# Metre: Map

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The metre (or meter) is the basic unit of length in the International System of Units (SI). 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 one ten-millionth of the distance from the Equator to the North Pole through Paris. In 1983, the metre was redefined as the distance travelled by light in free space in of a second.

The symbol for metre is m. Decimal multiples such as kilometre and centimetre are indicated by adding SI prefixes to metre.

## History

The word metre is from the Greek (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 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

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.

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.

### 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.

### 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:

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:
• 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 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.

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: with an estimated relative standard uncertainty (U) of . 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 ( ). Consequently, a practical realisation of the metre is usually delineated (not defined) today in labs as 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 of a second.
• 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."

## 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 is preferred among the majority of countries in the English-speaking world except in the United States, where the spelling is 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".

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.

The spelling (-)meter for measuring devices, is the only correct spelling regardless of country, such as: parking meter, speedometer. (Meter, the device, has the same derivation as the metre detailed in this article.

## Equivalents in other units

Metric unit
expressed in non-SI unit
Non-SI unit
expressed in metric unit
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".

"≈" means "is approximately equal to".

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

## Notes

1. See American and British English spelling differences#-re, -er
2. The BIPM does not distinguish between quantum vacuum and free space. Resolution 1 of the 17th CGPM (CGPM, 1984), retrieved from BIPM database (BIPM, n.d.) on 24 August 2008.
3. See Time Line for the Definition of the Meter (Penzes, 2005), published by the NIST; and these papers from the BIPM database; particularly Optical Frequency - Maintaining the SI Metre (National Research Council of Canada, 2008)
4. NIST: NIST-F1 Cesium Fountain Atomic Clock.
5. Taylor and Thompson (2008a), Appendix 1, p. 70.
6. Taylor and Thompson , Appendix 1, p. 77.
7. BIPM, 2006, p. 130ff.
8. 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 , as the "legal interpretation" of the SI for the United States (Turner).
9. Cambridge Advanced Learner's Dictionary (2008). Cambridge University Press. s.v. parking meter, meter, speedometer.
10. American Heritage Dictionary of the English Language. 3rd ed. (1992). Boston: Houghton Mifflin. s.v. meter.
11. 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, June 30, 1959, 8:45 a.m.)