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			{{short description|none}} <!-- "none" is preferred when the title is sufficiently descriptive; see ] -->
	{{outline|Outline of the metric system}}
			{{about|the history of the standards used in the metric system|history of adoption|Metrication}}
	]
			{{Use dmy dates|date=August 2018}}
			]
			The history of the ] began during the ] with measures of ] and ] derived from ], along with their ] multiples and fractions. The system became the standard of France and Europe within half a century. Other measures with unity ratios<ref group="Note">ratios of 1 between magnitudes of unit quantities</ref> were added, and the system went on to be adopted across the world.
	The origins of the ] date back to the sixteenth century when ] published details of his ] notation, and the seventeenth century when ] published a proposal for a decimal system of measurement based on natural units. The first practical realisation of the metric system came during the ], when the existing system of measure which had fallen into disrepute was replaced by a decimal system based on the ] and the ]. The metric system was, in the words of philosopher and mathematician ], "for all people for all time". The unit of length, the metre, was based on the dimensions of the ], and the unit of ], the kilogram, was based on the mass of ] having a ] of one ] or one thousandth of a ]. Reference copies for both units were manufactured and placed in the custody of the ].		The first practical realisation of the metric system came in 1799, during the ], after the existing system of measures had become impractical for trade, and was replaced by a decimal system based on the ] and the ]. The basic units were taken from the natural world. The unit of length, the metre, was based on the dimensions of the ], and the unit of ], the kilogram, was based on the mass of a ] of water of one ] (a cubic ]). Reference copies for both units were manufactured in platinum and remained the standards of measure for the next 90 years. After a period of reversion to the '']'' due to unpopularity of the metric system, the metrication of France and much of Europe was complete by the 1850s.
	During the first half of the nineteenth century, the metric system was adopted by the scientific community. In the middle of the century, ] put forward the concept of a coherent system where a small number of units of measure were defined as ], and all other units of measure, called ], were defined in terms of the base units. Maxwell proposed three base units – length, mass and time. This concept worked well with ], but attempts to describe ]s in terms of these units were beset with difficulties. By the end of the nineteenth century, four principal variants of the metric system were in place for the measurement of electromagnetic phenomena, three based on the ] (CGS system), and one on the metre-kilogram-second system of units (MKS system). This impasse was resolved by ], who in 1901 proved that a coherent system that incorporated electromagnetic units had to have an electromagnetic unit as the fourth base unit.		In the middle of the 19th century, ] conceived a coherent system where a small number of units of measure were defined as ], and all other units of measure, called ], were defined in terms of the base units. Maxwell proposed three base units for length, mass and time. Advances in ] in the 19th century necessitated additional units to be defined, and multiple incompatible systems of such units came into use; none could be reconciled with the existing dimensional system. The impasse was resolved by ], who in 1901 proved that a coherent system that incorporated electromagnetic units required a fourth base unit, of electromagnetism.
			The seminal 1875 ] resulted in the fashioning and distribution of metre and kilogram artefacts, the standards of the future coherent system that became the SI, and the creation of an international body '']'' or CGPM to oversee systems of weights and measures based on them.
	Until 1875, the French government owned the prototype metre and kilogram, but in that year the ] was signed, and control of the standards relating to mass and length passed to a trio of inter-governmental organisations, the senior of which was the ] (in French the ''Conférence générale des poids et mesures'' or CGPM). During the first half of the twentieth century, the CGPM cooperated with a number of other organisations, and by 1960 it had responsibility for defining temporal, electrical, thermal, molecular and luminar measurements, while other international organisations continued their roles in how these units of measurement were used.
	In 1960, the CGPM launched the ] (in French the ''Système international d'unités'' or SI) which had six base units, the metre, kilogram, ], ], ] (subsequently renamed the "kelvin") and ], and 22 derived units. The ] was added as a seventh base unit in 1971. During this period, the metre was redefined in terms of the ] of the waves from a particular light source, and the second was defined in terms of the ] of ] from another light source. By the end of the century, work was well under way to redefine the ampere, kilogram, mole and kelvin in terms of the basic ], thereby ensuring that all the base units were in theory available to everybody. It is expected that this work will be completed by 2014.{{update after|2014|12|31}}		In 1960, the CGPM launched the ] (in French the ''Système international d'unités'' or SI) with six "base units": the metre, kilogram, ], ], ] (subsequently renamed the "kelvin") and ], plus 16 more units derived from the base units. A seventh base unit, the ], and six other derived units were added later in the 20th century. During this period, the metre was redefined in terms of the speed of light, and the second was redefined based on the microwave ] of a ].
			Due to the instability of the ], a series of initiatives were undertaken, starting in the late 20th century, to redefine the ampere, kilogram, mole and kelvin in terms of invariant ], ultimately resulting in the ], which finally eliminated the need for any physical reference artefacts—notably, this enabled the retirement of the standard kilogram.
	==Universal measure==
	In the early ninth century, ] introduced standard units of measure for length and for mass throughout the ]. As the empire disintegrated these standards diverged and by the seventeenth century there were numerous units of measure within regions and different sizes having the same name across regions. The variations were promoted by local vested interests but hindered trade and taxation.<ref name="Larousse">{{LarousseXIXe | article = Métrique | volume = 11 | pages = 163–64}}.</ref><ref name="Nelson">{{citation | first = Robert A. | last = Nelson | title = Foundations of the international system of units (SI) | journal = Phys. Teacher | year = 1981 | page = 597 | url = http://plato.if.usp.br/1-2009/fmt0159n/PDFFiles/ThePhysTeacher_FoundationsOfTheSI.pdf}}.</ref>
			A fleeting hint of an ancient decimal or metric system may be found in the ], 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.
	In 1586, the Flemish mathematician ] published a small pamphlet called ''De Thiende'' ("the tenth"). Decimal fractions had been employed for the extraction of square roots some five centuries before his time, but it was Stevin who first introduced decimal numbers in daily life in Europe. He 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> Many twentieth century writers regarded the French cleric ] as the originator of the metric system,<ref>{{cite book
	|page = 140
	|title = The Basis of Measurement: Volume 1 - Historical Aspects
	|first1 = Thomas
	|last1 = McGreevy
	|first2 = Peter
	|last2 = Cunningham
	|year = 1995
	|isbn= {nowrap|0 948251 82 4}}
	|publisher = Picton Publishing (Chippenham) Ltd}}</ref> but in 2007 the late Pat Naughtin, a tireless metrication promoter from Australia,<ref>{{cite web |url=http://themetricmaven.com/?page_id=101 |title=Metrication Resources |publisher=The Metric Maven</ref> offered an interpretation of a few pages in a larger book by the English cleric ] (published two years before the publication of Mouton's book) suggesting that Wilkins had pre-empted the invention of the metric system by more than a century.<ref name=Naughtin>{{cite web
	|title = Aussie researcher challenges origins of metric system
	|url = http://www.abc.net.au/news/2007-07-15/aussie-researcher-challenges-origins-of-metric/2503194
	|date = 15 July 2007
	|publisher = ]
	|accessdate = 30 December 2012}}</ref> Some commentators appear to have followed Naughtin's cue, and now also mention Wilkins when discussing the origins of the metric system.<ref>{{cite journal
	|journal = International Journal of Applied Science and Technology
	|title = No Child Left Behind: Teaching the Metric System in US Schools
	|url = http://www.ijastnet.com/journals/Vol_2_No_4_April_2012/5.pdf
	|first1 = Kern W.
	|last1 = Craig
	|date = April 2012
	|issn = 2221-1004
	|at = 5. The Evolution of SI
	|volume = 2
	|number = 4
	|page = 44 - 48}}</ref><ref>{{cite conference
	|conference = Baroque Science workshop
	|date = 15-17 February 2008
	|title = The Hive and the Pendulum: Universal Metrology and Baroque Science
	|url = http://sydney.edu.au/science/hps/baroque_science/docs/February_2008_papers/Dew_The_Hive_and_the_Pendulum.pdf
	|first1 = Nicholas
	|last1 = Dew
	|page = 5}}</ref><ref>{{cite web
	|title = Celebrating metrology: 51 years of SI units
	|date = 20 June 2011
	|publisher = Institute of Physics
	|accessdate = 30 December 2012}}</ref>
	===Wilkins===
	], ], ] and ] would be related to each other.]]
	Writing in '']'', in 1668, ], first secretary of the ] proposed the concept of a "universal measure" and associated system of units based on a decimal system and natural phenomena.<ref>{{cite book
	|author= ]
	|year= 1668
	|title= An Essay towards a Real Character and a Philosophical Language
	|chapter = VII
	|pages= 190–194
	|publisher= The Royal Society
	|accessdate= 2011-03-06}}<br>;
	</ref><ref>{{cite video
	|url = http://news.bbc.co.uk/player/nol/newsid_6890000/newsid_6898200/6898274.stm?
	|title = Metric system 'was British'
	|publisher = ]
	|accessdate = 2011-03-06}}</ref> ] backed the proposal when he promoted the "''metro cattolico''"<ref>{{citation | title = Misura Universale | year = 1675}}.</ref> from which the word ''metre'' was to be derived.
	Wilkins' proposed a "seconds pendulum" (a ] with a half-period of one ]) as the unit of length: such pendulums had recently been demonstrated by ],<ref>{{MacTutor|title=Christiaan Huygens|id=Huygens|date=January 2004}}</ref> and their length is very close to one modern metre (as well as to length units which were then in use, such as the ]). However, it was soon discovered that the length of a seconds pendulum varies from place to place: French astronomer ] had measured the 0.3% difference in length between Cayenne (in French Guiana) and Paris.<ref>{{cite web
	|url = http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Richer.html
	|title = Jean Richer
	|first = J J O'Connor
	|last = E F Robertson
	|work = The MacTutor History of Mathematics archive
	|publisher = School of Mathematics and Statistics, ], Scotland
	|accessdate = 2011-03-06}}</ref><ref>{{citation
	| last1 = Poynting
	| first1 = John Henry
	| first2 = Joseph John
	| last2 = Thompson
	| title = A Textbook of Physics: Properties of Matter
	| edition = 4th
	| publisher = Charles Griffin
	| year = 1907
	| location = London
	| page Ε= 20
	| url = http://books.google.com/books?id=TL4KAAAAIAAJ&pg=PA20}}.</ref> Wilkins completed the system of measurement by proposing that ] and ] should be expressed as terns of the ] or the ] of the "universal measure" and that the base unit of ] should be derived from the volume of a cube of rainwater with sides equal to the "universal measure". In the words of Naughtin, "... he had every single element of the modern metric system" .<ref name=Naughtin/>
			== Age of Enlightenment ==
	===Mouton===
			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.
	In 1670, ], a French abbot and scientist, proposed a decimal system of measurement of length based on the circumference of the Earth. His suggestion was a unit, the milliare, be defined as a minute of arc along a meridian. He then suggested a system of sub-units, dividing successively by factors of ten into the centuria, decuria, virga, virgula, decima, centesima, and millesima.<ref name = Mouton>{{MacTutor|title=Gabriel Mouton|id=Mouton|date=January 2004}}</ref> His ideas attracted interest at the time, and were supported by both ] and ] in 1673,<ref>{{cite web
	|url = http://smdsi.quartier-rural.org/histoire/precurs.htm
	|title = Le système métrique des poids et des mesures
	|language = French
	|trans_title = The metric system of weights and measures
	|author = G. Bigourdan
	|year = 1901
	|location = Paris
	|accessdate = 2011-03-25}}</ref> and also studied at the Royal Society in London. In the same year, ] independently made proposals similar to those of Mouton.<ref name = Mouton/>
			=== Preamble ===
	===Leading up to the French Revolution===
			In the early ninth century, when much of what later became ] was part of France, units of measure had been standardised by the ]. 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, ] (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
			| url = https://www.bl.uk/magna-carta/articles/magna-carta-english-translation
			| publisher = British Library
			| access-date = 10 January 2018
			| archive-date = 17 January 2023
			| archive-url = https://web.archive.org/web/20230117040531/https://www.bl.uk/magna-carta/articles/magna-carta-english-translation
			| url-status = dead
			}}</ref>
			During the early ], ] were used in Europe to represent numbers,<ref>
	Whereas in England the ] in 1215 decreed that "there shall be one unit of measure throughout the realm",<ref>{{cite web
			{{cite journal
	|url = http://www.archives.gov/exhibits/featured_documents/magna_carta/translation.html
			| last1 = Durham | first1 = John W
	|title = Magna Charta translation
			| date = 2 December 1992
	|publisher = National Archives and Records Administration
			| title = The Introduction of "Arabic" Numerals in Euiropean Accounting
	|accessdate = 2011-03-25}}</ref> France had a multitude of units of measure.<ref name=histmet>{{cite web
			| journal = The Accounting Historians Journal
	|url = http://www.french-metrology.com/en/history/history-mesurement.asp
			| publisher = The ]
	|title = History of measurement
			| volume = 19
	|publisher = Métrologie française
			| pages = 27–28
	|accessdate = 2011-02-06}}</ref> It has been estimated that on the eve of the Revolution a quarter of a million different units of measure were in use in France; in many cases the quantity associated with each unit of measure differed from town to town and even from trade to trade.<ref name=Adletinto>{{cite book
			| jstor = 40698081
	|title = The Measure of all Things - The Seven -Year-Odyssey that Transformed the World
			| number = 2
	|last= Adler
			| doi = 10.2308/0148-4184.19.2.25
	|first= Ken
			}}<!--|access-date = 10 October 2013--></ref> but the ] represented numbers using the ], a ] that used ten symbols. In about 1202, ] published his book '']'' (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 ]s and ]s and there was no consistency in the way in which decimal fractions were represented.
	|year= 2002
	|publisher= Abacus
	|location= London
	|isbn= 0&nbsp;349&nbsp;11507&nbsp;9
	|pages= 2–3}}</ref> Although certain standards, such as the ''pied du roi'' (the King's foot) had a degree of pre-eminence and were used by scientists, many traders chose to use their own measuring devices, giving scope for fraud and hindering commerce and industry.<ref name=histmet/>
			] 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">
	By the mid eighteenth century the need for standardisation of weights and measures had become apparent - Spain aligned her units of measure with the royal units of France,<ref name = metricSpain/> and Peter the Great aligned the Russian units of measure with the English units.<ref>{{cite book
			{{cite book
	|url = http://www.archive.org/stream/modernmetrologym00jackrich/modernmetrologym00jackrich_djvu.txt
			| url = https://books.google.com/books?id=8kg-t6xsv48C&q=wilkins&pg=PA16
	|title = Modern metrology; a manual of the metrical units and systems of the present century (1882)
			| title = Smoot's Ear: The Measure of Humanity
	|last = Jackson
			| first1 = Robert
	|first = Lowis D'Aguilar
			| last1 = Tavernor
	|place = London
			| year = 2007
	|publisher = C Lockwood and co.
			| publisher = ]
	|page = 11
			| isbn = 978-0-300-12492-7
	|accessdate = 2011-03-25}}</ref> In 1783 the British inventor ] who was having difficulties in communicating with German scientists called for the creation of a global decimal measurement system.<ref>{{cite book
			}}</ref>{{rp|70}}<ref name=Alder/>{{rp|91}}
	|url = http://www.freeinfosociety.com/media/pdf/4750.pdf
	|title = James Watt
	|first = Andrew
	|last = Carnegie
	|pages = 59–60
	|date = May 1905
	|publisher = Doubleday, Page & Company
	|accessdate =20 October 2011}}</ref>
			=== 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 '']'' (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.
	In 1789 the French finances were in a perilous state and in May ] summoned the ]. On 14 July 1789, the mob stormed the ] and in August 1789 the nobility surrendered their privileges, including the right to control local weights and measures. Louis XVI charged a group of experts including such notables as ], ], ], ] and ] to produce the system of measures that would replace the disparate system then in place.<ref name=Adletinto/>
			=== Clocks and pendulums ===
	There was also a wish that the units of measure should be not dependent on an artifact owned by any one particular nation. ], at the prompting of the mathematician ], approached the British and the Americans in the early 1790s with proposals of a joint effort to define the metre using the length of a pendulum (as proposed by Wilkins) as the basis of the standard of length. On 13 July 1790 Thomas Jefferson presented to ] a document '']'' in which he advocated a decimal system that used traditional names for units (such as ten inches per foot). The report was considered but not adopted by Congress.<ref>{{cite web
			In 1656, Dutch scientist ] 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 ]), and this was not a good solution. A more uniform standard was needed.
	|url = http://avalon.law.yale.edu/18th_century/jeffplan.asp
	|title = Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States; Communicated to the House of Representatives July 13, 1790
	|date = 4 July 1790
	|location = ]
	|first1 = Thomas
	|last1 = ]
	|accessdate = 10 November 2012}}</ref> The proposal also received the support of the British Parliament, championed by ], but when the French overthrew their monarchy and decided to use the ] as their base unit, Britain withdrew support.<ref>{{cite book
	|title = The Measure of all Things – The Seven-Year-Odyssey that Transformed the World
	|last= Alder
	|first= Ken
	|year= 2002
	|publisher= Abacus
	|location= London
	|pages = 252–253
	|isbn= 0&nbsp;349&nbsp;11507&nbsp;9}}
	</ref>
			{{anchor|milliare}}
	] 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.<ref name="Larousse"/>
			In 1670, ], a French abbot and astronomer, published the book ''Observationes diametrorum solis et lunae apparentium'' ("Observations of the apparent diameters of the Sun and Moon") in which he proposed a decimal system of measurement of length for use by scientists in international communication, to be based on the dimensions of the Earth. The ''milliare'' would be defined as a ] along a ] (such as the ]) and would be divided into 10 centuria, the centuria into 10 decuria and so on, successive units being the virga, virgula, decima, centesima, and the millesima. Mouton used ] estimate that one degree of arc was 321,185 Bolognese feet. Mouton's experiments showed that a pendulum of length one virgula would beat 3959.2 times<ref group="Note">There were two beats in an oscillation.</ref> in half an hour.<ref>
	The French Revolution and subsequent Napoleonic Wars marked the end of the ]. The forces of change that had been brewing manifest themselves across all of France, including the way in which units of measure should be defined. The scientists of the day favoured the use of a system of units that were inter-related and which used a decimal basis.
			{{cite book
			| pages = 123–129
			| url = https://books.google.com/books?id=uYCNFkRgXCoC&q=mouton&pg=PA49
			| title = Revolution in Measurement: Western European Weights and Measures Since the Age of Science
			| first1 = Ronald Edward
			| last1 = Zupko
			| year = 1990
			| series = Memoirs of the American Philosophical Society, Volume 186
			| isbn = 978-0-87169-186-6
			| location = ]
			}}</ref><ref group="Note">the pendulum would have had a length of 205.6&nbsp;mm and the virgula was ~185.2&nbsp;mm.</ref> Mouton believed that, with this information, scientists in a foreign country would be able to construct a copy of the virgula for their own use.<ref name="Mouton">{{MacTutor|title=Gabriel Mouton|id=Mouton|date=June 2004}}</ref> Mouton's ideas attracted interest at the time; ] in his work ''Mesure de la Terre'' (1671) and Huygens in his work ''Horologium Oscillatorium sive de motu pendulorum'' ("Of oscillating clocks, or concerning the motion of pendulums", 1673) both proposing that a standard unit of length be tied to the beat frequency of a pendulum.<ref name="Bigourdan">
			{{cite web
			| url = http://smdsi.quartier-rural.org/histoire/precurs.htm
			| title = Le système métrique des poids et des mesures
			| language = fr
			| trans-title = The metric system of weights and measures
			| author = G. Bigourdan
			| quote = On voit que le projet de Mouton est, sans aucune différence de principe, celui qui a ét réalisé par notre Système métrique.
			| year = 1901
			| location = Paris
			| access-date = 25 March 2011
			}}</ref><ref name = Mouton/>
			=== Shape and size of the Earth ===
	==Revolutionary France (1795 - 1812)==
			{{main|Figure of the Earth}}
	] and ].]]
	Overtures made by the French government to the British and American governments for the establishment of a common system of weights and measures came to nothing and France decided to "go it alone".<ref>{{cite book
	|author = Adler
	|pages = 88–96}}</ref>
			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 ] 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 ].<ref name=mouton>US Metric Association </ref> Thus ] would be 21 600 (viz., 60 minutes of arc × 360 degrees in four 90-degree quadrants; a quadrant being the length of the quarter-circle from the ] to the ]).
	===Decimal time (1793)===
	Decimal time was introduced in the decree of 5 October 1793 under which the day was divided into 10 "decimal hours", the "hour" into 100 " decimal minutes" and the "decimal minute" into 100 "decimal seconds". The "decimal hour" corresponded to 2&nbsp;hr&nbsp;24&nbsp;min, the "decimal minute" to 1.44&nbsp;min and the "decimal second" to 0.864&nbsp;s. The revolutionary week was 10&nbsp;days, but there were still twelve months in a year.<ref>{{cite web
	|url = http://www.antique-horology.org/_Editorial/RepublicanCalendar/default.htm#Calendar%20and%20time
	|title = Dials & Symbols of the French revolution. The Republican Calendar and Decimal time
	|publisher = The Horological Foundation
	|accessdate = 2011-03-07}}</ref> The use of decimal time proved very unpopular, especially the ten day week and the calendar was officially discarded by Napoleon in 1806.
			In 1669, ], 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% (]).
	===Draft metric system (1795)===
