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The International System ofUnitsAnd its base units

ContentsArticlesOverview 1

International System of Units 1

Organisations 9

Metre Convention 9General Conference on Weights and Measures 12International Bureau of Weights and Measures 14International Committee for Weights and Measures 15

Base units 16

SI base unit 16Metre 19Kilogram 25Second 45Ampere 50Kelvin 52Mole 56Candela 59

Apprendix 63

SI derived unit 63Units accepted for use with SI 66

ReferencesArticle Sources and Contributors 68Image Sources, Licenses and Contributors 71

Article LicensesLicense 72

1

Overview

International System of Units

Cover of brochure The International Systemof Units [1].

The International System of Units [2] (abbreviated SI from the FrenchSystème international d'unités[3] ) is the modern form of the metric systemand is generally a system of units of measurement devised around sevenbase units and the convenience of the number ten. It is the world's mostwidely used system of measurement, both in everyday commerce and inscience.[4] [5] [6]

The older metric system included several groups of units. The SI wasdeveloped in 1960 from the old metre-kilogram-second system, rather thanthe centimetre-gram-second system, which, in turn, had a few variants.Because the SI is not static, units are created and definitions are modifiedthrough international agreement among many nations as the technology ofmeasurement progresses, and as the precision of measurements improves.

The system has been nearly globally adopted. Three principal exceptionsare Burma (Myanmar), Liberia, and the United States. The UnitedKingdom has officially adopted the International System of Units but notwith the intention of replacing customary measures entirely.

HistoryThe metric system was conceived by a group of scientists (among them, Antoine-Laurent Lavoisier, who is known asthe "father of modern chemistry") who had been commissioned by the assemblee nationale and Louis XVI of Franceto create a unified and rational system of measures.[7] On 1 August 1793, the National Convention adopted the newdecimal metre with a provisional length as well as the other decimal units with preliminary definitions and terms. On7 April 1795 (Loi du 18 germinal, an III) the terms gramme and kilogramme replaced the former terms gravet(correctly milligrave) and grave. On 10 December 1799 (a month after Napoleon's coup d'état), the metric systemwas definitively adopted in France.

Countries by date of metrication

The desire for internationalcooperation on metrology led to thesigning in 1875 of the MetreConvention, a treaty which establishedthree international organizations tooversee the keeping of metricstandards:

• General Conference on Weights andMeasures (Conférence générale despoids et mesures or CGPM) - ameeting every four to six years ofdelegates from all member states;

International System of Units 2

• International Bureau of Weights and Measures (Bureau international des poids et mesures or BIPM) - aninternational metrology centre at Sèvres in France; and

• International Committee for Weights and Measures (Comité international des poids et mesures or CIPM) - anadministrative committee which meets annually at the BIPM.

The history of the metric system has seen a number of variations, whose use has spread around the world, to replacemany traditional measurement systems. At the end of World War II a number of different systems of measurementwere still in use throughout the world. Some of these systems were metric-system variations, whereas others werebased on customary systems. It was recognised that additional steps were needed to promote a worldwidemeasurement system. As a result the 9th General Conference on Weights and Measures (CGPM), in 1948, asked theInternational Committee for Weights and Measures (CIPM) to conduct an international study of the measurementneeds of the scientific, technical, and educational communities.Based on the findings of this study, the 10th CGPM in 1954 decided that an international system should be derivedfrom six base units to provide for the measurement of temperature and optical radiation in addition to mechanicaland electromagnetic quantities. The six base units that were recommended are the metre, kilogram, second, ampere,degree Kelvin (later renamed the kelvin), and the candela. In 1960, the 11th CGPM named the system theInternational System of Units, abbreviated SI from the French name: Le Système international d'unités. The seventhbase unit, the mole, was added in 1971 by the 14th CGPM.One of the CIPM committees, the CCU, has proposed a number of changes to the definitions of the base units usedin SI .[8] The CIPM meeting of October 2010 found that the proposal was not fully complete,[9] and it is expectedthat the CGPM will consider the full proposal in 2015.

Related systemsThe definitions of the concepts 'quantity', 'unit', 'dimension' etc. used in measurement, are given in the InternationalVocabulary of Metrology.[10]

The quantities and equations which define the SI units are now referred to as the International System of Quantities(ISQ), and are set out in the ISO/IEC 80000 Quantities and Units.A readable discussion of the present units and standards is found at Brian W. Petley [11] International Union of Pureand Applied Physics I.U.P.A.P.- 39 (2004).

UnitsThe International System of Units consists of a set of units together with a set of prefixes. The units are divided intotwo classes—base units and derived units. There are seven base units, each representing, by convention, differentkinds of physical quantities.

SI base units[12] [13]

Name Unit symbol Quantity Symbol

metre m length l (a lowercase L)

kilogram kg mass m

second s time t

ampere A electric current I (a capital i)

kelvin K thermodynamic temperature T

candela cd luminous intensity Iv (a capital i with lowercase v subscript)

mole mol amount of substance n

International System of Units 3

There are an unlimited number of derived units formed from multiplication and division of the seven base units,[14]

for example the SI derived unit of speed is metre per second, m/s. Some derived units have special names; forexample, the unit of resistance, the ohm, symbol Ω, is uniquely defined by the relation Ω = m2·kg·s−3·A−2, whichfollows from the definition of the quantity electrical resistance. The radian and steradian, once given special status,are now considered derived units.[14]

A prefix may be added to a unit to produce a multiple of the original unit. All multiples are integer powers of ten,and beyond a hundred(th) all are integer powers of a thousand. For example, kilo- denotes a multiple of a thousandand milli- denotes a multiple of a thousandth; hence there are one thousand millimetres to the metre and onethousand metres to the kilometre. The prefixes are never combined: a millionth of a kilogram is a milligram not amicrokilogram.

Standard prefixes for the SI units of measure

Multiples Name deca- hecto- kilo- mega- giga- tera- peta- exa- zetta- yotta-

Symbol da h k M G T P E Z Y

Factor 100 101 102 103 106 109 1012 1015 1018 1021 1024

Fractions Name deci- centi- milli- micro- nano- pico- femto- atto- zepto- yocto-

Symbol d c m μ n p f a z y

Factor 100 10−1 10−2 10−3 10−6 10−9 10−12 10−15 10−18 10−21 10−24

In addition to the SI units, there is also a set of non-SI units accepted for use with SI which includes some commonlyused non-coherent units such as the litre.

Writing unit symbols and the values of quantities• The value of a quantity is written as a number followed by a space (representing a multiplication sign) and a unit

symbol; e.g., "2.21 kg", "7.3 × 102 m2", "22 K". This rule explicitly includes the percent sign (%). Exceptions arethe symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after thenumber with no intervening space.[15] [16]

• Symbols for derived units formed by multiplication are joined with a centre dot (·) or a non-break space, forexample, "N·m" or "N m".

• Symbols for derived units formed by division are joined with a solidus (⁄), or given as a negative exponent. Forexample, the "metre per second" can be written "m⁄s", "m s−1", "m·s−1" or . Only one solidus should be used;e.g., "kg⁄(m·s2)" or "kg·m−1·s−2" are acceptable but "kg⁄m⁄s2" is ambiguous and unacceptable. Many computerusers will type the / character provided on computer keyboards, which in turn produces the Unicode characterU+002F, which is named solidus but is distinct from the Unicode solidus character, U+2044.

• Symbols are mathematical entities, not abbreviations, and do not have an appended period/full stop (.).• Symbols are written in upright (Roman) type (m for metres, s for seconds), so as to differentiate from the italic

type used for quantities (m for mass, s for displacement). By consensus of international standards bodies, this ruleis applied independent of the font used for surrounding text.[17]

• Symbols for units are written in lower case (e.g., "m", "s", "mol"), except for symbols derived from the name of aperson (e.g., "Pa", "Hz", "K" for Pascal, Hertz, Kelvin).[18]

• The one exception is the litre, whose original symbol "l" is unsuitably similar to the numeral "1" or the uppercase letter "i" (depending on the typeface used), at least in many English-speaking countries. The American National Institute of Standards and Technology recommends that "L" be used instead, a usage which is common in the US, Canada and Australia (but not elsewhere). This has been accepted as an alternative by

International System of Units 4

the CGPM since 1979. The cursive ℓ is occasionally seen, especially in Japan and Greece, but this is notcurrently recommended by any standards body. For more information, see litre.

• A prefix is part of the unit, and its symbol is prepended to the unit symbol without a separator (e.g., "k" in "km","M" in "MPa", "G" in "GHz" and so on). Compound prefixes are not allowed.

• Symbols of units are not pluralised, for example "25 kg" (not "25 kgs").[17]

• The 10th resolution of CGPM in 2003 declared that "the symbol for the decimal marker shall be either the pointon the line or the comma on the line." In practice, the decimal point is used in English-speaking countries as wellas most of Asia and the comma in most continental European languages.

• Spaces may be used as a thousands separator (1000000) in contrast to commas or periods (1,000,000 or1.000.000) in order to reduce confusion resulting from the variation between these forms in different countries. Inprint, the space used for this purpose is typically narrower than that between words (commonly a thin space).

• Any line-break inside a number, inside a compound unit, or between number and unit should be avoided, but, ifnecessary, the last-named option should be used.

• In Chinese, Japanese, and Korean language computing (CJK), some of the commonly used units, prefix-unitcombinations, or unit-exponent combinations have been allocated predefined single characters taking up a fullsquare. Unicode includes these in its CJK Compatibility [19] and Letterlike Symbols [20] subranges for backcompatibility, without necessarily recommending future usage.

• When writing dimensionless quantities, the terms 'ppb' (parts per billion) and 'ppt' (parts per trillion) arerecognised as language-dependent terms, since the value of billion and trillion can vary from language tolanguage. SI, therefore, recommends avoiding these terms.[21] However, no alternative is suggested by theInternational Bureau of Weights and Measures (BIPM).

Writing the unit names• Names of units start with a lower-case letter, even when the symbol for the unit begins with a capital letter (e.g.,

newton, hertz, pascal). This also applies to 'degrees Celsius', since 'degree' is the unit.• Names of units are pluralised using the normal English grammar rules,[22] [23] for example, "henries" is the plural

of "henry".[22] :31 The units lux, hertz, and siemens are exceptions from this rule: they remain the same in singularand plural.

• The official US spellings for deca, metre, and litre are deka, meter, and liter, respectively.[24]

Realisation of unitsMetrologists carefully distinguish between the definition of a unit and its realisation. The definition of each base unitof the SI is drawn up so that it is unique and provides a sound theoretical basis upon which the most accurate andreproducible measurements can be made. The realisation of the definition of a unit is the procedure by which thedefinition may be used to establish the value and associated uncertainty of a quantity of the same kind as the unit. Adescription of how the definitions of some important units are realised in practice is given on the BIPM website.[25]

However, "any method consistent with the laws of physics could be used to realise any SI unit."[26] (p. 111).

International System of Units 5

Conversion factorsThe relationship between the units used in different systems is determined by convention or from the basic definitionof the units. Conversion of units from one system to another is accomplished by use of a conversion factor. There areseveral compilations of conversion factors; see, for example, Appendix B of NIST SP 811.[22]

Cultural issues

Three nations have not officially adopted the International System of Unitsas their primary or sole system of measurement: Myanmar (Burma),

Liberia, and the United States

The near-worldwide adoption of the metric systemas a tool of economy and everyday commerce wasbased to some extent on the lack of customarysystems in many countries to adequately describesome concepts, or as a result of an attempt tostandardise the many regional variations in thecustomary system. International factors alsoaffected the adoption of the metric system, asmany countries increased their trade. For use inscience, it simplifies dealing with very large andsmall quantities, since it lines up so well with thedecimal numeral system.

Many units in everyday and scientific use are not derived from the seven SI base units (metre, kilogram, second,ampere, kelvin, mole, and candela) combined with the SI prefixes. In some cases these deviations have beenapproved by the BIPM.[27] Some examples include:

• The many units of time (minute, min; hour, h; day, d) in use besides the SI second, and are specifically acceptedfor use according to table 6.[28]

• The year is specifically not included but has a recommended conversion factor.[29]

• The Celsius temperature scale; kelvins are rarely employed in everyday use.• Electric energy is often billed in kilowatt-hours instead of megajoules. Similarly, battery charge is often measured

as milliamperes-hour (mAh) instead of coulombs.• The nautical mile and knot (nautical mile per hour) used to measure travel distance and speed of ships and aircraft

(1 International nautical mile = 1852 m or approximately 1 minute of latitude). In addition to these, Annex 5 ofthe Convention on International Civil Aviation permits the "temporary use" of the foot for altitude.

• Astronomical distances measured in astronomical units, parsecs, and light-years instead of, for example,petametres (a light-year is about 9.461 Pm or about 9461000000000000 m).

• Atomic scale units used in physics and chemistry, such as the ångström, electron volt, atomic mass unit and barn.• Some physicists prefer the centimetre-gram-second (CGS) units, or systems based on physical constants, such as

Planck units, atomic units, or geometric units.• In some countries, the informal cup measurement has become 250 mL. Likewise, a 500 g metric pound is used in

many countries. Liquids, especially alcoholic ones, are often sold in units whose origins are historical (forexample, pints for beer and cider in glasses in the UK —although pint means 568 mL; champagne in Jeroboamsin France).

• A metric mile of 10 km is used in Norway and Sweden. The term metric mile is also used in some Englishspeaking countries for the 1500 m foot race.

• In the US, blood glucose measurements are recorded in milligrams per decilitre (mg/dL), which would normaliseto cg/L; in Canada, Australia, New Zealand, Oceania, and Europe, the standard is millimole per litre (mmol/L) ormM (millimolar).

• Blood pressure and atmospheric pressure are usually measured in mmHg and bars, respectively, instead of Pa.

International System of Units 6

The fine-tuning that has happened to the metric base-unit definitions over the past 200 years, as experts have triedperiodically to find more precise and reproducible methods, does not affect the everyday use of metric units. Sincemost non-SI units in common use, such as the US customary units, are defined in SI units,[30] any change in thedefinition of the SI units results in a change of the definition of the older units, as well.

International tradeOne of the European Union's (EU) objectives is the creation of a single market for trade. In order to achieve thisobjective, the EU standardised on using SI as the legal units of measure. At the time of writing (2009) it had issuedtwo units of measurement directives which catalogued the units of measure that might be used for, amongst otherthings, trade: the first was Directive 71/354/EEC[31] issued in 1971 which required member states to standardise onSI rather than use the variety of cgs and mks units then in use. The second was Directive 80/181/EEC[32] [33] [34] [35]

[36] issued in 1979 which replaced the first and which gave the United Kingdom and the Republic of Ireland anumber of derogations from the original directive.The directives gave a derogation from using SI units in areas where other units of measure had either been agreed byinternational treaty or which were in universal use in worldwide trade. They also permitted the use of supplementaryindicators alongside, but not in place of the units catalogued in the directive. In its original form, Directive80/181/EEC had a cut-off date for the use of such indicators, but with each amendment this date was moved until, in2009, supplementary indicators have been allowed indefinitely.

References[1] http:/ / www. bipm. org/ en/ publications/ brochure/[2] International Bureau of Weights and Measures (2006), The International System of Units (SI) (http:/ / www. bipm. org/ utils/ common/ pdf/

si_brochure_8_en. pdf) (8th ed.), ISBN 92-822-2213-6,[3] Resolution of the International Bureau of Weights and Measures establishing the International System of Units (http:/ / www. bipm. org/ en/

CGPM/ db/ 11/ 12/ )[4] Official BIPM definitions (http:/ / www. bipm. org/ en/ si/ base_units/ )[5] Essentials of the SI: Introduction (http:/ / www. physics. nist. gov/ cuu/ Units/ introduction. html)[6] An extensive presentation of the SI units is maintained on line by NIST (http:/ / www. physics. nist. gov/ cuu/ Units/ units. html), including a

diagram (http:/ / www. physics. nist. gov/ cuu/ Units/ SIdiagram. html) of the interrelations between the derived units based upon the SI units.Definitions of the basic units can be found on this site, as well as the CODATA report (http:/ / physics. nist. gov/ cuu/ Constants/ codata. pdf)listing values for special constants such as the electric constant, the magnetic constant and the speed of light, all of which have defined valuesas a result of the definition of the metre and ampere.

In the International System of Units (SI) (BIPM, 2006), the definition of the meter fixes the speed oflight in vacuum c0, the definition of the ampere fixes the magnetic constant (also called the permeabilityof vacuum) μ0, and the definition of the mole fixes the molar mass of the carbon 12 atom M(12C) tohave the exact values given in the table [Table 1, p.7]. Since the electric constant (also called thepermittivity of vacuum) is related to μ0 by ε0 = 1/μ0c0

2, it too is known exactly.– CODATA report

[7] "The name "kilogram"" (http:/ / www1. bipm. org/ en/ si/ history-si/ name_kg. html). . Retrieved 25 July 2006.[8] Ian Mills (29 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units" (http:/ / www. bipm. org/ utils/ en/

pdf/ si_brochure_draft_ch2. pdf). CCU. . Retrieved 2011-01-01.[9] Anon (November 2010). "BIPM Bulletin" (http:/ / www. bipm. org/ utils/ en/ pdf/ BIPM_Bulletin. pdf). BIPM. . Retrieved 2011-01-05.[10] "The International Vocabulary of Metrology (VIM)" (http:/ / www. bipm. org/ en/ publications/ guides/ vim. html). .[11] http:/ / www. physics. ohio-state. edu/ ~jossem/ IUPAP/ PhysicsNowText-A4-1. pdf[12] Barry N. Taylor & Ambler Thompson Ed. (2008). The International System of Units (SI) (http:/ / physics. nist. gov/ Pubs/ SP330/ sp330.

pdf). Gaithersburg, MD: National Institute of Standards and Technology. pp. 23. . Retrieved 18 June 2008.[13] Quantities Units and Symbols in Physical Chemistry (http:/ / old. iupac. org/ publications/ books/ author/ mills. html), IUPAC[14] Ambler Thompson and Barry N. Taylor, (2008), Guide for the Use of the International System of Units (SI) (http:/ / physics. nist. gov/ cuu/

pdf/ sp811. pdf), (Special publication 811), Gaithersburg, MD: National Institute of Standards and Technology, p. 3, footnote 2.[15] The International System of Units (SI) (http:/ / www. bipm. org/ utils/ common/ pdf/ si_brochure_8_en. pdf) (8 ed.). International Bureau of

Weights and Measures (BIPM). 2006. p. 133. .

International System of Units 7

[16] Thompson, A.; Taylor, B. N. (July 2008). "NIST Guide to SI Units — Rules and Style Conventions" (http:/ / physics. nist. gov/ Pubs/SP811/ sec07. html). National Institute of Standards and Technology. . Retrieved 29 December 2009.

[17] Bureau International des Poids et Mesures (2006). The International System of Units (SI) (http:/ / www. bipm. org/ utils/ common/ pdf/si_brochure_8_en. pdf). 8th ed.. . Retrieved 13 February 2008. Chapter 5.

[18] Ambler Thompson and Barry N. Taylor, (2008), Guide for the Use of the International System of Units (SI) (http:/ / physics. nist. gov/ cuu/pdf/ sp811. pdf), (Special publication 811), Gaithersburg, MD: National Institute of Standards and Technology, section 6.1.2

[19] http:/ / www. unicode. org/ charts/ PDF/ U3300. pdf[20] http:/ / www. unicode. org/ charts/ PDF/ U2100. pdf[21] http:/ / www. bipm. org/ en/ si/ si_brochure/ chapter5/ 5-3-7. html[22] Ambler Thompson & Barry N. Taylor (2008). NIST Special Publication 811: Guide for the Use of the International System of Units (SI)

(http:/ / physics. nist. gov/ cuu/ pdf/ sp811. pdf). National Institute of Standards and Technology. . Retrieved 18 June 2008.[23] Turner, James M. (9 May 2008). May 2008/pdf/E8-11058.pdf "Interpretation of the International System of Units (the Metric System of

Measurement) for the United States" (http:/ / www. gpo. gov/ fdsys/ pkg/ FR-16). Federal Register (National Archives and RecordsAdministration) 73 (96): 28432–3. FR Doc number E8-11058. May 2008/pdf/E8-11058.pdf. Retrieved 28 October 2009.

[24] "The International System of Units" (http:/ / physics. nist. gov/ Pubs/ SP330/ sp330. pdf). pp. iii. . Retrieved 27 May 2008.[25] SI Practical Realization brochure (http:/ / www. bipm. org/ en/ si/ si_brochure/ appendix2/ )[26] International Bureau of Weights and Measures (2006), The International System of Units (SI) (http:/ / www. bipm. org/ utils/ common/ pdf/

si_brochure_8_en. pdf) (8th ed.), p. 111, ISBN 92-822-2213-6,[27] BIPM - Table 8 (http:/ / www. bipm. org/ en/ si/ si_brochure/ chapter4/ table8. html)[28] BIPM - Table 6 (http:/ / www. bipm. org/ en/ si/ si_brochure/ chapter4/ table6. html)[29] NIST Guide to SI Units - Appendix B9. Conversion Factors (http:/ / physics. nist. gov/ Pubs/ SP811/ appenB9. html#TIME)[30] Mendenhall, T. C. (1893). "Fundamental Standards of Length and Mass". Reprinted in Barbrow, Louis E. and Judson, Lewis V. (1976).

