The history of the

metric system The metric system is a system of measurement that standardization, standardizes a set of base units and a nomenclature for describing relatively large and small quantities via decimal-based multiplicative unit prefixes. Though the rules gover ...

began during the

Age of Enlightenment The Age of Enlightenment (also the Age of Reason and the Enlightenment) was a Europe, European Intellect, intellectual and Philosophy, philosophical movement active from the late 17th to early 19th century. Chiefly valuing knowledge gained th ...

with measures of

length Length is a measure of distance. In the International System of Quantities, length is a quantity with Dimension (physical quantity), dimension distance. In most systems of measurement a Base unit (measurement), base unit for length is chosen, ...

and

weight In science and engineering, the weight of an object is a quantity associated with the gravitational force exerted on the object by other objects in its environment, although there is some variation and debate as to the exact definition. Some sta ...

derived from

nature Nature is an inherent character or constitution, particularly of the Ecosphere (planetary), ecosphere or the universe as a whole. In this general sense nature refers to the Scientific law, laws, elements and phenomenon, phenomena of the physic ...

, along with their

decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of th ...

multiples and fractions. The system became the standard of France and Europe within half a century. Other measures with unity ratiosratios of 1 between magnitudes of unit quantities 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 The kilogram (also spelled kilogramme) is the base unit of mass in the International System of Units (SI), equal to one thousand grams. It has the unit symbol kg. The word "kilogram" is formed from the combination of the metric prefix kilo- (m ...

and the

metre The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of ...

. The basic units were taken from the natural world. The unit of length, the metre, was based on the dimensions of the

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

, and the unit of

mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...

, the kilogram, was based on the mass of a

volume Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...

of water of one

litre The litre ( Commonwealth spelling) or liter ( American spelling) (SI symbols L and l, other symbol used: ℓ) is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metres (m3). A ...

(a cubic

decimetre The decimetre (or in American English; symbol: dm), is a unit of length in the International System of Units, equal to one tenth of a metre, ten centimetres, one hundred millimetres, and 3.937 inches. The common non- SI metric unit of volu ...

). 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 James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician who was responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism an ...

conceived a coherent system where a small number of units of measure were defined as

base units A base unit of measurement (also referred to as a base unit or fundamental unit) is a unit of measurement adopted for a '' base quantity''. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the ...

, 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 physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...

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 Giovanni Giorgi (November 27, 1871 – August 19, 1950) was an Italian physicist and electrical engineer who proposed the ''Giorgi system'' of measurement, the precursor to the International System of Units (SI). Early life Giovanni Giorgi was bo ...

, 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 The Metre Convention (), also known as the Treaty of the Metre, is an international treaty that was signed in Paris on 20 May 1875 by representatives of 17 nations: Argentina, Austria-Hungary, Belgium, Brazil, Denmark, France, Germany, Italy, ...

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 The General Conference on Weights and Measures (abbreviated CGPM from the ) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established in 1875 under the terms of the Metre C ...

'' or CGPM to oversee systems of weights and measures based on them. In 1960, the CGPM launched the

International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...

(in French the ''Système international d'unités'' or SI) with six "base units": the metre, kilogram,

second The second (symbol: s) is a unit of time derived from the division of the day first into 24 hours, then to 60 minutes, and finally to 60 seconds each (24 × 60 × 60 = 86400). The current and formal definition in the International System of U ...

ampere The ampere ( , ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to 1 c ...

, degree Kelvin (subsequently renamed the "kelvin") and

candela The candela (symbol: cd) is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to radi ...

, 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 Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

of a caesium atomic clock. Due to the instability of the

international prototype of the kilogram The International Prototype of the Kilogram (referred to by metrology, metrologists as the IPK or Le Grand K; sometimes called the ''wiktionary:ur-#Prefix, ur-kilogram'', or ''urkilogram'', particularly by German-language authors writing in Engli ...

, a series of initiatives were undertaken, starting in the late 20th century, to redefine the ampere, kilogram, mole and kelvin in terms of invariant constants of physics, ultimately resulting in the

2019 revision of the SI In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artefacts such as the standard kilogram. Effective 20 May 2019, the 144th ...

, 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 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 The Holy Roman Empire, also known as the Holy Roman Empire of the German Nation after 1512, was a polity in Central and Western Europe, usually headed by the Holy Roman Emperor. It developed in the Early Middle Ages, and lasted for a millennium ...

was part of France, units of measure had been standardised by the

Emperor Charlemagne Charlemagne ( ; 2 April 748 – 28 January 814) was King of the Franks from 768, King of the Lombards from 774, and Emperor of what is now known as the Carolingian Empire from 800, holding these titles until his death in 814. He united mo ...

. 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 (Medieval Latin for "Great Charter"), sometimes spelled Magna Charta, is a royal charter of rights agreed to by King John of England at Runnymede, near Windsor, on 15 June 1215. First drafted by the Archbishop of Canterbury, Cardin ...

(1215) had stipulated that "There shall be standard measures of wine, ale, and corn (the London quarter), throughout the kingdom. There shall also be a standard width of dyed cloth, russet, and haberject, namely two ells within the selvedges. Weights are to be standardised similarly." During the early

medieval era In the history of Europe, the Middle Ages or medieval period lasted approximately from the 5th to the late 15th centuries, similarly to the post-classical period of global history. It began with the fall of the Western Roman Empire and t ...

Roman numerals Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...

were used in Europe to represent numbers, but the

Arabs Arabs (, , ; , , ) are an ethnic group mainly inhabiting the Arab world in West Asia and North Africa. A significant Arab diaspora is present in various parts of the world. Arabs have been in the Fertile Crescent for thousands of yea ...

represented numbers using the Hindu numeral system, a

positional notation Positional notation, also known as place-value notation, positional numeral system, or simply place value, usually denotes the extension to any radix, base of the Hindu–Arabic numeral system (or decimal, decimal system). More generally, a posit ...

that used ten symbols. In about 1202,

Fibonacci Leonardo Bonacci ( – ), commonly known as Fibonacci, was an Italians, Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". The name he is commonly called, ''Fibonacci ...

published his book ''

Liber Abaci The or (Latin for "The Book of Calculation") was a 1202 Latin work on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci. It is primarily famous for introducing both base-10 positional notation and the symbols known as Arabic n ...

'' (Book of Calculation) which introduced the concept of positional notation into Europe. These symbols evolved into the numerals "0", "1", "2", etc. At that time, there was dispute regarding the difference between

rational number In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (for example, The set of all ...

s and

irrational number In mathematics, the irrational numbers are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, ...

s and there was no consistency in the way in which decimal fractions were represented.

