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The '''metre''' (symbol: '''m'''), spelled '''meter''' in the United States,<ref group="Note">The spelling "meter" is the official spelling in the United States, following the ''Government Printing Office Style Manual'' and the usage of the [[National Institute of Standards and Technology]] (NIST), which has responsibility for interpreting the [[International System of Units]] (SI) in the United States by authority of the Secretary of Commerce under 15&nbsp;U.S.C.&nbsp;205: see [http://ts.nist.gov/WeightsAndMeasures/Metric/upload/FRN_Vol_73_No_96_16May2008_SI_Interpretation.pdf 73&nbsp;FR&nbsp;28432–33] (No.&nbsp;96, May&nbsp;16, 2008) and {{NIST SP 330|pages=iii, 18}}. Outside the United States, "metre" is the normal spelling, following the usage of the [[International Bureau of Weights and Measures]] (BIPM): see {{SIbrochure8th|page=112}}.</ref> is the [[SI unit]] of [[length]] and one of the seven [[base unit]]s 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&nbsp;[[General Conference on Weights and Measures]] (CGPM) in 1983:<ref name="SI">{{SIbrochure8th|page=112}}.</ref><ref name="NIST">{{NIST SP 330|page=18}}.</ref>
{{quotation|The metre is the length of the path travelled by light in vacuum during a time interval of {{frac|{{nowrap|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]]: ''c''<sub>0</sub>&nbsp;= {{nowrap|299 792 458&nbsp;m s<sup>−1</sup>}}.<ref name="SI"/><ref name="NIST"/>

===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 10<sup>16</sup> per vertical metre, which is far less than the [[measurement uncertainty]] in Earth-based length measurements).<ref name="1-CI-2002">Recommendation 1 (CI-2002), [http://www.bipm.org/utils/en/pdf/CIPM2002-EN.pdf 91st Meeting of the International Committee for Weights and Measures], 2002.</ref> 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 (general relativity)|metric tensor]] which defines the gravitational field.<ref>{{citation | last = Guinot | first = B. | title = Application of general relativity to metrology | journal = Metrologia | year = 1997 | volume = 34 | issue = 3 | pages = 261–90 | doi = 10.1088/0026-1394/34/3/9}}.</ref>

==Realization==
The metre can be [[Realization|realized]] either directly, by measuring the time taken for light to travel a certain distance ("time-of-flight"), or by [[interferometry]].<ref name="1-CI-2002"/><ref name="MeP">{{citation | title = ''Mise en pratique'' for the definition of the metre | url = http://www.bipm.org/en/si/si_brochure/appendix2/mep.html | publisher = International Bureau of Weights and Measures | date = 2009 | accessdate = 2010-08-13}}.</ref> Time-of-flight measurements are usually used for long distances (more than a few tens of metres), while interferometry is the normal technique for the measurement of lengths less than a few metres. In either case, corrections may be necessary for gravitational effects, [[diffraction]] and, especially, the [[refractive index]] of the medium:<ref name="1-CI-2002"/> for measurements in air, there are conventionally accepted formulae to calculate the refractive index based on local temperature, pressure and [[carbon dioxide]] content.

There are, of course, many other methods for the routine measurement of length, such as rulers, tape measures, calipers, micrometers, etc. These are properly considered as [[representation (metrology)|representation]]s of the metre and, for accurate work, their [[calibration]] should be [[Metrological traceability|traceable]] to one of the realizations of the metre (usually through interferometry).

===Time-of-flight measurements===
The best-known example of time-of-flight realizations of the metre is [[radar]], where a pulse of [[electromagnetic radiation]] (in this case, usually [[radio wave]]s) is sent out towards a distant object and the time interval ''t'' between the outgoing pulse and the reflected radiation is measured. This gives the distance ''d'' between the observer and the object as:
:''d'' = ''t''/2''c''
Similar measurements have been made of the distance to the Moon and to the inner planets of the Solar System. It is also possible, with adequate [[clock synchronization]], to measure the distance from a distant emittor to a receiver; this is the principle behind the Global Positioning System (GPS) and similar systems such as GLONASS and Galileo.