Weights and measures standards of the United States: A brief history (NBS Special Publication 447). Washington D.C.: Superintendent ofDocuments. Viewed 23 August 2006 at (http:/ / physics. nist. gov/ Pubs/ SP447/ ) pp. 28–29.

[31] "Council Directive of 18 October 1971 on the approximation of laws of the member states relating to units of measurement, (71/354/EEC)"(http:/ / eur-lex. europa. eu/ Notice. do?mode=dbl& lang=en& lng1=en,nl& lng2=da,de,el,en,es,fr,it,nl,pt,& val=22924:cs& page=1&hwords=). . Retrieved 7 February 2009.

[32] The Council of the European Communities (21 December 1979). "Council Directive 80/181/EEC of 20 December 1979 on theapproximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC" (http:/ / eur-lex.europa. eu/ LexUriServ/ LexUriServ. do?uri=CONSLEG:1980L0181:19791221:EN:PDF). . Retrieved 7 February 2009.

[33] The Council of the European Communities (20 December 1984). "Council Directive 80/181/EEC of 20 December 1979 on theapproximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC" (http:/ / eur-lex.europa. eu/ LexUriServ/ LexUriServ. do?uri=CONSLEG:1980L0181:19841220:EN:PDF). . Retrieved 7 February 2009.

[34] The Council of the European Communities (30 November 1989). "Council Directive 80/181/EEC of 20 December 1979 on theapproximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC" (http:/ / eur-lex.europa. eu/ LexUriServ/ LexUriServ. do?uri=CONSLEG:1980L0181:19891130:EN:PDF). . Retrieved 7 February 2009.

[35] The Council of the European Communities (9 February 2000). "Council Directive 80/181/EEC of 20 December 1979 on the approximationof the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC" (http:/ / eur-lex. europa. eu/LexUriServ/ LexUriServ. do?uri=CONSLEG:1980L0181:20000209:EN:PDF). . Retrieved 7 February 2009.

[36] The Council of the European Communities (27 May 2009). "Council Directive 80/181/EEC of 20 December 1979 on the approximation ofthe laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC" (http:/ / eur-lex. europa. eu/LexUriServ/ LexUriServ. do?uri=CONSLEG:1980L0181:20090527:EN:PDF). . Retrieved 14 September 2009.

Further reading• International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry,

2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. Electronic version. (http:/ / www. iupac. org/publications/ books/ gbook/ green_book_2ed. pdf)

• Unit Systems in Electromagnetism (http:/ / info. ee. surrey. ac. uk/ Workshop/ advice/ coils/ unit_systems/ #rms)• MW Keller et al. (http:/ / qdev. boulder. nist. gov/ 817. 03/ pubs/ downloads/ set/ Watt_Triangle_sub1. pdf)

Metrology Triangle Using a Watt Balance, a Calculable Capacitor, and a Single-Electron Tunneling Device

International System of Units 8

External linksOfficial• BIPM Bureau International des Poids et Mesures (SI maintenance agency) (http:/ / www. bipm. org/ en/ si/ )

(home page)• BIPM brochure (http:/ / www. bipm. org/ en/ si/ si_brochure/ ) (SI reference)

• ISO 80000-1:2009 Quantities and units -- Part 1: General (http:/ / www. iso. org/ iso/ iso_catalogue/catalogue_ics/ catalogue_detail_ics. htm?csnumber=30669)

• NIST Official Publications (http:/ / physics. nist. gov/ cuu/ Units/ bibliography. html)• NIST Special Publication 330, 2008 Edition: The International System of Units (SI) (http:/ / physics. nist. gov/

Pubs/ SP330/ sp330. pdf)• NIST Special Pub 814: Interpretation of the SI for the United States and Federal Government Metric

Conversion Policy (http:/ / ts. nist. gov/ WeightsAndMeasures/ Metric/ pub814. cfm)• Weights and Measures Act, Canada (http:/ / laws. justice. gc. ca/ en/ ShowTdm/ cs/ W-6/ / / en)• IEEE/ASTM SI 10-2002 Standard for Use of the International System of Units (SI): The Modern Metric System

(http:/ / webstore. ansi. org/ ansidocstore/ product. asp?sku=SI10-2002) (ANSI approved, joint IEEE/ASTMstandard)

• Rules for SAE Use of SI (Metric) Units (http:/ / www. sae. org/ standardsdev/ tsb/ tsb003. pdf)• National Physical Laboratory, UK (http:/ / www. npl. co. uk/ server. php?show=category. 364)Information• International System of Units (http:/ / www. dmoz. org/ Science/ Reference/ Units_of_Measurement/ / ) at the

Open Directory Project• EngNet Metric Conversion Chart (http:/ / www. engnetglobal. com/ tips/ convert. aspx) Online Categorised

Metric Conversion Calculator• U.S. Metric Association. 2008. A Practical Guide to the International System of Units (http:/ / lamar. colostate.

edu/ ~hillger/ pdf/ Practical_Guide_to_the_SI. pdf)History• LaTeX SIunits package manual (ftp:/ / cam. ctan. org/ tex-archive/ macros/ latex/ contrib/ SIunits/ SIunits. pdf)

gives a historical background to the SI system.Research• The metrological triangle (http:/ / www. npl. co. uk/ server. php?show=ConWebDoc. 1835)• Recommendation of ICWM 1 (CI-2005) (http:/ / www. bipm. org/ cc/ CIPM/ Allowed/ 94/

CIPM-Recom1CI-2005-EN. pdf)Pro-metric advocacy groups• The UK Metric Association (http:/ / www. ukma. org. uk/ )• The US Metric Association (http:/ / www. metric. org/ )• Canadian Metric Association (http:/ / niagara. cioc. ca/ details. asp?RSN=5108& Number=0)• Metrication US (http:/ / www. metrication. us)Pro-customary measures pressure groups• Pro-customary measures groups (http:/ / www. dmoz. org/ Society/ Issues/ Government_Operations/

Anti-Metrication/ / ) at the Open Directory Project

9

Organisations

Metre ConventionThe Metre Convention of May 20, 1875 is a treaty which established three international organizations to overseethe keeping of metric standards. It is written in French, in which it is called the Convention du Mètre. In English it isalso called the Treaty of the Metre. It was revised in 1921. In 1960, the system of units it established was renamedthe "International System of Units" (Système international d'unités or SI).The Convention created three main organizations:• General Conference on Weights and Measures (Conférence générale des poids et mesures or CGPM) - a meeting

every four to six years of delegates from all member states;• International Bureau of Weights and Measures (Bureau international des poids et mesures or BIPM) - an

international metrology centre at Sèvres in France; and• International Committee for Weights and Measures (Comité international des poids et mesures or CIPM) - an

administrative committee which meets annually at the BIPM.

SignatoriesThere were originally 17 signatories to the treaty. This number grew to 21 in 1900, 32 in 1950, 44 by 1975, 48 by1997, and 49 by 2001. As of 31 December 2008[1] , there are 54 signatories (with year of accession in parentheses):• Argentina (1877)• Australia (1947)• Austria (1875)• Belgium (1875)• Brazil (1921)• Bulgaria (1911)• Cameroon (1970)• Canada (1907)• Chile (1908)• People's Republic of China (1977)• Croatia (2008)• Czech Republic (1922)• Denmark (1875)• Dominican Republic (1954)• Egypt (1962)• Finland (1923)• France (1875)• Germany (1875)• Greece (2001)• Hungary (1925)• India (1957)• Indonesia (1960)• Iran (1975)• Ireland (1925) (already accepted as Ireland was part of the UK when the UK signed)

Metre Convention 10

• Israel (1985)• Italy (1875)• Japan (1885)• Kazakhstan (2008)• Kenya (2010)• Korea (Democratic Republic of) [North] (1982)• Korea (Republic of) [South] (1959)• Malaysia (2001)• Mexico (1890)• The Netherlands (1929)• New Zealand (1991)• Norway (1875)• Pakistan (1973)• Poland (1925)• Portugal (1876)• Romania (1884)• Russian Federation (1875)• Serbia (1879)• Singapore (1994)• Slovakia (1922)• South Africa (1964)• Spain (1875)• Sweden (1875)• Switzerland (1875)• Thailand (1912)• Turkey (1875)• United Kingdom (1884)• United States (1878)• Uruguay (1908)• Venezuela (1879)Several other states have associate status:• Albania (September 10, 2007)• Antigua and Barbuda[2] October 10, 2005)• Barbados[2] October 10, 2005)• Belarus (May 5, 2003)• Belize[2] October 10, 2005)• Bolivia (April 4, 2008)• Costa Rica (January 29, 2004)• Cuba (December 19, 2000)• Dominica[2] October 10, 2005)• Ecuador (November 20, 2000)• Estonia (January 27, 2005)• Georgia (January 1, 2008)• Guyana[2] October 10, 2005)• Grenada[2] October 10, 2005)• Hong Kong (April 8, 2000)• Jamaica (September 15, 2003)

Metre Convention 11

• Kazakhstan (September 14, 2003)• Kenya (September 24, 2002)• Latvia (January 11, 2001)• Lithuania (March 12, 2001)• Macedonia (October 10, 2006)• Malta (April 11, 2001)• Moldova (January 1, 2007)• Panama (August 3, 2003)• Peru (Mai 28, 2009)• Philippines (June 1, 2002)• Taiwan (April 26, 2002)• Slovenia (June 2, 2003)• Saint Kitts and Nevis[2] October 10, 2005)• Saint Lucia[2] October 10, 2005)• Saint Vincent and the Grenadines[2] October 10, 2005)• Sri Lanka (August 3, 2007)[3]• Suriname[2] October 10, 2005)• Trinidad and Tobago[2] October 10, 2005)• Ukraine (August 19, 2002)• Vietnam (October 10, 2003)Note[1] "Member States and Associates" (http:/ / www. bipm. org/ en/ convention/ member_states/ ). Bureau International des Poids et Mesures.

2008-12-31. . Retrieved 2009-04-23.[2] Through CARICOM[3] http:/ / www. bipm. org/ jsp/ en/ ViewCountryDetails. jsp?ISO_CODE=LK

References

External links• http:/ / www. bipm. fr/ enus/ 1_Convention/ foreword. html

General Conference on Weights and Measures 12

General Conference on Weights and MeasuresThe General Conference on Weights and Measures is the English name of the Conférence générale des poids etmesures (CGPM, never GCWM). It is one of the three organizations established to maintain the InternationalSystem of Units (SI) under the terms of the Convention du Mètre (Metre Convention) of 1875. It meets in Sèvres (inthe southwestern suburbs of Paris) every four to six years. The CGPM represents 52 member states and 26 furtherassociate members.[1]

CGPM meetings

1st [2]

(1889)

kilogram defined as mass of the international prototype kilogram (IPK) made of platinum-iridium and kept at the International Bureauof Weights and Measures (Bureau international des poids et mesures), Sèvres, France. International prototype metre sanctioned.

2nd [3]

(1897)

No resolutions were passed by the 2nd CGPM.

3rd [4]

(1901)

litre redefined as volume of 1 kg of water. Clarified that kilograms are units of mass, "standard weight" defined, standard acceleration ofgravity defined endorsing use of grams force and making them well-defined.

4th [5]

(1907)

carat = 200 mg adopted.

5th [6]

(1913)

International Temperature Scale proposed.

6th [7]

(1921)

Metre Convention revised.

7th [8]

(1927)

Consultative Committee for Electricity (CCE) created.

8th [9]

(1933)

Need for absolute electrical unit identified.

9th [10]

(1948)ampere, bar, coulomb, farad, henry, joule, newton, ohm, volt, watt, weber defined. Chose degree Celsius from among the three namesthen in use. l (lowercase L) adopted as symbol for litre. Both the comma and dot on a line are accepted as decimal marker symbols.Symbols for the stere and second changed [11]. The universal return to the Long Scale numbering system was proposed but not adopted.

10th [12]

(1954)

kelvin, standard atmosphere defined. International System of Units (metre, kilogram, second, ampere, kelvin, candela) began.

11th [13]

(1960)

metre redefined in terms of wavelengths of light. Units: hertz, lumen, lux, tesla adopted. New metric system given the official symbol SIfor Système International d'Unités, the "modernized metric system". Prefixes pico-, nano-, micro-, mega-, giga- and tera- confirmed.

12th [14]

(1964)original definition of litre = 1 dm3 restored. atto- and femto- prefixes.

13th [15]

(1967)

second redefined as duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levelsof the ground state of the caesium-133 atom at a temperature of 0 K. Degree Kelvin renamed kelvin. Candela redefined.

14th [16]

(1971)

new SI base unit mole defined. pascal, siemens approved.

15th [17]

(1975)

peta- and exa- prefixes. gray and becquerel radiological units.

16th [18]

(1979)

candela, sievert defined. Both l and L provisionally allowed as symbols for litre.

General Conference on Weights and Measures 13

17th [19]

(1983)

metre redefined in terms of the speed of light, but keeps same length.

18th [20]

(1987)

conventional values adopted for Josephson constant, KJ, and von Klitzing constant, RK, preparing the way for alternative definitions ofthe ampere and kilogram.

19th [21]

(1991)

new prefixes yocto-, zepto-, zetta- and yotta-.

20th [22]

(1995)

SI supplementary units (radian and steradian) become derived units.

21st [23]

(1999)

new SI derived unit, the katal = mole per second, for the expression of catalytic activity.

22nd [24]

(2003)A comma or a dot on a line are reaffirmed as decimal marker symbols, and not as grouping symbols in order to facilitate reading;"numbers may be divided in groups of three in order to facilitate reading; neither dots nor commas are ever inserted in the spacesbetween groups".[25] .

23rd [26]

(2007)

clarification about the kelvin and thoughts about possible revision of certain base units

See also• International Bureau of Weights and Measures (BIPM)• International Committee for Weights and Measures• Institute for Reference Materials and Measurements (IRMM)• National Institute of Standards and Technology (NIST)

References[1] CGPM Member States (http:/ / www. bipm. org/ en/ convention/ member_states/ )[2] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=1[3] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=2[4] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=3[5] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=4[6] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=5[7] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=6[8] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=7[9] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=8[10] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=9[11] http:/ / www. bipm. org/ jsp/ en/ ViewCGPMResolution. jsp?CGPM=9& RES=7[12] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=10[13] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=11[14] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=12[15] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=13[16] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=14[17] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=15[18] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=16[19] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=17[20] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=18[21] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=19[22] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=20[23] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=21[24] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=22[25] http:/ / www. bipm. org/ jsp/ en/ ViewCGPMResolution. jsp?CGPM=22& RES=10[26] http:/ / www. bipm. org/ jsp/ en/ ListCGPMResolution. jsp?CGPM=23

International Bureau of Weights and Measures 14

International Bureau of Weights and Measures

International Bureau of Weightsand Measures

French: Bureau international despoids et mesures

Website bipm.org [1]

The bureau.

The International Bureau of Weights andMeasures (French: Bureau international des poidset mesures), is an international standardsorganisation, one of three such organisationsestablished to maintain the International System ofUnits (SI) under the terms of the Metre Convention(Convention du Mètre). The organisation is usuallyreferred to by its French initialism, BIPM.

The other organisations that maintain the SI system,also known by their French initialisms are theGeneral Conference on Weights and Measures(French: Conférence générale des poids et mesures)(CGPM) and the International Committee for Weights and Measures (French: Comité international des poids etmesures) (CIPM).

HistoryThe BIPM was created on 20 May 1875, following the signing of the Metre Convention, a treaty among 51 nations(as of August 2008).[2] It is based at the Pavillon de Breteuil in Sèvres, France, where it enjoys extraterritorial status.

FunctionUnder the authority of the Metric Convention, the BIPM helps to ensure uniformity of SI weights and measuresaround the world. It does so through a series of consultative committees, whose members are the national metrologylaboratories of the Convention's member states, and through its own laboratory work.The BIPM carries out measurement-related research. It takes part in and organises international comparisons ofnational measurement standards and performs calibrations for member states.The BIPM has an important role in maintaining accurate worldwide time of day. It combines, analyzes, and averagesthe official atomic time standards of member nations around the world to create a single, official CoordinatedUniversal Time (UTC).

International Bureau of Weights and Measures 15

References[1] http:/ / www. bipm. org/ en/ home/[2] "Brief history of the SI" (http:/ / www. bipm. org/ en/ si/ history-si/ ). BIPM. . Retrieved 2009-04-21.

External links• BIPM website (http:/ / www. bipm. org/ en/ home/ )

International Committee for Weights andMeasuresThe International Committee for Weights and Measures is the English name of the Comité international despoids et mesures (CIPM, sometimes written in English Comité International des Poids et Mesures). It consists ofeighteen persons from Member States of the Metre Convention (Convention du Mètre). Its principal task is to ensureworld-wide uniformity in units of measurement and it does this by direct action or by submitting proposals to theGeneral Conference on Weights and Measures (CGPM, Conférence générale des poids et mesures). Note that theabbreviation ICWM is not used.The secretariat is based at Sèvres, Hauts-de-Seine, France.A recent focus area of the CIPM has been the establishment of the CIPM Arrangement de reconnaissance mutuelle(Mutual Recognition Arrangement, MRA) which serves as the framework for the mutual acceptance ofmeasurements performed in the Member States of the Metre Convention.The CIPM meets annually at the International Bureau of Weights and Measures (BIPM, Bureau international despoids et mesures), and discusses reports presented to it by its Consultative Committees. It issues an Annual Reporton the administrative and financial position of the BIPM to the governments of the Member States of the MetreConvention.

External links• Mutual Recognition Arrangement (MRA) [1]

References[1] http:/ / www1. bipm. org/ en/ convention/ mra/

16

Base units

SI base unit[[| thumb| The seven SI base units and the interdependency of their definitions]] The International System of Units(SI) defines seven units of measure as a basic set from which all other SI units are derived. These SI base units andtheir physical quantities are:[1]

• metre for length• kilogram for mass• second for time• ampere for electric current• kelvin for temperature• candela for luminous intensity• mole for the amount of substance.The SI base quantities form a set of mutually independent dimensions as required by dimensional analysiscommonly employed in science and technology. However, in a given realization of these units they may well beinterdependent, i.e. defined in terms of each other.[1]

The names of all SI units are written in lowercase characters (e.g., the metre has the symbol m), except that thesymbols of units named after persons are written with an initial capital letter (e.g., the ampere has the uppercasesymbol A).Many other units, such as the litre, are formally not part of the SI, but are accepted for use with SI.

SI base units

Name Symbol Measure Definition Historical Origin / Justification

metre m length "The metre is the length of the path travelled by light invacuum during a time interval of 1/299 792 458 of asecond."17th CGPM (1983, Resolution 1, CR, 97)

1⁄10,000,000 of the distance from the Earth'sequator to the North Pole measured on thecircumference through Paris.

kilogram kg mass "The kilogram is the unit of mass; it is equal to the mass ofthe international prototype of the kilogram."3rd CGPM (1901, CR, 70)

The mass of one litre of water. A litre is onethousandth of a cubic metre.

second s time "The second is the duration of 9 192 631 770 periods of theradiation corresponding to the transition between the twohyperfine levels of the ground state of the caesium 133atom."13th CGPM (1967/68, Resolution 1; CR, 103)"This definition refers to a caesium atom at rest at atemperature of 0 K."(Added by CIPM in 1997)

The day is divided in 24 hours, each hourdivided in 60 minutes, each minute divided in60 seconds.A second is 1⁄(24 × 60 × 60) of the day

SI base unit 17

ampere A electric current "The ampere is that constant current which, if maintainedin two straight parallel conductors of infinite length, ofnegligible circular cross-section, and placed 1 metre apartin vacuum, would produce between these conductors aforce equal to 2 × 10−7 newton per metre of length."9th CGPM (1948)

The original "International Ampere" wasdefined electrochemically as the currentrequired to deposit 1.118 milligrams of silverper second from a solution of silver nitrate.Compared to the SI ampere, the difference is0.015%.

kelvin K thermodynamictemperature

"The kelvin, unit of thermodynamic temperature, is thefraction 1/273.16 of the thermodynamic temperature of thetriple point of water."13th CGPM (1967/68, Resolution 4; CR, 104)"This definition refers to water having the isotopiccomposition defined exactly by the following amount ofsubstance ratios: 0.000 155 76 mole of 2H per mole of 1H,0.000 379 9 mole of 17O per mole of 16O, and 0.002 005 2mole of 18O per mole of 16O."(Added by CIPM in 2005)

The Celsius scale: the Kelvin scale uses thedegree Celsius for its unit increment, but is athermodynamic scale (0 K is absolute zero).

mole mol amount ofsubstance

"1. The mole is the amount of substance of a system whichcontains as many elementary entities as there are atoms in0.012 kilogram of carbon 12; its symbol is “mol”. / 2. Whenthe mole is used, the elementary entities must be specifiedand may be atoms, molecules, ions, electrons, otherparticles, or specified groups of such particles."14th CGPM (1971, Resolution 3; CR, 78)"In this definition, it is understood that unbound atoms ofcarbon 12, at rest and in their ground state, are referred to."(Added by CIPM in 1980)

Atomic weight or molecular weight dividedby the molar mass constant, 1 g/mol.

candela cd luminousintensity

"The candela is the luminous intensity, in a given direction,of a source that emits monochromatic radiation offrequency 540 × 1012 hertz and that has a radiant intensityin that direction of 1/683 watt per steradian."16th CGPM (1979, Resolution 3; CR, 100)

The candlepower, which is based on the lightemitted from a burning candle of standardproperties.

