History of the Metric System

History of the metric system 1

History of the metric systemFor a topical guide to this subject, see Outline of the metric system.

Woodcut dated 1800 illustrating the six new decimalunits that became the legal norm across all France on 4

November 1800

Concepts similar to those behind the metric system had beendiscussed the 16th and 17th centuries. Simon Stevin hadpublished his ideas for a decimal notation and John Wilkins hadpublished a proposal for a decimal system of measurement basedon natural units. The first practical realisation of the metricsystem came in 1799, during the French Revolution, when theexisting system of measure, which had fallen into disrepute, wastemporarily replaced by a decimal system based on the kilogramand the metre. The work of reforming the old system of weightsand measures had the support of whoever was in power, includingLouis XVI. The metric system was to be, in the words ofphilosopher and mathematician Condorcet, "for all people for alltime". In the era of humanism, the basic units were taken from thenatural world: the unit of length, the metre, was based on thedimensions of the Earth, and the unit of mass, the kilogram, wasbased on the mass of water having a volume of one litre or onethousandth of a cubic metre. Reference copies for both units weremanufactured and placed in the custody of the French Academyof Sciences. By 1812, due to the unpopularity of the new metricsystem, France had reverted to a measurement system using unitssimilar to those of their old system.

In 1837 the metric system was re-adopted by France, and alsoduring the first half of the 19th century was adopted by thescientific community. In the middle of the century, James ClerkMaxwell put forward the concept of a coherent system where asmall number of units of measure were defined as base units, andall other units of measure, called derived units, were defined in terms of the base units. Maxwell proposed three baseunits: length, mass and time. This concept worked well with mechanics, but attempts to describe electromagneticforces in terms of these units encountered difficulties. By the end of the 19th century, four principal variants of themetric system were in use for the measurement of electromagnetic phenomena: three based on thecentimetre-gram-second system of units (CGS system), and one on the metre-kilogram-second system of units (MKSsystem). This impasse was resolved by Giovanni Giorgi, who in 1901 proved that a coherent system thatincorporated electromagnetic units had to have an electromagnetic unit as a fourth base unit.

Until 1875, the French government owned the prototype metre and kilogram, but in that year the Convention of themetre was signed, and control of the standards relating to mass and length passed to a trio of inter-governmentalorganisations, the senior of which was the General Conference on Weights and Measures (in French the Confrencegnrale des poids et mesures or CGPM). During the first half of the 20th century, the CGPM cooperated with anumber of other organisations, and by 1960 it had responsibility for defining temporal, electrical, thermal, molecularand luminar measurements, while other international organisations continued their roles in how these units ofmeasurement were used.In 1960, the CGPM launched the International System of Units (in French the Systme international d'units or SI) which had six "base units": the metre, kilogram, second, ampere, degree Kelvin (subsequently renamed the "kelvin")


and candela; as well as 22 further units derived from the base units. The mole was added as a seventh base unit in1971. During this period, the metre was redefined in terms of the wavelength of the waves from a particular lightsource, and the second was defined in terms of the frequency of radiation from another light source. By the end ofthe 20th century, work was well under way to redefine the ampere, kilogram, mole and kelvin in terms of the basicconstants of physics. It is expected that this work will be completed by 2014.

Development of underlying principlesThe first practical implementation of the metric system: 1089 was the system implemented by FrenchRevolutionaries towards the end of the 18th century. Its key features were that: It was decimal in nature. It derived its unit sizes from nature. Units that have different dimensions are related to each other in a rational manner. Prefixes are used to denote multiples and sub-multiples of its units.These features had already been explored and expounded by various scholars and academics in the two centuriesprior to the French metric system being implemented.Simon Stevin is credited with introducing the decimal system into general use in Europe. Twentieth-century writerssuch Bigourdan (France, 1901) and McGreevy (United Kingdom, 1995) credit the French cleric Gabriel Mouton(1670) as the originator of the metric system.:140 In 2007 a proposal for a coherent decimal system of measurementby the English cleric John Wilkins (1668) received publicity. Since then writers have also focused on Wilkins'proposals: Tavernor (2007):4651 gave both Wilkins and Mouton equal coverage while Quinn (2012) makes nomention of Mouton but states that "he [Wilkins] proposed essentially what became... the French decimal metricsystem".


Work of Simon Stevin

Frontspiece of the publication where John Wilkinsproposed a metric system of units in which length,

mass, volume and area would be related to each other

During the early medieval era, Roman numerals were used inEurope to represent numbers, but the Arabs represented numbersusing the Hindu numeral system, a positional notation that usedten symbols. In about 1202, Fibonacci published his book LiberAbaci (Book of Calculation) which introduced the concept ofpositional notation into Europe. These symbols evolved into thenumerals "0", "1", "2" etc.

At that time there was dispute regarding the difference betweenrational numbers and irrational numbers and there was noconsistency in the way in which decimal fractions wererepresented. In 1586, Simon Stevin published a small pamphletcalled De Thiende ("the tenth") which historians credit as being thebasis of modern notation for decimal fractions. Stevin felt that thisinnovation was so significant that he declared the universalintroduction of decimal coinage, measures, and weights to bemerely a question of time.:70:91

Work of John Wilkins

In the mid seventeenth century John Wilkins, the first secretary ofEngland's Royal Society, was asked by the society to devise a"universal standard of measure". In 1668 he attempted to codify allknowledge in his 621 page book An Essay towards a RealCharacter and a Philosophical Language. Four pages of Part II in Chapter VII were devoted to physicalmeasurement. Here Wilkins also proposed a decimal system of units of measure based on what he called a "universalmeasure" that was derived from nature for use between "learned men" of various nations.[1]

Wilkins considered the earth's meridian, atmospheric pressure[2] and, following a suggestion by Christopher Wrenand demonstrations by Christiaan Huygens, the pendulum as the source for his universal measure. He discardedatmospheric pressure as a candidate it was described by Torricelli in 1643 as being susceptible to variation (thelink between atmospheric pressure and weather was not understood at the time) and he discarded a meridian as beingtoo difficult to measure; leaving the pendulum as his preferred choice. He proposed that the length of a "secondspendulum"[3] (approximately 993mm) which he named the "standard" should be the basis of length. He proposedfurther that the "measure of capacity" (base unit of volume) should be defined as a cubic standard and that the"measure of weight" (base unit of weight [mass]) should be the weight of a cubic standard of rainwater. All multiplesand sub-multiples of each of these measures would be related to the base measure in a decimal manner. In short,Wilkins "proposed essentially what became... the French decimal metric system".

Work of Gabriel MoutonIn 1670, Gabriel Mouton, a French abbot and astronomer, published the book Observationes diametrorum solis et lunae apparentium 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 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 milles. Mouton used Riccioli's estimate that one degree of arc was 321,185 Bolognese feet, and his own experiments showed that a pendulum of length one virgula would beat 3959.2 times[4] in half an hour. Current pendulum theory shows that such a pendulum would have had an equivalent


length of 205.6mm using today's knowledge of the size of the earth, the virgula would have been approximately185.2mm.[5] He believed that with this information scientists in a foreign country would be able to construct a copyof the virgula for their own use.

17th Century developments

Comparison of Wilkins' "Bob" pendulum andJefferson's "rod" pendulum, both of which beat

once per second

Communication of metrological information was one of the issuesfacing mid-seventeenth century savants; many discussed the possibilityof scholarly communication using a so-called "universal measure" thatwas not tied to a particular national system of measurement. Mouton'sideas attracted interest at the time; Picard in his work Mesure de laTerre (1671) and Huygens in his work Horologium Oscillatorium sivede motu pendulorum (1673) both proposing that a standard unit oflength be tied to the beat frequency of a pendulum.

The French Academy of Sciences (Acadmie Royale des Sciences)interest in the pendulum experiments were effectively announced byPicard in his work Mesure de la Terre. The length of a "secondpendulum" was measured at a number of locations outside France, in1671 at Uraniborg, an island 26km north of Copenhagen and in 1672Jean Richer measured one at Cayenne in French Guiana, 5 north ofthe equator. There was no discernible difference between theUraniborg pendulum and the Paris one, but there was a 2.81mmdifference between the lengths of the Cayenne pendulum and that fromParis. Cooperation with the English Royal Society showed no discernible difference between pendulums measured inLondon and Paris, but measurements taken at Gore in Senegal, in West Africa were more in line with those taken atCayenne. Meanwhile, in England, Locke, in his work An Essay Concerning Human Understanding (1689), madereferences to the "philosopher's foot" which he defined as being one third of a "second pendulum" at 45 latitude.