Time-of-flight measurements are the only practical solution to measure long distances: it is possible with modern electronics (e.g. a good [[oscilloscope]]) to measure lengths of the order of one metre by time-of-flight methods, but the accuracy and precision are much lower than for interferometric measurements. In the context of [[general relativity]], raw time-of-flight measurements (unlike interferometry) do not necessarily correspond to [[proper length]], and so may need correction for gravitational effects to correspond to the definition of the metre.<ref name="1-CI-2002"/>

===Interferometry===
[[Interferometry]] relies on the calculation of the difference in the number of [[wavelength]]s of [[monochromatic light]] between two unequal optical paths: by multiplying by the wavelength of the light, the difference in path length is obtained in metres. The wavelength may be calculated by measuring the [[frequency]], but it is much more usual to use one of the "recommended radiations" on a list that is published periodically by the [[International Committee for Weights and Measures]] (CIPM). The vacuum wavelength is given by
:''λ'' = ''c''<sub>0</sub>/''f''
Two radiations in particular are relevant for high-precision interferometry:

{| class="wikitable"
|-
! Source
! Stabilizing line (<sup>127</sup>I<sub>2</sub>)
! <u>Frequency</u><br/>THz
! <u>Wavelength</u><br/>nm
! [[Measurement uncertainty|''u''<sub>r</sub>]]
|-
| [[Helium–neon laser]]
| a<sub>16</sub> component, R(127) 11-5 transition
| 473.612 353 604(10)
| 632.991 212 579(13)
| 2.1{{e|−11}}
|-
| [[Nd:YAG laser]]
| a<sub>10</sub> component, R(56) 32-0 transition
| 563.260 223 513(5)
| 532.245 036 104(5)
| 8.9{{e|−12}}
|-
|}

The [[Measurement uncertainty|uncertainty]] in the frequencies (and hence the wavelengths) of the recommended radiations is far lower than is required for most length measurements. For routine interferometry, it is usual to use the [[neon]] 3s<sub>2</sub>&rarr;2p<sub>4</sub> transition of an unstabilized helium–neon laser, and the CIPM has also published a recommended frequency for this line to avoid an excessive need for calibration of individual sources:<ref>Recommendation 2 (CI-2007), [http://www.bipm.org/utils/en/pdf/CIPM2007-EN.pdf 96th Meeting of the International Committee on Weights and Measures], 2007.</ref>
:''f'' = 473.6127(7) THz
:''λ'' = 632.9908(9) nm
:''u''<sub>r</sub> = 1.5{{e|−6}}

==History==
===Universal measure===
The standard measures of length in Europe diverged from one another following the fall of Charlemagne's 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.<ref name="Larousse">{{LarousseXIXe | article = Métrique | volume = 11 | pages = 163–64}}.</ref><ref name="Nelson">{{citation | first = Robert A. | last = Nelson | title = Foundations of the international system of units (SI) | journal = Phys. Teacher | year = 1981 | pages = 596–613 | url = http://plato.if.usp.br/1-2009/fmt0159n/PDFFiles/ThePhysTeacher_FoundationsOfTheSI.pdf}}.</ref>

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<ref>{{citation | first = John | last = Wilkins | authorlink = John Wilkins | title = An Essay Towards a Real Character, And a Philosophical Language | location = London | publisher = Gillibrand | year = 1668 | url = http://www.metricationmatters.com/docs/WilkinsTranslationLong.pdf}}.</ref>) or "''metro cattolico''" (Italian [[Tito Livio Burattini]]<ref>{{citation | title = Misura Universale | year = 1675}}.</ref>), 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.<ref>{{citation | last1 = Poynting | first1 = John Henry | first2 = Joseph John | last2 = Thompson | title = A Textbook of Physics: Properties of Matter | edition = 4th | publisher = Charles Griffin | year = 1907 | location = London | page = 20 | url = http://books.google.com/books?id=TL4KAAAAIAAJ&pg=PA20}}.</ref>

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.<ref name="Larousse"/><ref group="Note">The idea of the seconds pendulum as a length standard did not die completely, and such a standard was used to define the [[yard]] in the United Kingdom from 1843 to 1878.</ref>

