Metric system

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This article is about the metric system in general. Information about specific versions of the system, such as the International System of Units or the cgs system of units, can be found in those articles.

The metric system is for all people for all time (Condorcet 1791). Four measuring devices that have metric calibrations are shown. Three of the instruments, a tape measure calibrated in centimetres, a thermometer calibrated in degrees Celsius and a kilogram weight are for domestic use while the fourth, an electrical multimeter which measures volts, amps and ohms, is for use normal use by tradesmen.

The metric system is an international decimalised system of measurement. France was first to adopt it in 1799 and it is now the basic system of measurement used in almost every country in the world; the United States being the only industrialised country yet to adopt the International System of Units as its predominant system of measurement. Although the originators intended to devise a system that was equally accessible to all, it proved necessary to use prototype units under the custody of government or other approved authorities as standards. Until 1875, control of the prototype units of measure were maintained by the French Government when it passed to an inter-governmental organisation - the Conférence générale des poids et mesures (CGPM). It is now hoped that the last of these prototypes can be retired by 2015.

From its beginning, the main feature of the metric system was the standard set of inter-related base units and a standard set of prefixes in powers of ten. These base units are used to derive larger and smaller units and replaced a huge number of unstandardised units of measure that existed previously. While the system was first developed for commercial use, its coherent set of units made it particularly suitable for scientific and engineering purposes.

The uncoordinated use of the metric system by different scientific and engineering disciplines, particularly in the late nineteenth century, resulted in different choices of fundamental units, even though all were based on the same definitions of the metre) and the kilogram). During the twentieth century, efforts were made to rationalise these units and in 1960 the CGPM published the International System of Units ("Système international d'unités" in French, hence "SI") which, since then, has been the internationally recognised standard metric system.

Contents

[edit] Features of the metric system

Although the metric system has changed and developed since its inception, its basic features have remained constant.

[edit] A Universal System

Chinese expressway distances road sign in eastern Beijing. Although the primary text is in Chinese, the distances use internationally recognised characters.

The metric system was, in the words of the French philosopher Condorcet to be "for all people for all time".[1] It was designed for ordinary people, for engineers who worked in human-related measurements and for astronomers and physicists who worked with numbers both small and large, hence the huge range of prefixes that have now been defined in SI.[2]

The metric system was designed to be universal, that is, available to all. When the French Government first investigated the idea of overhauling their system of measurement, Talleyrand, in the late 1780s, acting on Concordet's advice, invited Riggs, a British Parliamentarian and Jefferson, the American Secretary of State to George Washington to work with the French is producing an international standard by promoting legislation in their respective legislative bodies. However, these overtures failed and the custody of the metric system remained in the hands of the French Government until 1875.[3]

To help make it universal, common symbols that are independent of language were developed. Thus the symbol "km" is used in French and in British English for "kilometre", in German and in American English for "kilometer", in Italian for "Chilometri", in Greek for "χιλιόμετρα", in Russian for "Километр" and so on.[4][5]

[edit] Decimal multiples

The metric system is decimal. All multiples and divisions of the base units are factors of the power of ten, am idea was first proposed by Stevin in 1586. [6] Thus all lengths and distances, for example, are measured in metres, millimetres (1/1 000 of a metre), or kilometres (1 000 m). There is no profusion of different units with different conversion factors, such as inches, feet, yards, fathoms, rods, chains, furlongs, miles, nautical miles, leagues, etc. The practical benefits of a decimal system have also been used to replace other non-decimal systems such as currencies, with decimal systems .

The simple decimal prefixes encouraged the adoption of the metric system; the use of base 10 arithmetic aids in unit conversion, as compared to 12 inches per foot, 3 feet per yard, et cetera. Differences in expressing units are simply a matter of shifting the decimal point or changing an exponent; for example, the speed of light may be expressed as 299,792.458 km/s or 2.99792458×108
 m/s.