In 1686 Englishman Newton, in his book Philosophi Naturalis Principia Mathematica, gave a theoreticalexplanation for the "bulging equator" which also explained the differences found in the lengths of the "secondpendulums", theories that were confirmed by the Acadmie's expedition to Peru in 1735.[6]

18th Century international cooperationIn the late eighteenth century proposals, similar to those of the seventeenth century for a universal measure, weremade for a common international system of measure in the spheres of commerce and technology; when the FrenchRevolutionaries implemented such a system, they drew on many of the seventeenth-century proposals.In the early ninth century, when much of what later became France was part of the Holy Roman Empire, units ofmeasure had been standardised by the Emperor Charlemagne. He had introduced standard units of measure forlength and for mass throughout his empire. As the empire disintegrated into separate nations, including France, thesestandards diverged. It has been estimated that on the eve of the Revolution, a quarter of a million different units ofmeasure were in use in France; in many cases the quantity associated with each unit of measure differed from townto town, and even from trade to trade.:23 Although certain standards, such as the pied du roi (the King's foot) had adegree of pre-eminence and were used by scientists, many traders chose to use their own measuring devices, givingscope for fraud and hindering commerce and industry. These variations were promoted by local vested interests, buthindered trade and taxation. In contrast, in England the Magna Carta (1215) had stipulated that "there shall be oneunit of measure throughout the realm".


James Watt, British inventor and advocate of aninternational decimalized system of measure

By the mid-eighteenth century, it had become apparent thatstandardisation of weights and measures between nations who tradedand exchanged scientific ideas with each other was necessary. Spain,for example, had aligned her units of measure with the royal units ofFrance, and Peter the Great aligned the Russian units of measure withthose of England. In 1783 the British inventor James Watt, who washaving difficulties in communicating with German scientists, called forthe creation of a global decimal measurement system, proposing asystem which, like the seventeenth-century proposal of Wilkins, usedthe density of water to link length and mass, and in 1788 the Frenchchemist Antoine Lavoisier commissioned a set of nine brasscylindersa [French] pound and decimal subdivisions thereof for hisexperimental work.:71

In 1789 French finances were in a perilous state, several years of poorharvests had resulted in hunger among the peasants and reforms werethwarted by vested interests. On 5 May 1789 Louis XVI summoned theEstates-General which has been in abeyance since 1614, triggering a series of events that were to culminate in theFrench Revolution. On 20 June 1789 the newly formed Assemble nationale (National Assembly) took an oath not todisband until a constitution had been drafted, resulting in the setting up, on 27 June 1789, of the Assemble nationaleconstituante (Constituent Assembly). On the same day, the Acadmie des sciences (Academy of Sciences) set up acommittee to investigate the reform of weights and measures which, due to their diverse nature, had become avehicle for corruption.:23:46

The Marquis de Condorcet "The metric systemis for all people for all time."

On 4 August 1789, three weeks after the storming of the Bastille, thenobility surrendered their privileges, including the right to control localweights and measures.:88 Talleyrand, Assemble representative of theclergy, revolutionary leader and former Bishop of Autun, at theprompting of the mathematician and secretary of the AcadmieCondorcet, approached the British and the Americans in early 1790with proposals of a joint effort to define a common standard of lengthbased on the length of a pendulum. Great Britain, represented by JohnRiggs Miller and the United States represented by Thomas Jeffersonagreed in principle to the proposal, but the choice of latitude for thependulum proved to be a sticking point: Jefferson opting for 38N,Talleyrand for 45N and Riggs-Miller for London's latitude.:9395 On 8May 1790 Talleyrand's proposal in the Assemble that the new measurebe defined at 45N "or whatever latitude might be preferred" won thesupport of all parties concerned. On 13 July 1790, Jefferson presenteda document Plan for Establishing Uniformity in the Coinage, Weights,and Measures of the United States to the U.S. Congress in which, likeWilkins, he advocated a decimal system in which units that usedtraditional names such as inches, feet, roods were related to each by the

powers of ten. Again, like Wilkins, he proposed a system of weights based around the weight of a cubic unit ofwater, but unlike Wilkins, he proposed a "rod pendulum" rather than a "bob pendulum". Riggs-Miller promotedTallyrand's proposal in the British House of Commons.


In response to Tallyrand's proposal of 1790, the Assemble set up a new committee under the auspices of theAcadmie to investigate weights and measures. The members were five of the most able scientists of thedayJean-Charles de Borda, Joseph-Louis Lagrange, Pierre-Simon Laplace, Gaspard Monge and Condorcet. Thecommittee, having decided that counting and weights and measures should use the same radix, debated the use of theduodecimal system as an alternative to the decimal system. Eventually the committee decided that the advantages ofdivisibility by three and four was outweighed by the complications of introducing a duodecimal system and on 27October 1790 recommended to the Assemble that currency, weights and measures should all be based on a decimalsystem. They also argued in favour of the decimalization of time and of angular measures.:7172 The committeeexamined three possible standards for length the length of pendulum that beat with a frequency of once a second at45 latitude, a quarter of the length of the equator and a quarter of the length of a meridian. The committee alsoproposed that the standard for weight should be the weight of distilled water held in cube with sides a decimalproportion of the standard for length.:5051 The committee's final report to the Assemble on 17 March 1791recommended the meridional definition for the unit of length. inventor of the repeating circle was appointedchairmanWikipedia:Please clarify.:2021 The proposal was accepted by the Assemble on 30 March 1791.Jefferson's report was considered but not adopted by the U.S. Congress, and Riggs-Miller lost his BritishParliamentary seat in the election of 1790. When the French later overthrew their monarchy, Britain withdrew hersupport.:252253 and France decided to "go it alone".:8896

Roles of Wilkins and MoutonIn the past many writers such as Bigourdan (France, 1903) and McGreevy (United Kingdom, 1995) credited Moutonas the "founding father" of the metric system.:140 In 2007 the late Australian metric campaigner Pat Naughtininvestigated Wilkins' proposal for a universal system of measurement in Wilkins' essay, a work that pre-datedMouton's proposal by two years. Wilkins' proposal, unlike Mouton's, discussed an integrated measurement systemthat encompassed length, volume and mass rather than just length.Wilkins' Essay was widely circulated at the time, but the main interest in the Essay was his proposal for aphilosophical language in general rather than just a universal standard for units of measure. Subsequent interest inWilkins' Essay was confined mainly to those interested in the field of onomasiology rather than metrology: forexample, Roget in the introduction of his Thesaurus (1852), noted Wilkins' Essay as being one of the leadingseventeenth-century works in onomasiology. British commentators of the Essay devoted little space to Wilkins'proposals of measurement; Vernon et al. (1802) made a passing comment on the section on measurements in aneight-page study of the Essay while Wright-Henderson (1910), in a four-page study of the Essay, made no commentsabout measurements at all.Mouton's proposals were taken seriously by, amongst others, the seventeenth-century scientists Jean Picard andChristiaan Huygens, but a hundred years were to elapse before the French again took interest in the underlyingtheory of the development of systems of measure.Shortly after the introduction of the metric system by the French, a letter by an anonymous but regular contributor toThe Philosophical Magazine (1805) noted the lack of acknowledgement by the French of Wilkins' publication. Thewriter accused the editors of the Encyclopdie of giving unwarranted attention to the work of Mouton and Huygensat the expense of Edward Wright who, in 1599 had proposed using the earth's meridian as a standard, and of Wilkinswho had proposed a measurement system. He took British writers to task for not "defending their countrymen". Hewent on to note that there was considerable communication between scientists on either side of the Channel,particularly with Huygens and Leibniz either visiting or being members of both the Royal Society and the AcadmieRoyale des Sciences.


