# History of the metric system

For a topical guide to this subject, see Outline of the metric system.
Woodcut dated 1800 illustrating the new decimal units which became the legal norm across all France on 4 November 1800

The concepts behind the metric system were developed in the 16th and 17th centuries when Simon Stevin published details of his decimal notation and John Wilkins published a proposal for a decimal system of measurement based on natural units. The first practical realisation of the metric system came during the French Revolution, when the existing system of measure which had fallen into disrepute was replaced by a decimal system based on the kilogram and the metre. The work of reforming the existing system of weights and measures had the support of whoever was in power, including Louis XVI. The metric system was, in the words of philosopher and mathematician Condorcet, "for all people for all time". 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 water having a volume of one litre or one thousandth of a cubic metre. Reference copies for both units were manufactured and placed in the custody of the French Academy of Sciences.

During the first half of the 19th century, the metric system was adopted by the scientific community. In the middle of the century, James Clerk Maxwell put forward the concept of 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: length, mass and time. This concept worked well with mechanics, but attempts to describe electromagnetic forces in terms of these units encountered difficulties. By the end of the 19th century, four principal variants of the metric system were in use for the measurement of electromagnetic phenomena: three based on the centimetre-gram-second system of units (CGS system), and one on the metre-kilogram-second system of units (MKS system). This impasse was resolved by Giovanni Giorgi, who in 1901 proved that a coherent system that incorporated electromagnetic units had to have an electromagnetic unit as the fourth base unit.

Until 1875, the French government owned the prototype metre and kilogram, but in that year the Convention of the metre 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 General Conference on Weights and Measures (in French the Conférence générale des poids et mesures or CGPM). During the first half of the 20th 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 International System of Units (in French the Système international d'unités 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 in 1971. During this period, the metre was redefined in terms of the wavelength of the waves from a particular light source, and the second was defined in terms of the frequency of radiation from another light source. By the end of the 20th century, work was well under way to redefine the ampere, kilogram, mole and kelvin in terms of the basic constants of physics. It is expected that this work will be completed by 2014.

## Development of underlying principles

The first practical implementation of the metric system[1]: 108–9 was the system implemented by French Revolutionaries 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 centuries prior to the French metric system being implemented.

Simon Stevin is credited with introducing the decimal system into general use in Europe.[2] Twentieth-century writers such Bigourdan (France, 1901) and McGreevy (United Kingdom, 1995) credit the French cleric Gabriel Mouton (1670) as the originator of the metric system.[3][4]:140 In 2007 a proposal for a coherent decimal system of measurement by the English cleric John Wilkins (1668) received publicity.[5][6][7] Since then writers have also focused on Wilkins' proposals: Tavernor (2007)[8]:46–51 gave both Wilkins and Mouton equal coverage while Quinn (2012)[9] makes no mention of Mouton but states that "he [Wilkins] proposed essentially what became ... the French decimal metric system".

### Work of Simon Stevin

Frontspiece of the publication where John Wilkins proposed 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 in Europe to represent numbers,[10] 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.[11][12]

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. In 1586, Simon Stevin published a small pamphlet called De Thiende ("the tenth") which historians credit as being the basis of modern notation for decimal fractions.[13] 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.[8]:70[2][14]:91

### Work of John Wilkins

In the mid seventeenth century John Wilkins, the first secretary of England's Royal Society, was asked by the society to devise a "universal standard of measure".[15] In 1668 he attempted to codify all knowledge in his 621 page book An Essay towards a Real Character and a Philosophical Language. Four pages of Part II in Chapter VII were devoted to physical measurement. Here Wilkins also proposed a decimal system of units of measure based on what he called a "universal measure" that was derived from nature for use between "learned men" of various nations.[16][17]

Wilkins considered the earth's meridian, atmospheric pressure[Note 1] and, following a suggestion by Christopher Wren and demonstrations by Christiaan Huygens, the pendulum as the source for his universal measure. He discarded atmospheric pressure as a candidate – it was described by Torricelli in 1643 as being susceptible to variation (the link between atmospheric pressure and weather was not understood at the time) and he discarded a meridian as being too difficult to measure; leaving the pendulum as his preferred choice. He proposed that the length of a "seconds pendulum"[Note 2] (approximately 993 mm) which he named the "standard" should be the basis of length.[18] He proposed further 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 multiples and 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".[9]

### Work of Gabriel Mouton

In 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 savants 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[Note 3] in half an hour.[19] Current pendulum theory shows that such a pendulum would have had an equivalent length of 205.6 mm – using today's knowledge of the size of the earth, the virgula would have been approximately 185.2 mm.[Note 4] He believed that with this information savants in a foreign country would be able to construct a copy of the virgula for their own use.[20]

