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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]}
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]}
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 ^{1}⁄_{4} 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]}
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]}
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]}
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:
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, λ_{HeNe}, 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]}
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]}
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:
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]}
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]}
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]}
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.
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:
The ancient Egyptian cubit was about ^{1}⁄_{2} 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 ^{1}⁄_{2} 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.
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