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A fleeting hint of an ancient decimal or metric system may be found in the [[Mohenjo-Daro#Ruler|Mohenjo-Daro ruler]], which uses a base length of {{convert|1.32|inch|mm|1}} and is very precisely divided with decimal markings. Bricks from that period are consistent with this unit, but this usage appears not to have survived, as later systems in India are non-metric, employing divisions into eighths, twelfths, and sixteenths.
== Age of Enlightenment ==
Foundational aspects of mathematics, together with an increased understanding of the natural world during the Enlightenment, set the stage for the emergence in the late 18th century of a system of measurement with rationally related units and rules for combining them.
=== Preamble ===
In the early ninth century, when much of what later became France was part of the [[Holy Roman Empire]], units of measure had been standardised by the [[Charlemagne|Emperor Charlemagne]]. He had introduced standard units of measure for length and for mass throughout his empire. As the empire disintegrated into separate nations, including France, these standards diverged. In England, [[Magna Carta]] (1215) had stipulated that "There shall be standard measures of wine, ale, and corn (the London quarter), throughout the kingdom. There shall also be a standard width of dyed cloth, russet, and haberject, namely two ells within the selvedges. Weights are to be standardised similarly."<ref>{{cite web
| title = English translation of Magna Carta
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| number = 2
| doi = 10.2308/0148-4184.19.2.25
}}<!--|access-date = 10 October 2013--></ref> but the [[Arabs]] represented numbers using the [[Hindu numeral system]], a [[positional notation]] that used ten symbols. In about 1202, [[Fibonacci]] published his book ''[[Liber Abaci]]'' (Book of Calculation) which introduced the concept of positional notation into Europe. These symbols evolved into the numerals "0", "1", "2", etc.<ref>{{MacTutor|class=HistTopics|id=Arabic_numerals|title=The Arabic numeral system|date=January 2001}}</ref><ref>{{MacTutor|id=Fibonacci|title = Leonardo Pisano Fibonacci|date = October 1998}}</ref> At that time, there was dispute regarding the difference between [[rational number]]s and [[irrational number]]s and there was no consistency in the way in which decimal fractions were represented.
[[Simon Stevin]] is credited with introducing the decimal system into general use in Europe.<ref name=Stevin_MacTutor/> In 1586, he published a small pamphlet called ''De Thiende'' ("the tenth") which historians credit as being the basis of modern notation for decimal fractions.<ref>{{MacTutor|class=HistTopics|id=Real_numbers_1|title=The real numbers: Pythagoras to Stevin|date=October 2005}}</ref> Stevin felt that this innovation was so significant that he declared the universal introduction of decimal coinage, measures, and weights to be merely a question of time.<ref name="Stevin_MacTutor">{{MacTutor|id=Stevin|title=Simon Stevin|date=January 2004}}</ref><ref name="TavernorB">{{cite book
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}}</ref>{{rp|70}}<ref name=Alder/>{{rp|91}}
=== Body measures and artifacts ===
Since the time of Charlemagne, the standard of length had been a measure of the body, that from fingertip to fingertip of the outstretched arms of a large man,<ref group="Note">just under 2 metres in today's units</ref> from a family of body measures called ''fathoms'', originally used among other things, to measure the depth of water. An artifact to represent the standard was cast in the most durable substance available in the Middle Ages, an iron bar {{Citation needed|date=February 2018}}. The problems of a non-reproducible artefact became apparent over the ages: it rusted, was stolen, beaten into a mortised wall until it bent, and was, at times, lost. When a new royal standard had to be cast, it was a different standard than the old one, so replicas of old ones and new ones came into existence and use. The artefact existed through the 18th century, and was called a ''teise'' or later, a ''[[toise]]'' (from Latin ''tense'': outstretched (arms)). This would lead to a search in the 18th century for a reproducible standard based on some invariant measure of the natural world.
=== Clocks and pendulums ===
In 1656, Dutch scientist [[Christiaan Huygens]] invented the pendulum clock, with its pendulum marking the seconds. This gave rise to proposals to use its length as a standard unit. But it became apparent that the pendulum lengths of calibrated clocks in different locations varied (due to local variations in the [[Gravity of Earth|acceleration due to gravity]]), and this was not a good solution. A more uniform standard was needed.
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}}</ref><ref name = Mouton/>
=== The shape and size of the Earth ===
{{main|Figure of the Earth}}
Since at least the Middle Ages, the Earth had been perceived as eternal, unchanging, and of symmetrical shape (close to a sphere), so it was natural that some fractional measure of its surface should be proposed as a standard of length. But first, scientific information about the shape and size of the Earth had to be obtained. One degree of arc would be 60 minutes of arc, on the equator; one [[#milliare|milliare]] would be one minute of arc, or 1 nautical mile, so 60 nautical miles would be one degree of arc on Earth's surface, taken as a [[sphere]].<ref name=mouton>US Metric Association [https://usma.org/origin-of-the-metric-system Origin of the metric system]</ref> Thus [[Earth's circumference#Earth's circumference in nautical miles|Earth's circumference in nautical miles]] would be 21 600 (viz., 60 minutes of arc
In 1669, [[Jean Picard]], a French astronomer, was the first person to measure the Earth accurately. In a survey spanning one degree of latitude, he erred by only 0.44% ([[Picard's arc measurement]]).