### 17th Century developments

Comparison of Wilkins' "Bob" pendulum and Jefferson's "rod" pendulum, both of which beat once per second

Communication of metrological information was one of the issues facing mid-seventeenth century savants; many discussed the possibility of scholarly communication using a so-called "universal measure" that was not tied to a particular national system of measurement.[21] 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 (1673) both proposing that a standard unit of length be tied to the beat frequency of a pendulum.[3][20]

The French Academy of Sciences (Académie Royale des Sciences) interest in the pendulum experiments were effectively announced by Picard in his work Mesure de la Terre. The length of a "second pendulum" was measured at a number of locations outside France, in 1671 at Uraniborg, an island 26 km north of Copenhagen and in 1672 Jean Richer measured one at Cayenne in French Guiana, 5° north of the equator. There was no discernible difference between the Uraniborg pendulum and the Paris one, but there was a 2.81 mm difference between the lengths of the Cayenne pendulum and that from Paris. Cooperation with the English Royal Society showed no discernible difference between pendulums measured in London and Paris, but measurements taken at Gorée in Senegal, in West Africa were more in line with those taken at Cayenne.[21][22][23] Meanwhile, in England, Locke, in his work An Essay Concerning Human Understanding (1689), made references to the "philosopher's foot" which he defined as being one third of a "second pendulum" at 45° latitude.[24]

In 1686 Englishman Newton, in his book Philosophiæ Naturalis Principia Mathematica, gave a theoretical explanation for the "bulging equator" which also explained the differences found in the lengths of the "second pendulums",[25] theories that were confirmed by the Académie's expedition to Peru in 1735.[26][Note 5]

### 18th Century international cooperation

In the late eighteenth century proposals, similar to those of the seventeenth century for a universal measure, were made for a common international system of measure in the spheres of commerce and technology; when the French Revolutionaries 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 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. 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.[14]: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.[27] These variations were promoted by local vested interests, but hindered trade and taxation.[28][29] In contrast, in England the Magna Carta (1215) had stipulated that "there shall be one unit of measure throughout the realm".[30]

James Watt, British inventor and advocate of an international decimalized system of measure[31]

By the mid eighteenth century, it had become apparent that standardisation of weights and measures between nations who traded and exchanged scientific ideas with each other was necessary. Spain, for example, had aligned her units of measure with the royal units of France,[32] and Peter the Great aligned the Russian units of measure with those of England.[33] 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, like the seventeenth century proposal of Wilkins, used the density of water to link length and mass[31] and in 1788 the French chemist Antoine Lavoisier commissioned a set of nine brass cylinders—a [French] pound and decimal subdivisions thereof for his experimental work.[8]:71

In 1789 the French finances were in a perilous state, several years of poor harvests had resulted in hunger among the peasants and reforms were thwarted by vested interests.[34] On 5 May 1789 Louis XVI summonsed the Estates-General which has been in abeyance since 1614 triggering a series of events that were to cumulate in the French Revolution. On 20 June 1789 the newly formed Assemblée nationale (National Assembly) took an oath not to disband until a constitution has been drafted resulting in the setting up, on 27 June 1789, of the Assemblée nationale constituante (Constituent Assembly). On the same day, the Académie des sciences (Academy of Sciences) set up a committee to investigate the reform of weights and measures which, due to their diverse nature, had become a vehicle for corruption.[14]:2–3[35]:46

The Marquis de Condorcet – "The metric system is for all people for all time."

On 4 August 1789, three weeks after the storming of the Bastille the nobility surrendered their privileges, including the right to control local weights and measures.[14]:88

Talleyrand, Assemblée representative of the clergy, revolutionary leader and former Bishop of Autun, at the prompting of the mathematician and secretary of the Académie Condorcet,[36] approached the British and the Americans in early 1790 with proposals of a joint effort to define a common standard of length based on the length of a pendulum. Great Britain, represented by John Riggs Miller and the United States represented by Thomas Jefferson agreed in principle to the proposal, but the choice of latitude for the pendulum proved to be a sticking point: Jefferson opting for 38°N, Talleyrand for 45°N and Riggs-Miller for London's latitude.[14]:93–95 On 8 May 1790 Talleyrand's proposal in the Assemblée that the new measure be defined at 45°N "or whatever latitude might be preferred"[37] won the support of all parties concerned.[28] On 13 July 1790, Jefferson presented a document Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States to the U.S. Congress in which, like Wilkins, he advocated a decimal system in which units that used traditional 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 of water, but unlike Wilkins, he proposed a "rod pendulum" rather than a "bob pendulum".[38] Riggs-Miller promoted Tallyrand's proposal in the British House of Commons.

