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History of the metre
Origins and values of the unit of length

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. 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.

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.

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:

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.

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Background

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.7

Universal measurement

Main article: History_of_measurement § Units_of_length

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.910 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. 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.

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.

The seconds pendulum

Galileo discovered gravitational acceleration explaining the fall of bodies at the surface of the Earth.11 He also observed the regularity of the period of swing of the pendulum and that this period depended on the length of the pendulum.12 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).1314 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).151617 He found the value of 36 pouces and 8 ⁠1/2⁠ lignes of the Toise of Châtelet, which had been recently renewed.181920

In 1675, Tito Livio Burattini suggested the term metro cattolico meaning universal measure for the unit of length based on the seconds pendulum.21 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.2223

Astronomy, physics and map making

The French Academy of Sciences, responsible for the concept and definition of the metre,24 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.25 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.26 That demonstrated Newton's law of universal gravitation.27

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.2829 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.303132

French revolution

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. In addition to rejecting standards created by the French royal establishment, basing units on fundamental physicals properties was an explicit goal. This effort culminated in the arc measurement of Delambre and Méchain aiming at defining the metre and determining the figure of the Earth.33: 52 

Meridional definition

See also: Earth's circumference § Historical use in the definition of units of measurement, and Meridian arc § History of measurement

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.34 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.3536

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,37 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.38 This value was set by legislation on 7 April 1795.39 It was therefore metal bars of 443.44 lignes that were distributed in France in 1795-1796.40 These metres were provisional (French: provisoire) because the expedition and the calculations to determine the definitive length of metre were not completed until 1799.4142

To decide the length of the Mètre des Archives, the Weights and Measures Commission adopted a value of ⁠1/334⁠ for the non-spherical shape of the Earth, known as the flattening. This was based on analysis by Pierre-Simon Laplace using the arc of Peru and the meridian arc of Delambre and Méchain,43 and was close to his previous estimate of ⁠1/336⁠ based on pendulum measurements.44

Mètre des Archives

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. In 1799, the metre was officially defined by an artifact made of platinum kept in the National Archives, the Mètre des Archives.45 A second platinum and twelve iron standards of the metre were made by Étienne Lenoir.46

One of the latter was brought to the United States in 1805 by Ferdinand Rudolph Hassler.47 It became known as the Committee Meter in the United States and served as standard of length in the United States Coast Survey until 1890. Hassler designed a calibration apparatus which instead of bringing different bars in actual contact during measurements,48 used only one bar calibrated on the Committee meter.49505152

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

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.5354 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 1855.55 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.5657

In the United States, the Metric Act of 1866 allowed the use of the metre in the United States,58 and in 1867 the General Conference of the European Arc Measurement (German: Europäische Gradmessung) established the International Bureau of Weights and Measures.5960

International prototype metre

In the late nineteenth century, a new international standard metre, called a "prototype",61 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.6263

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.6465 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 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.66 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).6768

As bar lengths vary with temperature, precise measurements required known and stable temperatures and could even be affected by a scientist's body heat,69 so standard metres were provided with precise thermometers. 70

The first (and only) follow-up comparison of the national standards with the international prototype was carried out between 1921 and 1936,7172 and indicated that the definition of the metre was preserved to within 0.2 μm.73 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 1927.74

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,75 that minimise shortening of the bar due to bending under its own weight.76 Because the prototype is a line standard, its full length is 102 cm, slightly longer than 1 metre.7778 Cross-sectionally, it measures 16 mm × 16 mm.79

From standard bars to wavelength of light

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.8081

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)82 and of Benoît, Fabry and Perot (1906),83 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)84 and later by the CIPM (1927).8586 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 1907.878889

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).90

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.9192

Accordingly, the 11th CGPM in 1960 agreed a new definition of the metre:93

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).9495 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

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.96 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.97

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.98 The asymmetry also affected the precision to which the wavelengths could be measured.99100

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 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.101102

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.103 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−1.104

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.105106 That same year, the 17th CGPM adopted a definition of the metre, in terms of the 1975 conventional value for the speed of light:107

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 2019:108

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).110111 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.112

Summary of definitions since 1798

Definitions of the metre since 1798113
Basis of definitionDateAbsoluteuncertaintyRelativeuncertainty
1⁄10,000,000 part of one half of a meridian, measurement by Delambre and Méchain17980.5–0.1 mm10−4
First prototype Mètre des Archives platinum bar standard17990.05–0.01 mm10−5
Platinum-iridium bar at melting point of ice (1st CGPM)18890.2–0.1 μm10−7
Platinum-iridium bar at melting point of ice, atmospheric pressure, supported by two rollers (7th CGPM)1927n/an/a
1,650,763.73 wavelengths of light from a specified transition in krypton-86 (11th CGPM)19600.01–0.005 μm10−8
Length of the path travelled by light in a vacuum in 1⁄299,792,458 of a second (17th CGPM)19830.1 nm10−10

See also

Notes

References

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