[edit] Prefixes

Metric prefixes in everyday use
Text Symbol Factor
tera T 1,000,000,000,000
giga G 1,000,000,000
mega M 1,000,000
kilo k 1,000
hecto h 100
deka da 10
(unit) (unit) 1
deci d 0.1
centi c 0.01
milli m 0.001
micro μ 0.000,001
nano n 0.000,000,001
pico p 0.000,000,000,001
Main article: SI prefix

All derived units use a common set of prefixes for each multiple. (This idea was first suggested by Mouton in 1670.[7]) Thus the prefix kilo is used for mass (kilogram) or length (kilometre) both indicating a thousand times the base unit. This did not prevent the popular use of names for some derived units such as the tonne which is a megagram; derived from old customary units and rounded to metric.

The function of the prefix is to multiply or divide the measure by a factor of ten, one hundred or a positive integer power of one thousand.[8] Initally positive powers of ten had Greek-derived prefixes and negative power of ten Latin-derived prefixes. However later SI extensions to the prefix system did not follow the Greek-greater-than-one/Latin-less-than-one convention.

The most familiar ones from everyday use are the kilo~ is of Greek origin, and the centi~ and milli~ which are of Latin origin. Most other metric measurements also use prefixes rooted in Latin or Greek: deci- has a Latin root, while nano-, micro-, deka-, hecto-, mega-, giga- have Greek roots.

[edit] Replicable prototypes

The initial way to establish a standard was to make prototypes of the base units and distribute copies to approved centres. This made the new standard reliant on the original prototypes, which would be in conflict with the previous goal, since all countries would have to refer to the one holding the prototypes.

Instead, where possible, definitions of the base units were developed so that any laboratory equipped with proper instruments would be able to construct their own copies of the standard. In the original version of the metric system the base units could be derived from the a specified length (the metre) and the weight [mass] of a specified volume (1⁄1000 of a cubic metre) of pure water. Initially the Assemblée Constituante considered defining the metre as the length of a pendulum that has a period of one second at 45°N and an altitide equal to sea level. The altitude and latitude were specified to accomodate variations in gravity - the specified latitude was a compromise between the latitude of London (51° 30'N), Paris (48° 50'N) and the median parallel of the United States (38°N) to accomodate variations.[9] However Borda persuaded the Assemblée Constituante that a survey having its ends at sea leval and based on a meridian that spanned at least 10% of the earth's quadrant would be more appropriate for such a basis.[10]

[edit] Realisability

K48, above, came from the second batch of kilogram replicas to be produced. It was delivered to Denmark in 1949 with an official mass of 1 kg + 81 µg. Like all other replicas, it is stored under two nested bell jars virtually all the time.

The base units used in the metric system must be realisable, ideally with reference to natural phenomena rather than unique artefacts. Each of the base units in SI is accompanied by a mise and practique published by the BIPM that describes in detail at least one way in which the base unit can be measured.[11]

Two of the base units originally depended on artefacts – the metre and the kilogram. The original prototypes of each artefact were adopted in 1799 and replaced in 1889. The 1889 prototypes used the best technology of the day to ensure stability.

In 1889 there was no generally accepted theory regarding the nature of light but by 1960 the wavelength of specific light spectra could give a more accurate and reproducible value than a prototype metre. In that year the prototype metre was replaced by a formal definition which defines the metre in terms of the wavelength of specified light spectra. By 1983, Einstein's theory of relativity, provided a yet better value so the metre was redefined in terms of the speed of light. These definitions give a much better reproducability and also allow anyone, anywhere to make their own "standard" metre (assuming that they have a good enough laboratory).[12]

Similarly, at the 13th convocation of the GCPM in 1968, the definitive second was redefined in terms of measurements taken from atomic clocks rather than from the earth's rotation;[13] in 2008 the solar day was 0.002 s longer than in 1820[14] but it was only in the 1960s that this could be measured more accurately using clocks rather than relying on astronomy.