Implementation in Revolutionary France (17921812)When the National Assembly accepted the committee's report on 30 March 1791, the Acadmie des sciences wasinstructed to implement the proposals. The Acadmie broke the tasks into five operations, allocating each part to aseparate working group::82

1. Measuring the difference in latitude between Dunkirk and Barcelona and triangulating between them (Cassini,Mchain, and Legendre)

2. Measuring the baselines used for the survey (Monge, Meusnier)3. Verifying the length of the second pendulum at 45 latitude (de Borda and de Coulomb).4. Verifying the weight in vacuo of a given volume of distilled water (Antoine Lavoisier and Ren Just Hay).5. Publishing conversion tables relating the new units of measure to the existing units of measure (Tillet).On 19 June 1791, the day before Louis XVI's flight to Varennes Cassini, Mchain, Legendre and Borda obtained aroyal audience where the king agreed to fund both the measurement of the meridian and repeating the measurementsmade by Cassini's father. The king's authorization arrived on 24 June 1791.:2021

During the political turmoil that followed the king's flight to Varennes, the reform of weights and measures and inparticular the measurement of the meridian continued albeit with interruptions, though the structure of thecommission changed with the changing political climate. In May 1792 Cassini, loyal to Louis XVI but not to theRevolution was replaced by Delambre and on 11 July 1792 the Commission formally proposed the names "metre","litre" and multipliers "centi", "kilo" etc. to the Assembly.:82

Louis XVI was executed on 21 January 1793 and on 8 August of that year, on the eve of the Reign of Terror the newde facto government executive, the Committee of Public Safety suppressed all academies and with it thecommission, requiring them to justify their existence. Antoine Franois, comte de Fourcroy, a member of theconvention argued that the importance of reforming weights and measures was such that the work of the commissionshould be allowed to continue. On 11 September 1793 the commission was reconstituted as the commissiontemporaire.On 7 April 1795 the metric system was formally defined in French law and provisional standards based on Cassini'ssurvey of 1740 adopted. On 22 October 1795 the work of the commission (since reconstituted as a three-man agencetemporaire under Legendre's directorship) was taken over by the newly formed National Institute of Arts andScience and under the new government, the Directory, was transferred to the "Office for Weights and Measures"under the Minister of the Interior.:9697

On 15 November 1798 Delambre and Mchain returned to Paris with their data, having completed the survey of theDunkirk-Barcelona meridian. The data was analysed and a prototype metre constructed from platinum with a lengthof 443.296 lignes.[7] At the same time a prototype kilogram was constructed the mass of a cube of water at 4C,each side of the cube being 0.1 metres. The prototype metre was presented to the French legislative assemblies on 22June 1799.:265266


Decimal time (1793)Main article: French Republican Calendar

A clock of the republican era showingboth decimal and standard time

The decree of 5 October 1793 introduced the Republican Calendar intoFrance and with it decimalised time. The day was divided into 10 "decimalhours", the "hour" into 100 "decimal minutes" and the "decimal minute" into100 "decimal seconds". The "decimal hour" corresponded to 2hr24min, the"decimal minute" to 1.44min and the "decimal second" to 0.864s. Therevolutionary week was 10days, but there were still twelve months in a year,each month consisting of three "weeks". Each year had five or six intercalarydays to make up the total of 365 or 366 days.

The implementation of decimal time proved an immense task and under thearticle 22 of the law of 18 Germinal, Year III (7 April 1795), the use ofdecimal time was no longer mandatory, though the Republican Calendar wasretained. On 1 January 1806, France reverted to the traditional timekeeping.

Repeating circle the instrument usedfor triangulation when measuring the

meridian

Angular measure (c. 1793)

Although there was no specific decree regarding angular measure which wasalso decimalised during the 1790s, it is reported to have been used in 1794,:51

but was not mentioned in the metric system decree of 1795. In particular, therepeating circle, invented in about 1787 by Borda, himself a strong proponentof decimalization, was adapted to use decimal angles.

A grade (or gon) was defined as being 1100 of a quadrant, making 400 gradesin a full circle. Fractions of the grade used the standard metric prefixes, thusone centigrade was 110000 of a quadrant, making one centigrade of longitudeapproximately one kilometre.

The adoption of the grade by the cartographic community was sufficient towarrant a mention in the Lexicographia-neologica Gallica in 1801 and its use

continued on military maps through the nineteenth century[8] into the twentieth century.[9] It appears not to have beenwidely used outside cartography. The centigrade, as an angular measure, was adopted for general use in a numbercountries, so in 1948 the General Conference on Weights and Measures (CGPM) recommended that the degreecentigrade, as used for the measurement of temperature, be renamed the degree Celsius. The SI Brochure (2006)notes that the gon is now a little-used alternative to the degree.


Draft metric system (1795)

The Paris meridian which passes through the ParisObservatory (Observatoire de Paris). The metre was

defined along this meridian using a survey thatstretched from Dunkirk to Barcelona.

In France, the metric system of measure was first given a legalbasis in 1795 by the French Revolutionary government. Article 5of the law of 18 Germinal, Year III (7 April 1795) defined six newdecimal units. The units and their preliminary values were:

The metre, for length defined as being one ten millionth ofthe distance between the North Pole and the Equator throughParis

The are(100m2) for area [of land] The stre(1m3) for volume of firewood The litre(1dm3) for volumes of liquid The gramme, for mass defined as being the mass of one cubic

centimetre of water The franc, for currencyDecimal multiples of these units were defined by Greek prefixes:"myria" (10,000), "kilo" (1000), "hecta" (100) and "deka" (10) andsubmultiples were defined by the Latin prefixes "deci" (0.1),"centi" (0.01) and "milli" (0.001). Using Cassini's survey of 1744,a provisional value of 443.44 lignes was assigned to the metrewhich, in turn, defined the other units of measure.:106

The final value of the metre was defined in 1799 when Delambreand Mchain presented the results of their survey between Dunkirk and Barcelona which fixed the length of themetre at 443.296 lignes. The law 19 Frimaire An VIII (10 December 1799) defined the metre in terms of this valueand the kilogramme as being 18827.15 grains. These definitions enabled reference copies of the kilograms andmetres to be constructed and these were used as the standards for the next 90 years.


Meridianal definition

Belfry, Dunkirk the northern end of the meridian arc

The question of measurement reform in France was placed in thehands of the French Academy of Sciences who appointed acommission chaired by Jean-Charles de Borda. Borda could besaid to have been a fanatic for decimalization: he had designed therepeating circle, a surveying instrument which allowed amuch-improved precision in the measurement of angles betweenlandmarks, but insisted that it be calibrated in "grades" (1100 of aquarter-circle) rather than degrees, with 100minutes to a gradeand 100seconds to a minute. The instrument was manufactured bytienne Lenoir. For Borda, the seconds pendulum was a poorchoice for a standard because the second (as a unit of time) wasinsufficiently decimal: he preferred the new system of 10hours tothe day, 100minutes to the hour and 100seconds to the minute.

Instead, the commission whose members included Lagrange,Laplace, Monge and Condorcet decided that the new measureshould be equal to one ten-millionth of the distance from the NorthPole to the Equator (the quadrant of the Earth's circumference),measured along the meridian passing through Paris. Apart fromthe obvious nationalistic considerations, the Paris meridian was

also a sound choice for practical scientific reasons: a portion of the quadrant from Dunkerque to Barcelona (about1000km, or one-tenth of the total) could be surveyed with start- and end-points at sea level, and that portion wasroughly in the middle of the quadrant, where the effects of the Earth's oblateness were expected to be the largest.

The north and south sections of the meridianal surveymet at Rodez cathederal, seen here dominating the

Rodez skyline

The task of surveying the meridian arc, which was authorized byLouis XVI:2133 and which was estimated to take two years, fell toPierre Mchain and Jean-Baptiste Delambre. The task eventuallytook more than six years (179298) with delays caused not onlyby unforeseen technical difficulties but also by the convulsedperiod of the aftermath of the Revolution. In the meantime, thecommission calculated a provisional value from older surveys of443.44lignes.[10]

The project was split into two parts the northern section of742.7km from the Belfry, Dunkirk to Rodez Cathederal whichwas surveyed by Delambre and the southern section of 333.0kmfrom Rodez to the Montjuc Fortress, Barcelona which wassurveyed by Mchain.: 227230[11]

Delambre used a baseline of about 10km in length along a straight road, located close to Melun. In an operationtaking six weeks, the baseline was accurately measured using four platinum rods, each of length two toise (about3.9m).: 227230 Thereafter he used, where possible, the triangulation points used by Cassini in his 1744 survey ofFrance. Mchain's baseline, of a similar length, and also on a straight section of road was in the Perpignan area.:240241 Although Mchain's sector was half the length of Delambre, it included the Pyrenees and hitherto unsurveyedparts of Spain. After the two surveyors met, each computed the other's baseline in order to cross-check their resultsand they then recomputed the kilometre. Their result came out at 0.144lignes shorter than the provisional value, adifference of about 0.03%.


