The history of the metric system began during the Age of Enlightenment with measures of length and weight derived from nature, along with their decimal multiples and fractions. The system became the standard of France and Europe within half a century. Other measures with unity ratios^{[Note 1]} were added, and the system went on to be adopted across the world.

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

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

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

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

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

A fleeting hint of an ancient decimal or metric system may be found in the Mohenjo-Daro ruler, which uses a base length of 1.32 inches (33.5 mm) and is very precisely divided with decimal markings. Bricks from that period are consistent with this unit, but this usage appears not to have survived, as later systems in India are non-metric, employing divisions into eighths, twelfths, and sixteenths.

Age of Enlightenment

Foundational aspects of mathematics, together with an increased understanding of the natural world during the Enlightenment, set the stage for the emergence in the late 18th century of a system of measurement with rationally related units and rules for combining them.

Preamble

In the early ninth century, when much of what later became Holy Roman Empire was part of France, units of measure had been standardised by the Emperor Charlemagne. He had introduced standard units of measure for length and for mass throughout his empire. As the empire disintegrated into separate nations, including France, these standards diverged. In England, Magna Carta (1215) had stipulated that "There shall be standard measures of wine, ale, and corn (the London quarter), throughout the kingdom. There shall also be a standard width of dyed cloth, russet, and haberject, namely two ells within the selvedges. Weights are to be standardised similarly."^[1]

During the early medieval era, Roman numerals were used in Europe to represent numbers,^[2] 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.^[3][4] At that time, there was dispute regarding the difference between rational numbers and irrational numbers and there was no consistency in the way in which decimal fractions were represented.

Simon Stevin is credited with introducing the decimal system into general use in Europe.^[5] In 1586, he published a small pamphlet called De Thiende ("the tenth") which historians credit as being the basis of modern notation for decimal fractions.^[6] 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.^{[5][7]: 70 [8]: 91}

Body measures and artifacts

Since the time of Charlemagne, the standard of length had been a measure of the body, that from fingertip to fingertip of the outstretched arms of a large man,^{[Note 2]} from a family of body measures called fathoms, originally used among other things, to measure the depth of water. An artifact to represent the standard was cast in the most durable substance available in the Middle Ages, an iron bar ^{[citation needed]}. The problems of a non-reproducible artefact became apparent over the ages: it rusted, was stolen, beaten into a mortised wall until it bent, and was, at times, lost. When a new royal standard had to be cast, it was a different standard than the old one, so replicas of old ones and new ones came into existence and use. The artefact existed through the 18th century, and was called a teise or later, a toise (from Latin tense: outstretched (arms)). This would lead to a search in the 18th century for a reproducible standard based on some invariant measure of the natural world.

Clocks and pendulums

In 1656, Dutch scientist Christiaan Huygens invented the pendulum clock, with its pendulum marking the seconds. This gave rise to proposals to use its length as a standard unit. But it became apparent that the pendulum lengths of calibrated clocks in different locations varied (due to local variations in the acceleration due to gravity), and this was not a good solution. A more uniform standard was needed.

In 1670, Gabriel Mouton, a French abbot and astronomer, published the book Observationes diametrorum solis et lunae apparentium ("Observations of the apparent diameters of the Sun and Moon") in which he proposed a decimal system of measurement of length for use by scientists in international communication, to be based on the dimensions of the Earth. The milliare would be defined as a minute of arc along a meridian (such as the Paris meridian) and would be divided into 10 centuria, the centuria into 10 decuria and so on, successive units being the virga, virgula, decima, centesima, and the millesima. Mouton used Riccioli's estimate that one degree of arc was 321,185 Bolognese feet. Mouton's experiments showed that a pendulum of length one virgula would beat 3959.2 times^{[Note 3]} in half an hour.^{[9][Note 4]} Mouton believed that, with this information, scientists in a foreign country would be able to construct a copy of the virgula for their own use.^[10] Mouton's ideas attracted interest at the time; Picard in his work Mesure de la Terre (1671) and Huygens in his work Horologium Oscillatorium sive de motu pendulorum ("Of oscillating clocks, or concerning the motion of pendulums", 1673) both proposing that a standard unit of length be tied to the beat frequency of a pendulum.^[11][10]