[edit] Coherence

The metric system is a coherent system - the various derived units are directly related to the base units without the need of intermediate conversion factors.[15] For example, the units of force, energy and power are chosen so that the equations

force = mass × acceleration
energy = force × distance
energy = power × time

hold without the introduction of constant factors. Many relationships in physics, including Einstein's equation e = mc2, do not require extraneous constants when expressed in coherent units.[16]

In SI, which is a coherent system, the unit of power is the "watt" which is defined as "one joule per second". In the foot-pound-second system of measurement, which is non-coherent, the unit of power is the "horsepower" which is defined as "550 foot-pounds per second".

Other defined units are derived in a similar way building up on the base units.

[edit] History

Countries by date of metrication. Colours red to green show the pattern of metrication from 1795 to 1998. Black identifies countries that have not adopted the metric system as the primary measurement system. White identifies countries that already used the metric system at the time they gained their independence.
See also: Metrication

The map on the left shows when the metric system was adopted by various countries.

In 1586, the Flemish mathematician Simon Stevin published a small pamphlet called De Thiende ("the tenth").[6] Decimal fractions had been employed for the extraction of square roots some five centuries before his time, but nobody used decimal numbers in daily life. Stevin declared that using decimals was so important that the universal introduction of decimal weights, measures and coinage was only a matter of time.

The idea of a metric system has been attributed to John Wilkins, first secretary of the Royal Society of London in 1668.[17][18][19] Two years later, in 1670, Gabriel Mouton, a French abbot and scientist, proposed a decimal system of measurement based on the circumference of the Earth. His suggestion was a unit, milliare, that was defined as a minute of arc along a meridian. He then suggested a system of sub-units, dividing successively by factors of ten into the centuria, decuria, virga, virgula, decima, centesima, and millesima.[7] His ideas attracted interest at the time, and were supported by both Jean Picard and Christiaan Huygens in 1673, and also studied at the Royal Society in London. In the same year, Gottfried Leibniz independently made proposals similar to those of Mouton.

In pre-revolutionary Europe, each state had its own system of units of measure. Some countries, such as Spain and Russia saw the advantages of harmonising their units of measure with those of their trading partners.[20] However, vested interests who profited from variations in units of measure opposed this. This was particularly prevelant in France where there was a huge inconsistency in the size of units of measure. [1] During the early years of the French Revolution, the leaders of the French revolutionary Assemblée Constituante decided that rather than standardising the size of the existing units, they would a introduce a completely new system based on the principals of logic and natural phenonena.[1]

Initially France attempted to work with other countries towards the adoption of a common set of units of measure. Among the supporters of such an international system of units was Thomas Jefferson who, in 1790, presented a document Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States to congress in which he advocated a decimal system that used traditional names for units (such as ten inches per foot).[21] The report was considered but not adopted by Congress. There was little support form other countries.

Woodcut dated 1800 illustrating the new decimal units which became the legal norm across all France on 4 November 1800

[edit] Original system

The law of 18 Germinal, Year III (7 April 1795) defined five units of measure:[22]

This system continued the tradition of having separate base units for geometrically related dimensions, e.g., metre for lengths, are (100 m2) for areas, stère (1 m3) for dry capacities, and litre (1 dm3) for liquid capacities. The hectare, equal to a hundred ares, is the area of a square 100 metres on a side (about 2.47 acres), and is still in use. The early metric system included only a few prefixes from milli (one thousandth) to myria (ten thousand), and they were based on powers of 10 unlike later prefixes added in the SI, which are based on powers of 1,000.

Originally the kilogram, the only base unit with a prefix, was called the "grave"; the "gram" being an alternative name for a thousandth of a grave. However, the word "grave" , being a synonym for the title "count" had aristocratic connotations and was renamed the kilogram.[24]

France officially adopted the metric system on 10 December 1799[25] with conversion being mandatory first in Paris and then across the provinces.

[edit] International adoption

The areas that were annexed by France during the Napoleonic era inherited the metric system. In 1812, Napoleon introduced a system known as mesures usuelles which used the names of pre-metric units of measure, but defined then in terms of metric units – for example, the livre metrique (metric pound) was 500 g and the toise metrique (metric fathom) was 2 metres.[26] After the Congress of Vienna in 1815, France lost the territories that she had annexed and they reverted to their pre-revolutionary units of measure.

