metrication.

References

Further reading

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See also
SI prefixes · Systems of measurement · Conversion of units
Wikipedia book Book:International System of Units  · Category Category:SI base units
SI units of length
yoctometre <<< zeptometre <<< attometre <<< femtometre <<< picometre <<< nanometre <<< micrometre <<< millimetre < centimetre < decimetre < metre < decametre < hectometre < kilometre <<< megametre <<< gigametre <<< terametre <<< petametre <<< exametre <<< zettametre <<< yottametre