	The implementation of decimal time proved an immense task and under the article 22 of the law of 18 Germinal, Year III (7 April 1795), the use of decimal time was no longer mandatory.<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)
	|language = French
	|trans_title = Decree regarding weights and measures: 18 Germinal Year III (7 April 1795)
	|publisher = Association Métrodiff
	|work = Le systeme metrique decimal
	|accessdate = 2011-02-07}}</ref> On 1 January 1806, France reverted to the traditional timekeeping.<ref>{{cite web
	|url = http://www.antique-horology.org/_Editorial/RepublicanCalendar/default.htm
	|accessdate = 2011-02-07
	|title = Dials & Symbols of the French revolution. The Republican Calendar and Decimal time.
	|publisher = The Horological Foundation}}</ref>
	]. The metre was defined along this meridian using a survey that stretched from ] to ].]]
			In '']'' (1686), Isaac Newton gave a theoretical explanation for the "bulging equator",<ref group="Note">The acceleration due to gravity at the poles is 9.832&nbsp;m/s<sup>−2</sup> and at the equator 9.780&nbsp;m/s<sup>−2</sup>, a difference of about 0.5%. {{Webarchive|url=https://web.archive.org/web/20130309080332/http://www.ucl.ac.uk/EarthSci/people/lidunka/GEOL2014/Geophysics2%20-%20Gravity/gravity.htm|date=9 March 2013}}</ref> which also explained the differences found in the lengths of the "second pendulums",<ref>
	The metric system of measure was first given a legal basis in 1795 by the ]ary government. Article 5 of the law of 18 Germinal, Year III (7 April 1795) defined five units of measure. The units and their preliminary values were:<ref name=18germ_3/>
			{{cite book
	*The ], for length - defined as being one ten millionth of the distance between the ] and the ] through ]
			| url = https://books.google.com/books?id=hMgXh8jMSGgC&q=newton+equatorial+bulge&pg=PA269
	*The ]&nbsp;(100&nbsp;m<sup>2</sup>) for area
			| page = 269
	*The ]&nbsp;(1&nbsp;m<sup>3</sup>) for volume of firewood
			| publisher = ]
	*The ]&nbsp;(1&nbsp;dm<sup>3</sup>) for volumes of liquid
			| year = 1989
	*The ], for mass - defined as being the mass of one cubic centimetre of water
			| isbn = 978-0-521-24254-7
			| title = Planetary astronomy from the Renaissance to the rise of astrophysics – Part A: tycho Brahe to Newton
			| editor1-first = R
			| editor1-last = Taton
			| editor2-first = C
			| editor2-last = Wilson
			}}</ref> theories that were confirmed by the ] to Peru undertaken by the ] in 1735.<ref>
			{{cite book
			| url = https://books.google.com/books?id=0UzjTJ4w9yEC&q=1738+peru+flattening&pg=PA63
			| title = Flattening the earth: two thousand years of map projections
			| first1 = John P
			| last1 = Snyder
			| year = 1993
			| publisher = ]
			| location = Chicago
			| page = 63
			| isbn = 978-0-226-76747-5
			}}
			</ref>{{efn |name=cassiniSurvey|1=]'s survey of Earth of 1713–1718<ref name=Cassini >]. ''On the size and features of Earth'', pages 14ff.</ref> }}
			=== Late 18th century: conflict and lassitude ===
	Decimal multiples and submultiples of these units would be defined by Greek ] - "myria", "kilo", "hecta" (100), "deka", "deci", "centi" and "milli". Using ] survey of 1744, a provisional value of 443.44 ''lignes'' was assigned to the metre which, in turn, defined the other units of measure.<ref>{{cite book
			], British inventor and advocate of an international decimalised system of measure<ref name=JamesWatt/>]]
	|author = Adler
			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">
	|page = 106}}</ref>
			{{cite web
			| url = http://www.2iceshs.cyfronet.pl/2ICESHS_Proceedings/Chapter_16/R-8_Navarro_Merino.pdf
			| title = The units of length in the Spanish treatises of military engineering
			| first1 = Juan Navarro
			| last1 = Loidi
			| first2 = Pilar Merino
			| last2 = Saenz
			| work = The Global and the Local: The History of Science and the Cultural Integration of Europe. Proceedings of the 2nd ICESHS
			| location = Cracow, Poland
			| date = 6–9 September 2006
			| publisher = The Press of the Polish Academy of Arts and Sciences
			| access-date = 17 March 2011
			}}</ref> and ] aligned the Russian units of measure with those of England.<ref>
			{{cite book
			| url = https://archive.org/stream/modernmetrologym00jackrich/modernmetrologym00jackrich_djvu.txt
			| title = Modern metrology; a manual of the metrical units and systems of the present century (1882)
			| last = Jackson
			| first = Lowis D'Aguilar
			| year = 1882
			| place = London
			| publisher = C Lockwood and co.
			| page = 11
			| access-date = 25 March 2011
			}}</ref> In 1783, the British inventor ], who was having difficulties in communicating with German scientists, called for the creation of a global decimal measurement system, proposing a system which used the density of water to link length and mass,<ref name="JamesWatt">
			{{cite book
			|url = http://www.freeinfosociety.com/media/pdf/4750.pdf
			|title = James Watt
			|first = Andrew
			|last = Carnegie
			|pages = 59–60
			|date = May 1905
			|publisher = Doubleday, Page & Company
			|access-date = 20 October 2011
			|archive-date = 13 August 2011
			|archive-url = https://web.archive.org/web/20110813070553/http://www.freeinfosociety.com/media/pdf/4750.pdf
			|url-status = dead
			}}</ref> and, in 1788, the French ] ] commissioned a set of nine brass cylinders (a pound and decimal subdivisions thereof) for his experimental work.<ref name=TavernorB/>{{rp|71}}
			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>
	The final value of the metre had to wait until 1799 when Delambre and Mechain presented the results of their ] which fixed the length of the metre at 443.296 ''lignes''. The law 19 Frimaire An VIII (10 December 1799) defined the metre in terms of this value and the kilogram as being 18827.15 ''grains''. These definitions enabled reference copies of the kilograms and metres to be constructed that were to used as standards for the next 90 years.<ref>{{cite web
	|url = http://www.culture.gouv.fr/culture/actualites/celebrations/metre.htm
	|language = French
	|title = Fixation de la longueur définitive du mètre
	|trans_title = Establishing the definitive metre
	|author = Suzanne Débarbat
	|publisher = Ministère de la culture et de la communication (] ministry of culture and communications)
	|accessdate = 2011-03-01}}</ref><ref>{{cite journal
	|url = http://docserver.ingentaconnect.com/deliver/connect/matthey/00321400/v44n3/s12.pdf?expires=1352558762&id=71401683&titleid=892&accname=Guest+User&checksum=3905710836BB9421D1322C998C9463CB
	|accessdate = 10 November 2012
	|title = The Foundation of the Metric System in France in the 1790s: The importance of Etienne Lenoir's platinum measuring instruments
	|first1 = William A.
	|last1 = Smeaton
	|location = ], United Kingdom
	|journal = Platinum Metals Rev.
	|year = 2000
	|volume = 44
	|number = 3
	|pages = 125–134}}</ref>
			== Implementation in Revolutionary France ==
	At the same time, a new decimal-based system for ] was implemented. The right angle was divided into 100 ] which in turn was divided in 100 ''centigrads''. An arc on the earth’s surface formed by an angle of one ''centigrade'' was one kilometre. The use of the ''centigrade'' was adopted for general use in a number countries and in 1948 the ] (CGPM) recommended that the degree centigrade (used for the measurement of temperature) be renamed the ].<ref>{{cite web
	|url = http://www.bipm.org/en/committees/cipm/cipm-1948.html
	|title = CIPM, 1948 and 9th CGPM, 1948
	|accessdate = 2011-02-08
	|publisher = ] (BIPM)}}</ref>
			=== Weights and measures of the ''Ancien Régime'' ===
	===Meridianal definition===
			{{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">
	The question of measurement reform was placed in the hands of the ] who appointed a commission chaired by ]. Borda could be said to have been a fanatic for decimalization: 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 "'']''" ({{frac|100}} of a quarter-circle) rather than ]s, with 100&nbsp;minutes to a ''grade'' and 100&nbsp;seconds to a minute.<ref>{{citation | title = Jean Charles de Borda | url = http://www-history.mcs.st-andrews.ac.uk/Biographies/Borda.html | publisher = MacTutor | accessdate = 2010-08-13}}.</ref> For Borda, the seconds pendulum was a poor choice for a standard because the second (as a unit of time) was insufficiently decimal: he preferred a system of 10&nbsp;hours to the day, 100&nbsp;minutes to the hour and 100&nbsp;seconds to the minute...
			{{cite book
			| isbn = 978-0-349-11507-8
			| author = Alder
			| title = The Measure of all Things – The Seven-Year-Odyssey that Transformed the World
			| year = 2004
			| publisher = Abacus
			}}</ref>{{rp|2–3}} Although certain standards, such as the ''pied du roi'' (the King's foot) had a degree of pre-eminence and were used by scientists, many traders chose to use their own measuring devices, giving scope for fraud and hindering commerce and industry.<ref name="histmet">
			{{cite web
			| url = http://www.french-metrology.com/en/history/history-mesurement.asp
			| title = History of measurement
			| publisher = Laboratoire national de métrologie et d'essais (LNE) (Métrologie française)
			| access-date = 6 February 2011
			| archive-date = 25 April 2011
			| archive-url = https://web.archive.org/web/20110425025041/http://www.french-metrology.com/en/history/history-mesurement.asp
			| url-status = dead
			}}</ref> These variations were promoted by local vested interests, but hindered trade and taxation.<ref name="Larousse">
			{{cite LarousseXIXe
			| title = Métrique
			| volume = 11
			| pages = 163–64
			}}</ref><ref name="Nelson">
			{{citation
			| first = Robert A.
			| last = Nelson
			| title = Foundations of the international system of units (SI)
			| journal = Physics Teacher
			| volume = 19
			| issue = 9
			| year = 1981
			| page = 597
			| url = https://www.physics.umd.edu/lecdem/services/refs_scanned_WIP/1%20-%20Krishna's%20LECDEM/A101/GetPDFServlet.pdf
			| bibcode = 1981PhTea..19..596N
			| doi = 10.1119/1.2340901
			}}{{Dead link|date=August 2024 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>
			=== Units of weight and length ===
	Instead, the commission – whose members included ], ], ] and ] – 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 ] passing through Paris.<ref name="Larousse"/> Apart from the obvious nationalistic considerations, the ] was also a sound choice for practical scientific reasons: a portion of the quadrant from Dunkerque to Barcelona (about 1000&nbsp;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.<ref name="Larousse"/>
			]
			In 1790, a panel of five leading French scientists was appointed by the ] to investigate weights and measures. They were ], ], ], ], and ].<ref name=Alder/>{{rp|2–3}}<ref name="Konvitz">
			{{cite book
			| title = Cartography in France, 1660–1848: Science, Engineering, and Statecraft
			| first1 = Josef
			| last1 = Konvitz
			| url = https://books.google.com/books?id=-I6WurxXeI0C
			| year = 1987
			| publisher = University of Chicago Press
			| 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 ], 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
			| volume = 1
			| date = January 1936
			| journal = Osiris
			| pages = 314–340
			| doi = 10.1086/368429
			| last1 = Hellman
			| 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
			| title = History of Binary and other Nondecimal Numeration
			| first1 = Anton
			| last1 = Glaser
			| publisher = Tomash
			| year = 1981
			| isbn = 978-0-938228-00-4
			| edition = Revised
			| orig-date = 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
			| author = Adams, John Quincy
			| location = Washington DC
			| publisher = ]
			| 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)
			|language = fr
			|trans-title = Decree regarding weights and measures: 18 Germinal Year III (7 April 1795)
			|work = Le systeme metrique decimal
			|publisher = Association Métrodiff
			|access-date = 7 February 2011
			|archive-url = https://web.archive.org/web/20160817122340/http://www.metrodiff.org/cmsms/index.php?page=18_germinal_an_3
			|archive-date = 17 August 2016
			}}</ref> The proposals were accepted by the ] on 30 March 1791.<ref name="LoisEtDecret">
			{{cite web
			| title = Lois et décrets
			| language = fr
			| trans-title = Laws and decrees
			| work = Histoire de la métrologie
			| publisher = Association Métrodiff
			| location = Paris
			| url = https://www.metrodiff.org/wp/metrologie/histoire-de-la-metrologie/lois-et-decrets/
			| access-date = 2 April 2020
			}}</ref>
			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 ]:<ref name="TavernorB"/>{{rp|82}}
	]
			* Measuring the difference in latitude between ] and ] and ] between them
	The task of surveying the ] fell to ] and ], and armed with letters of authorisation signed by ]<ref name="Adler 21–33">{{cite book
			* Measuring the baselines used for the survey
	|author = Adler
			* Verifying the length of the second pendulum at 45° latitude.
	|pages = 21–33}}</ref> the task took more than six years (1792–98).<ref>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 ], 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 (see Alder).</ref> In the meantime, the commission calculated a provisional value from older surveys of 443.44&nbsp;'']s''.<ref name="lignes">All values in ''lignes'' are referred to the '']'', not to the later value in '']''. 1&nbsp;'']''&nbsp;= 6&nbsp;'']s''; 1&nbsp;''pied''&nbsp;= 12&nbsp;'']s''; 1&nbsp;''pouce''&nbsp;= 12&nbsp;''lignes''; so 864&nbsp;''lignes''&nbsp;= 1&nbsp;''toise''.</ref>
			* 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 (]), measured along the ].<ref name="Larousse"/>
	The project was split into two parts - the northern section of 742.7&nbsp;km from the Belfry, ] to ] which was surveyed by Delambre and the southern section of 333.0&nbsp;km from ] to the ], ] which was surveyed by Méchain.<ref name="Adler 227–230">{{cite book
	|author = Adler
	|pages = 227–230}}</ref><ref>Distances measured using Google Earth. The coordinates are:<br> {{Coord|51|02|08|N|2|22|34|E|region:FR-O_type:landmark|name= Belfry, Dunkirk}} - Belfry, Dunkirk<br>
	{{Coord|44|25|57|N|2|34|24|E|region:FR-N_type:landmark|name=Rodez Cathederal}} - ] Cathederal<br>
	{{Coord|41|21|48|N|2|10|01|E|region:ES-CT_type:landmark|name= Montjuïc, Barcelona}} - ], ]</ref>
			Using ]'s survey of 1670 and ]'s survey of 1718,{{efn|name= cassiniSurvey}} a provisional value of 443.44 '']s'' was assigned to the metre which, in turn, defined the other units of measure.<ref name=Alder/>{{rp|106}}
	Delambre used a baseline of about 10&nbsp;km in length along a straight road, located close to ]. In an operation taking six weeks, the baseline was accurately measured using four platinum rods, each of length two ''toise'' (about 3.9&nbsp;m).<ref name="Adler 227–230"/> Thereafter he used, where possible, the triangulation points used by ] in his 1744 survey of France. Méchain's baseline, of a similar length, and also on a straight section of road was in the ] area.<ref>{{cite book
	|author = Adler
	|pages = 240–241}}</ref> Although Méchain's sector was half the length of Delambre, it included the ] 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&nbsp;''lignes'' shorter than the provisional value, a difference of about 0.03%.<ref name="Larousse"/>
			While ] were completing their survey, the commission had ordered a series of ] 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 would be selected.
	]
	===''Mètre des Archives''===
	While Méchain and Delambre were completing their survey, the commission had ordered a series of ] bars to be made based on the provisional metre. When the final result was known, the bar whose length was closest to the meridianal definition of the metre was selected and placed in the National Archives on 22&nbsp;June 1799 (4&nbsp;messidor An&nbsp;VII in the Republican calendar) as a permanent record of the result:<ref name="Larousse"/> this standard metre bar became known as the ''mètre des Archives''.
			After 1792, the name of the original defined unit of mass, "'']''", 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 "'']''". Consequently, the kilogram is the only ] that has an ] as part of its unit name.
	The ], that is the system of units based on the metre, was officially adopted in France on 10&nbsp;December 1799 (19&nbsp;frimaire An&nbsp;VIII) and became the sole legal system of weights and measures from 1801.
			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 ]) 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 ].<ref group="Note">from Latin ''gravitas'': "weight"</ref> This mass unit defined by ] and ] 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
			| work = Antoine-Laurent de Lavoisier (1743–1794 – Life and Works
			| publisher = Comité Lavoisier de l'Académie des Sciences de Paris
			| first = Jean-Pierre
			| 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&nbsp;°C—a highly stable temperature point—it was replaced with the temperature at which water reaches maximum density. This temperature, about 4&nbsp;°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 Metre, 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 ] 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-date=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 |pages=558–580 }}</ref>{{rp|{{citation|title=563–564| year=1810 | publisher=Baudouin, imprimeur de l'Institut National |url=https://books.google.com/books?id=AMNyANd13d4C&dq=%22moins%20dans%20les%20temp%C3%A9ratures%20faciles%20%C3%A0%20obtenir%2C%20c'est%20celle%22&pg=PA564}}}} This is a general mathematical fact: if a function {{math|''f''(·)}} of a variable {{math|''x''}} is sufficiently free of discontinuities, then, if one plots {{math|''f''}} vs. {{math|''x''}}, and looks at a point {{math|(''x''{{sub|max}}, ''f''(''x''{{sub|max}}))}} at which {{math|''f''}} has a 'peak' (meaning, {{math|''f''}} decreases no matter whether {{math|''x''}} is made a bit larger or a bit smaller than {{math|''x''{{sub|max}}}}), once notices that {{math|''f''}} is 'flat' at {{math|''x''{{sub|max}}}}—the tangent line to it at that point is horizontal, so the slope of {{math|''f''}} at {{math|''x''{{sub|max}}}} is zero. This is why {{math|''f''}} changes little from its maximum value if {{math|''x''}} is made slightly different from {{math|''x''{{sub|max}}}}.}} The final conclusion was that one cubic decimetre of water at its maximum density was equal to 99.92072% of the mass of the provisional kilogram.<ref>'' {{Webarchive|url=https://web.archive.org/web/20130821042634/http://www.sizes.com/units/kilogram.htm |date=21 August 2013 }}''</ref>
			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/>
	It soon became apparent that Méchain and Delambre's result (443.296&nbsp;''lignes'')<ref name="lignes"/> was slightly too short for the meridianal definition of the metre. ] and ] extended the survey to the island of Formentera in the western Mediterranean Sea in 1806–9, and found that one ten-millionth of the Earth's quadrant should be 443.31&nbsp;''lignes'': later work increased the value to 443.39&nbsp;''lignes''.<ref name="Larousse"/> The modern value, for the WGS&nbsp;84 reference spheroid, is {{nowrap|1.000 196 57}}&nbsp;m or {{nowrap|443.383 08}}&nbsp;''lignes''.<ref>The WGS&nbsp;84 reference spheroid has a semi-major axis of {{nowrap|6 378 137.0 m}} and a flattening of {{frac|{{nowrap|298.257 223 563}}}}.</ref>
			* The '']'', for length—defined as one ten-millionth of the distance between the ] and the ] through ]
			* The '']''&nbsp;(100&nbsp;m<sup>2</sup>) for area
			* The '']''&nbsp;(1&nbsp;m<sup>3</sup>) for volume of firewood
			* The '']''&nbsp;(1&nbsp;dm<sup>3</sup>) for volumes of liquid
			* The '']me'', for mass—defined as the mass of one cubic centimetre of water
			* The '']'', 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&nbsp;ares, or 1&nbsp;hm<sup>2</sup>) are still in use, but are not SI units.''
			Decimal multiples of these units were defined by Greek ]: ''"]"'' (10,000), ''"]"'' (1000), ''"]"'' (100), and ''"]"'' (10) and submultiples were defined by the Latin prefixes ''"]"'' (0.1), ''"]"'' (0.01), and ''"]"'' (0.001).<ref>
	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 meridianal definition. When, in 1867, it was proposed that a new international standard metre be created, 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 | accessdate = 2010-08-15}}.</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 | publisher = International Bureau of Weights and Measures | accessdate = 2010-08-15}}.</ref>
			{{cite journal
			| journal = A Journal of Natural Philosophy, Chemistry, and the Arts
			| title = An account of the New System of measures established in France
			| first1 = Ch
			| last1 = Coquebert
			| date = August 1797
			| volume = 1
			| pages = 193–200
			}}</ref>
			For purposes of commerce, units and prefixed-units of weight (mass) and capacity (volume) were prependable by the binary multipliers ''"]"'' (2) and ''"]"'' ({{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>
	===''Kilogramme des Archives''===
	A '''grave''' is a metallic reference standard of one thousand ]s that was used for a few years until it was replaced by the ] standard in 1799.
			The 1795 draft definitions enabled provisional copies of the kilograms and metres to be constructed.<ref>
	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 this was the ''definition'' of the gram, 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 “grave” (symbol '''G'''). This mass unit, whose name is derived from the word “gravity”, defined by ] and ] had been in use since 1793.<ref>{{cite web
			{{cite web
	|url =http://historyofscience.free.fr/Lavoisier-Friends/a_chap8_lavoisier.html
			| url = http://www.culture.gouv.fr/culture/actualites/celebrations/metre.htm
	|title = Chapter 8: Lavoisier, Arts and Trades
			| language = fr
	|work = Antoine-Laurent de Lavoisier (1743-1794 - Life and Works
			| title = Fixation de la longueur définitive du mètre
	|publisher = Comité Lavoisier de l'Académie des Sciences de Paris
			| trans-title = Establishing the definitive metre
	|first = Jean-Pierre
			| author = Suzanne Débarbat
	|last =Poirier
			| publisher = Ministère de la culture et de la communication (] ministry of culture and communications)
	|accessdate = 2011-08-04}}</ref> Notwithstanding that the ''definition'' of the base unit of mass was the gramme (alternatively “gravet”), this new, practical realisation would ultimately become the base unit of mass. A provisional kilogram standard was made and work was commissioned to determine precisely how massive a cubic decimetre (later to be defined as equal to one ]) of water was.
			| access-date = 1 March 2011
			}}</ref><ref>
			{{cite journal
			| url = http://www.platinummetalsreview.com/journal-archive/?decade=1991–2000
			| access-date = 10 November 2012
			| title = The Foundation of the Metric System in France in the 1790s: The importance of Etienne Lenoir's platinum measuring instruments
			| first1 = William A.
			| last1 = Smeaton
			| location = ], United Kingdom
			| journal = Platinum Metals Rev.
			| year = 2000
			| volume = 44
			| number = 3
			| pages = 125–134
			| doi = 10.1595/003214000X443125134
			| doi-access= free
			}}</ref>
			=== Meridional survey ===
	Although the decreed definition of the kilogram specified water at 0&nbsp;°C — a highly stable ''temperature'' point — the scientists tasked with producing the new practical realisation chose to redefine the standard and perform their measurements at the most stable ''density'' point: the temperature at which water reaches maximum density, which was measured at the time as 4&nbsp;°C.<ref>''L’Histoire Du Mètre, La Détermination De L’Unité De Poids'', link to Web site </ref> They concluded that one cubic decimetre of water at its maximum density was equal to 99.92072% of the mass of the provisional kilogram made earlier that year.<ref>''''</ref> Four years later in 1799, an all-platinum standard, the “Kilogramme des Archives”, was fabricated with the objective that it would equal, as close as was scientifically feasible for the day, to the mass of cubic decimetre of water at 4&nbsp;°C. The kilogram was defined to be equal to the mass of the Kilogramme des Archives and this standard stood for the next ninety years.