Simon Stevin Simon Stevin (; 1548–1620), sometimes called Stevinus, was a County_of_Flanders, Flemish mathematician, scientist and music theorist. He made various contributions in many areas of science and engineering, both theoretical and practical. He a ...

is credited with introducing the decimal system into general use in Europe. In 1586, he published a small pamphlet called ''De Thiende'' ("the tenth") which historians credit as being the basis of modern notation for decimal fractions. Stevin felt that this innovation was so significant that he declared the universal introduction of decimal coinage, measures, and weights to be merely a question of time.

Body measures and artifacts

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

Clocks and pendulums

In 1656, Dutch scientist

Christiaan Huygens Christiaan Huygens, Halen, Lord of Zeelhem, ( , ; ; also spelled Huyghens; ; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution ...

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 A minute of arc, arcminute (abbreviated as arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of a degree. Since one degree is of a turn, or complete rotation, one arcminute is of a tu ...

along a meridian (such as the

Paris meridian The Paris meridian is a meridian line running through the Paris Observatory in Paris, France – now longitude 2°20′14.02500″ East. It was a long-standing rival to the Greenwich meridian as the prime meridian of the world. The "Paris meri ...

) 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 timesThere were two beats in an oscillation. in half an hour.the pendulum would have had a length of 205.6 mm and the virgula was ~185.2 mm. Mouton believed that, with this information, scientists in a foreign country would be able to construct a copy of the virgula for their own use. Mouton's ideas attracted interest at the time;

Picard Picard may refer to: Places * Picard, Quebec, Canada * Picard, California, United States * Picard (crater), a lunar impact crater in Mare Crisium People and fictional characters * Picard (name), a list of people and fictional characters with th ...

in his work ''Mesure de la Terre'' (1671) and Huygens in his work ''Horologium Oscillatorium sive de motu pendulorum'' ("Of oscillating clocks, or concerning the motion of pendulums", 1673) both proposing that a standard unit of length be tied to the beat frequency of a pendulum.

Shape and size of the Earth

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 A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

.US Metric Associatio
Origin of the metric system
/ref> 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 The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is the point in the Northern Hemisphere where the Earth's rotation, Earth's axis of rotation meets its surface. It is called the True North Pole to distingu ...

to the

equator The equator is the circle of latitude that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern Hemispheres of Earth, hemispheres. It is an imaginary line located at 0 degrees latitude, about in circumferen ...

). 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 (English: ''The Mathematical Principles of Natural Philosophy''), often referred to as simply the (), is a book by Isaac Newton that expounds Newton's laws of motion and his law of universal gravitation. The ''Principia'' is written in Lati ...

'' (1686), Isaac Newton gave a theoretical explanation for the "bulging equator",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

which also explained the differences found in the lengths of the "second pendulums", theories that were confirmed by the

French Geodesic Mission The French Geodesic Mission to the Equator (), also called the French Geodesic Mission to Peru and the Spanish-French Geodesic Mission, was an 18th-century expedition to what is now Ecuador carried out for the purpose of performing an arc measu ...

to Peru undertaken by the

French Academy of Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...

in 1735.

Late 18th century: conflict and lassitude

By the mid-18th century, it had become apparent that it was necessary to standardise of weights and measures between nations who traded and exchanged scientific ideas with each other. Spain, for example, had aligned her units of measure with the royal units of France and

Peter the Great Peter I (, ; – ), better known as Peter the Great, was the Sovereign, Tsar and Grand Prince of all Russia, Tsar of all Russia from 1682 and the first Emperor of Russia, Emperor of all Russia from 1721 until his death in 1725. He reigned j ...

aligned the Russian units of measure with those of England. In 1783, the British inventor

James Watt James Watt (; 30 January 1736 (19 January 1736 OS) – 25 August 1819) was a Scottish inventor, mechanical engineer, and chemist who improved on Thomas Newcomen's 1712 Newcomen steam engine with his Watt steam engine in 1776, which was f ...

, who was having difficulties in communicating with German scientists, called for the creation of a global decimal measurement system, proposing a system which used the density of water to link length and mass, and, in 1788, the French

chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a graduated scientist trained in the study of chemistry, or an officially enrolled student in the field. Chemists study the composition of ...

Antoine Lavoisier Antoine-Laurent de Lavoisier ( ; ; 26 August 17438 May 1794), When reduced without charcoal, it gave off an air which supported respiration and combustion in an enhanced way. He concluded that this was just a pure form of common air and that i ...

commissioned a set of nine brass cylinders (a renchpound and decimal subdivisions thereof) for his experimental work. In 1790, a proposal floated by the French to Britain and the United States, to establish a uniform measure of length, a ''metre'' based on the period of a pendulum with a beat of one second, was defeated in the British Parliament and United States Congress. The underlying issue was failure to agree on the latitude for the definition, since gravitational acceleration, and, therefore, the length of the pendulum, varies (inter alia) with latitude: each party wanted a definition according to a major latitude passing through their own country. The direct consequences of the failure were the French unilateral development and deployment of the metric system and its spread by trade to the continent; the British adoption of the Imperial System of Measures throughout the realm in 1824; and the United States' retention of the British common system of measures in place at the time of the independence of the colonies. This was the position that continued for nearly the next 200 years.Much of the British Empire except the UK adopted the metric system early on; the UK partly adopted the metric system late in the 20th century.

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

Units of weight and length

In 1790, a panel of five leading French scientists was appointed by the ''Académie des sciences'' to investigate weights and measures. They were

Jean-Charles de Borda Jean-Charles, chevalier de Borda (4 May 1733 – 19 February 1799) was a French mathematician, physicist, and Navy officer. Biography Borda was born in the city of Dax to Jean‐Antoine de Borda and Jeanne‐Marie Thérèse de Lacroix. In 17 ...

Joseph-Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaPierre-Simon Laplace Pierre-Simon, Marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summariz ...

Gaspard Monge Gaspard Monge, Comte de Péluse (; 9 May 1746 – 28 July 1818) was a French mathematician, commonly presented as the inventor of descriptive geometry, (the mathematical basis of) technical drawing, and the father of differential geometry. Dur ...

, and

Nicolas de Condorcet Nicolas or Nicolás may refer to: People Given name * Nicolas (given name) Mononym * Nicolas (footballer, born 1999), Brazilian footballer * Nicolas (footballer, born 2000), Brazilian footballer Surname Nicolas * Dafydd Nicolas (c.1705–1774), ...

. 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 In a positional numeral system, the radix (radices) or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal system (the most common system in use today) the radix is ten, becaus ...