===Meridional definition===
The question of measurement reform was placed in the hands of the [[Academy of Sciences (France)|Academy of Sciences]] who appointed a commission chaired by [[Jean-Charles de Borda]]. Borda could be said to have been a fanatic for decimalization: he had invented the "repeating circle", a surveying instrument which allowed a much-improved precision in the measurement of angles between landmarks, but insisted that it be calibrated in "''[[grade]]s''" ({{frac|100}} of a quarter-circle) rather than [[degree]]s, with 100&nbsp;minutes to a ''grade'' and 100&nbsp;seconds to a minute.<ref>{{citation | title = Jean Charles de Borda | url = http://www-history.mcs.st-andrews.ac.uk/Biographies/Borda.html | publisher = MacTutor | accessdate = 2010-08-13}}.</ref> For Borda, the seconds pendulum was a poor choice for a standard because the second (as a unit of time) was insufficiently decimal: he preferred a system of 10&nbsp;hours to the day, 100&nbsp;minutes to the hour and 100&nbsp;seconds to the minute…

Instead, the commission – whose members included [[Joseph-Louis Lagrange|Lagrange]], [[Pierre-Simon Laplace|Laplace]], [[Gaspard Monge|Monge]] and [[Nicolas de Condorcet|Condorcet]] – decided that the new measure should be equal to one ten-millionth of the distance from the North Pole to the Equator (the quadrant of the Earth's circumference), measured along the meridian passing through Paris.<ref name="Larousse"/> Apart from the obvious nationalistic considerations, the Paris meridian was also a sound choice for practical scientific reasons: a portion of the quadrant from Dunkerque to Barcelona (about 1000&nbsp;km, or one-tenth of the total) could be surveyed with start- and end-points at sea level, and that portion was roughly in the middle of the quadrant, where the effects of the Earth's oblateness were expected to be the largest.<ref name="Larousse"/>

The task of surveying the meridian fell to [[Pierre Méchain]] and [[Jean-Baptiste Delambre]], and took more than six years (1792–98).<ref group="Note">The technical difficulties were not the only problems the surveyors had to face in the convulsed period of the aftermath of the Revolution: Méchain and Delambre, and later [[François Arago|Arago]], were imprisoned several times during their surveys, and Méchain died in 1804 of yellow fever, which he contracted while trying to improve his original results in northern Spain.</ref> In the meantime, the commission calculated a provisional value from older surveys of 443.44&nbsp;''[[ligne]]s''.<ref group="Note" name="lignes">All values in ''lignes'' are referred to the ''[[toise de Pérou]]'', not to the later value in ''[[mesures usuelles]]''. 1&nbsp;''[[toise]]''&nbsp;= 6&nbsp;''[[pied]]s''; 1&nbsp;''pied''&nbsp;= 12&nbsp;''[[pouce]]s''; 1&nbsp;''pouce''&nbsp;= 12&nbsp;''lignes''; so 864&nbsp;''lignes''&nbsp;= 1&nbsp;''toise''.</ref> Méchain and Delambre's result came out at 0.144&nbsp;''lignes'' shorter than this, a difference of  about 0.03%.<ref name="Larousse"/>

===''Mètre des Archives''===
While Méchain and Delambre were completing their survey, the comission had ordered a series of [[platinum]] bars to be made based on the provisional metre. When the final result was known, the bar whose length was closest to the meridional definition of the metre was selected and placed in the National Archives on 22&nbsp;June 1799 (4&nbsp;messidor An&nbsp;VII in the Republican calendar) as a permanent record of the result:<ref name="Larousse"/> this standard metre bar became known as the ''mètre des Archives''.

The [[metric system]], that is the system of units based on the metre, was officially adopted in France on 10&nbsp;December 1799 (19&nbsp;frimaire An&nbsp;VIII) and became the sole legal system of weights and measures from 1801. After the instauration of the Empire, in 1812, the old names for units of length were revived but the units redefined in terms of the metre: this system was known as ''[[mesures usuelles]]'', and lasted until 1840 when the decimal metric system was again made the sole legal measure.<ref name="Larousse"/> In the meantime, the Netherlands had adopted the metric system from 1816, the first of several countries to follow the French lead.