The shape and size of the Earth

Since at least the Middle Ages, the Earth had been perceived as eternal, unchanging, and of symmetrical shape (close to a sphere), so it was natural that some fractional measure of its surface should be proposed as a standard of length. But first, scientific information about the shape and size of the Earth had to be obtained. One degree of arc would be 60 minutes of arc, on the equator; one milliare would be one minute of arc, or 1 nautical mile, so 60 nautical miles would be one degree of arc on Earth's surface, taken as a sphere.^[12] Thus Earth's circumference in nautical miles would be 21 600 (viz., 60 minutes of arc × 360 degrees in four 90-degree quadrants; a quadrant being the length of the quarter-circle from the North Pole to the equator).

In 1669, Jean Picard, a French astronomer, was the first person to measure the Earth accurately. In a survey spanning one degree of latitude, he erred by only 0.44% (Picard's arc measurement).

In Philosophiæ Naturalis Principia Mathematica (1686), Isaac Newton gave a theoretical explanation for the "bulging equator",^{[Note 5]} which also explained the differences found in the lengths of the "second pendulums",^[13] theories that were confirmed by the French Geodesic Mission to Peru undertaken by the French Academy of Sciences in 1735.^[14][a]

Late 18th century: conflict and lassitude

By the mid-18th century, it had become apparent that it was necessary to standardise of weights and measures between nations who traded and exchanged scientific ideas with each other. Spain, for example, had aligned her units of measure with the royal units of France^[17] and Peter the Great aligned the Russian units of measure with those of England.^[18] In 1783, the British inventor James Watt, who was having difficulties in communicating with German scientists, called for the creation of a global decimal measurement system, proposing a system which used the density of water to link length and mass,^[16] and, in 1788, the French chemist Antoine Lavoisier commissioned a set of nine brass cylinders (a pound and decimal subdivisions thereof) for his experimental work.^[7]: 71

In 1790, a proposal floated by the French to Britain and the United States, to establish a uniform measure of length, a metre based on the period of a pendulum with a beat of one second, was defeated in the British Parliament and United States Congress. The underlying issue was failure to agree on the latitude for the definition, since gravitational acceleration, and, therefore, the length of the pendulum, varies (inter alia) with latitude: each party wanted a definition according to a major latitude passing through their own country. The direct consequences of the failure were the French unilateral development and deployment of the metric system and its spread by trade to the continent; the British adoption of the Imperial System of Measures throughout the realm in 1824; and the United States' retention of the British common system of measures in place at the time of the independence of the colonies. This was the position that continued for nearly the next 200 years.^{[Note 6]}

Implementation in Revolutionary France

Weights and measures of the Ancien Régime

It has been estimated that, on the eve of the Revolution in 1789, the eight hundred or so units of measure in use in France had up to a quarter of a million different definitions because the quantity associated with each unit could differ from town to town, and even from trade to trade.^[8]: 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.^[19] These variations were promoted by local vested interests, but hindered trade and taxation.^[20][21]

Units of weight and length

In 1790, a panel of five leading French scientists was appointed by the Académie des sciences to investigate weights and measures. They were Jean-Charles de Borda, Joseph-Louis Lagrange, Pierre-Simon Laplace, Gaspard Monge, and Nicolas de Condorcet.^{[8]: 2–3 [22]: 46} Over the following year, the panel, after studying various alternatives, made a series of recommendations regarding a new system of weights and measures, including that it should have a decimal radix, that the unit of length should be based on a fractional arc of a quadrant of the Earth's meridian, and that the unit of weight should be that of a cube of water whose dimension was a decimal fraction of the unit of length.^{[23][24][7]: 50–51 [25][26]} The proposals were accepted by the French Assembly on 30 March 1791.^[27]