Future redefinitionsThere have been several modifications to the definitions of the base units, and additions of base units, since theMetre Convention in 1875. Since the redefinition of the metre in 1960, the kilogram is the only unit which is directlydefined in terms of a physical artifact rather than a property of nature. However, the mole, the ampere and thecandela are also linked through their definitions to the mass of this platinum–iridium cylinder stored in a vault nearParis. It has long been an objective of metrology to find a way to define the kilogram in terms of a fundamentalconstant, in the same way that the metre is now defined in terms of the speed of light.The 21st General Conference on Weights and Measures (CGPM, 1999) placed these efforts on an official footing,and recommended "that national laboratories continue their efforts to refine experiments that link the unit of mass tofundamental or atomic constants with a view to a future redefinition of the kilogram." Two main possibilities haveattracted attention: the Planck constant and the Avogadro constant.In 2005, the International Committee for Weights and Measures (CIPM) approved the preparation of new definitionsfor the kilogram, the ampere, and the kelvin and it noted the possibility of a new definition for the mole based on theAvogadro constant.[2] The 23rd CGPM (2007) decided to postpone any legal change until the next GeneralConference in 2011.[3]

In a note to the CIPM in October 2009,[4] Ian Mills, the President of the CIPM Consultative Committee - Units (CCU) cataloged the uncertainties of the fundamental constants of physics according to the current definitions and

SI base unit 18

their values under the proposed new definition. He urged the CIPM to accept the proposed changes in the definitionof the kilogram, ampere, kelvin and mole so that they are referenced to the values of the fundamental constants,namely Planck's constant (h), the electron charge (e), Boltzmann's constant (k), and Avogadro's constant (NA).[5]

References[1] International Bureau of Weights and Measures (2006), The International System of Units (SI) (http:/ / www. bipm. org/ utils/ common/ pdf/

si_brochure_8_en. pdf) (8th ed.), ISBN 92-822-2213-6,[2] 94th Meeting of the International Committee for Weights and Measures (2005). Recommendation 1: Preparative steps towards new

definitions of the kilogram, the ampere, the kelvin and the mole in terms of fundamental constants (http:/ / www. bipm. org/ utils/ en/ pdf/CIPM2005-EN. pdf)

[3] 23rd General Conference on Weights and Measures (2007). Resolution 12: On the possible redefinition of certain base units of theInternational System of Units (SI) (http:/ / www. bipm. org/ utils/ en/ pdf/ Resol23CGPM-EN. pdf).

[4] Ian Mills, President of the CCU (2009-10). "Thoughts about the timing of the change from the Current SI to the New SI" (http:/ / www. bipm.org/ cc/ CIPM/ Allowed/ 98/ CIPM2009_49_TIMING_THE_NEW_SI. pdf). CIPM. . Retrieved 2010-02-23.

[5] Ian Mills (29 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units" (http:/ / www. bipm. org/ utils/ en/pdf/ si_brochure_draft_ch2. pdf). CCU. . Retrieved 2011-01-01.

External links• BIPM (http:/ / www. bipm. org/ en/ si/ base_units/ )• National Physical Laboratory (http:/ / www. npl. co. uk/ mass/ faqs/ kilogram. html)• NIST -SI (http:/ / physics. nist. gov/ cuu/ Units/ index. html)

Metre 19

Metre

1 metre =

SI units

100 cm 1000 mm

US customary / Imperial units

3.2808 ft 39.370 in

The metre (or meter), symbol m, is the base unit of length in the International System of Units (SI). Originallyintended to be one ten-millionth of the distance from the Earth's equator to the North Pole (at sea level), its definitionhas been periodically refined to reflect growing knowledge of metrology. Since 1983, it is defined as the distancetravelled by light in vacuum in 1⁄299,792,458 of a second.[1]

History

NameThe first recorded proposal for a decimal-based unit of length was the universal measure unit proposed by theEnglish philosopher John Wilkins in 1668.[2] [3] In 1675 the Italian scientist Tito Livio Burattini, in his work MisuraUniversale, used the words metro cattolico (metre catholic) which was derived from the Greek μέτρον καθολικόν(métron katholikón), "a universal measure". This word gave rise to the French mètre which in 1797 was introducedinto the English language.[4]

Belfry, Dunkirk - the northern end of the meridian arc

Meridional definition

In 1668 Wilkins proposed using Christopher Wren's suggestion ofa pendulum with a half-period of one second to measure a standardlength that Christiaan Huygens had observed to be 38 Rhinelandor 39¼ English inches (997 mm) in length.[2] [3] In the eighteenthcentury, there were two favoured approaches to the definition ofthe standard unit of length. One approach followed Wilkins indefining the metre as the length of a pendulum with a half-periodof one second, a 'seconds pendulum'. The other approachsuggested defining the metre as one ten-millionth of the length ofthe Earth's meridian along a quadrant, that is the distance from theEquator to the North Pole. In 1791, the French Academy ofSciences selected the meridional definition over the pendulardefinition because the force of gravity varies slightly over thesurface of the Earth, which affects the period of a pendulum.

In order to establish a universally accepted foundation for thedefinition of the metre, measurements of this meridian moreaccurate than those available at that time were imperative. TheFrench Academy of Sciences commissioned an expedition led by

Metre 20

Fortress of Montjuïc - the southerly end of the meridianarc

Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from1792 to 1799, which measured the distance between theDunkerque belfry and Montjuïc castle, Barcelona to estimate thelength of the meridian arc through Dunkerque (assumed to be thesame length as the Paris meridian). This portion of the meridianwas to serve as the basis for the length of the half meridian,connecting the North Pole with the Equator. The exact shape ofthe Earth is not a simple mathematical shape (sphere or ellipse) atthe level of precision required for defining a standard of length.The irregular and particular shape of the Earth (smoothed to sealevel) is called a Geoid, which means "Earth-shaped".

However, in 1793, France adopted as its official unit of length ametre based on provisional results from the expedition. Although it was later determined that the first prototypemetre bar was short by a fifth of a millimetre because of miscalculation of the flattening of the Earth, this lengthbecame the standard. The circumference of the Earth through the poles is therefore slightly more than forty millionmetres.

Prototype metre bar

Historical International Prototype Metre bar, made of analloy of platinum and iridium, that was the standard from

1889 to 1960.

In the 1870s and in light of modern precision, a series ofinternational conferences was held to devise new metricstandards. The Metre Convention (Convention du Mètre) of1875 mandated the establishment of a permanent InternationalBureau of Weights and Measures (BIPM: BureauInternational des Poids et Mesures) to be located in Sèvres,France. This new organisation would preserve the newprototype metre and kilogram standards when constructed,distribute national metric prototypes, and maintaincomparisons between them and non-metric measurementstandards. The organisation created a new prototype bar in1889 at the first General Conference on Weights andMeasures (CGPM: Conférence Générale des Poids etMesures), establishing the International Prototype Metre as the distance between two lines on a standard barcomposed of an alloy of ninety percent platinum and ten percent iridium, measured at the melting point of ice.[5]

The original international prototype of the metre is still kept at the BIPM under the conditions specified in 1889. Adiscussion of measurements of a standard metre bar and the errors encountered in making the measurements is foundin a NIST document.[6]

Standard wavelength of krypton-86 emissionIn 1893, the standard metre was first measured with an interferometer by Albert A. Michelson, the inventor of thedevice and an advocate of using some particular wavelength of light as a standard of distance. By 1925,interferometry was in regular use at the BIPM. However, the International Prototype Metre remained the standarduntil 1960, when the eleventh CGPM defined the metre in the new SI system as equal to 1,650,763.73 wavelengthsof the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum.

Metre 21

Speed of lightTo further reduce uncertainty, the seventeenth CGPM in 1983 replaced the definition of the metre with its currentdefinition, thus fixing the length of the metre in terms of the second and the speed of light:

The metre is the length of the path travelled by light in vacuum during a time interval of 1⁄299 792 458 of asecond.[1]

This definition fixed the speed of light in a vacuum at precisely 299,792,458 metres per second. Although the metreis now defined as the distance travelled by light in a given time, actual laboratory realisations of the metre are stilldelineated by measuring the wavelength of laser light of a standard type,[7] using interferometry to effectively countthe number of wavelengths in a metre. Three major factors limit the accuracy attainable with laser interferometers:[8]

• Uncertainty in vacuum wavelength of the source,• Uncertainty in the refractive index of the medium,• Laser count resolution of the interferometer.Use of the interferometer to define the metre is based upon the relation:

where λ is the determined wavelength; c is the speed of light in ideal vacuum; n is the refractive index of the mediumin which the measurement is made; and f is the frequency of the source. In this way the length is related to one of themost accurate measurements available: frequency.[8]

An intended byproduct of the 17th CGPM’s definition was that it enabled scientists to measure the wavelength oftheir lasers with one-fifth the uncertainty. To further facilitate reproducibility from lab to lab, the 17th CGPM alsomade the iodine-stabilised helium-neon laser “a recommended radiation” for realising the metre. For purposes ofdelineating the metre, the BIPM currently considers the HeNe laser wavelength to be as follows: λHeNe =632.99139822 nm with an estimated relative standard uncertainty (U) of 2.5 × 10−11.[9] This uncertainty is currentlythe limiting factor in laboratory realisations of the metre as it is several orders of magnitude poorer than that of thesecond (U = 5 × 10−16).[10] Consequently, a practical realisation of the metre is usually delineated (not defined)today in labs as 1579800.298728(39) wavelengths of helium-neon laser light in a vacuum.

Timeline of definition• 1790 May 8 – The French National Assembly decides that the length of the new metre would be equal to the

length of a pendulum with a half-period of one second.• 1791 March 30 – The French National Assembly accepts the proposal by the French Academy of Sciences that

the new definition for the metre be equal to one ten-millionth of the length of the Earth's meridian along aquadrant through Paris, that is the distance from the equator to the north pole.

• 1795 – Provisional metre bar constructed of brass.• 1799 December 10 – The French National Assembly specifies the platinum metre bar, constructed on 23 June

1799 and deposited in the National Archives, as the final standard.• 1889 September 28 – The first General Conference on Weights and Measures (CGPM) defines the metre as the

distance between two lines on a standard bar of an alloy of platinum with ten percent iridium, measured at themelting point of ice.

• 1927 October 6 – The seventh CGPM adjusts the definition of the metre to be the distance, at 0 °C, between theaxes of the two central lines marked on the prototype bar of platinum-iridium, this bar being subject to onestandard atmosphere of pressure and supported on two cylinders of at least one centimetre diameter,symmetrically placed in the same horizontal plane at a distance of 571 millimetres from each other.

• 1960 October 14 – The eleventh CGPM defines the metre to be equal to 1,650,763.73 wavelengths in vacuum ofthe radiation corresponding to the transition between the 2p10 and 5d5 quantum levels of the krypton-86 atom.[11]

Metre 22

• 1983 October 21 – The seventeenth CGPM defines the metre as equal to the distance travelled by light in vacuumduring a time interval of 1⁄299,792,458 of a second.[12]

• 2002  – The International Committee for Weights and Measures (CIPM) considers the metre to be a unit of properlength and thus recommends this definition be restricted to "lengths ℓ which are sufficiently short for the effectspredicted by general relativity to be negligible with respect to the uncertainties of realisation."[13]

Definitions of the metre since 1795 [14]

Basis of definition Date Absoluteuncertainty

Relativeuncertainty

1/10000000 part of the quarter of a meridian, measurement by Delambre and Mechain 1795 0.5–0.1 mm 10−4

First prototype Metre des Archives platinum bar standard 1799 0.05–0.01 mm 10−5

Platinum-iridium bar at melting point of ice (1st CGPM) 1889 0.2–0.1 µm 10−7

Platinum-iridium bar at melting point of ice, atmospheric pressure, supported by two rollers (7th CGPM) 1927 n.a. n.a.

Hyperfine atomic transition; 1650763.73 wavelengths of light from a specified transition in Krypton 86 (11thCGPM)

1960 0.01–0.005 µm 10−8

Distance traversed in vacuum by light in 1/299792458 of a second (17th CGPM ) 1983 0.1 nm 10−10

SI prefixed forms of metreSI prefixes are often employed to denote decimal multiples and submultiples of the metre, as shown in the tablebelow. As indicated in the table, some are commonly used, while others are not. Long distances are usuallyexpressed in km, astronomical units, light-years, or parsecs, rather than in Mm, Gm, Tm, Pm, Em, Zm or Ym; "30cm", "30 m", and "300 m" are more common than "3 dm", "3 dam", and "3 hm", respectively.

SI multiples for metre (m)

Submultiples Multiples

Value Symbol Name Value Symbol Name

10−1 m dm decimetre 101 m dam decametre

10−2 m cm centimetre 102 m hm hectometre

10−3 m mm millimetre 103 m km kilometre

10−6 m µm micrometre 106 m Mm megametre

10−9 m nm nanometre 109 m Gm gigametre

10−12 m pm picometre 1012 m Tm terametre

10−15 m fm femtometre 1015 m Pm petametre

10−18 m am attometre 1018 m Em exametre

10−21 m zm zeptometre 1021 m Zm zettametre

10−24 m ym yoctometre 1024 m Ym yottametre

Common prefixed units are in bold face.

The term micron is often used instead of micrometre, but this practice is officially discouraged.[15]

Metre 23

SpellingMetre is used as the standard spelling of the metric unit for length in all English speaking nations except the USA.[16]

The most recent official brochure, written in 2006, about the International System of Units (SI), Bureau internationaldes poids et mesures, was written in French by the International Bureau of Weights and Measures. An Englishtranslation (using the spelling: metre) is included to make the SI standard "more widely accessible".[17]

In 2008, the U.S. English translation published by the U.S. National Institute of Standards and Technology chose touse meter in accordance with the United States Government Printing Office Style Manual.[18]

Measuring devices (such as parking meter, speedometer) are traditionally spelt "...meter" in all countries.[19] Theword "meter", signifying any such device, has the same derivation as the word "metre", denoting the unit of lengththis article is about.[20]

Equivalents in other units

Metric unitexpressed in non-SI units  

Non-SI unitexpressed in metric units

1 metre ≈ 39.37 inches 1 inch ≡ 0.0254 metres

1 centimetre ≈ 0.3937 inch 1 inch ≡ 2.54 centimetres

1 millimetre ≈ 0.03937 inch 1 inch ≡ 25.4 millimetres

1 metre ≡ 1×1010 Ångström 1 Ångström ≡ 1×10−10 metre

1 nanometre ≡ 10 Ångström 1 Ångström ≡ 100 picometres

Within this table, "inch" means "international inch".[21]

"≈" means "is approximately equal to"."≡" means "equals by definition" or equivalently, "is exactly equal to".A simple mnemonic aid exists to assist with conversion;

1 metre is equivalent to 3 feet, 3 and 3/8 inches.[22] This gives an over-estimate of 0.125 mm.

Notes[1] 17th General Conference on Weights and Measures (1983), Resolution 1.[2] An Essay towards a Real Character and a Philosophical Language (Reproduction) (http:/ / www. metricationmatters. com/ docs/

WilkinsTranslationLong. pdf)[3] An Essay towards a Real Character and a Philosophical Language (Transcription) (http:/ / www. metricationmatters. com/ docs/

WilkinsTranslationShort. pdf)[4] meter. (2009). In Merriam-Webster Online Dictionary (http:/ / www. merriam-webster. com/ dictionary/ meter). Retrieved 8 December 2009.[5] National Institute of Standards and Technology 2003; Historical context of the SI: Unit of length (meter)[6] Beers & Penzes 1992[7] See, for example, Iodine-Stabilised Lasers Iodine-Stabilised Lasers (http:/ / www. npl. co. uk/ science-technology/ time-frequency/

optical-frequency-standards-and-metrology/ research/ iodine-stabilised-lasers) on the National Physical Laboratory website[8] Zagar, 1999, pp. 6–67ff[9] See Penzes 2005 and these papers (http:/ / search. bipm. org/ bipm/ en/

C=eJw9xrFygjAYAOA8Sr3r0DrBIQrdgKIIiBgqyNQD8huBECCmWN6!Tp2!b0Sylgw!3jyI4KUDKeAdMQQccRSLnny7nLL6fkPDrecg6wopiEHXFU!LYRD97zP3qkMcJhCI*O*1cYcRgT!nTeUGj8Y6Yc9gG7edBMlK39oue7wywoWW2CIoI9oWS2*8VPcHLa6UQxxt!mzVNIwUrcOlb48NhVNTqXHi5nO0KPA6TcrEUfGPNHYbevZI7OoX1tKDIF1ALSPNtYHNUeiUSUbjpPVb86j7dr!m532uYwe!KD4qqYDSlNN1CT6fp92VKmZo0gvZph5GfyXiXFA_?action=s&q=title:(HeNe+ OR+ metre)& x=0& y=0& resetcontext=) from the BIPM database, as well as Maintaining the SI unit of length (http:/ / www.nrc-cnrc. gc. ca/ eng/ projects/ inms/ si-length. html) (National Research Council of Canada, 2010)

[10] NIST: NIST-F1 Cesium Fountain Atomic Clock (http:/ / tf. nist. gov/ timefreq/ cesium/ fountain. htm).[11] National Institute of Standards and Technology (http:/ / physics. nist. gov/ Pubs/ SP447/ app6. pdf)[12] Taylor and Thompson (2008a), Appendix 1, p. 70.[13] Taylor and Thompson (2008a), Appendix 1, p. 77.

Metre 24

[14] Cardarelli, Francois Encydopaedia of scientific units, weights, and measures: their SI equivalences and origins, Springer-Verlag LondonLimited 2003, ISBN 1-85233-682-X, page 5, table 2.1, data from Giacomo, P., Du platine a la lumiere, Bull. Bur. Nat. Metrologie, 102 (1995)5–14.

[15] NIST Guide to the SI: #5.2.3 Other Unacceptable Units - Retrieved 12 March 2010 (http:/ / physics. nist. gov/ Pubs/ SP811/ sec05. html)[16] http:/ / www. metricationmatters. com/ docs/ Spelling_metre_or_meter. pdf[17] BIPM, 2006, p. 130ff.[18] The Metric Conversion Act of 1975 gives the Secretary of Commerce of the US the responsibility of interpreting or modifying the SI for use

in the US. The Secretary of Commerce delegated this authority to the Director of the National Institute of Standards and Technology (NIST)(Turner). In 2008, NIST published the US version (Taylor and Thompson, 2008a) of the English text of the eighth edition of the BIPMpublication Le Système international d'unités (SI) (BIPM, 2006). In the NIST publication, the spellings "meter", "liter" and "deka" are usedrather than "metre", "litre" and "deca" as in the original BIPM English text (Taylor and Thompson, 2008a, p. iii). The Director of the NISTofficially recognised this publication, together with Taylor and Thompson (2008b), as the "legal interpretation" of the SI for the United States(Turner).

[19] Cambridge Advanced Learner's Dictionary (http:/ / dictionary. cambridge. org/ results. asp?searchword=parking+ meter) (2008). CambridgeUniversity Press. s.v. parking meter, meter, speedometer.

[20] American Heritage Dictionary of the English Language. 3rd ed. (1992). Boston: Houghton Mifflin. s.v. meter.[21] A. V. Astin & H. Arnold Karo, (1959), Refinement of values for the yard and the pound (http:/ / www. ngs. noaa. gov/ PUBS_LIB/

FedRegister/ FRdoc59-5442. pdf), Washington DC: National Bureau of Standards, republished on National Geodetic Survey web site and theFederal Register (Doc. 59-5442, Filed, 30 June 1959, 8:45 a.m.)

[22] Well-known conversion, publicised at time of metrication.

References• 17th General Conference on Weights and Measures. (1983). Resolution 1. (http:/ / www. bipm. org/ en/ CGPM/

db/ 17/ 1/ ) International Bureau of Weights and Measures.• Beers, J.S. & Penzes, W. B. (1992). NIST Length Scale Interferometer Measurement Assurance. (http:/ / ts. nist.

gov/ MeasurementServices/ Calibrations/ upload/ 4998. pdf) (NISTIR 4998). National Institute of Standards andTechnology.

• Bureau International des Poids et Mesures. (2006). The International System of Units (SI) (http:/ / www1. bipm.org/ utils/ common/ pdf/ si_brochure_8. pdf). Retrieved 18 August 2008.• HTML version (http:/ / www. bipm. org/ en/ si/ si_brochure/ ). Retrieved 24 August 2008.