In response to Tallyrand's proposal of 1790, the Assemblée set up a new committee under the auspices of the Académie to investigate weights and measures. The members were five of the most able scientists of the day—Jean-Charles de Borda, Joseph-Louis Lagrange, Pierre-Simon Laplace, Gaspard Monge and Condorcet. The committee, having decided that counting and weights and measures should use the same radix, debated the use of the duodecimal system as an alternative to the decimal system. Eventually the committee decided that the advantages of divisibility by three and four was outweighed by the complications of introducing a duodecimal system and on 27 October 1790 recommended to the Assemblée that currency, weights and measures should all be based on a decimal system. They also argued in favour of the decimalization of time and of angular measures.[8]:71–72 The committee examined three possible standards for length – the length of pendulum that beat with a frequency of once a second at 45° latitude, a quarter of the length of the equator and a quarter of the length of a meridian. The committee also proposed that the standard for weight should be the weight of distilled water held in cube with sides a decimal proportion of the standard for length.[8]:50–51[39][40] The committee's final report to the Assemblée on 17 March 1791 recommended the meridional definition for the unit of length.[41][42] inventor of the repeating circle was appointed chairman.[14]:20–21 The proposal was accepted by the Assemblée on 30 March 1791.[37]

Jefferson's report was considered but not adopted by the U.S. Congress and Riggs-Miller lost his British Parliamentary seat in the election of 1790.[43] When the French later overthrew their monarchy Britain withdrew her support.[14]:252–253 and France decided to "go it alone".[14]:88–96

### Roles of Wilkins and Mouton

In the past many writers such as Bigourdan (France, 1903) and McGreevy (United Kingdom, 1995) credited Mouton as the "founding father" of the metric system.[3][4]:140 In 2007 the Australian researcher Pat Naughtin "rediscovered" Wilkins proposal for a universal system of measurement in Wilkins' Essay, a work that predated Mouton's proposal by two years.[5][7] Wilkins' proposal, unlike Mouton's proposal, discussed an integrated measurement system that 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 a philosophical language in general rather than just a universal standard for units of measure.[15] Subsequent interest in Wilkins' Essay was confined mainly to those interested in the field of onomasiology rather than metrology: for example, Roget in the introduction of his Thesaurus (1852), noted Wilkins' Essay as being one of the leading seventeenth-century works in onomasiology.[44] British commentators of the Essay devoted little space to Wilkins' proposals of measurement; Vernon et al. (1802) made a passing comment to the section on measurements in an eight-page study of the Essay[45] while Wright-Henderson (1910), in a four-page study of the Essay, made no comments about measurements at all.[46]

Mouton's proposals were taken seriously by, amongst others, the seventeenth century scientists Jean Picard and Christiaan Huygens but a hundred years were to elapse before the French again took interest in the underlying theory of the development of systems of measure.[20]

Shortly after the introduction of the metric system by the French, a letter by an anonymous but regular contributor to the The Philosophical Magazine (1805) noted the lack of acknowledgement by the French of Wilkins' publication. The writer accused the editors of Encyclopédie of giving unwarranted attention to the work of Mouton and Huygens at the expense of Edward Wright who, in 1599 had proposed using the earth's meridian as a standard and of Wilkins who had proposed a measurement system. He took British writers to task for not "defending their countrymen". He went on to note that there was considerable communication between savants on either side of the Channel, particularly with Huygens and Liebnitz either visiting or being members of both the Royal Society and the Académie Royale des Sciences.[47]

## Implementation in Revolutionary France (1792–1812)

When the National Assembly accepted the committee's report on 30 March 1791, 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:[8]:82

1. Measuring the difference in latitude between Dunkirk and Barcelona and triangulating between them (Cassini, Méchain, 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 René Just Haüy).
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, Méchain, Legendre and Borda obtained a royal audience where the king agreed to fund both the measurement of the meridian and repeating the measurements made by Cassini's father. The king's authorization arrived on 24 June 1791.[14]:20–21

During the political turmoil that followed the king's flight to Varennes, the reform of weights and measures and in particular the measurement of the meridian continued albeit with interruptions, though the structure of the commission changed with the changing political climate. In May 1792 Cassini, loyal to Louis XVI but not to the Revolution was replaced by Delambre[48] and on 11 July 1792 the Commission formally proposed the names "metre", "litre" and multipliers "centi", "kilo" etc. to the Assembly.[8]: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 new de facto government executive, the Committee of Public Safety suppressed all academies and with it the commission, requiring them to justify their existence. Antoine François, comte de Fourcroy, a member of the convention argued that the importance of reforming weights and measures was such that the work of the commission should be allowed to continue. On 11 September 1793 the commission was reconstituted as the commission temporaire.[49]

On 7 April 1795 the metric system was formally defined in French law and provisional standards based on Cassini's survey of 1740 adopted. On 22 October 1795 the work of the commission (since reconstituted as a three-man agence temporaire under Legendre's directorship) was taken over by the newly formed National Institute of Arts and Science and under the new government, the Directory, was transferred to the "Office for Weights and Measures" under the Minister of the Interior.[8]:96–97