			{{further|Arc measurement}}
			], seen here dominating the Rodez skyline]]
	Note that the new metric system did not come into effect until after the ], when the new revolutionary government captured the idea of the metric system. The decision of the Republican government to name this new unit the “kilogramme” had been mainly politically motivated, because the name “grave” was at that time considered politically incorrect as it resembled the aristocratic German title of the ], an alternative name for the title of ] that, like other nobility titles, was inconsistent with the ].<ref></ref> Accordingly, the ''name'' of the original, defined unit of mass, “gramme”, which was too small to serve as a practical realisation, was adopted and the new prefix “kilo” was appended to it to form the name “kilogramme”. Consequently, the kilogram is the only ] that has an ] as part of its unit name.
			The task of surveying the ], which was estimated to take two years, fell to ] and ]. The task eventually took more than six years (1792–1798) with delays caused not only by unforeseen technical difficulties but also by the convulsed period of the aftermath of the Revolution.<ref name=Alder/> Apart from the obvious nationalistic considerations, the ] was also a sound choice for practical scientific reasons: a portion of the quadrant from Dunkirk to Barcelona (about 1000&nbsp;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.<ref name="Larousse"/>
			The project was split into two parts—the northern section of 742.7&nbsp;km from the Belfry, ] to ] which was surveyed by Delambre and the southern section of 333.0&nbsp;km from ] to the ], ] which was surveyed by Méchain.<ref name=Alder/>{{rp| 227–230}}<ref group="Note">Distances measured using Google Earth. The coordinates are:<br /> {{Coord|51|02|08|N|2|22|34|E|region:FR-O_type:landmark|name= Belfry, Dunkirk}} – Belfry, Dunkirk<br />
	==Worldwide adoption of the metric system==
			{{Coord|44|25|57|N|2|34|24|E|region:FR-N_type:landmark|name=Rodez Cathedral}} – ] Cathedral<br />
			{{Coord|41|21|48|N|2|10|01|E|region:ES-CT_type:landmark|name= Montjuïc, Barcelona}} – ], ]</ref>
			] (''Observatoire de Paris''). The metre was defined along this meridian using a survey that stretched from ] to ].]]
			Delambre used a baseline of about 10&nbsp;km in length along a straight road, located close to ]. In an operation taking six weeks, the baseline was accurately measured using four platinum rods, each of length two ''toises'' (about 3.9&nbsp;m).<ref name=Alder/>{{rp| 227–230}} Thereafter he used, where possible, the triangulation points used by ] in his 1744 survey of France. Méchain's baseline, of a similar length, and also on a straight section of road was in the ] area.<ref name=Alder/>{{rp| 240–241}} Although Méchain's sector was half the length of Delambre, it included the ] 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 metre as 443.296&nbsp;''lignes'',<ref name="Larousse"/><ref name="lignes" group="Note">All values in ''lignes'' are referred to the ''toise de Pérou'', not to the later value in '']''. 1&nbsp;'']''&nbsp;= 6&nbsp;'']s''; 1&nbsp;''pied''&nbsp;= 12&nbsp;'']s''; 1&nbsp;''pouce''&nbsp;= 12&nbsp;''lignes''; so 1&nbsp;''toise''&nbsp;= 864&nbsp;''lignes''.</ref> notably shorter than the 1795 provisional value of 443.44&nbsp;''lignes''. On 15 November 1798, Delambre and Méchain returned to Paris with their data, having completed the survey. The final value of the ''mètre'' was defined in 1799 as the computed value from the survey.
	During the nineteenth century the metric system proved a convenient political compromise during the unification processes in the Netherlands, Germany and Italy. Spain found it expedient in 1858 to follow the French example and within a decade ] had also adopted the metric system. There was considerable resistance to metrication in the United Kingdom and in the United States, though once the United Kingdom announced its metrication program in 1965, the ] followed suit.
			: ''Historical note:'' It soon became apparent that Méchain and Delambre's result (443.296&nbsp;''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&nbsp;84 reference spheroid of {{nowrap|1.000 196 57}}&nbsp;m is {{nowrap|443.383 08}}&nbsp;''lignes''.</ref>
	===France: Mesures usuelles (1812 - 1839)===
			{{clear}}
	{{main|Mesures usuelles}}
	The introduction of the metric system into France in 1795 was done on a district by district basis with Paris being the first district, but it was, in terms of modern standards, poorly managed. Although thousands of pamphlets were distributed, the Agency of Weights and Measures who oversaw the introduction underestimated the work involved. Paris alone needed 500,000 metre sticks, yet one month after the metre became the sole legal unit of measure, they only had 25,000 in store.<ref>{{cite book |author = Adler |page = 269}}</ref> This, combined with other excesses of the Revolution and the high level of illiteracy made the metric system unpopular.
			=== The French metric system ===
	Napoleon himself ridiculed the metric system, but as an able administrator, recognised the value of a sound basis for a system of measurement and under the ''décret impérial du 12 février 1812'' (imperial decree of 12 February 1812), a new system of measure - the ''mesure uselles'' or "customary measures" was introduced for use in small retail businesses - all government, legal and similar works still had to use the metric system and the metric system continued to be taught at all levels of education.<ref name=Fevier>{{cite web
			In June 1799, platinum prototypes were fabricated according to the measured quantities, the ''mètre des archives'' defined to be a length of 443.296&nbsp;lignes, and the ''kilogramme des archives'' defined to be a weight of 18827.15 ],<ref>
	|url = http://www.industrie.gouv.fr/metro/aquoisert/metre.htm
			{{cite journal
	|title = Un historique du mètre
			|title= On the Science of Weighing and Measuring, and the Standards of Weight and Measure*
	|language = French
			|last= CHISHOLM
	|author = Denis Février
			|first= H.W.
	|publisher = Ministère de l'Economie, des Finances et de l'Industrie
			|date= 9 October 1873
	|accessdate = 2011-03-10}}</ref> The names of many units used during the ancien regime were reintroduced, but were redefined in terms of metric units. Thus the ''toise'' was defined as being two metres with six ''pied'' making up one ''toise'', twelve ''pouce'' making up one ''pied'' and twelve ''lignes'' making up one ''pouce''. Likewise the ''livre'' was defined as being 500&nbsp;g, each ''livre'' comprising sixteen ''once'' and each ''once'' eight ''gros'' and the ''aune'' as 120 centimetres.<ref name=H&H>{{cite web
			|journal= Nature
	|url = http://www.archive.org/stream/outlinesofevolut00halluoft/outlinesofevolut00halluoft_djvu.txt
			|volume= 8
	|title = Outlines of the evolution of weights and measures and the metric system
			|issue= 206
	|first1 = William
			|pages= 489–491
	|last1 = Hallock
			|doi= 10.1038/008489a0
	|first2 = Herbert T
			|bibcode= 1873Natur...8..489C
	|last2 = Wade
			|s2cid= 3968820
	|publisher = The Macmillan Company
			|doi-access= free
	|year = 1906
			}}</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.
	|pages = 66–69
	|location = London}}</ref>
			Despite the law, the populace continued to use the old measures. In 1812, Napoleon revoked the law and issued one called the '']'', 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 '']'', originally a unit of mass derived from the Roman ''libra'' (as was the English ]), but now meaning 500&nbsp;grams, are still in use today.
	===The Dutch metric system===
	The Netherlands first used the metric system and then, in 1812, the ] when it was part of the ]. Under the Royal decree of 27 March 1817 (''Koningklijk besluit van den 27 Maart 1817''), the newly-formed ] abandoned the mesures usuelles in favour of the "Dutch" ] (''Nederlands metrisch stelsel'') in which metric units were given the names of units of measure that were then in use. Examples include the ''ons'' (ounce) which was defined as being 100&nbsp;g:<ref>{{cite book
	|url = http://books.google.co.uk/books?id=XYVbAAAAQAAJ&printsec=frontcover#v=onepage&q&f=false
	|title = Allereerste Gronden der Cijferkunst
	|author = Jacob de Gelder
	|location = 's Gravenhage and Amsterdam
	|language = Dutch
	|year = 1824
	|pages = 155–157
	|publisher = de Gebroeders van Cleef
	|trans_title = Introduction to Numeracy
	|accessdate = 2011-03-02}}</ref>
			== Development of non-coherent metric systems ==
	===The German Zollverein===
			At the start of the nineteenth century, the French Academy of Sciences' artefacts for ] and ] were the only nascent units of the metric system that were defined in terms of formal ]. 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 (ca. 1724) and Celsius (ca. 1742) scales of temperature existed, and varied instruments for measuring units or degrees of them. The ]/] unit model had not yet been elaborated, nor was it known how many ] might be interrelated.
	]
	At the outbreak of the French Revolution, much of modern-day Germany and Austria were part of the ] which has become a loose federation of kingdoms, principalities, free cities, bishoprics and other fiefdoms, each with its own system of measurement, though in most cases such system were loosely derived from the ] system instituted by ] a thousand years earlier.
			A model of interrelated units was first proposed in 1861 by the ] (BAAS) based on what came to be called the "mechanical" units (length, mass, and time). Over the following decades, this foundation enabled ], ], and ]{{when|date=January 2018}} units to be correlated.
	During the Napoleonic era, there was a move among some of the German states to reform their systems of measurement using the prototype metre and kilogram as the basis of the new units. ], in 1810, for example, redefined the ''ruthe'' (rods) as being 3.0&nbsp;m exactly and defined the subunits of the ''ruthe'' as 1 ''ruthe'' = 10&nbsp;''fuβ'' (feet) = 100&nbsp;''zoll'' (inches) = 1,000&nbsp;''linie'' (lines) = 10,000&nbsp;''punkt'' (points) while the ''pfund'' was defined as being 500&nbsp;g, divided into 30&nbsp;loth, each of 16.67&nbsp;g.<ref name=Europa1842>{{cite web
	|url = http://home.fonline.de/fo0126//geschichte/groessen/mas1.htm
	|title = Amtliche Maßeinheiten in Europa 1842
	|language = German
	|trans_title = Official units of measure in Europe 1842
	|postscript = Text version of Malaisé's book
	|accessdate = 2011-03-26}}</ref><ref>{{cite book
	|url = http://home.fonline.de/rs-ebs/geschichte/buch/titel.htm
	|title = Theoretisch-practischer Unterricht im Rechnen
	|language = German
	|trans_title = Theoritcal and practical instruction in arithmetic
	|author = Ferdinand Malaisé
	|place = München
	|year = 1842
	|pages = 307–322
	|accessdate = 2011-03-26}}</ref> ], in its reform of 1811, trimmed the Bavarian ''pfund'' from 561.288&nbsp;g to 560&nbsp;g exactly, consisting of 32 ''loth'', each of 17.5&nbsp;g<ref>{{cite web
	|url = http://www.digitalis.uni-koeln.de/Grebenau/grebenau_index.html
	|title =Tabellen zur Umwandlung des bayerischen Masses und Gewichtes in metrisches Maß und Gewicht und umgekehrt
	|language = German
	|trans_title = Conversion tables for converting between Bavarian units of measure and metric units
	|location = Munich
	|author =Heinrich Grebenau
	|year = 1870
	|accessdate = 2011-03-07}}</ref> while the ]n pfund remained at 467.711&nbsp;g.<ref>{{Cite thesis
	|degree= Dr.&nbsp;med.&nbsp;vet
	|chapter= 2.1
	|title= ''Der Marstall des Schlosses Anholt (16. bis 18. Jahrhundert) - Quellen und Materialien zur Geschichte der Pferdehaltung im Münsterland''
	|url= http://elib.tiho-hannover.de/dissertations/parrass_ss06.pdf
	|author= Silke Parras
	|year= 2006
	|publisher= ''Tierärztliche Hochschule Hannover''
	|accessdate= 2011-03-07}}</ref>
			=== Time ===
	After the ] there was a degree of commercial cooperation between the various German states resulting in the setting of the German Customs Union ('']''). There were however still many barriers to trade until ] took the lead in establishing the General German Commercial Code in 1856. As part of the code the ''Zollverein'' introduce the ''Zollpfund'' (Customs Pound) which was defined to be exactly 500&nbsp;g and which could be split into 30&nbsp;'lot'.<ref name=Zollmuseum>{{cite web
	|url = http://www.zoll.de/h0_wir_ueber_uns/h0_zollmuseum/d0_gewinnspiel/c0_Archiv/a0_2006/y02_fundstueck_november_2006/index.html
	|title = Fundstück des Monats November 2006
	|language = German
	|trans_title = Exhibit of the month - November 2006
	|publisher = Bundesministerium der FinanzenQuelle: www.zoll.de
	|date = 4 June 2009
	|accessdate = 2011-03-07}}</ref> This unit was used for inter-state movement of goods, but was not applied in all states for internal use.
			In 1832, German mathematician ] made the first absolute measurements of the ] 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's 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.
	Although the Zollverein collapsed after the ] of 1866, the metric system became the official system of measurement in the newly formed ] in 1871<ref>{{cite web
	|url = http://www.csi.tu-darmstadt.de/media/csi/institutes/nearwallreactiveflows/bilderdateien_1/messtechnik/mtmnormen.pdf
	|title = Metrologie
	|language = German
	|author = Andreas Dreizler et al
	|date = 20 April 2009
	|publisher = Technische Universität Darmstaft
	|accessdate = 2011-03-28}}</ref> and of Austria in 1875.<ref name=PopularScience>{{cite journal
	|journal = Popular Science Monthly
	|url = http://books.google.co.uk/books?id=IyUDAAAAMBAJ&pg=PA394&lpg=PA394&dq=The+Metric+System+-+Shall+it+be+compulsory&source=bl&ots=lrnmZ5tWi2&sig=5w7UFhDue7LjnLlG93bz2SOIA4E&hl=en&ei=Z0vVTdr8C42LhQejoKnlCw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CB0Q6AEwAA#v=onepage&q=The%20Metric%20System%20-%20Shall%20it%20be%20compulsory&f=false
	|title = The Metric System - Shall it be compulsory?
	|author = W Leconte Stephens
	|date = March 1904
	|pages = 394–405
	|accessdate = 2011-05-17}}</ref> The Zollpfund ceased to be legal in Germany after 1877.<ref name=Zollmuseum/>
	===Italy===		=== Work and energy ===
			] was transferred to the water, heating it up.]]
	], Toscana]]
			In a paper published in 1843, ] first demonstrated a means of measuring the ] transferred between different systems when work is done thereby relating ]'s ], defined in 1824 as "the amount of heat required to raise the temperature of 1&nbsp;kg of water from 0 to 1&nbsp;°C at 1 atmosphere of pressure" to ].<ref>
	The ], a North Italian republic set up by Napoleon in 1797 with its capital at ] first adopted a modified form of the metric system based in the ''braccio cisalpino'' (Cisalpine cubit) which was defined to be half a metre.<ref name = metricItaly>{{cite web
			{{cite journal
	|url = http://www.2iceshs.cyfronet.pl/2ICESHS_Proceedings/Chapter_16/R-8_Borgato.pdf
			| last1 = Hargrove
	|title = The first applications of the metric system in Italy
			| first1 = JL
	|author = Maria Teresa Borgato
			| date = December 2006
	|work = The Global and the Local:The History of Science and the Cultural Integration of Europe. Proceedings of the 2nd ICESHS
			| title = History of the calorie in nutrition
	|location = Cracow, Poland
			| journal = ]
	|date = 6-9 September 2006
			| location = Bethesda, Maryland
	|publisher = The Press of the Polish Academy of Arts and Sciences
			| volume = 136
	|accessdate = 2011-03-17}}</ref> In 1802 the Cisalpine Republic was renamed the ], with Napoleon as its head of state. The following year the Cisalpine system of measure was replaced by the metric system.<ref name = metricItaly/>
			| issue = 12
			| pages = 2957–61
			| doi = 10.1093/jn/136.12.2957
			| 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
			| publisher = ], ] and the ]
			| location = London, York and Bradford
			| access-date = 8 July 2013
			}}</ref> Energy became the unifying concept of nineteenth century ],<ref>
			{{cite journal
			| journal = Current Science
			| volume = 100
			| issue = 4
			| date = 25 February 2011
			| url = http://www.currentscience.ac.in/Volumes/100/04/0563.pdf
			| title = How the electric telegraph shaped electromagnetism
			| author = Kapil Subramanian
			| access-date = 12 May 2011
			}}</ref> initially by bringing ] and ] together and later adding ].
			=== The first structured metric system: CGS ===
	In 1806, the Italian Republic was replaced by the ] with Napoleon as its emperor. By 1812, all of Italy from Rome northwards was under the control of Napoleon, either as French Departments or as part of the Kingdom of Italy ensuring the metric system was in use throughout this region.
			In 1861, a committee of the ] (BAAS) including ], ], and ] 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
			| chapter = First Report – Cambridge 3 October 1862
			| pages = 1–3
			| first1 = William
			| last1 = Thomson
			| first2 = James Prescott
			| last2 = Joule
			| first3 = James Clerk
			| last3 = Maxwell
			| first4 = Flemming
			| last4 = Jenkin
			| editor1-first = Flemming
			| editor1-last = Jenkin
			| location = London
			| 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
			| chapter = Second report – Newcastle-upon-Tyne 26 August 1863
			| pages = 39–41
			| first1 = William
			| last1 = Thomson
			| first2 = James Prescott
			| last2 = Joule
			| first3 = James Clerk
			| last3 = Maxwell
			| first4 = Flemming
			| last4 = Jenkin
			| editor1-first = Flemming
			| editor1-last = Jenkin
			| location = London
			| 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 '']''). All other units of measure could be derived (hence '']'') 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
			| author = J C Maxwell
			| year = 1873
			| publisher = Clarendon Press
			| location = Oxford
			| url = https://archive.org/details/electricandmagne01maxwrich
			| pages = –3
			| access-date = 12 May 2011
			}}</ref><ref name="Maxwell2">
			{{cite book
			| title = A treatise on electricity and magnetism
			| volume = 2
			| author = J C Maxwell
			| year = 1873
			| publisher = Clarendon Press
			| location = Oxford
			| url = https://archive.org/stream/electricandmag02maxwrich
			| pages = 242–245
			| access-date = 12 May 2011
			}}</ref>
			In 1861, before{{clarify|date=January 2020}}{{Fix|text=at?}} a meeting of the BAAS, ] and ] proposed the names of ], ], and ] in honour of ], ], and ] respectively for the practical units based on the CGS absolute system. This was supported by Thomson (Lord Kelvin).<ref>
	After the ], the various Italian states reverted to their original system of measurements, but in 1845 the ] passed legislation to introduce the metric system within five years. By 1860, most of Italy had been unified under the King of Sardinia ] and under ''Law 132 of 28 July 28, 1861'' the metric system became the official system of measurement throughout the kingdom. Numerous ''Tavole di ragguaglio'' (Conversion Tables) were displayed in shops until 31 December 1870.<ref name = metricItaly/>
			{{cite web
			|url = http://www.iec.ch/about/history/beginning/lord_kelvin.htm
			|title = In the beginning&nbsp;... Lord Kelvin
			|author = Silvanus P. Thompson
			|publisher = International Electrotechnical Commission
			|access-date = 10 May 2011
			|archive-date = 23 December 2016
			|archive-url = https://web.archive.org/web/20161223214939/http://www.iec.ch/about/history/beginning/lord_kelvin.htm
			}}</ref> The concept of naming units of measure after noteworthy scientists was subsequently used for other units.
			In 1873, another committee of the BAAS (which also included Maxwell and Thomson) tasked with "the Selection and Nomenclature of Dynamical and Electrical Units" recommended using the ]. The committee also recommended the names of "]" and "]" for the cgs units of force and energy.<ref name="BAASReport">
	===Spain===
			{{cite journal
			| journal = Report on the Forty-third Meeting of the British Association for the Advancement of Science Held at Bradford in September 1873
			| year = 1874
			| title = First Report of the Committee for the Selection and Nomenclature of Dynamical and Electrical Units
			| volume = 43
			| editor = Professor Everett
			| publisher = British Association for the Advancement of Science
			| pages = 222–225
			| url = https://www.biodiversitylibrary.org/item/94452
			| access-date = 10 May 2011
			}}</ref><ref name=Maxwell2/><ref>
			{{cite web
			| url = http://www.sizes.com/units/sys_cgs.htm
			| title = centimeter–gram–second systems of units
			| work = Sizes, Inc
			| date = 6 August 2001
			| access-date = 7 April 2011
			}}</ref> The cgs system became the basis for scientific work for the next seventy years.
			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).
	Until the ascent of the ] monarchy in Spain in 1700, each of the regions of Spain retained their own system of measurement. The new Bourbon monarchy tried to centralise control and with it the system of measurement. There were debates regarding the desirability of retaining the ] units of measure or, in the interests of harmonisation, adopting the French system.<ref name = metricSpain>{{cite web
	|url = http://www.2iceshs.cyfronet.pl/2ICESHS_Proceedings/Chapter_16/R-8_Navarro_Merino.pdf
	|title = The units of length in the Spanish treatises of military engineering
	|first1 = Juan Navarro
	|last1 = Loidi
	|first2 = Pilar Merino
	|last2 = Saenz
	|work = The Global and the Local:The History of Science and the Cultural Integration of Europe. Proceedings of the 2nd ICESHS
	|location = Cracow, Poland
	|date = 6-9 September 2006
	|publisher = The Press of the Polish Academy of Arts and Sciences
	|accessdate = 2011-03-17}}></ref> Although Spain assisted Machain in his meridian survey, the Government feared the French revolutionary movement and reinforced the Castilian units of measure to counter such movements. By 1849 however, it proved difficult to maintain the old system and in that year the metric system became the legal system of measure in Spain.<ref name = metricSpain/>
			=== Electrical units ===
	===United Kingdom and the Commonwealth===
			{| class="wikitable floatright"
	{{main|Metrication in the United Kingdom|Metrication of British Transport}}
			|+ Symbols used in this section
	In 1824 the Weights and Measures Act imposed one standard 'imperial' system of weights and measures on the British Empire.<ref>{{cite web
	|url = http://www.parliament.uk/about/living-heritage/transformingsociety/tradeindustry/industrycommunity/keydates/
	|title = Industry and community - Key dates
	|publisher = United Kingdom Parliament
	|accessdate = 2011-03-28}}</ref> The effect of this act was to standardise existing British units of measure rather than to align them with the metric system.
	During the next eighty years a number of Parliamentary select committees recommended the adoption of the metric system each with a greater degree of urgency, but Parliament prevaricated. A Select Committee report of 1862 recommended compulsory metrication, but with an "Intermediate permissive phase", Parliament responded in 1864 by legalising metric units only for 'contracts and dealings'.<ref name = Hyttel>
	{{Cite thesis
	|degree=BA
	|title= Working man's pint - An investigation of the implementation of the metric system in Britain 1851-1979
	|url= http://ukma.org.uk/sites/default/files/hyttel_metrication.pdf
	|author=Frederik Hyttel
	|date = May 2009
	|publisher= Bath Spa University
	|location = ], United Kingdom