Following acceptance, the Académie des sciences was instructed to implement the proposals. The Académie broke the tasks into five operations, allocating each part to a separate working group:^[7]: 82

• Measuring the difference in latitude between Dunkirk and Barcelona and triangulating between them
• Measuring the baselines used for the survey
• Verifying the length of the second pendulum at 45° latitude.
• Verifying the weight in a vacuum of a given volume of distilled water.
• Publishing conversion tables relating the new units of measure to the existing units of measure.

The panel decided that the new measure of length should be equal to one ten-millionth of the distance from the North Pole to the Equator (Earth quadrant), measured along the Paris meridian.^[20]

Using Jean Picard's survey of 1670 and Jacques Cassini's survey of 1718,^[a] a provisional value of 443.44 lignes was assigned to the metre which, in turn, defined the other units of measure.^[8]: 106

While Méchain and Delambre were completing their survey, the commission had ordered a series of platinum bars to be made based on the provisional metre. When the final result was known, the bar whose length was closest to the meridional definition of the metre would be selected.

After 1792, the name of the original defined unit of mass, "gramme", which was too small to serve as a practical realisation for many purposes, was adopted, the new prefix "kilo" was added to it to form the name "kilogramme". Consequently, the kilogram is the only SI base unit that has an SI prefix as part of its unit name. A provisional kilogram standard was made and work was commissioned to determine the precise mass of a cubic decimetre (later to be defined as equal to one litre) of water. The regulation of trade and commerce required a "practical realisation": a single-piece, metallic reference standard that was one thousand times more massive that would be known as the grave.^{[Note 8]} This mass unit defined by Lavoisier and René Just Haüy had been in use since 1793.^[28] This new, practical realisation would ultimately become the base unit of mass. On 7 April 1795, the gramme, upon which the kilogram is based, was decreed to be equal to "the absolute weight of a volume of pure water equal to a cube of one hundredth of a metre, and at the temperature of the melting ice".^[26] Although the definition of the kilogramme specified water at 0 °C—a highly stable temperature point—it was replaced with the temperature at which water reaches maximum density. This temperature, about 4 °C, was not accurately known, but one of the advantages of the new definition was that the precise Celsius value of the temperature was not actually important.^{[29][Note 9]} The final conclusion was that one cubic decimetre of water at its maximum density was equal to 99.92072% of the mass of the provisional kilogram.^[32]

On 7 April 1795, the metric system was formally defined in French law.^{[Note 10]} It defined six new decimal units:^[26]

• The mètre, for length—defined as one ten-millionth of the distance between the North Pole and the Equator through Paris
• The are (100 m²) for area
• The stère (1 m³) for volume of firewood
• The litre (1 dm³) for volumes of liquid
• The gramme, for mass—defined as the mass of one cubic centimetre of water
• The franc, for currency.

Historical note: only the metre and (kilo)gramme defined here went on to become part of later metric systems. Litres and to a lesser extent hectares (100 ares, or 1 hm²) are still in use, but are not official SI units.

Decimal multiples of these units were defined by Greek prefixes: "myria-" (10,000), "kilo-" (1000), "hecto-" (100), and "deka-" (10) and submultiples were defined by the Latin prefixes "deci-" (0.1), "centi-" (0.01), and "milli-" (0.001).^[33]

For purposes of commerce, units and prefixed-units of weight (mass) and capacity (volume) were prependable by the binary multipliers "double-" (2) and "demi-" (1⁄2), as in double-litre, demi-litre; or double-hectogramme, demi-hectogramme, etc.^{[Note 11]}

The 1795 draft definitions enabled provisional copies of the kilograms and metres to be constructed.^[34][35]