On 15 November 1798 Delambre and Méchain returned to Paris with their data, having completed the survey of the Dunkirk-Barcelona meridian. The data was analysed and a prototype metre constructed from platinum with a length of 443.296 lignes.[Note 6] At the same time a prototype kilogram was constructed – the mass of a cube of water at 4°C, each side of the cube being 0.1 metres. The prototype metre was presented to the French legislative assemblies on 22 June 1799.[14]:265–266[50]

### Decimal time (1793)

A clock of the republican era showing both decimal and standard time

The decree of 5 October 1793 introduced the Republican Calendar into France and with it decimalised time.[51] 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 hr 24 min, the "decimal minute" to 1.44 min and the "decimal second" to 0.864 s. The revolutionary week was 10 days, but there were still twelve months in a year, each month consisting of three "weeks". Each year had five or six intercalary days to make up the total of 365 or 366 days.[37][52]

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, though the Republican Calendar was retained.[40] On 1 January 1806, France reverted to the traditional timekeeping.[52]

Repeating circle – the instrument used for triangulation when measuring the meridian

### Angular measure (c. 1793)

Although there was no specific decree regarding angular measure which was also decimalised during the 1790s, it is reported to have been used in 1794,[35]:51 but was not mentioned in the metric system decree of 1795.[40] In particular, the repeating circle, invented in about 1787 by Borda, himself a strong proponent of decimalization, was adapted to use decimal angles.[53]

A grade (or gon) was defined as being 1100 of a quadrant, making 400 grades in a full circle. Fractions of the grade used the standard metric prefixes, thus one centigrade was 110000 of a quadrant, making one centigrade of longitude approximately one kilometre.

The adoption of the grade by the cartographic community was sufficient to warrant a mention in the Lexicographia-neologica Gallica[54] in 1801 and its use continued on military maps through the nineteenth century[55] into the twentieth century.[56] It appears not to have been widely used outside cartography.[57] The centigrade, as an angular measure, was adopted for general use in a number countries, so in 1948 the General Conference on Weights and Measures (CGPM) recommended that the degree centigrade, as used for the measurement of temperature, be renamed the degree Celsius.[58] The SI Brochure (2006) notes that the gon is now a little-used alternative to the degree.[59]

### Draft metric system (1795)

The Paris meridian which passes through the Paris Observatory (Observatoire de Paris). The metre was defined along this meridian using a survey that stretched from Dunkirk to Barcelona.

In France, the metric system of measure was first given a legal basis in 1795 by the French Revolutionary 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:[40]

• The metre, for length – defined as being one ten millionth of the distance between the North Pole and the Equator through Paris
• The are (100 m2) for area [of land]
• The stère (1 m3) for volume of firewood
• The litre (1 dm3) for volumes of liquid
• The gramme, for mass – defined as being the mass of one cubic centimetre of water

Decimal multiples of these units were defined by Greek prefixes: "myria" (10,000), "kilo" (1000), "hecta" (100) and "deka" (10) and submultiples were defined by the Latin prefixes "deci" (0.1), "centi" (0.01) and "milli" (0.001).[60] Using Cassini's survey of 1744, a provisional value of 443.44 lignes was assigned to the metre which, in turn, defined the other units of measure.[14]:106

The final value of the metre was defined in 1799 when Delambre and Méchain presented the results of their survey between Dunkirk and Barcelona 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 kilogramme as being 18827.15 grains. These definitions enabled reference copies of the kilograms and metres to be constructed and these were used as the standards for the next 90 years.[61][62]

### Meridianal definition

Belfry, Dunkirk – the northern end of the meridian arc

The question of measurement reform in France was placed in the hands of the French Academy of Sciences who appointed a commission chaired by Jean-Charles de Borda. Borda could be said to have been a fanatic for decimalization: he had designed the repeating circle, a surveying instrument which allowed a much-improved precision in the measurement of angles between landmarks, but insisted that it be calibrated in "grades" (1100 of a quarter-circle) rather than degrees, with 100 minutes to a grade and 100 seconds to a minute.[63] The instrument was manufactured by Étienne Lenoir.[64] 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 the new system of 10 hours to the day, 100 minutes to the hour and 100 seconds to the minute.