In 1817, the Netherlands reintroduced the metric system, but used pre-revolutionary names – for example 1 cm became the duim (thumb), the ons (ounce) became 100 g and so on.[27] Certain German states adopted similar systems[28][29] and in 1852 the German Zollverein (customs union) adopted the zollpfund (customs pound) of 500 g for intrastate commerce.[30] In 1872 the newly-formed German Empire adopted the metric system as its official system of weights and measures[31] and the newly-formed Kingdom of Italy likewise, following the lead given by Piedmont, adopted the metric system in 1861.[32]

The Exposition Universelle (1867) (Paris exhibition) devoted a stand to the metric system and by the end of the century every European country except Russia and the United Kingdom had adopted the metric system.

[edit] International Standards

In the 1861, a committee of the British Association for Advancement of Science (BAAS) including William Thomson (later Lord Kelvin), James Clerk Maxwell and John Prescott Joule introduced the concept of a coherent system of units based on the metre, gram and second which, in 1873, was extended to include electrical units.

Seal of the International Bureau for Weights and Measures (BIPM)

On 20 May 1875 an international treaty known as the Convention du Mètre (Metre Convention)[33] was signed by 17 states. This treaty established the following organisations to conduct international activities relating to a uniform system for measurements:[34]

  • Conférence générale des poids et mesures (CGPM), an intergovernmental conference of official delegates of member nations and the supreme authority for all actions;
  • Comité international des poids et mesures (CIPM), consisting of selected scientists and metrologists, which prepares and executes the decisions of the CGPM and is responsible for the supervision of the International Bureau of Weights and Measures;
  • Bureau international des poids et mesures (BIPM), 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 and maintenance of the international prototype standards.

In 1881, first International Electrical Congress adopted the BAAS recommendations on electrical units, followed by a series of congresses in which further units of measure were defined.[35]

[edit] Variants of the metric system

A number of variants of the metric system evolved, all using the Mètre des Archives and Kilogramme des Archives as their base units, but differing in the definitions of the various derived units.

James Clerk Maxwell played a major role in developing the concept of a coherent cgs system and in extending the metric system to include electrical units.

[edit] Centimetre-gram-second systems

The centimetre gram second system of units (CGS) was the first coherent metric system, having been developed in the 1860s and promoted by Maxwell and Thomson. In 1874 this system was formally promoted by the British Association for the Advancement of Science (BAAS).[36] The system's characteristics are that density is expressed in g/cm3, force expressed in dynes and mechanical energy in ergs. Thermal energy was defined in calories, one calorie being the energy required to raise the temperature of one gram of water from 15.5 °C to 16.5 °C. The meeting also proposed two sets of units for electrical and magnetic properties - the electrostatic set of units and the electomagnetic set of units.

[edit] Metre-kilogram-second systems

The cgs units of electricty were cumbersome to work with. This was remedied at the 1893 International Electrical Congress held in Chicago by defining the "international" ampere and ohm using definitions based on the metre, kilogram and second.[37] In 1901, Giorgi showed that by adding an electrical unit as a fourth base units, the various anomalies in electromagnetic systems could be resolved. The metre-kilogram-second-coulomb (MKSC) and metre-kilogram-second-ampere (MKSA) systems are examples such systems.[38]

The International System of Units (System international units or SI) is the current international standard metric system and the system most widely used around the world. It is an extension of Giorgi's MKSA system; its base units are the metre, kilogram, second, ampere, kelvin, candela and mole. Proposals have been made to change the definitions of four of the base units at the 24th meeting of the CGPM in October 2011. These changes should not affect the average person.[39]

[edit] Metre-tonne-second systems

The metre-tonne-second system of units (MTS) was based on the metre, tonne and second - the units of force is the sthène and the unit of pressure is the pièze. It was invented in France in industry and was mostly used in the Soviet Union from 1933 to 1955.[35][40]

[edit] Gravitational systems

Gravitational metric systems use the kilogram-force (kilopond) as a base unit of force, with mass measured in a unit known as the hyl, TME, mug or metric slug. Note these are not part of the International System of Units (SI).

