history of the metre#Krypton standard

{{Multiple issues|{{Synthesis|section|date=January 2025}}

{{Overly detailed|section|date=January 2025}}}}

{{main|History_of_measurement#Units_of_length}}

Historically, units of measurement varied greatly, even when called by the same name. Some kingdoms and other polities standardised some measurements, but in others, such as France before the French Revolution, units could still vary from place to place. During the Scientific Revolution, various "universal measures" of length were proposed which would be based on reproducible natural phenomena, in particular the pendulum and the Earth.

In around 1602, Galileo observed that the regular swing of the pendulum depended on its length.{{Cite web |title=Museo Galileo - In depth - Pendulum |url=https://catalogue.museogalileo.it/indepth/Pendulum.html |access-date=2025-01-29 |website=catalogue.museogalileo.it}} In 1645 Giovanni Battista Riccioli determined the length of a pendulum whose swing is one second each way, a "seconds pendulum".{{Cite book |last=Guedj |first=Denis |title=Le mètre du monde |date=2011 |publisher=Éd. du Seuil |isbn=978-2-7578-2490-0 |location=Paris |page=38 |oclc=758713673 |author-link=Denis Guedj}}{{efn|At the time the second was defined as a fraction of the Earth's rotation time and determined by clocks whose precision was checked by astronomical observations. In 1936 French and German astronomers found that Earth rotation's speed is irregular. Since 1967 atomic clocks define the second. For further information see atomic time.}} In 1671, Jean Picard proposed this length as a unit of measurement to be called the Rayon Astronomique (astronomical radius).{{Cite book |last=Picard |first=Jean |url=https://gallica.bnf.fr/ark:/12148/btv1b7300361b/f13.image |title=Mesure de la terre |date=1671 |pages=3–4 |language=fr |author-link=Jean Picard |via=Gallica}}{{Cite book |last=Picard |first=Jean |author-link=Jean Picard |url=https://gallica.bnf.fr/ark:/12148/btv1b7300361b/f41.image |title=Mesure de la terre |date=1671 |page=23 |language=fr |access-date=5 September 2018 |via=Gallica}} In 1675, Tito Livio Burattini suggested calling it {{Lang|it|metro cattolico}} (universal measure).{{cite book |last1=Lucendo |first1=Jorge |url=https://books.google.com/books?id=4l3eDwAAQBAJ&pg=PT246 |title=Centuries of Inventions: Encyclopedia and History of Inventions |date=23 April 2020 |publisher=Jorge Lucendo |page=246 |language=en |access-date=2 August 2021}} However in 1671–1673, astronomer Jean Richer discovered that the length of a seconds pendulum also varies from place to place by as much as 0.28%.{{cite web |date=25 March 2021 |title=Science. 1791, l'adoption révolutionnaire du mètre |url=https://www.humanite.fr/science-1791-ladoption-revolutionnaire-du-metre-702009 |access-date=3 August 2021 |website=humanite.fr |language=fr}}{{cite book |last1=Poynting |first1=John Henry |url=https://archive.org/details/bub_gb_TL4KAAAAIAAJ |title=A Textbook of Physics: Properties of Matter |last2=Thompson |first2=Joseph John |publisher=Charles Griffin |year=1907 |edition=4th |location=London |pages=9, 20}}

In the 18th century, the French Academy of Sciences organised work on cartography and geodesy which included measuring the size and shape of the Earth.{{Cite web |title=Academy of Sciences |url=https://www.britannica.com/topic/Academy-of-Sciences-French-organization |access-date=2025-02-15 |website=www.britannica.com |language=en}} Through surveys in Ecuador and Lapland it was found that the earth is not a perfect sphere but rather an oblate spheroid.{{Cite EB1911|wstitle=Earth, Figure of the|volume=8|pages=801–813|short=1}}

Using a decimal scale for measurements was proposed by Simon Stevin, a Flemish mathematician in 1586.{{Cn|date=June 2025}}

{{anchor|Mètre des Archives}}

{{see also|Earth's circumference#Historical use in the definition of units of measurement|Meridian arc#History of measurement}}