Instead, the commission – whose members included Lagrange, Laplace, Monge and Condorcet – decided that the new measure should be equal to one ten-millionth of the distance from the North Pole to the Equator (the quadrant of the Earth's circumference), measured along the meridian passing through Paris.[28] Apart from the obvious nationalistic considerations, the Paris meridian was also a sound choice for practical scientific reasons: a portion of the quadrant from Dunkerque 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.[28]

The north and south sections of the meridianal survey met at Rodez cathederal, seen here dominating the Rodez skyline

The task of surveying the meridian arc, which was authorized by Louis XVI[14]:21–33 and which was estimated to take two years, fell to Pierre Méchain and Jean-Baptiste Delambre. The task eventually took more than six years (1792–98) with delays caused not only by unforeseen technical difficulties but also by the convulsed period of the aftermath of the Revolution.[14] In the meantime, the commission calculated a provisional value from older surveys of 443.44 lignes.[Note 7]

The project was split into two parts – the northern section of 742.7 km from the Belfry, Dunkirk to Rodez Cathederal 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.[14]: 227–230[Note 8]

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 toise (about 3.9 m).[14]: 227–230 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.[14]: 240–241 Although Méchain's sector was half the length of Delambre, it included the Pyrenees and hitherto unsurveyed parts of Spain. After the two surveyors met, each computed the other's baseline in order to cross-check their results and they then recomputed the kilometre. Their result came out at 0.144 lignes shorter than the provisional value, a difference of about 0.03%.[28]

Fortress of Montjuïc – the southern end of the meridian arc

### Mètre des Archives

While Méchain and Delambre were completing their survey, the commission had ordered a series of platinum bars to be made based on the provisional metre. When the final result was known, the bar whose length was closest to the meridianal definition of the metre was selected and placed in the French National Archives on 22 June 1799 (4 messidor An VII in the Republican calendar) as a permanent record of the result:[28] this standard metre bar became known as the mètre des Archives.

The metric system, that is the system of units based on the metre, was officially adopted in France on 10 December 1799 (19 frimaire An VIII) and became the sole legal system of weights and measures there from 1801.

It soon became apparent that Méchain and Delambre's result (443.296 lignes)[Note 7] was slightly too short for the meridianal definition of the metre. Arago and Biot 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 lignes: later work increased the value to 443.39 lignes.[28] The modern value, for the WGS 84 reference spheroid, is 1.000 196 57 m or 443.383 08 lignes.[Note 9]

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".[65][66]

### Kilogramme des Archives

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".[40] 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 René Just Haüy had been in use since 1793.[67] 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 the precise mass of a cubic decimetre (later to be defined as equal to one litre) of water.

Although the decreed definition of the kilogramme specified water at 0 °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 °C.[68] 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.[69] 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 °C. The kilogramme was defined 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 for the title of Count that, like other nobility titles, was inconsistent with the new French Republic notion of equality (égalité).[70] 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 SI base unit that has an SI prefix as part of its unit name.

## Adoption of the metric weights and measures

During the nineteenth century the metric system of weights and measures 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 Latin America 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 Commonwealth followed suit.

### France

Napoleon Bonparte introduced the 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.[14]: 269 This, combined with other excesses of the Revolution and the high level of illiteracy made the metric system 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 under the décret impérial du 12 février 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 and similar works still had to use the metric system and the metric system continued to be taught at all levels of education.[71] 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 g, each livre comprising sixteen once and each once eight gros and the aune as 120 centimetres.[72]

Louis Philippe I by means of the La loi du 4 juillet 1837 (the law of 4 July 1837) effectively revoked the use of mesures uselles by reaffirming the laws of measurement of 1795 and 1799 to be used from 1 May 1840.[27][73] However, many units of measure, such as the livre (for half a kilogram), remained in colloquial use for many years.[73][Note 10]

### The Dutch metric system

The Netherlands first used the metric system and then, in 1812, the mesures usuelles when it was part of the First French Empire. Under the Royal decree of 27 March 1817 (Koningklijk besluit van den 27 Maart 1817), the newly formed 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 100 g.[74]

### The German Zollverein

Stone marking the Austro-Hungarian/Italian border at Pontebba displaying myriametres (10 km), a unit used in Central Europe in the 19th century.[75]

At the outbreak of the French Revolution, much of modern-day Germany and Austria were part of the Holy Roman Empire 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 Carolingian system instituted by Charlemagne a thousand years earlier.

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. Baden, in 1810, for example, redefined the Ruthe (rods) as being 3.0 m exactly and defined the subunits of the Ruthe as 1 Ruthe = 10 Fuß (feet) = 100 Zoll (inches) = 1,000 Linie (lines) = 10,000 Punkt (points) while the Pfund was defined as being 500 g, divided into 30 Loth, each of 16.67 g.[75][76] Bavaria, in its reform of 1811, trimmed the Bavarian Pfund from 561.288 g to 560 g exactly, consisting of 32 Loth, each of 17.5 g[77] while the Prussian Pfund remained at 467.711 g.[78]

After the Congress of Vienna there was a degree of commercial cooperation between the various German states resulting in the setting of 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. As part of the code the Zollverein introduce the Zollpfund (Customs Pound) which was defined to be exactly 500 g and which could be split into 30 'lot'.[79] This unit was used for inter-state movement of goods, but was not applied in all states for internal use.