	|accessdate= 2011-03-29}}</ref> Initially the United Kingdom declined to sign the ], but did so in 1883. Meanwhile British scientists and technologists were at the forefront of the metrication movement - it was the ] that promoted the cgs system of units as a coherent system and it was the British firm ] that was accepted by the CGPM in 1889 to cast the international prototype metre and kilogram.
	In 1895 another Parliamentary select committee recommended the compulsory adoption of the metric system after a two-year permissive period, the 1897 Weights and Measures Act legalised the metric units for trade, but did not make them mandatory.<ref name = Hyttel/> A bill to make the metric system compulsory in order to enable British industrial base to fight off the challenge of the nascent German base passed through the House of Lords in 1904, but did not pass in the House of Commons before the next general election was called. Following opposition by the Lancashire cotton industry, a similar bill was defeated in 1907 in the House of Commons by 150 votes to 118.<ref name = Hyttel/>
	In 1965 Britain commenced an official program of metrication that, as of 2012, had not been completed. The British metrication program signaled the start of metrication programs elsewhere in the ], though India had started her program before in 1959, six years before the United Kingdom. South Africa (then not a member of the Commonwealth) set up a Metrication Advisory Board in 1967, New Zealand set up its Metric Advisory Board in 1969, Australia passed the Metric Conversion Act in 1970 and Canada appointed a Metrication Commission in 1971. Metrication in Australia, New Zealand and South Africa was essentially complete within a decade while metrication in India and Canada is not complete. In addition the ] and ] are still in widespread use in India. Most other Commonwealth countries adopted the metric system during the 1970s.<ref>{{cite web
	|url = http://lamar.colostate.edu/~hillger/internat.htm
	|title = Metrication status and history
	|publisher = United States Metrication Association
	|year = 2009
	|accessdate = 2011-05-19}}</ref>
	===United States===
	{{main|Metrication in the United States}}
	The United States government acquired copies of the French metre and kilogram for reference purposes in 1805 and 1820 respectively. In 1866 the ] passed a bill making it lawful to use the metric system in the United States. The bill, which was permissive rather than mandatory in nature, defined the metric system in terms of ] rather than with reference to the international prototype metre and kilogram.<ref>{{cite web
	|url=http://lamar.colostate.edu/~hillger/laws/metric-act-bill.html
	|title=H.R. 596, An Act to authorize the use of the metric system of weights and measures
	|author=29th Congress of the United States, Session 1
	|date=May 13, 1866
	|accessdate = 2011-05-19}}</ref><ref>{{cite web
	|url = http://www.nist.gov/pml/pubs/sp447/index.cfm
	|title = Use of metric system officially permitted
	|work = Weights and Measures Standards of the United States: A brief history
	|first1 = Louis E.
	|last1 = Barbrow
	|first2 = Lewis V.
	|last2 = Judson
	|publisher = NIST
	|year = 1976
	|accessdate = 2011-05-19}}</ref> By 1893, the reference standards for customary units had become unreliable. Moreover, the United States, being a signatory of the Metre Convention was in possession of national prototype metres and kilograms that were calibrated against those in use elsewhere in the world. This led to the ] which redefined the customary units by referring to the national metric prototypes, but used the conversion factors of the 1866 act.<ref>{{cite web
	|url = http://physics.nist.gov/Pubs/SP447/sec07.pdf
	|title = The Mendenhall Order
	|work = Weights and Measures Standards of the United States: A brief history
	|first1 = Louis E.
	|last1 = Barbrow
	|first2 = Lewis V.
	|last2 = Judson
	|publisher = NIST
	|year = 1976
	|accessdate = 2011-05-19}}</ref> In 1896 a bill that would make the metric system mandatory in the United States was presented to Congress. Of the 29 people who gave evidence before the congressional committee who were considering the bill, 23 were in favour of the bill, but six were against. Four of the six dissenters represented manufacturing interests and the other two the United States Revenue service. The grounds cited were the cost and inconvenience of the change-over. Subsequent bills suffered a similar fate.<ref name=PopularScience/>
	==Development of a coherent metric system==
	From its inception, the metric system was designed in such a manner that the various units of measure were linked to each other. At the start of the nineteenth century, length, mass and temperature were the only base units that had been standardised. The beginnings of a coherent system were in place with the units of area and volume linked to the unit of length, though at the time science did not understand the concepts of base units and derived units, nor how many physical quantities were inter-related.
	===Time, work and energy===
	In 1832 ] made the first absolute measurements of the ] using a decimal system based using the millimetre, gram, and second as the units of measure for length, mass, and time respectively, thereby implicitly making time a base dimension of the metric system.<ref name=SIbrochureHistory>{{SIbrochure8th|page=109}}</ref>
	] was transferred to the water, heating it up.]]
	In a paper published in 1843, ] first demonstrated a means of measuring the ] transferred between different systems when work is done thereby relating ]'s ], defined in 1824, to ].<ref>{{cite web
	|url = http://www.sussex.ac.uk/chemistry/documents/a_thermodynamics_history.pdf
	|title = A Very Brief History of Thermodynamics
	|author = John Murrell
	|publisher = Chemistry Department, ]
	|accessdate = 2011-03-10}}</ref> Energy became the unifying concept of nineteenth century ],<ref>{{cite journal
	|journal = Current Science
	|volume = 100
	|issue = 4
	|date = 25 February 2011
	|url = http://www.currentscience.ac.in/Volumes/100/04/0563.pdf
	|title = How the electric telegraph shaped electromagnetism
	|author = Kapil Subramanian
	|accessdate = 2011-05-12}}</ref> initially by bringing ] and ] together and ] and ultimately ] leading to ] equation <math>E = mc^2</math>. The CGS unit of energy was the "]", but the SI unit of energy was named the "]" in honour of Joule.
	In 1861 a committee of the ] (BAAS) including ], ] and Joule among its members was tasked with investigating the "Standards of Electrical Resistance". 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
	|url = http://www.archive.org/stream/reportscommitte00maxwgoog
	|chapter = First Report – Cambridge 3 October 1862
	|pages = 1–3
	|first1 = William
	|last1 =Thomson
	|first2 =James Prescott
	|last2 =Joule
	|first3 = James Clerk
	|last3 =Maxwell
	|first4 =Flemming
	|last4 =Jenkin
	|editor1-first = Flemming
	|editor1-last =Jenkin
	|location = London
	|year =1873
	|accessdate = 2011-05-12}}</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
	|url = http://www.archive.org/stream/reportscommitte00maxwgoog
	|chapter = Second report - Newcastle-upon-Tyne 26 August 1863
	|pages = 39–41
	|first1 = William
	|last1 =Thomson
	|first2 =James Prescott
	|last2 =Joule
	|first3 = James Clerk
	|last3 =Maxwell
	|first4 =Flemming
	|last4 =Jenkin
	|editor1-first = Flemming
	|editor1-last =Jenkin
	|location = London
	|year =1873
	|accessdate = 2011-05-12}}</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 '']''). All other units of measure could be derived (hence '']'') 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
	|author = J C Maxwell
	|year = 1873
	|publisher = Clarenden Press
	|location = Oxford
	|url = http://www.archive.org/details/electricandmagne01maxwrich
	|pages = 1–3
	|accessdate = 2011-05-12}}</ref><ref name=Maxwell2>{{cite book
	|title = A treatise on electricity and magnetism
	|volume = 2
	|author = J C Maxwell
	|year = 1873
	|publisher = Clarenden Press
	|location = Oxford
	|url = http://www.archive.org/stream/electricandmag02maxwrich
	|pages = 242–245
	|accessdate = 2011-05-12}}</ref>
	In 1873, another committee of the BAAS that also counted Maxwell and Thomson among its members and tasked with "the Selection and Nomenclature of Dynamical and Electrical Units" recommended using the ]. The committee also recommended the names of "]" and "]" for the CGS units of force and energy.<ref name=Maxwell2/><ref>{{cite journal
	|journal = Report on the Forty-third Meeting of the British Association for the Advancement of Science held at Bradford in September 1873
	|year = 1874
	|title = First Report of the Committee for the Selection and Nomenclature of Dynamical and Electrical Units
	|editor = Professor Everett
	|publisher = British Association for the Advancement of Science
	|pages= 222–225
	|url = http://www.biodiversitylibrary.org/item/94452
	|accessdate = 2011-05-10}}</ref><ref>{{cite web
	|url = http://www.sizes.com/units/sys_cgs.htm
	|title = centimeter-gram-second systems of units
	|work = Sizes, Inc
	|date = 6 August 2001
	|accessdate = 2011-04-07}}</ref> The CGS system became the basis for scientific work for the next seventy years.
	===Electrical units===
	In the 1820s ] formulated ] which can be extended to relate power to current, potential difference (voltage) and resistance. During the following decades the realisation of a coherent system of units that incorporated the measurement of electromagnetic phenomena and Ohm's law was beset with problems - at least four different systems of units were devised. In the three CGS systems, the constants <math>k_e</math> and <math>k_m</math> and consequently <math>\epsilon_0</math> and <math>\mu_0</math> were dimensionless.
	{| class="infobox bordered" style="font-size: 95%;"
	|- style="border-bottom-width=0; background:lightyellow;"
	|-		|-
			! Symbols
	|- align="center"
			! Meaning
	|'''Symbols used in this section'''
	{| class="wikitable"
	|-		|-
			| style="text-align:center;" |<math>F_\text{m}, F_\text{e}</math>
	!Symbol
			|electromagnetic and electrostatic forces
	!Meaning
	|-		|-
			| style="text-align:center;" |<math>I_\text{1}, I_\text{2}</math>
	|- align="center"
			|electric currents in conductors
	|<math>F_\mathrm{m}, F_\mathrm{e}</math>
	|Electromagnetic<br>and<br>Electrostatic<br>forces
	|-		|-
			| style="text-align:center;" |<math>q_\text{1}, q_\text{2}</math>
	|- align="center"
			|electrical charges
	|<math>I_\mathrm{1}, I_\mathrm{2}</math>
	|Electrical current<br>in conductors
	|-		|-
	|- align="center"		| style="text-align:center;" |<math>L</math>
			|conductor length
	|<math>q_\mathrm{1}, q_\mathrm{2}</math>
	|Electrical charges
	|-		|-
	|- align="center"		| style="text-align:center;" |<math>r</math>
			|distance between charges/conductors
	|<math>L</math>
	|Conductor length
	|-		|-
	|- align="center"		| style="text-align:center;" |<math>\epsilon_0</math>
			|]<ref group="Note" name="foo">The electric constant, termed the ''permittivity'' of free space (vacuum, such as might be found in a vacuum tube) is a physical electric constant with the unit farad per metre that represents the ability of vacuum to support an electric field. <br/>The magnetic constant termed the ''permeability'' of free space is a physical magnetic constant with units henries/metre that represents the ability of vacuum to support a magnetic field. <br/>Iron, for example, has both high permittivity because it readily conducts electricity and high permeability because it makes a good magnet. vacuum does not "conduct" electricity very well, nor can it be easily "magnetised", so the electric and magnetic constants of vacuum are tiny.</ref>
	|<math>r</math>
	|distance between <br>charges/conductors
	|-		|-
	|- align="center"		| style="text-align:center;" |<math>\mu_0</math>
			|]<ref group=Note name=foo/>
	|<math>\epsilon_0</math>
	|permittivity of<br>free space
	|-		|-
	|align="center"|<math>\mu_0</math>		| style="text-align:center;" |<math>k_\text{m}, k_\text{e}</math>
			|constants of proportionality
	|permeability of<br>free space
	|-		|-
	|- align="center"		| style="text-align:center;" |<math>c</math>
			|]<ref>A large constant, about 300,000,000 metres/second.</ref>
	|<math>k_\mathrm{m}, k_\mathrm{e}</math>
	|System of unit <br>dependant constants
	|-		|-
	|align="center"|<math>c</math>		| style="text-align:center;" |<math>4\pi</math>
			|] surrounding a point<ref group="Note">This factor appears in Maxwell's equations and represents the fact that electric and magnetic fields may be considered as point quantities that propagate equally in all directions, i.e. spherically</ref>
	|Speed of light
	|}		|-
			| style="text-align:center;" |<math>P</math>
			|electric power
			|-
			| style="text-align:center;" |<math>V</math>
			|electric potential
			|-
			| style="text-align:center;" |<math>I</math>
			|electric current
			|-
			| style="text-align:center;" |<math>E</math>
			|energy
			|-
			| style="text-align:center;" |<math>Q</math>
			|electric charge
			|-
			| style="text-align:center;" |<math>\mathsf{M, L, T}</math>
			|dimensions: mass, length, time
	|}		|}
			In the 1820s, ] formulated ], 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
			| last1 = Booth
			| publisher = Letts Educational
			| isbn = 184315-3025
			| location = London
			| year = 2003
			| at = Chapter 2 – Electricity
			}}</ref> During the following decades, the realisation of a coherent system of units that incorporated the measurement of electromagnetic phenomena and Ohm's law was beset with problems—several different systems of units were devised.
			In the three CGS systems, the constants <math>k_\text{e}</math> and <math>k_\text{m}</math> and consequently <math>\epsilon_0</math> and <math>\mu_0</math> were dimensionless, and thus did not require any units to define them.
	:<br>'''Electromagnetic system of units'''
	:In 1820s ] discovered a relationship between the force between two current-carrying conductors, now known as ] which can be written
	::<math> F_\mathrm{m} = 2 k_\mathrm{m} \frac {I_1 I_2 } {r}</math> where <math> k_\mathrm{m} = \frac {\mu_0}{ 4 \pi} \ </math> (SI units)
			The electrical units of measure did not easily fit into the coherent system of mechanical units defined by the BAAS. Using ], 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/>
	:In 1833 Gauss pointed out the possibility of equating this force with its mechanical equivalent. This proposal received further support from ] in 1851.<ref name=satellite>{{cite web
	|url = http://www.satellitetoday.com/via/The-International-System-of-Units_32466_p3.html
	|title = The International System of Units
	|publisher = Satellite Today
	|date = 1 February 2000
	|accessdate = 2011-04-05}}</ref> The ] was one of the two systems of units identified in the BAAS report of 1862 and defined in the refport of 1873. In this system, current is defined by setting the ] <math>k_\mathrm{m}</math> to unity and potential difference is defined in such a way as to ensure the unit of power calculated by the relation <math> P = VI</math> is identical to the unit of power required to move a mass of one gram a distance of one centimetre in one second when opposed by a force of one dyne. The electromagnetic units of measure were known as the abampere, the abvolt, the abcoulomb 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-"
	|author = Russ Rowlett
	|publisher = University of North Carolina at Chapel Hill
	|date = 4 December 2008
	|accessdate = 2011-05-12}}</ref>
	:'''Electrostatic system of units'''		==== Electromagnetic (absolute) system of units (EMU) ====
			The ] was developed from ]'s discovery in the 1820s of a relationship between currents in two conductors and the force between them now known as ]:
	:In 1783 Coulomb discovered and published the relationship between the force exerted between two charged bodies. This relationship, now known as ] can be written
	::<math>F_\mathrm{e} = k_\mathrm{e} \frac{q_1q_2}{r^2}</math> where <math>k_\mathrm{e} = \frac{1}{4 \pi \epsilon_0}</math> (SI units)		: <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 ] in 1851.<ref name="satellite">
	:The ] was the second of the two systems of units identified in the 1862 BAAS report and defined in the report of 1873. In this system unit for charge is defined by setting the ] (<math>k_\mathrm{e}</math>) to unity and the unit for potential difference were defined to ensure the unit of energy calculated by the relation <math> E = QV</math> is one erg. The electrostatic units of measure are now known as the statampere, the statvolt, the statcoulomb and so on.<ref>{{cite web
			{{cite web
	|url = http://www.unc.edu/~rowlett/units/dictA.html#stat
			| url = http://www.highbeam.com/doc/1G1-60048223.html
	|title = How Many? A Dictionary of Units of Measurement: "stat-"
			| archive-url = https://web.archive.org/web/20161018205901/https://www.highbeam.com/doc/1G1-60048223.html
	|author = Russ Rowlett
			| archive-date = 18 October 2016 <!--http://www.satellitetoday.com/via/The-International-System-of-Units_32466_p3.html-->
	|publisher = University of North Carolina at Chapel Hill
			| title = The International System of Units
	|date = 1 September 2004
			| publisher = Satellite Today
	|accessdate = 2011-05-12}}</ref>
			| date = 1 February 2000
			| access-date = 5 April 2011
			}}</ref> In this system, current is defined by setting the ] <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-"
			|author = Russ Rowlett
			|publisher = University of North Carolina at Chapel Hill
			|date = 4 December 2008
			|access-date = 12 May 2011
			|archive-date = 20 December 2008
			|archive-url = https://web.archive.org/web/20081220111445/http://www.unc.edu/~rowlett/units/dictA.html#ab
			}}</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
			|date = 9 June 2007
			|publisher = Sizes, Inc
			|access-date = 10 May 2011
			|archive-date = 9 October 2019
			|archive-url = https://web.archive.org/web/20191009124952/https://www.sizes.com/units/farad.htm
			|url-status = dead
			}}</ref>
	:'''Gaussian system of units'''		==== Electrostatic system of units (ESU) ====
			The ] was based on Coulomb's quantification in 1783 of the force acting between two charged bodies. This relationship, now known as ], can be written
	:In 1888 ] verified ] and in so doing realised that the CGS system of electromagnetic units to were related to the CGS system of electrostatic units by the relationship:
	::<math>c^2 = \frac{1}{\epsilon_0 \mu_0}</math><ref>{{cite web		: <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)
	|url = http://www.wbabin.net/science/danescu.pdf
	|title = The evolution of the Gaussian Units
	|author = Dan Petru Danescu
	|publisher = The general journal of science
	|date = 9 January 2009
	|accessdate = 2011-05-07}}</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
	|work = Physics 221A, Fall 2010, Appendix A
	|publisher = Department of Physics University of California
	|location = Berkeley
	|accessdate = 2011-05-07}}</ref>
	: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 ] and ]) and ESU units elsewhere. He named this combined set of units "]". This set of units has been recognised as being particularly useful in theoretical physics.{{SIBrochure8th|page 128}}
			In this system, the unit for charge is defined by setting the ] (<math>k_\text{e}</math>) to unity and the unit for electric potential was defined to ensure the unit of energy calculated by the relation <math> E = QV</math> is one erg. The electrostatic units of measure were the statampere, statvolt, and so on.<ref>
	:'''Practical system of units'''
			{{cite web
	:The CGS units of measure used in scientific work were not practical when used in engineering leading to the development of the practical system of electric units. At the time that this system of units was proposed, the dimensions of electrical resistance was modelled as the ratio of length to time (ie a velocity). The most practical unit for resistance was multiples of {{nowrap|10<sup>8</sup> m/s}} - the base unit of length was the length of the Earth's quadrant, the base unit of time the second and the base unit of mass was {{nowrap|10<sup>-11</sup> g}}, the latter having been chosen to allow conversion back to the CGS system.<ref name=Maxwell2/> The names, but not the values, ], ], ] and ] were carried over from the CGS system. The system was adopted at the International Electrical Congress (IEC) in 1881.<ref>{{cite web
	|url = http://physics.nist.gov/cuu/Units/history.html		|url = http://www.unc.edu/~rowlett/units/dictA.html#stat
	|title = A brief history of SI		|title = How Many? A Dictionary of Units of Measurement: "stat-"
			|author = Russ Rowlett
	|publisher = NIST
			|publisher = University of North Carolina at Chapel Hill
	|accessdate = 2011-03-29}}</ref> This system was formalised as the ] at the 1893 congress of the IEC in Chicago where the volt, amp and ohm were formally defined. The SI units with these names are very close, but not identical to the "practical units".
			|date = 1 September 2004
			|access-date = 12 May 2011
			|archive-date = 20 December 2008
			|archive-url = https://web.archive.org/web/20081220111445/http://www.unc.edu/~rowlett/units/dictA.html#stat
			}}</ref>
	===A coherent system===		==== Gaussian system of units ====
			The ] was based on ]'s realisation,{{citation needed|date=January 2018}} while verifying ] in 1888, that the electromagnetic and electrostatic units were related by:
	The electrical units of measure did not easily fit into the coherent system using length, mass and time as its base units as proposed in the 1861 BAAS paper. Using ] the dimensions of charge as defined by the ESU system of units was identical to the dimensions of current as defined by the EMU system of units <math>M^\frac{1}{2}L^\frac{3}{2}T^{-1}</math> while resistance had the same dimensions as velocity in the EMU system of units, but had the dimensions of the inverse of velocity in the ESU system of units.<ref name=Maxwell2/>
			: <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
			|author = Dan Petru Danescu
			|publisher = The general journal of science
			|date = 9 January 2009
			|access-date = 7 May 2011
			|archive-url = https://web.archive.org/web/20120312010853/http://www.wbabin.net/science/danescu.pdf
			|archive-date = 12 March 2012
			}}</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
			| work = Physics 221A, Fall 2010, Appendix A
			| publisher = Department of Physics University of California
			| location = Berkeley
			| access-date = 7 May 2011
			}}</ref>
			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 ] and ]) and ESU units elsewhere. He named this combined set of units "]". This set of units has been recognised as being particularly useful in theoretical physics.<ref name=SIBrochure/>{{rp|128}}
			==== Quadrant–eleventhgram–second (QES) or International system of units <span class="anchor" id="Quad–eleventhgram–second"></span><span class="anchor" id="QES"></span><span class="anchor" id="International system of units"></span> ====
			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>&nbsp;m (the ], nominally the ]), the unit of mass was an unnamed unit equal to 10<sup>−11</sup>&nbsp;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
			|volume = XV
			|number = 67
			|date = January 1981
			|publisher = ]
			|location = Geneva
			|url = http://www.iec.ch/about/history/documents/pdf/75th%20anniversary%20IEC%20Bulletin.pdf
			|access-date = 23 October 2013
			|archive-date = 30 October 2012
			|archive-url = https://web.archive.org/web/20121030084345/http://www.iec.ch/about/history/documents/pdf/75th%20anniversary%20IEC%20Bulletin.pdf
			|url-status = dead
			}}</ref> The system was formalised as the ] 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
			| last1 = McGreevy
			| first2 = Peter
			| last2 = Cunningham
			| year = 1995
			| isbn = 978-0-948251-82-5
			| quote = (pg 140) The originator of the metric system might be said to be Gabriel Mouton.
			| publisher = Picton Publishing (Chippenham) Ltd
			}}</ref>{{rp|155–156}}