Fortress of Montjuc the southern end of the meridianarc

Mtre des Archives

While Mchain and Delambre were completing their survey, thecommission had ordered a series of platinum bars to be madebased on the provisional metre. When the final result was known,the bar whose length was closest to the meridianal definition of themetre was selected and placed in the French National Archives on22June 1799 (4messidor AnVII in the Republican calendar) as apermanent record of the result: this standard metre bar becameknown as the mtre des Archives.

The metric system, that is the system of units based on the metre,was officially adopted in France on 10December 1799(19frimaire AnVIII) and became the sole legal system of weights

and measures there from 1801.

It soon became apparent that Mchain and Delambre's result (443.296lignes) was slightly too short for themeridianal definition of the metre. Arago and Biot extended the survey to the island of Formentera in the westernMediterranean Sea in 18069, and found that one ten-millionth of the Earth's quadrant should be 443.31lignes: laterwork increased the value to 443.39lignes. The modern value, for the WGS84 reference spheroid, is 1.000 196 57mor 443.383 08lignes.[12]

Nevertheless, the mtre des Archives remained the legal and practical standard for the metre in France, even once itwas known that it did not exactly correspond to the meridianal definition. When, in 1867, it was proposed that a newinternational standard metre be created, the length was taken to be that of the mtre des Archives "in the state inwhich it shall be found".

Kilogramme des Archives

On 7 April 1795, the gramme, upon which the kilogram is based, was decreed to be equal to "the absolute weight ofa volume of pure water equal to a cube of one hundredth of a metre, and at the temperature of the melting ice".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 Lavoisier and Ren JustHay had been in use since 1793. 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 provisionalkilogram standard was made and work was commissioned to determine the precise mass of a cubic decimetre (laterto be defined as equal to one litre) of water.Although the decreed definition of the kilogramme specified water at 0C a highly stable temperature point the scientists tasked with producing the new practical realisation chose to redefine the standard and perform theirmeasurements at the most stable density point: the temperature at which water reaches maximum density, which wasmeasured at the time as 4C.[13] They concluded that one cubic decimetre of water at its maximum density wasequal to 99.92072% of the mass of the provisional kilogram made earlier that year.[14] Four years later in 1799, anall-platinum standard, the "Kilogramme des Archives", was fabricated with the objective that it would equal, as closeas was scientifically feasible for the day, to the mass of cubic decimetre of water at 4C. The kilogramme wasdefined to be equal to the mass of the Kilogramme des Archives and this standard stood for the next ninety years.Note that the new metric system did not come into effect in France until after the French Revolution, 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 Graf, an alternative name forthe title of Count that, like other nobility titles, was inconsistent with the new French Republic notion of equality(galit).[15] Accordingly, the name of the original, defined unit of mass, "gramme", which was too small to serve asa practical realisation, was adopted and the new prefix "kilo" was appended 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.

Adoption of the metric weights and measuresDuring the nineteenth century the metric system of weights and measures proved a convenient political compromiseduring the unification processes in the Netherlands, Germany and Italy. Spain found it expedient in 1858 to followthe French example and within a decade Latin America had also adopted the metric system. There was considerableresistance to metrication in the United Kingdom and in the United States, though once the United Kingdomannounced its metrication program in 1965, the Commonwealth followed suit.

France

Napoleon Bonaparte introduced theMesures usuelles.

Main articles: Mesures usuelles and Units of measurement in FranceThe introduction of the metric system into France in 1795 was done on adistrict by district basis with Paris being the first district, but it was, in termsof modern standards, poorly managed. Although thousands of pamphlets weredistributed, the Agency of Weights and Measures who oversaw theintroduction underestimated the work involved. Paris alone needed 500,000metre sticks, yet one month after the metre became the sole legal unit ofmeasure, they only had 25,000 in store.: 269 This, combined with otherexcesses of the Revolution and the high level of illiteracy made the metricsystem unpopular.

Napoleon himself ridiculed the metric system, but as an able administrator,recognised the value of a sound basis for a system of measurement and underthe dcret imprial du 12 fvrier 1812 (imperial decree of 12 February 1812),a new system of measure the mesures usuelles or "customary measures"was introduced for use in small retail businesses all government, legal andsimilar works still had to use the metric system and the metric systemcontinued to be taught at all levels of education. The names of many unitsused during the ancien regime were reintroduced, but were redefined in termsof metric units. Thus the toise was defined as being two metres with six pied making up one toise, twelve poucemaking up one pied and twelve lignes making up one pouce. Likewise the livre was defined as being 500g, eachlivre comprising sixteen once and each once eight gros and the aune as 120 centimetres.

Louis Philippe I by means of the La loi du 4 juillet 1837 (the law of 4 July 1837) effectively revoked the use ofmesures uselles by reaffirming the laws of measurement of 1795 and 1799 to be used from 1 May 1840. However,many units of measure, such as the livre (for half a kilogram), remained in colloquial use for many years.[16]

The Dutch metric systemThe Netherlands first used the metric system and then, in 1812, the mesures usuelles when it was part of the FirstFrench Empire. Under the Royal decree of 27 March 1817 (Koningklijk besluit van den 27 Maart 1817), the newlyformed Kingdom of the Netherlands abandoned the mesures usuelles in favour of the "Dutch" metric system(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 100g.


The German Zollverein

Stone marking the Austro-Hungarian/Italianborder at Pontebba displaying myriametres

(10km), a unit used in Central Europe in the 19thcentury.

At the outbreak of the French Revolution, much of modern-dayGermany and Austria were part of the Holy Roman Empire which hasbecome a loose federation of kingdoms, principalities, free cities,bishoprics and other fiefdoms, each with its own system ofmeasurement, though in most cases such system were loosely derivedfrom the Carolingian system instituted by Charlemagne a thousandyears earlier.

During the Napoleonic era, there was a move among some of theGerman states to reform their systems of measurement using theprototype metre and kilogram as the basis of the new units. Baden, in1810, for example, redefined the Ruthe (rods) as being 3.0m exactlyand defined the subunits of the Ruthe as 1 Ruthe = 10Fu (feet) =100Zoll (inches) = 1,000Linie (lines) = 10,000Punkt (points) whilethe Pfund was defined as being 500g, divided into 30Loth, each of16.67g. Bavaria, in its reform of 1811, trimmed the Bavarian Pfundfrom 561.288g to 560g exactly, consisting of 32 Loth, each of 17.5gwhile the Prussian Pfund remained at 467.711g.

After the Congress of Vienna there was a degree of commercialcooperation between the various German states resulting in the settingof the German Customs Union (Zollverein). There were however still

many barriers to trade until Bavaria took the lead in establishing the General German Commercial Code in 1856. Aspart of the code the Zollverein introduce the Zollpfund (Customs Pound) which was defined to be exactly 500g andwhich could be split into 30'lot'. This unit was used for inter-state movement of goods, but was not applied in allstates for internal use.

Although the Zollverein collapsed after the Austro-Prussian War of 1866, the metric system became the officialsystem of measurement in the newly formed German Empire in 1872:350 and of Austria in 1875. The Zollpfundceased to be legal in Germany after 1877.


Italy

Tablet showing conversions of legacy units ofweights and measures to metric units,

Vicopisano, Tuscany

The Cisalpine Republic, a North Italian republic set up by Napoleon in1797 with its capital at Milan first adopted a modified form of themetric system based in the braccio cisalpino (Cisalpine cubit) whichwas defined to be half a metre. In 1802 the Cisalpine Republic wasrenamed the Italian Republic, with Napoleon as its head of state. Thefollowing year the Cisalpine system of measure was replaced by themetric system.

In 1806, the Italian Republic was replaced by the Kingdom of Italywith Napoleon as its emperor. By 1812, all of Italy from Romenorthwards was under the control of Napoleon, either as FrenchDepartments or as part of the Kingdom of Italy ensuring the metricsystem was in use throughout this region.

After the Congress of Vienna, the various Italian states reverted to theiroriginal system of measurements, but in 1845 the Kingdom ofPiedmont and Sardinia passed legislation to introduce the metricsystem within five years. By 1860, most of Italy had been unifiedunder the King of Sardinia Victor Emmanuel II and under Law 132 of28 July 28, 1861 the metric system became the official system ofmeasurement throughout the kingdom. Numerous Tavole di ragguaglio (Conversion Tables) were displayed in shopsuntil 31 December 1870.