Meridional survey

The task of surveying the meridian arc, which was estimated to take two years, fell to Pierre Méchain and Jean-Baptiste Delambre. The task eventually took more than six years (1792–1798) with delays caused not only by unforeseen technical difficulties but also by the convulsed period of the aftermath of the Revolution.^[8] Apart from the obvious nationalistic considerations, the Paris meridian was also a sound choice for practical scientific reasons: a portion of the quadrant from Dunkirk to Barcelona (about 1000 km, or one-tenth of the total) could be surveyed with start- and end-points at sea level, and that portion was roughly in the middle of the quadrant, where the effects of the Earth's oblateness were expected to be the largest.^[20]

The project was split into two parts—the northern section of 742.7 km from the Belfry, Dunkirk to Rodez Cathedral which was surveyed by Delambre and the southern section of 333.0 km from Rodez to the Montjuïc Fortress, Barcelona which was surveyed by Méchain.^{[8]: 227–230 [Note 12]}

Delambre used a baseline of about 10 km in length along a straight road, located close to Melun. In an operation taking six weeks, the baseline was accurately measured using four platinum rods, each of length two toises (about 3.9 m).^{[8]: 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.^{[8]: 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 metre as 443.296 lignes,^{[20][Note 13]} notably shorter than the 1795 provisional value of 443.44 lignes. On 15 November 1798, Delambre and Méchain returned to Paris with their data, having completed the survey. The final value of the mètre was defined in 1799 as the computed value from the survey.

Historical note: It soon became apparent that Méchain and Delambre's result (443.296 lignes) was slightly too short for the meridional definition of the metre. Méchain had made a small error measuring the latitude of Barcelona, so he remeasured it, but kept the second set of measurements secret.^{[Note 14]}

The French metric system

In June 1799, platinum prototypes were fabricated according to the measured quantities, the mètre des archives defined to be a length of 443.296 lignes, and the kilogramme des archives defined to be a weight of 18827.15 grains of the livre poids de marc,^[36] and entered into the French National Archives. In December of that year, the metric system based on them became by law the sole system of weights and measures in France from 1801 until 1812.

Despite the law, the populace continued to use the old measures. In 1812, Napoleon revoked the law and issued one called the mesures usuelles, restoring the names and quantities of the customary measures but redefined as round multiples of the metric units, so it was a kind of hybrid system. In 1837, after the collapse of the Napoleonic Empire, the new Assembly reimposed the metric system defined by the laws of 1795 and 1799, to take effect in 1840. The metrication of France took until about 1858 to be completed. Some of the old unit names, especially the livre, originally a unit of mass derived from the Roman libra (as was the English pound), but now meaning 500 grams, are still in use today.

Development of non-coherent metric systems

At the start of the nineteenth century, the French Academy of Sciences' artefacts for length and mass were the only nascent units of the metric system that were defined in terms of formal standards. Other units based on them, except the litre, proved to be short-lived. Pendulum clocks that could keep time in seconds had been in use for about 150 years, but their geometries were local to both latitude and altitude, so there was no standard of timekeeping. Nor had a unit of time been recognised as an essential base unit for the derivation of things like force and acceleration. Some quantities of electricity, like charge and potential, had been identified, but names and interrelationships of units were not yet established.^{[Note 15]} Both Fahrenheit (ca. 1724) and Celsius (ca. 1742) scales of temperature existed, and varied instruments for measuring units or degrees of them. The base/derived unit model had not yet been elaborated, nor was it known how many physical quantities might be interrelated.

A model of interrelated units was first proposed in 1861 by the British Association for the Advancement of Science (BAAS) based on what came to be called the "mechanical" units (length, mass, and time). Over the following decades, this foundation enabled mechanical, electrical, and thermal^[when?] units to be correlated.