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| page = 63
| isbn = 978-0-226-76747-5
}}
</ref>{{efn |name=cassiniSurvey|1=[[Jacques Cassini]]'s survey of Earth of 1713–1718<ref name=Cassini >[[Jacques Cassini]]. [https://gallica.bnf.fr/ark:/12148/bpt6k853732m/f30.item (1720) De la grandeur et de la figure de la Terre] ''On the size and features of Earth'', pages 14ff.</ref> }}
=== Late 18th century: conflict and lassitude ===
[[File:Watt James von Breda.jpg|upright|thumb|[[James Watt]], British inventor and advocate of an international decimalised system of measure<ref name=JamesWatt/>]]
By the mid-18th century, it had become apparent that it was necessary to standardise of weights and measures between nations who traded and exchanged scientific ideas with each other. Spain, for example, had aligned her units of measure with the royal units of France<ref name="metricSpain">{{cite web
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In 1790, a proposal floated by the French to Britain and the United States, to establish a uniform measure of length, a ''metre'' based on the period of a pendulum with a beat of one second, was defeated in the British Parliament and United States Congress. The underlying issue was failure to agree on the latitude for the definition, since gravitational acceleration, and, therefore, the length of the pendulum, varies (inter alia) with latitude: each party wanted a definition according to a major latitude passing through their own country. The direct consequences of the failure were the French unilateral development and deployment of the metric system and its spread by trade to the continent; the British adoption of the Imperial System of Measures throughout the realm in 1824; and the United States' retention of the British common system of measures in place at the time of the independence of the colonies. This was the position that continued for nearly the next 200 years.<ref group="Note">Much of the British Empire except the UK adopted the metric system early on; the UK partly adopted the metric system late in the 20th century.</ref>
== Implementation in Revolutionary France ==
=== Weights and measures of the ''Ancien Régime'' ===
{{Further|French units of measurement}}
It has been estimated that, on the eve of the Revolution in 1789, the eight hundred or so units of measure in use in France had up to a quarter of a million different definitions because the quantity associated with each unit could differ from town to town, and even from trade to trade.<ref name="Alder">{{cite book
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}}</ref>
===
[[File:Nicolas de Condorcet.PNG|upright|left|thumb|The Marquis de Condorcet – 18th century French firebrand of the metric system<ref group="Note">Condorcet is universally misquoted as saying that "the metric system is for all people for all time". His remarks were probably between 1790 and 1792. The names 'metre' and 'metre-system' i.e. 'metric system' were not yet defined. Condorcet actually said, "measurement of an eternal and perfectly spherical earth is a measurement for all people for all time". He did not know what, if any, units of length or other measure would be derived from this. His political advocacy eventually resulted in him committing suicide rather than be executed by the Revolutionaries.</ref>]]
In 1790, a panel of five leading French scientists was appointed by the [[French Academy of Sciences|''Académie des sciences'']] to investigate weights and measures. They were [[Jean-Charles de Borda]], [[Joseph-Louis Lagrange]], [[Pierre-Simon Laplace]], [[Gaspard Monge]], and [[Nicolas de Condorcet]].<ref name=Alder/>{{rp|2–3}}<ref name="Konvitz">
{{cite book | title = Cartography in France, 1660–1848: Science, Engineering, and Statecraft
| first1 = Josef
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| isbn = 978-0-226-45094-0
}}</ref>{{rp|46}}
Over the following year, the panel, after studying various alternatives, made a series of recommendations regarding a new system of weights and measures, including that it should have a decimal [[radix]], that the unit of length should be based on a fractional arc of a quadrant of the Earth's meridian, and that the unit of weight should be that of a cube of water whose dimension was a decimal fraction of the unit of length.<ref>
{{cite journal | title = Legendre and the French Reform of Weights and Measures
| publisher = University of Chicago Press
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| first1 = C. Doris|author1-link=C. Doris Hellman
|jstor = 301613| s2cid = 144499554
}}</ref><ref name="Glasser">
{{cite book | url = http://www.eipiphiny.org/books/history-of-binary.pdf
| pages = 71–72
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| orig-year = 1971
| access-date = 5 April 2013
}}</ref><ref name="TavernorB"/>{{rp|50–51}}<ref name="Adams">
{{cite book | url = https://archive.org/details/reportuponweight1821unit
| title = Report upon Weights and Measures
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| date = 22 February 1821
| author-link = John Quincy Adams
}}</ref><ref name="18germ_3">
{{cite web |url = http://www.metrodiff.org/cmsms/index.php?page=18_germinal_an_3
|title = Décret relatif aux poids et aux mesures. 18 germinal an 3 (7 avril 1795)
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|archive-date = 17 August 2016
|url-status = dead
}}</ref> The proposals were accepted by the [[National Constituent Assembly (France)|French Assembly]] on 30 March 1791.<ref name="LoisEtDecret">
{{cite web | title = Lois et décrets
| language = fr
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Following acceptance, the ''Académie des sciences'' was instructed to implement the proposals. The ''Académie'' broke the tasks into five operations, allocating each part to a separate [[working group]]:<ref name="TavernorB"/>{{rp|82}}
* Measuring the difference in latitude between [[Dunkirk]] and [[Barcelona]] and [[Triangulation|triangulating]] between them
* Measuring the baselines used for the survey
* Verifying the length of the second pendulum at 45° latitude.
* Verifying the weight in a vacuum of a given volume of distilled water.
* Publishing conversion tables relating the new units of measure to the existing units of measure.
The panel decided that the new measure of length should be equal to one ten-millionth of the distance from the North Pole to the Equator ([[Earth quadrant]]), measured along the [[Paris meridian]].<ref name="Larousse"/>
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After 1792, the name of the original defined unit of mass, "''[[gramme]]''", which was too small to serve as a practical realisation for many purposes, was adopted, the new prefix "kilo" was added to it to form the name "''[[kilogramme]]''". Consequently, the kilogram is the only [[SI base unit]] that has an [[SI prefix]] as part of its unit name.
A provisional kilogram standard was made and work was commissioned to determine the precise mass of a cubic decimetre (later to be defined as equal to one [[litre]]) of water.
The regulation of trade and commerce required a "practical realisation": a single-piece, metallic reference standard that was one thousand times more massive that would be known as the [[grave (unit)|''grave'']].<ref group="Note">from Latin ''gravitas'': "weight"</ref> This mass unit defined by [[Antoine Lavoisier|Lavoisier]] and [[René Just Haüy]] had been in use since 1793.<ref>
{{cite web | url = http://historyofscience.free.fr/Lavoisier-Friends/a_chap8_lavoisier.html
| title = Chapter 8: Lavoisier, Arts and Trades
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| last = Poirier
| access-date = 4 August 2011
}}</ref> This new, practical realisation would ultimately become the base unit of mass. On 7 April 1795, the ''gramme'', upon which the kilogram is based, was decreed to be equal to "the absolute weight of a volume of pure water equal to a cube of one hundredth of a metre, and at the temperature of the melting ice".<ref name=18germ_3/> Although the definition of the ''kilogramme'' specified water at 0 °C—a highly stable temperature point—it was replaced with the temperature at which water reaches maximum density. This temperature, about 4 °C, was not accurately known, but one of the advantages of the new definition was that the precise Celsius value of the temperature was not actually important.<ref>