SpainUntil the ascent of the Bourbon monarchy in Spain in 1700, each of the regions of Spain retained its own system ofmeasurement. The new Bourbon monarchy tried to centralise control and with it the system of measurement. Therewere debates regarding the desirability of retaining the Castilian units of measure or, in the interests ofharmonisation, adopting the French system. Although Spain assisted Mchain in his meridian survey, theGovernment feared the French revolutionary movement and reinforced the Castilian units of measure to counter suchmovements. By 1849 however, it proved difficult to maintain the old system and in that year the metric systembecame the legal system of measure in Spain.

United Kingdom and the CommonwealthMain articles: Metrication in the United Kingdom and Metrication of British transportIn 1824 the Weights and Measures Act imposed one standard 'imperial' system of weights and measures on theBritish Empire. The effect of this act was to standardise existing British units of measure rather than to align themwith the metric system.During the next eighty years a number of Parliamentary select committees recommended the adoption of the metricsystem each with a greater degree of urgency, but Parliament prevaricated. A Select Committee report of 1862recommended compulsory metrication, but with an "Intermediate permissive phase", Parliament responded in 1864by legalising metric units only for 'contracts and dealings'. Initially the United Kingdom declined to sign the Treatyof the Metre, but did so in 1883. Meanwhile British scientists and technologists were at the forefront of themetrication movement it was the British Association for the Advancement of Science that promoted the cgs systemof units as a coherent system: 109 and it was the British firm Johnson Matthey that was accepted by the CGPM in1889 to cast the international prototype metre and kilogram.


In 1895 another Parliamentary select committee recommended the compulsory adoption of the metric system after atwo-year permissive period, the 1897 Weights and Measures Act legalised the metric units for trade, but did notmake them mandatory. A bill to make the metric system compulsory in order to enable British industrial base to fightoff the challenge of the nascent German base passed through the House of Lords in 1904, but did not pass in theHouse of Commons before the next general election was called. Following opposition by the Lancashire cottonindustry, a similar bill was defeated in 1907 in the House of Commons by 150 votes to 118.In 1965 Britain commenced an official program of metrication that, as of 2012, had not been completed. The Britishmetrication program signalled the start of metrication programs elsewhere in the Commonwealth, though India hadstarted its program before in 1959, six years before the United Kingdom. South Africa (then not a member of theCommonwealth) set up a Metrication Advisory Board in 1967, New Zealand set up its Metric Advisory Board in1969, 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 metricationin India and Canada is not complete. In addition the lakh and crore are still in widespread use in India. Most otherCommonwealth countries adopted the metric system during the 1970s.

United StatesMain article: Metrication in the United StatesThe United States government acquired copies of the French metre and kilogram for reference purposes in 1805 and1820 respectively. In 1866 the United States Congress passed a bill making it lawful to use the metric system in theUnited States. The bill, which was permissive rather than mandatory in nature, defined the metric system in terms ofcustomary units rather than with reference to the international prototype metre and kilogram.:1013 By 1893, thereference standards for customary units had become unreliable. Moreover, the United States, being a signatory of theMetre Convention was in possession of national prototype metres and kilograms that were calibrated against those inuse elsewhere in the world. This led to the Mendenhall Order which redefined the customary units by referring to thenational metric prototypes, but used the conversion factors of the 1866 act.:1620 In 1896 a bill that would make themetric system mandatory in the United States was presented to Congress. Of the 29 people who gave evidencebefore 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. The bill was not enacted. Subsequent billssuffered a similar fate.

Development of a coherent metric systemFrom its inception, the metric system was designed in such a manner that the various units of measure were linked toeach other. At the start of the nineteenth century, length, mass, time and temperature were the only base unit unitsthat were defined in terms of formal standards. The beginnings of a coherent system were in place with the units ofarea and volume linked to the unit of length, though at the time science did not understand the concepts of base unitsand derived units, nor how many physical quantities were inter-related. This concept, which enabled thermal,mechanical, electrical and relativistic systems to be interlinked was first formally proposed in 1861 using length,mass and time as base units. The absence of an electrical base unit resulted in a number of different electricalsystems being developed in the latter half of the nineteenth century. The need for such a unit to resolve theseproblems was identified by Giorgi in 1901. The SI standard which was published in 1960 defined a single coherentsystem based on six units.:109


Time, work and energyIn 1832 Carl-Friedrich Gauss made the first absolute measurements of the Earth's magnetic field using a decimalsystem based on the use of the millimetre, milligram, and second as the base unit of time.:109 In his paper, he alsopresented his results using the metre and gram instead of the millimetre and milligram, also using the Parisian lineand the Berlin pound[17] instead of the millimetre and milligram.

Joule's apparatus for measuring the mechanicalequivalent of heat. As the weight dropped,

potential energy was transferred to the water,heating it up.

In a paper published in 1843, James Prescott Joule first demonstrated ameans of measuring the energy transferred between different systemswhen work is done thereby relating Nicolas Clment's calorie, definedin 1824, to mechanical work. Energy became the unifying concept ofnineteenth century science, initially by bringing thermodynamics andmechanics together and later adding electrical technology andrelativistic physics leading to Einstein's equation . TheCGS unit of energy was the "erg", while the SI unit of energy wasnamed the "joule" in honour of Joule.

In 1861 a committee of the British Association for Advancement ofScience (BAAS) including William Thomson (later Lord Kelvin),James Clerk Maxwell and Joule among its members was tasked withinvestigating the "Standards of Electrical Resistance". In their firstreport (1862) they laid the ground rules for their work the metricsystem was to be used, measures of electrical energy must have the same units as measures of mechanical energyand two sets of electromagnetic units would have to be derived an electromagnetic system and an electrostaticsystem. In the second report (1863) they introduced the concept of a coherent system of units whereby units oflength, mass and time were identified as "fundamental units" (now known as base units). All other units of measurecould be derived (hence derived units) from these base units. The metre, gram and second were chosen as base units.

In 1873, another committee of the BAAS that also counted Maxwell and Thomson among its members and taskedwith "the Selection and Nomenclature of Dynamical and Electrical Units" recommended using the CGS(centimetre-gram-second) system of units. The committee also recommended the names of "dyne" and "erg" for theCGS units of force and energy. The CGS system became the basis for scientific work for the next seventy years.

Electrical unitsIn the 1820s Georg Ohm formulated Ohms Law which can be extended to relate power to current, potentialdifference (voltage) and resistance. During the following decades the realisation of a coherent system of units thatincorporated the measurement of electromagnetic phenomena and Ohm's law was beset with problems at least fourdifferent systems of units were devised. In the three CGS systems, the constants and and consequently and were dimensionless.

Symbols used in this section


Symbol Meaning

Electromagneticand

Electrostaticforces

Electrical currentin conductors

Electrical charges

Conductor length

distance betweencharges/conductors

permittivity offree space

permeability offree space

System of unitdependant constants

Speed of light

Electromagnetic system of units (EMU)

The Electromagnetic system of units (EMU) was developed from Andr-Marie Ampre's discovery in 1820sof a relationship between the force between two current-carrying conductors. This relationship is now knownas Ampere's law which can be written

where (SI units)

In 1833 Gauss pointed out the possibility of equating this force with its mechanical equivalent. This proposalreceived further support from Wilhelm Weber in 1851. The electromagnetic (or absolute) system of units wasone of the two systems of units identified in the BAAS report of 1862 and defined in the report of 1873. In thissystem, current is defined by setting the magnetic force constant to unity and potential difference isdefined in such a way as to ensure the unit of power calculated by the relation is identical to theunit of power required to move a mass of one gram a distance of one centimetre in one second when opposedby a force of one dyne. The electromagnetic units of measure were known as the abampere, the abvolt, theabcoulomb and so on.Electrostatic system of units (ESU)

The Electrostatic system of units (ESU) was based on Coulomb's discovery in 1783 of the relationshipbetween the force exerted between two charged bodies. This relationship, now known as Coulomb's law canbe written

where (SI units)

The electrostatic system was the second of the two systems of units identified in the 1862 BAAS report anddefined in the report of 1873. In this system unit for charge is defined by setting the Coulomb force constant (

) to unity and the unit for potential difference were defined to ensure the unit of energy calculated by therelation is one erg. The electrostatic units of measure are now known as the statampere, thestatvolt, the statcoulomb and so on.Gaussian system of units


The Gaussian system of units was based on Heinrich Hertz realization, made in 1888 while verifyingMaxwell's Equations, that the CGS system of electromagnetic units to were related to the CGS system ofelectrostatic units by the relationship:

Using this relationship, he proposed merging the EMU and the ESU systems into one system using the EMUunits for magnetic quantities (subsequently named the gauss and maxwell) and ESU units elsewhere. Henamed this combined set of units "Gaussian units". This set of units has been recognised as being particularlyuseful in theoretical physics.:128

Practical system of units

The CGS units of measure used in scientific work were not practical when used in engineering leading to thedevelopment of the practical system of electric units. At the time that this system of units was proposed, thedimension of electrical resistance was modelled in the EMU system as the ratio L/T and in the ESU system asits inverse T/L.The unit of length adopted for the practical system was the 108 m (approximately the length of the Earth'squadrant), the unit of time was the second and the unit of mass an unnamed unit equal to 1011 g and thedefinitions of electrical units were based on those of the EMU system. The names, but not the values, amp,volt, farad and ohm were carried over from the EMU system. The system was adopted at the First InternationalElectrical Congress (IEC) in 1881. The second IEC congress (1889) defined the joule and the watt at thepractical units of energy and power respectively. The units were formalised as the International System ofElectrical and Magnetic Units at the 1893 congress of the IEC in Chicago where the volt, amp and ohm wereformally defined. The SI units with these names are very close, but not identical to the "practical units".

A coherent systemThe electrical units of measure did not easily fit into the coherent system using length, mass and time as its baseunits as proposed in the 1861 BAAS paper. Using dimensional analysis the dimensions of charge as defined by theESU system of units was identical to the dimensions of current as defined by the EMU system of units while resistance had the same dimensions as velocity in the EMU system of units, but had the dimensions of theinverse of velocity in the ESU system of units.From mid-1890s onwards Giovanni Giorgi and Oliver Heaviside corresponded with each other regarding theseanomalous results. This led to Giorgi presenting a paper to the congress of the Associazione Elettrotecnica Italiana(A.E.I.)[18] in October 1901 in which he showed that a coherent electro-mechanical system of units could beobtained by adding a fourth base unit of an electrical nature (ampere, volt or ohm) to the three base units proposed inthe 1861 BAAS report. This gave the constants ke and km physical dimensions and hence the electro-mechanicalquantities 0 and 0 were also given physical dimensions. His work also recognized the unifying concept that energyplayed in the establishment of a coherent, rational system of units with the joule as the unit of energy and theelectrical units in the practical system of units remaining unchanged.:156

The 1893 definitions of the ampere and the ohm by the IEC led to the joule as being defined in accordance with theIEC resolutions being 0.02% larger than the joule as defined in accordance with the artefacts helds by the BIPM. In1908, the IEC prefixed the units of measure that they had defined with the word "international", hence the"international ampere", "international volt" etc.:155156 It took more than thirty years before Giorgi's work wasaccepted in practice by the IEC. In 1946 the CIPM formally adopted a definition of the ampere based on the originalEMU definition and redefined the ohm in terms of other base units. In 1960, Giorgi's proposals were adopted as thebasis of the Systme International d'Units (International System of Units), the SI.:109


Naming the units of measureIn 1861, 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 centimetre-gramme-secondabsolute system. This was supported by Thomson (Lord Kelvin) These names were later scaled for use in thePractical System. The concept of naming units of measure after noteworthy scientists was subsequently used forother units.

Convention of the metreMain article: Metre Convention

Seal of the International Bureau ofWeights and Measures (BIPM)

With increasing international adoption of the metre, the short-comings of themtre des Archives as a standard became ever more apparent. Countrieswhich adopted the metre as a legal measure purchased standard metre barsthat were intended to be equal in length to the mtre des Archives, but therewas no systematic way of ensuring that the countries were actually working tothe same standard. The meridianal definition, which had been intended toensure international reproducibility, quickly proved so impractical that is wasall but abandoned in favour of the artefact standards, but the mtre desArchives (and most of its copies) were "end standards": such standards (barswhich are exactly one metre in length) are prone to wear with use, anddifferent standard bars could be expected to wear at different rates.

The International Conference on Geodesy in 1867 called for the creation of anew, international prototype metre[19] 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 betweentwo lines marked on the bar, so avoiding the wear problems of end standards. The French government gave practicalsupport to the creation of an International Metre Commission, which met in Paris in 1870 and again in 1872 with theparticipation of about thirty countries.

On 20 May 1875 an international treaty known as the Convention du Mtre (Metre Convention) was signed by 17states.[20] This treaty established the following organisations to conduct international activities relating to a uniformsystem for measurements:

Confrence gnrale des poids et mesures (CGPM or General Conference on Weights and Measures), anintergovernmental conference of official delegates of member nations and the supreme authority for allactions;

Comit 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 andis 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), apermanent laboratory and world centre of scientific metrology, the activities of which include theestablishment of the basic standards and scales of the principal physical quantities, maintenance of theinternational prototype standards and oversight of regular comparisons between the international prototype andthe various national standards.

The international prototype metre and 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 asnational prototypes.

Twentieth century

U.S. national standard of the metre, showing thebar number (#27), the Tresca cross-section and

one of the lines

At the beginning of the twentieth century, the BIPM had custody oftwo artefacts one to define length and the other to define mass. Otherunits of measure which did not rely on specific artefacts werecontrolled by other bodies. In the scientific world, quantum theory wasin its infancy and Einstein had yet to publish his theories of relativity.By the end of the century, a coherent system of units was in placeunder the control of the bodies set up by the Treaty of the Metre, thedefinition of the second relied on quantum theory, the definition of themetre relied on the theory of relativity and plans were being made torelegate the international prototype kilogram to the archives.

Metre

The first (and only) follow-up comparison of the national standardswith the international prototype metre was carried out between 1921 and 1936, and indicated that the definition ofthe metre was preserved to within 0.2m. During this follow-up comparison, the way in which the prototype metreshould be measured was more clearly definedthe 1889 definition had defined the metre as being the length of theprototype at the definition of melting ice, but in 1927 the 7thCGPM extended this definition was to specify that theprototype metre shall be "supported on two cylinders of at least one centimetre diameter, symmetrically placed in thesame horizontal plane at a distance of 571mm from each other".:14243, 148 The choice of 571mm represents theAiry points of the prototypethe points at which the bending or droop of the bar is minimized.

In 1887 Michelson proposed the use of optical interferometers for the measurement of length, work whichcontributed to him being awarded the Nobel Prize in 1907. In 1952 the CIPM proposed the use of wavelength of aspecific light source as the standard for defining length and in 1960 the CGPM accepted this proposal using radiationcorresponding to a transition between specified energy levels of the krypton 86 atom as the new standard for themetre. By 1975, when the second had been defined in terms of a physical phenomenon rather than the earth's rotationand Einstein's assertion that the speed of light was constant, the CGPM authorised the CIPM to investigate the use ofthe speed of light as the basis for the definition of the metre. This proposal was accepted in 1983.


Kilogram

Mass drift over time of national prototypes K21K40, plus two of the IPK's sister copies:K32 and K8(41). [21] The above are all relative measurements; no historical

mass-measurement data is available to determine which of the prototypes has been moststable 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 simplygained less than the others.

Although the definition of the kilogramremained unchanged throughout thetwentieth century, the 3rd CGPM in1901 clarified that the kilogram was aunit of mass, not of weight. Theoriginal batch of 40 prototypes(adopted in 1889) were supplementedfrom time to time with furtherprototypes for use by new signatoriesto the Metre Convention.

During the course of the century, thevarious national prototypes of thekilogram were recalibrated against theInternational Prototype Kilogram(IPK) and therefore against each other.The initial 1889 starting-value offsetsof the national prototypes relative tothe IPK were nulled. and anysubsequent mass changes beingrelative to the IPK. A technique for steam cleaning the prototypes to remove any contaminants was developed in1946 as part of the second recalibration.

The third periodic recalibration in 1988-9 revealed that the average difference between the IPK and adjusted baselinefor the national prototypes was 50g in 1889 the baseline of the national prototypes had been adjusted so that thedifference was zero. As the IPK is the definitive kilogram, there is no way of telling whether the IPK had been losingmass or the national prototypes had been gaining mass.