• Bureau International des Poids et Mesures. (n.d.). Resolutions of the CGPM (http:/ / www. bipm. fr/ en/convention/ resolutions. html) (search facility). Retrieved 3 June 2006.

• Bureau International des Poids et Mesures. (n.d.). The BIPM and the evolution of the definition of the metre (http:// www1. bipm. org/ en/ si/ history-si/ evolution_metre. html). Retrieved 3 June 2006.

• Layer, H.P. (2008). Length—Evolution from Measurement Standard to a Fundamental Constant (http:/ / www.mel. nist. gov/ div821/ museum/ length. htm). Gaithersburg, MD: National Institute of Standards and Technology.Retrieved 18 August 2008.

• Mohr, P., Taylor, B.N., and David B. Newell, D. (28 December 2007). CODATA Recommended Values of theFundamental Physical Constants: 2006 (http:/ / physics. nist. gov/ cuu/ Constants/ codata. pdf). Gaithersburg,MD: National Institute of Standards and Technology. Retrieved 18 August 2008.

• National Institute of Standards and Technology. (December 2003). The NIST Reference on Constants, Units, andUncertainty: International System of Units (SI) (http:/ / physics. nist. gov/ cuu/ Units/ index. html) (web site):• SI base units (http:/ / physics. nist. gov/ cuu/ Units/ units. html). Retrieved 18 August 2008.• Definitions of the SI base units (http:/ / physics. nist. gov/ cuu/ Units/ current. html). Retrieved 18 August

2008.• Historical context of the SI: Metre (http:/ / physics. nist. gov/ cuu/ Units/ meter. html). Retrieved 26 May 2010.

• National Research Council Canada. (5 February 2010). Maintaining the SI unit of length (http:/ / www. nrc-cnrc.gc. ca/ eng/ projects/ inms/ si-length. html). Retrieved 4 December 2010.

• Penzes, W. (29 December 2005). Time Line for the Definition of the Meter (http:/ / www. nist. gov/ pml/ div681/

museum-timeline. cfm). Gaithersburg, MD: National Institute of Standards and Technology — Precision

Metre 25

Engineering Division. Retrieved 4 December 2010.• Taylor, B.N. and Thompson, A. (Eds.). (2008a). The International System of Units (SI) (http:/ / physics. nist. gov/

Pubs/ SP330/ sp330. pdf). United States version of the English text of the eighth edition (2006) of theInternational Bureau of Weights and Measures publication Le Système International d’ Unités (SI) (SpecialPublication 330). Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 18 August 2008.

• Taylor, B.N. and Thompson, A. (2008b). Guide for the Use of the International System of Units (http:/ / physics.nist. gov/ cuu/ pdf/ sp811. pdf) (Special Publication 811). Gaithersburg, MD: National Institute of Standards andTechnology. Retrieved 23 August 2008.

• Tibo Qorl. (2005) The History of the Meter (http:/ / histoire. du. metre. free. fr/ en/ ) (Translated by SibilleRouzaud). Retrieved 18 August 2008.

• Turner, J. (Deputy Director of the National Institute of Standards and Technology). (16 May 2008)."Interpretation of the International System of Units (the Metric System of Measurement) for the United States"(http:/ / ts. nist. gov/ WeightsAndMeasures/ Metric/ upload/FRN_Vol_73_No_96_16May2008_SI_Interpretation. pdf). Federal Register Vol. 73, No. 96, p. 28432-3.

• Zagar, B.G. (1999). Laser interferometer displacement sensors (http:/ / books. google. com/books?id=VXQdq0B3tnUC& pg=PT164#PPT160,M1) in J.G. Webster (ed.). The Measurement, Instrumentation,and Sensors Handbook. CRC Press. isbn=0849383471.

Further reading• Alder, Ken. (2002). The Measure of All Things : The Seven-Year Odyssey and Hidden Error That Transformed

the World. Free Press, New York ISBN 0-7432-1675-X

Kilogram

Kilogram

A computer-generated image of the International Prototype Kilogram (“IPK”). The IPK is the kilogram. It sits next to an inch-basedruler for scale. The IPK is made of a platinum-iridium alloy and is stored in a vault at the BIPM in Sèvres, France. Like the other

prototypes, the edges of the IPK have a four-angle chamfer to minimize wear. For other kilogram-related images, see Externallinks, below.

Unit information

Unit system: SI base unit

Unit of... Mass

Symbol: kg

Kilogram 26

Unit conversions

1 kg in... is equal to...

U.S. customary    ≈ 2.205 pounds

Natural units    ≈ 4.59 × 107 Planck masses≈1.356392733(68) × 1050 hertz [1]

The kilogram (symbol: kg) is the base unit of mass in the International System of Units (SI, from the French LeSystème International d’Unités),[2] which is the modern standard governing the metric system. The kilogram isdefined as being equal to the mass of the International Prototype Kilogram[3] (IPK),[4] which is almost exactly equalto the mass of one liter of water. It is the only SI base unit with an SI prefix as part of its name. It is also the only SIunit that is still defined by an artifact rather than a fundamental physical property that can be reproduced in differentlaboratories.In everyday usage, the mass of an object, which is measured in kilograms, is often referred to as its weight.However, the term weight in strict scientific contexts refers to the gravitational force of an object. Throughout mostof the world, force is measured with the SI unit newton and the non-SI unit kilogram-force. Similarly, theavoirdupois (or international) pound, used in both the Imperial system and U.S. customary units, is a unit of massand its related unit of force is the pound-force. The avoirdupois pound is defined as exactly 0.45359237 kg,[5]

making one kilogram approximately equal to 2.2046 avoirdupois pounds.Many units in the SI system are defined relative to the kilogram so its stability is important. After the InternationalPrototype Kilogram had been found to vary in mass over time, the International Committee for Weights andMeasures (known also by its French-language initials CIPM) recommended in 2005 that the kilogram be redefined interms of a fundamental constant of nature.[6] No final decision is expected before 2011.[7]

Nature of mass

The chains on the swing hold all the child’s weight. If one were to standbehind her at the bottom of the arc and try to stop her, one would beacting against her inertia, which arises purely from mass, not weight.

The kilogram is a unit of mass, the measurement ofwhich corresponds to the general, everyday notion ofhow “heavy” something is. However, mass is actuallyan inertial property; that is, the tendency of an objectto remain at constant velocity unless acted upon byan outside force. According to Sir Isaac Newton's324-year-old laws of motion and an importantformula that sprang from his work, F = ma, an objectwith a mass, m, of one kilogram will accelerate, a, atone meter per second per second (about one-tenth theacceleration due to earth’s gravity)[8] when actedupon by a force, F, of one newton.

While the weight of matter is entirely dependentupon the strength of gravity, the mass of matter isinvariant.[9] Accordingly, for astronauts inmicrogravity, no effort is required to hold objects offthe cabin floor; they are “weightless”. However, since objects in microgravity still retain their mass and inertia, anastronaut must exert ten times as much force to accelerate a 10‑kilogram object at the same rate as a 1‑kilogramobject.

On earth, a common swing set can demonstrate the relationship of force, mass, and acceleration without beingappreciably influenced by weight (downward force). If one were to stand behind a large adult sitting stationary in a

Kilogram 27

swing and give him a strong push, the adult would accelerate relatively slowly and swing only a limited distanceforwards before beginning to swing backwards. Exerting that same effort while pushing on a small child wouldproduce much greater acceleration.

History

Early definitionsOn 7 April 1795, the gram was decreed in France to be equal to “the absolute weight of a volume of water equal tothe cube of the hundredth part of the meter, at the temperature of melting ice.”[10] The concept of using a specifiedvolume of water to define a unit measure of mass was first advanced by the English philosopher John Wilkins in1668.[11] [12]

Since trade and commerce typically involve items significantly more massive than one gram, and since a massstandard made of water would be inconvenient and unstable, the regulation of commerce necessitated themanufacture of a practical realization of the water-based definition of mass. Accordingly, a provisional massstandard was made as a single-piece, metallic artifact one thousand times more massive than the gram—thekilogram.At the same time, work was commissioned to precisely determine the mass of a cubic decimeter (one liter) ofwater.[13] [10] Although the decreed definition of the kilogram specified water at 0 °C—its highly stable temperaturepoint—the French chemist, Louis Lefèvre-Gineau and the Italian naturalist, Giovanni Fabbroni after several years ofresearch chose to redefine the standard in 1799 to water’s most stable density point: the temperature at which waterreaches maximum density, which was measured at the time as 4 °C.[14] [15] They concluded that one cubic decimeterof water at its maximum density was equal to 99.9265% of the target mass of the provisional kilogram standardmade four years earlier.[16] [17] That same year, 1799, an all-platinum kilogram prototype was fabricated with theobjective that it would equal, as close as was scientifically feasible for the day, the mass of one cubic decimeter ofwater at 4 °C. The prototype was presented to the Archives of the Republic in June and on 10 December 1799, theprototype was formally ratified as the Kilogramme des Archives (Kilogram of the Archives) and the kilogram wasdefined as being equal to its mass. This standard stood for the next ninety years.

International Prototype KilogramThe Metre Convention was signed on 20 May 1875 and established the SI system, which since 1889 defines themagnitude of the kilogram to be equal to the mass of the International Prototype Kilogram,[3] often referred to in theprofessional metrology world as the “IPK”. The IPK is made of a platinum alloy known as “Pt‑10Ir”, which is 90%platinum and 10% iridium (by mass) and is machined into a right-circular cylinder (height = diameter) of39.17 millimeters to minimize its surface area.[18] The addition of 10% iridium improved upon the all-platinumKilogram of the Archives by greatly increasing hardness while still retaining platinum’s many virtues: extremeresistance to oxidation, extremely high density, satisfactory electrical and thermal conductivities, and low magneticsusceptibility. The IPK and its six sister copies are stored at the International Bureau of Weights and Measures(known by its French-language initials BIPM) in an environmentally monitored safe in the lower vault located in thebasement of the BIPM’s House of Breteuil in Sèvres on the outskirts of Paris (see External images, below forphotographs). Three independently controlled keys are required to open the vault. Official copies of the IPK weremade available to other nations to serve as their national standards. These are compared to the IPK roughly every 50years.The IPK is one of three cylinders made in 1879. In 1883, it was found to be indistinguishable from the mass of theKilogram of the Archives made eighty-four years prior, and was formally ratified as the kilogram by the 1st CGPMin 1889.[18]

Kilogram 28

Modern measurements of Vienna Standard Mean Ocean Water, which is pure distilled water with an isotopiccomposition representative of the average of the world’s oceans, show it has a density of 0.999975 ±0.000001 kg/Lat its point of maximum density (3.984 °C) under one standard atmosphere (760 torr) of pressure.[19] Thus, a cubicdecimeter of water at its point of maximum density is only 25 parts per million less massive than the IPK. This smalldifference, and the fact that the mass of the IPK was indistinguishable from the mass of the Kilogram of theArchives, speaks to the scientists’ skills over 212 years ago when they made their measurements of water’s propertiesand fabricated the Kilogram of the Archives.

Stability of the International Prototype Kilogram

Mass drift over time of national prototypes K21–K40, plus two of the IPK’s sister copies:K32 and K8(41).[20] All mass changes are relative to the IPK. The initial 1889

starting-value offsets relative to the IPK have been nulled.[21] The above are all relativemeasurements; no historical mass-measurement data is available to determine which of

the prototypes has been most stable relative to an invariant of nature. There is the distinctpossibility that all the prototypes gained mass over 100 years and that K21, K35, K40,

and the IPK simply gained less than the others.

By definition, the error in the measuredvalue of the IPK’s mass is exactly zero;the IPK is the kilogram. However, anychanges in the IPK’s mass over timecan be deduced by comparing its massto that of its official copies storedthroughout the world, a process called“periodic verification.” For instance,the U.S. owns four 90% platinum /10% iridium (Pt‑10Ir) kilogramstandards, two of which, K4 and K20,are from the original batch of 40replicas delivered in 1884.[22] The K20prototype was designated as theprimary national standard of mass forthe U.S. Both of these, as well as thosefrom other nations, are periodicallyreturned to the BIPM forverification.[23]

Note that none of the replicas has a mass precisely equal to that of the IPK; their masses are calibrated anddocumented as offset values. For instance, K20, the U.S.’s primary standard, originally had an official mass of 1 kg −39 micrograms (µg) in 1889; that is to say, K20 was 39 µg less than the IPK. A verification performed in 1948showed a mass of 1 kg − 19 µg. The latest verification performed in 1999 shows a mass precisely identical to itsoriginal 1889 value. Quite unlike transient variations such as this, the U.S.’s check standard, K4, has persistentlydeclined in mass relative to the IPK—and for an identifiable reason. Check standards are used much more often thanprimary standards and are prone to scratches and other wear. K4 was originally delivered with an official mass of 1kg − 75 µg in 1889, but as of 1989 was officially calibrated at 1 kg − 106 µg and ten years later was 1 kg − 116 µg.Over a period of 110 years, K4 lost 41 µg relative to the IPK.[24]

Beyond the simple wear that check standards can experience, the mass of even the carefully stored national prototypes can drift relative to the IPK for a variety of reasons, some known and some unknown. Since the IPK and its replicas are stored in air (albeit under two or more nested bell jars), they gain mass through adsorption of atmospheric contamination onto their surfaces. Accordingly, they are cleaned in a process the BIPM developed between 1939 and 1946 known as “the BIPM cleaning method” that comprises lightly rubbing with a chamois soaked in equal parts ether and ethanol, followed by steam cleaning with bi-distilled water, and allowing the prototypes to settle for 7–10 days before verification.[25] Cleaning the prototypes removes between 5 and 60 µg of contamination depending largely on the time elapsed since the last cleaning. Further, a second cleaning can remove up to 10 µg

Kilogram 29

more. After cleaning—even when they are stored under their bell jars—the IPK and its replicas immediately begingaining mass again. The BIPM even developed a model of this gain and concluded that it averaged 1.11 µg permonth for the first 3 months after cleaning and then decreased to an average of about 1 µg per year thereafter. Sincecheck standards like K4 are not cleaned for routine calibrations of other mass standards—a precaution to minimizethe potential for wear and handling damage—the BIPM’s model of time-dependent mass gain has been used as an“after cleaning” correction factor.

K48, above, came from the second batch of kilogram replicas tobe produced. It was delivered to Denmark in 1949 with an

official mass of 1 kg + 81 µg. Like all other replicas, it is storedunder two nested bell jars virtually all the time. Still, its mass

and that of the IPK diverged markedly in only 40 years; the massof K48 was certified as 1 kg + 112 µg during the 1988–1992

periodic verification.[21]

Because the first forty official copies are made of the samealloy as the IPK and are stored under similar conditions,periodic verifications using a large number ofreplicas—especially the national primary standards, whichare rarely used—can convincingly demonstrate the stabilityof the IPK. What has become clear after the third periodicverification performed between 1988 and 1992 is thatmasses of the entire worldwide ensemble of prototypeshave been slowly but inexorably diverging from eachother. It is also clear that the mass of the IPK lost perhaps50 µg over the last century, and possibly significantlymore, in comparison to its official copies.[21] [26] Thereason for this drift has eluded physicists who havededicated their careers to the SI unit of mass. No plausiblemechanism has been proposed to explain either a steadydecrease in the mass of the IPK, or an increase in that of itsreplicas dispersed throughout the world.[27] [28] [29] [30]

This relative nature of the changes amongst the world’skilogram prototypes is often misreported in the popularpress, and even some notable scientific magazines, whichoften state that the IPK simply “lost 50 µg” and omit thevery important caveat of “in comparison to its officialcopies.”[31] Moreover, there are no technical meansavailable to determine whether or not the entire worldwide

ensemble of prototypes suffers from even greater long-term trends upwards or downwards because their mass“relative to an invariant of nature is unknown at a level below 1000 µg over a period of 100 or even 50 years.”[26]

Given the lack of data identifying which of the world’s kilogram prototypes has been most stable in absolute terms, itis equally as valid to state that the first batch of replicas has, as a group, gained an average of about 25 µg over onehundred years in comparison to the IPK.[32]

What is known specifically about the IPK is that it exhibits a short-term instability of about 30 µg over a period ofabout a month in its after-cleaned mass.[33] The precise reason for this short-term instability is not understood but isthought to entail surface effects: microscopic differences between the prototypes’ polished surfaces, possiblyaggravated by hydrogen absorption due to catalysis of the volatile organic compounds that slowly deposit onto theprototypes as well as the hydrocarbon-based solvents used to clean them.[30] [34]

Scientists are seeing far greater variability in the prototypes than previously believed. The increasing divergence inthe masses of the world’s prototypes and the short-term instability in the IPK has prompted research into improvedmethods to obtain a smooth surface finish using diamond-turning on newly manufactured replicas and has intensifiedthe search for a new definition of the kilogram. See Proposed future definitions, below.[35]

Kilogram 30

Importance of the kilogram

The magnitude of many of the units comprising the SI system ofmeasurement, including most of those used in the measurement ofelectricity and light, are highly dependent upon the stability of a

132-year-old, golf ball-size cylinder of metal stored in a vault in France.

The stability of the IPK is crucial because thekilogram underpins much of the SI system ofmeasurement as it is currently defined andstructured. For instance, the newton is defined as theforce necessary to accelerate one kilogram at onemeter per second squared. If the mass of the IPKwere to change slightly, so too must the newton by aproportional degree. In turn, the pascal, the SI unitof pressure, is defined in terms of the newton. Thischain of dependency follows to many other SI unitsof measure. For instance, the joule, the SI unit ofenergy, is defined as that expended when a force ofone newton acts through one meter. Next to beaffected is the SI unit of power, the watt, which isone joule per second. The ampere too is definedrelative to the newton, and ultimately, the kilogram.With the magnitude of the primary units ofelectricity thus determined by the kilogram, so toofollow many others; namely, the coulomb, volt,tesla, and weber. Even units used in the measure oflight would be affected; the candela—following thechange in the watt—would in turn affect the lumenand lux.

Because the magnitude of many of the unitscomprising the SI system of measurement is ultimately defined by the mass of a 132-year-old, golf ball-sized pieceof metal, the quality of the IPK must be diligently protected to preserve the integrity of the SI system. Yet, in spite ofthe best stewardship, the average mass of the worldwide ensemble of prototypes and the mass of the IPK have likelydiverged another 5.1 µg since the third periodic verification 22 years ago.[36] Further, the world’s national metrologylaboratories must wait for the fourth periodic verification to confirm whether the historical trendspersisted.

Fortunately, definitions of the SI units are quite different from their practical realizations. For instance, the meter isdefined as the distance light travels in a vacuum during a time interval of 1⁄299,792,458 of a second. However, themeter’s practical realization typically takes the form of a helium-neon laser, and the meter’s length isdelineated—not defined—as 1579800.298728 wavelengths of light from this laser. Now suppose that the officialmeasurement of the second was found to have drifted by a few parts per billion (it is actually exquisitely stable).There would be no automatic effect on the meter because the second—and thus the meter’s length—is abstracted viathe laser comprising the meter’s practical realization. Scientists performing meter calibrations would simply continueto measure out the same number of laser wavelengths until an agreement was reached to do otherwise. The same istrue with regard to the real-world dependency on the kilogram: if the mass of the IPK was found to have changedslightly, there would be no automatic effect upon the other units of measure because their practical realizationsprovide an insulating layer of abstraction. Any discrepancy would eventually have to be reconciled though becausethe virtue of the SI system is its precise mathematical and logical harmony amongst its units. If the IPK’s value weredefinitively proven to have changed, one solution would be to simply redefine the kilogram as being equal to themass of the IPK plus an offset value, similarly to what is currently done with its replicas; e.g., “the kilogram is equalto the mass of the IPK + 42 parts per billion” (equivalent to 42 µg).

Kilogram 31

The long-term solution to this problem, however, is to liberate the SI system’s dependency on the IPK by developinga practical realization of the kilogram that can be reproduced in different laboratories by following a writtenspecification. The units of measure in such a practical realization would have their magnitudes precisely defined andexpressed in terms of fundamental physical constants. While major portions of the SI system would still be based onthe kilogram, the kilogram would in turn be based on invariant, universal constants of nature. While this is aworthwhile objective and much work towards that end is ongoing, no alternative has yet achieved the uncertainty ofa couple parts in 108 (~20 µg) required to improve upon the IPK. However, as of April 2007, the U.S.’s NationalInstitute of Standards and Technology (NIST) had an implementation of the watt balance that was approaching thisgoal, with a demonstrated uncertainty of 36 µg.[37] See Watt balance, below.

Proposed future definitionsIn the following sections, wherever numeric equalities are shown in ‘concise form’—such as1.85487(14) × 1043—the two digits between the parentheses denote the uncertainty at 1σ standard deviation(68% confidence level) in the two least significant digits of the significand.