[edit] Usage in English-speaking countries

English-speaking countries vary in their use of the metric system. Australia and New Zealand are almost totally metric, other countries are partly metric while the United States still uses their customary units in everyday life.

[edit] Degree of usage

According to the American Central Intelligence Agency's Factbook, the International System of Units is the official system of measurement for all nations in the world except for Burma, Liberia and the United States.[41] (Some sources, though, identify Liberia as metric.[42][43][44]) However, a number of other jurisdictions have laws mandating or permitting other systems of measurement in some or all contexts, such as the United Kingdom – where for example the traffic sign regulations (TSRGD) only allow distance signs displaying imperial units (miles or yards)[45] – or Hong Kong.[46] In the United States, metric units are widely used in science, military, and partially in industry, but customary units predominate in household use. At retail stores, the litre is a commonly used unit for volume, especially on bottles of beverages, and milligrams are used to denominate the amounts of medications, rather than grains. Also, other standardised measuring systems other than metric are still in universal international use, such as nautical miles and knots in international aviation.

[edit] Variations in spelling

Although the symbol for the kilometre throughout the world is "km", there is no consistency in the spelling of the name "kilometre". Variants include Chilometro (Italian), Kilometer (German), kilomètre (French), χιλιόμετρο (Greek), quilómetro (Portuguese) and Километър (Bulgarian).[47] Similar variations are found with the spelling of other units of measure in various countries including differences in American English and British spelling. For example meter and liter are used in the United States whereas metre and litre are used in the United Kingdom. In addition, the official US spelling for the rarely used SI prefix for ten is deka. In American English the term metric ton is the normal usage whereas in other varieties of English tonne is common. Gram is also sometimes spelled gramme in English-speaking countries other than the United States, though this older usage is declining.[48]

The US government has approved this terminology for official use. In scientific contexts, only the symbols are used;[citation needed] since these are universally the same, the differences do not arise in practice in scientific use.

[edit] Conversion and calculation errors

The dual usage of metric and non metric units can result in serious errors. These include:

  • According to the National Transportation Safety Board, the confusion between pounds and kilograms means that aircraft are sometimes overloaded.[49]
  • The Institute for Safe Medication Practices has reported that confusion between grains and grams is sometimes the reason for medical errors. One example given is a case where a patient received phenobarbital 0.5 grams instead of 0.5 grains (0.03 grams) after the prescriber misread the prescription.[50]
  • The Canadian "Gimli Glider" accident in 1983, when a Boeing 767 jet ran out of fuel in mid-flight because of two mistakes in figuring the fuel supply of Air Canada's first aircraft to use metric measurements,[51]
  • NASA's 1999 loss of the $125 million Mars Climate Orbiter because one engineering team used metric units while another used US customary units for a calculation.[52]

[edit] Conversion between SI and legacy units

Main article: Conversion of units

During its evolution, the metric system has adopted many units of measure. The introdution of SI rationalised both the way in which units of measure were defiend and also the list of units in use. These are now catalogued in the official SI Brouchure.[53] The table below lists the units of measure in this catalogue and gives the shows the conversion factors them and the equivalent units that were in use on the eve of the adoption of SI.