{{Cite web |title=L'Histoire Du Mètre, La Détermination De L'Unité De Poids |trans-title=The History of the Meter, the Determination of the Unit of Weight |url=http://histoire.du.metre.free.fr/fr/index.htm |access-date=2022-08-12 |website=histoire.du.metre.free.fr |language=fr }}</ref>{{refn|group="Note"|There were three reasons for the change from the freezing point to the point of maximum density:<br> 1. It proved difficult to achieve the freezing point precisely. As [[Jean Henri van Swinden|van Swinden]] wrote in his report, ''whatever care citizens Lefévre-Gineau and Fabbroni took, by surrounding the vase that contained the water with a large quantity of crushed ice, and frequently renewing it, they never succeeded in lowering the centigrade thermometer below two-tenths of a degree; and the average water temperature during the course of their experiments was 3/10'';<ref name="van Swinden 1799 suite"> {{cite journal|author-last=van Swinden |author-first=Jean Henri|author-link=Jean Henri van Swinden|title=Suite Du Rapport. Fait à l'Institut national des sciences et arts, le 29 prairial an 7, au non de la classe des sciences mathématiques et physiques. Sur la mesure de la méridienne de France, et les résultats qui en ont été déduits pour déterminer les bases du nouveau systéme métrique|journal=Journal de Physique, de Chimie, d'Historie Naturelle et des Arts|volume=VI (XLIX)|year=1799|orig-year=Fructidor an 7 (Aug/Sep 1799)|url=https://books.google.com/books?id=JEVRAQAAMAAJ&dq=%22S%20U%20I%20T%20E%20D%20U%20R%20APP%20O%20R%20T%22&pg=PA161|pages=161–177}}</ref>{{rp|{{citation|title=168| year=1799 | publisher=Fuchs |url=https://books.google.com/books?id=DOUPAAAAQAAJ&dq=%22Mais%2C%20quelques%20soins%20que%20se%20soient%20donn%C3%A9s%20les%20citoyens%20Lef%C3%A9vre-Gineau%20et%20Fabbroni%22&pg=PA168}}}}<br> 2. This maximum of water density as a function of temperature can be detected 'independent of temperature awareness',<ref name="van Swinden 1799 suite"/>{{rp|{{citation|title=170| year=1799 | publisher=Bachelier |url=https://books.google.com/books?id=PZ7OAAAAMAAJ&dq=%22ind%C3%A9pendante%20de%20la%20connoissance%20de%20la%20temp%C3%A9rature%22&pg=PA170}}}} that is, without having to know the precise numerical value of the temperature. First note that if we are extracting net heat from the water, say by bringing it in thermal contact with e.g. ice, then we know, even without any direct temperature measurement, that the water temperature is going down. Given that, the procedure for determining the point of maximum density of water is as follows. As one weighs a submerged object, one notices that, as the water is being cooled (again, no direct temperature measurement is required to know that the water is being cooled), the apparent weight goes down, reaches a minimum (that's the point of maximum density of water), and then goes back up. In the course of this process, the precise value of the temperature is of no interest and the maximum of density is determined directly by the weighing, as opposed to by measuring the temperature of the water and making sure it matches some predetermined value. The advantage is both practical and conceptual. On the practical side, precision thermometry is difficult, and this procedure makes it unnecessary. On the conceptual side, the procedure makes the definition of the unit of mass completely independent from the definition of a temperature scale.<br> 3. The point of maximum density is also the point where the density depends the least on small changes in temperature.<ref>{{cite encyclopedia |last=Trallès |first=M. |editor-last1=Méchain |editor-first1=Pierre |editor-link1=Pierre Méchain|editor-last2=Delambre |editor-first2=Jean B. J. |editor-link2=Jean Baptiste Joseph Delambre |encyclopedia=Base du système métrique décimal, ou mesure de l'arc du méridien compris entre les parallèles de Dunkerque et Barcelone executée en 1792 et années suivantes: suite des Mémoires de l'Institut |title=Rapport de M. Trallès a la Commission, sur l'unité de poids du système métrique décimal, d'après le travail de M. Lefèvre–Gineau, le 11 prairial an 7|url=https://books.google.com/books?id=jpdOAAAAcAAJ&dq=%22de%20M.%20Trall%C3%A8s%20a%20la%20Commission%22&pg=PA558 |year=1810 |volume=3 On 7 April 1795, the metric system was formally defined in French law.<ref group="Note">Article 5 of the law of 18 Germinal, Year III</ref> It defined six new decimal units:<ref name=18germ_3/>
* The ''[[metre|mètre]]'', for length—defined as one ten-millionth of the distance between the [[North Pole]] and the [[Equator]] through [[Paris]]
* The ''[[Hectare|are]]'' (100 m<sup>2</sup>) for area [of land]
* The ''[[stère]]'' (1 m<sup>3</sup>) for volume of firewood
* The ''[[litre]]'' (1 dm<sup>3</sup>) for volumes of liquid
* The ''[[gram]]me'', for mass—defined as the mass of one cubic centimetre of water
* The ''[[French franc|franc]], for currency.
: ''Historical note: only the metre and (kilo)gramme defined here went on to become part of later metric systems. Litres and to a lesser extent hectares (100 ares, or 1 hm<sup>2</sup>) are still in use, but are not official SI units.''
Decimal multiples of these units were defined by Greek [[SI prefix|prefixes]]: ''"[[myria-]]"'' (10,000), ''"[[kilo-]]"'' (1000), ''"[[hecto-]]"'' (100), and ''"[[deka-]]"'' (10) and submultiples were defined by the Latin prefixes ''"[[deci-]]"'' (0.1), ''"[[centi-]]"'' (0.01), and ''"[[milli-]]"'' (0.001).<ref>{{cite journal
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For purposes of commerce, units and prefixed-units of weight (mass) and capacity (volume) were prependable by the binary multipliers ''"[[double-]]"'' (2) and ''"[[demi (metric prefix)|demi-]]"'' ({{fraction|1|2}}), as in ''double-litre'', ''demi-litre''; or ''double-hectogramme'', ''demi-hectogramme'', etc.<ref group="Note">Article 8 of the law of 18 Germinal, Year III</ref>
The 1795 draft definitions enabled provisional copies of the kilograms and metres to be constructed.<ref>
{{cite web | url = http://www.culture.gouv.fr/culture/actualites/celebrations/metre.htm
| language = fr
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| publisher = Ministère de la culture et de la communication ([[French language|French]] ministry of culture and communications)
| access-date = 1 March 2011
}}</ref><ref>
{{cite journal | url = http://www.platinummetalsreview.com/journal-archive/?decade=1991–2000
| access-date = 10 November 2012
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}}</ref>
=== Meridional survey ===
{{further|Arc measurement}}
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:''Historical note:'' It soon became apparent that Méchain and Delambre's result (443.296 ''lignes'') was slightly too short for the meridional definition of the metre. Méchain had made a small error measuring the latitude of Barcelona, so he remeasured it, but kept the second set of measurements secret.<ref group="Note">The modern value, for the WGS 84 reference spheroid of {{nowrap|1.000 196 57}} m is {{nowrap|443.383 08}} ''lignes''.</ref>
{{clear}}
=== The French metric system ===
In June 1799, platinum prototypes were fabricated according to the measured quantities, the ''mètre des archives'' defined to be a length of 443.296 lignes, and the ''kilogramme des archives'' defined to be a weight of 18827.15 [[Units of measurement in France before the French Revolution#Mass|grains of the ''livre poids de marc'']],<ref>
{{cite journal |url= https://www.nature.com/articles/008489a0
|title= On the Science of Weighing and Measuring, and the Standards of Weight and Measure*
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|bibcode= 1873Natur...8..489C
|s2cid= 3968820
|access-date= 21 August 2020
}}</ref> and entered into the French National Archives. In December of that year, the metric system based on them became by law the sole system of weights and measures in France from 1801 until 1812. Despite the law, the populace continued to use the old measures. In 1812, Napoleon revoked the law and issued one called the ''[[mesures usuelles]]'', restoring the names and quantities of the customary measures but redefined as round multiples of the metric units, so it was a kind of hybrid system. In 1837, after the collapse of the Napoleonic Empire, the new Assembly reimposed the metric system defined by the laws of 1795 and 1799, to take effect in 1840. The metrication of France took until about 1858 to be completed. Some of the old unit names, especially the ''[[Pound (mass)#French livre|livre]]'', originally a unit of mass derived from the Roman ''libra'' (as was the English [[Pound (mass)|pound]]), but now meaning 500 grams, are still in use today.
== Development of non-coherent metric systems ==
At the start of the nineteenth century, the French Academy of Sciences' artefacts for [[length]] and [[mass]] were the only nascent units of the metric system that were defined in terms of formal [[Standard (metrology)|standards]]. Other units based on them, except the ''litre'', proved to be short-lived. Pendulum clocks that could keep time in seconds had been in use for about 150 years, but their geometries were local to both latitude and altitude, so there was no standard of timekeeping. Nor had a unit of time been recognised as an essential base unit for the derivation of things like force and acceleration. Some quantities of electricity, like charge and potential, had been identified, but names and interrelationships of units were not yet established.<ref group="Note">Ohm's Law wasn't discovered until 1824, for example.</ref> Both Fahrenheit (
A model of interrelated units was first proposed in 1861 by the [[British Association for the Advancement of Science]] (BAAS) based on what came to be called the "mechanical" units (length, mass, and time). Over the following decades, this foundation enabled [[Machine (mechanical)|mechanical]], [[electricity|electrical]], and [[thermodynamics|thermal]]{{when|date=January 2018}} units to be correlated.