Time

In 1832, German mathematician Carl-Friedrich Gauss made the first absolute measurements of the Earth's magnetic field using a decimal system based on the use of the millimetre, milligram, and second as the base unit of time.^[37]: 109 Gauss' second was based on astronomical observations of the rotation of the Earth, and was the sexagesimal second of the ancients: a partitioning of the solar day into two cycles of 12 periods, and each period divided into 60 intervals, and each interval so divided again, so that a second was 1/86,400th of the day.^{[Note 16]} This effectively established a time dimension as a necessary constituent of any useful system of measures, and the astronomical second as the base unit.

Work and energy

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In a paper published in 1843, James Prescott Joule first demonstrated a means of measuring the energy transferred between different systems when work is done thereby relating Nicolas Clément's calorie, defined in 1824 as "the amount of heat required to raise the temperature of 1 kg of water from 0 to 1 °C at 1 atmosphere of pressure" to mechanical work.^[38][39] Energy became the unifying concept of nineteenth century science,^[40] initially by bringing thermodynamics and mechanics together and later adding electrical technology.

The first structured metric system: CGS

In 1861, a committee of the British Association for the Advancement of Science (BAAS) including William Thomson (later Lord Kelvin), James Clerk Maxwell, and James Prescott Joule among its members was tasked with investigating the "Standards of Electrical Resistance".^{[clarification needed]} In their first report (1862),^[41] 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),^[42] 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.^[43][44]

In 1861, before^{[clarification needed][at?]} a meeting of the BAAS, Charles Bright and Latimer Clark proposed the names of ohm, volt, and farad in honour of Georg Ohm, Alessandro Volta, and Michael Faraday respectively for the practical units based on the CGS absolute system. This was supported by Thomson (Lord Kelvin).^[45] The concept of naming units of measure after noteworthy scientists was subsequently used for other units.

In 1873, another committee of the BAAS (which also included Maxwell and Thomson) tasked with "the Selection and Nomenclature of Dynamical and Electrical Units" recommended using the cgs system of units. The committee also recommended the names of "dyne" and "erg" for the cgs units of force and energy.^[46][44][47] The cgs system became the basis for scientific work for the next seventy years.

The reports recognised two centimetre–gram–second based systems for electrical units: the Electromagnetic (or absolute) system of units (EMU) and the Electrostatic system of units (ESU).

Electrical units

Symbols used in this section

Symbols	Meaning
${\displaystyle F_{\text{m}},F_{\text{e}}}$	electromagnetic and electrostatic forces
${\displaystyle I_{\text{1}},I_{\text{2}}}$	electric currents in conductors
${\displaystyle q_{\text{1}},q_{\text{2}}}$	electrical charges
${\displaystyle L}$	conductor length
${\displaystyle r}$	distance between charges/conductors
${\displaystyle \epsilon _{0}}$	electric constant[Note 17]
${\displaystyle \mu _{0}}$	magnetic constant[Note 17]
${\displaystyle k_{\text{m}},k_{\text{e}}}$	constants of proportionality
${\displaystyle c}$	speed of light[48]
${\displaystyle 4\pi }$	steradians surrounding a point[Note 18]
${\displaystyle P}$	electric power
${\displaystyle V}$	electric potential
${\displaystyle I}$	electric current
${\displaystyle E}$	energy
${\displaystyle Q}$	electric charge
${\displaystyle {\mathsf {M,L,T}}}$	dimensions: mass, length, time

In the 1820s, Georg Ohm formulated Ohm's Law, which can be extended to relate power to current, electric potential (voltage), and resistance.^[49][50] During the following decades, the realisation of a coherent system of units that incorporated the measurement of electromagnetic phenomena and Ohm's law was beset with problems—several different systems of units were devised.

In the three CGS systems, the constants ${\displaystyle k_{\text{e}}}$ and ${\displaystyle k_{\text{m}}}$ and consequently ${\displaystyle {\mathrm{ϵ<!--\; ϵ\; -->}}_0}$Zdroj:https://en.wikipedia.org?pojem=History_of_the_metric_system
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