Subway
The meter (symbol: m) is the coherent unit of length in the International System of Units. It is defined as the distance that light travels in a vacuum in an interval of 1/299792458 s.
The meter was originally defined in 1793 as one ten millionth of the distance from the Equator to the North Pole along a great circle, so the circumference of the Earth is approximately 40,000 kilometers. In 1799 the meter was redefined in terms of a prototype meter bar (the actual bar used was changed in 1889). In 1960, the meter was redefined in terms of a certain number of wavelengths from a certain krypton-86 emission line. The current definition was adopted in 1983 and slightly modified in 2002 to clarify that the meter is a proper measure of length.
History of the subway and its definitions
The word meter comes from the Greek μέτρον (metron, measure); from here it passed into French as mètre. Its use in the modern sense of unit of measure was introduced by the Italian scientist Tito Livio Burattini in his work Misura Universale of 1675 to change the name to metro cattolico the universal measure proposed by the English philosopher John Wilkins in 1668.
In 1668 Wilkins made his proposal for universal measurement using Christopher Wren's suggestion of a pendulum with a half-period of one second to measure a standard length of 997 mm in length that Christiaan Huygens had observed.
During the 18th century there were two predominant trends regarding the definition of the standard unit of length. One of these, following Wilkins, suggested the definition of the meter as the length of a pendulum with a half-period of one second. Meanwhile, the other proposed a definition based on the length of the terrestrial meridian between the equator and the north pole: one ten-millionth of the length of half of the terrestrial meridian. In 1791, the French Academy of Sciences opted for the second definition against that based on the pendulum because the force of gravity varies significantly along the surface of the Earth and this variation affects the period of the pendulum.
The meter was defined in 1791 by the French Academy of Sciences as the ten-millionth part of the quadrant of a terrestrial meridian; specifically, the distance across the Earth's surface from the north pole to the equator passing through the Paris meridian (more precisely through the Paris observatory). This meridian had already been measured previously in 1669 by Jean Picard (Paris-Amiens section), extended to Dunkirk and Perpignan in 1718 by Jean-Dominique Cassini (Giovanni Cassini) and revised in 1739 by LaCaille. The Academy of Sciences created a commission made up of Borde, Condorcet, Lagrange, Lavoisier, Tillet, later adding Laplace and Monge, who commissioned Pierre-François André Méchain (1744-1804) and Jean-Baptiste Joseph Delambre (1749-1822) to carry out the measurements. pertinent geodesics to calculate the arc of the meridian and to be able to deduce the length of the meter. The measurement task was extended from 1792 to 1798, among other reasons due to the French Revolutionary Wars. These measures were carried out in a first phase between Dunkerque and Barcelona. Specifically, the Paris meridian reaches the sea at Ocata beach, in El Masnou. In a second phase, the measurements were extended to the Balearic Islands, between 1806 and 1808. The French scientist Francesc Aragón, who explains in his memoirs that he met Méchain when he was measuring the arc of the meridian through Roussillon, was one of the members of the second expedition that he completed, extending them to Alicante, Ibiza and Mallorca, the measures that allowed us to confirm this first definition. When the French war broke out, Francesc Aragón avoided lynching thanks to his knowledge of Catalan, but he had to take refuge in the Bellver castle prison with his assistants, and they could not return to France until a year later.. In 1795 France adopted the meter as the official unit of length.
Throughout history, attempts were made to unify the different measures with the aim of simplifying exchanges, facilitating trade and the fair collection of taxes. In the French Revolution of 1789, along with other challenges considered necessary for the new times, Scientific Commissions were appointed to standardize weights and measures, including length. The task was arduous and complicated; it was considered as a pattern of the length of a pendulum of seconds at a latitude of 45°, but it would end up discarded as not being a completely objective model; it would finally be agreed to measure a meridian arc to establish, on it and therefore on the Earth itself, the pattern of the meter. Those in charge of said measurement were Jean-Baptiste Joseph Delambre and Pierre Méchain, who between 1791 and 1798 and through a triangulation system from Dunkirk to Barcelona they established the measure of said meridian arc on which the meter was established. They had the collaboration of the Spanish mathematician and astronomer José Chaix Isniel, who was commissioned by the government of Spain between 1791 and 1793 to collaborate with the project led by Méchain.
1792 Definition
Initially, this unit of length was created by the French Academy of Sciences in 1792 and defined as one ten-millionth of the distance that separates the north pole from the terrestrial equator line, through the terrestrial surface.
New pattern of 1889
On September 28, 1889, the International Commission of Weights and Measures adopted new prototypes for the meter and, later, for the kilogram, which materialized in a standard meter of platinum and iridium deposited in chests located in the basements of the Breteuil pavilion in Sèvres, Office of Weights and Measures, on the outskirts of Paris.
