Metre

The metre (or meter), 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, its definition has been periodically refined to reflect growing knowledge of metrology. Since 1983, it is defined as the distance travelled by light in vacuum in of a second.

History

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. In 1675 the Italian scientist Tito Livio Burattini, in his work Misura Universale, used the words metro cattolico ( ) which was derived from the Greek (métron katholikón), "a ". This word gave rise to the French mètre which in 1797 was introduced into the English language.

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.

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.

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:

of a second.

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:

:$\backslash lambda\; =\; \backslash frac\{c\}\{n\; f\}\; \backslash \; ,$

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. 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 14 – 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) considers the metre to be a unit of proper length and thus 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."

Within this table, "inch" means "international inch".

"≈" means "is approximately equal to".

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

A simple mnemonic aid exists to assist with conversion; :1 metre is equivalent to 3 feet, 3 and 3/8 inches. This gives an over-estimate of 0.125 mm.

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

17th General Conference on Weights and Measures. (1983). Resolution 1. International Bureau of Weights and Measures. Beers, J.S. & Penzes, W. B. (1992). NIST Length Scale Interferometer Measurement Assurance. (NISTIR 4998). National Institute of Standards and Technology. 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 26 May 2010.

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.

Zagar, B.G. (1999). Laser interferometer displacement sensors in J.G. Webster (ed.). The Measurement, Instrumentation, and Sensors Handbook. CRC Press. isbn=0849383471.

Further reading

Alder, Ken. (2002). The Measure of All Things : The Seven-Year Odyssey and Hidden Error That Transformed the World. Free Press, New York ISBN 0-7432-1657-X

Category:SI base units Category:Units of length