It soon became apparent that Méchain and Delambre's result (443.296&nbsp;''lignes'')<ref group="Note" name="lignes"/> was slightly too short for the meridional definition of the metre. [[François Arago|Arago]] and [[Jean-Baptiste Biot|Biot]] extended the survey to the island of Formentera in the western Mediterranean Sea in 1806–9, and found that one ten-millionth of the Earth's quadrant should be 443.31&nbsp;''lignes'': later work increased the value to 443.39&nbsp;''lignes''.<ref name="Larousse"/> The modern value, for the WGS&nbsp;84 reference spheroid, is {{nowrap|1.000 196 57}}&nbsp;m or {{nowrap|443.383 08}}&nbsp;''lignes''.<ref group="Note">The WGS&nbsp;84 reference spheroid has a semi-major axis of {{nowrap|6 378 137.0 m}} and a flattening of {{frac|{{nowrap|298.257 223 563}}}}.</ref>

Nevertheless, the ''mètre des Archives'' remained the legal and practical standard for the metre in France, even once it was known that it did not exactly correspond to the meridional definition. When it was decided (in 1867) to create a new international standard metre, the length was taken to be that of the ''mètre des Archives'' "in the state in which it shall be found".<ref name="MComm">{{citation | title = The International Metre Commission (1870-1872) | url = http://www.bipm.org/en/si/history-si/commission.html | publisher = International Bureau of Weights and Measures | accessdate = 2010-08-15}}.</ref><ref name="BIPMhist">{{citation | title = The BIPM and the evolution of the definition of the metre | url = http://www.bipm.org/en/si/history-si/evolution_metre.html | publisher = International Bureau of Weights and Measures | accessdate = 2010-08-15}}.</ref>

The only significant international use of the meridional definition of the metre, apart from Méchain and Delambre's original survey, was the initial work conducted by the [[British Association for the Advancement of Science]] (B.A.) on electrical units which was to lead to the [[International System of Electrical and Magnetic Units]]. It was often claimed that the international electrical units formed a coherent set of absolute units in the "QES system", where the unit length was the quadrant of the Earth's polar circumference, the unit mass was the "eleventh-gram" or 10<sup>−11</sup>&nbsp;grams and the unit time was the [[second]].<ref name="EBunits">{{citation | contribution = Units, Physical | title = Encyclopædia Britannica | volume = 27 | year = 1911 | edition = 11th | pages = 738–45}}.</ref><ref>{{citation | title = Rationalised versus Unrationalised Practical Electromagnetic Units | first = Arthur E. | last = Kennelly | journal = Proc. Am. Phil. Soc. | volume = 70 | issue = 2 | year = 1931 | pages = 103–19 }}.</ref> Nevertheless, the precision of absolute electrical measurements in the late nineteenth century was not such that the 0.02% difference in the definitions of the metre had any practical significance.<ref name="EBunits"/>

===International prototype metre===
With increasing international adoption of the metre, the short-comings of the ''mètre des Archives'' as a standard became ever more apparent. Countries which adopted the metre as a legal measure purchased standard metre bars that were intended to be equal in length to the ''mètre des Archives'', but there was no systematic way of ensuring that the countries were actually working to the same standard. The meridional definition, which had been intended to ensure international reproduceability, quickly proved so impractical that is was all but abandoned in favour of the artefact standards, but the ''mètre des Archives'' (and most of its copies) were "end standards": such standards (bars which are exactly one metre in length) are prone to wear with use, and different standard bars could be expected to wear at different rates.<ref>{{LarousseXIXe| article = Mètre | volume = 17 | page = 1587}}.</ref>

The International Conference on Geodesy in 1867 called for the creation of a new, international prototype metre<ref name="MComm"/><ref name="BIPMhist"/><ref group="Note">The term "prototype" does not imply that it was the first in a series and that other standard metres would come after it: the "prototype" metre was the one that came first in the logical chain of comparisons, that is the metre to which all other standards were compared.</ref> and to arrange a system where national standards could be compared with it. The international prototype would also be a "line standard", that is the metre was defined as the distance between two lines marked on the bar, so avoiding the wear problems of end standards. The French government gave practical support to the creation of an International Metre Commission, which met in Paris in 1870 and again in 1872 with the participation of about thirty countries.<ref name="MComm"/>

The international nature of the standards was ensured by a treaty – the [[Metre Convention]] – signed in Paris on 20&nbsp;May 1875. This set up an international organization, the ''[[Bureau international des poids et mesures]]'' (BIPM), to conserve the prototypes (which were to be the joint property of the signatory nations) and to carry out regular comparisons with national standards. In recognition of the role of France in designing the metric system, the BIPM is based in Sèvres, just outside Paris, but it enjoys the usual privileges of an international organization and is under the ultimate control of a diplomatic conference (the ''[[Conférence générale des poids et mesures]]'', CGPM) and not of the French government.<ref name="Nelson"/><ref>Article 3, [[Metre Convention]].</ref>