=== Time ===
In 1832, German mathematician [[Carl Friedrich Gauss|Carl-Friedrich Gauss]] made the first absolute measurements of the [[Earth's magnetic field]] using a decimal system based on the use of the millimetre, milligram, and second as the base unit of time.<ref name="SIBrochure">{{SIBrochure8th}}</ref>{{rp|109}} Gauss' second was based on astronomical observations of the rotation of the Earth, and was the sexagesimal second of the ancients: a partitioning of the solar day into two cycles of 12 periods, and each period divided into 60 intervals, and each interval so divided again, so that a second was 1/86,400th of the day.<ref group="Note">It is certain, however, that 170 years after the invention of pendulum clocks, that Gauss had sufficiently accurate mechanical clocks for his work.</ref> This effectively established a time dimension as a necessary constituent of any useful system of measures, and the astronomical second as the base unit.
=== Work and energy ===
{{Off topic|date=January 2023|James Prescott Joule|Work and energy section relevance}}
[[File:Joule's Apparatus (Harper's Scan).png|right|thumb|Joule's apparatus for measuring the mechanical equivalent of heat. As the weight dropped, [[potential energy]] was transferred to the water, heating it up.]]
In a paper published in 1843, [[James Prescott Joule]] first demonstrated a means of measuring the [[energy]] transferred between different systems when work is done thereby relating [[Nicolas Clément]]'s [[calorie]], defined in 1824 as "the amount of heat required to raise the temperature of 1 kg of water from 0 to 1 °C at 1 atmosphere of pressure" to [[Work (physics)|mechanical work]].<ref>
{{cite journal | last1 = Hargrove
| first1 = JL
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| pmid = 17116702
| doi-access= free
}}<!--|access-date =8 July 2013--></ref><ref>
{{cite web | url = http://www.scienceandsociety.co.uk/results.asp?image=10301513&screenwidth=1069
| title = Joule's was friction apparatus, 1843
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| location = London, York and Bradford
| access-date = 8 July 2013
}}</ref> Energy became the unifying concept of nineteenth century [[science]],<ref>
{{cite journal | journal = Current Science
| volume = 100
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}}</ref> initially by bringing [[thermodynamics]] and [[mechanics]] together and later adding [[Electricity|electrical technology]].
=== The first structured metric system: CGS ===
In 1861, a committee of the [[British Association for the Advancement of Science]] (BAAS) including [[William Thomson, 1st Baron Kelvin|William Thomson (later Lord Kelvin)]], [[James Clerk Maxwell]], and [[James Prescott Joule]] among its members was tasked with investigating the "Standards of Electrical Resistance".{{clarify|reason=telegraphy?|date=January 2018}} In their first report (1862),<ref>
{{cite book | title = Reports on the Committee on Standards of Electrical Resistance – Appointed by the British Association for the Advancement of Science
| chapter-url = https://archive.org/stream/reportscommitte00maxwgoog
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| year = 1873
| access-date = 12 May 2011
}}</ref> they laid the ground rules for their work—the metric system was to be used, measures of electrical energy must have the same units as measures of mechanical energy, and two sets of electromagnetic units would have to be derived—an electromagnetic system and an electrostatic system. In the second report (1863),<ref>
{{cite book | title = Reports on the Committee on Standards of Electrical Resistance – Appointed by the British Association for the Advancement of Science
| chapter-url = https://archive.org/stream/reportscommitte00maxwgoog
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| year = 1873
| access-date = 12 May 2011
}}</ref> they introduced the concept of a coherent system of units whereby units of length, mass, and time were identified as "fundamental units" (now known as ''[[SI base unit|base units]]''). All other units of measure could be derived (hence ''[[SI derived unit|derived units]]'') from these base units. The metre, gram, and second were chosen as base units.<ref name="Maxwell1">
{{cite book | title = A treatise on electricity and magnetism
| volume = 1
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| pages = [https://archive.org/details/electricandmagne01maxwrich/page/1 1]–3
| access-date = 12 May 2011
}}</ref><ref name="Maxwell2">
{{cite book | title = A treatise on electricity and magnetism
| volume = 2
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}}</ref>
In 1861, before{{clarify|date=January 2020}}{{Fix|text=at?}} a meeting of the BAAS, [[Charles Tilston Bright|Charles Bright]] and [[Latimer Clark]] proposed the names of [[ohm]], [[volt]], and [[farad]] in honour of [[Georg Ohm]], [[Alessandro Volta]], and [[Michael Faraday]] respectively for the practical units based on the CGS absolute system. This was supported by Thomson (Lord Kelvin).<ref>
{{cite web |url = http://www.iec.ch/about/history/beginning/lord_kelvin.htm
|title = In the beginning ... Lord Kelvin
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The reports recognised two centimetre–gram–second based systems for electrical units: the Electromagnetic (or absolute) system of units (EMU) and the Electrostatic system of units (ESU).