, that the unit of length should be based on a fractional arc of a quadrant of the Earth's meridian, and that the unit of weight should be that of a cube of water whose dimension was a decimal fraction of the unit of length. The proposals were accepted by the French Assembly on 30 March 1791. Following acceptance, the ''Académie des sciences'' was instructed to implement the proposals. The ''Académie'' broke the tasks into five operations, allocating each part to a separate

working group A working group is a group of experts working together to achieve specified goals. Such groups are domain-specific and focus on discussion or activity around a specific subject area. The term can sometimes refer to an interdisciplinary collab ...

: * Measuring the difference in latitude between

Dunkirk Dunkirk ( ; ; ; Picard language, Picard: ''Dunkèke''; ; or ) is a major port city in the Departments of France, department of Nord (French department), Nord in northern France. It lies from the Belgium, Belgian border. It has the third-larg ...

and

Barcelona Barcelona ( ; ; ) is a city on the northeastern coast of Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second-most populous municipality of Spain. With a population of 1.6 million within c ...

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 In geodesy and navigation, a meridian arc is the curve between two points near the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length. Both the practical determination of meridian ...

), measured along the

. Using Jean Picard's survey of 1670 and Jacques Cassini's survey of 1718, a provisional value of 443.44 '' lignes'' was assigned to the metre which, in turn, defined the other units of measure. While Méchain and Delambre were completing their survey, the commission had ordered a series of

platinum Platinum is a chemical element; it has Symbol (chemistry), symbol Pt and atomic number 78. It is a density, dense, malleable, ductility, ductile, highly unreactive, precious metal, precious, silverish-white transition metal. Its name origina ...

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 The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which al ...

that has an

SI prefix The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official st ...

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

) 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''.from Latin ''gravitas'': "weight" This mass unit defined by

Lavoisier Antoine-Laurent de Lavoisier ( ; ; 26 August 17438 May 1794),
CNRS (

René Just Haüy René Just Haüy () FRS MWS FRSE (28 February 1743 – 1 June 1822) was a French priest and mineralogist, commonly styled the Abbé Haüy after he was made an honorary canon of Notre-Dame de Paris, Notre Dame. Due to his innovative work on cryst ...

had been in use since 1793. This new, practical realisation would ultimately become the base unit of mass. On 7 April 1795, the ''gramme'', upon which the kilogram is based, was decreed to be equal to "the absolute weight of a volume of pure water equal to a cube of one hundredth of a metre, and at the temperature of the melting ice". Although the definition of the ''kilogramme'' specified water at 0 °C—a highly stable temperature point—it was replaced with the temperature at which water reaches maximum density. This temperature, about 4 °C, was not accurately known, but one of the advantages of the new definition was that the precise Celsius value of the temperature was not actually important. The final conclusion was that one cubic decimetre of water at its maximum density was equal to 99.92072% of the mass of the provisional kilogram. On 7 April 1795, the metric system was formally defined in French law.Article 5 of the law of 18 Germinal, Year III It defined six new decimal units: * The '' mètre'', for length—defined as one ten-millionth of the distance between the

and the

Equator The equator is the circle of latitude that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern Hemispheres of Earth, hemispheres. It is an imaginary line located at 0 degrees latitude, about in circumferen ...

through

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

* The '' are'' (100 m²) for area f land* The '' stère'' (1 m³) for volume of firewood * The ''

'' (1 dm³) for volumes of liquid * The ''

gram The gram (originally gramme; SI unit symbol g) is a Physical unit, unit of mass in the International System of Units (SI) equal to one thousandth of a kilogram. Originally defined in 1795 as "the absolute Mass versus weight, weight of a volume ...

me'', for mass—defined as the mass of one cubic centimetre of water * The ''

franc The franc is any of various units of currency. One franc is typically divided into 100 centimes. The name is said to derive from the Latin inscription ''francorum rex'' (King of the Franks) used on early French coins and until the 18th century ...

'', 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 SI units.'' Decimal multiples of these units were defined by Greek

prefixes A prefix is an affix which is placed before the stem of a word. Particularly in the study of languages, a prefix is also called a preformative, because it alters the form of the word to which it is affixed. Prefixes, like other affixes, can b ...

: ''"

myria- Myria- (symbol my) is a now obsolete decimal prefix, decimal metric prefix denoting a factor of 104 (ten thousand). It originates from the Greek language, Greek μύριοι (''mýrioi'') (myriad). The prefix was part of the original metric syst ...

"'' (10,000), ''"

kilo- Kilo is a decimal prefix, decimal metric prefix, unit prefix in the metric system denoting multiplication by one thousand (103). It is used in the International System of Units, where it has the symbol k, in Letter case, lowercase. The prefix ' ...

"'' (1000), ''"

hecto- ''Hecto'' (symbol: h) is a decimal unit prefix in the metric system denoting a factor of one hundred. It was adopted as a multiplier in 1795, and comes from the Greek , meaning "hundred". In 19th century English it was sometimes spelled "hecato" ...

"'' (100), and ''" deka-"'' (10) and submultiples were defined by the Latin prefixes ''"

deci- ''Deci'' (symbol d) is a decimal unit prefix in the metric system denoting a factor of one tenth. Proposed in 1793, and adopted in 1795, the prefix comes from the Latin , meaning "tenth". Since 1960, the prefix is part of the International Syste ...

"'' (0.1), ''" centi-"'' (0.01), and ''" milli-"'' (0.001). For purposes of commerce, units and prefixed-units of weight (mass) and capacity (volume) were prependable by the binary multipliers ''" double-"'' (2) and ''" demi-"'' (), as in ''double-litre'', ''demi-litre''; or ''double-hectogramme'', ''demi-hectogramme'', etc.Article 8 of the law of 18 Germinal, Year III The 1795 draft definitions enabled provisional copies of the kilograms and metres to be constructed.

Meridional survey

The task of surveying the

meridian arc In geodesy and navigation, a meridian arc is the curve (geometry), curve between two points near the Earth's surface having the same longitude. The term may refer either to a arc (geometry), segment of the meridian (geography), meridian, or to its ...

, which was estimated to take two years, fell to

Pierre Méchain Pierre François André Méchain (; 16 August 1744 – 20 September 1804) was a French astronomer and surveyor who, with Charles Messier, was a major contributor to the early study of deep-sky objects and comets. Life Pierre Méchain was bo ...

and Jean-Baptiste Delambre. The task eventually took more than six years (1792–1798) with delays caused not only by unforeseen technical difficulties but also by the convulsed period of the aftermath of the Revolution. Apart from the obvious nationalistic considerations, the

was also a sound choice for practical scientific reasons: a portion of the quadrant from Dunkirk to Barcelona (about 1000 km, or one-tenth of the total) could be surveyed with start- and end-points at sea level, and that portion was roughly in the middle of the quadrant, where the effects of the Earth's oblateness were expected to be the largest. The project was split into two parts—the northern section of 742.7 km from the Belfry,

to Rodez Cathedral which was surveyed by Delambre and the southern section of 333.0 km from

Rodez Rodez (, , ; , ) is a small city and commune in the South of France, about 150 km northeast of Toulouse. It is the prefecture of the department of Aveyron, region of Occitania (formerly Midi-Pyrénées). Rodez is the seat of the communau ...

to the Montjuïc Fortress,

which was surveyed by Méchain.Distances measured using Google Earth. The coordinates are:
– Belfry, Dunkirk
–

Cathedral
–

Montjuïc Montjuïc () is a hill in Barcelona, Catalonia, Spain. Montjuïc or Montjuich, meaning "Jewish Mountain" in medieval Latin and Catalan, is a broad, shallow hill in Barcelona with a rich history. It was the birthplace of the city, and its st ...