Although the Zollverein collapsed after the Austro-Prussian War of 1866, the metric system became the official system of measurement in the newly formed German Empire in 1872[14]:350 and of Austria in 1875.[80] The Zollpfund ceased to be legal in Germany after 1877.[81]

### Italy

Tablet showing conversions of legacy units of weights and measures to metric units, Vicopisano, Tuscany

The Cisalpine Republic, a North Italian republic set up by Napoleon in 1797 with its capital at Milan first adopted a modified form of the metric system based in the braccio cisalpino (Cisalpine cubit) which was defined to be half a metre.[82] In 1802 the Cisalpine Republic was renamed the Italian Republic, with Napoleon as its head of state. The following year the Cisalpine system of measure was replaced by the metric system.[82]

In 1806, the Italian Republic was replaced by the Kingdom of Italy 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.

After the Congress of Vienna, the various Italian states reverted to their original system of measurements, but in 1845 the Kingdom of Piedmont and Sardinia passed legislation to introduce the metric system within five years. By 1860, most of Italy had been unified under the King of Sardinia Victor Emmanuel II 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.[82]

### Spain

Until the ascent of the Bourbon monarchy in Spain in 1700, each of the regions of Spain retained its 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 Castilian units of measure or, in the interests of harmonisation, adopting the French system.[32] Although Spain assisted Méchain 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.[32]

### United Kingdom and the Commonwealth

In 1824 the Weights and Measures Act imposed one standard 'imperial' system of weights and measures on the British Empire.[83] 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'.[84] Initially the United Kingdom declined to sign the Treaty of the Metre, but did so in 1883. Meanwhile British scientists and technologists were at the forefront of the metrication movement – it was the British Association for the Advancement of Science that promoted the cgs system of units as a coherent system[1]: 109 and it was the British firm Johnson Matthey that was accepted by the CGPM in 1889 to cast the international prototype metre and kilogram.[85]

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.[84] 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.[84]

In 1965 Britain commenced an official program of metrication that, as of 2012, had not been completed. The British metrication program signalled the start of metrication programs elsewhere in the Commonwealth, though India had started its 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 lakh and crore are still in widespread use in India. Most other Commonwealth countries adopted the metric system during the 1970s.[86]

### 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 United States Congress 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 customary units rather than with reference to the international prototype metre and kilogram.[87][88]:10–13 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 Mendenhall Order which redefined the customary units by referring to the national metric prototypes, but used the conversion factors of the 1866 act.[88]:16–20 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.[80]

## 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, time and temperature were the only base unit units that were defined in terms of formal standards. 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. 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 electrical systems being developed in the latter half of the nineteenth century. The need for such a unit to resolve these problems was identified by Giorgi in 1901. The SI standard which was published in 1960 defined a single coherent system based on six units.[1]:109

### Time, work and energy

In 1832 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.[1]:109 In his paper, he also presented his results using the metre and gram instead of the millimetre and milligram, also using the Parisian line and the Berlin pound[Note 11]instead of the millimetre and milligram.[89]

Joule's apparatus for measuring the mechanical equivalent of heat. As the weight dropped, potential energy was transferred to the water, heating it up.

In a paper published in 1843, James Prescott Joule first demonstrated a means of measuring the energy transferred between different systems when work is done thereby relating Nicolas Clément's calorie, defined in 1824, to mechanical work.[90][91] Energy became the unifying concept of nineteenth century science,[92] initially by bringing thermodynamics and mechanics together and later adding electrical technology and relativistic physics leading to Einstein's equation $E = mc^2$. The CGS unit of energy was the "erg",[93] while the SI unit of energy was named the "joule" in honour of Joule. [94]

In 1861 a committee of the British Association for Advancement of Science (BAAS) including William Thomson (later Lord Kelvin), James Clerk Maxwell and Joule among its members was tasked with investigating the "Standards of Electrical Resistance". In their first report (1862)[95] 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)[96] 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.[97][98]

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 CGS (centimetre-gram-second) system of units. The committee also recommended the names of "dyne" and "erg" for the CGS units of force and energy.[98][93][99] The CGS system became the basis for scientific work for the next seventy years.

### Electrical units

In the 1820s Georg Ohm formulated Ohms Law which can be extended to relate power to current, potential difference (voltage) and resistance.[100][101] 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 $k_e$ and $k_m$ and consequently $\epsilon_0$ and $\mu_0$ were dimensionless.