=== Electrical units ===
{| class="wikitable floatright"
|+Symbols used in this section
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|-
| style="text-align:center;" |<math>\epsilon_0</math>
|[[electric constant]]<ref group="Note" name="foo">The electric constant, termed the ''permittivity'' of free space (
|-
| style="text-align:center;" |<math>\mu_0</math>
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|dimensions: mass, length, time
|}
In the 1820s, [[Georg Ohm]] formulated [[Ohm's Law]], which can be extended to relate power to current, electric potential (voltage), and resistance.<ref>{{MacTutor|title=Georg Simon Ohm|id=Ohm|date=January 2000}}</ref><ref>
{{cite book | title = Revise AS Physics
| first1 = Graham
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The electrical units of measure did not easily fit into the coherent system of mechanical units defined by the BAAS. Using [[dimensional analysis]], the dimensions of voltage <math>\mathsf{M}^\frac{1}{2}\mathsf{L}^\frac{1}{2}\mathsf{T}^{-1}</math> in the ESU system were identical to the dimensions of current in the EMU system, while resistance had dimensions of velocity in the EMU system, but the inverse of velocity in the ESU system.<ref name=Maxwell2/>
==== Electromagnetic (absolute) system of units (EMU) ====
The [[Centimetre–gram–second system of units#Electromagnetic units (EMU)|Electromagnetic system of units (EMU)]] was developed from [[André-Marie Ampère]]'s discovery in the 1820s of a relationship between currents in two conductors and the force between them now known as [[Ampère's force law|Ampere's law]]:
: <math> \frac {F_\text{m}} {L} = 2 k_\text{m} \frac {I_1 I_2 } {r}</math> where <math> k_\text{m} = \frac {\mu_0}{ 4 \pi} \ </math> (SI units)▼
In 1833, Gauss pointed out the possibility of equating this force with its mechanical equivalent. This proposal received further support from [[Wilhelm Eduard Weber|Wilhelm Weber]] in 1851.<ref name="satellite">
▲:<math> \frac {F_\text{m}} {L} = 2 k_\text{m} \frac {I_1 I_2 } {r}</math> where <math> k_\text{m} = \frac {\mu_0}{ 4 \pi} \ </math> (SI units)
{{cite web
▲In 1833, Gauss pointed out the possibility of equating this force with its mechanical equivalent. This proposal received further support from [[Wilhelm Eduard Weber|Wilhelm Weber]] in 1851.<ref name="satellite">{{cite web
| url = http://www.highbeam.com/doc/1G1-60048223.html| archive-url = https://web.archive.org/web/20161018205901/https://www.highbeam.com/doc/1G1-60048223.html| url-status = dead| archive-date = 18 October 2016 <!--http://www.satellitetoday.com/via/The-International-System-of-Units_32466_p3.html-->
| title = The International System of Units
Line 563 ⟶ 583:
| date = 1 February 2000
| access-date = 5 April 2011
}}</ref> In this system, current is defined by setting the [[Ampère's force law|magnetic force constant]] <math>k_\mathrm{m}</math> to unity and electric potential is defined in such a way as to ensure the unit of power calculated by the relation <math> P = VI</math> is an erg/second. The electromagnetic units of measure were known as the abampere, abvolt, and so on.<ref>
{{cite web |url = http://www.unc.edu/~rowlett/units/dictA.html#ab
|title = How Many? A Dictionary of Units of Measurement: "ab-"
Line 573 ⟶ 594:
|archive-url = https://web.archive.org/web/20081220111445/http://www.unc.edu/~rowlett/units/dictA.html#ab
|url-status = dead
}}</ref> These units were later scaled for use in the International System.<ref>
{{cite web | url = http://www.sizes.com/units/farad.htm
| title = farad
Line 581 ⟶ 603:
}}</ref>
==== Electrostatic system of units (ESU) ====
The [[Electrostatic units|Electrostatic system of units (ESU)]] was based on Coulomb's quantification in 1783 of the force acting between two charged bodies. This relationship, now known as [[Coulomb's law]], can be written
:<math>F_\mathrm{e} = k_\text{e} \frac{q_1q_2}{r^2},</math> where <math>k_\text{e} = \frac{1}{4 \pi \epsilon_0}</math> (SI units)
Line 597 ⟶ 619:
}}</ref>
==== Gaussian system of units ====
The [[Gaussian units|Gaussian system of units]] was based on [[Heinrich Hertz]]'s realisation,{{citation needed|date=January 2018}} while verifying [[Maxwell's equations]] in 1888, that the electromagnetic and electrostatic units were related by:
: <math>c^2 = \frac{1}{\epsilon_0 \mu_0}</math><ref>
{{cite web |url = http://www.wbabin.net/science/danescu.pdf
|title = The evolution of the Gaussian Units
Line 609 ⟶ 632:
|archive-date = 12 March 2012
|url-status = dead
}}</ref><ref>
{{cite web | url = http://bohr.physics.berkeley.edu/classes/221/1011/notes/emunits.pdf
| title = Gaussian, SI and Other Systems of Units in Electromagnetic Theory
Line 620 ⟶ 644:
Using this relationship, he proposed merging the EMU and the ESU systems into one system using the EMU units for magnetic quantities (subsequently named the [[Gauss (unit)|gauss]] and [[Maxwell (unit)|maxwell]]) and ESU units elsewhere. He named this combined set of units "[[Gaussian units]]". This set of units has been recognised as being particularly useful in theoretical physics.<ref name=SIBrochure/>{{rp|128}}
The CGS units of measure used in scientific work were not practical for engineering, leading to the development of a more applicable system of electric units especially for telegraphy. The unit of length was 10<sup>7</sup> m (the [[hebdometre]], nominally the [[Earth quadrant]]), the unit of mass was an unnamed unit equal to 10<sup>−11</sup> g and the unit of time was the second. The units of mass and length were scaled incongruously to yield more consistent and usable electric units in terms of mechanical measures. Informally called the "practical" system, it was properly termed the quadrant–eleventhgram–second (QES) system of units according to convention.
The definitions of electrical units incorporated the magnetic constant like the EMU system, and the names of the units were carried over from that system, but scaled according to the defined mechanical units.<ref>
{{cite journal | journal = IEC Bulletin
| title = 1981 ... A year of anniversaries
Line 634 ⟶ 658:
| url = http://www.iec.ch/about/history/documents/pdf/75th%20anniversary%20IEC%20Bulletin.pdf
| access-date = 23 October 2013
}}</ref> The system was formalised as the [[International System of Electrical and Magnetic Units|International system]] late in the 19th century and its units later designated the "international ampere", "international volt", etc.<ref name="McGreevy">
{{cite book | title = The Basis of Measurement: Volume 1 – Historical Aspects
| first1 = Thomas
Line 646 ⟶ 671:
}}</ref>{{rp|155–156}}
==== Heaviside–Lorentz system of units ====
The factor <math>4\pi</math> that occurs in Maxwell's equations in the gaussian system (and the other CGS systems) comes from the <math>4\pi</math> steradians surrounding a point, such as a point electric charge. This factor could be eliminated from contexts that do not involve spherical coordinates by incorporating the factor into the definitions of the quantities involved. The system was proposed by Oliver Heaviside in 1883 and is also known as the "rationalised Gaussian system of units". The SI later adopted rationalised units based on Heaviside's rationalisation scheme.
=== Thermodynamics ===
Maxwell and Boltzmann had produced theories describing the interrelationship of temperature, pressure, and volume of a gas on a microscopic scale but otherwise, in 1900, there was no understanding of the microscopic nature of temperature.<ref name="Pledge">
{{cite book | title = Science since 1500
| author = H.T.Pledge
| orig-year
| year = 1959
| chapter = Chapter XXI: Quantum Theory
| pages = 271–275
| publisher = Harper Torchbooks
}}</ref><ref>
{{cite web | url = http://www.uic.edu/labs/trl/1.OnlineMaterials/BasicPrinciplesByTWLeland.pdf
| title = Basic Principles of Classical and Statistical Thermodynamics
Line 669 ⟶ 696:
By the end of the nineteenth century, the fundamental macroscopic laws of thermodynamics had been formulated and, although techniques existed to measure temperature using empirical techniques, the scientific understanding{{clarify|date=January 2018}} of the nature of temperature was minimal.