Delambre used a baseline of about 10 km in length along a straight road, located close to

Melun Melun () is a commune in the Seine-et-Marne department in the Île-de-France region, north-central France. It is located on the southeastern outskirts of Paris, about from the centre of the capital. Melun is the prefecture of Seine-et-Marne, ...

. In an operation taking six weeks, the baseline was accurately measured using four platinum rods, each of length two ''toises'' (about 3.9 m). Thereafter he used, where possible, the triangulation points used by Cassini in his 1744 survey of France. Méchain's baseline, of a similar length, and also on a straight section of road was in the

Perpignan Perpignan (, , ; ; ) is the prefectures in France, prefecture of the Pyrénées-Orientales departments of France, department in Southern France, in the heart of the plain of Roussillon, at the foot of the Pyrenees a few kilometres from the Me ...

area. Although Méchain's sector was half the length of Delambre, it included the

Pyrenees The Pyrenees are a mountain range straddling the border of France and Spain. They extend nearly from their union with the Cantabrian Mountains to Cap de Creus on the Mediterranean coast, reaching a maximum elevation of at the peak of Aneto. ...

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'',All values in ''lignes'' are referred to the ''toise de Pérou'', not to the later value in '' mesures usuelles''. 1 '' toise'' = 6 '' pieds''; 1 ''pied'' = 12 '' pouces''; 1 ''pouce'' = 12 ''lignes''; so 1 ''toise'' = 864 ''lignes''. notably shorter than the 1795 provisional value of 443.44 ''lignes''. On 15 November 1798, Delambre and Méchain returned to Paris with their data, having completed the survey. The final value of the ''mètre'' was defined in 1799 as the computed value from the survey. : ''Historical note:'' It soon became apparent that Méchain and Delambre's result (443.296 ''lignes'') was slightly too short for the meridional definition of the metre. Méchain had made a small error measuring the latitude of Barcelona, so he remeasured it, but kept the second set of measurements secret.The modern value, for the WGS 84 reference spheroid of m is ''lignes''.

The French metric system

In June 1799, platinum prototypes were fabricated according to the measured quantities, the ''mètre des archives'' defined to be a length of 443.296 lignes, and the ''kilogramme des archives'' defined to be a weight of 18827.15 grains of the ''livre poids de marc'', and entered into the French National Archives. In December of that year, the metric system based on them became by law the sole system of weights and measures in France from 1801 until 1812. Despite the law, the populace continued to use the old measures. In 1812, Napoleon revoked the law and issued one called the '' mesures usuelles'', restoring the names and quantities of the customary measures but redefined as round multiples of the metric units, so it was a kind of hybrid system. In 1837, after the collapse of the Napoleonic Empire, the new Assembly reimposed the metric system defined by the laws of 1795 and 1799, to take effect in 1840. The metrication of France took until about 1858 to be completed. Some of the old unit names, especially the ''

livre Livre may refer to: Currency * French livre, one of a number of obsolete units of currency of France * Livre tournois, one particular obsolete unit of currency of France * Livre parisis, another particular obsolete unit of currency of France * Fre ...

'', 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

and

were the only nascent units of the metric system that were defined in terms of formal

standards Standard may refer to: Symbols * Colours, standards and guidons, kinds of military signs * Standard (emblem), a type of a large symbol or emblem used for identification Norms, conventions or requirements * Standard (metrology), an object t ...

. 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.Ohm's Law wasn't discovered until 1824, for example. 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 A physical quantity (or simply quantity) is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a '' numerical value'' and a '' ...

might be interrelated. A model of interrelated units was first proposed in 1861 by the

British Association for the Advancement of Science The British Science Association (BSA) is a Charitable organization, charity and learned society founded in 1831 to aid in the promotion and development of science. Until 2009 it was known as the British Association for the Advancement of Scienc ...

(BAAS) based on what came to be called the "mechanical" units (length, mass, and time). Over the following decades, this foundation enabled

mechanical Mechanical may refer to: Machine * Machine (mechanical), a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement * Mechanical calculator, a device used to perform the basic operations o ...

electrical Electricity is the set of physical phenomena associated with the presence and motion of matter possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwel ...

, and thermal units to be correlated.

Time

In 1832, German mathematician Carl-Friedrich Gauss made the first absolute measurements of the

Earth's magnetic field Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from structure of Earth, Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from ...

using a decimal system based on the use of the millimetre, milligram, and second as the base unit of time. Gauss's second was based on astronomical observations of the rotation of the Earth, and was the sexagesimal second of the ancients: a partitioning of the solar day into two cycles of 12 periods, and each period divided into 60 intervals, and each interval so divided again, so that a second was 1/86,400th of the day.It is certain, however, that 170 years after the invention of pendulum clocks, that Gauss had sufficiently accurate mechanical clocks for his work. This effectively established a time dimension as a necessary constituent of any useful system of measures, and the astronomical second as the base unit.

Work and energy

In a paper published in 1843, James Prescott Joule first demonstrated a means of measuring the

energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...

transferred between different systems when work is done thereby relating

Nicolas Clément Nicolas Clément (12 January 1779 – 21 November 1841) was a French physicist and chemist. He was a colleague of Charles Desormes, with whom he conducted the Clément-Desormes experiment. The two chemists are also credited with determining a ...

calorie The calorie is a unit of energy that originated from the caloric theory of heat. The large calorie, food calorie, dietary calorie, kilocalorie, or kilogram calorie is defined as the amount of heat needed to raise the temperature of one liter o ...

, 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 In science, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force stre ...

. Energy became the unifying concept of nineteenth century

science Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...

, initially by bringing

thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

and

mechanics Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of ...

together and later adding electrical technology.

