Metre
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The metre (symbol: m), spelled meter in the United States, is the SI unit of length and one of the seven base units in the International System of Units. The name is derived from the Greek μέτρον (metron) meaning "measure", and gives rise to the term "metric system", a system of units of which the metre is one.
The metre was conceived in the aftermath of the French Revolution (1789) as a replacement for the old units of length that were associated with the ancien régime. Although there was initially considerable resistance to the adoption of the new units in France (including an official reversion to the mesures usuelles ["normal units"] for a period), the metre gained following in continental Europe during the mid nineteenth century, particularly in scientific usage, and was consacrated as an international measurement unit by the Metre Convention of 1875.
Definition
The current definition of the metre was agreed at the 17th General Conference on Weights and Measures (CGPM) in 1983:[1]
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.
This definition has the effect that the speed of light in vacuum has an exact, defined value in SI units: 299 792 458 m s−1.
Relativity
The metre is considered to be a unit of proper length. As such, the definition is only adequate in itself for measurements in an area where the local gravitational field can be considered to be uniform, a condition which is met by almost all measurements on the surface of the Earth (the Earth's gravitational field varies by about one part in 1016 per vertical metre, which is far less than the measurement uncertainty in Earth-based length measurements).[2] For astronomical measurements, the effects of general relativity cannot be ignored and the definition of the metre must be completed with a description of the metric tensor which defines the gravitational field.[3]
Realization
The metre can be realized either directly, by measuring the time taken for light to travel a certain distance, or by interferometry.[2][4]
Time-of-flight measurements
Interferometry
| Source | Stabilizing line (127I2) | Frequency THz |
Wavelength nm |
ur |
|---|---|---|---|---|
| Helium–neon laser | a16 component, R(127) 11-5 transition | 473.612 353 604(10) | 632.991 212 579(13) | 2.1 × 10−11 |
| Nd:YAG laser | a10 component, R(56) 32-0 transition | 563.260 223 513(5) | 532.245 036 104(5) | 8.9 × 10−12 |
For an unstabilized helium–neon laser (Ne 3s2→2p4 transition):[5]
- f = 473.612 7 THz
- λ = 632.990 8 nm
- ur = 1.5 × 10−6
History
Universal measure
The standard measures of length in Europe diverged from one another following the fall of the Roman Empire: while measures could be standardized within a given jurisdiction (which was often little more than a single market town), they were numerous varieties of measure between regions. Indeed, as the measures were often used as the basis for taxation (of cloth, for example), the use of a certain measure was associated with the sovereignty of a given ruler and often dictated by law.
Nevertheless, with the increasing scientific activity of the seventeenth century came calls for the institution of a "universal measure" (as Englishman John Wilkins called it[6]) or "metro cattolico" (Italian Tito Livio Burattini[7]), which would be based on a natural phenomenon rather than royal decree, and would also be decimal rather than the various systems of multipliers, often duodecimal, that coexisted at the time.
Wilkins' idea was to choose the length of a "seconds pendulum" (a pendulum with a half-period of one second) as the unit length: such pendulums had recently been demonstrated by Christiaan Huygens, and their length is very close to one modern metre (as well as to length units which were then in use, such as the yard). However, it was soon discovered that the length of a seconds pendulum varies from place to place: French astronomer Jean Richer had measured the 0.3% difference in length between Cayenne (in French Guiana) and Paris.[8]
Little practical progress was made towards the establishment of the "universal measure" until the French Revolution of 1789. France was particularly affected by the proliferation of length measures, and the need for reform was widely accepted across all political viewpoints, even if needed the push of revolution to bring it about. Talleyrand resurrected the idea of the seconds pendulum before the Constituant Assembly in 1790, suggesting that the new measure be defined at 45°N (a latitude that, in France, runs just north of Bordeaux and just south of Grenoble): dispite the support of the Assembly, and of Great Britain and the newly independent United States, nothing came of Talleyrand's proposal.[Note 1]
Meridional definition
Mètre des archives
International prototype metre
Krypton standard
Notes and references
Notes
References
- ↑ The International System of Units (SI), 8th ed.; International Bureau of Weights and Measures: Sèvres, France, 2006; p 112. ISBN 92-822-2213-6, <http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf>.
- ↑ 2.0 2.1 Recommendation 1 (CI-2002), 91st Meeting of the International Committee on Weights and Measures, 2002.
- ↑ Guinot, B. Application of general relativity to metrology. Metrologia 1997, 34 (3), 261–90. DOI: 10.1088/0026-1394/34/3/9.
- ↑ Mise en pratique for the definition of the metre; Interntional Bureau for Weights and Measures, 2009, <http://www.bipm.org/en/si/si_brochure/appendix2/mep.html>. (accessed 13 August 2010).
- ↑ Recommendation 2 (CI-2007), 96th Meeting of the International Committee on Weights and Measures, 2007.
- ↑ Wilkins, John An Essay Towards a Real Character, And a Philosophical Language; Gillibrand: London, 1668, <http://www.metricationmatters.com/docs/WilkinsTranslationLong.pdf>.
- ↑ Misura Universale, 1675.
- ↑ Poynting, John Henry; Thompson, Joseph John A Textbook of Physics: Properties of Matter, 4th ed.; Charles Griffin: London, 1907; p 20, <http://books.google.com/books?id=TL4KAAAAIAAJ&pg=PA20>.
External links
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See also the corresponding article on Wikipedia. |
- meter (metre) at Sizes.com
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