In 1790, during the French Revolution, the National Convention tasked the French Academy of Sciences with reforming the units of measurement. The Academy formed a commission, which rejected using the pendulum as a unit of length{{Cite LarousseXIXe|title=Métrique|volume=11|pages=163–164}} and decided that the new measure should be equal to one ten-millionth of the distance from the North Pole to the Equator (a quadrant of the Earth's circumference). This was to be measured along the meridian passing through the Panthéon in Paris.{{Cite web |title=L'histoire des unités {{!}} Réseau National de la Métrologie Française |url=https://metrologie-francaise.lne.fr/fr/metrologie/histoire-des-unites |access-date=2023-10-06 |website=metrologie-francaise.lne.fr}}{{Cite web |last=Ramani |first=Madhvi |date=24 September 2018 |title=How France created the metric system |url=http://www.bbc.com/travel/story/20180923-how-france-created-the-metric-system |access-date=2019-05-21 |website=www.bbc.com |language=en}}

File:First Metre, Paris.jpg

However, pending completion of that work, a measurement from Dunkirk to Collioure made in 1740 was used, and following legislation on 7 April 1795,{{Cite web |last=Maury |first=Jean-Pierre |date=2007 |title=Grandes lois de la République: les mesures républicaines |url=https://mjp.univ-perp.fr/france/1793mesures.htm |website=Digithèque de matériaux juridiques et politiques}} provisional metal metre bars were distributed in France in 1795-1796.{{cite book |author=National Industrial Conference Board |url=https://books.google.com/books?id=tSUoAAAAYAAJ&pg=PA10 |title=The metric versus the English system of weights and measures ... |publisher=The Century Co. |year=1921 |pages=10–11 |access-date=5 April 2011}}

File:Kilometre definition.svg was one ten-millionth of the Earth quadrant, the distance from the North Pole to the Equator, after the arc measurement of Delambre and Méchain.]]

In 1799, the measurement of part of the meridian, from Dunkirk to Barcelona, was completed and a correction for the Earth's non-spherical shape calculated from that and another survey.{{Cite journal |last=Nyblom |first=Jukka |date=2023-04-25 |title=How did the meter acquire its definitive length? |journal=GEM - International Journal on Geomathematics |language=en |volume=14 |issue=1 |page=10 |bibcode=2023IJGm...14...10N |doi=10.1007/s13137-023-00218-9 |issn=1869-2680 |doi-access=free}}{{Cite journal |last1=Débarbat |first1=Suzanne |last2=Quinn |first2=Terry |date=2019-01-01 |title=Les origines du système métrique en France et la Convention du mètre de 1875, qui a ouvert la voie au Système international d'unités et à sa révision de 2018 |journal=Comptes Rendus Physique |series=The new International System of Units / Le nouveau Système international d’unités |volume=20 |issue=1 |pages=6–21 |bibcode=2019CRPhy..20....6D |doi=10.1016/j.crhy.2018.12.002 |issn=1631-0705 |s2cid=126724939 |doi-access=free}} A metre bar was accordingly made of platinum and designated by law as the primary standard metre. This was kept in the National Archives and known as the {{Lang|fr|Mètre des Archives}}.{{sfn|Bigourdan|1901|pp=8,158–159,176–177}}

Another platinum metre, calibrated against the {{Lang|fr|Mètre des Archives}}, and twelve iron ones were made as secondary standards.{{Cite book |last=Wolf |first=M. C |title=Recherches historiques sur les étalons de poids et mesures de l'observatoire et les appareils qui ont servi a les construire. |date=1882 |publisher=Gauthier-Villars |location=Paris |pages=7–8, 20, 32 |language=French |oclc=16069502}}

One of the iron metre standards was brought to the United States in 1805.{{Cite book |url=https://play.google.com/store/books/details?id=NiEEAQAAIAAJ |title=NIST Special Publication |date=1966 |publisher=U.S. Government Printing Office |page=529 |language=en}} It became known as the Committee Meter in the United States and served as a standard of length in the United States Coast Survey until 1890.{{Cite journal |last=Cajori |first=Florian |date=1921 |title=Swiss Geodesy and the United States Coast Survey |url=https://www.jstor.org/stable/6721 |journal=The Scientific Monthly |volume=13 |issue=2 |pages=117–129 |bibcode=1921SciMo..13..117C |issn=0096-3771}}{{Cite journal |last1=Clarke |first1=Alexander Ross |last2=James |first2=Henry |date=1 January 1873 |title=XIII. Results of the comparisons of the standards of length of England, Austria, Spain, United States, Cape of Good Hope, and of a second Russian standard, made at the Ordnance Survey Office, Southampton. With a preface and notes on the Greek and Egyptian measures of length by Sir Henry James |journal=Philosophical Transactions of the Royal Society of London |language=en |volume=163 |pages=445–469 |doi=10.1098/rstl.1873.0014 |issn=0261-0523 |doi-access=free}}{{Cite book |last1=American Philosophical Society. |url=https://www.biodiversitylibrary.org/item/26092 |title=Transactions of the American Philosophical Society |last2=Society |first2=American Philosophical |last3=Poupard |first3=James |date=1825 |volume=new ser.:v.2 (1825) |location=Philadelphia [etc.] |pages=234–278}}