1960s definition
The 11th Conference on Weights and Measures adopted a new definition of the meter: "1,650,763.73 times the vacuum wavelength of orange radiation from the krypton 86 atom." The precision was fifty times higher than that of the 1889 pattern. (Equivalences: one fathom = 2.09 m; one span = 0.2089 m).
Definition in terms of the speed of light
This is the current definition, adopted in 1983 by the 17th General Conference on Weights and Measures. It is defined as the distance that light travels in a vacuum in an interval of 1/299,792,458 s. He fixed the length of the meter as a function of seconds and the speed of light:
The metro is the length of the journey through the light in the vacuum during an interval of time 1♪299,792,458 seconds.
This definition pegs the speed of light in a vacuum at exactly 299,792,458 m/s (meters per second). A byproduct of the 17th CGPM definition was that it allowed scientists to compare their lasers carefully using frequency, which results in wavelengths with one-fifth the uncertainty involved in direct comparison of wavelengths, thanks to the fact that those of interferometer errors were eliminated. To further facilitate laboratory reproducibility the 17th CGPM also made the stabilized iodine laser helium-neon "a recommended radiation" for the realization of the meter. In order to delineate the meter, the BIPM currently considers the HeNe laser wavelength has to be as follows: λHeNe = 632,991,212.58 fm with an estimated relative standard uncertainty (U) of 2.1×10−11. This uncertainty is currently a limiting factor in laboratory realizations of the meter, and one that is several orders of magnitude poorer than that of the second, based on cesium source atomic clock (1=U = 5×10−16). Therefore, a realization of the meter is normally delineated (not defined) today to laboratories as 1,579,800.762042(33) wavelengths of helium-neon laser light in a vacuum, the indicated error is only that of determining the frequency. This notation in keys expressing the error is explained in the article on measurement uncertainty.
The practical realization of the meter is subject to uncertainties in the characterization of the medium, various uncertainties of interferometry, and uncertainty in the measurement of the source frequency. A medium commonly used is air, and the Institute National Standards and Technology has created an online calculator to convert wavelengths in a vacuum to wavelengths in air. According to the description by NIST, in air, the uncertainties in the characterization of the mean are dominated by errors in the search for temperature and pressure. Errors in the theoretical formulas used are secondary. By implementing a refractive index correction of this type, an approximation of the meter realization can be implemented in air, such as using the meter formulation as 1.579. 800.762042(33) wavelengths of helium-neon laser light in a vacuum, and convert the wavelengths in a vacuum to wavelengths in air. Of course, air is only one possible medium to use in a meter realization, and any partial vacuum can be used, or some inert atmosphere such as helium gas, provided the appropriate corrections for refractive index are implemented.
Unit of length in meters
Although measurement is currently defined as the length of the path traveled by light in a given time, laboratory measurements of length in meters were determined by counting the number of wavelengths of laser light of one of the standard types set to length, and conversion of the selected unit of wavelength to meters. There are three main factors that limit the accuracy achievable with laser interferometers for a length measurement:
- Uncertainty in the wavelength of the vacuum source,
- Uncertainty in the media refraction index,
- Minimum value of interferometer resolution.
Of these, the last one is peculiar to the interferometer itself. The conversion of a length in wavelengths to a length in meters is based on the relationship:
- λ λ =cnf{displaystyle lambda ={frac {c}{nf}}{ }
which converts the wavelength unit λ λ {displaystyle lambda } in meters cthe speed of light in the vacuum, in m/s. Here. n is the refraction rate of the means in which the measurement is performed, and f is the frequency of measurement of the source. Although the conversion of wavelengths to meters introduces an additional error in the total length due to measurement errors in the determination of the refractive index and the frequency, the measurement of the frequency is one of the most accurate measures available.
Evolution of the definition of the meter
- May 8, 1790: the French National Assembly decided that the length of the new metro must be equal to the length of a pendulum with a semi-period of a second.
- March 26, 1791: the French National Assembly accepts the proposal of the French Academy of Sciences and decrees that the new definition of the metro is equal to a ten-millionth part of the length of a quarter of the land meridian. From then on it will begin to measure a meridian arch between Dunkirk and Barcelona that would serve as the basis for the new definition of the metro.
- 1795: In July a provisional pattern is built in brass and is sent to the Public Instruction Committee.
- December 10, 1799: the French National Assembly establishes by law the prototype of the metro as a pattern of measures of length to the Republic. The final prototype had been presented on June 22, 1799, was a complete plan built in platinum and rectangular section, this first definitive prototype was deposited to the National Archive of France.
- September 28, 1889: the first General Conference of Weights and Measures (GPM) held in Paris, defines the metro as the distance between two lines marked in a platinum bar with 10% measured iridium at the ice melting temperature.