			==== Heaviside–Lorentz system of units ====
	From mid 1890s onwards ] and ] corresponded with each other regarding these anomalous results.<ref name=IECGiorgi>{{cite web
			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.
	|url = http://www.iec.ch/about/history/beginning/giovanni_giorgi.htm
	|title = In the beginning... Giovanni Giorgi
	|year = 2011
	|publisher = ]
	|accessdate = 2011-04-05}}</ref> This led to Giorgi presenting a paper to the congress of the Associazione Elettrotecnica Italiana (A.E.I.)<ref>] (in Italian)</ref> in October 1901 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 (ampere, volt or ohm) to the three base units proposed in the 1861 BAAS report. This gave the constants ''k<sub>e</sub>'' and ''k<sub>m</sub>'' physical dimensions and hence the electrco-mechanical quantities ε<sub>0</sub> and µ<sub>0</sub> were also given physical dimensions.<ref name=IECGiorgi/>
			=== Thermodynamics ===
	It took more than thirty years before Giorgi's work was accepted in practice by international organisations and nearly another thirty years before they were incorporated as the basis of the ''Système International d'Unités'' (International System of Units), the SI.
			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-date = 1939
			| 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
			| author = Thomas W. Leland
			| editor = G.A. Mansoori
			| publisher = Department of Chemical Engineering, University of Illinois at Chicago
			| access-date = 10 May 2011
			}}</ref>
			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.
	===Naming the units of measure===
	In 1861, ] and ] proposed the names of ], ], and ] in honour of ], ] and ] respectively for the practical units based on the centimetre-gramme-second 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
	|author =Silvanus P. Thompson
	|publisher =International Electrotechnical Commission
	|accessdate = 2011-05-10}}</ref> These names were later scaled for use in the Practical System.<ref>{{cite web
	|url = http://www.sizes.com/units/farad.htm
	|title = farad
	|date = 9 June 2007
	|publisher = Sizes, Inc
	|accessdate = 2011-05-10}}</ref> The concept of naming units of measure after noteworthy scientists was subsequently used for other units.
	==Convention of the metre==		== Convention of the metre ==
	{{main|Metre Convention}}		{{main|Metre Convention}}
	] (BIPM)]]		] (BIPM)]]
	With increasing international adoption of the metre, the short-comings 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 meridianal definition, which had been intended to ensure international reproducibility, quickly proved so impractical that is was all but abandoned in favour of the artifact 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>{{LarousseXIXe| article = Mètre | volume = 17 | page = 1587}}.</ref>		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>
			{{cite LarousseXIXe
			| title = Mètre
			| volume = 17
			| page = 1587
			}}</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">
	The International Conference on Geodesy in 1867 called for the creation of a new, international prototype metre<ref name="MComm"/><ref name="BIPMhist"/><ref>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.</ref> and to arrange 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.<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
			| publisher = International Bureau of Weights and Measures
			| access-date = 15 August 2010
			| archive-url = https://web.archive.org/web/20110607152538/http://www1.bipm.org/en/si/history-si/evolution_metre.html
			| archive-date = 7 June 2011
			}}</ref> The International Conference on Geodesy in 1867 called for the creation of a new ]<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 ''Convention du Mètre'' (]) was signed by 17 states.<ref name="Nelson"/><ref>Text of the treaty: {{cite web		On 20 May 1875, an international treaty known as the ] (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		| url = http://www.bipm.org/utils/en/pdf/metre_convention.pdf
	|title = Convention du mètre		| title = Convention du mètre
	|language = French		| language = fr
			| access-date = 8 March 2011
	|accessdate = 2011-03-08}}</ref> This treaty established the following organisations to conduct international activities relating to a uniform system for measurements:
			}}</ref> This treaty established the following organisations to conduct international activities relating to a uniform system for measurements:
	]
	:*] (CGPM), an intergovernmental conference of official delegates of member nations and the supreme authority for all actions;		:* '']'' (CGPM or General Conference on Weights and Measures), an intergovernmental conference of official delegates of member nations and the supreme authority for all actions;
	:*] (CIPM), consisting of selected scientists and ]s, which prepares and executes the decisions of the CGPM and is responsible for the supervision of the International Bureau of Weights and Measures;		:* '']'' (CIPM or International Committee for Weights and Measures), consisting of selected scientists and ]s, which prepares and executes the decisions of the CGPM and is responsible for the supervision of the International Bureau of Weights and Measures;
	:*] (BIPM), 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.		:* '']'' (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 metres and kilograms were both made from a 90%&nbsp;], 10%&nbsp;] alloy which is exceptionally hard and which has good electrical and thermal conductivity properties. The prototype had a special X-shaped (]) 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 ] delivered 30 prototype metres and 40 prototype kilograms. At the first meeting of the ] in 1889 bar No.&nbsp;6 and cylinder No.&nbsp;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>{{cite journal		The ] and ] were both made from a 90%&nbsp;], 10%&nbsp;] alloy which is exceptionally hard and which has good electrical and thermal conductivity properties. The prototype had a special X-shaped (]) 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 ] delivered 30 prototype metres and 40 prototype kilograms. At the first meeting of the ] in 1889, bar No.&nbsp;6 and cylinder No.&nbsp;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		|last1 = Jabbour
	|first1= Z.J.		|first1 = Z.J.
	|last2= Yaniv		|last2 = Yaniv
	|first2= S.L.		|first2 = S.L.
	|year= 2001		|year = 2001
	|title= The Kilogram and Measurements of Mass and Force		|title = The Kilogram and Measurements of Mass and Force
	|journal= J. Res. Natl. Inst. Stand. Technol.		|journal = J. Res. Natl. Inst. Stand. Technol.
	|volume= 106		|volume = 106
	|issue= 1		|issue = 1
	|pages= 25–46		|pages = 25–46
	|publisher= ] (NIST		|publisher = ] (NIST
	|url= http://nvl.nist.gov/pub/nistpubs/jres/106/1/j61jab.pdf		|url = http://nvl.nist.gov/pub/nistpubs/jres/106/1/j61jab.pdf
			|access-date = 28 March 2011
	|accessdate= 2011-03-28}}</ref>
			|doi = 10.6028/jres.106.003
			|pmid = 27500016
			|pmc = 4865288
			|archive-url = https://web.archive.org/web/20110604144310/http://nvl.nist.gov/pub/nistpubs/jres/106/1/j61jab.pdf
			|archive-date = 4 June 2011
			}}</ref>
			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.
	==Twentieth century==
			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 ], not of ]. 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 ].<ref>
	At the beginning of the twentieth century, the BIPM had custody of two artifacts - one to define length and the other to define mass. Other units of measure which did not rely on specific artifacts were controlled by other bodies. In the scientific world, quantum theory was in its infancy and ] had yet to publish his theories of relativity. By the end of the century, a coherent system of units was in place under the control of the bodies set up by the ], the definition of the second relied on quantum theory, the definition of the metre relied on the theory of relativity and plans were being made to relegate the international prototype kilogram to the archives.
			{{cite journal
			|url = http://www.platinummetalsreview.com/pdf/pmr-v17-i2-066-068.pdf
			|title = Standard Kilogram Weights – A Story of Precision Fabrication
			|journal = Platinum Metals Review
			|author = F. J. Smith
			|year = 1973
			|volume = 17
			|issue = 2
			|pages = 66–68
			|doi = 10.1595/003214073X1726668
			|s2cid = 267431184
			|access-date = 11 May 2011
			|archive-date = 9 June 2011
			|archive-url = https://web.archive.org/web/20110609194754/http://www.platinummetalsreview.com/pdf/pmr-v17-i2-066-068.pdf
			|url-status = dead
			}}</ref>
			In 1921, the Treaty of the Metre was extended to cover electrical units, with the CGPM merging its work with that of the IEC.
	===Metre===
	The first (and only) follow-up comparison of the national standards with the international prototype 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&nbsp;µm.<ref name="Barrell">{{citation
	| first = H.
	| last = Barrel
	| title = The Metre
	| journal = Contemp. Phys.
	| year = 1962
	| volume = 3
	| issue = 6
	| pages = 415–34
	| 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 definition of melting ice, but in 1927 the 7th&nbsp;CGPM extended this definition was 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&nbsp;mm from each other".<ref name="oldSI">{{SIbrochure8th|pages=142–43, 148}}.</ref> The choice of 571&nbsp;mm represents the ] of the prototype—the points at which the bending or droop of the bar is minimized.<ref>{{citation
	| last = Phelps
	| first = F. M., III
	| year = 1966
	| title = Airy Points of a Meter Bar
	| journal = Am. J. Phys.
	| volume = 34
	| issue = 5
	| pages = 419–22
	| doi = 10.1119/1.1973011
	| bibcode=1966AmJPh..34..419P}}.</ref>
			== Measurement systems before World War II ==
	In 1887 ] proposed the use of optical interferometers for the measurement of length, work which contributed to him being awarded the ] in 1907. In 1952 the CIPM proposed the use of wavelength of a specific light source as the standard for defining length and in 1960 the CGPM accepted this proposal using radiation corresponding to a transition between specified energy levels of the krypton 86 atom as the new standard for the metre. By 1975, when the second had been defined in terms of a physical phenomena rather than the earth's rotation and Einstein's assertion that the ] was constant, 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
			] and one of the lines]]
	|url = http://physics.nist.gov/cuu/Units/meter.html
			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.
	|title = Base unit definitions: Meter
	|publisher = ]
	|accessdate = 2011-11-15}}</ref>
	===Kilogram===		=== 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 ] 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">
	]: K32 and K8(41).<ref group="Note">Prototype No. 8(41) was accidentally stamped with the number 41, but its accessories carry the proper number 8. Since there is no prototype marked 8, this prototype is referred to as 8(41).<sub>{{nbsp}}</sub></ref> The above are all ''relative'' measurements; no historical mass-measurement data is available to determine which of the prototypes has been most stable relative to an invariant of nature. There is the distinct possibility that ''all'' the prototypes gained mass over 100 years and that K21, K35, K40, and the IPK simply ''gained less'' than the others.]]
			{{cite web
			|url = http://www.iec.ch/about/history/beginning/giovanni_giorgi.htm
			|title = Historical figures&nbsp;... Giovanni Giorgi
			|year = 2011
			|publisher = ]
			|access-date = 5 April 2011
			|archive-date = 15 May 2011
			|archive-url = https://web.archive.org/web/20110515134553/http://www.iec.ch/about/history/beginning/giovanni_giorgi.htm
			}}</ref> His work also recognised the relevance of energy in the establishment of a coherent, rational system of units, with the ] 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 ===
	Although the definition of the kilogram remained unchanged throughout the twentieth century, the 3rd CGPM in 1901 clarified that the kilogram was a unit of ], not of ]. 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 ].<ref>{{cite journal
			] calibrated in ], a ] calibrated in ], a ] weight (mass) and an electrical ] which measures ], ] and ]s]]
	|url = http://www.platinummetalsreview.com/pdf/pmr-v17-i2-066-068.pdf
	|title = Standard Kilogram Weights - A Story of Precision Fabrication
	|journal = Platinum Metals Review
	|author = F. J. Smith
	|year = 1973
	|volume= 17
	|issue = 2
	|pages = 66–68}}</ref>
			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.
	During the course of the century, the various national prototypes of the kilogram were recalibrated against the international prototype and therefore against each other. The initial 1889 starting-value offsets of the national prototypes relative to the IPK were nulled.<ref name="Girard">{{Cite journal |title=The Third Periodic Verification of National Prototypes of the Kilogram (1988–1992) |author=G.{{nbsp}}Girard |journal=Metrologia |volume=31 |issue=4 |year=1994 |pages=317–336 |doi=10.1088/0026-1394/31/4/007|bibcode = 1994Metro..31..317G }}</ref> and any subsequent mass changes being relative to the IPK. A technique for steam cleaning the prototypes to remove any contaminants was developed in 1946 as part of the second recalibration.<ref>{{cite web
	|url = http://www.bipm.org/utils/en/pdf/Monographie1990-1-EN.pdf
	|title = Le nettoyage-lavage des prototypes du kilogramme au BIPM - The washing and cleaning of kilogram prototypes at the BIPM
	|author = G.Girard
	|date = October 1990
	|publisher = Bureau International des poids et mesures
	|accessdate = 2011-04-02}}</ref>
			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 ] 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&nbsp;μm.<ref name="Barrell">
	The third periodic recalibration in 1988-9 revealed that the average difference between International Prototype Kilogram and adjusted baseline for the national prototypes was 50&nbsp;μg - in 1889 the baseline of the national prototypes had been adjusted so that the difference was zero. As the IPK is the definitive kilogram, there is no way of telling whether the IPK had been losing mass or the national prototypes had been gaining mass.
			{{citation
			| first = H.
			| last = Barrel
			| title = The Metre
			| journal = Contemp. Phys.
			| year = 1962
			| volume = 3
			| issue = 6
			| pages = 415–34
			| 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&nbsp;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&nbsp;mm from each other".<ref name=SIBrochure/>{{rp|142–43,148}} The choice of 571&nbsp;mm represents the ] of the prototype—the points at which the bending or droop of the bar is minimised.<ref>
			{{citation
			| last = Phelps
			| first = F. M. III
			| year = 1966
			| title = Airy Points of a Meter Bar
			| journal = Am. J. Phys.
			| volume = 34
			| issue = 5
			| pages = 419–22
			| doi = 10.1119/1.1973011
			| bibcode = 1966AmJPh..34..419P
			}}</ref>
			== Working draft of SI: ''Practical system of units'' ==
	===Time===
			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>
	Until the advent of the atomic clock, the most reliable timekeeper available to mankind was the earth's rotation. It was natural therefore that the astronomers under the auspice of the International Astronomical Union (IAU) took the lead in maintaining the standards relating to time.<ref name=satellite/> During the twentieth 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
			{{cite conference
	|url = http://tycho.usno.navy.mil/leapsec.html
			| url = http://www.bipm.org/en/CGPM/db/9/6/
	|title = Leap seconds
			| title = Resolution 6 – Proposal for establishing a practical system of units of measurement
	|publisher = Time Service Department, U.S. Naval Observatory
			| conference = 9th Conférence Générale des Poids et Mesures (CGPM)
	|accessdate = 2011-04-29}}</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&nbsp;BC.<ref>{{cite journal
			| date = 12–21 October 1948
	|url = http://hbar.phys.msu.ru/gorm/atext/histecl.htm
			| access-date = 8 May 2011
	|journal = Scientific American
			}}</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.
	|volume = 247
	|issue = 4
	|pages = 154–163
	|author = F. Richard Stephenson
	|title = Historical Eclipses
	|year = 1982
	|accessdate = 2011-04-18|bibcode = 1982SciAm.247..154S }}</ref>
			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>
	In 1956 the 10th CGPM instructed the CIPM to prepare a definition of the second; in 1958 the definition was published stating that the second would be calculated by extrapolation using earth's rotational speed in 1900.<ref name=LeapSeconds/> Astronomers from the ] (USNO) and the ] determined a relationship between the frequency of radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom and the estimated rate of rotation of the earth in 1900. Their value was adopted in 1968 by the 13th CGPM.
			{{cite conference
			| url = http://www.bipm.org/en/CGPM/db/10/6/
			| title = Resolution 6 – Practical system of units
			| conference = 10th Conférence Générale des Poids et Mesures (CGPM)
			| 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 ] and ] 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
			| conference = 9th Conférence Générale des Poids et Mesures (CGPM)
			| date = 12–21 October 1948
			| access-date = 27 November 2022
			}}</ref>
	===Electrical units===		=== Time ===
			Until the advent of the ], the most reliable timekeeper available to humanity was the Earth's rotation. It was natural, therefore, that the astronomers under the auspices of the ] (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">
	] calibrated in ], a ] calibrated in ], a ] weight (mass) and an electrical ] which measures ], ] and ]s.]]
			{{cite web
	In 1921 the Treaty of the Metre was extended to cover electrical units with the CGPM merging its work with that of the IEC. 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 proposal be adopted was accepted, but no decision was made as to which electrical unit should be the fourth base unit. In 1935 Sears proposed that this should be the ampere, but ] prevented this being formalised until 1946. The definitions for absolute electrical system became effective from 1 January 1948.<ref name=satellite/>
			| url = http://tycho.usno.navy.mil/leapsec.html
			| title = Leap seconds
			| publisher = Time Service Department, U.S. Naval Observatory
			| access-date = 29 April 2011
			| 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&nbsp;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
			| archive-date = 15 January 2019
			| journal = Scientific American
			| volume = 247
			| issue = 4
			| pages = 154–163
			| author = F. Richard Stephenson
			| title = Historical Eclipses
			| year = 1982
			| access-date = 18 April 2011
			| bibcode = 1982SciAm.247d.154S
			}}</ref> In 1956, the 10th CGPM instructed the CIPM to prepare a definition of the second; in 1958, the definition was published stating that the second (called an ''ephemeris'' second) would be calculated by extrapolation using Earth's rotational speed in 1900.<ref name=LeapSeconds/>
	===Temperature===		=== 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">
	At the start of the twentieth century, the fundamental macroscopic laws of thermodynamics had been formulated and although techniques existed to measure temperature using empirical techniques, the scientific understanding of the nature of temperature was minimal. Maxwell and Boltzmann had produced theories describing the inter-relational of temperature, pressure and volume of a gas on a microscopic scale but otherwise, in 1900, there was no understanding of the microscopic or quantum nature of temperature.<ref name=Pledge>{{cite book
			{{cite book
	|title = Science since 1500
			| title = Dictionary of Weights, Measures and Units
	|author = H.T.Pledge
			| url = https://archive.org/details/dictionaryofweig0000fenn
	|origyear = 1939
			| url-access = registration
	|year = 1959
			| first1 = Donald
	|chapter = Chapter XXI: Quantum Theory
			| last1 = Fenna
	|pages = 271–275
	|publisher = Harper Torchbooks}}</ref><ref>{{cite web		| publisher = ]
			| location = Oxford
	|url = http://www.uic.edu/labs/trl/1.OnlineMaterials/BasicPrinciplesByTWLeland.pdf
			| year = 2002
	|title = Basic Principles of Classical and Statistical Thermodynamics
			| isbn = 978-0-19-860522-5
	|author = Thomas W. Leland
			}}</ref> The definitions for the absolute electrical system,{{clarify|date=January 2020}} based on the ampere, were formalised in 1948.<ref>
	|editor = G.A. Mansoori
			{{cite book
	|publisher = Department of Chemical Engineering, University of Illinois at Chicago
			| series = ''La metrologia ai confini tra fisica e tecnologia'' (Metrology at the Frontiers of Physics and Technology)
	|accessdate = 2011-05-10}}</ref> Within the metric system, temperature was expressed in degrees Centigrade with the definition that ice melted at 0&nbsp;°C and at standard atmospheric pressure, water boiled at 100&nbsp;°C. A series of lookup tables defined temperature in terms of inter-related empirical measurements made using various devices.
			| title = The continuing evolution in the definitions and realisations of the SI units of measurement
			| first1 = B.W.
			| last1 = Pretley
			| editor-first1 = L
			| editor-last1 = Crovini
			| editor-first2 = T.J
			| editor-last2 = Quinn
			| publisher = Societa Italiana di Fisica
			| location = Bologna
			| 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
			| publisher = NIST
			| access-date = 29 March 2011
			}}</ref>
			=== Temperature ===
	When, in 1948 the CGPM was charged with producing a coherent system of units of measure, definitions relating to temperature had to be clarified. At the 9th CGPM, the centigrade temperature scale was renamed the celsius temperature scale and the scale itself was fixed by defining the triple point of water as 0.01&nbsp;°C,<ref name=CGPM_9_3>{{cite conference
			In the Celsius scale from the 18th century, temperature was expressed in degrees Celsius with the definition that ice melted at 0&nbsp;°C and (at standard atmospheric pressure) water boiled at 100&nbsp;°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 ] (CGPM) recommended that the degree Celsius, as used for the measurement of temperature, be renamed the ].)<ref>
	|url = http://www.bipm.org/en/CGPM/db/9/3/
			{{cite web
	|title = Resolution 3 - Triple point of water; thermodynamic scale with a single fixed point; unit of quantity of heat (joule)
			| url = http://www.bipm.org/en/committees/cipm/cipm-1948.html
	|conference = 9th Conférence Générale des Poids et Mesures (CGPM)
	|date = 12–21 October 1948		| title = CIPM, 1948 and 9th CGPM, 1948
			| access-date = 8 February 2011
	|accessdate = 2011-05-08}}</ref> though the CGPM left the formal definition of absolute zero until the 10th GCPM when the name "degrees Kelvin" was assigned to the absolute temperature scale and triple point of water was defined as being 273.16&nbsp;°K.<ref>{{cite conference
			| publisher = ] (BIPM)
	|url = http://www.bipm.org/jsp/en/ListCGPMResolution.jsp?CGPM=13
			}}</ref>
	|title = Resolution 3 - Definition of the thermodynamic temperature scale and
	|conference = 10th Conférence Générale des Poids et Mesures (CGPM)
	|date = 5–14 October 1954
	|accessdate = 2011-05-08}}</ref> In 1967, at the 13th GCPM the degree Kelvin (°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)
	|conference = 9th Conférence Générale des Poids et Mesures (CGPM)
	|date = 12–21 October 1948
	|accessdate = 2011-05-08}}</ref>
			At the 9th CGPM, the Celsius temperature scale was renamed the ] scale, and the scale itself was fixed by defining the ] as 0.01&nbsp;°C,<ref name="CGPM_9_3">
	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
			{{cite conference
	|url = http://www.bipm.org/utils/common/pdf/its-90/ITS-90_Techniques.pdf
			| url = http://www.bipm.org/en/CGPM/db/9/3/