In 1855, the Dufour map (French: Carte Dufour), the first topographic map of Switzerland for which the metre was adopted as the unit of length, won the gold medal at the Exposition Universelle.{{Cite news |last=Abplanalp |first=Andrej |date=2019-07-14 |title=Henri Dufour et la carte de la Suisse |url=https://blog.nationalmuseum.ch/fr/2019/07/dufour-le-cartographe/ |archive-url=http://web.archive.org/web/20241225163218/https://blog.nationalmuseum.ch/fr/2019/07/dufour-le-cartographe/ |archive-date=2024-12-25 |access-date=2025-01-25 |work=Musée national - Blog sur l'histoire suisse |language=de-DE}}{{Cite journal |last=Dufour |first=G.-H. |date=1861 |title=Notice sur la carte de la Suisse dressée par l'État Major Fédéral |url=https://www.persee.fr/doc/globe_0398-3412_1861_num_2_1_7582 |journal=Le Globe. Revue genevoise de géographie |volume=2 |issue=1 |pages=5–22 |doi=10.3406/globe.1861.7582}}

On the sidelines of the Exposition Universelle (1855) and the second Congress of Statistics held in Paris, an association with a view to obtaining a uniform decimal system of measures, weights and currencies was created in 1855.{{Cite book |last=Quinn |first=T. J. |title=From artefacts to atoms: the BIPM and the search for ultimate measurement standards |date=2012 |publisher=Oxford University Press |isbn=978-0-19-990991-9 |location=Oxford |pages=9, 11, 14, 20, 37–38, 91–92, 70–72, 114–117, 144–147, 8 |oclc=861693071}} A Committee for Weights and Measures and Monies (French: Comité des poids, mesures et monnaies) was created during the Exposition Universelle (1867) in Paris and called for the international adoption of the metric system.

In the United States, the Metric Act of 1866 allowed the use of the metre in the United States,{{Cite web |title=Metric Act of 1866 – US Metric Association |url=https://usma.org/laws-and-bills/metric-act-of-1866#locale-notification |access-date=2021-03-15 |website=usma.org}} and in 1867 the General Conference of the European Arc Measurement (German: Europäische Gradmessung) established the International Bureau of Weights and Measures.{{Cite book |url=http://gfzpublic.gfz-potsdam.de/pubman/item/escidoc:108187:4/component/escidoc:272449/Generalbericht.mitteleurop%C3%A4ische.Gradmessung%201867.pdf |title=Bericht über die Verhandlungen der vom 30. September bis 7. October 1867 zu BERLIN abgehaltenen allgemeinen Conferenz der Europäischen Gradmessung |publisher=Central-Bureau der Europäischen Gradmessung |year=1868 |location=Berlin |pages=123–134 |language=german}}{{Cite journal |last=Quinn |first=Terry |date=2019 |title=Wilhelm Foerster's Role in the Metre Convention of 1875 and in the Early Years of the International Committee for Weights and Measures |journal=Annalen der Physik |language=en |volume=531 |issue=5 |page=2 |bibcode=2019AnP...53100355Q |doi=10.1002/andp.201800355 |issn=1521-3889 |s2cid=125240402 |doi-access=free}}

At the Metre Convention of 1875 the metre was adopted as an international scientific unit of length.

