History of the metre
Origins and values of the unit of length From Wikipedia, the free encyclopedia
During the French Revolution, the traditional units of measure were to be replaced by consistent measures based on natural phenomena. As a base unit of length, scientists had favoured the seconds pendulum (a pendulum with a half-period of one second) one century earlier, but this was rejected as it had been discovered that this length varied from place to place with local gravity. A new unit of length, the metre was introduced – defined as one ten-millionth of the shortest distance from the North Pole to the equator passing through Paris, assuming an Earth flattening of 1/334.
Following the arc measurement of Delambre and Méchain, the historical French official standard of the metre was made available in the form of the Mètre des Archives, a platinum bar held in Paris. During the mid nineteenth century, following the American Revolution and independence of Latin America, the metre gained adoption in Americas, particularly in scientific usage, and it was officially established as an international measurement unit by the Metre Convention of 1875 at the beginning of the Second Industrial Revolution.
The Mètre des Archives and its copies such as the Committee Meter were replaced from 1889 at the initiative of the International Geodetic Association by thirty platinum-iridium bars kept across the globe.[2] A better standardisation of the new prototypes of the metre and their comparison with each other and with the historical standard involved the development of specialised measuring equipment and the definition of a reproducible temperature scale.[3]
In collaboration with the International Geodetic Association created to measure the Earth, the International Bureau of Weights and Measures became the world reference center for the measurement of geodetic bases thanks to the discovery of invar, an alloy of nickel and iron with a coefficient of thermal expansion close to zero.[4][5]
Progress in science finally allowed the definition of the metre to be dematerialised; thus in 1960 a new definition based on a specific number of wavelengths of light from a specific transition in krypton-86 allowed the standard to be universally available by measurement. In 1983 this was updated to a length defined in terms of the speed of light; this definition was reworded in 2019:[6]
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 c to be 299792458 when expressed in the unit m⋅s−1, where the second is defined in terms of the caesium frequency ΔνCs.
Where older traditional length measures are still used, they are now defined in terms of the metre – for example the yard has since 1959 officially been defined as exactly 0.9144 metre.[7]
Background
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Perspective
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The arc measurement of Delambre and Méchain that defined the metre was the culmination of a proposal that began during the Scientific Revolution. That proposal grew out of governmental efforts to create the Paris Observatory and the French Academy of Sciences focused on astronomy, map making and geodesy.[8]
Universal measurement
Before the establishment of the decimal metric system in France during the French Revolution in the late 18th century,[8] many units of length were based on parts of the human body.[9][10] Units in use varied by location and the advantages of the decimal system were known only among scientists. Efforts to standardise measurements can be traced back at least as far as the 10th century Saxon king Edgar in England.[11]: 73 These efforts continued in the United Kingdom culminating in the Imperial system of measurement established by the Weights and Measures Act 1824. British exploration and colonisation and trade spread these standard but not decimal units worldwide.[11]: 78
Using a decimal scale for measurements was proposed by Simon Stevin, a Flemish mathematician in 1586. Proposals for decimal measurement systems from scientists and mathematicians also lead to proposals to base units on reproducible natural phenomena, such as the motion of a pendulum or a fraction of a meridian.[11]: 85
The seconds pendulum
Galileo discovered gravitational acceleration explaining the fall of bodies at the surface of the Earth.[12] He also observed the regularity of the period of swing of the pendulum and that this period depended on the length of the pendulum.[13] In 1645 Giovanni Battista Riccioli was the first to determine the length of a "seconds pendulum" (a pendulum with a half-period of one second).[14][Note 1] In 1671, Jean Picard also measured the length of a seconds pendulum at Paris Observatory and proposed this unit of measurement to be called the astronomical radius (French: Rayon Astronomique).[15][16][17] He found the value of 36 pouces and 8 1/2 lignes of the Toise of Châtelet, which had been recently renewed.[17][18][19]
In 1675, Tito Livio Burattini suggested the term metro cattolico meaning universal measure for the unit of length based on the seconds pendulum.[20] French astronomer Jean Richer discovered that a length derived from a seconds pendulum varies from place to place: had measured the 0.28% difference in length between Cayenne (in French Guiana) and Paris.[21][17]
Astronomy, physics and map making
The French Academy of Sciences, responsible for the concept and definition of the metre,[20] was established in 1666 and in the 18th century it organised important work in determining the first reasonably accurate distance to the Sun, geodesy and cartography.[22] Among the results that would impact the definition of the metre: Earth proved to be an oblate spheroid through geodetic surveys in Ecuador and Lapland.[23] That demonstrated Newton's law of universal gravitation.[24]
Geodetic surveys found practical applications in French cartography and in the Anglo-French Survey, which aimed to connect Paris and Greenwich Observatories and led to the Principal Triangulation of Great Britain.[25][26] The unit of length used by the French was the Toise de Paris, while the English one was the yard, which became the geodetic unit used in the British Empire.[27][28][29]