Symbols used in this section
Symbol Meaning
$F_\mathrm{m}, F_\mathrm{e}$ Electromagnetic
and
Electrostatic
forces
$I_\mathrm{1}, I_\mathrm{2}$ Electrical current
in conductors
$q_\mathrm{1}, q_\mathrm{2}$ Electrical charges
$L$ Conductor length
$r$ distance between
charges/conductors
$\epsilon_0$ permittivity of
free space
$\mu_0$ permeability of
free space
$k_\mathrm{m}, k_\mathrm{e}$ System of unit
dependant constants
$c$ Speed of light
Electromagnetic system of units (EMU)
The Electromagnetic system of units (EMU) was developed from André-Marie Ampère's discovery in 1820s of a relationship between the force between two current-carrying conductors. This relationship is now known as Ampere's law which can be written
$F_\mathrm{m} = 2 k_\mathrm{m} \frac {I_1 I_2 } {r}$ where $k_\mathrm{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.[102] The electromagnetic (or absolute) system of units was one of the two systems of units identified in the BAAS report of 1862 and defined in the report of 1873. In this system, current is defined by setting the magnetic force constant $k_\mathrm{m}$ to unity and potential difference is defined in such a way as to ensure the unit of power calculated by the relation $P = VI$ 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.[103]
Electrostatic system of units (ESU)
The Electrostatic system of units (ESU) was based on Coulomb's discovery in 1783 of the relationship between the force exerted between two charged bodies. This relationship, now known as Coulomb's law can be written
$F_\mathrm{e} = k_\mathrm{e} \frac{q_1q_2}{r^2}$ where $k_\mathrm{e} = \frac{1}{4 \pi \epsilon_0}$ (SI units)
The electrostatic system 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 Coulomb force constant ($k_\mathrm{e}$) to unity and the unit for potential difference were defined to ensure the unit of energy calculated by the relation $E = QV$ is one erg. The electrostatic units of measure are now known as the statampere, the statvolt, the statcoulomb and so on.[104]
Gaussian system of units
The Gaussian system of units was based on Heinrich Hertz realization, made in 1888 while verifying Maxwell's Equations, that the CGS system of electromagnetic units to were related to the CGS system of electrostatic units by the relationship:
$c^2 = \frac{1}{\epsilon_0 \mu_0}$[105][106]
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.[1]:128
Practical system of units
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 dimension of electrical resistance was modelled in the EMU system as the ratio L/T and in the ESU system as its inverse – T/L.[98]
The unit of length adopted for the practical system was the 108 m (approximately the length of the Earth's quadrant), the unit of time was the second and the unit of mass an unnamed unit equal to 10−11 g and the definitions 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 International Electrical Congress (IEC) in 1881.[107] The second IEC congress (1889) defined the joule and the watt at the practical units of energy and power respectively.[108] The units were formalised as the International System of Electrical and Magnetic Units 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".[109]

### A coherent system

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 dimensional analysis 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 $M^\frac{1}{2}L^\frac{3}{2}T^{-1}$ 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.[98]

From mid-1890s onwards Giovanni Giorgi and Oliver Heaviside corresponded with each other regarding these anomalous results.[110] This led to Giorgi presenting a paper to the congress of the Associazione Elettrotecnica Italiana (A.E.I.)[111] 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 ke and km physical dimensions and hence the electrco-mechanical quantities ε0 and µ0 were also given physical dimensions.[110] His work also recognized the unifying concept that energy played in the establishment of a coherent, rational system of units with the joule as the unit of energy and the electrical units in the practical system of units remaining unchanged.[112] [4]:156

The 1893 definitions of the ampere and the ohm by the IEC led to the joule as being defined in accordance with the IEC resolutions being 0.02% larger than the joule as defined in accordance with the artifacts helds by the BIPM. In 1908, the IEC prefixed the units of measure that they had defined with the word "internation", hence the "international ampere", "international volt" etc.[4]:155–156 It took more than thirty years before Giorgi's work was accepted in practice by the IEC. 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.[108] In 1960, Giorgi's proposals were adopted as the basis of the Système International d'Unités (International System of Units), the SI.[1]:109

### Naming the units of measure

In 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-second absolute system. This was supported by Thomson (Lord Kelvin)[113] These names were later scaled for use in the Practical System.[114] The concept of naming units of measure after noteworthy scientists was subsequently used for other units.

## Convention of the metre

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.[115]

The International Conference on Geodesy in 1867 called for the creation of a new, international prototype metre[65][66][116] 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.[65]

On 20 May 1875 an international treaty known as the Convention du Mètre (Metre Convention) was signed by 17 states.[29][117] 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 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.[29] 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.[85]

## Twentieth century

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

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 Einstein 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 Treaty of the Metre, 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.