Parameter Dimension SI unit and symbol Legacy unit and symbol Conversion
factor[54][55][56]
Time T second (s) second (s) 1
Length L metre (m) centimetre (cm)
ångstrom (Å)		 0.01
10-10
Mass M kilogram (kg) gram (g) 0.001
Electric current I ampere (A) international ampere
abampere or Biot
statampere		 1.000022
10.0
3.335641×10-10
Temperature Θ kelvin (K)
degrees celsius (°C)		 centigrade (°C) K = °C + 273.15
1
Luminous intensity J candela (cd) international candle 0.982
Amount of substance N mole (mol) No legacy unit n/a
Frequency T − 1 hertz (Hz) cycles per second align="center" 1
Energy L2MT − 2 joule (J) erg (erg) 10-7
Power L2MT − 3 watt (W) (erg/s)
Horsepower (HP)
Pferdestärke (PS)		 10-7
745.7
735.5
Force LMT − 2 newton (N) dyne (dyn) 10-5
Pressure L − 1MT − 2 pascal (Pa) barye (Ba) 0.1
Electric charge IT coulomb (C) abcoulomb
statcoulomb or Franklin		 10
3.335641×10-10
Potential difference L2MT − 3I − 1 volt (V) international volt
abvolt
statvolt		 1.00034
10-8
2.997925×102
Capacitance L − 2M − 1T4I2 farad (F) abfarad
statfarad		 109
1.112650×10-12
Inductance L2MT − 2I − 2 henry (H) abhenry
stathenry		 10-9
8.987552×1011
Electric resistance L2MT − 3I − 2 ohm (Ω) international ohm
abohm
statohm		 1.00049
10-9
8.987552×1011
Electric conductance L − 2M − 1T3I2 siemen (S) mho
abmho
statmho		 0.99951
109
1.112650×10-12
Magnetic flux L2MT − 2I − 1 weber (Wb) maxwell (Mx) 10-4
Magnetic flux density MT − 2I − 1 tesla (T) gauss (G) 1×10-8
Magnetic field strength IL − 2 (A/m2) oersted (Oe) 103/4π = 79.57747
Dynamic viscosity ML − 1T − 1 (Pa·s) poise (P) 0.1
kinematic viscosity L2T − 1 (m2s-1) stokes (St) 10-4
Luminous flux J lumen (lm) Stilb (unit) (sb) 104
Illuminance JL − 2 lux (lx) phot (ph) 104
[radioactive] activity T − 1 bequerel (Bq) curie (Ci) 3.70×1010
Absorbed [radiation] dose L2T − 2 gray (Gy) roentgen (R)
rad (rad)		 2.58×10−4
0.01
Radiation dose equivalent L2T − 2 sievert Roentgen equivalent man (rem) 0.01
Catalytic activity NT-1 katal (kat) No legacy unit n/a

Many non-SI units have been approved by the CGPM for use with SI and have been allocated unique symbols to simplify interantional recognition. These units include:

Parameter Dimension Unit and symbol Equivalence
Mass M tonne (t) 1000 kg
Area L2 hectare (ha) 0.01 km2
104 m2
Volume L3 litre (L or l) 0.001 m3
Time T minute (min)
hour (h)		 60 s = 1 min
60 min = 1 h
Pressure L − 1MT − 2 bar 100 kPa

[edit] See also
  • Metrication, the process of introducing the SI metric system as the worldwide standard for physical measurements
    (a long-term series of independent and systematic conversions from the various separate local systems of weights and measures)