	|title = Techniques for Approximating the International Temperature Scale of 1990
			| title = Resolution 3 – Triple point of water; thermodynamic scale with a single fixed point; unit of quantity of heat (joule)
	|publisher = ]
			| conference = 9th Conférence Générale des Poids et Mesures (CGPM)
	|location = Sèvres
			| date = 12–21 October 1948
	|year = 1997
			| access-date = 8 May 2011
	|origyear = 1990
	|accessdate = 2011-05-10}}</ref> Increasingly the use of the Boltzmann Relationship was used as the reference point and it appears likely that in 2015 the CGPM will redefine temperature in terms of the Boltzmann constant rather than the triple point of water.<ref name="draft"/>		}}</ref> though the CGPM left the formal definition of absolute zero until the 10th CGPM when the name "]" was assigned to the absolute temperature scale, and the triple point of water was defined as being {{not a typo|273.16&nbsp;°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
			| conference = 10th Conférence Générale des Poids et Mesures (CGPM)
			| date = 5–14 October 1954
			| access-date = 8 May 2011
			}}</ref>
	===Luminosity===		=== Luminosity ===
	Prior to 1937, the ] (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 ] (cd) which was defined as "the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per ]".<ref>{{cite book | title = The Metric System: The International System of Units (SI) | author = Barry N. Taylor | publisher = U. S. Department of Commerce | year = 1992 | isbn = 0-941375-74-9 | page = 18 | url = http://books.google.com/books?id=y2-BDaoBVnwC&pg=PA18&dq=%22value+of+the+new+candle+is+such+that+the+brightness+of+the+full+radiator%22&as_brr=3&ei=elatR_S1FofgswPvu430BQ&sig=yl2AU7A-R1O9e5ZuEzuLwekiM2E }} (NIST Special Publication 330, 1991 ed.)</ref> was ratified by the GCPM in 1948 and in 1960 was adopted as an SI base unit. The definition proved difficult to implement so in 1967, the definition was revised and the reference to the radiation source was replaced by defining the candles in terms of the power of a specified wavelength of visible light.<ref>{{SIBrochure8th|page 115}}</ref>
			Before 1937, the ] (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 ] (cd), which was defined as "the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per ]",<ref>
	In 2007 the CIPM and the CIE agreed a program of cooperation with the CIPM taking the lead in defining the use of units of measure and the CIE taking the lead in defining the behaviour of the human eye.<ref>{{cite web
			{{cite book
	|url =http://www.bipm.org/en/bipm/mou/cie.html
			| title = The Metric System: The International System of Units (SI)
	|title = Agreement with the CIE
			| author = Barry N. Taylor
	|publisher = BIPM
			| publisher = U. S. Department of Commerce
	|accessdate = 2011-05-10}}</ref>
			| year = 1992
			| isbn = 978-0-941375-74-0
			| page = 18
			| url = https://books.google.com/books?id=y2-BDaoBVnwC&q=%22value+of+the+new+candle+is+such+that+the+brightness+of+the+full+radiator%22&pg=PA18
			}} (NIST Special Publication 330, 1991 ed.)</ref> was ratified by the CGPM in 1948.
	===Mole===		=== Derived units ===
	The mole was originally known as a gram-atom or a gram-molecule - the amount of a substance measured in grams divided by its ]. Originally chemists and physicists had differing views regarding the definition of the atomic weight - both assigned a value of 16&nbsp;] (amu) to oxygen, but physicists defined oxygen in terms of the <sup>16</sup>O isotope whereas chemists assigned 16&nbsp;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 ]<ref>{{cite web
	|url = http://www.physics.umanitoba.ca/IUPAP/C2role.html
	|title = Role of the SUNAMCO Commission
	|publisher = ]
	|accessdate = 2011-05-10}}</ref> (IUPAP) and the ] (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>{{SIBrochure8th|pp 114 - 115}}</ref>
			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}}
	'']]
	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
	|conference = 9th Conférence Générale des Poids et Mesures (CGPM)
	|date = 12–21 October 1948
	|accessdate = 2011-05-08}}</ref> At the same time the CGPM formally adopted a recommendation for the writing and printing of unit symbols and of numbers.<ref>{{cite conference
	|url = http://www.bipm.org/en/CGPM/db/9/7/
	|title = Resolution 7 - Writing and printing of unit symbols and of numbers
	|conference = 9th Conférence Générale des Poids et Mesures (CGPM)
	|date = 12–21 October 1948
	|accessdate = 2011-05-08}}</ref> The recommendation also catalogued the recommended symbols for the most important ] and ] units of measure and for the first time the CGPM made recommendations concerning derived units.
			== International System of Units (SI) ==
	The CIPM's draft proposal, which was an extensive revision and simplification of the metric unit definitions, symbols and terminology based on the MKS system of units, was put to the 10th CGPM in 1954. In accordance with Giorgi's proposals of 1901, the CIPM also recommended that the ampere be the base unit from which electromechanical 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 metre, ampere, second and kilogram. After negotiations with the CIS and IUPAP, two further base units, the degree kelvin and the candela were also proposed as base units.<ref>{{cite conference
			{{main|International System of Units#Evolution of the SI}}
	|url = http://www.bipm.org/en/CGPM/db/10/6/
	|title = Resolution 6 - Practical system of units
	|conference = 10th Conférence Générale des Poids et Mesures (CGPM)
	|date = 5–14 October 1954
	|accessdate = 2011-05-08}}</ref> The full system and name "Système International d'Unités" were adopted at the 11th CGPM.<ref>{{cite conference
	|url = http://www.bipm.org/en/CGPM/db/11/12/
	|title = Resolution 12 - Système International d'Unités
	|conference = 11th Conférence Générale des Poids et Mesures (CGPM)
	|date = 11–20 October 1960
	|accessdate = 2011-05-08}}</ref>
			In 1952, the CIPM proposed the use of wavelength of a specific light source as the standard for defining length, and, in 1960, the CGPM accepted this proposal using radiation corresponding to a transition between specified energy levels of the krypton 86 atom as the new standard for the metre. The standard metre artefact was retired.
	During the years that followed the definitions of the base units and particularly the ''mise en pratique''<ref>{{cite web
	|url = http://www.bipm.org/en/si/si_brochure/appendix2/
	|title = Practical realization of the definitions of some important units
	|work = SI brochure, Appendix 2
	|publisher = BIPM
	|date = 9 September 2010
	|accessdate = 2011-05-05}}</ref> to realise these definitions have been refined.
			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>
	===The "New SI"===
	{{main|New SI definitions}}
	]
			== Evolution of the modern SI ==
	When the metre was redefined in 1960, the kilogram was the only SI base unit that relied on a specific artifact. Moreover, after the 1996-1998 recalibration a clear divergence between the various prototype kilograms was observed.
			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 ===
	At its 23rd meeting (2007), the CGPM mandated the CIPM to investigate the use of natural constants as the basis for all units of measure rather than the artifacts that were then in use. At a meeting of the CCU held in ] in September 2010, a resolution<ref>{{cite web
			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>
	|url = http://www.bipm.org/utils/en/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf
			{{cite web
	|title = On the possible future revision of the International System of Units, the SI
			| url = http://www.bipm.org/utils/common/pdf/its-90/ITS-90_Techniques.pdf
	|author = Ian Mills
			| title = Techniques for Approximating the International Temperature Scale of 1990
	|publisher = CCU
			| publisher = ]
	|date = 29 September 2010
			| location = Sèvres
	|accessdate = 2011-01-01}}</ref> and draft changes to the SI brochure that were to be presented to the next meeting of the CIPM in October 2010 were agreed to in principle.<ref name="draft">{{cite web
			| year = 1997
	|url = http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf
			| orig-date = 1990
	|title = Draft Chapter 2 for SI Brochure, following redefinitions of the base units
			| access-date = 10 May 2011
	|author = Ian Mills
			}}</ref>
	|publisher = CCU
	|date = 29 September 2010
	|accessdate = 2011-01-01}}</ref> The proposals that the CCU put forward were:
	:*In addition to the speed of light, four constants of nature—], an ], ] and ] be defined to have exact values.
	:*The international prototype kilogram be retired
	:*The current definitions of the kilogram, ], ] and ] be revised.
	:*The wording of the definitions of all the base units be tightened up
			The mole was originally known as a gram-atom or a gram-molecule—the amount of a substance measured in grams divided by its ]. Originally chemists and physicists had differing views regarding the definition of the atomic weight—both assigned a value of 16&nbsp;] (amu) to oxygen, but physicists defined oxygen in terms of the <sup>16</sup>O isotope whereas chemists assigned 16&nbsp;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 ]<ref>
	The CIPM meeting of October 2010 found that "the conditions set by the General Conference at its 23rd meeting have not yet been fully met. For this reason the CIPM does not propose a revision of the SI at the present time";<ref>{{cite web
			{{cite journal
	|url = http://www.bipm.org/en/si/new_si/
			|url = http://materia.ro/FACULTATE/DATA/Atomic%20Mass.pdf
	|title = Towards the "new SI"
			|title = Atomic Weights of the Elements: Review 2000 (IUPAC Technical Report)
	|publisher = ] (BIPM)
			|access-date = 6 July 2013
	|accessdate = 2011-02-20}}</ref> however the CIPM presented a resolution for consideration at the 24th CGPM (17–21 October 2011) to agree the new definitions in principle, but not to implement them until the details have been finalised.<ref>{{cite web
			|first1 = JR
	|url = http://www.bipm.org/utils/common/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf
			|last1 = de Laeter
	|title = On the possible future revision of the International System of Units, the SI - Draft Resolution A
			|first2 = JK
	|publisher = ] (CIPM)
			|last2 = Böhlke
	|accessdate = 2011-07-14}}</ref> This resolution was accepted by the conference<ref>{{cite conference
			|first3 = P
	|url= http://www.bipm.org/utils/en/pdf/24_CGPM_Resolution_1.pdf
			|last3 = de Bièvre
	|title= Resolution 1 - On the possible future revision of the International System of Units, the SI
			|first4 = H
	|conference= 24th meeting of the General Conference on Weights and Measures
			|last4 = Hidaka
	|location = ], France
			|first5 = Peiser
	|date = 17 - 21 October 2011
			|last5 = HS
	|accessdate = 2011-10-25}}</ref> and in addition the CGPM moved the date of the 25th meeting forward from 2015 to 2014.<ref>{{cite press release
			|first6 = KJR
	| url = http://www.bipm.org/utils/en/pdf/Press_release_resolution_1_CGPM.pdf
			|last6 = Rosman
	| title = General Conference on Weights and Measures approves possible changes to the International System of Units, including redefinition of the kilogram.
			|first7 = PDP
	| publisher = ]
			|last7 = Taylor
	| location = Sèvres, France
			|journal = Pure Appl. Chem.
	| date = 23 October 2011
			|volume = 75
	| accessdate = 2011-10-25}}</ref>
			|number = 6
			|pages = 690–691
			|publisher = ]
			|year = 2003
			|doi = 10.1351/pac200375060683
			|s2cid = 96800435
			|archive-url = https://web.archive.org/web/20130123190239/http://materia.ro/FACULTATE/DATA/Atomic%20Mass.pdf
			|archive-date = 23 January 2013
			}}</ref> (IUPAP) and the ] (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 ===
	==Notes==
			The second major trend in the post-modern SI was the migration of unit definitions in terms of physical constants of nature.
	{{Reflist|group=Note}}
			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)
			| conference = 9th Conférence Générale des Poids et Mesures (CGPM)
			| date = 12–21 October 1948
			| access-date = 8 May 2011
			}}</ref>
			Astronomers from the ] (USNO) and the ] 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
			| publisher = ]
			| access-date = 15 November 2011
			}}</ref>
			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 ===
			]: K32 and K8(41).<ref name="Girard">
			{{cite journal
			| title = The Third Periodic Verification of National Prototypes of the Kilogram (1988–1992)
			| author = G. Girard
			| journal = Metrologia
			| volume = 31
			| issue = 4
			| year = 1994
			| pages = 317–336
			| doi = 10.1088/0026-1394/31/4/007
			| bibcode = 1994Metro..31..317G
			| s2cid = 250743540
			}}</ref>
			<ref group="Note">Prototype No. 8(41) was accidentally stamped with the number 41, but its accessories carry the proper number 8. Since there is no prototype marked 8, this prototype is referred to as 8(41).<sub zoompage-fontsize="9">{{nbsp}}</sub></ref> The above are all ''relative'' measurements; no historical mass-measurement data is available to determine which of the prototypes has been most stable relative to an invariant of nature. There is the distinct possibility that ''all'' the prototypes gained mass over 100 years and that K21, K35, K40, and the IPK simply ''gained less'' than the others.]]
			After the metre was redefined in 1960, the kilogram remained the only SI base defined by a physical artefact. During the years that followed, the definitions of the base units and particularly the ''mise en pratique''<ref>
			{{cite web
			| url = http://www.bipm.org/en/si/si_brochure/appendix2/
			| title = Practical realization of the definitions of some important units
			| work = SI brochure, Appendix 2
			| publisher = BIPM
			| date = 9 September 2010
			| access-date = 5 May 2011
			}}</ref> to realise these definitions have been refined.
			The third periodic recalibration in 1988–1989 revealed that the average difference between the IPK and adjusted baseline for the national prototypes was 50&nbsp;μg—in 1889, the baseline of the national prototypes had been adjusted so that the difference was zero. As the IPK is the definitive kilogram, there is no way of telling whether the IPK had been losing mass or the national prototypes had been gaining mass.<ref name="Girard"/>
			During the course of the century, the various national prototypes of the kilogram were recalibrated against the ] (IPK) and, therefore, against each other. The initial 1889 starting-value offsets of the national prototypes relative to the IPK were nulled,<ref name="Girard"/> with any subsequent mass changes being relative to the IPK.
			=== Proposed replacements for the IPK ===
			]
			{{main|Alternative approaches to redefining the kilogram}}
			A number of replacements were proposed for the IPK.
			From the early 1990s, the ] worked on creating a 1&nbsp;kg, 94&nbsp;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
			| first = Robin
			| last = Materese
			| date = 14 May 2018
			| website = nist.gov
			}}</ref>
			Other groups worked on concepts such as creating a reference mass via precise ] of gold or bismuth atoms, and defining the kilogram in terms of the ] by relating it to forces generated by electromagnetic repulsion of electric currents.<ref name="Treese2018">{{Cite book|title=History and measurement of the base and derived units|last=Treese|first=Steven A.|publisher=Springer|year=2018|isbn=978-3-319-77577-7|location=Cham, Switzerland|page=92|oclc=1036766223}}</ref>
			Eventually, the choices were narrowed down to the use of the ] and the International Avogadro Project sphere.<ref name=Treese2018/>
			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 ==
			] after the 2019 revision: Dependence of base unit definitions on ]s with fixed numerical values and on other base units.]]
			{{main|2019 revision of the SI}}
			At its 23rd meeting (2007), the CGPM mandated the CIPM to investigate the use of natural constants as the basis for all units of measure rather than the artefacts that were then in use.
			The following year, this was endorsed by the ] (IUPAP).<ref>{{cite web |url=http://iupap.org/wp-content/uploads/2013/08/file_50095.pdf |title=Resolution proposal submitted to the IUPAP Assembly by Commission C2 (SUNAMCO) |publisher=International Union of Pure and Applied Physics |year=2008 |access-date=6 September 2015 |archive-url=https://web.archive.org/web/20160305121825/http://iupap.org/wp-content/uploads/2013/08/file_50095.pdf |archive-date=5 March 2016 |url-status=live }}</ref> At a meeting of the CCU held in ], in September 2010, a resolution<ref>{{cite web |url=http://www.bipm.org/utils/en/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf |title=On the possible future revision of the International System of Units, the SI |first=Ian |last=Mills |publisher=CCU |date=29 September 2010 |access-date=1 January 2011 |archive-url=https://web.archive.org/web/20120113075832/http://www.bipm.org/utils/en/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf |archive-date=13 January 2012 |url-status=live}}</ref> and draft changes to the SI brochure that were to be presented to the next meeting of the CIPM in October 2010 were agreed in principle.<ref name="draft">{{cite web |url=http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf |title=Draft Chapter 2 for SI Brochure, following redefinitions of the base units |first=Ian |last=Mills |publisher=CCU |date=29 September 2010 |access-date=1 January 2011 |archive-url=https://web.archive.org/web/20120316100258/http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf |archive-date=16 March 2012 |url-status=live }}</ref> The CIPM meeting of October 2010 found that "the conditions set by the General Conference at its 23rd meeting have not yet been fully met.{{#tag:ref|In particular the CIPM was to prepare a detailed ''mise en pratique'' for each of the new definitions of the kilogram, ampere, kelvin and mole set by the 23rd ].<ref>{{cite web |url=http://www.bipm.org/en/CGPM/db/23/12 |title=Resolution 12 of the 23rd meeting of the CGPM (2007) |location=Sèvres, France |publisher=] |access-date=2013-06-21 |archive-url=https://web.archive.org/web/20130421103428/http://www.bipm.org/en/CGPM/db/23/12/ |archive-date=21 April 2013 |url-status=live }}</ref>|group=Note}} For this reason the CIPM does not propose a revision of the SI at the present time".<ref>{{cite web |url=http://www.bipm.org/en/si/new_si/ |title=Towards the "new SI" |publisher=] (BIPM) |access-date=20 February 2011 |archive-url=https://web.archive.org/web/20110514140824/http://www.bipm.org/en/si/new_si/ |archive-date=14 May 2011 |url-status=live }}</ref> The CIPM, however, presented a resolution for consideration at the 24th CGPM (17–21 October 2011) to agree to the new definitions in principle, but not to implement them until the details had been finalised.<ref>{{cite web |url=http://www.bipm.org/utils/common/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf |title=On the possible future revision of the International System of Units, the SI – Draft Resolution A |publisher=] (CIPM) |access-date=14 July 2011 |archive-url=https://web.archive.org/web/20110806053509/http://www.bipm.org/utils/common/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf |archive-date=6 August 2011 |url-status=live }}</ref>
			In the revision, four of the seven SI base units—the ], ], ], and ]—were redefined by setting exact numerical values for the ] (''{{Math|h}}''), the ] (''{{Math|e}}''), the ] ({{math|''k''<sub>B</sub>}}), and the ] ({{Math|''N''<sub>A</sub>}}), respectively. The ], ], and ] were already ] by ]s and were subject to correction to their definitions. The new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements.<ref name="Kuehne">
			{{cite web
			|first = Michael |last = Kühne
			|title = Redefinition of the SI
			|url = http://www.its9.org/symposium_program.html#SI_Redefinition_Keynote_Abstract
			|work = Keynote address, ITS<sup>9</sup> (Ninth International Temperature Symposium)
			|location = Los Angeles
			|access-date = 1 March 2012
			|date = 22 March 2012
			|publisher = NIST
			|archive-url = https://web.archive.org/web/20130618064512/http://www.its9.org/symposium_program.html
			|archive-date = 18 June 2013
			}}</ref><ref name="Brochure9_2019">
			{{cite web
			|title = 9th edition of the SI Brochure
			|publisher = BIPM
			|url = https://www.bipm.org/en/publications/si-brochure/
			|date = 2019
			|access-date = 20 May 2019
			}}
			</ref>
			This resolution was accepted by the conference,<ref name="Resolution">{{Citation |title=24th meeting of the General Conference on Weights and Measures |contribution=Resolution 1: On the possible future revision of the International System of Units, the SI |contribution-url=http://www.bipm.org/utils/en/pdf/24_CGPM_Resolution_1.pdf |publisher=International Bureau for Weights and Measures |location=Sèvres, France |date=21 October 2011 |mode=cs1}} It was not expected to be adopted until some prerequisite conditions are met, and in any case not before 2014. See{{cite journal |title=Possible changes to the international system of units |journal=IUPAC Wire |volume=34 |issue=1 |date=January–February 2012}}</ref> and, in addition, the CGPM moved the date of the 25th meeting forward from 2015 to 2014.<ref>{{cite press release |url=http://www.bipm.org/utils/en/pdf/Press_release_resolution_1_CGPM.pdf |title=General Conference on Weights and Measures approves possible changes to the International System of Units, including redefinition of the kilogram. |publisher=] |location=Sèvres, France |date=23 October 2011 |access-date=25 October 2011 |archive-url=https://web.archive.org/web/20120209175127/http://www.bipm.org/utils/en/pdf/Press_release_resolution_1_CGPM.pdf |archive-date=9 February 2012 |url-status=live }}</ref><ref name="Mohr">{{cite web |title=Redefining the SI base units |author=Mohr, Peter |date=2 November 2011 |work=NIST Newsletter |url=https://www.nist.gov/pml/newsletter/siredef.cfm |publisher=NIST |access-date=1 March 2012 |archive-url=https://web.archive.org/web/20160812012223/http://nist.gov/pml/newsletter/siredef.cfm |archive-date=12 August 2016 |url-status=live }}</ref> At the 25th meeting on 18 to 20 November 2014, it was found that "despite the data do not yet appear to be sufficiently robust for the CGPM to adopt the revised SI at its 25th meeting",<ref>{{cite web |title=Resolutions adopted by the CGPM at its 25th meeting (18–20 November 2014) |url=http://www.bipm.org/utils/common/pdf/CGPM-2014/25th-CGPM-Resolutions.pdf |publisher=International Bureau for Weights and Measures |location=Sèvres, France |date=21 November 2014 |access-date=1 December 2014 |archive-url=https://web.archive.org/web/20150325103457/http://www.bipm.org/utils/common/pdf/CGPM-2014/25th-CGPM-Resolutions.pdf |archive-date=25 March 2015 |url-status=live }}</ref> thus postponing the revision to the next meeting in 2018.
	==References==
	{{Reflist|30em}}
			Measurements accurate enough to meet the conditions were available in 2017 and the revision<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.
	==Further reading==
	*{{cite book
	|title = The Measure of all Things - The Seven-Year-Odyssey that Transformed the World
	|last= Adler
	|first= Ken
	|year= 2002
	|publisher= Abacus
	|location= London
	|isbn= 0&nbsp;349&nbsp;11507&nbsp;9}}
	==External links==		== See also ==
			* ]
	*{{cite web|
			* ]
	|url = http://www.metricationmatters.com/docs/MetricationTimeline.pdf
			* ]
	|first1 = Pat
	|last1 = Naughtin
	|title = A chronological history of the modern metric system
	|year = 2009
	|accessdate = 2011-09-15}}
			== Notes ==
	{{systems of measurement}}
			{{reflist|group=Note}}
			{{notelist}}
			== References ==
	{{systems}}
			{{reflist}}
	{{metrication}}		{{Good Article}}
			{{Systems of measurement}}
			{{Systems}}
			{{Metrication}}
			]
	{{DEFAULTSORT:History of the Metric System}}
	]		]
			]

