meter

The metre or meter (from the Greek μέτρον /΄metron/)^[1] is a unit of proper length.^[2] It is the basic unit of length in the metric system and in the International System of Units (SI), used around the world for general and scientific purposes. Historically, the metre was defined by the French Academy of Sciences as the length between two marks on a platinum-iridium bar, which was designed to represent ¹⁄_10,000,000 of the distance from the equator to the north pole through Paris. In 1983, it was redefined by the International Bureau of Weights and Measures (BIPM) as the distance travelled by light in free space in ¹⁄_299,792,458 of a second.^[3]

The symbol for metre is a lower case m. Decimal multiples and submultiples of the metre, such as kilometre (1000 metres) and centimetre (¹⁄₁₀₀ metre), are indicated by adding SI prefixes to metre.

History

The word metre is from the Greek μέτρον (métron), "a measure", via the French mètre. It was first introduced in modern usage (metro cattolico) by Italian scientist Tito Livio Burattini in his work Misura Universale in 1675, in order to rename the universal measure unit proposed by John Wilkins in 1668. Its first recorded usage in English meaning this unit of length is from 1797.

Meridional definition

In the eighteenth century, there were two favoured approaches to the definition of the standard unit of length. One approach suggested 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 Bureau des Longitudes commissioned an expedition led by Delambre and Pierre Méchain, lasting from 1792 to 1799, which measured the length of the meridian 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.

However, in 1793, France adopted as its official unit of length a metre based on provisional results from the expedition as its official unit of length. Although it was later determined that the first prototype metre bar was short by a fifth of a millimetre due to 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 were 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.

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. The original international prototype of the metre is still kept at the BIPM under the conditions specified in 1889.

Standard wavelength of helium-neon laser 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 time 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.^[3]

This definition effectively fixed the speed of light in a vacuum at precisely 299,792,458 metres per second. Although the metre is now defined in terms of time-of-flight, actual laboratory realizations 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:^[4]

• Uncertainty in vacuum wavelength of the source,
• Uncertainty in the refractive index of the medium,
• Laser count resolution of the interferometer.

Use of the interferometer to determine the metre is based upon the relation:

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.^[4]

An intended byproduct of the 17^th 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 17^th 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: λ_HeNe = 632.99139822 nm with an estimated relative standard uncertainty (U) of 2.5×10⁻¹¹.^[5] 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).^[6] 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

• 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.
• 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.
• 1889 September 28 — The first 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 ten percent iridium, measured at the melting point of ice.
• 1927 October 6 — The seventh CGPM adjusts the definition of the metre to be the distance, at 0 °C, 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 one centimetre diameter, symmetrically placed in the same horizontal plane at a distance of 571 millimetres from each other.
• 1960 October 20 — The eleventh CGPM defines the metre to be equal to 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between the 2p¹⁰ and 5d⁵ quantum levels of the krypton-86 atom.
• 1983 October 21 — The seventeenth CGPM defines the metre as equal to the distance travelled by light in vacuum during a time interval of ¹⁄_299,792,458 of a second.^[7]
• 2002 — The International Committee for Weights and Measures (CIPM) 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."^[2]

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.

Spelling

Two spellings of the name of the unit are common in English: metre and meter (U.S.).^[1] The most recent official brochure about the International System of Units (SI) was written in French by the International Bureau of Weights and Measures (BIPM: Bureau international des poids et mesures), in 2006. An English translation is included to make the SI standard "more widely accessible".^[8] The UK English spelling is preferred among the majority of the English-speaking world apart from the United States, as meter is commonly used to describe counting machines such as parking meters and electrical meters. In 2008, the U.S. English translation published by the U.S. National Institute of Science and Technology chose to use meter in accordance with the United States Government Printing Office Style Manual.^[9]

Equivalents in other units

Within this table, "inch" means "international inch".^[10]

See also

• Conversion of units for comparisons with other units
• International System of Units
• ISO 1 – standard reference temperature for length measurements
• Metre Convention
• Metric system
• Metrication
• Orders of magnitude (length)
• SI prefix
• Speed of light

Notes

References

• Bureau International des Poids et Mesures. (2006). The International System of Units (SI). 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.
• 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: Metre. Retrieved 18 August 2008.
• National Research Council Canada. (16 May 2008). Optical Frequency - Maintaining the SI Metre. Retrieved 18 August 2008.
• 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 3 June 2006.
• 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.