The construction of the international prototype metre and the copies which would be national standards was at the limits of the technology of its time. The bars were to be made of a special alloy, 90%&nbsp;[[platinum]] and 10%&nbsp;[[iridium]], which is significantly harder than pure platinum, and have a special X-shaped cross section (a "Tresca section", named after French engineer [[Henri Tresca]]) to minimise the effects of torsional strain during length comparisons.<ref name="Nelson"/> The first castings proved unsatisfactory, and the job was given to the London firm of [[Johnson Matthey]] who succeded in producing thirty bars to the required specification: one of these (No.&nbsp;6) was determined to be identical in length to the ''mètre des Archives'', and was consacrated as the international prototype metre at the first meeting of the CGPM in 1889. The other bars, duely calibrated against the international prototype, were distributed to the signatory nations of the Metre Convention for use as national standards:<ref name="BIPMhist"/> for example, the United States received No.&nbsp;27 with a calibrated length of {{nowrap|0.999 9984 m ± 0.2 µm}} (1.6&nbsp;µm short of the international prototype).<ref>{{citation | title = National Prototype Meter No.&nbsp;27 | url = http://museum.nist.gov/object.asp?ObjID=37 | publisher = National Institute of Standards and Technology | accessdate = 2010-08-17}}.</ref>

The first (and only) follow-up comparison of the national standards with the international prototype was carried out between 1921 and 1936,<ref name="Nelson"/><ref name="BIPMhist"/> and indicated that the definition of the metre was preserved to with 0.2&nbsp;µm.<ref name="Barrell">{{citation | first = H. | last = Barrel | title = The Metre | journal = Contemp. Phys. | year = 1962 | volume = 3 | issue = 6 | pages = 415–34 | doi = 10.1080/00107516208217499}}.</ref> At this time, it was decided that a more formal definition of the metre was required (the 1889 decision had said merely that the "prototype, at the temperature of melting ice, shall henceforth represent the metric unit of length"), and this was agreed at the 7th&nbsp;CGPM in 1927:<ref name="oldSI">{{SIbrochure8th|pages=142–43, 148}}.</ref>
{{quotation|The unit of length is the metre, defined by the distance, at 0°, between the axes of the two central lines marked on the bar of platinum–iridium kept at the ''Bureau International des Poids et Mesures'' and declared Prototype of the metre by the 1st&nbsp;''Conférence Générale des Poids et Mesures'', this bar being subject to standard atmospheric pressure and supported on two cylinders of at least one centimetre diameter, symmetrically placed in the same horizontal plane at a distance of 571&nbsp;mm from each other.}}
The support requirements represent the [[Airy points]] of the prototype, that is the points, separated by {{frac|5|9}} of the total length of the bar, at which the bending or droop of the bar is minimized.<ref>{{citation | last = Phelps | first = F. M., III | year = 1966 | title = Airy Points of a Meter Bar | journal = Am. J. Phys. | volume = 34 | issue = 5 | pages = 419–22 | doi = 10.1119/1.1973011}}.</ref>