---

Latest revision as of 16:02, 13 September 2024

This article is about the history of the standards used in the metric system. For history of adoption, see Metrication.

The history of the metric system began during the Age of Enlightenment with measures of length and weight derived from nature, along with their decimal multiples and fractions. The system became the standard of France and Europe within half a century. Other measures with unity ratios were added, and the system went on to be adopted across the world.

The first practical realisation of the metric system came in 1799, during the French Revolution, after the existing system of measures had become impractical for trade, and was replaced by a decimal system based on the kilogram and the metre. The basic units were taken from the natural world. The unit of length, the metre, was based on the dimensions of the Earth, and the unit of mass, the kilogram, was based on the mass of a volume of water of one litre (a cubic decimetre). Reference copies for both units were manufactured in platinum and remained the standards of measure for the next 90 years. After a period of reversion to the mesures usuelles due to unpopularity of the metric system, the metrication of France and much of Europe was complete by the 1850s.

In the middle of the 19th century, James Clerk Maxwell conceived a coherent system where a small number of units of measure were defined as base units, and all other units of measure, called derived units, were defined in terms of the base units. Maxwell proposed three base units for length, mass and time. Advances in electromagnetism in the 19th century necessitated additional units to be defined, and multiple incompatible systems of such units came into use; none could be reconciled with the existing dimensional system. The impasse was resolved by Giovanni Giorgi, who in 1901 proved that a coherent system that incorporated electromagnetic units required a fourth base unit, of electromagnetism.

The seminal 1875 Treaty of the Metre resulted in the fashioning and distribution of metre and kilogram artefacts, the standards of the future coherent system that became the SI, and the creation of an international body Conférence générale des poids et mesures or CGPM to oversee systems of weights and measures based on them.

In 1960, the CGPM launched the International System of Units (in French the Système international d'unités or SI) with six "base units": the metre, kilogram, second, ampere, degree Kelvin (subsequently renamed the "kelvin") and candela, plus 16 more units derived from the base units. A seventh base unit, the mole, and six other derived units were added later in the 20th century. During this period, the metre was redefined in terms of the speed of light, and the second was redefined based on the microwave frequency of a caesium atomic clock.

Due to the instability of the international prototype of the kilogram, a series of initiatives were undertaken, starting in the late 20th century, to redefine the ampere, kilogram, mole and kelvin in terms of invariant constants of physics, ultimately resulting in the 2019 revision of the SI, which finally eliminated the need for any physical reference artefacts—notably, this enabled the retirement of the standard kilogram.

A fleeting hint of an ancient decimal or metric system may be found in the Mohenjo-Daro ruler, which uses a base length of 1.32 inches (33.5 mm) 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 Holy Roman Empire was part of France, units of measure had been standardised by the 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."

During the early medieval era, Roman numerals were used in Europe to represent numbers, 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. At that time, there was dispute regarding the difference between rational numbers and irrational numbers 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. 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. 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.

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, 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 . 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 acceleration due to gravity), and this was not a good solution. A more uniform standard was needed.

In 1670, Gabriel Mouton, a French abbot and astronomer, published the book Observationes diametrorum solis et lunae apparentium ("Observations of the apparent diameters of the Sun and Moon") in which he proposed a decimal system of measurement of length for use by scientists in international communication, to be based on the dimensions of the Earth. The milliare would be defined as a minute of arc along a meridian (such as the Paris meridian) and would be divided into 10 centuria, the centuria into 10 decuria and so on, successive units being the virga, virgula, decima, centesima, and the millesima. Mouton used Riccioli's estimate that one degree of arc was 321,185 Bolognese feet. Mouton's experiments showed that a pendulum of length one virgula would beat 3959.2 times in half an hour. Mouton believed that, with this information, scientists in a foreign country would be able to construct a copy of the virgula for their own use. Mouton's ideas attracted interest at the time; Picard in his work Mesure de la Terre (1671) and Huygens in his work Horologium Oscillatorium sive de motu pendulorum ("Of oscillating clocks, or concerning the motion of pendulums", 1673) both proposing that a standard unit of length be tied to the beat frequency of a pendulum.

Shape and size of the Earth

Main article: 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 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. Thus Earth's circumference in nautical miles would be 21 600 (viz., 60 minutes of arc × 360 degrees in four 90-degree quadrants; a quadrant being the length of the quarter-circle from the North Pole to the equator).

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).

In Philosophiæ Naturalis Principia Mathematica (1686), Isaac Newton gave a theoretical explanation for the "bulging equator", which also explained the differences found in the lengths of the "second pendulums", theories that were confirmed by the French Geodesic Mission to Peru undertaken by the French Academy of Sciences in 1735.

Late 18th century: conflict and lassitude

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 and Peter the Great aligned the Russian units of measure with those of England. In 1783, the British inventor James Watt, who was having difficulties in communicating with German scientists, called for the creation of a global decimal measurement system, proposing a system which used the density of water to link length and mass, and, in 1788, the French chemist Antoine Lavoisier commissioned a set of nine brass cylinders (a pound and decimal subdivisions thereof) for his experimental work.

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.

Implementation in Revolutionary France

Weights and measures of the Ancien Régime

Further information: 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. Although certain standards, such as the pied du roi (the King's foot) had a degree of pre-eminence and were used by scientists, many traders chose to use their own measuring devices, giving scope for fraud and hindering commerce and industry. These variations were promoted by local vested interests, but hindered trade and taxation.

Units of weight and length

In 1790, a panel of five leading French scientists was appointed by the 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. 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. The proposals were accepted by the French Assembly on 30 March 1791.

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:

• Measuring the difference in latitude between Dunkirk and Barcelona and 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.

Using Jean Picard's survey of 1670 and Jacques Cassini's survey of 1718, a provisional value of 443.44 lignes was assigned to the metre which, in turn, defined the other units of measure.

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 would be selected.

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. This mass unit defined by Lavoisier and René Just Haüy had been in use since 1793. 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". 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. The final conclusion was that one cubic decimetre of water at its maximum density was equal to 99.92072% of the mass of the provisional kilogram.

On 7 April 1795, the metric system was formally defined in French law. It defined six new decimal units:

• The mètre, for length—defined as one ten-millionth of the distance between the North Pole and the Equator through Paris
• The are (100 m) for area
• The stère (1 m) for volume of firewood
• The litre (1 dm) for volumes of liquid
• The gramme, for mass—defined as the mass of one cubic centimetre of water
• The 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) are still in use, but are not SI units.

Decimal multiples of these units were defined by Greek 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).

For purposes of commerce, units and prefixed-units of weight (mass) and capacity (volume) were prependable by the binary multipliers "double-" (2) and "demi-" (1⁄2), as in double-litre, demi-litre; or double-hectogramme, demi-hectogramme, etc.

The 1795 draft definitions enabled provisional copies of the kilograms and metres to be constructed.

Meridional survey

Further information: Arc measurement

The task of surveying the meridian arc, which was estimated to take two years, fell to Pierre Méchain and Jean-Baptiste Delambre. The task eventually took more than six years (1792–1798) with delays caused not only by unforeseen technical difficulties but also by the convulsed period of the aftermath of the Revolution. Apart from the obvious nationalistic considerations, 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.

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.

Delambre used a baseline of about 10 km in length along a straight road, located close to Melun. In an operation taking six weeks, the baseline was accurately measured using four platinum rods, each of length two toises (about 3.9 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, and also on a straight section of road was in the Perpignan area. 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 metre as 443.296 lignes, notably shorter than the 1795 provisional value of 443.44 lignes. On 15 November 1798, Delambre and Méchain returned to Paris with their data, having completed the survey. The final value of the mètre was defined in 1799 as the computed value from the survey.

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.

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 grains of the livre poids de marc, 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 livre, originally a unit of mass derived from the Roman libra (as was the English 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 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. Both Fahrenheit (ca. 1724) and Celsius (ca. 1742) scales of temperature existed, and varied instruments for measuring units or degrees of them. The base/derived unit model had not yet been elaborated, nor was it known how many physical quantities might be interrelated.

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 mechanical, electrical, and thermal units to be correlated.

Time

In 1832, German mathematician 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. Gauss's 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. 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

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 mechanical work. Energy became the unifying concept of nineteenth century science, initially by bringing thermodynamics and mechanics together and later adding 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 (later Lord Kelvin), James Clerk Maxwell, and James Prescott Joule among its members was tasked with investigating the "Standards of Electrical Resistance". In their first report (1862), 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), 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 base units). All other units of measure could be derived (hence derived units) from these base units. The metre, gram, and second were chosen as base units.

In 1861, before a meeting of the BAAS, 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). The concept of naming units of measure after noteworthy scientists was subsequently used for other units.

In 1873, another committee of the BAAS (which also included Maxwell and Thomson) tasked with "the Selection and Nomenclature of Dynamical and Electrical Units" recommended using the cgs system of units. The committee also recommended the names of "dyne" and "erg" for the cgs units of force and energy. The cgs system became the basis for scientific work for the next seventy years.

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

Symbols used in this section

Symbols	Meaning
${\displaystyle F_{\text{m}},F_{\text{e}}}$	electromagnetic and electrostatic forces
${\displaystyle I_{\text{1}},I_{\text{2}}}$	electric currents in conductors
${\displaystyle q_{\text{1}},q_{\text{2}}}$	electrical charges
${\displaystyle L}$	conductor length
${\displaystyle r}$	distance between charges/conductors
${\displaystyle \epsilon _{0}}$	electric constant
${\displaystyle \mu _{0}}$	magnetic constant
${\displaystyle k_{\text{m}},k_{\text{e}}}$	constants of proportionality
${\displaystyle c}$	speed of light
${\displaystyle 4\pi }$	steradians surrounding a point
${\displaystyle P}$	electric power
${\displaystyle V}$	electric potential
${\displaystyle I}$	electric current
${\displaystyle E}$	energy
${\displaystyle Q}$	electric charge
${\displaystyle {\mathsf {M,L,T}}}$	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. During the following decades, the realisation of a coherent system of units that incorporated the measurement of electromagnetic phenomena and Ohm's law was beset with problems—several different systems of units were devised.

In the three CGS systems, the constants ${\displaystyle k_{\text{e}}}$ and ${\displaystyle k_{\text{m}}}$ and consequently ${\displaystyle \epsilon _{0}}$ and ${\displaystyle \mu _{0}}$ were dimensionless, and thus did not require any units to define them.

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 ${\displaystyle {\mathsf {M}}^{\frac {1}{2}}{\mathsf {L}}^{\frac {1}{2}}{\mathsf {T}}^{-1}}$ 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.

Electromagnetic (absolute) system of units (EMU)

The 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 Ampere's law:

${\displaystyle {\frac {F_{\text{m}}}{L}}=2k_{\text{m}}{\frac {I_{1}I_{2}}{r}}}$ where ${\displaystyle k_{\text{m}}={\frac {\mu _{0}}{4\pi }}\ }$ (SI units)

In 1833, Gauss pointed out the possibility of equating this force with its mechanical equivalent. This proposal received further support from Wilhelm Weber in 1851. In this system, current is defined by setting the magnetic force constant ${\displaystyle k_{\mathrm {m} }}$ to unity and electric potential is defined in such a way as to ensure the unit of power calculated by the relation ${\displaystyle P=VI}$ is an erg/second. The electromagnetic units of measure were known as the abampere, abvolt, and so on. These units were later scaled for use in the International System.

Electrostatic system of units (ESU)

The 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

${\displaystyle F_{\mathrm {e} }=k_{\text{e}}{\frac {q_{1}q_{2}}{r^{2}}},}$ where ${\displaystyle k_{\text{e}}={\frac {1}{4\pi \epsilon _{0}}}}$ (SI units)

In this system, the unit for charge is defined by setting the Coulomb force constant (${\displaystyle k_{\text{e}}}$) to unity and the unit for electric potential was defined to ensure the unit of energy calculated by the relation ${\displaystyle E=QV}$ is one erg. The electrostatic units of measure were the statampere, statvolt, and so on.

Gaussian system of units

The Gaussian system of units was based on Heinrich Hertz's realisation, while verifying Maxwell's equations in 1888, that the electromagnetic and electrostatic units were related by:

${\displaystyle c^{2}={\frac {1}{\epsilon _{0}\mu _{0}}}}$

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 and 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.

Quadrant–eleventhgram–second (QES) or International system of units

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 m (the hebdometre, nominally the Earth quadrant), the unit of mass was an unnamed unit equal to 10 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. The system was formalised as the International system late in the 19th century and its units later designated the "international ampere", "international volt", etc.

Heaviside–Lorentz system of units

The factor ${\displaystyle 4\pi }$ that occurs in Maxwell's equations in the gaussian system (and the other CGS systems) comes from the ${\displaystyle 4\pi }$ 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.

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 of the nature of temperature was minimal.

Convention of the metre

Main article: Metre Convention

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.

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". The International Conference on Geodesy in 1867 called for the creation of a new international prototype of the metre 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.

On 20 May 1875, an international treaty known as the Convention du Mètre (Metre Convention) was signed by 17 states. 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 metrologists, 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 (Tresca) cross section to minimise the effects of torsional strain during length comparisons 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.

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.

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

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 Giorgi in 1901. This led to Giorgi presenting a paper in October 1901 to the congress of the Associazione Elettrotecnica Italiana (A.E.I.) 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_e and k_m and hence also to the electro-mechanical quantities ε₀ (permittivity of free space) and μ₀ (permeability of free space). 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. 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

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 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, and indicated that the definition of the metre was preserved to within 0.2 μm. 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". 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.

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. 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. 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 and CGS units of measure.

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—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. In 1956, the 10th CGPM instructed the CIPM to prepare a definition of the second; in 1958, the definition was published stating that the second (called an ephemeris second) would be calculated by extrapolation using Earth's rotational speed in 1900.

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. The definitions for the absolute electrical system, based on the ampere, were formalised in 1948. The draft proposed units with these names are very close, but not identical, to the international units.

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 degree Celsius.)

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, though the CGPM left the formal definition of absolute zero until the 10th CGPM when the name "Kelvin" was assigned to the absolute temperature scale, and the triple point of water was defined as being 273.16 °K.

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", 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 article: International System of Units § Evolution of the SI

In 1952, the CIPM proposed the use of wavelength of a specific light source as the standard for defining length, and, in 1960, the CGPM accepted this proposal using radiation corresponding to a transition between specified energy levels of the krypton 86 atom as the new standard for the metre. The standard metre artefact was retired.

In 1960, Giorgi's proposals were adopted as the basis of the Système International d'Unités (International System of Units), the SI. This initial definition of the SI included six base units, the metre, kilogram, second, ampere, degree Kelvin, and candela, and sixteen coherent derived units.

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.

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 O isotope whereas chemists assigned 16 amu to O, O and O isotopes mixed in the proportion that they occur in nature. Finally, an agreement between the International Union of Pure and Applied Physics (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 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.

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 (°K) was renamed the "kelvin" (K).

Astronomers from the US Naval Observatory (USNO) and the 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.

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, which is close to the frequency where the human eye, when adapted to bright conditions, has greatest sensitivity.

Kilogram artefact instability

After the metre was redefined in 1960, the kilogram remained the only SI base defined by a physical artefact. During the years that followed, the definitions of the base units and particularly the mise en pratique to realise these definitions have been refined.

The third periodic recalibration in 1988–1989 revealed that the average difference between the IPK and adjusted baseline for the national prototypes was 50 μg—in 1889, the baseline of the national prototypes had been adjusted so that the difference was zero. As the IPK is the definitive kilogram, there is no way of telling whether the IPK had been losing mass or the national prototypes had been gaining mass.

During the course of the century, the various national prototypes of the kilogram were recalibrated against the international prototype of the kilogram (IPK) and, therefore, against each other. The initial 1889 starting-value offsets of the national prototypes relative to the IPK were nulled, with any subsequent mass changes being relative to the IPK.

Proposed replacements for the IPK

Main article: Alternative approaches to redefining the kilogram

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.

Other groups worked on concepts such as creating a reference mass via precise electrodeposition of gold or bismuth atoms, and defining the kilogram in terms of the ampere by relating it to forces generated by electromagnetic repulsion of electric currents.

Eventually, the choices were narrowed down to the use of the Watt balance and the International Avogadro Project sphere.

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

Main article: 2019 revision of the SI

At its 23rd meeting (2007), the CGPM mandated the CIPM to investigate the use of natural constants as the basis for all units of measure rather than the artefacts that were then in use.

The following year, this was endorsed by the International Union of Pure and Applied Physics (IUPAP). At a meeting of the CCU held in Reading, United Kingdom, in September 2010, a resolution and draft changes to the SI brochure that were to be presented to the next meeting of the CIPM in October 2010 were agreed in principle. The CIPM meeting of October 2010 found that "the conditions set by the General Conference at its 23rd meeting have not yet been fully met. For this reason the CIPM does not propose a revision of the SI at the present time". The CIPM, however, presented a resolution for consideration at the 24th CGPM (17–21 October 2011) to agree to the new definitions in principle, but not to implement them until the details had been finalised.

In the revision, four of the seven SI base units—the kilogram, ampere, kelvin, and mole—were redefined by setting exact numerical values for the Planck constant (h), the elementary electric charge (e), the Boltzmann constant (k_B), and the Avogadro constant (N_A), respectively. The second, metre, and candela were already defined by physical constants and were subject to correction to their definitions. The new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements.

This resolution was accepted by the conference, and, in addition, the CGPM moved the date of the 25th meeting forward from 2015 to 2014. At the 25th meeting on 18 to 20 November 2014, it was found that "despite the data do not yet appear to be sufficiently robust for the CGPM to adopt the revised SI at its 25th meeting", thus postponing the revision to the next meeting in 2018.

Measurements accurate enough to meet the conditions were available in 2017 and the revision 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
• History of measurement
• Metrication

Notes

1. ratios of 1 between magnitudes of unit quantities
2. just under 2 metres in today's units
3. There were two beats in an oscillation.
4. the pendulum would have had a length of 205.6 mm and the virgula was ~185.2 mm.
5. The acceleration due to gravity at the poles is 9.832 m/s and at the equator 9.780 m/s, a difference of about 0.5%. Archived 9 March 2013 at the Wayback Machine
6. 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.
7. 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.
8. from Latin gravitas: "weight"
9. There were three reasons for the change from the freezing point to the point of maximum density:
   1. It proved difficult to achieve the freezing point precisely. As 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;
   2. This maximum of water density as a function of temperature can be detected 'independent of temperature awareness', 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.
   3. The point of maximum density is also the point where the density depends the least on small changes in temperature. This is a general mathematical fact: if a function f(·) of a variable x is sufficiently free of discontinuities, then, if one plots f vs. x, and looks at a point (x_max, f(x_max)) at which f has a 'peak' (meaning, f decreases no matter whether x is made a bit larger or a bit smaller than x_max), once notices that f is 'flat' at x_max—the tangent line to it at that point is horizontal, so the slope of f at x_max is zero. This is why f changes little from its maximum value if x is made slightly different from x_max.
10. Article 5 of the law of 18 Germinal, Year III
11. Article 8 of the law of 18 Germinal, Year III
12. Distances measured using Google Earth. The coordinates are:
    51°02′08″N 2°22′34″E / 51.03556°N 2.37611°E / 51.03556; 2.37611 (Belfry, Dunkirk) – Belfry, Dunkirk
    44°25′57″N 2°34′24″E / 44.43250°N 2.57333°E / 44.43250; 2.57333 (Rodez Cathedral) – Rodez Cathedral
    41°21′48″N 2°10′01″E / 41.36333°N 2.16694°E / 41.36333; 2.16694 (Montjuïc, Barcelona) – Montjuïc, Barcelona
13. 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 1 toise = 864 lignes.
14. The modern value, for the WGS 84 reference spheroid of 1.000 196 57 m is 443.383 08 lignes.
15. Ohm's Law wasn't discovered until 1824, for example.
16. It is certain, however, that 170 years after the invention of pendulum clocks, that Gauss had sufficiently accurate mechanical clocks for his work.
17. ^ The electric constant, termed the permittivity of free space (vacuum, such as might be found in a vacuum tube) is a physical electric constant with the unit farad per metre that represents the ability of vacuum to support an electric field.
    The magnetic constant termed the permeability of free space is a physical magnetic constant with units henries/metre that represents the ability of vacuum to support a magnetic field.
    Iron, for example, has both high permittivity because it readily conducts electricity and high permeability because it makes a good magnet. vacuum does not "conduct" electricity very well, nor can it be easily "magnetised", so the electric and magnetic constants of vacuum are tiny.
18. This factor appears in Maxwell's equations and represents the fact that electric and magnetic fields may be considered as point quantities that propagate equally in all directions, i.e. spherically
19. 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.
20. Prototype No. 8(41) was accidentally stamped with the number 41, but its accessories carry the proper number 8. Since there is no prototype marked 8, this prototype is referred to as 8(41). 
21. In particular the CIPM was to prepare a detailed mise en pratique for each of the new definitions of the kilogram, ampere, kelvin and mole set by the 23rd CGPM.