The kilogram is the only SI unit that is still defined by an artifact. Note that the meter was also once defined as anartifact (a single platinum-iridium bar with two marks on it). However, it was eventually redefined in terms ofinvariant, fundamental constants of nature (the wavelength of light emitted by krypton, and later the speed of light)so that the standard can be reproduced in different laboratories by following a written specification. Today,physicists are investigating various approaches to doing the same with the kilogram.In October 2010, the International Committee for Weights and Measures (known by its French-language initialsCIPM) voted to submit a resolution for consideration at the General Conference on Weights and Measures (CGPM),that the kilogram be defined in terms of the Planck constant, h.[38] [39] Such a definition would theoretically permitany apparatus that was capable of delineating the kilogram in terms of the Planck constant to be used as long as itpossessed sufficient precision, accuracy and stability. To date, there is one general type of apparatus showing suchpromise: the watt balance, which is discussed in detail below.In getting to the threshold of replacing the last artifact that underpins much of the International System of Units (SI),a variety of other fundamentally different technologies were considered and explored over many years. Some of theapproaches are fundamentally very different from each other. They too are covered below. Some of thesenow-abandoned approaches were based on equipment and procedures that would have enabled the reproducibleproduction of new, kilogram-mass prototypes on demand (albeit with extraordinary effort) using measurementtechniques and material properties that are ultimately based on, or traceable to, fundamental constants. Others werebased on devices that measured either the acceleration or weight of hand-tuned, kilogram test masses and whichexpressed their magnitudes in electrical terms via special components that permit traceability to fundamentalconstants. Measuring the weight of test masses would have required the precise measurement of the strength ofgravity in laboratories. All approaches would have precisely fixed one or more constants of nature at a defined value.

Kilogram 32

The watt balance

The NIST’s watt balance is a project of the U.S. Government to develop an “electronickilogram.” The vacuum chamber dome, which lowers over the entire apparatus, is

visible at top.

The watt balance is essentially asingle-pan weighing scale that measuresthe electric power necessary to oppose theweight of a kilogram test mass as it ispulled by earth’s gravity. It is a variationof an ampere balance in that it employs anextra calibration step that nulls the effectof geometry. The electric potential in thewatt balance is delineated by a Josephsonvoltage standard, which allows voltage tobe linked to an invariant constant ofnature with extremely high precision andstability. Its circuit resistance is calibratedagainst a quantum Hall resistancestandard.

The watt balance requires exquisitelyprecise measurement of gravity in alaboratory (see “FG‑5 absolutegravimeter” in External images, below).For instance, the NIST compensates forearth’s gravity gradient of 3.09 µGal per centimeter when the elevation of the center of the gravimeter differs fromthat of the nearby test mass in the watt balance; a change in the weight of a one-kilogram test mass that equates toabout 3.16 µg/cm.

In April 2007, the NIST’s implementation of the watt balance demonstrated a combined relative standard uncertainty(CRSU) of 36 µg and a short-term resolution of 10–15 µg.[37] [40] The UK’s National Physical Laboratory’s wattbalance demonstrated a CRSU of 70.3 µg in 2007.[41] That watt balance was disassembled and shipped in 2009 toCanada’s Institute for National Measurement Standards (part of the National Research Council), where research anddevelopment with the device could continue.

If the CGPM adopts the new proposal and the new definition of the kilogram becomes part of the SI, the Planckconstant (h), which is a measure that relates the energy of photons to their frequency, would be precisely fixed; forexample, to h = 6.626069 × 10−34 J·s (from the 2006 CODATA value of 6.62606896(33) × 10−34 J·s).[42] Onceagreed upon internationally, the kilogram would no longer be defined as the mass of the IPK. With the definition ofthe kilogram in terms of electric power and a frequency (the Planck constant’s J·s), electric power would be directlyidentical to mechanical power by definition rather than being a derivative. All the remaining units in theInternational System of Units (the SI) that today have dependencies upon the kilogram and the joule would also fallin place, their magnitudes ultimately defined, in part, in terms photon oscillations rather than a 132-year-old metalartifact stored in a vault.

Kilogram 33

Gravity is measured with exceptional precision with the help of alaser interferometer. The laser’s pattern of interference

fringes—the dark and light bands above—blooms at an ever fasterrate as a free-falling corner reflector drops inside an absolute

gravimeter. The pattern’s frequency sweep is timed by an atomicclock.

Gravity and the nature of the watt balance, whichoscillates test masses up and down against gravity, areexploited so that mechanical power is compared againstelectrical power, which is the square of voltage divided byelectrical resistance. However, the force of gravity variessignificantly—nearly one percent—depending uponwhere on earth’s surface the measurement is made (seeEarth’s gravity ). Even more problematic, there are subtleseasonal variations in gravity due to changes inunderground water tables, and even semimonthly anddiurnal changes due to tidal distortions in the earth’sshape caused by the moon. Although gravity would not bea term in the definition of the kilogram, gravity would bea crucial term used in the delineation of the kilogramwhen relating energy to power. Accordingly, the ‘gravity’term must be measured with at least as much precisionand accuracy as are the other terms. It is therefore highlydesirable that gravity measurements also be traceable to

fundamental constants of nature. For the most precise work in mass metrology, gravitational acceleration ismeasured using dropping-mass absolute gravimeters that contain an iodine-stabilized helium–neon laserinterferometer. The fringe-signal, frequency-sweep output from the interferometer is measured with a rubidiumatomic clock. Since this type of dropping-mass gravimeter derives its accuracy and stability from the constancy ofthe speed of light as well as the innate properties of helium, neon, and rubidium atoms, the ‘gravity’ term in thedelineation of an all-electronic kilogram is also measured in terms of invariants of nature—and with very highprecision. For instance, in the basement of the NIST’s Gaithersburg facility in 2009, when measuring the gravityacting upon Pt‑10Ir test masses (which are denser, smaller, and have a slightly lower center of gravity inside the wattbalance than stainless steel masses), the measured value was typically within 8 ppb of 9.80101644 m/s2.[43]

The virtue of electronic realizations like the watt balance is that the definition and dissemination of the kilogramwould no longer be dependent upon the stability of kilogram prototypes, which must be very carefully handled andstored. It would free physicists from the need to rely on assumptions about the stability of those prototypes,including those that would be manufactured under atom-counting schemes. Instead, hand-tuned, close-approximationmass standards would simply be weighed and documented as being equal to one kilogram plus an offset value. Withthe watt balance, the kilogram would not only be delineated in electrical and gravity terms, all of which are traceableto invariants of nature; it would be defined in electrical terms in a manner that is directly traceable to just twofundamental constants of nature. Mass artifacts—physical objects calibrated in a watt balance, including theIPK—would become transfer standards.Scales like the watt balance also permit more flexibility in choosing materials with especially desirable properties formass standards. For instance, Pt‑10Ir could continue to be used so that the specific gravity of newly produced massstandards would be the same as existing national primary and check standards (≈21.55 g/ml). This would reduce therelative uncertainty when making mass comparisons in air. Alternately, entirely different materials and constructionscould be explored with the objective of producing mass standards with greater stability. For instance,osmium-iridium alloys could be investigated if platinum’s propensity to absorb hydrogen (due to catalysis of VOCsand hydrocarbon-based cleaning solvents) and atmospheric mercury proved to be sources of instability. Also,vapor-deposited, protective ceramic coatings like nitrides could be investigated for their suitability to isolate thesenew alloys.

Kilogram 34

The challenge with watt balances is not only in reducing their uncertainty, but also in making them truly practicalrealizations of the kilogram. Nearly every aspect of watt balances and their support equipment requires suchextraordinarily precise and accurate, state-of-the-art technology that—unlike a device like an atomic clock—fewcountries would currently choose to fund their operation. For instance, the NIST’s watt balance used four resistancestandards in 2007, each of which was rotated through the watt balance every two to six weeks after being calibratedin a different part of NIST headquarters facility in Gaithersburg, Maryland. It was found that simply moving theresistance standards down the hall to the watt balance after calibration altered their values 10 ppb (equivalent to10 µg) or more.[44] Present-day technology is insufficient to permit stable operation of watt balances between evenbiannual calibrations. If the kilogram is defined in terms of the Planck constant, it is likely there will only be afew—at most—watt balances initially operating in the world.Alternative approaches to redefining the kilogram that were fundamentally different from the watt balance wereexplored to varying degrees with some abandoned, as follows:

Atom-counting approaches

Carbon-12

Though not offering a practical realization, this definition would precisely define the magnitude of the kilogram interms of a certain number of carbon‑12 atoms. Carbon‑12 (12C) is an isotope of carbon. The mole is currentlydefined as “the quantity of entities (elementary particles like atoms or molecules) equal to the number of atoms in 12grams of carbon‑12.” Thus, the current definition of the mole requires that 1000⁄12 (83⅓) moles of 12C has a mass ofprecisely one kilogram. The number of atoms in a mole, a quantity known as the Avogadro constant, isexperimentally determined, and the current best estimate of its value is 6.02214179(30) × 1023 entities per mole(CODATA, 2006). This new definition of the kilogram proposes to fix the Avogadro constant at precisely6.02214179 × 1023 with the kilogram being defined as “the mass equal to that of 1000⁄12 · 6.02214179 × 1023 atoms of12C.”The accuracy of the measured value of the Avogadro constant is currently limited by the uncertainty in the value ofthe Planck constant—a measure relating the energy of photons to their frequency. That relative standard uncertaintyhas been 50 parts per billion (ppb) since 2006. By fixing the Avogadro constant, the practical effect of this proposalwould be that the uncertainty in the mass of a 12C atom—and the magnitude of the kilogram—could be no betterthan the current 50 ppb uncertainty in the Planck constant. Under this proposal, the magnitude of the kilogram wouldbe subject to future refinement as improved measurements of the value of the Planck constant become available;electronic realizations of the kilogram would be recalibrated as required. Conversely, an electronic definition of thekilogram (see Electronic approaches, below), which would precisely fix the Planck constant, would continue toallow 83⅓ moles of 12C to have a mass of precisely one kilogram but the number of atoms comprising a mole (theAvogadro constant) would continue to be subject to future refinement.A variation on a 12C-based definition proposes to define the Avogadro constant as being precisely 84,446,8863

(≈6.02214098 × 1023) atoms. An imaginary realization of a 12-gram mass prototype would be a cube of 12C atomsmeasuring precisely 84,446,886 atoms across on a side. With this proposal, the kilogram would be defined as “themass equal to 84,446,8863 × 83⅓ atoms of 12C.” The value 84,446,886 was chosen because it has a special property;its cube (the proposed new value for the Avogadro constant) is evenly divisible by twelve. Thus with this definitionof the kilogram, there would be an integer number of atoms in one gram of 12C: 50,184,508,190,229,061,679,538atoms.[45] [46]

Kilogram 35

Avogadro project

One of the master opticians at the AustralianCentre for Precision Optics [47] (ACPO) is

holding a 1 kg, single-crystal silicon sphere forthe Avogadro project. These spheres are amongthe roundest man-made objects in the world. If

the best of these spheres were scaled to the size ofearth, its high point—a continent-size

area—would gently rise to a maximum elevationof only 2.4 meters above “sea level.”[48]

Another Avogadro constant-based approach, known as the Avogadroproject, would define and delineate the kilogram as a softball-size(93.6 mm diameter) sphere of silicon atoms. Silicon was chosenbecause a commercial infrastructure with mature processes for creatingdefect-free, ultra-pure monocrystalline silicon already exists to servicethe semiconductor industry. To make a practical realization of thekilogram, a silicon boule (a rod-like, single-crystal ingot) would beproduced. Its isotopic composition would be measured with a massspectrometer to determine its average relative atomic mass. The boulewould be cut, ground, and polished into spheres. The size of a selectsphere would be measured using optical interferometry to anuncertainty of about 0.3 nm on the radius—roughly a single atomiclayer. The precise lattice spacing between the atoms in its crystalstructure (≈192 pm) would be measured using a scanning X-rayinterferometer. This permits its atomic spacing to be determined withan uncertainty of only three parts per billion. With the size of thesphere, its average atomic mass, and its atomic spacing known, therequired sphere diameter can be calculated with sufficient precisionand uncertainty to enable it to be finish-polished to a target mass of onekilogram.

Experiments are being performed on the Avogadro Project’s siliconspheres to determine whether their masses are most stable when storedin a vacuum, a partial vacuum, or ambient pressure. However, notechnical means currently exist to prove a long-term stability any better than that of the IPK’s because the mostsensitive and accurate measurements of mass are made with dual-pan balances like the BIPM’s FB‑2 flexure-stripbalance (see External links, below). Balances can only compare the mass of a silicon sphere to that of a referencemass. Given the latest understanding of the lack of long-term mass stability with the IPK and its replicas, there is noknown, perfectly stable mass artifact to compare against. Single-pan scales, which measure weight relative to aninvariant of nature, are not precise to the necessary long-term uncertainty of 10–20 parts per billion. Another issue tobe overcome is that silicon oxidizes and forms a thin layer (equivalent to 5–20 silicon atoms) of silicon dioxide(quartz) and silicon monoxide. This layer slightly increases the mass of the sphere, an effect which must beaccounted for when polishing the sphere to its finish dimension. Oxidation is not an issue with platinum and iridium,both of which are noble metals that are roughly as cathodic as oxygen and therefore don’t oxidize unless coaxed todo so in the laboratory. The presence of the thin oxide layer on a silicon-sphere mass prototype places additionalrestrictions on the procedures that might be suitable to clean it to avoid changing the layer’s thickness or oxidestoichiometry.

All silicon-based approaches would fix the Avogadro constant but vary in the details of the definition of the kilogram. One approach would use silicon with all three of its natural isotopes present. About 7.78% of silicon comprises the two heavier isotopes: 29Si and 30Si. As described in Carbon‑12 above, this method would define the magnitude of the kilogram in terms of a certain number of 12C atoms by fixing the Avogadro constant; the silicon sphere would be the practical realization. This approach could accurately delineate the magnitude of the kilogram because the masses of the three silicon nuclides relative to 12C are known with great precision (relative uncertainties of 1 ppb or better). An alternative method for creating a silicon sphere-based kilogram proposes to use isotopic separation techniques to enrich the silicon until it is nearly pure 28Si, which has a relative atomic mass of 27.9769265325(19). With this approach, the Avogadro constant would not only be fixed, but so too would the

Kilogram 36

atomic mass of 28Si. As such, the definition of the kilogram would be decoupled from 12C and the kilogram wouldinstead be defined as 1000⁄27.9769265325 · 6.02214179 × 1023 atoms of 28Si (≈35.74374043 fixed moles of 28Si atoms).Physicists could elect to define the kilogram in terms of 28Si even when kilogram prototypes are made of naturalsilicon (all three isotopes present). Even with a kilogram definition based on theoretically pure 28Si, a silicon-sphereprototype made of only nearly pure 28Si would necessarily deviate slightly from the defined number of moles ofsilicon to compensate for various chemical and isotopic impurities as well as the effect of surface oxides.[49]

Ion accumulation

Another Avogadro-based approach, ion accumulation, since abandoned, would have defined and delineated thekilogram by precisely creating new metal prototypes on demand. It would have done so by accumulating gold orbismuth ions (atoms stripped of an electron) and counted them by measuring the electrical current required toneutralize the ions. Gold (197Au) and bismuth (209Bi) were chosen because they can be safely handled and have thetwo highest atomic masses among the mononuclidic elements that is effectively non-radioactive (bismuth) or isperfectly stable (gold). See also Table of nuclides.[50]

With a gold-based definition of the kilogram for instance, the relative atomic mass of gold could have been fixed asprecisely 196.9665687, from the current value of 196.9665687(6). As with a definition based upon carbon‑12, theAvogadro constant would also have been fixed. The kilogram would then have been defined as “the mass equal tothat of precisely 1000⁄196.9665687 · 6.02214179 × 1023 atoms of gold” (precisely 3,057,443,620,887,933,963,384,315atoms of gold or about 5.07700371 fixed moles).In 2003, German experiments with gold at a current of only 10 µA demonstrated a relative uncertainty of 1.5%.[51]

Follow-on experiments using bismuth ions and a current of 30 mA were expected to accumulate a mass of 30 g in sixdays and to have a relative uncertainty of better than 1 part in 106.[52] Ultimately, ion‑accumulation approachesproved to be unsuitable. Measurements required months and the data proved too erratic for the technique to beconsidered a viable future replacement to the IPK.[53]

Among the many technical challenges of the ion-deposition apparatus was obtaining a sufficiently high ion current(mass deposition rate) while simultaneously decelerating the ions so they could all deposit onto a target electrodeembedded in a balance pan. Experiments with gold showed the ions had to be decelerated to very low energies toavoid sputtering effects—an phenomenon whereby ions that had already been counted ricochet off the targetelectrode or even dislodged atoms that had already been deposited. The deposited mass fraction in the 2003 Germanexperiments only approached very close to 100% at ion energies of less than around 1 eV (<1 km/s for gold).[51]

If the kilogram had been defined as a precise quantity of gold or bismuth atoms deposited with an electric current,not only would the Avogadro constant and the atomic mass of gold or bismuth had to have been precisely fixed, butalso the value of the elementary charge (e), likely to 1.602176487 × 10−19 C (from the present 2006 CODATA valueof 1.602176487(40) × 10−19). Doing so would have effectively defined the ampere as a flow of 1⁄1.602176487 × 10−19(6,241,509,647,120,417,390) electrons per second past a fixed point in an electric circuit. The SI unit of mass wouldhave been fully defined by having precisely fixed the values of the Avogadro constant and elementary charge, and byexploiting the fact that the atomic masses of bismuth and gold atoms are invariant, universal constants of nature.Beyond the slow speed of making a new mass standard and the poor reproducibility, there were other intrinsic shortcomings to the ion‑accumulation approach that proved to be formidable obstacles to ion-accumulation-based techniques becoming a practical realization. The apparatus necessarily required that the deposition chamber have an integral balance system to enable the convenient calibration of a reasonable quantity of transfer standards relative to any single internal ion-deposited prototype. Furthermore, the mass prototypes produced by ion deposition techniques would have been nothing like the freestanding platinum-iridium prototypes currently in use; they would have been deposited onto—and become part of—an electrode imbedded into one pan of a special balance integrated into the device. Moreover, the ion-deposited mass wouldn’t have had a hard, highly polished surface that can be vigorously cleaned like those of current prototypes. Gold, while dense and a noble metal (resistant to oxidation and the

Kilogram 37

formation of other compounds), is extremely soft so an internal gold prototype would have to be kept well isolatedand scrupulously clean to avoid contamination and the potential of wear from having to remove the contamination.Bismuth, which is an inexpensive metal used in low-temperature solders, slowly oxidizes when exposed toroom-temperature air and forms other chemical compounds and so would not have produced stable reference massesunless it was continually maintained in a vacuum or inert atmosphere.

Ampere-based force

A magnet floating above a superconductor bathedin liquid nitrogen demonstrates perfect

diamagnetic levitation via the Meissner effect.Experiments with an ampere-based definition of

the kilogram flipped this arrangementupside-down: an electric field accelerated a

superconducting test mass supported by fixedmagnets.

This approach would define the kilogram as “the mass which would beaccelerated at precisely 2 × 10−7 m/s2 when subjected to the per-meterforce between two straight parallel conductors of infinite length, ofnegligible circular cross section, placed one meter apart in vacuum,through which flow a constant current of 1⁄1.602176487 × 10−19(≈6,241,509,647,120,417,390) elementary charges per second.”

Effectively, this would define the kilogram as a derivative of theampere rather than present relationship, which defines the ampere as aderivative of the kilogram. This redefinition of the kilogram wouldspecify elementary charge (e) as precisely 1.602176487 × 10−19

coulomb rather than the current 2006 CODATA value of1.602176487(40) × 10−19. Effectively, the coulomb would be the sumof 6,241,509,647,120,417,390 elementary charges. It would necessarilyfollow that the ampere (one coulomb per second) would also becomean electrical current of this precise quantity of elementary charges persecond passing a given point in an electric circuit.

The virtue of a practical realization based upon this definition is thatunlike the watt balance and other scale-based methods, all of whichrequire the careful characterization of gravity in the laboratory, this method delineates the magnitude of the kilogramdirectly in the very terms that define the nature of mass: acceleration due to an applied force. Unfortunately, it isextremely difficult to develop a practical realization based upon accelerating masses. Experiments over a period ofyears in Japan with a superconducting, 30 g mass supported by diamagnetic levitation never achieved an uncertaintybetter than ten parts per million. Magnetic hysteresis was one of the limiting issues. Other groups performed similarresearch that used different techniques to levitate the mass.[54] [55]

Kilogram 38

SI multiplesBecause SI prefixes may not be concatenated (serially linked) within the name or symbol for a unit of measure, SIprefixes are used with the gram, not the kilogram, which already has a prefix as part of its name.[56] For instance,one-millionth of a kilogram is 1 mg (one milligram), not 1 µkg (one microkilogram).