The first structured metric system: CGS

In 1861, a committee of the

(BAAS) including William Thomson (later Lord Kelvin),

, and James Prescott Joule among its members was tasked with investigating the "Standards of Electrical Resistance". In their first report (1862), they laid the ground rules for their work—the metric system was to be used, measures of electrical energy must have the same units as measures of mechanical energy, and two sets of electromagnetic units would have to be derived—an electromagnetic system and an electrostatic system. In the second report (1863), they introduced the concept of a coherent system of units whereby units of length, mass, and time were identified as "fundamental units" (now known as ''

''). All other units of measure could be derived (hence '' derived units'') from these base units. The metre, gram, and second were chosen as base units. In 1861, before a meeting of the BAAS, Charles Bright and

Latimer Clark Josiah Latimer Clark FRS FRAS (10 March 1822 – 30 October 1898), was an English electrical engineer, born in Great Marlow, Buckinghamshire. Biography Josiah Latimer Clark was born in Great Marlow, Buckinghamshire, and was the younger bro ...

proposed the names of

ohm Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm. Ohm or OHM may also refer to: People * Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm'' * Germán Ohm (born 1936), Mexican boxer * Jörg Ohm (1 ...

volt The volt (symbol: V) is the unit of electric potential, Voltage#Galvani potential vs. electrochemical potential, electric potential difference (voltage), and electromotive force in the International System of Units, International System of Uni ...

, and

farad The farad (symbol: F) is the unit of electrical capacitance, the ability of a body to store an electrical charge, in the International System of Units, International System of Units (SI), equivalent to 1 coulomb per volt (C/V). It is named afte ...

in honour of

Georg Ohm Georg Simon Ohm (; ; 16 March 1789 – 6 July 1854) was a German mathematician and physicist. As a school teacher, Ohm began his research with the new electrochemical cell, invented by Italian scientist Alessandro Volta. Using equipment of his o ...

Alessandro Volta Alessandro Giuseppe Antonio Anastasio Volta (, ; ; 18 February 1745 – 5 March 1827) was an Italian chemist and physicist who was a pioneer of electricity and Power (physics), power, and is credited as the inventor of the electric battery a ...

, and

Michael Faraday Michael Faraday (; 22 September 1791 – 25 August 1867) was an English chemist and physicist who contributed to the study of electrochemistry and electromagnetism. His main discoveries include the principles underlying electromagnetic inducti ...

respectively for the practical units based on the CGS absolute system. This was supported by Thomson (Lord Kelvin). The concept of naming units of measure after noteworthy scientists was subsequently used for other units. In 1873, another committee of the BAAS (which also included Maxwell and Thomson) tasked with "the Selection and Nomenclature of Dynamical and Electrical Units" recommended using the cgs system of units. The committee also recommended the names of "

dyne The dyne (symbol: dyn; ) is a derived units of measurement, unit of force (physics), force specified in the centimetre–gram–second system of units, centimetre–gram–second (CGS) system of units, a predecessor of the modern International S ...

" and "

erg The erg is a unit of energy equal to 10−7joules (100Nano-, nJ). It is not an SI unit, instead originating from the centimetre–gram–second system of units (CGS). Its name is derived from (), a Greek language, Greek word meaning 'work' or ' ...

" for the cgs units of force and energy. The cgs system became the basis for scientific work for the next seventy years. The reports recognised two centimetre–gram–second based systems for electrical units: the Electromagnetic (or absolute) system of units (EMU) and the Electrostatic system of units (ESU).

Electrical units

In the 1820s,

formulated

Ohm's Law Ohm's law states that the electric current through a Electrical conductor, conductor between two Node (circuits), points is directly Proportionality (mathematics), proportional to the voltage across the two points. Introducing the constant of ...

, which can be extended to relate power to current, electric potential (voltage), and resistance. During the following decades, the realisation of a coherent system of units that incorporated the measurement of electromagnetic phenomena and Ohm's law was beset with problems—several different systems of units were devised. In the three CGS systems, the constants

k_\text

and

k_\text

and consequently

\epsilon_0

and

\mu_0

were dimensionless, and thus did not require any units to define them. The electrical units of measure did not easily fit into the coherent system of mechanical units defined by the BAAS. Using dimensional analysis, the dimensions of voltage

\mathsf^\frac\mathsf^\frac\mathsf^

in the ESU system were identical to the dimensions of current in the EMU system, while resistance had dimensions of velocity in the EMU system, but the inverse of velocity in the ESU system.

Electromagnetic (absolute) system of units (EMU)

The Electromagnetic system of units (EMU) was developed from

André-Marie Ampère André-Marie Ampère (, ; ; 20 January 177510 June 1836) was a French physicist and mathematician who was one of the founders of the science of classical electromagnetism, which he referred to as ''electrodynamics''. He is also the inventor of ...

's discovery in the 1820s of a relationship between currents in two conductors and the force between them now known as Ampere's law: :

\frac   = 2 k_\text \frac

where

k_\text = \frac  \

(SI units) In 1833, Gauss pointed out the possibility of equating this force with its mechanical equivalent. This proposal received further support from Wilhelm Weber in 1851. In this system, current is defined by setting the magnetic force constant

k_\mathrm

to unity and electric potential is defined in such a way as to ensure the unit of power calculated by the relation

P = VI

is an erg/second. The electromagnetic units of measure were known as the abampere, abvolt, and so on. These units were later scaled for use in the International System.

Electrostatic system of units (ESU)

The Electrostatic system of units (ESU) was based on Coulomb's quantification in 1783 of the force acting between two charged bodies. This relationship, now known as

Coulomb's law Coulomb's inverse-square law, or simply Coulomb's law, is an experimental scientific law, law of physics that calculates the amount of force (physics), force between two electric charge, electrically charged particles at rest. This electric for ...

, can be written :

F_\mathrm = k_\text \frac,

where

k_\text = \frac

(SI units) In this system, the unit for charge is defined by setting the Coulomb force constant (

k_\text

) to unity and the unit for electric potential was defined to ensure the unit of energy calculated by the relation

E = QV

is one erg. The electrostatic units of measure were the statampere, statvolt, and so on.

Gaussian system of units

The Gaussian system of units was based on

Heinrich Hertz Heinrich Rudolf Hertz (; ; 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's equations of electromagnetism. Biography Heinri ...

's realisation, while verifying

Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, Electrical network, electr ...

in 1888, that the electromagnetic and electrostatic units were related by: :

c^2 = \frac

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 Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observat ...

and

maxwell Maxwell may refer to: People * Maxwell (surname), including a list of people and fictional characters with the name ** James Clerk Maxwell, mathematician and physicist * Justice Maxwell (disambiguation) * Maxwell baronets, in the Baronetage of N ...

) and ESU units elsewhere. He named this combined set of units "

Gaussian units Gaussian units constitute a metric system of units of measurement. This system is the most common of the several electromagnetic unit systems based on the centimetre–gram–second system of units (CGS). It is also called the Gaussian unit syst ...