== International prototype metre ==

File:US_National_Length_Meter.JPG and given to the United States,{{Cite book |last=Quinn |first=Terry |title=From artefacts to atoms: the BIPM and the search for ultimate measurement standards |date=2012 |publisher=Oxford University Press |isbn=978-0-19-530786-3 |location=New York |page=144}} which served as the standard for American cartography from 1890 replacing the Committee Meter, an authentic copy of the Mètre des Archives produced in 1799 in Paris, which Ferdinand Rudolph Hassler had brought to the United States in 1805.|left]]

In the late nineteenth century, a new international standard metre, called a "prototype",{{efn|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 chain of comparisons, the metre to which all other standards were compared.}} was made along with copies to serve as national standards. It was a "line standard", with the metre was defined as the distance between two lines marked on the bar, to make any wear at the ends irrelevant.{{Cite book |last=Fischer |first=Stéphane |url=https://institutions.ville-geneve.ch/fileadmin/user_upload/mhn/images/votre_visite/site_mhs/9_Pied_au_metre_online.pdf |title=Du pied au mètre du marc au kilo |date=June 2010 |publisher=Musée d'histoire des sciences |isbn= |edition=2020 |location=Genève |page=16 |language=fr |issn=2673-6586}}{{Cite book |last=Quinn |first=Terry J. |title=From artefacts to atoms: the BIPM and the search for ultimate measurement standards |date=2012 |publisher=Oxford University Press |isbn=978-0-19-530786-3 |location=New York & Oxford |page=13, 56-57}}

The construction was at the limits of technology. The bars were made of a special alloy, 90% platinum and 10% iridium, 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. The first castings proved unsatisfactory, and the job was given to the London firm of Johnson Matthey who succeeded in producing thirty bars to the required specification. One of these, No. 6, was determined to be identical in length to the {{lang|fr|mètre des Archives}}, and was designated the international prototype metre at the first meeting of the CGPM in 1889. The other bars, duly calibrated against the international prototype, were distributed to the signatory nations of the Metre Convention for use as national standards.{{citation |title=The BIPM and the evolution of the definition of the metre |url=http://www.bipm.org/en/measurement-units/history-si/evolution-metre.html |access-date=30 August 2016 |publisher=International Bureau of Weights and Measures}} For example, the United States received No. 27 with a calibrated length of {{nowrap|{{val|0.9999984}} m ± 0.2 μm}} (1.6 μm short of the international prototype).{{citation |title=National Prototype Meter No. 27 |url=http://museum.nist.gov/object.asp?ObjID=37 |access-date=17 August 2010 |archive-url=https://web.archive.org/web/20080916030206/http://museum.nist.gov/object.asp?ObjID=37 |publisher=National Institute of Standards and Technology |archive-date=16 September 2008}}

As bar lengths vary with temperature, precise measurements required known and stable temperatures and could even be affected by a scientist's body heat,{{Cite web |last=Guillaume |first=Charles-Édouard |date=11 December 1920 |title=Nobel lecture: Invar and Elinvar |url=https://www.nobelprize.org/prizes/physics/1920/guillaume/lecture/ |access-date=21 May 2020 |website=NobelPrize.org |page=445 |language=en-US}} so standard metres were provided with precise thermometers. {{Cite book |url=https://books.google.com/books?id=jTA8AQAAMAAJ |title=Comptes rendus des séances de la ... Conférence générale des poids et mesures |date=1890 |publisher=Gauthier-Villars |page=25 |language=fr}}

The first (and only) follow-up comparison of the national standards with the international prototype was carried out between 1921 and 1936, and indicated that the definition of the metre was preserved to within 0.2 μm.{{cite journal | first=H. | last=Barrell | title=The Metre | journal=Contemporary Physics | year=1962 | volume=3 | issue=6 | pages=415–434 | doi=10.1080/00107516208217499 | bibcode=1962ConPh...3..415B}} 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 CGPM in 1927.{{SIbrochure8th|pages=142–143, 148}}

{{blockquote|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 {{lang|fr|Bureau International des Poids et Mesures}} and declared Prototype of the metre by the 1st {{lang|fr|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 mm from each other.}}