SI multiples for gram (g)

Submultiples Multiples

Value Symbol Name Value Symbol Name

10−1 g dg decigram 101 g dag decagram

10−2 g cg centigram 102 g hg hectogram

10−3 g mg milligram 103 g kg kilogram

10−6 g µg microgram (mcg) 106 g Mg megagram (tonne)

10−9 g ng nanogram 109 g Gg gigagram

10−12 g pg picogram 1012 g Tg teragram

10−15 g fg femtogram 1015 g Pg petagram

10−18 g ag attogram 1018 g Eg exagram

10−21 g zg zeptogram 1021 g Zg zettagram

10−24 g yg yoctogram 1024 g Yg yottagram

Common prefixes are in bold face.[57]

• When the Greek lowercase “µ” (mu) in the symbol of microgram is typographically unavailable, it isoccasionally—although not properly—replaced by Latin lowercase “u”.

• The microgram is often abbreviated “mcg”, particularly in pharmaceutical and nutritional supplement labeling, toavoid confusion since the “µ” prefix is not well recognized outside of technical disciplines.[58] Note however, thatthe abbreviation “mcg”, is also the symbol for an obsolete CGS unit of measure known as the “millicentigram”,which is equal to 10 µg.

• The unit name “megagram” is rarely used, and even then, typically only in technical fields in contexts whereespecially rigorous consistency with the units of measure is desired. For most purposes, the unit “tonne” is insteadused. The tonne and its symbol, t, were adopted by the CIPM in 1879. It is a non-SI unit accepted by the BIPMfor use with the SI. According to the BIPM, “In English speaking countries this unit is usually called ‘metricton’.”[59] Note also that the unit name “megatonne” or “megaton” (Mt) is often used in general-interest literature ongreenhouse gas emissions whereas the equivalent value in scientific papers on the subject is often the “teragram”(Tg).

Kilogram 39

Glossary• Abstracted: Isolated and its effect changed in form, often simplified or made more accessible in the process.• Artifact: A simple human-made object used directly as a comparative standard in the measurement of a physical

quantity.• Check standard:

1. A standard body’s backup replica of the International Prototype Kilogram (IPK).2. A secondary kilogram mass standard used as a stand-in for the primary standard during routine calibrations.

• Definition: A formal, specific, and exact specification.• Delineation: The physical means used to mark a boundary or express the magnitude of an entity.• Disseminate: To widely distribute the magnitude of a unit of measure, typically via replicas and transfer

standards.• IPK: Abbreviation of “International Prototype Kilogram” (CG image), the mass artifact in France internationally

recognized as having the defining mass of precisely one kilogram.• Magnitude: The extent or numeric value of a property• National prototype: A replica of the IPK possessed by a nation.• Practical realization: A readily reproducible apparatus to conveniently delineate the magnitude of a unit of

measure.• Primary national standard:

1. A replica of the IPK possessed by a nation2. The least used replica of the IPK when a nation possesses more than one.

• Prototype:1. A human-made object that serves as the defining comparative standard in the measurement of a physical

quantity.2. A human-made object that serves as the comparative standard in the measurement of a physical quantity.3. The IPK and any of its replicas

• Replica: An official copy of the IPK.• Sister copy: One of six official copies of the IPK that are stored in the same safe as the IPK and are used as check

standards by the BIPM.• Transfer standard: An artifact or apparatus that reproduces the magnitude of a unit of measure in a different,

usually more practical, form.

See also

• 1795 in science • Metric system• 1799 in science • Metric ton• Inertia • Mass• International System of Units (SI) • Mass versus weight• International Bureau of Weights and Measures (BIPM) • Milligrams per cent• International Committee for Weights and Measures (CIPM) • National Institute of Standards and Technology (NIST)• General Conference on Weights and Measures (CGPM) • Newton• Gram • SI base units• Grave (orig. name of the kilogram, history of) • Standard gravity• Gravimetry • Watt balance• Kilogram-force • Weight• Liter

Kilogram 40

Notes[1] One kilogram at rest has an equivalent energy approximately equal to the energy of photons whose frequencies sum to this value.[2] The spelling kilogram is the modern spelling used by the International Bureau of Weights and Measures (BIPM), the U.S. National Institute

of Standards and Technology (NIST), the UK’s National Measurement Office, National Research Council Canada, and Australia’s NationalMeasurement Institute. The traditional British-English spelling kilogramme is sometimes also used.

[3] "Resolution of the 1st CGPM (1889)" (http:/ / www. bipm. org/ en/ CGPM/ db/ 1/ 1/ ). BIPM. .[4] Also known by its French-language name Le Grand K.[5] "Appendix 8 – Customary System of Weights and Measures" (http:/ / physics. nist. gov/ Pubs/ SP447/ app8. pdf) (1.6 MB PDF). National

Bureau of Standards (predecessor of the NIST). ."Frequently Asked Questions" (http:/ / inms-ienm. nrc-cnrc. gc. ca/ faq_mech_e. html#Q1). National Research Council Canada. ."Converting Measurements to Metric—NIST FAQs" (http:/ / www. nist. gov/ public_affairs/ faqs/ qmetric. htm). NIST. ."Metric Conversions" (http:/ / www. nmo. bis. gov. uk/ faqs. aspx?ID=8). UK National Measurement Office. ."Fed-Std-376B, Preferred Metric Units for General Use By the Federal Government" (http:/ / ts. nist. gov/ WeightsAndMeasures/ Metric/upload/ fs376-b. pdf) (294 KB PDF). NIST. .

[6] 94th Meeting of the International Committee for Weights and Measures (2005) Recommendation 1: Preparative steps towards new definitionsof the kilogram, the ampere, the kelvin and the mole in terms of fundamental constants (http:/ / www. bipm. org/ utils/ en/ pdf/CIPM2005-EN. pdf)

[7] 23rd General Conference on Weights and Measures (2007). Resolution 12: On the possible redefinition of certain base units of theInternational System of Units (SI) (http:/ / www. bipm. org/ utils/ en/ pdf/ Resol23CGPM-EN. pdf).

[8] In professional metrology (the science of measurement), the acceleration of earth’s gravity is taken as standard gravity (symbol: gn), which isdefined as precisely 9.80665 meters per square second (m/s2). The expression “1 m/s2 ” means that for every second that elapses, velocitychanges an additional 1 meter per second. In more familiar terms: an acceleration of 1 m/s2 can also be expressed as a rate of change invelocity of precisely 3.6 km/h per second (≈2.2 mph per second).

[9] Matter has invariant mass assuming it is not traveling at a relativistic speed with respect to an observer. According to Einstein’s theory ofspecial relativity, the relativistic mass (apparent mass with respect to an observer) of an object or particle with rest mass m0 increases with itsspeed as M = γm0 (where γ is the Lorentz factor). This effect is vanishingly small at everyday speeds, which are many orders of magnitude lessthan the speed of light. For example, to change the mass of a kilogram by 1 μg (1 ppb, about the level of detection by current technology)would require moving it at 0.0045% of the speed of light relative to an observer, which is 13.4 km/s (30,000 mph).

As regards the kilogram, relativity’s effect upon the constancy of matter’s mass is simply an interesting scientificphenomenon that has zero effect on the definition of the kilogram and its practical realizations.[10] "Decree on weights and measures" (http:/ / smdsi. quartier-rural. org/ histoire/ 18germ_3. htm). 7 April 1795. . "Gramme, le poids absolu

d'un volume d'eau pure égal au cube de la centième partie du mètre , et à la température de la glace fondante."[11] An Essay towards a Real Character and a Philosophical Language (Reproduction) (http:/ / www. metricationmatters. com/ docs/

WilkinsTranslationLong. pdf)[12] An Essay towards a Real Character and a Philosophical Language (Transcription) (http:/ / www. metricationmatters. com/ docs/

WilkinsTranslationShort. pdf)[13] The same decree also defined the liter as follows: “Liter: the measure of volume, both for liquid and solids, for which the displacement

would be that of a cube [with sides measuring] one-tenth of a meter.” Original text: “Litre, la mesure de capacité, tant pour les liquides quepour les matières sèches, dont la contenance sera celle du cube de la dixièrne partie du mètre.”

[14] Modern measurements show the temperature at which water reaches maximum density is 3.984 °C. However, the scientists at the close ofthe 18th century concluded that the temperature was 4 °C.

[15] "L'histoire du mètre, la détermination de l'unité de poids" (http:/ / histoire. du. metre. free. fr/ fr/ index. htm). .[16] The provisional kilogram standard had been fabricated in accordance with a single, inaccurate measurement of the density of water made

earlier by Antoine Lavoisier and René Just Haüy, which showed that one cubic decimeter of distilled water at 0 °C had a mass of 18,841grains in France’s soon-to-be-obsoleted poids de marc system. The newer, highly accurate measurements by Lefèvre‑Gineau and Fabbroniconcluded that the mass of a cubic decimeter of water at the new temperature of 4 °C—a condition at which water is denser—was actually lessmassive, at 18,827.15 grains, than the earlier inaccurate value assumed for 0 °C water.

France’s metric system had been championed by Charles Maurice de Talleyrand‑Périgord. On 30 March 1791, fourdays after Talleyrand forwarded a specific proposal on how to proceed with the project, the French governmentordered a committee known as the Academy to commence work on accurately determining the magnitude of the baseunits of the new metric system. The Academy divided the task among five commissions. The commission chargedwith determining the mass of a cubic decimeter of water originally comprised Lavoisier and Haüy but their work wasfinished by Louis Lefèvre‑Gineau and Giovanni Fabbroni.Neither Lavoisier nor Haüy can be blamed for participating in an initial—and inaccurate—measurement and for leaving the final work to Lefèvre‑Gineau and Fabbroni to finish in 1799. As a member of the Ferme générale,

Kilogram 41

Lavoisier was also one of France’s 28 tax collectors. He was consequently convicted of treason during the waningdays of the Reign of Terror period of the French Revolution and beheaded on 8 May 1794. Lavoisier’s partner, Haüy,was also thrown into prison and was himself at risk of going to the guillotine but his life was spared after a renownedFrench naturalist interceded.[17] Ronald Edward Zupko (1990). Revolution in Measurement: Western European Weights and Measures Since the Age of Science. DIANE

Publishing.[18] New Techniques in the Manufacture of Platinum-Iridium Mass Standards, T. J. Quinn, Platinum Metals Rev., 1986, 30, (2), pp. 74–79[19] Isotopic composition and temperature per London South Bank University’s “List of physicochemical data concerning water” (http:/ / www1.

lsbu. ac. uk/ water/ data. html), density and uncertainty per NIST Standard Reference Database Number 69 (http:/ / webbook. nist. gov/chemistry/ ) (retrieved 5 April 2010)

[20] Prototype No. 8(41) was accidentally stamped with the number 41, but its accessories carry the proper number 8. Since there is no prototypemarked 8, this prototype is referred to as 8(41).

[21] G. Girard (1994). "The Third Periodic Verification of National Prototypes of the Kilogram (1988–1992)". Metrologia 31 (4): 317–336.doi:10.1088/0026-1394/31/4/007.

[22] The other two Pt‑10Ir standards owned by the U.S. are K79, from a new series of prototypes (K64–K80) that were diamond-turned directlyto a finish mass, and K85, which is used for watt balance experiments (see Watt balance, above).

[23] Extraordinary care is exercised when transporting prototypes. In 1984, the K4 and K20 prototypes were hand-carried in the passengersection of separate commercial airliners.

[24] Z. J. Jabbour; S. L. Yaniv (Jan–Feb 2001). 3.5 "The Kilogram and Measurements of Mass and Force" (http:/ / nvl. nist. gov/ pub/ nistpubs/jres/ 106/ 1/ j61jab. pdf). J. Res. Natl. Inst. Stand. Technol. 106 (1): 25–46. 3.5.

[25] Before the BIPM’s published report in 1994 detailing the relative change in mass of the prototypes, different standard bodies used differenttechniques to clean their prototypes. The NIST’s practice before then was to soak and rinse its two prototypes first in benzene, then in ethanol,and to then clean them with a jet of bi-distilled water steam.

[26] Mills, Ian M.; Mohr, Peter J; Quinn, Terry J; Taylor, Barry N; Williams, Edwin R (April 2005). "Redefinition of the kilogram: a decisionwhose time has come" (http:/ / membership. acs. org/ N/ NOME/ appendix_i pt_1_082007. pdf). Metrologia 42 (2): 71–80.doi:10.1088/0026-1394/42/2/001. . Retrieved 25 November 2009.

[27] Note that if the ∆ 50 µg between the IPK and its replicas was entirely due to wear, the IPK would have to have lost 150 million billion moreplatinum and iridium atoms over the last century than its replicas. That there would be this much wear, much less a difference of thismagnitude, is thought unlikely; 50 µg is roughly the mass of a fingerprint. Specialists at the BIPM in 1946 carefully conducted cleaningexperiments and concluded that even vigorous rubbing with a chamois—if done carefully—did not alter the prototypes’ mass. More recentcleaning experiments at the BIPM, which were conducted on one particular prototype (K63), and which benefited from the then-new NBS‑2balance, demonstrated 2 µg stability.

Many theories have been advanced to explain the divergence in the masses of the prototypes. One theory posits thatthe relative change in mass between the IPK and its replicas is not one of loss at all and is instead a simple matterthat the IPK has gained less than the replicas. This theory begins with the observation that the IPK is uniquely storedunder three nested bell jars whereas its six sister copies stored alongside it in the vault as well as the other replicasdispersed throughout the world are stored under only two. This theory is also founded on two other facts: thatplatinum has a strong affinity for mercury, and that atmospheric mercury is significantly more abundant in theatmosphere today than at the time the IPK and its replicas were manufactured. The burning of coal is a majorcontributor to atmospheric mercury and both Denmark and Germany have high coal shares in electrical generation.Conversely, electrical generation in France, where the IPK is stored, is mostly nuclear. This theory is supported bythe fact that the mass divergence rate—relative to the IPK—of Denmark’s prototype, K48, since it took possession in1949 is an especially high 78 µg per century while that of Germany’s prototype has been even greater at 126µg/century ever since it took possession of K55 in 1954. However, still other data for other replicas isn’t supportiveof this theory. This mercury absorption theory is just one of many advanced by the specialists to account for therelative change in mass. To date, each theory has either proven implausible, or there are insufficient data or technicalmeans to either prove or disprove it.[28] Davis, Richard (December 2003). "The SI unit of mass" (http:/ / charm. physics. ucsb. edu/ courses/ ph21_05/ kilogrampaper. pdf).

Metrologia 40 (6): 299–305. doi:10.1088/0026-1394/40/6/001. . Retrieved 25 November 2009.[29] R. S. Davis (July–August 1985). "Recalibration of the U.S. National Prototype Kilogram" (http:/ / nvl. nist. gov/ pub/ nistpubs/ jres/ 090/ 4/

V90-4. pdf). Journal of Research of the National Bureau of Standards 90 (4). .[30] Conjecture why the IPK drifts, R. Steiner, NIST, 11 Sept. 2007.[31] Even well respected organizations incorrectly represent the relative nature of the mass divergence as being one of mass loss, as exemplified

by this site at Science Daily (http:/ / www. sciencedaily. com/ releases/ 2007/ 09/ 070921110735. htm), and this site at PhysOrg.com (http:/ /

Kilogram 42

www. physorg. com/ news109595312. html), and this site at Sandia National Laboratories. (http:/ / www. sandia. gov/ LabNews/ 080201.html) The root of the problem is often the reporters’ failure to correctly interpret or paraphrase nuanced scientific concepts, as exemplified bythis 12 September 2007 story (http:/ / www. physorg. com/ news108836759. html) by the Associated Press published on PhysOrg.com. In thatAP story, Richard Davis—who used to be the NIST’s kilogram specialist and now works for the BIPM in France—was correctly quoted by theAP when he stated that the mass change is a relative issue. Then the AP summarized the nature of issue with this lead-in to the story: “Akilogram just isn't what it used to be. The 118-year-old cylinder that is the international prototype for the metric mass, kept tightly under lockand key outside Paris, is mysteriously losing weight — if ever so slightly.” Like many of the above-linked sites, the AP also misreported theage of the IPK, using the date of its adoption as the mass prototype, not the date of the cylinder’s manufacture. This is a mistake evenScientific American fell victim to in a print edition.

[32] The mean change in mass of the first batch of replicas relative to the IPK over one hundred years is +23.5 µg with a standard deviation of30 µg. Per The Third Periodic Verification of National Prototypes of the Kilogram (1988–1992), G. Girard, Metrologia 31 (1994) Pg. 323,Table 3. Data is for prototypes K1, K5, K6, K7, K8(41), K12, K16, K18, K20, K21, K24, K32, K34, K35, K36, K37, K38, and K40; andexcludes K2, K23, and K39, which are treated as outliers. This is a larger data set than is shown in the chart at the top of this section, whichcorresponds to Figure 7 of G. Girard’s paper.

[33] Report to the CGPM, 14th meeting of the Consultative Committee for Units (CCU), April 2001, 2. (ii); General Conference on Weights andMeasures, 22nd Meeting, October 2003, which stated “The kilogram is in need of a new definition because the mass of the prototype is knownto vary by several parts in 108 over periods of time of the order of a month…” ( 3.2 MB ZIP file, here (http:/ / www. bipm. org/ utils/ en/ zip/CGPM22. zip)).

[34] BBC, Getting the measure of a kilogram (http:/ / news. bbc. co. uk/ 1/ hi/ sci/ tech/ 7084099. stm).[35] General section citations: Recalibration of the U.S. National Prototype Kilogram, R. S. Davis, Journal of Research of the National Bureau of

Standards, 90, No. 4, July–August 1985 ( 5.5 MB PDF, here (http:/ / nvl. nist. gov/ pub/ nistpubs/ jres/ 090/ 4/ V90-4. pdf)); and The Kilogramand Measurements of Mass and Force, Z. J. Jabbour et al., J. Res. Natl. Inst. Stand. Technol. 106, 2001, 25–46 ( 3.5 MB PDF, here (http:/ /nvl. nist. gov/ pub/ nistpubs/ jres/ 106/ 1/ j61jab. pdf))

[36] Assuming the past trend continues, whereby the mean change in mass of the first batch of replicas relative to the IPK over one hundred yearswas +23.5 σ30 µg.

[37] Uncertainty Improvements of the NIST Electronic Kilogram, RL Steiner et al., Instrumentation and Measurement, IEEE Transactions on, 56Issue 2, April 2007, 592–596

[38] NIST Backs Proposal for a Revamped System of Measurement Units (http:/ / www. nist. gov/ pml/ wmd/ 20101026_si. cfm)[39] Ian Mills (29 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units" (http:/ / www. bipm. org/ utils/

en/ pdf/ si_brochure_draft_ch2. pdf). CCU. . Retrieved 1 January 2011.[40] The combined relative standard uncertainty (CRSU) of these measurements, as with all other tolerances and uncertainties in this article

unless otherwise noted, have a 1σ standard deviation, which equates to a confidence level of about 68%; that is to say, 68% of themeasurements fall within the stated tolerance.

[41] "An initial measurement of Planck's constant using the NPL Mark II watt balance", I.A. Robinson et al., Metrologia 44 (2007), 427–440;NPL: NPL Watt Balance (http:/ / www. npl. co. uk/ server. php?show=ConWebDoc. 2029)

[42] The Planck constant’s unit of measure “joule-second” (J·s) may be more easily understood when expressed as a “joule per hertz” (J/Hz).Universally, an individual photon has an energy that is proportional to its frequency. This relationship is 6.62606896(33) × 10−34 J/Hz and1.50919045(8) × 1033 Hz/J.

[43] R. Steiner, Watts in the watt balance, NIST, 16 Oct. 2009.[44] R. Steiner, No FG-5?, NIST, 30 Nov. 2007. “We rotate between about 4 resistance standards, transferring from the calibration lab to my lab

every 2–6 weeks. Resistors do not transfer well, and sometimes shift at each transfer by 10 ppb or more.”[45] Georgia Tech, “A Better Definition for the Kilogram?” (http:/ / gtresearchnews. gatech. edu/ definition-kilogram/ ) 21 September 2007 (press

release).[46] The uncertainty in the Avogadro constant narrowed since this proposal was first submitted to American Scientist for publication. The 2006

CODATA value for the Avogadro constant has a relative standard uncertainty of 50 parts per billion and the only cube root values within thisuncertainty must fall within the range of 84,446,889.8 ±1.4; that is, there are only three integer cube roots (…89, …90, and …91) in this rangeand the value 84,446,886 falls outside of it. Unfortunately, none of the three integer values within the range possess the property of their cubesbeing divisible by twelve; one gram of 12C could not comprise an integer number of atoms. If the value 84,446,886 was adopted to define thekilogram, many other constants of nature and electrical units would have to be revised an average of about 0.13 part per million. Thestraightforward adjustment to this approach advanced by the group would instead define the kilogram as “the mass equal to 84,446,8903 ×83⅓ atoms of carbon‑12.” This proposed value for the Avogadro constant (≈6.02214184 × 1023) falls neatly within the 2006 CODATA valueof 6.02214179(30) × 1023 and the proposed definition of the kilogram produces an integer number of atoms in 12 grams of carbon‑12(602,214,183,858,071,454,769,000 atoms), but not for 1 gram or 1 kilogram.