TimeUntil the advent of the atomic clock, the most reliable timekeeper available to mankind was the earth's rotation. Itwas natural therefore that the astronomers under the auspice of the International Astronomical Union (IAU) took thelead in maintaining the standards relating to time. In 1988, responsibility for timekeeping passed to the BIPM whotook on the role of coordinating a number of atomic clocks scattered around the globe. During the twentieth centuryit became apparent that the earth's rotation was slowing down resulting in days becoming 1.4 milliseconds longereach century this was verified by comparing the calculated timings of eclipses of the sun with those observed inantiquity going back to Chinese records of 763BC.In 1956 the 10th CGPM instructed the CIPM to prepare a definition of the second; in 1958 the definition waspublished stating that the second would be calculated by extrapolation using earth's rotational speed in 1900.Astronomers from the US Naval Observatory (USNO) and the National Physical Laboratory determined arelationship between the frequency of radiation corresponding to the transition between the two hyperfine levels ofthe ground state of the caesium 133 atom and the estimated rate of rotation of the earth in 1900. Their value wasadopted in 1968 by the 13th CGPM.


Electrical units

Four domestic quality contemporary measuring devicesthat have metric calibrations a tape measure

calibrated in centimetres, a thermometer calibrated indegrees Celsius, a kilogram weight (mass) and an

electrical multimeter which measures volts, amps andohms

In 1921 the Treaty of the Metre was extended to cover electricalunits with the CGPM merging its work with that of the IEC. At the8th CGPM in 1933 the need to replace the "International"electrical units with "absolute" units was raised. The IEC proposalthat Giorgi's proposal be adopted was accepted, but no decisionwas made as to which electrical unit should be the fourth base unit.In 1935 Sears proposed that this should be the ampere, but WorldWar II prevented this being formalised until 1946. The definitionsfor absolute electrical system based on the ampere was formalizedin 1948.

Temperature

At the start of the twentieth century, the fundamental macroscopiclaws of thermodynamics had been formulated and althoughtechniques existed to measure temperature using empiricaltechniques, the scientific understanding of the nature oftemperature was minimal. Maxwell and Boltzmann had producedtheories describing the inter-relational of temperature, pressureand volume of a gas on a microscopic scale but otherwise, in 1900,there was no understanding of the microscopic or quantum natureof temperature. Within the metric system, temperature wasexpressed in degrees Centigrade with the definition that ice meltedat 0C and at standard atmospheric pressure, water boiled at 100C. A series of lookup tables defined temperaturein terms of inter-related empirical measurements made using various devices.When, in 1948 the CGPM was charged with producing a coherent system of units of measure, definitions relating totemperature had to be clarified. At the 9th CGPM, the centigrade temperature scale was renamed the Celsiustemperature scale and the scale itself was fixed by defining the triple point of water as 0.01C, though the CGPMleft the formal definition of absolute zero until the 10th GCPM when the name "Kelvin" was assigned to the absolutetemperature scale and triple point of water was defined as being 273.16K. In 1967, at the 13th GCPM the degreeKelvin (K) was renamed the "kelvin" (K).

Over the ensuing years, the BIPM developed and maintained cross-correlations relating various measuring devicessuch as thermocouples, light spectra and the like to the equivalent temperatures. Increasingly the use of theBoltzmann Relationship was used as the reference point and it appears likely that in 2015 the CGPM will redefinetemperature in terms of the Boltzmann constant rather than the triple point of water.

LuminosityPrior to 1937, the International Commission on Illumination (CIE from its French title, the CommissionInternationale de l'Eclairage) in conjunction with the CIPM produced a standard for luminous intensity to replace thevarious national standards. This standard, the candela (cd) which was defined as "the brightness of the full radiator atthe temperature of solidification of platinum is 60 new candles per square centimetre".[22] was ratified by the GCPMin 1948 and in 1960 was adopted as an SI base unit. The definition proved difficult to implement so in 1967, thedefinition was revised and the reference to the radiation source was replaced by defining the candles in terms of thepower of a specified wavelength of visible light.: 115


In 2007 the CIPM and the CIE agreed a program of cooperation with the CIPM taking the lead in defining the use ofunits of measure and the CIE taking the lead in defining the behaviour of the human eye.

MoleThe mole was originally known as a gram-atom or a gram-molecule the amount of a substance measured in gramsdivided by its atomic weight. Originally chemists and physicists had differing views regarding the definition of theatomic weight both assigned a value of 16atomic mass units (amu) to oxygen, but physicists defined oxygen interms of the 16O isotope whereas chemists assigned 16amu to 16O, 17O and 18O isotopes mixed in the proportionthat 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 in1959/60, both parties agreeing to define the atomic weight of 12C as being exactly 12 amu. This agreement wasconfirmed by ISO and in 1969 the CIPM recommended its inclusion in SI as a base unit. This was done in 1971 atthe 14th CGPM.:114115

International System of Units (SI)Main article: International System of UnitsThe 9th CGPM met in 1948, fifteen years after the 8th CGPM. In response to formal requests made by theInternational Union of Pure and Applied Physics and by the French government to establish a practical system ofunits of measure, the CGPM requested the CIPM to prepare recommendations for a single practical system of unitsof measurement, suitable for adoption by all countries adhering to the Metre Convention. At the same time theCGPM formally adopted a recommendation for the writing and printing of unit symbols and of numbers. Therecommendation also catalogued the recommended symbols for the most important MKS and CGS units of measureand for the first time the CGPM made recommendations concerning derived units.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 withGiorgi's proposals of 1901, the CIPM also recommended that the ampere be the base unit from whichelectromechanical would be derived. The definitions for the ohm and volt that had previously been in use werediscarded and these units became derived units based on the metre, ampere, second and kilogram. After negotiationswith the CIS and IUPAP, two further base units, the degree kelvin and the candela were also proposed as base units.The full system and name "Systme International d'Units" were adopted at the 11th CGPM.During the years that followed the definitions of the base units and particularly the mise en pratique to realise thesedefinitions have been refined.


Proposed revision of unit definitionsMain article: New SI definitions

Relations between proposed SI units definitions (in colour) and withseven fundamental constants of nature (in grey) with fixed numerical

values in the proposed system

After the metre was redefined in 1960, the kilogramremained the only SI base defined by a physicalexample or artefact. Moreover, after the 19961998recalibration a clear divergence between the variousprototype kilograms was observed.

At its 23rd meeting (2007), the CGPM mandated theCIPM to investigate the use of natural constants as thebasis for all units of measure rather than the artefactsthat were then in use. At a meeting of the CCU held inReading, United Kingdom in September 2010, aresolution and draft changes to the SI brochure thatwere to be presented to the next meeting of the CIPMin October 2010 were agreed to in principle. Theproposals that the CCU put forward were that:

in addition to the speed of light, four constants ofnaturePlanck's constant, an elementary charge,Boltzmann constant and Avogadro's numberbedefined to have exact values;

the international prototype kilogram be retired; the current definitions of the kilogram, ampere, kelvin and mole be revised; the wording of the definitions of all the base units be tightened up.

The CIPM meeting of October 2010 found that "the conditions set by the General Conference at its 23rd meetinghave not yet been fully met. For this reason the CIPM does not propose a revision of the SI at the present time";however the CIPM presented a resolution for consideration at the 24th CGPM (1721 October 2011) to agree thenew definitions in principle, but not to implement them until the details have been finalised. This resolution wasaccepted by the conference and in addition the CGPM moved the date of the 25th meeting forward from 2015 to2014.

Notes[1] Transcription of relevant pages (126 kB) the associated PDF file is over 25 MB in length (http:/ / www. metricationmatters. com/ docs/

WilkinsTranslationShort. pdf)[2] Described by Wilkins as the "quicksilver experiment" an experiment in which Torricelli demonstrated the existence of atmospheric pressure

using what would today be called a mercury barometer[3] A "seconds pendulum" is a pendulum with a half-period of one second)[4][4] There were two beats in an oscillation.[5][5] Derived from the knowledge that the earth's circumference is approximately 40,000km.[6] The acceleration due to gravity at the poles is 9.832m/s2 and at the equator 9.780m/s2, a difference of about 0.5%. (http:/ / www. ucl. ac.

uk/ EarthSci/ people/ lidunka/ GEOL2014/ Geophysics2 - Gravity/ gravity. htm)[7] The French pied (foot) has 12 pouce (inches) and each pouce has 12 lignes (lines). The French units are 6.57% larger than their English

counterparts.[8] For example this 1852military map of Paris[9] For example this 1902 military map of Paris.[10] All values in lignes are referred to the toise de Prou, not to the later value in mesures usuelles. 1toise= 6pieds; 1pied= 12pouces;

1pouce= 12lignes; so 864lignes= 1toise.[11] Distances measured using Google Earth. The coordinates are:

Belfry, Dunkirk Rodez Cathederal


Montjuc, Barcelona[12][12] The WGS84 reference spheroid has a semi-major axis of and a flattening of .[13] L'Histoire Du Mtre, La Dtermination De L'Unit De Poids, link to Web site here. (http:/ / histoire. du. metre. free. fr/ fr/ index. htm)[14] History of the kilogram (http:/ / www. sizes. com/ units/ kilogram. htm)[15] BIPM the name "kilogram" (http:/ / www. bipm. org/ en/ si/ history-si/ name_kg. html)[16][16] Crease (2011) refers to:[17] The Parisian line = of a Parisian pied or foot or 1.066 English lines. The Berlin (or Prussian) pfund or pound was 468g or about 1.032

imperial pounds.[18] it:Associazione Elettrotecnica Italiana (in Italian)[19][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" 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][20] Text of the treaty:[21][21] 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).[22][22] (NIST Special Publication 330, 1991 ed.)

