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The metre (Commonwealth spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure", and cognate with Sanskrit , meaning "measured") is the base unit of length in the International System of Units (SI). The SI unit symbol is m. The metre is currently defined as the length of the path travelled by light in a vacuum in of a second. 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  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.

Spelling

''Metre'' is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States and the Philippines, which use ''meter.'' Other Germanic languages, such as German, Dutch, and the Scandinavian languages, likewise spell the word ''meter.'' Measuring devices (such as ammeter, speedometer) are spelled "-meter" in all variants of English. The suffix "-meter" has the same Greek origin as the unit of length.

Etymology

The etymological roots of ''metre'' can be traced to the Greek verb () (to measure, count or compare) and noun () (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 (), French (), English and other languages. Ultimately the word came from the sanskrit "mita", meaning "measured". The motto () 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 ) in English began at least as early as 1797.Oxford English Dictionary, Clarendon Press 2nd ed.1989, vol.IX p.697 col.3.

History of definition

Meridional definition

International prototype metre bar

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. 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 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum.

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: ::The metre is the length of the path travelled by light in vacuum during a time interval of of a second. This definition fixed the speed of light in vacuum at exactly metres per second (≈). 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. For the purpose of delineating the metre, the BIPM currently considers the HeNe laser wavelength, , to be with an estimated relative standard uncertainty (''U'') of .The term "relative standard uncertainty" is explained by NIST on their web site: 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 (). Consequently, a realisation of the metre is usually delineated (not defined) today in labs as wavelengths of helium-neon laser light in a vacuum, the error stated being only that of frequency determination. 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. 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.The formulas used in the calculator and the documentation behind them are found at The choice is offered to use either th
modified Edlén equation
or th
Ciddor equation
The documentation provide
a discussion of how to choose
between the two possibilities.
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. 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 wavelengths of helium–neon laser light in 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. 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, and converting the selected unit of wavelength to metres. Three major factors limit the accuracy attainable with laser interferometers for a length measurement: A more detailed listing of errors can be found in Zagar, 1999, pp. 6–65''ff''. * 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 :$\lambda = \frac$ 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.

Timeline

Early adoptions of the metre internationally

Triangulation near New York City, 1817. After the July Revolution of 1830 the metre became the definitive French standard from 1840. At that time it had already been adopted by Ferdinand Rudolph Hassler for the U.S Survey of the Coast. "The unit of length to which all distances measured in the Coast Survey are referred is the French metre, an authentic copy of which is preserved in the archives of the Coast Survey Office. It is the property of the American Philosophical Society, to whom it was presented by Mr. Hassler, who had received it from Tralles, a member of the French Committee charged with the construction of the standard metre by comparison with the toise, which had served as unit of length in the measurement of the meridional arcs in France and Peru. It possesses all the authenticity of any original metre extant, bearing not only the stamp of the Committee but also the original mark by which it was distinguished from the other bars during the operation of standardising. It is always designated as the Committee metre" (French : ''Mètre des Archives''). In 1830 President Andrew Jackson mandated Ferdinand Rudolf Hassler to work out new standards for all U.S. states. According to the decision of the Congress of the United States, the British Parliamentary Standard from 1758 was introduced as the unit of length. Another geodesist with metrology skills was to play a pivotal role in the process of internationalization of weights and measures, Carlos Ibáñez e Ibáñez de Ibero who would become the first president of both the International Geodetic Association and the International Committee for Weights and Measures.

SI prefixed forms of metre

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.

Equivalents in other units

Within this table, "inch" and "yard" mean "international inch" and "international yard" respectively, though approximate conversions in the left 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 inches and to yards. A simple mnemonic aid exists to assist with conversion, as three "3"s: : 1 metre is nearly equivalent to 3feet inches. This gives an overestimate of 0.125mm; 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 0.5m (surviving rods are 523–529mm). Scottish and English definitions of the ell (two cubits) were 941mm (0.941m) and 1143mm (1.143m) respectively. The ancient Parisian ''toise'' (fathom) was slightly shorter than 2m and was standardised at exactly 2m in the mesures usuelles system, such that 1m was exactly toise. The Russian verst was 1.0668km. The Swedish mil was 10.688km, but was changed to 10km when Sweden converted to metric units.

* Conversion of units for comparisons with other units * International System of Units * Introduction to the metric system * ISO 1standard reference temperature for length measurements * Length measurement * Metre Convention * Metric system * Metric prefix * Metrication * Orders of magnitude (length) * SI prefix * Speed of light * Vertical metre

Notes

References

* * 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) * * * * *

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. * * Republic of the Philippines. (2 December 1978).

'. Author. * Republic of the Philippines. (10 October 1991). ''ttps://www.officialgazette.gov.ph/downloads/1991/10oct/19911010-RA-7160-CCA.pdf Republic Act No. 7160: The Local Government Code of the Philippines'. Author. * Supreme Court of the Philippines (Second Division). (20 January 2010).
G.R. No. 185240
'. Author. * 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. * 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. * Zagar, B.G. (1999)
Laser interferometer displacement sensors
in J.G. Webster (ed.). ''The Measurement, Instrumentation, and Sensors Handbook.'' CRC Press. . {{Authority control Category:Metrology Category:SI base units Category:UCUM base units Category:Units of length