===Krypton standard===
The first [[Interferometry|interferometric]] measurements carried out using the international prototype metre were those of [[Albert A. Michelson|Michelson]] and [[Benoît]] (1892–93)<ref>{{citation | first1 = A. A. | last1 = Michelson | authorlink1 = Albert A. Michelson | first2 = J.-R. | last2 = Benoît | title =   Détermination expérimentale de la valeur du mètre en longueurs d'ondes lumineuses | journal = Trav. Mem. Bur. Int. Poids Mes. | volume = 11 | issue = 3 | pages = 85 | year = 1895}}.</ref> and of Benoît, [[Charles Fabry|Fabry]] and [[Alfred Perot|Perot]] (1906),<ref>{{citation | last1 = Benoit | first1 = R. | last2 = Fabry | first2 = Ch. | authorlink2 = Charles Fabry | last3 = Perot | first3 = A. | authorlink3 = Alfred Perot | year = 1907 | title = Nouvelle détermination du Mètre en longueurs d'ondes lumieuses | journal = C. R. Hebd. Acad. Sci. Paris | volume = 144 | pages = 1082–86 | url = http://gallica.bnf.fr/ark:/12148/bpt6k3098j.image.f1082.langFR}}.</ref> both using the red line of [[cadmium]]. These results, which gave the [[wavelength]] of the cadmium line (''λ''&nbsp;≈ 644&nbsp;nm), led to the definition of the [[angstrom]] as a secondary unit of length for spectroscopic measurements, first by the [[International Union for Solar Research]] (1907)<ref>{{citation | journal = Trans. Int. Union Solar Res. | volume = 2 | pages = 28 | year = 1907}}.</ref> and later by the [[CIPM]] (1927).<ref name="BIPMhist"/><ref name="Hollberg">{{citation | first1 = L. | last1 = Hollberg | first2 = C. W. | last2 = Oates | first3 = G. | last3 = Wilpers | first4 = C. W. | last4 = Hoyt | first5 =  Z. W. | last5 = Barber | first6 = S. A. | last6 = Diddams | first7 = W. H. | last7 = Oskay | first8 = J. C. | last8 = Bergquist | title = Optical frequency/wavelength references | journal = J. Phys. B: At. Mol. Opt. Phys. | volume = 38 | year = 2005 | pages = S469–S495 | doi = 10.1088/0953-4075/38/9/003}}.</ref><ref group="Note">The IUSR (later to become the [[International Astronomical Union]]) defined the angstrom such that the wavelength (in air) of the cadmium line was {{nowrap|6438.469 63}}&nbsp;Å.</ref> Michelson's work in "measuring" the prototype metre to within {{frac|10}} of a wavelength ({{nowrap|< 0.1}}&nbsp;µm) was one of the reasons for which he was awarded the [[Nobel Prize in Physics]] in 1907.<ref name="Nelson"/><ref name="BIPMhist"/><ref>{{citation | title = Nobel Prize in Physics 1907 – Presentation Speech | url = http://nobelprize.org/nobel_prizes/physics/laureates/1907/press.html | publisher = Nobel Foundation | accessdate = 2010-08-14}}.</ref>

By the 1950s, interferometry had become the method of choice for precise measurements of length but there remained a practical problem imposed by the system of units used. The natural unit for expressing a length measured by interferometry was the angstrom, but this result then had to be converted into metres using an experimental conversion factor – the wavelength of light used, but measured in metres rather than in angstroms. This added an additional [[measurement uncertainty]] to any length result in metres, over and above the uncertainty of the actual interferometric measurement. The solution was to define the metre in the same manner as the angstrom had been defined in 1907, that is in terms of the best interferometric wavelength available.

Advances in both experimental technique and theory showed that the cadmium line was actually a cluster of closely separated lines, and that this was due to the presence of different [[isotope]]s in natural cadmium (eight in total). To get the most precisely defined line, it was necessary to use a monoisotopic source and this source should contain an isotope with even numbers of protons and neutrons (so as to have zero [[nuclear spin]]).<ref name="Nelson"/> Several isotopes of cadmium, [[krypton]] and [[mercury]] both fulfill the condition of zero nuclear spin and have bright lines in the visible region of the spectrum. Krypton is a gas at room temperature, allowing for easier [[isotopic enrichment]] and lower operating temperatures for the lamp (which reduces [[Doppler broadening|broadening]] of the line due to the [[Doppler effect]]), and so it was decided to select the orange line of [[krypton-86]] (''λ''&nbsp;≈ 606&nbsp;nm) as the new wavelength standard.<ref name="Nelson"/><ref>{{citation | title = The International Length Standard | first1 = K. M. | last1 = Baird | first2 = L. E. | last2 = Howlett | journal = Appl. Opt. | volume = 2 | issue = 5 | pages = 455–63 | year = 1963 | doi = 10.1364/AO.2.000455}}.</ref> Accordingly, the 11th&nbsp;[[CGPM]] in 1960 agreed a new definition of the metre:<ref name="oldSI"/>
{{quotation|The metre is the length equal to {{nowrap|1 650 763.73}}&nbsp;wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p<sub>10</sub> and 5d<sub>5</sub> of the krypton&nbsp;86 atom.}}
The measurement of the wavelength of the krypton line was ''not'' made directly against the international prototype metre: instead the ratio of the wavelength of the krypton line to that of the cadmium line was determined in vacuum, and this was compared to the 1906 Fabry–Perot determination of the wavelength of the cadmium line in air (with a correction for the [[refractive index]] of air).<ref name="Nelson"/><ref name="Barrell"/> In this way, the new definition of the metre was [[Metrological traceability|traceable]] to both the old prototype metre and the old definition of the angstrom.