== Convention of the metre ==
{{main|Metre Convention}}
[[File:Metric seal.svg|thumb|upright=0.75|Seal of the [[International Bureau of Weights and Measures]] (BIPM)]]
With increasing international adoption of the metre, the shortcomings of the ''mètre des Archives'' as a standard became ever more apparent. Countries which adopted the metre as a legal measure purchased standard metre bars that were 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.<ref>
{{ | title = Mètre
| volume = 17
Line 678 ⟶ 706:
}}</ref>
In 1867, it was proposed that a new international standard metre be created, and the length was taken to be that of the ''mètre des Archives'' "in the state in which it shall be found".<ref name="MComm">
{{citation | title = The International Metre Commission (1870–1872)
| url = http://www.bipm.org/en/si/history-si/commission.html
| publisher = International Bureau of Weights and Measures
| access-date = 15 August 2010
}}</ref><ref name="BIPMhist">
{{citation | title = The BIPM and the evolution of the definition of the metre
| url = http://www.bipm.org/en/si/history-si/evolution_metre.html
Line 693 ⟶ 723:
}}</ref> The International Conference on Geodesy in 1867 called for the creation of a new [[international prototype of the metre]]<ref name="MComm"/><ref name="BIPMhist"/><ref group="Note">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" of the metre was the one that came first in the logical chain of comparisons, that is the metre to which all other standards were compared.</ref> and of a system by which 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.<ref name="MComm"/>
On 20 May 1875, an international treaty known as the [[Metre Convention|''Convention du Mètre'']] (Metre Convention) was signed by 17 states.<ref name="Nelson"/><ref>
Text of the treaty: {{cite web | url = http://www.bipm.org/utils/en/pdf/metre_convention.pdf
| title = Convention du mètre
Line 699 ⟶ 731:
| access-date = 8 March 2011
}}</ref> This treaty established the following organisations to conduct international activities relating to a uniform system for measurements:
:* ''[[Conférence générale des poids et mesures]]'' (CGPM or General Conference on Weights and Measures), an intergovernmental conference of official delegates of member nations and the supreme authority for all actions;
:* ''[[Comité international des poids et mesures]]'' (CIPM or International Committee for Weights and Measures), consisting of selected scientists and [[metrologist]]s, which prepares and executes the decisions of the CGPM and is responsible for the supervision of the International Bureau of Weights and Measures;
:* ''[[Bureau international des poids et mesures]]'' (BIPM or International Bureau of Weights and Measures), a permanent laboratory and world centre of scientific metrology, the activities of which include the establishment of the basic standards and scales of the principal physical quantities, maintenance of the international prototype standards, and oversight of regular comparisons between the international prototype and the various national standards.
The [[international prototype of the metre]] and [[international prototype of the kilogram]] were both made from a 90% [[platinum]], 10% [[iridium]] alloy which is exceptionally hard and which has good electrical and thermal conductivity properties. The prototype had a special X-shaped ([[Henri Tresca|Tresca]]) cross section to minimise the effects of torsional strain during length comparisons<ref name="Nelson"/> and the prototype kilograms were cylindrical in shape. The London firm [[Johnson Matthey]] delivered 30 prototype metres and 40 prototype kilograms. At the first meeting of the [[CGPM]] in 1889, bar No. 6 and cylinder No. X were accepted as the international prototypes. The remainder were either kept as BIPM working copies or distributed to member states as national prototypes.<ref name="CGPMprototypes">
{{cite journal |last1 = Jabbour
|first1 = Z.J.
Line 716 ⟶ 749:
|publisher = [[National Institute of Standards and Technology]] (NIST
|url = http://nvl.nist.gov/pub/nistpubs/jres/106/1/j61jab.pdf
|access-date
|doi = 10.6028/jres.106.003
|pmid = 27500016
Line 727 ⟶ 760:
Following the Convention of the Metre, in 1889, the BIPM had custody of two artefacts—one to define length and the other to define mass. Other units of measure which did not rely on specific artefacts were controlled by other bodies.
Although the definition of the kilogram remained unchanged throughout the 20th century, the 3rd CGPM in 1901 clarified that the kilogram was a unit of [[mass]], not of [[weight]]. The original batch of 40 prototypes (adopted in 1889) were supplemented from time to time with further prototypes for use by new signatories to the [[Metre Convention]].<ref>
{{cite journal | url = http://www.platinummetalsreview.com/pdf/pmr-v17-i2-066-068.pdf
| title = Standard Kilogram Weights – A Story of Precision Fabrication
Line 740 ⟶ 774:
In 1921, the Treaty of the Metre was extended to cover electrical units, with the CGPM merging its work with that of the IEC.
== Measurement systems before World War II ==
[[File:US National Length Meter.JPG|left|thumb|U.S. national prototype of the metre, showing the bar number (#27), the [[Henri Tresca|Tresca cross-section]] and one of the lines]]
The 20th century history of measurement is marked by five periods: the 1901 definition of the coherent MKS system; the intervening 50 years of coexistence of the MKS, cgs and common systems of measures; the 1948 ''Practical system of units'' prototype of the SI; the introduction of the SI in 1960; and the evolution of the SI in the latter half century.
=== A coherent system ===
The need for an independent electromagnetic dimension to resolve the difficulties related to defining such units in terms of length, mass, and time was identified by [[Giovanni Giorgi|Giorgi]] in 1901. This led to Giorgi presenting a paper in October 1901 to the congress of the Associazione Elettrotecnica Italiana (A.E.I.)<ref>''Unità razionali di elettromagnetismo'', Giorgi (1901)</ref> in which he showed that a coherent electro-mechanical system of units could be obtained by adding a fourth base unit of an electrical nature (e.g., ampere, volt, or ohm) to the three base units proposed in the 1861 BAAS report. This gave physical dimensions to the constants ''k''<sub>e</sub> and ''k''<sub>m</sub> and hence also to the electro-mechanical quantities ''ε''<sub>0</sub> (permittivity of free space) and ''μ''<sub>0</sub> (permeability of free space).<ref name="IECGiorgi">
{{cite web |url = http://www.iec.ch/about/history/beginning/giovanni_giorgi.htm
|title = Historical figures ... Giovanni Giorgi
Line 756 ⟶ 791:
}}</ref> His work also recognised the relevance of energy in the establishment of a coherent, rational system of units, with the [[joule]] as the unit of energy, and the electrical units in the International System of Units remaining unchanged.<ref name=McGreevy/>{{rp|156}} However, it took more than thirty years before Giorgi's work was accepted in practice by the IEC.
=== Systems of measurement in the industrial era ===
[[File:FourMetricInstruments.JPG|thumb|upright| Four domestic quality contemporary measuring devices that have metric calibrations – a [[tape measure]] calibrated in [[centimetres]], a [[thermometer]] calibrated in [[degrees Celsius]], a [[kilogram]] weight (mass) and an electrical [[multimeter]] which measures [[volts]], [[ampere|amps]] and [[ohm]]s]]
As industry developed around the world, the cgs system of units as adopted by the British Association for the Advancement of Science in 1873 with its plethora of electrical units continued to be the dominant system of measurement, and remained so for at least the next 60 years. The advantages were several: it had a comprehensive set of derived units which, while not quite coherent, were at least homologous; the MKS system lacked a defined unit of electromagnetism at all; the MKS units were inconveniently large for the sciences; customary systems of measures held sway in the United States, Britain, and the British empire, and even to some extent in France, the birthplace of the metric system, which inhibited adoption of any competing system. Finally, war, nationalism, and other political forces inhibited development of the science favouring a coherent system of units.