[47] http:/ / www. acpo. csiro. au/[48] The sphere shown in the photograph has an out-of-roundness value (peak to valley on the radius) of 50 nm. According to ACPO, they

improved on that with an out-of-roundness of 35 nm. On the 93.6 mm diameter sphere, an out-of-roundness of 35 nm (undulations of ±17.5 nm) is a fractional roundness (∆r /r ) = 3.7 × 10−7. Scaled to the size of earth, this is equivalent to a maximum deviation from sea level of only 2.4 m. The roundness of that ACPO sphere is exceeded only by two of the four fused-quartz gyroscope rotors flown on Gravity Probe B, which were manufactured in the late 1990s and given their final figure at the W.W. Hansen Experimental Physics Lab (http:/ / hepl.

Kilogram 43

stanford. edu/ ) at Stanford University. Particularly, “Gyro 4” is recorded in the Guinness database of world records (their database, not in theirbook) as the world’s roundest man-made object. According to a published report ( 221 kB PDF, here (http:/ / aa. stanford. edu/ aeroastro/posters2007/ Polhode_Motion. pdf)) and the GP‑B public affairs coordinator at Stanford University, of the four gyroscopes onboard the probe,Gyro 4 has a maximum surface undulation from a perfect sphere of 3.4 ±0.4 nm on the 38.1 mm diameter sphere, which is a ∆r /r =1.8 × 10−7. Scaled to the size of earth, this is equivalent to an undulation the size of North America rising slowly up out of the sea (inmolecular-layer terraces 11.9 cm high), reaching a maximum elevation of 1.14 ±0.13 m in Nebraska, and then gradually sloping back down tosea level on the other side of the continent.

[49] NPL: Avogadro Project (http:/ / www. npl. co. uk/ server. php?show=ConWebDoc. 2050); Australian National Measurement Institute:Redefining the kilogram through the Avogadro constant (http:/ / www. measurement. gov. au/ index. cfm?event=object. showContent&objectID=7CBA5E62-BCD6-81AC-15017BE81748EF4B); and Australian Centre for Precision Optics: The Avogadro Project (http:/ / www.acpo. csiro. au/ avogadro. htm)

[50] In 2003, the same year the first gold-deposition experiments were conducted, physicists found that the only naturally occurring isotope ofbismuth, 209Bi, is actually very slightly radioactive, with the longest known radioactive half-life of any naturally occurring element that decaysvia alpha radiation—a half-life of 19 ± 2 × 1018 yr. As this is 1.4 billion times the age of the universe, 209Bi is considered a stable isotope formost practical applications (those unrelated to such disciplines as nucleocosmochronology and geochronology). In other terms,99.999999983% of the bismuth that existed on earth 4.567 billion years ago still exists today. Only two mononuclidic elements are heavierthan bismuth and only one approaches its stability: thorium. Long considered a possible replacement for uranium in nuclear reactors, thoriumcan cause cancer when inhaled because it is over 1.2 billion times more radioactive than bismuth. It also has such a strong tendency to oxidizethat its powders are pyrophoric. These characteristics make thorium unsuitable in ion-deposition experiments. See also Isotopes of bismuth,Isotopes of gold and Isotopes of thorium.

[51] The German national metrology institute, known as the Physikalisch-Technische Bundesanstalt (PTB): Working group 1.24, IonAccumulation (http:/ / www. ptb. de/ en/ org/ 1/ 12/ 124/ ionenex. htm)

[52] General Conference on Weights and Measures, 22nd Meeting, October 2003 (http:/ / www. bipm. org/ utils/ en/ zip/ CGPM22. zip) (3.2 MBZIP file).

[53] Bowers, Mary, The Caravan (magazine), 1–15 September 2009: “Why the World is Losing Weight” (http:/ / www. marybowers. org. uk/18_The Caravan September 1-15. pdf)

[54] NIST. "Beyond the kilogram: redefining the International System of Units" (http:/ / web. archive. org/ web/ 20080522131052/ http:/ / www.nist. gov/ public_affairs/ newsfromnist_beyond_the_kilogram. htm). Press release. Archived from the original (http:/ / www. nist. gov/public_affairs/ newsfromnist_beyond_the_kilogram. htm) on 22 May 2008. .

[55] Robinson, I.A. (April 2009). "Toward a Final Result From the NPL Mark II Watt Balance". IEEE Transactions on Instrumentation andMeasurement 58 (4): 936–941. doi:10.1109/TIM.2008.2008090.

[56] BIPM: SI Brochure: Section 3.2, The kilogram (http:/ / www. bipm. org/ en/ si/ si_brochure/ chapter3/ 3-2. html)[57] Criterion: A combined total of at least 250,000 Google hits on both the modern spelling (‑gram) and the traditional British spelling

(‑gramme).[58] The practice of using the abbreviation “mcg” rather than the SI symbol “µg” was formally mandated for medical practitioners in 2004 by the

Joint Commission on Accreditation of Healthcare Organizations (JCAHO) in their “Do Not Use” List: Abbreviations, Acronyms, and Symbols(http:/ / www. aapmr. org/ hpl/ pracguide/ jcahosymbols. htm) because hand-written expressions of “µg” can be confused with “mg”, resultingin a thousand-fold overdosing. The mandate was also adopted by the Institute for Safe Medication Practices. (http:/ / www. ismp. org/ )

[59] BIPM: SI Brochure: Section 4.1, Non-SI units accepted for use with the SI, and units based on fundamental constants: Table 6 (http:/ /www. bipm. org/ en/ si/ si_brochure/ chapter4/ table6. html)

References

External links

Kilogram 44

External images

BIPM: The IPK in three nested bell jars (http:/ / www. bipm. org/ en/ scientific/ mass/ pictures_mass/ prototype. html)

NIST: K20, the US National Prototype Kilogram (http:/ / patapsco. nist. gov/ imagegallery/ retrieve. cfm?imageid=49& dpi=72&fileformat=jpg) resting on an egg crate fluorescent light panel

BIPM: Steam cleaning a 1 kg prototype before a mass comparison (http:/ / www. bipm. org/ en/ scientific/ mass/ pictures_mass/cleaning. html)

BIPM: The IPK and its six sister copies in their vault (http:/ / www. bipm. org/ en/ scientific/ mass/ pictures_mass/ vault. html)

The Age: Silicon sphere for the Avogadro Project (http:/ / www. theage. com. au/ ffximage/ 2007/ 06/ 14/rgN1506_csiro_wideweb__470x343,0. jpg)

NPL: The NPL’s Watt Balance project (http:/ / www. npl. co. uk/ server. php?show=conMediaFile. 1083)

NIST: This particular Rueprecht Balance (http:/ / museum. nist. gov/ object. asp?ObjID=51), an Austrian-made precision balance, wasused by the NIST from 1945 until 1960

BIPM: The FB‑2 flexure-strip balance (http:/ / www. bipm. org/ en/ scientific/ mass/ research_mass/ flexure-strip. html), the BIPM’smodern precision balance featuring a standard deviation of one ten-billionth of a kilogram (0.1 µg)

BIPM: Mettler HK1000 balance (http:/ / www. bipm. org/ en/ scientific/ mass/ pictures_mass/ mettler. html), featuring 1 µg resolutionand a 4 kg maximum mass. Also used by NIST and Sandia National Laboratories’ Primary Standards Laboratory

Micro-g LaCoste: FG‑5 absolute gravimeter, (http:/ / www. microglacoste. com/ images/ FG5. small. jpg) ( diagram (http:/ / www.microglacoste. com/ images/ fg5schem. jpg)), used in national laboratories to measure gravity to 2 µGal accuracy

• National Institute of Standards and Technology (NIST): NIST Improves Accuracy of ‘Watt Balance’ Method forDefining the Kilogram (http:/ / www. nist. gov/ public_affairs/ releases/ electrokilogram. htm)

• The UK’s National Physical Laboratory (NPL): An overview of the problems with an artifact-based kilogram(http:/ / www. npl. co. uk/ server. php?show=ConWebDoc. 2087)

• NPL: Avogadro Project (http:/ / www. npl. co. uk/ server. php?show=ConWebDoc. 2050)• NPL: NPL watt balance (http:/ / www. npl. co. uk/ server. php?show=ConWebDoc. 2029)• Metrology in France: Watt balance (http:/ / www. metrologiefrancaise. com/ en/ feature/ watt-balance. asp)• Australian National Measurement Institute: Redefining the kilogram through the Avogadro constant (http:/ /

www. measurement. gov. au/ index. cfm?event=object. showContent&objectID=7CBA5E62-BCD6-81AC-15017BE81748EF4B)

• International Bureau of Weights and Measures (BIPM): Home page (http:/ / www. bipm. org/ en/ home/ )• NZZ Folio: What a kilogram really weighs (http:/ / www. nzzfolio. ch/ www/

d80bd71b-b264-4db4-afd0-277884b93470/ showarticle/ fb0ba22e-46b7-43a5-8320-ef16483b7e91. aspx)• NPL: What are the differences between mass, weight, force and load? (http:/ / www. npl. co. uk/ server.

php?show=ConWebDoc. 1380)• BBC: Getting the measure of a kilogram (http:/ / news. bbc. co. uk/ 1/ hi/ sci/ tech/ 7084099. stm)• NPR: This Kilogram Has A Weight-Loss Problem (http:/ / www. npr. org/ templates/ story/ story.

php?storyId=112003322), an interview with National Institute of Standards and Technology physicist RichardSteiner

• Nature: Elemental shift for kilo (http:/ / www. nature. com/ news/ 2010/ 101019/ pdf/ 467892a. pdf), article aboutthe silicone-28 sphere

Second 45

Second

A light flashing once persecond.

The second (SI symbol: s), sometimes abbreviated sec., is a unit of time, and is theInternational System of Units (SI) base unit of time.[1] It may be measured using a clock.

Early definitions of the second were based on the apparent motion of the sun around theearth.[2] The solar day was divided into 24 hours, each of which contained 60 minutes of60 seconds each, so the second was 1⁄86 400 of the mean solar day. However, 19th- and20th century astronomical observations revealed that this average time is lengthening,and thus the sun/earth motion is no longer considered a suitable basis for definition. Withthe advent of atomic clocks, it became feasible to define the second based onfundamental properties of nature. Since 1967, the second has been defined to be

the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfinelevels of the ground state of the caesium 133 atom.[1]

SI prefixes are frequently combined with the word second to denote subdivisions of the second, e.g., the millisecond(one thousandth of a second), the microsecond (one millionth of a second), and the nanosecond (one billionth of asecond). Though SI prefixes may also be used to form multiples of the second such as kilosecond (one thousandseconds), such units are rarely used in practice. The more common larger non-SI units of time are not formed bypowers of ten; instead, the second is multiplied by 60 to form a minute, which is multiplied by 60 to form an hour,which is multiplied by 24 to form a day.The second is also the base unit of time in the centimetre-gram-second, metre-kilogram-second, metre-tonne-second,and foot-pound-second systems of units.

International secondUnder the International System of Units (via the International Committee for Weights and Measures, or CIPM),since 1967 the second has been defined as the duration of 9192631770 periods of the radiation corresponding to thetransition between the two hyperfine levels of the ground state of the caesium 133 atom.[1] In 1997 CIPM added thatthe periods would be defined for a caesium atom at rest, and approaching the theoretical temperature of absolutezero, and in 1999, it included corrections from ambient radiation.[1]

This definition refers to a caesium atom at rest at a temperature of 0 K (absolute zero). Absolute zero implies nomovement, and therefore zero external radiation affects (i.e., zero local electric and magnetic fields). The secondthus defined is consistent with the ephemeris second, which was based on astronomical measurements. (See Historybelow.)The realization of the standard second is described briefly in a special publication from the National Institute ofScience and Technology,[3] and in detail by the National Research Council of Canada.[4]

Second 46

Equivalence to other units of time1 international second is equal to:• 1/60 minute (but see also leap second)• 1/3,600 hour• 1/86,400 day (IAU system of units)• 1/31,557,600 Julian year (IAU system of units)

History

Before mechanical clocksThe Egyptians subdivided daytime and nighttime into twelve hours each since at least 2000 BC, hence the seasonalvariation of their hours. The Hellenistic astronomers Hipparchus (c. 150 BC) and Ptolemy (c. AD 150) subdividedthe day sexagesimally and also used a mean hour (1⁄24 day), simple fractions of an hour (1⁄4, 2⁄3, etc.) andtime-degrees (1⁄360 day or four modern minutes), but not modern minutes or seconds.[5]

The day was subdivided sexagesimally, that is by 1⁄60, by 1⁄60 of that, by 1⁄60 of that, etc., to at least six places afterthe sexagesimal point (a precision of less than 2 microseconds) by the Babylonians after 300 BC, but they did notsexagesimally subdivide smaller units of time. For example, six fractional sexagesimal places of a day was used intheir specification of the length of the year, although they were unable to measure such a small fraction of a day inreal time. As another example, they specified that the mean synodic month was 29;31,50,8,20 days (four fractionalsexagesimal positions), which was repeated by Hipparchus and Ptolemy sexagesimally, and is currently the meansynodic month of the Hebrew calendar, though restated as 29 days 12 hours 793 halakim (where 1 hour = 1080halakim).[6] The Babylonians did not use the hour, but did use a double-hour lasting 120 modern minutes, atime-degree lasting four modern minutes, and a barleycorn lasting 31⁄3 modern seconds (the helek of the modernHebrew calendar).[7]

In 1000, the Persian scholar al-Biruni gave the times of the new moons of specific weeks as a number of days, hours,minutes, seconds, thirds, and fourths after noon Sunday.[8] In 1267, the medieval scientist Roger Bacon stated thetimes of full moons as a number of hours, minutes, seconds, thirds, and fourths (horae, minuta, secunda, tertia, andquarta) after noon on specified calendar dates.[9] Although a third for 1⁄60 of a second remains in some languages, forexample Polish (tercja) and Turkish (salise), the modern second is subdivided decimally.

Seconds measured by mechanical clocksThe earliest clocks to display seconds appeared during the last half of the 16th century. The earliest spring-driventimepiece with a second hand which marked seconds is an unsigned clock depicting Orpheus in the Fremersdorfcollection, dated between 1560 and 1570.[10] :417–418[11] During the 3rd quarter of the 16th century, Taqi al-Din builta clock with marks every five seconds.[12] [13] In 1579, Jost Bürgi built a clock for William of Hesse that markedseconds.[10] :105 In 1581, Tycho Brahe redesigned clocks that displayed minutes at his observatory so they alsodisplayed seconds. In 1587 he complained that his four clocks disagreed by plus or minus four seconds.[10] :104

The second first became accurately measurable with the development of pendulum clocks keeping mean time (asopposed to the apparent time displayed by sundials), specifically in 1670 when William Clement added a secondspendulum to the original pendulum clock of Christian Huygens.[14] The seconds pendulum has a period of twoseconds, one second for a swing forward and one second for a swing back, enabling the longcase clock incorporatingit to tick seconds. From this time, a second hand that rotated once per minute in a small subdial began to be added tothe clock faces of precision clocks.

Second 47

Modern measurementsIn 1956 the second was defined in terms of the period of revolution of the Earth around the Sun for a particularepoch, because by then it had become recognized that the Earth's rotation on its own axis was not sufficientlyuniform as a standard of time. The Earth's motion was described in Newcomb's Tables of the Sun (1895), whichprovide a formula estimating the motion of the Sun relative to the epoch 1900 based on astronomical observationsmade between 1750 and 1892.[15] The second thus defined is

the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.[15]

This definition was ratified by the Eleventh General Conference on Weights and Measures in 1960. The tropicalyear in the definition was not measured, but calculated from a formula describing a mean tropical year that decreasedlinearly over time, hence the curious reference to a specific instantaneous tropical year. This definition of the secondwas in conformity with the ephemeris time scale adopted by the IAU in 1952,[16] defined as the measure of time thatbrings the observed positions of the celestial bodies into accord with the Newtonian dynamical theories of theirmotion (those accepted for use during most of the 20th century being Newcomb's Tables of the Sun, used from 1900through 1983, and Brown's Tables of the Moon, used from 1923 through 1983).[15]

With the development of the atomic clock, it was decided to use atomic clocks as the basis of the definition of thesecond, rather than the revolution of the Earth around the Sun.Following several years of work, Louis Essen from the National Physical Laboratory (Teddington, England) andWilliam Markowitz from the United States Naval Observatory (USNO) determined the relationship between thehyperfine transition frequency of the caesium atom and the ephemeris second.[15] [17] Using a common-viewmeasurement method based on the received signals from radio station WWV,[18] they determined the orbital motionof the Moon about the Earth, from which the apparent motion of the Sun could be inferred, in terms of time asmeasured by an atomic clock. They found that the second of ephemeris time (ET) had the duration of 9,192,631,770± 20 cycles of the chosen caesium frequency.[17] As a result, in 1967 the Thirteenth General Conference on Weightsand Measures defined the second of atomic time in the International System of Units as

FOCS 1, a continuous cold caesium fountainatomic clock in Switzerland, started operating in

2004 at an uncertainty of one second in 30million years.

the duration of 9,192,631,770 periods of the radiationcorresponding to the transition between the two hyperfine levelsof the ground state of the caesium-133 atom.[15]

This SI second, referred to atomic time, was later verified to be inagreement, within 1 part in 1010, with the second of ephemeris time asdetermined from lunar observations.[19] (Nevertheless, this SI secondwas already, when adopted, a little shorter than the then-current valueof the second of mean solar time.[20] [21] )

During the 1970s it was realized that gravitational time dilation causedthe second produced by each atomic clock to differ depending on itsaltitude. A uniform second was produced by correcting the output ofeach atomic clock to mean sea level (the rotating geoid), lengtheningthe second by about 1×10−10. This correction was applied at thebeginning of 1977 and formalized in 1980. In relativistic terms, the SI second is defined as the proper time on therotating geoid.[22]

The definition of the second was later refined at the 1997 meeting of the BIPM to include the statementThis definition refers to a caesium atom at rest at a temperature of 0 K.

The revised definition seems to imply that the ideal atomic clock contains a single caesium atom at rest emitting asingle frequency. In practice, however, the definition means that high-precision realizations of the second shouldcompensate for the effects of the ambient temperature (black-body radiation) within which atomic clocks operate,and extrapolate accordingly to the value of the second at a temperature of absolute zero.

Second 48

Today, the atomic clock operating in the microwave region is challenged by atomic clocks operating in the opticalregion. To quote Ludlow et al.,[23] “In recent years, optical atomic clocks have become increasingly competitive inperformance with their microwave counterparts. The overall accuracy of single trapped ion based optical standardsclosely approaches that of the state-of-the-art caesium fountain standards. Large ensembles of ultracold alkalineearth atoms have provided impressive clock stability for short averaging times, surpassing that of single-ion basedsystems. So far, interrogation of neutral atom based optical standards has been carried out primarily in free space,unavoidably including atomic motional effects that typically limit the overall system accuracy. An alternativeapproach is to explore the ultranarrow optical transitions of atoms held in an optical lattice. The atoms are tightlylocalized so that Doppler and photon-recoil related effects on the transition frequency are eliminated.”The NRC [24] attaches a "relative uncertainty" of 2.5×10−11 (limited by day-to-day and device-to-devicereproducibility) to their atomic clock based upon the 127I2 molecule, and is advocating use of an 88Sr ion trap instead(relative uncertainty due to linewidth of 2.2×10−15). See magneto-optical trap and "Trapped ion optical frequencystandards" [25]. National Physical Laboratory. Such uncertainties rival that of the NIST F-1 caesium atomic clock inthe microwave region, estimated as a few parts in 1016 averaged over a day.[26] [27]

SI multiplesSI prefixes are commonly used to measure time less than a second, but rarely for multiples of a second. Instead, thenon-SI units minutes, hours, days, Julian years, Julian centuries, and Julian millennia are used.