These support locations are at the Bessel points of the prototype{{snd}}the support points, separated by 0.5594 of the total length of the bar,{{cite journal | first=F. M. III | last=Phelps | date=1966 | title=Airy Points of a Meter Bar | journal=American Journal of Physics | volume=34 | issue=5 | pages=419–422 | doi=10.1119/1.1973011 |bibcode=1966AmJPh..34..419P}} that minimise shortening of the bar due to bending under its own weight.{{Cite book|editor-last1=Page |editor-first1=Chester H. |editor-last2=Vigoureux |editor-first2=Paul |title=The International Bureau of Weights and Measures, 1875–1975: translation of the BIPM centennial volume |publication-date=1975 |publisher=U.S. Dept. of Commerce, National Bureau of Standards |page=67 |url=https://www.govinfo.gov/content/pkg/GOVPUB-C13-d7a59c174a3b5aab60e6a2d262a5e88f/pdf/GOVPUB-C13-d7a59c174a3b5aab60e6a2d262a5e88f.pdf#page=78}} Because the prototype is a line standard, its full length is 102 cm, slightly longer than 1 metre.{{Cite web |title=National Bureau of Standards Replica Meter Standard |work=Smithsonian Institution |url=https://www.si.edu/object/national-bureau-standards-replica-meter-standard%3Anmah_905325 |quote=This aluminum bar, with an X-shaped cross-section, is a replica of the platinum international meter prototype housed in Paris and used as a standard for the metric system from 1889 to 1960. ... Like an actual meter standard, the bar is 102 centimeters long and there are marks 1 centimeter from each end on this side to show the precise length of a meter.}}{{Cite web |title=Histoire du mètre |trans-title=History of the meter |author=Direction générale des Entreprises |url=https://metrologie.entreprises.gouv.fr/fr/point-d-histoire/histoire-du-metre |language=fr |archive-url=http://web.archive.org/web/20240604013118/https://metrologie.entreprises.gouv.fr/fr/point-d-histoire/histoire-du-metre |archive-date=4 June 2024}} Cross-sectionally, it measures 16 mm × 16 mm.{{Cite book |author-last=Gupta |author-first=S.V. |publication-date=2020 |title=Units of measurement: history, fundamentals and redefining the SI base units (2nd ed) |publisher=Springer |page=108}}

Charles Sanders Peirce's work promoted the advent of American science at the forefront of global metrology. Alongside his intercomparisons of artifacts of the metre and contributions to gravimetry through improvement of reversible pendulum, Peirce was the first to tie experimentally the metre to the wave length of a spectral line. According to him the standard length might be compared with that of a wave of light identified by a line in the solar spectrum. Albert Abraham Michelson soon took up the idea and improved it.{{Cite journal |last=Crease |first=Robert P. |date=2009-12-01 |title=Charles Sanders Peirce and the first absolute measurement standard |url=https://pubs.aip.org/physicstoday/article/62/12/39/390647/Charles-Sanders-Peirce-and-the-first-absolute |journal=Physics Today |volume=62 |issue=12 |pages=39–44 |bibcode=2009PhT....62l..39C |doi=10.1063/1.3273015 |issn=0031-9228|url-access=subscription }}{{Cite journal |last=Lenzen |first=Victor F. |date=1965 |title=The Contributions of Charles S. Peirce to Metrology |url=https://www.jstor.org/stable/985776 |journal=Proceedings of the American Philosophical Society |volume=109 |issue=1 |pages=29–46 |jstor=985776 |issn=0003-049X}}