". This set of units has been recognised as being particularly useful in theoretical physics.

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

The CGS units of measure used in scientific work were not practical for engineering, leading to the development of a more applicable system of electric units especially for telegraphy. The unit of length was 10⁷ m (the hebdometre, nominally the

), the unit of mass was an unnamed unit equal to 10⁻¹¹ g and the unit of time was the second. The units of mass and length were scaled incongruously to yield more consistent and usable electric units in terms of mechanical measures. Informally called the "practical" system, it was properly termed the quadrant–eleventhgram–second (QES) system of units according to convention. The definitions of electrical units incorporated the magnetic constant like the EMU system, and the names of the units were carried over from that system, but scaled according to the defined mechanical units. The system was formalised as the International system late in the 19th century and its units later designated the "international ampere", "international volt", etc.

Heaviside–Lorentz system of units

The factor

4\pi

that occurs in Maxwell's equations in the gaussian system (and the other CGS systems) comes from the

4\pi

steradians surrounding a point, such as a point electric charge. This factor could be eliminated from contexts that do not involve spherical coordinates by incorporating the factor into the definitions of the quantities involved. The system was proposed by Oliver Heaviside in 1883 and is also known as the "rationalised Gaussian system of units". The SI later adopted rationalised units based on Heaviside's rationalisation scheme.

Thermodynamics

Maxwell and Boltzmann had produced theories describing the interrelationship of temperature, pressure, and volume of a gas on a microscopic scale but otherwise, in 1900, there was no understanding of the microscopic nature of temperature. By the end of the nineteenth century, the fundamental macroscopic laws of thermodynamics had been formulated and, although techniques existed to measure temperature using empirical techniques, the scientific understanding of the nature of temperature was minimal.

Convention of the metre

With increasing international adoption of the metre, the shortcomings of the ''mètre des Archives'' as a standard became ever more apparent. Countries which adopted the metre as a legal measure purchased standard metre bars that were intended to be equal in length to the ''mètre des Archives'', but there was no systematic way of ensuring that the countries were actually working to the same standard. The meridional definition, which had been intended to ensure international reproducibility, quickly proved so impractical that it was all but abandoned in favour of the artefact standards, but the ''mètre des Archives'' (and most of its copies) were "end standards": such standards (bars which are exactly one metre in length) are prone to wear with use, and different standard bars could be expected to wear at different rates. In 1867, it was proposed that a new international standard metre be created, and the length was taken to be that of the ''mètre des Archives'' "in the state in which it shall be found". The International Conference on Geodesy in 1867 called for the creation of a new international prototype of the metreThe term "prototype" does not imply that it was the first in a series and that other standard metres would come after it: the "prototype" of the metre was the one that came first in the logical chain of comparisons, that is the metre to which all other standards were compared. and of a system by which national standards could be compared with it. The international prototype would also be a "line standard", that is the metre was defined as the distance between two lines marked on the bar, so avoiding the wear problems of end standards. The French government gave practical support to the creation of an International Metre Commission, which met in Paris in 1870 and again in 1872 with the participation of about thirty countries. On 20 May 1875, an international treaty known as the ''Convention du Mètre'' (Metre Convention) was signed by 17 states. This treaty established the following organisations to conduct international activities relating to a uniform system for measurements: :* ''

'' (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 The International Bureau of Weights and Measures (, BIPM) is an intergovernmental organisation, through which its 64 member-states act on measurement standards in areas including chemistry, ionising radiation, physical metrology, as well as t ...

'' (BIPM or International Bureau of Weights and Measures), a permanent laboratory and world centre of scientific metrology, the activities of which include the establishment of the basic standards and scales of the principal physical quantities, maintenance of the international prototype standards, and oversight of regular comparisons between the international prototype and the various national standards. The international prototype of the metre and

were both made from a 90%

, 10%

iridium Iridium is a chemical element; it has the symbol Ir and atomic number 77. This very hard, brittle, silvery-white transition metal of the platinum group, is considered the second-densest naturally occurring metal (after osmium) with a density ...

alloy which is exceptionally hard and which has good electrical and thermal conductivity properties. The prototype had a special X-shaped ( Tresca) cross section to minimise the effects of torsional strain during length comparisons and the prototype kilograms were cylindrical in shape. The London firm Johnson Matthey delivered 30 prototype metres and 40 prototype kilograms. At the first meeting of the

CGPM The General Conference on Weights and Measures (abbreviated CGPM from the ) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established in 1875 under the terms of the Metre ...

in 1889, bar No. 6 and cylinder No. X were accepted as the international prototypes. The remainder were either kept as BIPM working copies or distributed to member states as national prototypes. Following the Convention of the Metre, in 1889, the BIPM had custody of two artefacts—one to define length and the other to define mass. Other units of measure which did not rely on specific artefacts were controlled by other bodies. Although the definition of the kilogram remained unchanged throughout the 20th century, the 3rd CGPM in 1901 clarified that the kilogram was a unit of

, not of

. The original batch of 40 prototypes (adopted in 1889) were supplemented from time to time with further prototypes for use by new signatories to the

Metre Convention The Metre Convention (), also known as the Treaty of the Metre, is an international treaty that was signed in Paris on 20 May 1875 by representatives of 17 nations: Argentina, Austria-Hungary, Belgium, Brazil, Denmark, France, German Empire, Ge ...

. In 1921, the Treaty of the Metre was extended to cover electrical units, with the CGPM merging its work with that of the IEC.

Measurement systems before World War II

The 20th century history of measurement is marked by five periods: the 1901 definition of the coherent MKS system; the intervening 50 years of coexistence of the MKS, cgs and common systems of measures; the 1948 ''Practical system of units'' prototype of the SI; the introduction of the SI in 1960; and the evolution of the SI in the latter half century.

A coherent system

The need for an independent electromagnetic dimension to resolve the difficulties related to defining such units in terms of length, mass, and time was identified by Giorgi in 1901. This led to Giorgi presenting a paper in October 1901 to the congress of the Associazione Elettrotecnica Italiana (A.E.I.) in which he showed that a coherent electro-mechanical system of units could be obtained by adding a fourth base unit of an electrical nature (e.g., ampere, volt, or ohm) to the three base units proposed in the 1861 BAAS report. This gave physical dimensions to the constants ''k''_e and ''k''_m and hence also to the electro-mechanical quantities ''ε''₀ (permittivity of free space) and ''μ''₀ (permeability of free space). His work also recognised the relevance of energy in the establishment of a coherent, rational system of units, with the

joule The joule ( , or ; symbol: J) is the unit of energy in the International System of Units (SI). In terms of SI base units, one joule corresponds to one kilogram- metre squared per second squared One joule is equal to the amount of work d ...

as the unit of energy, and the electrical units in the International System of Units remaining unchanged. However, it took more than thirty years before Giorgi's work was accepted in practice by the IEC.