===Speed of light standard===
The krypton-86 discharge lamp operating at the [[triple point]] of [[nitrogen]] (63.14&nbsp;K, −210.01&nbsp;°C) was the state of the art light source for interferometry in 1960, but it was soon to be supeceded by a new invention – the [[laser]], of which the first working version was constructed in the same year as the redefinition of the metre.<ref>{{citation | last = Maiman | first = T. H. | year = 1960 | title = Stimulated optical radiation in ruby | journal = Nature | volume = 187 | pages = 493–94 | doi = 10.1038/187493a0}}.</ref> Laser light is usually highly monochromatic, and is also coherent (all the light has the same [[phase (wave)|phase]], unlike the light from a discharge lamp), both of which are advantageous for inteferometry.<ref name="Nelson"/>

The shortcomings of the krypton standard were demonstrated by the measurement of the wavelength of the light from a [[methane]]-stabilized [[helium–neon laser]] (''λ''&nbsp;≈ 3.39&nbsp;µm). The krypton line was found to be asymmetrical, so two different wavelengths could be found for the laser light depending on which point on the kyrpton line was taken for reference.<ref group="Note">Taking the point of highest intensity as the reference wavelength, the methane line had a wavelength of {{nowrap|3.392 231 404(12)}}&nbsp;µm; taking the intensity-weighted mean point ("centre of gravity") of the krypton line as the standard, the wavelength of the methane line is {{nowrap|3.392 231 376(12)}}&nbsp;µm.</ref> The asymmetry also affected the precision to which the wavelengths could be measured.<ref name="SoL">{{citation | first1 = K. M. | last1 = Evenson | first2 = J. S. | last2 = Wells | first3 = F. R. | last3 = Petersen | first4 = B. L. | last4 = Danielson | first5 = G. W. | last5 = Day | first6 = R. L. | last6 = Barger | first7 = J. L. | last7 = Hall | title = Speed of Light from Direct Frequency and Wavelength Measurements of the Methane-Stabilized Laser | journal = Phys. Rev. Lett. | volume = 29 | pages = 1346–49 | year = 1972 | doi = 10.1103/PhysRevLett.29.1346}}.</ref><ref>{{citation | first1 = R. L. | last1 = Barger | first2 = J. L. | last2 = Hall | title = Wavelength of the 3.39-μm laser-saturated absorption line of methane | journal = Appl. Phys. Lett. | volume = 22 | pages = 196–99 | year = 1973 | doi = 10.1063/1.1654608}}.</ref>

Developments in electronics also made it possible for the first time to measure the frequency of light in or near the visible region of the spectrum, instead of inferring the frequency from the wavelength and the [[speed of light]]. Although visible and infrared frequencies were still too high to be directly measured, it was possible to construct a "chain" of laser frequencies that, by suitable multiplication, differ from each other by only a directly measureable frequency in the [[microwave]] region. The frequency of the light from the methane-stabilized laser was found to be {{nowrap|88.376 181 627(50)}}&nbsp;THz.<ref name="SoL"/><ref>{{citation | first1 = K. M. | last1 = Evenson | first2 = G. W. | last2 = Day | first3 = J. S. | last3 = Wells | first4 = L. O. | last4 = Mullen | title = Extension of Absolute Frequency Measurements to the cw He☒Ne Laser at 88&nbsp;THz (3.39&nbsp;μ) | journal = Appl. Phys. Lett. | volume = 20 | pages = 133–34 | year = 1972 | doi = 10.1063/1.1654077}}.</ref>