References

Article Sources and Contributors 26

Article Sources and ContributorsHistory of the metric system Source: http://en.wikipedia.org/w/index.php?oldid=624483287 Contributors: A. Parrot, Arch dude, Arjayay, Awien, BarrelProof, Bender235, Bo Jacoby, Boson,Carminowe of Hendra, Ceinturion, Cobulator, Comp.arch, CopperSquare, Coreyemotela, Credibility gap, Crusoe8181, Dawnseeker2000, DeFacto, Des Titres, Doctormatt, Download, Drmies,Drpickem, Ehrenkater, Eikob, Ergative rlt, Ericl, Fraggle81, Frakturfreak, Fruitpunchline, Future Perfect at Sunrise, Gaius Cornelius, Garamond Lethe, Gilliam, Ginsuloft, Glacialfox, GroundZero, GroveGuy, Iajanus, J991, JOHNDOE, Jc3s5h, Jdaloner, Jdoniach, John of Reading, Keith D, Khazar2, LilHelpa, LittleWink, Lklundin, Martinvl, Mcoupal, MeasureIT, Metron, Mild BillHiccup, Mr Stephen, Muhandes, Myasuda, NebY, Nerlost, Orenburg1, PBS, PKT, Peter Horn, Piledhigheranddeeper, Pyrotec, Reywas92, Rjwilmsi, Sander1453, Scartboy, Srice13,Stevengriffiths, StoneProphet, Sun Creator, Tbhotch, The Rambling Man, WOSlinker, Widr, Will Bradshaw, Wolsunger, Woohookitty, Ymblanter, 54 , anonymous edits

Image Sources, Licenses and ContributorsFile:Poids et mesures.png Source: http://en.wikipedia.org/w/index.php?title=File:Poids_et_mesures.png License: Public Domain Contributors: Pollllux, PyrotecFile:Wilkins An Essay towards a real.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Wilkins_An_Essay_towards_a_real.jpg License: Public Domain Contributors: Martinvl,Valrie75File:MetricPendulums2.svg Source: http://en.wikipedia.org/w/index.php?title=File:MetricPendulums2.svg License: Creative Commons Attribution-Sharealike 3.0 Contributors: User:MartinvlFile:Watt James von Breda.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Watt_James_von_Breda.jpg License: Public Domain Contributors: Astrochemist, Connormah,Dcoetzee, Diomede, Hystrix, Jvsfan, Martin H., VictuallersFile:Nicolas de Condorcet.PNG Source: http://en.wikipedia.org/w/index.php?title=File:Nicolas_de_Condorcet.PNG License: Public Domain Contributors: Beria, Coyau, Ecummenic,Graphium, Mathiasrex, 1 anonymous editsFile:Horloge-republicaine4.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Horloge-republicaine4.jpg License: Public Domain Contributors: CopyRighter, Dahn, Future Perfect atSunrise, Martinvl, Mate2code, Rama, RighterCopy, Wst, Yonatanh, 2 anonymous editsFile:Cercle-reflexion-Lenoir.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Cercle-reflexion-Lenoir.jpg License: GNU Free Documentation License Contributors: Karel K.,Mcapdevila, Paris 16, Pline, Rama, Roomba, WstFile:Obs-Paris-meridienne.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Obs-Paris-meridienne.jpg License: Creative Commons Attribution-ShareAlike 3.0 UnportedContributors: Bohme, Clicgauche, Damouns, FredA, Gilles MAIRET, Olivier, Paris 16, Tevatron, 1 anonymous editsFile:Dunkerque Belfort.JPG Source: http://en.wikipedia.org/w/index.php?title=File:Dunkerque_Belfort.JPG License: Creative Commons Attribution-Sharealike 3.0 Contributors: WelleschikFile:Rodez-coquelicots480.JPG Source: http://en.wikipedia.org/w/index.php?title=File:Rodez-coquelicots480.JPG License: Creative Commons Attribution-Sharealike 3.0,2.5,2.0,1.0Contributors: AnRo0002, Kilom691, Pauzies, TangopasoFile:Monjuic's castle in Barcelona.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Monjuic's_castle_in_Barcelona.jpg License: Creative Commons Attribution-ShareAlike 3.0Unported Contributors: Gepardenforellenfischer, Jordiferrer, Marb, Pyrotec, 1 anonymous editsFile:Jacques-Louis David - The Emperor Napoleon in His Study at the Tuileries - Google Art Project 2.jpg Source:http://en.wikipedia.org/w/index.php?title=File:Jacques-Louis_David_-_The_Emperor_Napoleon_in_His_Study_at_the_Tuileries_-_Google_Art_Project_2.jpg License: Public DomainContributors: Artwork, INS Pirat, LouisKenzo, Moe Epsilon, Paris 16, SteinsplitterFile:Alter Grenzstein Pontebba 01.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Alter_Grenzstein_Pontebba_01.jpg License: GNU Free Documentation License Contributors:User Johann Jaritz on de.wikipediaFile:Vicopisano-misure antiche.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Vicopisano-misure_antiche.jpg License: Creative Commons Attribution-Sharealike 3.0Contributors: Davide PapaliniFile:Joule's Apparatus (Harper's Scan).png Source: http://en.wikipedia.org/w/index.php?title=File:Joule's_Apparatus_(Harper's_Scan).png License: Public Domain Contributors:Ariadacapo, Chowbok, Martinvl, Pieter Kuiper, 1 anonymous editsFile:Metric seal.svg Source: http://en.wikipedia.org/w/index.php?title=File:Metric_seal.svg License: Public Domain Contributors: en:user:SsolbergjFile:US National Length Meter.JPG Source: http://en.wikipedia.org/w/index.php?title=File:US_National_Length_Meter.JPG License: Public Domain Contributors: Chetvorno, Man vyi,Mormegil, Mu, 1 anonymous editsFile:Prototype mass drifts.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Prototype_mass_drifts.jpg License: GNU Free Documentation License Contributors: Original uploaderwas Greg L at en.wikipediaFile:FourMetricInstruments.JPG Source: http://en.wikipedia.org/w/index.php?title=File:FourMetricInstruments.JPG License: Creative Commons Attribution-Sharealike 3.0 Contributors:MartinvlFile:Relations between new SI units definitions.png Source: http://en.wikipedia.org/w/index.php?title=File:Relations_between_new_SI_units_definitions.png License: Creative CommonsAttribution-Share Alike Contributors: Wikipetzi

LicenseCreative Commons Attribution-Share Alike 3.0//creativecommons.org/licenses/by-sa/3.0/

History of the metric systemDevelopment of underlying principlesWork of Simon StevinWork of John WilkinsWork of Gabriel Mouton17th Century developments18th Century international cooperationRoles of Wilkins and Mouton

Implementation in Revolutionary France (17921812)Decimal time (1793)Angular measure (c. 1793)Draft metric system (1795)Meridianal definitionMtre des ArchivesKilogramme des Archives

Adoption of the metric weights and measuresFranceThe Dutch metric systemThe German ZollvereinItalySpainUnited Kingdom and the CommonwealthUnited States

Development of a coherent metric systemTime, work and energyElectrical unitsA coherent systemNaming the units of measure

Convention of the metreTwentieth centuryMetreKilogramTimeElectrical unitsTemperatureLuminosityMole

International System of Units (SI)Proposed revision of unit definitions

NotesReferences

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History of the Metric System

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