[edit] Notes and references

  1. ^ a b c Adler - Prologue, p 1
  2. ^ SI Brochure - §3.1 SI prefixes - p 103
  3. ^ Adler; page 92
  4. ^ "Online Translation- Offering hundreds of dictionaries and translation in more than 800 language pairs". Babylon. http://translation.babylon.com/. Retrieved 2011-01-24. 
  5. ^ International vocabulary of metrology — Basic and general concepts and associated terms (VIM). Joint Committee for Guides in Metrology/International Bureau for Weights and Measures. 2008. p. 9. http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf. Retrieved 2011-03-05. 
  6. ^ a b O'Connor, John J.; Robertson, Edmund F. (January 2004), "Simon Stevin", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Stevin.html .
  7. ^ a b O'Connor, John J.; Robertson, Edmund F. (January 2004), "Gabriel Mouton", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Mouton.html .
  8. ^ The factor ten thousand was also once used. The corresponding prefixes myria~ 104 and myrio~ 10-4 were both Greek-derived.
  9. ^ Adler, p93-95
  10. ^ Adler, p96
  11. ^ "What is a mise en pratique?". BIPM. 2011. http://www.bipm.org/en/si/new_si/mise-en-pratique.html. Retrieved 2011-03-11. 
  12. ^ "The BIPM and the evolution of the definition of the metre". BIPM. http://www.bipm.org/en/si/history-si/evolution_metre.html. Retrieved 2011-03-11. 
  13. ^ SI Brochure - Appendix 1 - p 120
  14. ^ "Leap Seconds". Time Service Dept., U.S. Naval Observatory. http://tycho.usno.navy.mil/leapsec.html. Retrieved 2011-03-11. 
  15. ^ SI brochure - §1.2 Two classes of SI Units - p92
  16. ^ Michael Good. "Some Derivations of E = mc2". http://www.unc.edu/~mgood/research/RestEnergy.pdf. Retrieved 2011-03-18. 
  17. ^ An Essay towards a Real Character and a Philosophical Language (Reproduction)
  18. ^ An Essay towards a Real Character and a Philosophical Language (Transcription)
  19. ^ Metric system 'was British' - from the BBC video news
  20. ^ Loidi, Juan Navarro; Saenz, Pilar Merino (6-9 Septembe 2006). "The units of length in the Spanish treatises of military engineering". The Global and the Local:The History of Science and the Cultural Integration of Europe. Proceedings of the 2nd ICESHS. The Press of the Polish Academy of Arts and Sciences. http://www.2iceshs.cyfronet.pl/2ICESHS_Proceedings/Chapter_16/R-8_Navarro_Merino.pdf. Retrieved 2011-03-17. >
  21. ^ Thomas Jefferson (4 July 1790). "Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States". http://avalon.law.yale.edu/18th_century/jeffplan.asp. Retrieved 2011-04-19. 
  22. ^ "La loi du 18 Germinal an 3 « la mesure [républicaine de superficie pour les terrains, égale à un carré de dix mètres de côté » [The law of 18 Germanial year 3 "The republican measures of land area equal to a square with sides of ten metres"]"] (in French). Le CIV (Centre d'Instruction de Vilgénis) - Forum des Anciens. http://aviatechno.free.fr/unites/nouveausys.php. Retrieved 2010-03-02. 
  23. ^ Thierry Thomasset. "Le stère" (in French). Tout sur les unités de mesure [All the units of measure]. Université de Technologie de Compiègne. http://www.utc.fr/~tthomass/Themes/Unites/unites/infos/stere/Le%20stere.pdf. Retrieved 2011-03-21. 
  24. ^ Nelson, Robert A (February 2000). "The International System of Units: Its History and Use in Science and Industry". Applied Technology Institute. http://www.aticourses.com/international_system_units.htm. Retrieved 12 April 2007. 
  25. ^ National Industrial Conference Board (1921). The metric versus the English system of weights and measures .... The Century Co. pp. 10–11. http://books.google.com/books?id=tSUoAAAAYAAJ&pg=PA10. Retrieved 5 April 2011. 
  26. ^ Denis Février. "Un historique du mètre" (in French). Ministère de l'Economie, des Finances et de l'Industrie. http://www.industrie.gouv.fr/metro/aquoisert/metre.htm. Retrieved 2011-03-10. 
  27. ^ Jacob de Gelder (1824) (in Dutch). Allereerste Gronden der Cijferkunst [Introduction to Numeracy]. 's Gravenhage and Amsterdam: de Gebroeders van Cleef. pp. 163–176. http://books.google.co.uk/books?id=XYVbAAAAQAAJ&printsec=frontcover#v=onepage&q&f=false. Retrieved 2011-03-02. 
  28. ^ Ferdinand Malaisé (1842) (in German). Theoretisch-practischer Unterricht im Rechnen [Theoritcal and practical instruction in arithmetic]. München. pp. 307–322. http://home.fonline.de/rs-ebs/geschichte/buch/titel.htm. Retrieved 2011-03-26. 
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