### Metre

The first (and only) follow-up comparison of the national standards with the international prototype metre was carried out between 1921 and 1936,[29][66] and indicated that the definition of the metre was preserved to within 0.2 µm.[118] 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 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 mm from each other".[1]:142–43, 148 The choice of 571 mm represents the Airy points of the prototype—the points at which the bending or droop of the bar is minimized.[119]

In 1887 Michelson proposed the use of optical interferometers for the measurement of length, work which contributed to him being awarded the Nobel Prize 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 phenomenon rather than the earth's rotation and Einstein's assertion that the speed of light 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.[120]

### Kilogram

Mass drift over time of national prototypes K21–K40, plus two of the IPK's sister copies: K32 and K8(41).[121] [Note 12] 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.

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 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.[122]

During the course of the century, the various national prototypes of the kilogram were recalibrated against the International Prototype Kilogram (IPK) and therefore against each other. The initial 1889 starting-value offsets of the national prototypes relative to the IPK were nulled.[121] 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.[123]

The third periodic recalibration in 1988-9 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.[121]

### Time

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. In 1988, responsibility for timekeeping passed to the BIPM who took on the role of coordinating a number of atomic clocks scattered around the globe.[124] 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[125] – 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.[126]

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.[125] 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 value was adopted in 1968 by the 13th CGPM.

### Electrical units

Four domestic quality contemporary measuring devices that have metric calibrations – a tape measure calibrated in centimetres, a thermometer calibrated in degrees Celsius, a kilogram weight (mass) and an electrical multimeter which measures volts, amps and ohms

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 World War II prevented this being formalised until 1946. The definitions for absolute electrical system based on the ampere was formalized in 1948.[127]

### Temperature

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.[128][129] Within the metric system, temperature was expressed in degrees Centigrade 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 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 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 °C,[130] though the CGPM left the formal definition of absolute zero until the 10th GCPM when the name "Kelvin" was assigned to the absolute temperature scale and triple point of water was defined as being 273.16 °K.[131] In 1967, at the 13th GCPM the degree Kelvin (°K) was renamed the "kelvin" (K).[132]

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.[133] 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.[134]

### Luminosity

Prior to 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".[135] 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.[1]: 115

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.[136]

### Mole

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 16O isotope whereas chemists assigned 16 amu to 16O, 17O and 18O isotopes mixed in the proportion that they occur in nature. Finally an agreement between the International Union of Pure and Applied Physics[137] (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 12C 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.[1]:114–115

## International System of Units (SI)

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.[138] At the same time the CGPM formally adopted a recommendation for the writing and printing of unit symbols and of numbers.[139] The recommendation also catalogued the recommended symbols for the most important MKS and CGS units of measure and 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 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.[140] The full system and name "Système International d'Unités" were adopted at the 11th CGPM.[141]

During the years that followed the definitions of the base units and particularly the mise en pratique[142] to realise these definitions have been refined.

### The "New SI"

Relations between proposed SI units definitions (in colour) and with seven fundamental constants of nature (in grey) with fixed numerical values in the proposed system

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.

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 Reading, United Kingdom in September 2010, a resolution[143] 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.[134] The proposals that the CCU put forward were that:

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";[144] 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.[145] This resolution was accepted by the conference[146] and in addition the CGPM moved the date of the 25th meeting forward from 2015 to 2014.[147]

## Notes

1. ^ 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
2. ^ A "seconds pendulum" is a pendulum with a half-period of one second)
3. ^ There were two beats in an oscillation.
4. ^ Derived from the knowledge that the earth's circumference is approximately 40,000 km.
5. ^ The acceleration due to gravity at the poles is 9.832 m/s−2 and at the equator 9.780 m/s−2, a difference of about 0.5%.[1]
6. ^ 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.
7. ^ a b All values in lignes are referred to the toise de Pérou, not to the later value in mesures usuelles. 1 toise = 6 pieds; 1 pied = 12 pouces; 1 pouce = 12 lignes; so 864 lignes = 1 toise.
8. ^ Distances measured using Google Earth. The coordinates are:
51°02′08″N 2°22′34″E﻿ / ﻿51.03556°N 2.37611°E – Belfry, Dunkirk
44°25′57″N 2°34′24″E﻿ / ﻿44.43250°N 2.57333°ERodez Cathederal
41°21′48″N 2°10′01″E﻿ / ﻿41.36333°N 2.16694°EMontjuïc, Barcelona
9. ^ The WGS 84 reference spheroid has a semi-major axis of 6 378 137.0 m and a flattening of 1298.257 223 563.
10. ^ Crease (2011) refers to: Kennelly, Arthur E. (1928). Vestiges of Pre-metric Weights and Measures Persisting in Metric-system Europe, 1926-27. New York: Macmillan. p. vii.
11. ^ The Parisian line = 1144 of a Parisian pied or foot or 1.066 English lines. The Berlin (or Prussian) pfund or pound was 468 g or about 1.032 imperial pounds.
12. ^ 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).

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