At the 8th CGPM in 1933, the need to replace the "international" electrical units with "absolute" units was raised. The IEC proposal that Giorgi's 'system', denoted informally as MKSX, be adopted was accepted, but no decision was made as to which electrical unit should be the fourth base unit. In 1935, J. E. Sears<ref>Superintendent of the Metrology Department of the National Physical Laboratory, UK</ref>{{citation needed|date=December 2017}} proposed that this should be the ampere, but [[World War II]] prevented this being formalised until 1946. The first (and only) follow-up comparison of the national standards with the international prototype of the metre was carried out between 1921 and 1936,<ref name="Nelson"/><ref name="BIPMhist"/> and indicated that the definition of the metre was preserved to within 0.2 μm.<ref name="Barrell">
{{citation | first = H.
| last = Barrel
Line 772 ⟶ 808:
| doi = 10.1080/00107516208217499
| bibcode = 1962ConPh...3..415B
}}</ref> During this follow-up comparison, the way in which the prototype metre should be measured was more clearly defined—the 1889 definition had defined the metre as being the length of the prototype at the temperature of melting ice, but, in 1927, the 7th CGPM extended this definition to specify that the prototype metre shall be "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".<ref name=SIBrochure/>{{rp|142–43,148}} The choice of 571 mm represents the [[Airy points]] of the prototype—the points at which the bending or droop of the bar is minimised.<ref>
{{citation | last = Phelps
| first = F. M., III
Line 785 ⟶ 822:
}}</ref>
== Working draft of SI: ''Practical system of units'' ==
The 9th CGPM met in 1948, fifteen years after the 8th CGPM. In response to formal requests made by the International Union of Pure and Applied Physics and by the French government to establish a practical system of units of measure, the CGPM requested the CIPM to prepare recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention.<ref>
{{cite conference | url = http://www.bipm.org/en/CGPM/db/9/6/
| title = Resolution 6 – Proposal for establishing a practical system of units of measurement
Line 794 ⟶ 832:
}}</ref> The CIPM's draft proposal was an extensive revision and simplification of the metric unit definitions, symbols, and terminology based on the MKS system of units.
Following astronomical observations, the second was set as a fraction of the year 1900. The electromagnetic base unit, as required by Giorgi, was accepted as the ampere. After negotiations with the CIS and IUPAP, two additional units—the degree kelvin and the candela—were also proposed as base units.<ref>
{{cite conference | url = http://www.bipm.org/en/CGPM/db/10/6/
| title = Resolution 6 – Practical system of units
Line 800 ⟶ 839:
| date = 5–14 October 1954
| access-date = 8 May 2011
}}</ref> For the first time, the CGPM made recommendations concerning derived units. At the same time, the CGPM adopted conventions for the writing and printing of unit symbols and numbers and catalogued the symbols for the most important [[MKS system of units|MKS]] and [[Centimetre gram second system of units|CGS]] units of measure.<ref>
{{cite conference | url = https://www.bipm.org/en/committees/cg/cgpm/9-1948/resolution-7
| title = Resolution 7 – Writing and printing of unit symbols and of numbers
Line 808 ⟶ 848:
}}</ref>
=== Time ===
Until the advent of the [[atomic clock]], the most reliable timekeeper available to humanity was the Earth's rotation. It was natural, therefore, that the astronomers under the auspices of the [[International Astronomical Union]] (IAU) took the lead in maintaining the standards relating to time. During the 20th century, it became apparent that the Earth's rotation was slowing down, resulting in days becoming 1.4 milliseconds longer each century<ref name="LeapSeconds">
{{cite web | url = http://tycho.usno.navy.mil/leapsec.html
| title = Leap seconds
Line 817 ⟶ 858:
| archive-url = https://web.archive.org/web/20150312003149/http://tycho.usno.navy.mil/leapsec.html
| archive-date = 12 March 2015
}}</ref>—this was verified by comparing the calculated timings of eclipses of the Sun with those observed in antiquity going back to Chinese records of 763 BC.<ref>
{{cite journal | url = http://hbar.phys.msu.ru/gorm/atext/histecl.htm
| archive-url = https://web.archive.org/web/20190115083621/http://hbar.phys.msu.ru/gorm/atext/histecl.htm
Line 834 ⟶ 876:
=== Electrical unit ===
Per Giorgi's proposals of 1901, the CIPM also recommended that the ampere be the base unit from which electromechanical units would be derived. The definitions for the ohm and volt that had previously been in use were discarded, and these units became derived units based on the ampere. In 1946, the CIPM formally adopted a definition of the ampere based on the original EMU definition and redefined the ohm in terms of other base units.<ref name="Fenna">
{{cite book | title = Dictionary of Weights, Measures and Units
| url = https://archive.org/details/dictionaryofweig0000fenn
Line 844 ⟶ 887:
| year = 2002
| isbn = 978-0-19-860522-5
}}</ref> The definitions for the absolute electrical system,{{clarify|date=January 2020}} based on the ampere, were formalised in 1948.<ref>
{{cite book | series = ''La metrologia ai confini tra fisica e tecnologia'' (Metrology at the Frontiers of Physics and Technology)
| title = The continuing evolution in the definitions and realisations of the SI units of measurement
Line 857 ⟶ 901:
| isbn = 978-0-444-89770-1
| year = 1992
}}</ref> The draft proposed units with these names are very close, but not identical, to the international units.<ref name="NISTHistory">
{{cite web | url = http://physics.nist.gov/cuu/Units/history.html
| title = A brief history of SI
Line 864 ⟶ 909:
}}</ref>
=== Temperature ===
In the Celsius scale from the 18th century, temperature was expressed in degrees Celsius with the definition that ice melted at 0 °C and (at standard atmospheric pressure) water boiled at 100 °C. A series of lookup tables defined temperature in terms of interrelated empirical measurements made using various devices. In 1948, definitions relating to temperature had to be clarified. (The degree, as an angular measure, was adopted for general use in many countries, so, in 1948, the [[General Conference on Weights and Measures]] (CGPM) recommended that the degree Celsius, as used for the measurement of temperature, be renamed the [[Celsius|degree Celsius]].)<ref>{{cite web
| url = http://www.bipm.org/en/committees/cipm/cipm-1948.html
Line 873 ⟶ 917:
}}</ref>
At the 9th CGPM, the Celsius temperature scale was renamed the [[Celsius]] scale, and the scale itself was fixed by defining the [[triple point of water]] as 0.01 °C,<ref name="CGPM_9_3">
{{cite conference | url = http://www.bipm.org/en/CGPM/db/9/3/
| title = Resolution 3 – Triple point of water; thermodynamic scale with a single fixed point; unit of quantity of heat (joule)
Line 879 ⟶ 924:
| date = 12–21 October 1948
| access-date = 8 May 2011
}}</ref> though the CGPM left the formal definition of absolute zero until the 10th CGPM when the name "[[degrees Kelvin|Kelvin]]" was assigned to the absolute temperature scale, and the triple point of water was defined as being {{not a typo|273.16 °K}}.<ref>
{{cite conference | url = http://www.bipm.org/jsp/en/ListCGPMResolution.jsp?CGPM=13
| title = Resolution 3 – Definition of the thermodynamic temperature scale and
Line 887 ⟶ 933:
}}</ref>
=== Luminosity ===
Before 1937, the [[International Commission on Illumination]] (CIE from its French title, the ''Commission Internationale de l'Eclairage''), in conjunction with the CIPM, produced a standard for luminous intensity to replace the various national standards. This standard, the [[candela]] (cd), which was defined as "the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per [[square centimetre]]",<ref>
{{cite book | title = The Metric System: The International System of Units (SI)
| author = Barry N. Taylor
Line 899 ⟶ 946:
}} (NIST Special Publication 330, 1991 ed.)</ref> was ratified by the CGPM in 1948.