1. ^ Jacques Cassini's survey of Earth of 1713–1718

References

1. "English translation of Magna Carta". British Library. Archived from the original on 17 January 2023. Retrieved 10 January 2018.
2. Durham, John W (2 December 1992). "The Introduction of "Arabic" Numerals in Euiropean Accounting". The Accounting Historians Journal. 19 (2). The Academy of Accounting Historians: 27–28. doi:10.2308/0148-4184.19.2.25. JSTOR 40698081.
3. O'Connor, John J.; Robertson, Edmund F. (January 2001), "The Arabic numeral system", MacTutor History of Mathematics Archive, University of St Andrews
4. O'Connor, John J.; Robertson, Edmund F. (October 1998), "Leonardo Pisano Fibonacci", MacTutor History of Mathematics Archive, University of St Andrews
5. ^ O'Connor, John J.; Robertson, Edmund F. (January 2004), "Simon Stevin", MacTutor History of Mathematics Archive, University of St Andrews
6. O'Connor, John J.; Robertson, Edmund F. (October 2005), "The real numbers: Pythagoras to Stevin", MacTutor History of Mathematics Archive, University of St Andrews
7. ^ Tavernor, Robert (2007). Smoot's Ear: The Measure of Humanity. Yale University Press. ISBN 978-0-300-12492-7.
8. ^ Alder (2004). The Measure of all Things – The Seven-Year-Odyssey that Transformed the World. Abacus. ISBN 978-0-349-11507-8.
9. Zupko, Ronald Edward (1990). Revolution in Measurement: Western European Weights and Measures Since the Age of Science. Memoirs of the American Philosophical Society, Volume 186. Philadelphia. pp. 123–129. ISBN 978-0-87169-186-6.{{cite book}}: CS1 maint: location missing publisher (link)
10. ^ O'Connor, John J.; Robertson, Edmund F. (June 2004), "Gabriel Mouton", MacTutor History of Mathematics Archive, University of St Andrews
11. G. Bigourdan (1901). "Le système métrique des poids et des mesures" [The metric system of weights and measures] (in French). Paris. Retrieved 25 March 2011. On voit que le projet de Mouton est, sans aucune différence de principe, celui qui a ét réalisé par notre Système métrique.
12. US Metric Association Origin of the metric system
13. Taton, R; Wilson, C, eds. (1989). Planetary astronomy from the Renaissance to the rise of astrophysics – Part A: tycho Brahe to Newton. Cambridge University Press. p. 269. ISBN 978-0-521-24254-7.
14. Snyder, John P (1993). Flattening the earth: two thousand years of map projections. Chicago: University of Chicago Press. p. 63. ISBN 978-0-226-76747-5.
15. Jacques Cassini. (1720) De la grandeur et de la figure de la Terre On the size and features of Earth, pages 14ff.
16. ^ Carnegie, Andrew (May 1905). James Watt (PDF). Doubleday, Page & Company. pp. 59–60. Archived from the original (PDF) on 13 August 2011. Retrieved 20 October 2011.
17. Loidi, Juan Navarro; Saenz, Pilar Merino (6–9 September 2006). "The units of length in the Spanish treatises of military engineering" (PDF). The Global and the Local: The History of Science and the Cultural Integration of Europe. Proceedings of the 2nd ICESHS. Cracow, Poland: The Press of the Polish Academy of Arts and Sciences. Retrieved 17 March 2011.
18. Jackson, Lowis D'Aguilar (1882). Modern metrology; a manual of the metrical units and systems of the present century (1882). London: C Lockwood and co. p. 11. Retrieved 25 March 2011.
19. "History of measurement". Laboratoire national de métrologie et d'essais (LNE) (Métrologie française). Archived from the original on 25 April 2011. Retrieved 6 February 2011.
20. ^  Larousse, Pierre, ed. (1874), "Métrique", Grand dictionnaire universel du XIXe siècle, vol. 11, Paris: Pierre Larousse, pp. 163–64
21. ^ Nelson, Robert A. (1981), "Foundations of the international system of units (SI)" (PDF), Physics Teacher, 19 (9): 597, Bibcode:1981PhTea..19..596N, doi:10.1119/1.2340901
22. Konvitz, Josef (1987). Cartography in France, 1660–1848: Science, Engineering, and Statecraft. University of Chicago Press. ISBN 978-0-226-45094-0.
23. Hellman, C. Doris (January 1936). "Legendre and the French Reform of Weights and Measures". Osiris. 1. University of Chicago Press: 314–340. doi:10.1086/368429. JSTOR 301613. S2CID 144499554.
24. Glaser, Anton (1981) . History of Binary and other Nondecimal Numeration (PDF) (Revised ed.). Tomash. pp. 71–72. ISBN 978-0-938228-00-4. Retrieved 5 April 2013.
25. Adams, John Quincy (22 February 1821). Report upon Weights and Measures. Washington DC: Office of the Secretary of State of the United States.
26. ^ "Décret relatif aux poids et aux mesures. 18 germinal an 3 (7 avril 1795)" [Decree regarding weights and measures: 18 Germinal Year III (7 April 1795)]. Le systeme metrique decimal (in French). Association Métrodiff. Archived from the original on 17 August 2016. Retrieved 7 February 2011.
27. "Lois et décrets" [Laws and decrees]. Histoire de la métrologie (in French). Paris: Association Métrodiff. Retrieved 2 April 2020.
28. Poirier, Jean-Pierre. "Chapter 8: Lavoisier, Arts and Trades". Antoine-Laurent de Lavoisier (1743–1794 – Life and Works. Comité Lavoisier de l'Académie des Sciences de Paris. Retrieved 4 August 2011.
29. "L'Histoire Du Mètre, La Détermination De L'Unité De Poids" [The History of the Metre, the Determination of the Unit of Weight]. histoire.du.metre.free.fr (in French). Retrieved 12 August 2022.
30. ^ van Swinden, Jean Henri (1799) . "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 de Physique, de Chimie, d'Historie Naturelle et des Arts. VI (XLIX): 161–177.
31. Trallès, M. (1810). "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". In Méchain, Pierre; Delambre, Jean B. J. (eds.). 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. Vol. 3. pp. 558–580.
32. History of the kilogram Archived 21 August 2013 at the Wayback Machine
33. Coquebert, Ch (August 1797). "An account of the New System of measures established in France". A Journal of Natural Philosophy, Chemistry, and the Arts. 1: 193–200.
34. Suzanne Débarbat. "Fixation de la longueur définitive du mètre" [Establishing the definitive metre] (in French). Ministère de la culture et de la communication (French ministry of culture and communications). Retrieved 1 March 2011.
35. Smeaton, William A. (2000). "The Foundation of the Metric System in France in the 1790s: The importance of Etienne Lenoir's platinum measuring instruments". Platinum Metals Rev. 44 (3). Ely, Cambridgeshire, United Kingdom: 125–134. doi:10.1595/003214000X443125134. Retrieved 10 November 2012.
36. CHISHOLM, H.W. (9 October 1873). "On the Science of Weighing and Measuring, and the Standards of Weight and Measure*". Nature. 8 (206): 489–491. Bibcode:1873Natur...8..489C. doi:10.1038/008489a0. S2CID 3968820.
37. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), ISBN 92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021
38. Hargrove, JL (December 2006). "History of the calorie in nutrition". Journal of Nutrition. 136 (12). Bethesda, Maryland: 2957–61. doi:10.1093/jn/136.12.2957. PMID 17116702.
39. "Joule's was friction apparatus, 1843". London, York and Bradford: Science Museum, National Railway Museum and the National Media Museum. Retrieved 8 July 2013.
40. Kapil Subramanian (25 February 2011). "How the electric telegraph shaped electromagnetism" (PDF). Current Science. 100 (4). Retrieved 12 May 2011.
41. Thomson, William; Joule, James Prescott; Maxwell, James Clerk; Jenkin, Flemming (1873). "First Report – Cambridge 3 October 1862". In Jenkin, Flemming (ed.). Reports on the Committee on Standards of Electrical Resistance – Appointed by the British Association for the Advancement of Science. London. pp. 1–3. Retrieved 12 May 2011.{{cite book}}: CS1 maint: location missing publisher (link)
42. Thomson, William; Joule, James Prescott; Maxwell, James Clerk; Jenkin, Flemming (1873). "Second report – Newcastle-upon-Tyne 26 August 1863". In Jenkin, Flemming (ed.). Reports on the Committee on Standards of Electrical Resistance – Appointed by the British Association for the Advancement of Science. London. pp. 39–41. Retrieved 12 May 2011.{{cite book}}: CS1 maint: location missing publisher (link)
43. J C Maxwell (1873). A treatise on electricity and magnetism. Vol. 1. Oxford: Clarendon Press. pp. 1–3. Retrieved 12 May 2011.
44. ^ J C Maxwell (1873). A treatise on electricity and magnetism. Vol. 2. Oxford: Clarendon Press. pp. 242–245. Retrieved 12 May 2011.
45. Silvanus P. Thompson. "In the beginning ... Lord Kelvin". International Electrotechnical Commission. Archived from the original on 23 December 2016. Retrieved 10 May 2011.
46. Professor Everett, ed. (1874). "First Report of the Committee for the Selection and Nomenclature of Dynamical and Electrical Units". Report on the Forty-third Meeting of the British Association for the Advancement of Science Held at Bradford in September 1873. 43. British Association for the Advancement of Science: 222–225. Retrieved 10 May 2011.
47. "centimeter–gram–second systems of units". Sizes, Inc. 6 August 2001. Retrieved 7 April 2011.
48. A large constant, about 300,000,000 metres/second.
49. O'Connor, John J.; Robertson, Edmund F. (January 2000), "Georg Simon Ohm", MacTutor History of Mathematics Archive, University of St Andrews
50. Booth, Graham (2003). Revise AS Physics. London: Letts Educational. Chapter 2 – Electricity. ISBN 184315-3025.
51. "The International System of Units". Satellite Today. 1 February 2000. Archived from the original on 18 October 2016. Retrieved 5 April 2011.
52. Russ Rowlett (4 December 2008). "How Many? A Dictionary of Units of Measurement: "ab-"". University of North Carolina at Chapel Hill. Archived from the original on 20 December 2008. Retrieved 12 May 2011.
53. "farad". Sizes, Inc. 9 June 2007. Archived from the original on 9 October 2019. Retrieved 10 May 2011.
54. Russ Rowlett (1 September 2004). "How Many? A Dictionary of Units of Measurement: "stat-"". University of North Carolina at Chapel Hill. Archived from the original on 20 December 2008. Retrieved 12 May 2011.
55. Dan Petru Danescu (9 January 2009). "The evolution of the Gaussian Units" (PDF). The general journal of science. Archived from the original (PDF) on 12 March 2012. Retrieved 7 May 2011.
56. "Gaussian, SI and Other Systems of Units in Electromagnetic Theory" (PDF). Physics 221A, Fall 2010, Appendix A. Berkeley: Department of Physics University of California. Retrieved 7 May 2011.
57. "1981 ... A year of anniversaries" (PDF). IEC Bulletin. XV (67). Geneva: International Electrotechnical Commission. January 1981. Archived from the original (PDF) on 30 October 2012. Retrieved 23 October 2013.
58. ^ McGreevy, Thomas; Cunningham, Peter (1995). The Basis of Measurement: Volume 1 – Historical Aspects. Picton Publishing (Chippenham) Ltd. ISBN 978-0-948251-82-5. (pg 140) The originator of the metric system might be said to be Gabriel Mouton.
59. H.T.Pledge (1959) . "Chapter XXI: Quantum Theory". Science since 1500. Harper Torchbooks. pp. 271–275.
60. Thomas W. Leland. G.A. Mansoori (ed.). "Basic Principles of Classical and Statistical Thermodynamics" (PDF). Department of Chemical Engineering, University of Illinois at Chicago. Retrieved 10 May 2011.
61.  "Mètre", Grand dictionnaire universel du XIXe siècle, vol. 17 (Suppl. 2), Paris: Pierre Larousse, 1890, p. 1587
62. ^ The International Metre Commission (1870–1872), International Bureau of Weights and Measures, retrieved 15 August 2010
63. ^ The BIPM and the evolution of the definition of the metre, International Bureau of Weights and Measures, archived from the original on 7 June 2011, retrieved 15 August 2010
64. Text of the treaty: "Convention du mètre" (PDF) (in French). Retrieved 8 March 2011.
65. Jabbour, Z.J.; Yaniv, S.L. (2001). "The Kilogram and Measurements of Mass and Force" (PDF). J. Res. Natl. Inst. Stand. Technol. 106 (1). National Institute of Standards and Technology (NIST: 25–46. doi:10.6028/jres.106.003. PMC 4865288. PMID 27500016. Archived from the original (PDF) on 4 June 2011. Retrieved 28 March 2011.
66. F. J. Smith (1973). "Standard Kilogram Weights – A Story of Precision Fabrication" (PDF). Platinum Metals Review. 17 (2): 66–68. doi:10.1595/003214073X1726668. S2CID 267431184. Archived from the original (PDF) on 9 June 2011. Retrieved 11 May 2011.
67. Unità razionali di elettromagnetismo, Giorgi (1901)
68. "Historical figures ... Giovanni Giorgi". International Electrotechnical Commission. 2011. Archived from the original on 15 May 2011. Retrieved 5 April 2011.
69. Superintendent of the Metrology Department of the National Physical Laboratory, UK
70. Barrel, H. (1962), "The Metre", Contemp. Phys., 3 (6): 415–34, Bibcode:1962ConPh...3..415B, doi:10.1080/00107516208217499
71. Phelps, F. M. III (1966), "Airy Points of a Meter Bar", Am. J. Phys., 34 (5): 419–22, Bibcode:1966AmJPh..34..419P, doi:10.1119/1.1973011
72. Resolution 6 – Proposal for establishing a practical system of units of measurement. 9th Conférence Générale des Poids et Mesures (CGPM). 12–21 October 1948. Retrieved 8 May 2011.
73. Resolution 6 – Practical system of units. 10th Conférence Générale des Poids et Mesures (CGPM). 5–14 October 1954. Retrieved 8 May 2011.
74. Resolution 7 – Writing and printing of unit symbols and of numbers. 9th Conférence Générale des Poids et Mesures (CGPM). 12–21 October 1948. Retrieved 27 November 2022.
75. ^ "Leap seconds". Time Service Department, U.S. Naval Observatory. Archived from the original on 12 March 2015. Retrieved 29 April 2011.
76. F. Richard Stephenson (1982). "Historical Eclipses". Scientific American. 247 (4): 154–163. Bibcode:1982SciAm.247d.154S. Archived from the original on 15 January 2019. Retrieved 18 April 2011.
77. Fenna, Donald (2002). Dictionary of Weights, Measures and Units. Oxford: Oxford University Press. ISBN 978-0-19-860522-5.
78. Pretley, B.W. (1992). Crovini, L; Quinn, T.J (eds.). The continuing evolution in the definitions and realisations of the SI units of measurement. La metrologia ai confini tra fisica e tecnologia (Metrology at the Frontiers of Physics and Technology). Bologna: Societa Italiana di Fisica. ISBN 978-0-444-89770-1.
79. "A brief history of SI". NIST. Retrieved 29 March 2011.
80. "CIPM, 1948 and 9th CGPM, 1948". International Bureau of Weights and Measures (BIPM). Retrieved 8 February 2011.
81. Resolution 3 – Triple point of water; thermodynamic scale with a single fixed point; unit of quantity of heat (joule). 9th Conférence Générale des Poids et Mesures (CGPM). 12–21 October 1948. Retrieved 8 May 2011.
82. Resolution 3 – Definition of the thermodynamic temperature scale and. 10th Conférence Générale des Poids et Mesures (CGPM). 5–14 October 1954. Retrieved 8 May 2011.
83. Barry N. Taylor (1992). The Metric System: The International System of Units (SI). U. S. Department of Commerce. p. 18. ISBN 978-0-941375-74-0. (NIST Special Publication 330, 1991 ed.)
84. radian, steradian, hertz, newton, joule, watt, coloumb, volt, farad, ohm, weber, tesla, henry, degree Celsius, lumen, lux
85. "Techniques for Approximating the International Temperature Scale of 1990" (PDF). Sèvres: BIPM. 1997 . Retrieved 10 May 2011.
86. de Laeter, JR; Böhlke, JK; de Bièvre, P; Hidaka, H; HS, Peiser; Rosman, KJR; Taylor, PDP (2003). "Atomic Weights of the Elements: Review 2000 (IUPAC Technical Report)" (PDF). Pure Appl. Chem. 75 (6). International Union of Pure and Applied Chemistry: 690–691. doi:10.1351/pac200375060683. S2CID 96800435. Archived from the original (PDF) on 23 January 2013. Retrieved 6 July 2013.
87. Resolution 3 – SI unit of thermodynamic temperature (kelvin) and Resolution 4 – Definition of the SI unit of thermodynamic temperature (kelvin). 9th Conférence Générale des Poids et Mesures (CGPM). 12–21 October 1948. Retrieved 8 May 2011.
88. "Base unit definitions: Meter". NIST. Retrieved 15 November 2011.
89. ^ G. Girard (1994). "The Third Periodic Verification of National Prototypes of the Kilogram (1988–1992)". Metrologia. 31 (4): 317–336. Bibcode:1994Metro..31..317G. doi:10.1088/0026-1394/31/4/007. S2CID 250743540.
90. "Practical realization of the definitions of some important units". SI brochure, Appendix 2. BIPM. 9 September 2010. Retrieved 5 May 2011.
91. Materese, Robin (14 May 2018). "Kilogram: Introduction". nist.gov.
92. ^ Treese, Steven A. (2018). History and measurement of the base and derived units. Cham, Switzerland: Springer. p. 92. ISBN 978-3-319-77577-7. OCLC 1036766223.
93. "Resolution proposal submitted to the IUPAP Assembly by Commission C2 (SUNAMCO)" (PDF). International Union of Pure and Applied Physics. 2008. Archived (PDF) from the original on 5 March 2016. Retrieved 6 September 2015.
94. Mills, Ian (29 September 2010). "On the possible future revision of the International System of Units, the SI" (PDF). CCU. Archived (PDF) from the original on 13 January 2012. Retrieved 1 January 2011.
95. Mills, Ian (29 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units" (PDF). CCU. Archived (PDF) from the original on 16 March 2012. Retrieved 1 January 2011.
96. "Resolution 12 of the 23rd meeting of the CGPM (2007)". Sèvres, France: General Conference on Weights and Measures. Archived from the original on 21 April 2013. Retrieved 21 June 2013.
97. "Towards the "new SI"". International Bureau of Weights and Measures (BIPM). Archived from the original on 14 May 2011. Retrieved 20 February 2011.
98. "On the possible future revision of the International System of Units, the SI – Draft Resolution A" (PDF). International Committee for Weights and Measures (CIPM). Archived (PDF) from the original on 6 August 2011. Retrieved 14 July 2011.
99. Kühne, Michael (22 March 2012). "Redefinition of the SI". Keynote address, ITS (Ninth International Temperature Symposium). Los Angeles: NIST. Archived from the original on 18 June 2013. Retrieved 1 March 2012.
100. "9th edition of the SI Brochure". BIPM. 2019. Retrieved 20 May 2019.
101. "Resolution 1: On the possible future revision of the International System of Units, the SI" (PDF). 24th meeting of the General Conference on Weights and Measures. Sèvres, France: International Bureau for Weights and Measures. 21 October 2011. It was not expected to be adopted until some prerequisite conditions are met, and in any case not before 2014. See"Possible changes to the international system of units". IUPAC Wire. 34 (1). January–February 2012.
102. "General Conference on Weights and Measures approves possible changes to the International System of Units, including redefinition of the kilogram" (PDF) (Press release). Sèvres, France: General Conference on Weights and Measures. 23 October 2011. Archived (PDF) from the original on 9 February 2012. Retrieved 25 October 2011.
103. Mohr, Peter (2 November 2011). "Redefining the SI base units". NIST Newsletter. NIST. Archived from the original on 12 August 2016. Retrieved 1 March 2012.
104. "Resolutions adopted by the CGPM at its 25th meeting (18–20 November 2014)" (PDF). Sèvres, France: International Bureau for Weights and Measures. 21 November 2014. Archived (PDF) from the original on 25 March 2015. Retrieved 1 December 2014.
105. "Draft Resolution A "On the revision of the International System of units (SI)" to be submitted to the CGPM at its 26th meeting (2018)" (PDF). Archived (PDF) from the original on 29 April 2018. Retrieved 5 May 2018.

v t e Systems of measurement
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