File:Krypton-86-lamp NIST 49.jpg

The first interferometric measurements carried out using the international prototype metre were those of Albert A. Michelson and Jean-René Benoît (1892–1893){{cite journal | first1=A.A. | last1=Michelson | author-link1=Albert A. Michelson | first2=Jean-René | last2=Benoît | title=Détermination expérimentale de la valeur du mètre en longueurs d'ondes lumineuses | language=fr | journal=Travaux et Mémoires du Bureau International des Poids et Mesures | volume=11 | issue=3 | page=85 | year=1895}} and of Benoît, Fabry and Perot (1906),{{cite journal | last1=Benoît | first1=Jean-René | last2=Fabry | first2=Charles | author-link2=Charles Fabry | last3=Perot | first3=A. | author-link3=Alfred Perot | year=1907 | title=Nouvelle détermination du Mètre en longueurs d'ondes lumieuses | language=fr | journal=Comptes rendus hebdomadaires des séances de l'Académie des sciences | volume=144 | pages=1082–1086 | url=http://gallica.bnf.fr/ark:/12148/bpt6k3098j.image.f1082.langFR}} both using the red line of cadmium. These results, which gave the wavelength of the cadmium line (λ ≈ 644 nm), led to the definition of the ångström as a secondary unit of length for spectroscopic measurements, first by the International Union for Cooperation in Solar Research (1907){{cite journal | journal=Transactions of the International Union for Cooperation in Solar Research | title=Détermination de la valeur en Ångströms de la longeur d'onde de la raie rouge du Cadmium considérée comme étalon primaire | language=fr | trans-title=Determination of the value in Ångströms of the wavelength of the red line of cadmium under consideration as a primary standard | volume=2 | pages=18–34 | date=21 May 1907 | bibcode=1908TIUCS...2...17.}} and later by the CIPM (1927).{{cite journal | 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=Journal of Physics B: Atomic, Molecular and Optical Physics | volume=38 | issue=9 | year=2005 | pages=S469–S495 | doi=10.1088/0953-4075/38/9/003 | bibcode=2005JPhB...38S.469H | s2cid=53495023 | url=http://tf.nist.gov/general/pdf/2020.pdf}} Michelson's work in "measuring" the prototype metre to within {{frac|10}} of a wavelength ({{nowrap|< 0.1}} μm) was one of the reasons for which he was awarded the Nobel Prize in Physics in 1907.{{citation | title=Nobel Prize in Physics 1907 – Presentation Speech | url=http://nobelprize.org/nobel_prizes/physics/laureates/1907/press.html | publisher=Nobel Foundation | access-date=14 August 2010}}

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 ångström, 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 ångströms. 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 isotopes 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).

Several isotopes of cadmium, krypton and mercury both fulfil 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 broadening of the line due to the Doppler effect), and so it was decided to select the orange line of krypton-86 (λ ≈ 606 nm) as the new wavelength standard.{{cite journal | title=The International Length Standard | first1=K.M. | last1=Baird | first2=L.E. | last2=Howlett | journal=Applied Optics | volume=2 | issue=5 | pages=455–463 | year=1963 | doi=10.1364/AO.2.000455 | bibcode=1963ApOpt...2..455B}}

Accordingly, the 11th CGPM in 1960 agreed a new definition of the metre:

{{blockquote|The metre is the length equal to {{nowrap|1 650 763.73}} wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p₁₀ and 5d₅ of the krypton 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. This was then 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). In this way, the new definition of the metre was traceable to both the old prototype metre and the old definition of the angstrom.

File:Laser DSC09088.JPG at the Kastler-Brossel Laboratory at Univ. Paris 6]]

{{See also|Metre#Speed of light definition}}

The krypton-86 discharge lamp operating at the triple point of nitrogen (63.14 K, −210.01 °C) was the state-of-the-art light source for interferometry in 1960, but it was soon to be superseded by a new invention: the laser, of which the first working version was constructed in the same year as the redefinition of the metre.{{cite journal | last=Maiman | first=T.H. | s2cid=4224209 | year=1960 | title=Stimulated optical radiation in ruby | journal=Nature | volume=187 | pages=493–494 | doi=10.1038/187493a0 | bibcode=1960Natur.187..493M | issue=4736}} Laser light is usually highly monochromatic, and is also coherent (all the light has the same phase, unlike the light from a discharge lamp), both of which are advantageous for interferometry.

The shortcomings of the krypton standard were demonstrated by the measurement of the wavelength of the light from a methane-stabilised helium–neon laser (λ ≈ 3.39 μm). The krypton line was found to be asymmetrical, so different wavelengths could be found for the laser light depending on which point on the krypton line was taken for reference.{{efn|Taking the point of highest intensity as the reference wavelength, the methane line had a wavelength of {{nowrap|3.392 231 404(12)}} 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)}} μm.}} The asymmetry also affected the precision to which the wavelengths could be measured.{{cite journal | 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=Physical Review Letters | volume=29 | issue=19 | pages=1346–1349 | year=1972 | doi=10.1103/PhysRevLett.29.1346 | bibcode=1972PhRvL..29.1346E}}{{cite journal | first1=R.L. | last1=Barger | first2=J.L. | last2=Hall | s2cid=1841238 | title=Wavelength of the 3.39-μm laser-saturated absorption line of methane | journal=Applied Physics Letters | volume=22 | issue=4 | pages=196–199 | year=1973 | doi=10.1063/1.1654608 | bibcode=1973ApPhL..22..196B}}