French revolution
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Perspective
Despite scientific progresses in the field of geodesy, little practical advance 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; the conflicts related to units helped precipitate the revolution.[11]: 86 In addition to rejecting standards created by the French royal establishment, basing units on fundamental physicals properties was an explicit goal.[11]: 111 This effort culminated in the arc measurement of Delambre and Méchain aiming at defining the metre and determining the figure of the Earth.[30]: 52
Meridional definition
The question of measurement reform was placed in the hands of the French Academy of Sciences, who appointed a commission chaired by Jean-Charles de Borda. Talleyrand resurrected the idea of the seconds pendulum before the Constituent 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): despite the support of the Assembly, nothing came of Talleyrand's proposal.[32] Instead of the seconds pendulum method, the commission of the French Academy of Sciences – whose members included Borda, Lagrange, Laplace, Monge and 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 at the longitude of Paris pantheon, which became the central geodetic station in Paris.[33][34]
To put into practice the decision taken by the National Convention, on 1 August 1793, to disseminate the new units of the decimal metric system,[35] it was decided to establish the length of the metre based on a fraction of the meridian in the process of being measured. The decision was taken to fix the length of a metre determined by the measurement of the Meridian of France from Dunkirk to Collioure, which, in 1740, had been carried out by Nicolas Louis de Lacaille and Cesar-François Cassini de Thury. The length of the metre was established, in relation to the toise of the Academy also called toise of Peru, at 3 feet 11.44 lines, taken at 13 degrees of the temperature scale of René-Antoine Ferchault de Réaumur in use at the time.[8] This value was set by legislation on 7 April 1795.[35] It was therefore metal bars of 443.44 lignes that were distributed in France in 1795-1796.[36] These metres were provisional (French: provisoire) because the expedition and the calculations to determine the definitive length of metre were not completed until 1799.[37][8]
The definitive length of the Mètre des Archives required a value for the non-spherical shape of the Earth, known as the flattening of the Earth. The Weights and Measures Commission would, in 1799, adopt a flattening of based on analysis by Pierre-Simon Laplace who combined the arc of Peru and the data of the meridian arc of Delambre and Méchain.[37] Combining these two data sets Laplace succeeded to estimate the flattening anew and was happy to find the suitable value 1/334. It also fitted well with his estimate 1/336 based on 15 pendulum measurements.[24]
Emerging geodetic standard
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At that time, units of measurement were defined by primary standards, and unique artifacts made of different alloys with distinct coefficients of expansion were the legal basis of units of length. A wrought iron ruler, the Toise of Peru, also called Toise de l'Académie, was the French primary standard of the toise, and the metre was officially defined by an artifact made of platinum kept in the National Archives.[38] Besides the latter, another platinum and twelve iron standards of the metre were made by Étienne Lenoir in 1799.[39] One of them became known as the Committee Meter in the United States and served as standard of length in the United States Coast Survey until 1890.[40] According to geodesists, these standards were secondary standards deduced from the Toise of Peru. In Europe, except Spain,[41] surveyors continued to use measuring instruments calibrated on the Toise of Peru.[42] Among these, the toise of Bessel and the apparatus of Borda were respectively the main references for geodesy in Prussia and in France. These measuring devices consisted of bimetallic rulers in platinum and brass or iron and zinc fixed together at one extremity to assess the variations in length produced by any change in temperature. The combination of two bars made of two different metals allowed to take thermal expansion into account without measuring the temperature.[43][44] A French scientific instrument maker, Jean Nicolas Fortin, made three direct copies of the Toise of Peru, one for Friedrich Georg Wilhelm von Struve, a second for Heinrich Christian Schumacher in 1821 and a third for Friedrich Wilhelm Bessel in 1823. In 1831, Henri-Prudence Gambey also realised a copy of the Toise of Peru which was kept at Altona Observatory.[39][45]
United States
In 1816, Ferdinand Rudolph Hassler was appointed first Superintendent of the Survey of the Coast.[46][47] Trained in geodesy in Switzerland, France and Germany, Hassler had brought a standard metre made in Paris to the United States in October 1805. He designed a baseline apparatus which instead of bringing different bars in actual contact during measurements,[47] used only one bar calibrated on the Committee meter, an authenthic copy of the Mètre des Archives,[40][28] and optical contact.[47][48] Thus the metre became the unit of length for geodesy in the United States.[49] This would result in the Metre Convention of 1875, when the metre was adopted as an international scientific unit of length for the convenience of continental European geodesists following forerunners such as Ferdinand Rudolph Hassler later Carlos Ibáñez e Ibáñez de Ibero.[50][41][51][52][49][53][8]
In 1830, Hassler became head of the Office of Weights and Measures, which became a part of the Survey of the Coast. He compared various units of length used in the United States at that time and measured coefficients of expansion to assess temperature effects on the measurements.[54]