Systems of measurement in the industrial era

As industry developed around the world, the cgs system of units as adopted by the British Association for the Advancement of Science in 1873 with its plethora of electrical units continued to be the dominant system of measurement, and remained so for at least the next 60 years. The advantages were several: it had a comprehensive set of derived units which, while not quite coherent, were at least homologous; the MKS system lacked a defined unit of electromagnetism at all; the MKS units were inconveniently large for the sciences; customary systems of measures held sway in the United States, Britain, and the British empire, and even to some extent in France, the birthplace of the metric system, which inhibited adoption of any competing system. Finally, war, nationalism, and other political forces inhibited development of the science favouring a coherent system of units. At the 8th CGPM in 1933, the need to replace the "international" electrical units with "absolute" units was raised. The IEC proposal that Giorgi's 'system', denoted informally as MKSX, be adopted was accepted, but no decision was made as to which electrical unit should be the fourth base unit. In 1935, J. E. Sears proposed that this should be the ampere, but

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

prevented this being formalised until 1946. The first (and only) follow-up comparison of the national standards with the international prototype of the metre was carried out between 1921 and 1936, and indicated that the definition of the metre was preserved to within 0.2 μm. During this follow-up comparison, the way in which the prototype metre should be measured was more clearly defined—the 1889 definition had defined the metre as being the length of the prototype at the temperature of melting ice, but, in 1927, the 7th CGPM extended this definition to specify that the prototype metre shall be "supported on two cylinders of at least one centimetre diameter, symmetrically placed in the same horizontal plane at a distance of 571 mm from each other". The choice of 571 mm represents the Airy points of the prototype—the points at which the bending or droop of the bar is minimised.

Working draft of SI: ''Practical system of units''

The 9th CGPM met in 1948, fifteen years after the 8th CGPM. In response to formal requests made by the International Union of Pure and Applied Physics and by the French government to establish a practical system of units of measure, the CGPM requested the CIPM to prepare recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention. The CIPM's draft proposal was an extensive revision and simplification of the metric unit definitions, symbols, and terminology based on the MKS system of units. Following astronomical observations, the second was set as a fraction of the year 1900. The electromagnetic base unit, as required by Giorgi, was accepted as the ampere. After negotiations with the CIS and IUPAP, two additional units—the degree kelvin and the candela—were also proposed as base units. For the first time, the CGPM made recommendations concerning derived units. At the same time, the CGPM adopted conventions for the writing and printing of unit symbols and numbers and catalogued the symbols for the most important MKS and CGS units of measure.

Time

Until the advent of the

atomic clock An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions betwee ...

, the most reliable timekeeper available to humanity was the Earth's rotation. It was natural, therefore, that the astronomers under the auspices of the

International Astronomical Union The International Astronomical Union (IAU; , UAI) is an international non-governmental organization (INGO) with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach, education, and developmen ...

(IAU) took the lead in maintaining the standards relating to time. During the 20th century, it became apparent that the Earth's rotation was slowing down, resulting in days becoming 1.4 milliseconds longer each century —this was verified by comparing the calculated timings of eclipses of the Sun with those observed in antiquity going back to Chinese records of 763 BC. In 1956, the 10th CGPM instructed the CIPM to prepare a definition of the second; in 1958, the definition was published stating that the second (called an ''ephemeris'' second) would be calculated by extrapolation using Earth's rotational speed in 1900.

Electrical unit

Per Giorgi's proposals of 1901, the CIPM also recommended that the ampere be the base unit from which electromechanical units would be derived. The definitions for the ohm and volt that had previously been in use were discarded, and these units became derived units based on the ampere. In 1946, the CIPM formally adopted a definition of the ampere based on the original EMU definition and redefined the ohm in terms of other base units. The definitions for the absolute electrical system, based on the ampere, were formalised in 1948. The draft proposed units with these names are very close, but not identical, to the international units.

Temperature

In the Celsius scale from the 18th century, temperature was expressed in degrees Celsius with the definition that ice melted at 0 °C and (at standard atmospheric pressure) water boiled at 100 °C. A series of lookup tables defined temperature in terms of interrelated empirical measurements made using various devices. In 1948, definitions relating to temperature had to be clarified. (The degree, as an angular measure, was adopted for general use in many countries, so, in 1948, the

General Conference on Weights and Measures The General Conference on Weights and Measures (abbreviated CGPM from the ) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established in 1875 under the terms of the Metre C ...

(CGPM) recommended that the degree Celsius, as used for the measurement of temperature, be renamed the degree Celsius.) At the 9th CGPM, the Celsius temperature scale was renamed the

Celsius The degree Celsius is the unit of temperature on the Celsius temperature scale "Celsius temperature scale, also called centigrade temperature scale, scale based on 0 ° for the melting point of water and 100 ° for the boiling point ...

scale, and the scale itself was fixed by defining the

triple point of water Water () is a polar inorganic compound that is at room temperature a tasteless and odorless liquid, which is nearly colorless apart from an inherent hint of blue. It is by far the most studied chemical compound and is described as the "uni ...

as 0.01 °C, though the CGPM left the formal definition of absolute zero until the 10th CGPM when the name "

Kelvin The kelvin (symbol: K) is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By de ...

" was assigned to the absolute temperature scale, and the triple point of water was defined as being .

Luminosity

Before 1937, the

International Commission on Illumination The International Commission on Illumination (usually abbreviated CIE for its French name Commission internationale de l'éclairage) is the international authority on light, illumination, colour, and colour spaces. It was established in 1913 a ...

(CIE from its French title, the ''Commission Internationale de l'Eclairage''), in conjunction with the CIPM, produced a standard for luminous intensity to replace the various national standards. This standard, the

(cd), which was defined as "the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per

square centimetre The square metre ( international spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the unit of area in the International System of Units (SI) with symbol m2. It is the area of a square w ...

", was ratified by the CGPM in 1948.

Derived units

The newly accepted definition of the ampere allowed practical and useful coherent definitions of a set of electromagnetic derived units, including farad, henry, watt, tesla, weber, volt, ohm, and coulomb. Two derived units, lux and lumen, were based on the new candela, and one, degree Celsius, equivalent to the degree Kelvin. Five other miscellaneous derived units completed the draft proposal: radian, steradian, hertz, joule, and newton.

International System of Units (SI)

In 1952, the CIPM proposed the use of wavelength of a specific light source as the standard for defining length, and, in 1960, the CGPM accepted this proposal using radiation corresponding to a transition between specified energy levels of the krypton 86 atom as the new standard for the metre. The standard metre artefact was retired. In 1960, Giorgi's proposals were adopted as the basis of the ''Système International d'Unités'' (International System of Units), the SI. This initial definition of the SI included six base units, the metre, kilogram, second, ampere, degree Kelvin, and candela, and sixteen coherent derived units.

