History of the metre
In the aftermath of the French Revolution (1789), the traditional units of measure used in the Ancien Régime were replaced. The livre monetary unit was replaced by the decimal franc, and a new unit of length was introduced which became known as the metre. Although there was initially considerable resistance to the adoption of the new metric system in France (including a period of official reversion to customary units, mesures usuelles), the metre gained adoption in continental Europe during the mid nineteenth century, particularly in scientific usage, and was officially established as an international measurement unit by the Metre Convention of 1875.
History of definition
|Basis of definition||Date||Absolute uncertainty||Relative uncertainty|
|1⁄10,000,000 part of one half of a meridian, measurement by Delambre and Méchain||1795||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|
The standard measures of length in Europe diverged from one another after the fall of the Carolingian Empire (around 888): while measures could be standardized within a given jurisdiction (which was often little more than a single market town), there were numerous variations of measure between regions. Indeed, as the measures were often used as the basis for taxation (of cloth, for example), the use of a particular measure was associated with the sovereignty of a given ruler and often dictated by law.
Nevertheless, with the increasing scientific activity of the 17th century came calls for the institution of a "universal measure" (as Englishman John Wilkins called it) or "metro cattolico" (Italian Tito Livio Burattini), which would be based on natural phenomena rather than royal decree, and would also be decimal rather than using the various systems of subdivision, often duodecimal, which 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 of length: such pendulums had recently been demonstrated by Christiaan Huygens, and their length is quite close to one modern metre (as well as to some other 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.
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 it needed the push of revolution to bring it about. 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, and of Great Britain and the newly independent United States, nothing came of Talleyrand's proposal.[Note 1]
The question of measurement reform was placed in the hands of the Academy of Sciences, who appointed a commission chaired by Jean-Charles de Borda. Borda was an avid supporter of decimalisation: 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 "grades" (1⁄100 of a quarter-circle) rather than degrees, with 100 minutes to a grade and 100 seconds to a minute. Borda considered that the seconds pendulum was a poor choice for a standard because the existing second (as a unit of time) was not part of the proposed decimal system of time measurement - a system of 10 hours to the day, 100 minutes to the hour and 100 seconds to the minute - introduced in 1793.
Instead of the seconds pendulum method, the commission – whose members included 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. Apart from the obvious consideration of safe access for French surveyors, the Paris meridian was also a sound choice for practical scientific reasons: a portion of the quadrant from Dunkirk to Barcelona (about 1000 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[clarification needed].
The task of surveying the meridian arc fell to Pierre Méchain and Jean-Baptiste Delambre, and took more than six years (1792–1798). 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 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. In the meantime, the commission calculated a provisional value from older surveys of 443.44 lignes.[Note 2] This value was set by legislation on 7 April 1795.
The project was split into two parts – the northern section of 742.7 km from the belfry, Dunkirk to Rodez Cathedral which was surveyed by Delambre and the southern section of 333.0 km from Rodez to the Montjuïc Fortress, Barcelona which was surveyed by Méchain.[Note 3]
Delambre used a baseline of about 10 km (6,075.90 toise) in length along a straight road between Melun and Lieusaint. In an operation taking six weeks, the baseline was accurately measured using four platinum rods, each of length two toise (about 1.949 m). Thereafter he used, where possible, the triangulation points used by Cassini in his 1744 survey of France. Méchain's baseline, of a similar length (6,006.25 toise), and also on a straight section of road between Vernet (in the Perpignan area) and Salces (now Salses-le-Chateau). Although Méchain's sector was half the length of Delambre, it included the Pyrenees and hitherto unsurveyed parts of Spain. After the two surveyors met, each computed the other's baseline in order to cross-check their results and they then recomputed the kilometre. Their result came out at 0.144 lignes shorter than the provisional value, a difference of about 0.03%.
Mètre des Archives
While Méchain and Delambre were completing their survey, the commission 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 June 1799 (4 messidor An VII in the Republican calendar) as a permanent record of the result. 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 December 1799 (19 frimaire An VIII) and became the sole legal system of weights and measures from 1801. After the restoration 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. 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 lignes)[Note 2] was slightly too short for the meridional definition of the metre. Arago and Biot extended the survey to the island of Formentera in the western Mediterranean Sea in 1806–1809, and found that one ten-millionth of the Earth's quadrant should be 443.31 lignes: later work increased the value to 443.39 lignes. The modern value, for the WGS 84 reference spheroid, is 19657 m or 1.00008 443.383lignes.[Note 4]
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".
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 quadrant-eleventh-gram-second system (aka "QES system" or "Q.E.S. system"), where the unit length was the quadrant of the Earth's polar circumference, the unit mass was the "eleventh-gram" or 10−11 grams and the unit time was the second. 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.
International prototype metre
With increasing international adoption of the metre, the shortcomings of the mètre des Archives as a standard became ever more apparent. Countries that adopted the metre as a legal measure purchased standard metre bars 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 reproducibility, quickly proved so impractical that it 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.
The International Conference on Geodesy in 1867 called for the creation of a new, international prototype metre (IPM)[Note 5] and the arrangement of 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.
The standards' international nature was ensured by a treaty, the Metre Convention, signed in Paris on 20 May 1875. The treaty established an international organisation, the Bureau international des poids et mesures (BIPM), to conserve the prototypes—which would be the joint property of the signatory nations—and to carry out regular comparisons with national standards. In recognition of France's role in designing the metric system, the BIPM is based in Sèvres, just outside Paris. However, as an international organisation, the BIPM is under the ultimate control of a diplomatic conference, the Conférence générale des poids et mesures (CGPM) rather than the French government.
The construction of the international prototype metre and the copies which would be national standards was at the limits of the technology of the time. The bars were to be made of a special alloy, 90% platinum and 10% 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. 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. For example, the United States received No. 27 with a calibrated length of 0.999 9984 m ± 0.2 µm (1.6 µm short of the international prototype).
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. 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.
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.
The first interferometric measurements carried out using the international prototype metre were those of Albert A. Michelson and Jean-René Benoît (1892–1893) and of Benoît, Fabry and Perot (1906), 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) and later by the CIPM (1927).[Note 6] 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.
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 ångström 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. Accordingly, the 11th CGPM in 1960 agreed a new definition of the metre:
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). In this way, the new definition of the metre was traceable to both the old prototype metre and the old definition of the ångström.
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. 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-stabilized 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 7] The asymmetry also affected the precision to which the wavelengths could be measured.
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-stabilized laser was found to be 88.376 181 627(50) THz.
Independent measurements of frequency and wavelength are, in effect, a measurement of the speed of light (c = fλ), and the results from the methane-stabilized 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 8] 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.
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 nm line of the helium–neon laser, stabilized using molecular iodine. That same year, the 17th CGPM adopted the current definition of the metre, in terms of the 1975 conventional value for the speed of light:
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.
The concept of defining a unit of length in terms of a time received some comment, although it was similar to 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 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 realized 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 stabilize a laser source, the advantages of flexibility are obvious.
- 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.
- All values in lignes are referred to the toise de Pérou, not to the later value in mesures usuelles. 1 toise = 6 pieds; 1 pied = 12 pouces; 1 pouce = 12 lignes; so 864 lignes = 1 toise.
- Distances measured using Google Earth. The coordinates are:
– Belfry, Dunkirk
– Rodez Cathedral
– Montjuïc, Barcelona
- The WGS 84 reference spheroid has a semi-major axis of 378137.0 m and a flattening of 61⁄223563298.257.
- 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.
- The IUSR (later to become the International Astronomical Union) defined the ångström such that the wavelength (in air) of the cadmium line was 6438.469 63 Å.
- 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.
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