Independent measurements of frequency and wavelength are, in effect, a measurement of the speed of light (''c''&nbsp;= ''fλ''), and the results from the methane-stabilized laser gave the speed of light with an [[Measurement uncertainty|uncertainty]] almost 100-times lower than previous measurements in the microwave region. Or, somewhat inconveniently, the results gave ''two'' values for the speed of light, depending on which point on the krypton line was chosen to define the metre.<ref group="Note">The measured speed of light was {{nowrap|299 792.4562(11)&nbsp;km s<sup>−1</sup>}} for the "centre-of-gravity" definition and {{nowrap|299 792.4587(11)&nbsp;km s<sup>−1</sup>}} for the maximum-intensity definition, with a relative uncertainty ''u''<sub>r</sub>&nbsp;= 3.5{{e|−9}}.</ref> The ambiguity was resolved in 1975, when the 15th&nbsp;[[CGPM]] approved a conventional value of the speed of light as exactly {{nowrap|299 792 458&nbsp;m s<sup>−1</sup>}}.<ref>[http://www.bipm.org/en/CGPM/db/15/2/ Resolution 2], 15th&nbsp;Meeting of the [[General Conference on Weights and Measures]], 1975.</ref>

Nevertheless, the infrared light from a methane-stabilized laser was inconvenient for use in practical interferometry. It was not until 1983 that the chain of frequency measurements reached the 633&nbsp;nm line of the helium–neon laser, which can be stabilized (if necessary) against absorptions of molecular [[iodine]].<ref>{{citation | last1 = Pollock | first1 = C. R. | last2 = Jennings | first2 = D. A. | last3 = Petersen | first3 = F. R. | last4 = Wells | first4 = J. S. | last5 = Drullinger | first5 = R. E. | last6 = Beaty | first6 = E. C. | last7 = Evenson | first7 = K. M. | year = 1983 | title = Direct frequency measurements of transitions at 520&nbsp;THz (576&nbsp;nm) in iodine and 260&nbsp;THz (1.15&nbsp;µm) in neon | journal = Opt. Lett. | volume = 8 | issue = 3 | pages = 133–35 | doi = 10.1364/OL.8.000133}}. {{citation | last1 = Jennings | first1 = D. A. | last2 = Pollock | first2 = C. R. | last3 = Petersen | first3 = F. R. | last4 = Drullinger | first4 = R. E. | last5 = Evenson | first5 = K. M. | last6 = Wells | first6 = J. S. | last7 = Hall | first7 = J. L. | last8 = Layer | first8 = H. P. | title = Direct frequency measurement of the I<sub>2</sub>-stabilized He–Ne 473-THz (633-nm) laser | journal = Opt. Lett. | year = 1983 | volume = 8 | issue = 3 | pages = 136–38 | doi = 10.1364/OL.8.000136}}.</ref> That same year, the 17th&nbsp;CGPM adopted the current definition of the metre, in terms of the 1975 conventional value for the speed of light:<ref>[http://www.bipm.org/en/CGPM/db/17/1/ Resolution 1], 17th&nbsp;Meeting of the [[General Conference on Weights and Measures]], 1983.</ref>
{{quotation|The metre is the length of the path travelled by light in vacuum during a time interval of {{frac|{{nowrap|299 792 458}}}} of a second.}}
The concept of define a unit of length in terms of a time received some comment,<ref name="NewScientist">{{citation | last = Wilkie | first = Tom | title = Time to remeasure the metre | url = http://books.google.com/books?id=pKU5MXqo4UYC&pg=PA258#v=onepage&q&f=false | journal = New Scientist | year = 1983 | issue = 27 October | pages = 258–63}}.</ref> although it is no different from [[John Wilkins|Wilkins']] original proposal in 1668 to define the universal unit of length in terms of the seconds pendulum. In both cases, the practical issue is that time can be measured more accurately than length (one part in 10<sup>13</sup> as opposed to four parts in 10<sup>9</sup> in 1983).<ref name="Hollberg"/><ref name="NewScientist"/> The definition in terms of the speed of light also means that the metre can be [[Realization|realized]] using any light source of known frequency, rather than defining a "preferred" source in advance: given that there are more than 22,000&nbsp;lines in the visible spectrum of iodine, any of which could be potentially used to stabilize a laser source, the advantages of flexibity are obvious.<ref name="NewScientist"/>

==Notes and references==
===Notes===
{{reflist|group=Note}}

===References===
{{reflist|2}}

==External links==
{{Wikipedia|Metre}}
*[http://www.sizes.com/units/meter.htm meter (metre)] at Sizes.com

[[Category:SI units]]
[[Category:Units of length]]

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