In 1834, Hassler, measured at Fire Island the first baseline of the Survey of the Coast,[55] shortly before Louis Puissant declared to the French Academy of Sciences in 1836 that Jean Baptiste Joseph Delambre and Pierre Méchain had made errors in the meridian arc measurement, which had been used to determine the length of the metre.[56][57]
Europe
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.[59][60] However, the baselines for this map were measured in 1834 with three toises long measuring rods calibrated on a toise made in 1821 by Jean Nicolas Fortin for Friedrich Georg Wilhelm von Struve.[61][29] The Spanish standard, a geodetic measuring device calibrated on the metre devised by Carlos Ibáñez e Ibáñez de Ibero and Frutos Saavedra Meneses, was also displayed by Jean Brunner at the Exhibition.[62][63]
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.[42] Under the impetus of this association, a Committee for Weights and Measures and Monies (French: Comité des poids, mesures et monnaies) would be created during the Exposition Universelle (1867) in Paris and would call for the international adoption of the metric system.[4][42]
In 1866, an important concern was that the Toise of Peru, the standard of the toise constructed in 1735 for the French Geodesic Mission to the Equator, might be so much damaged that comparison with it would be worthless,[64] while Bessel had questioned the accuracy of copies of this standard belonging to Altona and Koenigsberg Observatories, which he had compared to each other about 1840.[65][39] This assertion was particularly worrying, because when the primary Imperial yard standard had partially been destroyed in 1834, a new standard of reference was constructed using copies of the "Standard Yard, 1760", instead of the pendulum's length as provided for in the Weights and Measures Act 1824,[66] because the pendulum method proved unreliable.[67][68] Nevertheless Ferdinand Rudolph Hassler's use of the metre and the creation of the Office of Standard Weights and Measures as an office within the Coast Survey contributed to the introduction of the Metric Act of 1866 allowing the use of the metre in the United States,[69] and preceded the choice of the metre as international scientific unit of length and the proposal by the 1867 General Conference of the European Arc Measurement (German: Europäische Gradmessung) to establish the International Bureau of Weights and Measures.[53][70]
Egypt
Egyptian astronomy has ancient roots which were revived in the 19th century by the modernist impetus of Muhammad Ali who founded in Sabtieh, Boulaq district, in Cairo an Observatory which he was keen to keep in harmony with the progress of this science still in progress.[71][72] In 1858, a Technical Commission was set up to continue, by adopting the procedures instituted in Europe, the cadastre work inaugurated under Muhammad Ali. This Commission suggested to Viceroy Mohammed Sa'id Pasha the idea of buying geodetic devices which were ordered in France. While Mahmud Ahmad Hamdi al-Falaki was in charge, in Egypt, of the direction of the work of the general map, the viceroy entrusted to Ismail Mustafa al-Falaki the study, in Europe, of the precision apparatus calibrated against the metre intended to measure the geodesic bases and already built by Jean Brunner in Paris. Ismail Mustafa had the task to carry out the experiments necessary for determining the expansion coefficients of the two platinum and brass bars, and to compare the Egyptian standard with a known standard. The Spanish standard designed by Carlos Ibáñez e Ibáñez de Ibero and Frutos Saavedra Meneses was chosen for this purpose, as it had served as a model for the construction of the Egyptian standard.[72][71] In addition, the Spanish standard had been compared with Borda's double-toise N° 1, which served as a comparison module for the measurement of all geodesic bases in France,[73][74] and was also to be compared to the Ibáñez apparatus.[75][73] In 1954, the connection of the southerly extension of the Struve Geodetic Arc with an arc running northwards from South Africa through Egypt would bring the course of a major meridian arc back to land where Eratosthenes had founded geodesy.[76]
International prototype metre
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Perspective
For metrology the matter of expansibility was fundamental; as a matter of fact, the temperature measuring error related to the length measurement in proportion to the expansibility of the standard and the constantly renewed efforts of metrologists to protect their measuring instruments against the interfering influence of temperature revealed clearly the importance they attached to the expansion-induced errors. It was common knowledge, for instance, that effective measurements were possible only inside a building, the rooms of which were well protected against the changes in outside temperature, and the very presence of the observer created an interference against which it was often necessary to take strict precautions.[78] Thus, the Contracting States also received a collection of thermometers whose accuracy made it possible to ensure that of length measurements.[79] 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.[80][81]
The construction of the international prototype metre and the copies which were the national standards was at the limits of the technology of the time. The bars were made of a special alloy, 90% platinum and 10% iridium, which was 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.[7][81] 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 mètre des Archives, and was consecrated as 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.[82] For example, the United States received No. 27 with a calibrated length of 0.9999984 m ± 0.2 μm (1.6 μm short of the international prototype).[83][42]
