Metre

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

The metre (meter in the US), 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 1 ⁄ 299,792,458 of a second.[1]

Contents

History

Main article: History of the metre

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 μέτρον καθολικόν (métron katholikón), "a universal measure". This word gave rise to the French mètre which in 1797 was introduced into the English language.[3]

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.

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

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 1 ⁄ 299,792,458 of a second.[1]

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. For purposes of delineating the metre, the BIPM currently considers the HeNe laser wavelength to be as follows: λHeNe = 632 991 212.58 fm with an estimated relative standard uncertainty (U ) of 2.1×10−11.[7][8] 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 ).[9] Consequently, a realisation of the metre is usually delineated (not defined) today in labs as 1,579,800.762042(33) wavelengths of helium-neon laser light in vacuum, the error stated being only that of frequency determination.[10] 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, in addition to various uncertainties of interferometry, and to uncertainties in measuring the frequency of the source.[11] A commonly used medium is air, and NIST has set up an on-line calculator to convert wavelengths in vacuum to wavelengths in air.[12] As described by NIST, in air the uncertainties in characterising the medium are dominated by errors in finding temperature and pressure, and errors in the theoretical formulas used are secondary.[13] By implementing a refractive index correction such as this, an approximate realization of the metre can be implemented in air, for example, using the formulation of the metre as 1,579,800.762042(33) wavelengths of helium-neon laser light in vacuum, and converting the wavelengths in vacuum to wavelengths in air. Of course, air is only one possible medium to use in a realization 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.[14]

Length measurement in metres

Although the metre is now defined as the path length travelled by light in a given time, actual 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,[15] and converting the selected unit of wavelength to metres. Three major factors limit the accuracy attainable with laser interferometers for a length measurement:[16][11]

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 vacuum in m/s. Here n is the refractive index of the medium in which the measurement is made; and f is taken for the conversion here as the measured frequency of the source. Although conversion from wavelengths to metres introduces additional error in the overall length due to measurement error in determining the refractive index and the frequency, measurement of frequency is one of the most accurate measurements available.[16]

Timeline of definition

Definitions of the metre since 1795 [20]
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 (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.

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.[21]

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.[22]

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".[23]

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.[24]

Measuring devices (such as parking meter, speedometer) are traditionally spelt "...meter" in all countries.[25] The word "meter", signifying any such device, has the same derivation as the word "metre", denoting the unit of length this article is about.[26]

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).[27] 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 10000⁄254 inches and to 10000⁄9144 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.[28] This gives an over-estimate of 0.125 mm.

The ancient Egyptian cubit was about ½ m (surviving rods are 52.3–52.9 cm). The ancient Paris toise (fathom) was slightly shorter than 2 m, and was standardized at exactly 2 m in the mesures usuelles system, such that 1 m was exactly ½ toise. The Russian verst was 1.0668 km, and Swedish mil was 10.688 km.

See also

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. ^ 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. ^ 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. http://physics.nist.gov/cgi-bin/cuu/Info/Constants/definitions.html. Retrieved 2011-12-19. 
  8. ^ Iodine (λ≈633nm), National Research Council 2010
  9. ^ National Institute of Standards and Technology 2011.
  10. ^ "Iodine (λ ≈ 633 nm)". MEP (Mise en Pratique) 2003. BIPM. http://www.bipm.org/utils/common/pdf/mep/M-e-P_I2_633.pdf. Retrieved 2011-12-16. 
  11. ^ a b A more detailed listing of errors can be found in John S Beers, William B Penzes (December 1992). "§4 Re-evaluation of measurement errors". NIST length scale interferometer measurement assurance; NIST document NISTIR 4998. pp. 9 ff. http://www.nist.gov/calibrations/upload/4998.pdf. Retrieved 2011-12-17. 
  12. ^ 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. http://emtoolbox.nist.gov/Wavelength/Documentation.asp. Retrieved 2011-12-16.  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.
  13. ^ "§VI: Uncertainty and range of validity". Engineering metrology toolbox: Refractive index of air calculator. NIST. September 23, 2010. http://emtoolbox.nist.gov/Wavelength/Documentation.asp#UncertaintyandRangeofValidity. Retrieved 2011-12-16. 
  14. ^ F. B. Dunning, Randall G. Hulet (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 0124759777. http://books.google.com/books?id=FV4Y39AGYuYC&pg=PA316. "The error [introduced by using air] can be reduced tenfold if the chamber is filled with an atmosphere of helium rather than air." 
  15. ^ National Physical Laboratory 2010
  16. ^ a b Zagar, 1999, pp. 6–65ff
  17. ^ Barbrow & Judson 1976, appendix 6.
  18. ^ Taylor and Thompson (2008a), Appendix 1, p. 70.
  19. ^ Taylor and Thompson (2008a), Appendix 1, p. 77.
  20. ^ Cardarelli 2003
  21. ^ Taylor & Thompson 2003, p. 11.
  22. ^ Naughtin 2008
  23. ^ BIPM, 2006, p. 130ff.
  24. ^ 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).
  25. ^ Cambridge Advanced Learner's Dictionary 2008, s.v. parking meter, meter, speedometer.
  26. ^ American Heritage Dictionary 1992, s.v. meter.
  27. ^ Astin & Karo 1959.
  28. ^ Well-known conversion, publicised at time of metrication.

References

Further reading

Base units
Ampere · Candela · Kelvin · Kilogram · Metre · Mole · Second
Derived units
Becquerel · Coulomb · degree Celsius · Farad · Gray · Henry · Hertz · Joule · Katal · Lumen · Lux · Newton · Ohm · Pascal · Radian · Siemens · Sievert · Steradian · Tesla · Volt · Watt · Weber
Accepted for use
with SI
See also
Book:International System of Units  · Category:SI base units
SI units of length