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,{{explain|date=July 2017}} 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 measurable frequency in the microwave region. The frequency of the light from the methane-stabilised laser was found to be {{nowrap|88.376 181 627(50)}} THz.{{cite journal | first1=K.M. | last1=Evenson | first2=G. W. | last2=Day | first3=J.S. | last3=Wells | first4=L.O. | last4=Mullen | s2cid=118871648 | title=Extension of Absolute Frequency Measurements to the cw He☒Ne Laser at 88 THz (3.39 μ) | journal=Applied Physics Letters | volume=20 | issue=3 | pages=133–134 | year=1972 | doi=10.1063/1.1654077 | bibcode=1972ApPhL..20..133E}}

Independent measurements of frequency and wavelength are, in effect, a measurement of the speed of light (c = fλ), and the results from the methane-stabilised laser gave the value for the speed of light with an 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.{{efn|1=The measured speed of light was {{nowrap|299 792.4562(11) km s⁻¹}} for the "centre-of-gravity" definition and {{nowrap|299 792.4587(11) km s⁻¹}} for the maximum-intensity definition, with a relative uncertainty u_r = 3.5{{e|−9}}.}} This ambiguity was resolved in 1975, when the 15th CGPM approved a conventional value of the speed of light as exactly {{nowrap|299 792 458 m s⁻¹}}.{{cite conference |url=http://www.bipm.org/en/CGPM/db/15/2/ |title=Resolution 2 of the 15th CGPM |publisher=International Bureau of Weights and Measures |conference=15th Meeting of the General Conference on Weights and Measures |year=1975}}

Nevertheless, the infrared light from a methane-stabilised laser was inconvenient for use in practical interferometry. It was not until 1983 that the chain of frequency measurements reached the 633 nm line of the helium–neon laser, stabilised using molecular iodine.{{cite journal | 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. | s2cid=42447654 | year=1983 | title=Direct frequency measurements of transitions at 520 THz (576 nm) in iodine and 260 THz (1.15 μm) in neon | journal=Optics Letters | volume=8 | issue=3 | pages=133–135 | doi=10.1364/OL.8.000133 | pmid=19714161 | bibcode=1983OptL....8..133P}}{{cite journal | 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 I₂-stabilized He–Ne 473-THz (633-nm) laser | journal=Optics Letters | year=1983 | volume=8 | issue=3 | pages=136–138 | doi=10.1364/OL.8.000136 | pmid=19714162 | bibcode=1983OptL....8..136J}} That same year, the 17th CGPM adopted a definition of the metre, in terms of the 1975 conventional value for the speed of light:{{citation | url=http://www.bipm.org/en/CGPM/db/17/1/ | title=Resolution 1, 17th Meeting of the General Conference on Weights and Measures | date=1983}}

:The metre is the length of the path travelled by light in vacuum during a time interval of {{frac|1|299,792,458}} of a second.

This definition was reworded in 2019:

:The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum {{mvar|c}} to be {{val|299792458}} when expressed in the unit m⋅s{{sup|−1}}, where the second is defined in terms of the caesium frequency {{math|Δν_Cs}}.

The concept of defining a unit of length in terms of a time received some comment.{{cite journal | last=Wilkie | first=Tom | title=Time to remeasure the metre | url=https://books.google.com/books?id=pKU5MXqo4UYC&pg=PA258 | journal=New Scientist | date=27 October 1983 | issue=27 October 1983 | pages=258–263}} In both cases, the practical issue is that time can be measured more accurately than length (one part in 10¹³ for a second using a caesium clock as opposed to four parts in 10⁹ for the metre in 1983). The definition in terms of the speed of light also means that the metre can be realised using any light source of known frequency, rather than defining a "preferred" source in advance. Given that there are more than 22,000 lines in the visible spectrum of iodine, any of which could be potentially used to stabilise a laser source, the advantages of flexibility are obvious.

• Hebdomometre
• Length measurement
• History of geodesy#Prime_meridian_and_standard_of_length
• {{section link|Seconds pendulum|Relationship to the figure of the Earth}}
• Paris meridian#History

{{Notelist}}

{{Reflist|2}}

• {{cite EB1911|wstitle=Metric System |volume= 18 |page= 299}}

*

Metre