The first (and only) follow-up comparison of the national standards with the international prototype was carried out between 1921 and 1936,[7][82] and indicated that the definition of the metre was preserved to within 0.2 μm.[84] 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.[85]
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 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 – the support points, separated by 0.5594 of the total length of the bar,[86] that minimise shortening of the bar due to bending under its own weight.[87] Because the prototype is a line standard, its full length is 102 cm, slightly longer than 1 metre.[88][89] Cross-sectionally, it measures 16 mm × 16 mm.[90]
The comparison of the new prototypes of the metre with each other involved the development of special measuring equipment and the definition of a reproducible temperature scale. The BIPM's thermometry work led to the discovery of special alloys of iron–nickel, in particular invar, whose practically negligible coefficient of expansion made it possible to develop simpler baseline measurement methods, and for which its director, the Swiss physicist Charles-Edouard Guillaume, was granted the Nobel Prize in Physics in 1920. Guillaume's Nobel Prize marked the end of an era in which metrology was leaving the field of geodesy to become a technological application of physics.[91][5][92]
In 1883, at its seventh General Conference in Rome, the International Geodetic Association would also consider the choice of an international prime meridian and would propose the Greenwich meridian hoping that Great Britain might respond in favour of the unification of weights and measures, by adhering to the Metre Convention.[93]
In 1889 the General Conference on Weights and Measures met at Sèvres, the seat of the International Bureau. It performed the first great deed dictated by the motto inscribed in the pediment of the splendid edifice that is the metric system: "A tous les temps, à tous les peuples" (For all times, to all peoples); and this deed consisted in the approval and distribution, among the governments of the states supporting the Metre Convention, of prototype standards of hitherto unknown precision intended to propagate the metric unit throughout the whole world.[78][Note 2]
From standard bars to wavelength of light
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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.[68][94]
Interferometric options
The first interferometric measurements carried out using the international prototype metre were those of Albert A. Michelson and Jean-René Benoît (1892–1893)[95] and of Benoît, Fabry and Perot (1906),[96] 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)[97] and later by the CIPM (1927).[82][98] Michelson's work in "measuring" the prototype metre to within 1⁄10 of a wavelength (< 0.1 μm) was one of the reasons for which he was awarded the Nobel Prize in Physics in 1907.[7][82][99]
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).[7]
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 standard
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.[7][100]
Accordingly, the 11th CGPM in 1960 agreed a new definition of the metre:[85]
The metre is the length equal to 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).[7][84] In this way, the new definition of the metre was 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 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.[101] 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.[7]
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.[Note 3] The asymmetry also affected the precision to which the wavelengths could be measured.[102][103]
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,[further explanation needed] 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 88.376 181 627(50) THz.[102][104]
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.[Note 4] This ambiguity was resolved in 1975, when the 15th CGPM approved a conventional value of the speed of light as exactly 299 792 458 m s−1.[105]
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.[106][107] That same year, the 17th CGPM adopted a definition of the metre, in terms of the 1975 conventional value for the speed of light:[108]
- 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 was reworded in 2019:[6]
- 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 c to be 299792458 when expressed in the unit m⋅s−1, where the second is defined in terms of the caesium frequency ΔνCs.
The concept of defining a unit of length in terms of a time received some comment.[109] 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).[98][109] 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.[109]
Summary of definitions since 1798
| Basis of definition | Date | Absolute uncertainty |
Relative uncertainty |
|---|---|---|---|
| 1⁄10,000,000 part of one half of a meridian, measurement by Delambre and Méchain | 1798 | 0.5–0.1 mm | 10−4 |
| First prototype Mètre des Archives platinum bar standard | 1799 | 0.05–0.01 mm | 10−5 |
| Platinum-iridium bar at melting point of ice (1st CGPM) | 1889 | 0.2–0.1 μm | 10−7 |
| Platinum-iridium bar at melting point of ice, atmospheric pressure, supported by two rollers (7th CGPM) | 1927 | n/a | n/a |
| 1,650,763.73 wavelengths of light from a specified transition in krypton-86 (11th CGPM) | 1960 | 0.01–0.005 μm | 10−8 |
| Length of the path travelled by light in a vacuum in 1⁄299,792,458 of a second (17th CGPM) | 1983 | 0.1 nm | 10−10 |
See also
Notes
- 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.
- 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.
- Taking the point of highest intensity as the reference wavelength, the methane line had a wavelength of 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 3.392 231 376(12) μm.
- The measured speed of light was 299 792.4562(11) km s−1 for the "centre-of-gravity" definition and 299 792.4587(11) km s−1 for the maximum-intensity definition, with a relative uncertainty ur = 3.5×10−9.
References
External links
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