=== Derived units ===
The newly accepted definition of the ampere allowed practical and useful coherent definitions of a set of electromagnetic derived units, including farad, henry, watt, tesla, weber, volt, ohm, and coulomb. Two derived units, lux and lumen, were based on the new candela, and one, degree Celsius, equivalent to the degree Kelvin. Five other miscellaneous derived units completed the draft proposal: radian, steradian, hertz, joule, and newton.
== International System of Units (SI) ==
{{main|International System of Units#Evolution of the SI}}
Line 910 ⟶ 957:
In 1960, Giorgi's proposals were adopted as the basis of the ''Système International d'Unités'' (International System of Units), the SI.<ref name=SIBrochure/>{{rp|109}} This initial definition of the SI included six base units, the metre, kilogram, second, ampere, degree Kelvin, and candela, and sixteen coherent derived units.<ref>radian, steradian, hertz, newton, joule, watt, coloumb, volt, farad, ohm, weber, tesla, henry, degree Celsius, lumen, lux</ref>
== Evolution of the modern SI ==
The evolution of the SI after its publication in 1960 has seen the addition of a seventh base unit, the ''mole'', and six more derived units, the ''pascal'' for pressure, the ''gray'', ''sievert'', and ''becquerel'' for radiation, the ''siemens'' for electrical conductance, and ''katal'' for catalytic (enzymatic) activity. Several units have also been redefined in terms of physical constants.
=== New base and derived units ===
Over the ensuing years, the BIPM developed and maintained cross-correlations relating various measuring devices such as thermocouples, light spectra, and the like to the equivalent temperatures.<ref>
{{cite web | url = http://www.bipm.org/utils/common/pdf/its-90/ITS-90_Techniques.pdf
| title = Techniques for Approximating the International Temperature Scale of 1990
Line 924 ⟶ 972:
}}</ref>
The mole was originally known as a gram-atom or a gram-molecule—the amount of a substance measured in grams divided by its [[atomic weight]]. Originally chemists and physicists had differing views regarding the definition of the atomic weight—both assigned a value of 16 [[atomic mass units]] (amu) to oxygen, but physicists defined oxygen in terms of the <sup>16</sup>O isotope whereas chemists assigned 16 amu to <sup>16</sup>O, <sup>17</sup>O and <sup>18</sup>O isotopes mixed in the proportion that they occur in nature. Finally, an agreement between the [[International Union of Pure and Applied Physics]]<ref>
{{cite journal |url = http://materia.ro/FACULTATE/DATA/Atomic%20Mass.pdf
|title = Atomic Weights of the Elements: Review 2000 (IUPAC Technical Report)
Line 955 ⟶ 1,004:
}}</ref> (IUPAP) and the [[International Union of Pure and Applied Chemistry]] (IUPAC) brought this duality to an end in 1959/60, both parties agreeing to define the atomic weight of <sup>12</sup>C as being exactly 12 amu. This agreement was confirmed by ISO and in 1969 the CIPM recommended its inclusion in SI as a base unit. This was done in 1971 at the 14th CGPM.<ref name=SIBrochure/>{{rp|114–115}}
=== Start of migration to constant definitions ===
The second major trend in the post-modern SI was the migration of unit definitions in terms of physical constants of nature.
In 1967, at the 13th CGPM, the degree Kelvin ({{not a typo|°K}}) was renamed the "kelvin" (K).<ref>
{{cite conference | url = http://www.bipm.org/en/CGPM/db/9/6/
| title = Resolution 3 – SI unit of thermodynamic temperature (kelvin) and Resolution 4 – Definition of the SI unit of thermodynamic temperature (kelvin)
Line 968 ⟶ 1,018:
Astronomers from the [[US Naval Observatory]] (USNO) and the [[National Physical Laboratory (United Kingdom)|National Physical Laboratory]] determined a relationship between the frequency of radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom and the estimated rate of rotation of the earth in 1900. Their atomic definition of the second was adopted in 1968 by the 13th CGPM.
By 1975, when the second had been defined in terms of a physical phenomenon rather than the earth's rotation, the CGPM authorised the CIPM to investigate the use of the speed of light as the basis for the definition of the metre. This proposal was accepted in 1983.<ref>
{{cite web | url = http://physics.nist.gov/cuu/Units/meter.html
| title = Base unit definitions: Meter
Line 977 ⟶ 1,028:
The candela definition proved difficult to implement so, in 1979, the definition was revised and the reference to the radiation source was replaced by defining the candela in terms of the power of a specified frequency of monochromatic yellowish-green visible light,<ref name=SIBrochure/>{{rp| 115}} which is close to the frequency where the human eye, when adapted to bright conditions, has greatest sensitivity.
=== Kilogram artefact instability ===
[[File:Prototype mass drifts.jpg|thumb|right|upright=1.3|Mass drift over time of national prototypes {{nowrap|K21–K40}}, plus two of the IPK's [[Kilogram#International prototype kilogram sister copy|sister copies]]: K32 and K8(41).<ref name="Girard">
{{ | title = The Third Periodic Verification of National Prototypes of the Kilogram (1988–1992)
| author = G. Girard
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A number of replacements were proposed for the IPK.
From the early 1990s, the [[International Avogadro Project]] worked on creating a 1 kg, 94 mm, sphere made of a uniform silicon-28 crystal, with the intention of being able replace the IPK with a physical object which would be precisely reproducible from an exact specification. Due to its precise construction, the Avogadro Project's sphere is likely to be the most precisely spherical object ever created by humans.<ref>
{{cite web | url = https://www.nist.gov/physical-measurement-laboratory/silicon-spheres-and-international-avogadro-project
| title = Kilogram: Introduction
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Ultimately, a decision was made not to create any physical replacement for the IPK, but instead to define all SI units in terms of assigning precise values to a number of physical constants which had previously been measured in terms of the earlier unit definitions.
== Redefinition in terms of fundamental constants ==
[[File:Unit relations in the new SI.svg|thumb|upright=1.35|The [[International System of Units|SI system]] after the 2019 redefinition: Dependence of base unit definitions on [[physical constant]]s with fixed numerical values and on other base units.]]
{{main|2019 redefinition of the SI base units}}
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Measurements accurate enough to meet the conditions were available in 2017 and the redefinition<ref name="draft-resolution-A">{{cite web |title=Draft Resolution A "On the revision of the International System of units (SI)" to be submitted to the CGPM at its 26th meeting (2018) |url=https://www.bipm.org/utils/en/pdf/CGPM/Draft-Resolution-A-EN.pdf |access-date=5 May 2018 |archive-url=https://web.archive.org/web/20180429025229/https://www.bipm.org/utils/en/pdf/CGPM/Draft-Resolution-A-EN.pdf |archive-date=29 April 2018 |url-status=live }}</ref> was adopted at the 26th CGPM (13–16 November 2018), with the changes finally coming into force in 2019, creating a system of definitions which is intended to be stable for the long term.
== See also ==
*[[History of the metre]]
== Notes ==
{{Reflist|group=Note}}
{{Notelist}}
== References ==
{{reflist}}
== External links ==
{{Good Article}}
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