- October 6, 1927: the 7th CGPM adjusts the definition of the metro as the distance to 0 °C between the two central lines axles marked on the platinum-irdium bar of the prototype, with the bar subject to a standard atmospheric pressure conditions and supported by two cylinders at least one centimeter in diameter placed in a symmetrical way to the same horizontal plan and at a distance of 571 mm (milimeters).
- October 20, 1960: the 11th CGPM defined the subway as 1 650 763.73 times the wavelength in the radiation vacuum that corresponds to the transition between quantum levels 2p10 and 5d5 of the krypton-86 atom.
- October 21, 1983: the 17th meeting of the GFCM established the current definition of the subway, the length traveled by the light in the vacuum at a time of 1/299,792,458 seconds. This definition has the advantage that the speed of light to vacuum is a fundamental physical constant, which makes the definition of the independent metro of any material reference object.
| Basis of definition | Date | Uncertainty absolute | Uncertainty relative |
|---|---|---|---|
| 1♪10,000,000 part of the fourth part of a meridian astronomical measurement of Bessel (443,44 lines) | 1792 | 0.5-0.1mm (millimeters) | 10−4 |
| 1♪10,000,000 part of the fourth part of a meridian measured by Delambre and Méchain (443,296 lines) | 1795 | 0.5-0.1mm | 10−4 |
| First prototypeMetro des Archives, the standard platinum bar | 1799 | 0.05-0.01mm | 10−5 |
| Platinum-irdium bar at its ice melting point (1.a CGPM) | 1889 | 0.2-0.1μm (micrometers) | 10−7 |
| Platinum-irdium bar at its ice melting point, atmospheric pressure, supported by two rollers (7.a CGPM) | 1927 | No. | No. |
| Hyperphine atomic transition; 1,650,763.73 light wavelengths of a transition specified in krypton-86 (11.a CGPM) | 1960 | 0.01-0.005μm | 10−8 |
| Longitude of the trajectory traveled by light in the void in 1♪299,792,458 second (17th CGPM) | 1983 | 0.1nm | 10−10 |
Spelling
Metre is the standard spelling of the metric unit of length in almost all English-speaking nations, except the United States and the Philippines, which use meter. Other Germanic languages, such as German, Dutch, and Scandinavian languages, also spell the word meter.
Measuring devices (such as ammeter, speedometer) are written -meter in all variants of English. The suffix "-meter" has the same Greek origin as the unit of length.
Etymology
The word meter comes from the Greek term μέτρον (metron), which means 'measure'. It was used in France under the name mètre to designate the pattern of measuring length.
| Basis of definition | Date | Uncertainty absolute | Uncertainty relative |
|---|---|---|---|
| 1/10 000 part of the distance between the north pole and the equator along the line of the meridian that passes through Paris | 1795 | 0.5-0.1 (millimeters) | 10−4 |
| First prototype Metre des Archives standard platinum bar. | 1799 | 0.05-0.01 mm | 10−5 |
| Platinum-irdium bar at the ice melting point (1.a General Conference of Weights and Measures) | 1889 | 0.2-0.1 μm (micrometers) | 10−7 |
| Platinum-irdium bar at the ice melting point, atmospheric pressure, supported by two rollers (7.a CGPM) | 1927 | No. | No. |
| Hyperfine atomic transition; 1 650 763.73 wavelengths of transition light with krypton 86 (11.a CGPM) | 1960 | 0.01-0.005 μm | 10−8 |
| Distance traveled by light in vacuum in 1/299 792 458 part of a second (17th CGPM) | 1983 | 0.1 nm | 10−10 |
Multiples and submultiples of the meter
| Submultiplos | Multiple | |||||
|---|---|---|---|---|---|---|
| Value | Symbol | Name | Value | Symbol | Name | |
| 10−1 m | dm | decimeter | 101 m | dam | decameter | |
| 10−2 m | cm | centimeter | 102 m | hm | hectometer | |
| 10−3 m | mm | millimeter | 103 m | km | kilometer | |
| 10−6 m | μm | micrometer (micrometer) | 106 m | Mm. | meter | |
| 10−9 m | nm | nanometer | 109 m | Gm | gigameter | |
| 10−12 m | pm | picometer | 1012 m | Tm | Thermal | |
| 10−15 m | fm | femometer (fermi) | 1015 m | Pm | petameter | |
| 10−18 m | am | Attometer | 1018 m | Em | Diameter | |
| 10−21 m | zm | zeptometer | 1021 m | Zm | zettámetro | |
| 10−24 m | ym | Yoctometer | 1024 m | Ym | Yotttámeter | |
| 10−27 m | rm | rhetorometer | 1027 m | Rm | ronnameter | |
| 10−30 m | qm | . | 1030 m | Qm | the diameter | |
| The most common prefixes appear in bold. | ||||||
Subway equivalences
- 1 metre equals:
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