Evolution of the modern SI

The evolution of the SI after its publication in 1960 has seen the addition of a seventh base unit, the ''mole'', and six more derived units, the ''pascal'' for pressure, the ''gray'', ''sievert'', and ''becquerel'' for radiation, the ''siemens'' for electrical conductance, and ''katal'' for catalytic (enzymatic) activity. Several units have also been redefined in terms of physical constants.

New base and derived units

Over the ensuing years, the BIPM developed and maintained cross-correlations relating various measuring devices such as thermocouples, light spectra, and the like to the equivalent temperatures. The mole was originally known as a gram-atom or a gram-molecule—the amount of a substance measured in grams divided by its

atomic weight Relative atomic mass (symbol: ''A''; sometimes abbreviated RAM or r.a.m.), also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a giv ...

. 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 The International Union of Pure and Applied Physics (IUPAP; ) is an international non-governmental organization whose mission is to assist in the worldwide development of physics, to foster international cooperation in physics, and to help in the ...

(IUPAP) and the

International Union of Pure and Applied Chemistry The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...

(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.

Start of migration to constant definitions

The second major trend in the post-modern SI was the migration of unit definitions in terms of physical constants of nature. In 1967, at the 13th CGPM, the degree Kelvin () was renamed the "kelvin" (K). Astronomers from the US Naval Observatory (USNO) and the National Physical Laboratory determined a relationship between the frequency of radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom and the estimated rate of rotation of the earth in 1900. Their atomic definition of the second was adopted in 1968 by the 13th CGPM. By 1975, when the second had been defined in terms of a physical phenomenon rather than the earth's rotation, the CGPM authorised the CIPM to investigate the use of the speed of light as the basis for the definition of the metre. This proposal was accepted in 1983. The candela definition proved difficult to implement so, in 1979, the definition was revised and the reference to the radiation source was replaced by defining the candela in terms of the power of a specified frequency of monochromatic yellowish-green visible light, which is close to the frequency where the human eye, when adapted to bright conditions, has greatest sensitivity.

Kilogram artefact instability

After the metre was redefined in 1960, the kilogram remained the only SI base defined by a physical artefact. During the years that followed, the definitions of the base units and particularly the ''mise en pratique'' to realise these definitions have been refined. The third periodic recalibration in 1988–1989 revealed that the average difference between the IPK and adjusted baseline for the national prototypes was 50 μg—in 1889, the baseline of the national prototypes had been adjusted so that the difference was zero. As the IPK is the definitive kilogram, there is no way of telling whether the IPK had been losing mass or the national prototypes had been gaining mass. During the course of the century, the various national prototypes of the kilogram were recalibrated against the

(IPK) and, therefore, against each other. The initial 1889 starting-value offsets of the national prototypes relative to the IPK were nulled, with any subsequent mass changes being relative to the IPK.

Proposed replacements for the IPK

A number of replacements were proposed for the IPK. From the early 1990s, the International Avogadro Project worked on creating a 1 kg, 94 mm, sphere made of a uniform silicon-28 crystal, with the intention of being able replace the IPK with a physical object which would be precisely reproducible from an exact specification. Due to its precise construction, the Avogadro Project's sphere is likely to be the most precisely spherical object ever created by humans. Other groups worked on concepts such as creating a reference mass via precise electrodeposition of gold or bismuth atoms, and defining the kilogram in terms of the

by relating it to forces generated by electromagnetic repulsion of electric currents. Eventually, the choices were narrowed down to the use of the Watt balance and the International Avogadro Project sphere. Ultimately, a decision was made not to create any physical replacement for the IPK, but instead to define all SI units in terms of assigning precise values to a number of physical constants which had previously been measured in terms of the earlier unit definitions.

Redefinition in terms of fundamental constants

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

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

kelvin The kelvin (symbol: K) is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By de ...

, and mole—were redefined by setting exact numerical values for the

Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

('), the

elementary electric charge The elementary charge, usually denoted by , is a fundamental physical constant, defined as the electric charge carried by a single proton (+1 ''e'') or, equivalently, the magnitude of the negative electric charge carried by a single electron, ...

('), the

Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative thermal energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the ...

(), and the

Avogadro constant The Avogadro constant, commonly denoted or , is an SI defining constant with an exact value of when expressed in reciprocal moles. It defines the ratio of the number of constituent particles to the amount of substance in a sample, where th ...

(), respectively. The

, and

were already defined by

physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that cannot be explained by a theory and therefore must be measured experimentally. It is distinct from a mathematical constant, which has a ...

s and were subject to correction to their definitions. The new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. This resolution was accepted by the conference, It was not expected to be adopted until some prerequisite conditions are met, and in any case not before 2014. See and, in addition, the CGPM moved the date of the 25th meeting forward from 2015 to 2014. At the 25th meeting on 18 to 20 November 2014, it was found that "despite rogress in the necessary requirementsthe data do not yet appear to be sufficiently robust for the CGPM to adopt the revised SI at its 25th meeting", thus postponing the revision to the next meeting in 2018. Measurements accurate enough to meet the conditions were available in 2017 and the revision was adopted at the 26th CGPM (13–16 November 2018), with the changes finally coming into force in 2019, creating a system of definitions which is intended to be stable for the long term.

Notes

References

{{Metrication Metrication

Metric system The metric system is a system of measurement that standardization, standardizes a set of base units and a nomenclature for describing relatively large and small quantities via decimal-based multiplicative unit prefixes. Though the rules gover ...

Age of Enlightenment

Preamble

Body measures and artifacts

Clocks and pendulums

Shape and size of the Earth

Late 18th century: conflict and lassitude

Implementation in Revolutionary France

Weights and measures of the ''Ancien Régime''

Units of weight and length

Meridional survey

The French metric system

Development of non-coherent metric systems

Time

Work and energy

The first structured metric system: CGS

Electrical units

Electromagnetic (absolute) system of units (EMU)

Electrostatic system of units (ESU)

Gaussian system of units

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

Heaviside–Lorentz system of units

Thermodynamics

Convention of the metre

Measurement systems before World War II

A coherent system

Systems of measurement in the industrial era

Working draft of SI: ''Practical system of units''

Time

Electrical unit

Temperature

Luminosity

Derived units

International System of Units (SI)

Evolution of the modern SI

New base and derived units

Start of migration to constant definitions

Kilogram artefact instability

Proposed replacements for the IPK

Redefinition in terms of fundamental constants

See also

Notes

References