SI multiples for second (s)

Submultiples Multiples

Value Symbol Name Value Symbol Name

10−1 s ds decisecond 101 s das decasecond

10−2 s cs centisecond 102 s hs hectosecond

10−3 s ms millisecond 103 s ks kilosecond

10−6 s µs microsecond 106 s Ms megasecond

10−9 s ns nanosecond 109 s Gs gigasecond

10−12 s ps picosecond 1012 s Ts terasecond

10−15 s fs femtosecond 1015 s Ps petasecond

10−18 s as attosecond 1018 s Es exasecond

10−21 s zs zeptosecond 1021 s Zs zettasecond

10−24 s ys yoctosecond 1024 s Ys yottasecond

Common prefixes are in bold

Other current definitionsFor specialized purposes, a second may be used as a unit of time in time scales where the precise length differsslightly from the SI definition. One such time scale is UT1, a form of universal time. McCarthy and Seidelmannrefrain from stating that the SI second is the legal standard for timekeeping throughout the world, saying only that"over the years UTC [which ticks SI seconds] has become either the basis for legal time of many countries, oraccepted as the de facto basis for standard civil time".[28]

Second 49

References[1] "Official BIPM definition" (http:/ / www. bipm. org/ en/ si/ si_brochure/ chapter2/ 2-1/ second. html). BIPM. . Retrieved 2008.[2] Jones, Tony (2000). Splitting the second: the story of atomic time (http:/ / books. google. be/ books?id=krZBQbnHTY0C). Institute of Physics

Pub. ISBN 0750306408. .[3] BN Taylor, A Thompson (Eds.), ed (2008). "Appendix 2" (http:/ / physics. nist. gov/ Pubs/ SP330/ sp330. pdf). The International System of

Units (SI). NIST Special Publication. 330. pp. 53 ff. . Retrieved 2009-08-19.[4] "NRC's Cesium Fountain Clock - FCs1" (http:/ / www. nrc-cnrc. gc. ca/ eng/ projects/ inms/ fountain-clock. html). National Research Council

of Canada. . Retrieved 2009-08-19.[5] G. J. Toomer, Ptolemey's Almagest (Princeton, New Jersey: Princeton University Press, 1998) 6–7, 23, 211–216.[6] O Neugebauer (1975). A history of ancient mathematical astronomy. Springer-Verlag. ISBN 038706995X.[7] See page 325 in O Neugebauer (1949). "The astronomy of Maimonides and its sources". Hebrew Union College Annual 22: 321–360.[8] al-Biruni (1879). The chronology of ancient nations: an English version of the Arabic text of the Athâr-ul-Bâkiya of Albîrûnî, or "Vestiges of

the Past" (http:/ / books. google. com/ ?id=pFIEAAAAIAAJ& pg=PA148#v=onepage& q=). Sachau C Edward. pp. 147–149. .[9] R Bacon (2000) [1928]. The Opus Majus of Roger Bacon. BR Belle. University of Pennsylvania Press. table facing page 231.

ISBN 9781855068568.[10] David S. Landes, Revolution in time (Cambridge, Massachusetts: Harvard University Press, 1983).[11] Johann Willsberger, Clocks & watches (New York, Dial Press, 1975) full page color photo: 4th caption page, 3rd photo thereafter (neither

pages nor photos are numbered).[12] Taqi al-Din (http:/ / books. google. com/ books?id=raKRY3KQspsC& pg=PA934)[13] The astronomical clock of Taqi al-Din: Virtual reconstruction (http:/ / muslimheritage. com/ topics/ default. cfm?ArticleID=947).[14] See page 2 in J Chappell (2002). "The Long Case Clock: The Science and Engineering that Goes Into a Grandfather Clock" (http:/ / illumin.

usc. edu/ article. php?articleID=64& page=1). Illumin 1 (0): 1. .[15] "Leap Seconds" (http:/ / tycho. usno. navy. mil/ leapsec. html). Time Service Department, United States Naval Observatory. . Retrieved

2006-12-31.[16] Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac (prepared jointly by the

Nautical Almanac Offices of the United Kingdom and the United States of America, HMSO, London, 1961), at Sect. 1C, p.9), stating that at aconference "in March 1950 to discuss the fundamental constants of astronomy ... the recommendations with the most far-reachingconsequences were those that defined ephemeris time and brought the lunar ephemeris into accordance with the solar ephemeris in terms ofephemeris time. These recommendations were addressed to the International Astronomical Union and were formally adopted by Commission4 and the General Assembly of the Union in Rome in September 1952."

[17] W Markowitz, RG Hall, L Essen, JVL Parry (1958). "Frequency of cesium in terms of ephemeris time" (http:/ / www. leapsecond. com/history/ 1958-PhysRev-v1-n3-Markowitz-Hall-Essen-Parry. pdf). Physical Review Letters 1: 105–107. doi:10.1103/PhysRevLett.1.105. .

[18] S Leschiutta (2005). "The definition of the 'atomic' second". Metrologia 42 (3): S10–S19. doi:10.1088/0026-1394/42/3/S03.[19] W Markowitz (1988). AK Babcock, GA Wilkins. ed. The Earth's Rotation and Reference Frames for Geodesy and Geophysics. IAU

Sumposia #128. pp. 413–418. Bibcode: 1988IAUS..128..413M.[20] DD McCarthy, C Hackman, R Nelson (2008). "The Physical Basis of the Leap Second". Astronomical Journal 136: 1906–1908.

doi:10.1088/0004-6256/136/5/1906. "... the SI second is equivalent to an older measure of the second of UT1, which was too small to startwith and further, as the duration of the UT1 second increases, the discrepancy widens.".

[21] In the late 1950s, the caesium standard was used to measure both the current mean length of the second of mean solar time (UT2)(9192631830 cycles) and also the second of ephemeris time (ET) (9192631770 ± 20 cycles), see L Essen (1968). "Time Scales" (http:/ / www.leapsecond. com/ history/ 1968-Metrologia-v4-n4-Essen. pdf). Metrologia 4: 161–165. doi:10.1088/0026-1394/4/4/003. .. As noted in page162, the 9192631770 figure was chosen for the SI second. L Essen in the same 1968 article stated that this value "seemed reasonable in viewof the variations in UT2".

[22] See page 515 in RA Nelsonet al.; McCarthy, D D; Malys, S; Levine, J; Guinot, B; Fliegel, H F; Beard, R L; Bartholomew, T R (2000). "Theleap second: its history and possible future" (http:/ / www. cl. cam. ac. uk/ ~mgk25/ time/ metrologia-leapsecond. pdf). Metrologia 38:509–529. doi:10.1088/0026-1394/38/6/6. .

[23] AD Ludlow et al. (2006). "Systematic study of the 87Sr clock transition in an optical lattice". Physical Review Letters 96: 033003.doi:10.1103/PhysRevLett.96.033003. arXiv:physics/0508041.

[24] http:/ / inms-ienm. nrc-cnrc. gc. ca/ research/ optical_frequency_projects_e. html#optical[25] http:/ / www. npl. co. uk/ server. php?show=ConWebDoc. 1086[26] R Wynands, S Weyers (2005). "Atomic fountain clocks". Metrologia 42: S64–S79. doi:10.1088/0026-1394/42/3/S08.[27] "NIST-F1 Cesium Fountain Atomic Clock" (http:/ / tf. nist. gov/ cesium/ fountain. htm). NIST. . Retrieved 2009-08-19.[28] McCarty, D. D.; Seidelmann, P. K. (2009). TIME From Earth Rotation to Atomic Physics. Weinheim: WILEY-VCH Verlag GmbH & Co..

pp. 68, 232.

Second 50

External links• National Physical Laboratory: Trapped ion optical frequency standards (http:/ / www. npl. co. uk/ server.

php?show=ConWebDoc. 1086)• High-accuracy strontium ion optical clock; National Physical Laboratory (2005) (http:/ / resource. npl. co. uk/

docs/ networks/ time/ meeting3/ klein. pdf)• National Research Council of Canada: Optical frequency standard based on a single trapped ion (http:/ /

inms-ienm. nrc-cnrc. gc. ca/ research/ optical_frequency_projects_e. html#optical)• NIST: Definition of the second; notice the cesium atom must be in its ground state at 0 K (http:/ / physics. nist.

gov/ cuu/ Units/ second. html)• Official BIPM definition of the second (http:/ / www. bipm. org/ en/ si/ si_brochure/ chapter2/ 2-1/ second. html)• Seconds and leap seconds by the USNO (http:/ / tycho. usno. navy. mil/ leapsec. html)• The leap second: its history and possible future (http:/ / www. cl. cam. ac. uk/ ~mgk25/ time/

metrologia-leapsecond. pdf)• What is a Cesium atom clock? (http:/ / inms-ienm. nrc-cnrc. gc. ca/ faq_time_e. html#10)

Ampere

Current can be measured by a galvanometer, via thedeflection of a magnetic needle in the magnetic field

created by the current.

The ampere (symbol: A) is the SI unit of electric current[1]

(symbol: I) and is one of the seven[2] SI base units. It is namedafter André-Marie Ampère (1775–1836), French mathematicianand physicist, considered the father of electrodynamics. Inpractice, its name is often shortened to amp.

In practical terms, the ampere is a measure of the amount ofelectric charge passing a point per unit time. Around 6.241 × 1018

electrons, or one coulomb, passing a given point each secondconstitutes one ampere.[3]

Definition

Ampère's force law[4] [5] states that there is an attractive forcebetween two parallel wires carrying an electric current. This force is used in the formal definition of the amperewhich states that it is "the constant current which will produce an attractive force of 2 × 10–7 newton per metre oflength between two straight, parallel conductors of infinite length and negligible circular cross section placed onemetre apart in a vacuum".[1] [6]

In terms of Ampère's force law,

so

The SI unit of charge, the coulomb, "is the quantity of electricity carried in 1 second by a current of 1 ampere."[7]

Conversely, a current of one ampere is one coulomb of charge going past a given point per second:

That is, in general, charge Q is determined by steady current I flowing for a time t as Q = It.

Ampere 51

HistoryThe ampere was originally defined as one tenth of the CGS system electromagnetic unit of current (now known asthe abampere), the amount of current which generates a force of two dynes per centimetre of length between twowires one centimetre apart.[8] The size of the unit was chosen so that the units derived from it in the MKSA systemwould be conveniently sized.The "international ampere" was an early realisation of the ampere, defined as the current that would deposit0.001118000 grams of silver per second from a silver nitrate solution.[9] Later, more accurate measurements revealedthat this current is 0.99985 A.

RealisationThe ampere is most accurately realised using a watt balance, but is in practice maintained via Ohm's Law from theunits of electromotive force and resistance, the volt and the ohm, since the latter two can be tied to physicalphenomena that are relatively easy to reproduce, the Josephson junction and the quantum Hall effect,respectively.[10]

At present, techniques to establish the realisation of an ampere have a relative uncertainty of approximately a fewparts in 107, and involve realisations of the watt, the ohm and the volt.[11]

Proposed future definitionRather than a definition in terms of the force between two current-carrying wires, it has been proposed to define theampere in terms of the rate of flow of elementary charges.[12] Since a coulomb is approximately equal to6.24150948 × 1018 elementary charges, one ampere is approximately equivalent to 6.24150948 × 1018 elementarycharges, such as electrons, moving past a boundary in one second. The proposed change would define 1 A as beingthe current in the direction of flow of a particular number of elementary charges per second. In 2005, theInternational Committee for Weights and Measures (CIPM) agreed to study the proposed change, and, depending onthe outcome of experiments over the next few years, to formally propose the change at the 24th General Conferenceon Weights and Measures (CGPM) in 2011.[13] [14]

See also• Ammeter• Ampacity (current-carrying capacity)• Electric shock• Hydraulic analogy• Magnetic constant

References[1] BIPM official definition (http:/ / www. bipm. org/ en/ si/ si_brochure/ chapter2/ 2-1/ ampere. html)[2] The other six are the metre, kelvin, second, mole, candela and the kilogram[3] Bodanis, David. (2005). Electric Universe. New York: Three Rivers Press[4] Raymond A Serway & Jewett JW (2006). Serway's principles of physics: a calculus based text (http:/ / books. google. com/

books?id=1DZz341Pp50C& pg=RA1-PA746& dq=wire+ "magnetic+ force"& lr=& as_brr=0&sig=4vMV_CH6Nm8ZkgjtDJFlupekYoA#PRA1-PA746,M1) (Fourth Edition ed.). Belmont, CA: Thompson Brooks/Cole. p. 746.ISBN 053449143X. .

[5] Beyond the Kilogram: Redefining the International System of Units (http:/ / www. nist. gov/ public_affairs/newsfromnist_beyond_the_kilogram. htm)(2006). National Institute of Standards and Technology. Square brackets appear in original.Retrieved March 2008.

[6] Paul M. S. Monk, Physical Chemistry: Understanding our Chemical World, John Wiley and Sons, 2004 online (http:/ / books. google. com/

books?vid=ISBN0471491802& id=LupAi35QjhoC& pg=PA16& lpg=PA16& ots=IMiGyIL-67& dq=ampere+ definition+ si&

Ampere 52

sig=9Y0k0wgvymmLNYFMcXodwJZwvAM).[7] Bureau International des Poids et Mesures. (2006). The International System of Units (SI) (http:/ / www. bipm. org/ utils/ common/ pdf/

si_brochure_8_en. pdf), 8th ed. p. 144.[8] A short history of the SI units in electricity (http:/ / alpha. montclair. edu/ ~kowalskiL/ SI/ SI_PAGE. HTML)[9] History of the ampere (http:/ / www. sizes. com/ units/ ampHist. htm)[10] Practical realisation of unit definitions: Electrical quantities (http:/ / www. bipm. org/ en/ si/ si_brochure/ appendix2/ electrical. html)[11] BIPM SI brochure; Appendix 2 (http:/ / www. bipm. org/ en/ si/ si_brochure/ appendix2/ electrical. html)[12] Beyond the Kilogram: Redefining the International System of Units (http:/ / www. nist. gov/ public_affairs/

newsfromnist_beyond_the_kilogram. htm)[13] International Committee for Weights and Measures (CIPM) Recommendation 1 (CI-2005) (http:/ / www. bipm. org/ cc/ CIPM/ Allowed/ 94/

CIPM-Recom1CI-2005-EN. pdf): Preparative steps towards new definitions of the kilogram, the ampere, the kelvin and the mole in terms offundamental constants

[14] Ian Mills (29 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units" (http:/ / www. bipm. org/ utils/en/ pdf/ si_brochure_draft_ch2. pdf). CCU. . Retrieved 2011-01-01.

External links• The NIST Reference on Constants, Units, and Uncertainty (http:/ / physics. nist. gov/ cuu/ )• A short history of the SI units in electricity (http:/ / alpha. montclair. edu/ ~kowalskiL/ SI/ SI_PAGE. HTML)• NIST Definition of ampere and μ0 (http:/ / physics. nist. gov/ cuu/ Units/ ampere. html)

Kelvin

Kelvin temperature conversion formulae

from Kelvin to Kelvin

Celsius [°C] = [K] − 273.15 [K] = [°C] + 273.15

Fahrenheit [°F] = [K] × 9⁄5 − 459.67 [K] = ([°F] + 459.67) × 5⁄9Rankine [°R] = [K] × 9⁄5 [K] = [°R] × 5⁄9

For temperature intervals rather than specific temperatures,1 K = 1 °C = 1.8 °F = 1.8 °R

Comparisons among various temperature scales

The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System ofUnits (SI) and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scaleusing as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description ofthermodynamics. The reference point that defines the Kelvin scale is the triple point of water at 273.16K (0.01degrees Celsius). The kelvin is defined as 1/273.16 of the difference between these two reference points.The Kelvin scale is named after the Belfast-born engineer and physicist William Thomson, 1st Baron Kelvin(1824–1907), who wrote of the need for an "absolute thermometric scale". Unlike the degree Fahrenheit and degreeCelsius, the kelvin is not referred to or typeset as a degree. The kelvin is the primary unit of measurement in thephysical sciences, but is often used in conjunction with the degree Celsius, which has the same magnitude. Absolutezero at 0kelvin is −273.15 degrees Celsius.

Kelvin 53

History1848

Lord Kelvin (William Thomson), wrote in his paper, On an Absolute Thermometric Scale, of the need for ascale whereby "infinite cold" (absolute zero) was the scale’s null point, and which used the degree Celsius forits unit increment. Thomson calculated that absolute zero was equivalent to −273 °C on the air thermometersof the time.[1] This absolute scale is known today as the Kelvin thermodynamic temperature scale. Thomson’svalue of "−273" was the reciprocal of 0.00366—the accepted expansion coefficient of gas per degree Celsiusrelative to the ice point, giving a remarkable consistency to the currently accepted value.

1954

Resolution 3 of the 10th CGPM gave the Kelvin scale its modern definition by designating the triple point ofwater as its second defining point and assigned its temperature to exactly 273.16 kelvin.[2]

1967/1968

Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbolK, replacing "degree absolute", symbol °K.[3] Furthermore, feeling it useful to more explicitly define themagnitude of the unit increment, the 13th CGPM also held in Resolution 4 that "The kelvin, unit ofthermodynamic temperature, is equal to the fraction 1/273.16 of the thermodynamic temperature of the triplepoint of water."[4]

2005

The Comité International des Poids et Mesures (CIPM), a committee of the CGPM, affirmed that for thepurposes of delineating the temperature of the triple point of water, the definition of the Kelvinthermodynamic temperature scale would refer to water having an isotopic composition specified asVSMOW.[5]

Usage conventionsWhen reference is made to the unit kelvin (either a specific temperature or a temperature interval), kelvin is alwaysspelled with a lowercase k unless it is the first word in a sentence.[6] When reference is made to the "Kelvin scale",the word "kelvin"—which is normally a noun—functions adjectivally to modify the noun "scale" and is capitalized.Until the 13th General Conference on Weights and Measures (CGPM) in 1967–1968, the unit kelvin was called a"degree", the same as with the other temperature scales at the time. It was distinguished from the other scales witheither the adjective suffix "Kelvin" ("degree Kelvin") or with "absolute" ("degree absolute") and its symbol was °K.The latter (degree absolute), which was the unit’s official name from 1948 until 1954, was rather ambiguous since itcould also be interpreted as referring to the Rankine scale. Before the 13th CGPM, the plural form was "degreesabsolute". The 13th CGPM changed the name to simply "kelvin" (symbol K).[7] The omission of "degree" indicatesthat it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales, but rather an absolute unitof measure which can be manipulated algebraically (e.g., multiplied by two to indicate twice the amount of "meanenergy" available among elementary degrees of freedom of the system).

This SI unit is named after William Thomson, 1st Baron Kelvin. As with every SI unit whose name is derivedfrom the proper name of a person, the first letter of its symbol is uppercase (K). When an SI unit is spelled outin English, it should always begin with a lowercase letter (kelvin), except where any word would becapitalized, such as at the beginning of a sentence or in capitalized material such as a title. Note that "degreeCelsius" conforms to this rule because the "d" is lowercase.—Based on The International System of Units [8], section 5.2.

The kelvin symbol is always a roman, non-italic capital K. In the SI naming convention, all symbols named after a person are capitalized; in the case of the kelvin, capitalizing also distinguishes the symbol from the SI prefix "kilo",

Kelvin 54

which has the lowercase k as its symbol. The admonition against italicizing the symbol K applies to all SI unitsymbols; only symbols for variables and constants (e.g., P = pressure, and c = 299,792,458 m/s) are italicized inscientific and engineering papers. As with most other SI unit symbols (angle symbols, e.g. 45° 3′ 4″, are theexception) there is a space between the numeric value and the kelvin symbol (e.g. "99.987 K").[9] [10]

Unicode provides a compatibility character for the kelvin at U+212A (decimal 8490), for compatibility with CJKencodings that provide such a character (as such, in most fonts the width is the same as for fullwidth characters).

Use in conjunction with CelsiusIn science and in engineering, the Celsius scale and the kelvin are often used simultaneously in the same article (e.g.,"...its measured value was 0.01028 °C with an uncertainty of 60 µK..."). This practice is permissible because thedegree Celsius is a special name for the kelvin for use in expressing Celsius temperatures and the magnitude of thedegree Celsius is exactly equal to that of the kelvin.[11] Notwithstanding that the official endorsement provided byResolution 3 of the 13th CGPM states, "a temperature interval may also be expressed in degrees Celsius," thepractice of simultaneously using both "°C" and "K" remains widespread throughout the scientific world as the use ofSI prefixed forms of the degree Celsius (such as "µ°C" or "microdegrees Celsius") to express a temperature intervalhas not been widely adopted.[3]

Proposed redefinitionIn 2005 the CIPM embarked on a program to redefine, amongst others, the Kelvin using a more rigorous basis thanwas in use. The current (2010) definition is unsatisfactory for temperatures below 20 K and above 1300 K.[12] It isanticipated that the program will be completed in time for its adoption by the CGPM at its 2011 meeting. Thecommittee proposes defining the kelvin as the temperature scale for which Boltzmann's constant is1.3806505 × 10−23 J/K exactly.[13]

From a scientific point of view, this will link temperature to the rest of SI and result in a stable definition that isindependent of any particular substance. From a practical point of view the redefinition will pass unnoticed; waterwill still freeze at 0 °C (273.15 K).[14]

Practical uses

Color temperatureThe kelvin is often used in the measure of the color temperature of light sources. Color temperature is based upon theprinciple that a black body radiator emits light whose color depends on the temperature of the radiator. Black bodieswith temperatures below about 4000 K appear reddish whereas those above about 7500 K appear bluish. Colortemperature is important in the fields of image projection and photography where a color temperature ofapproximately 5600 K is required to match "daylight" film emulsions. In astronomy, the stellar classification of starsand their place on the Hertzsprung–Russell diagram are based, in part, upon their surface temperature, known aseffective temperature. The photosphere of the Sun, for instance, has an effective temperature of 5778 K.

Kelvin 55

Kelvin as a measure of noiseIn electronics, the kelvin is used as an indicator of how noisy a circuit is in relation to an ultimate noise floor, i.e. thenoise temperature. The so-called Johnson–Nyquist noise of discrete resistors and capacitors is a type of thermalnoise derived from the Boltzmann constant and can be used to determine the noise temperature of a circuit using theFriis formulas for noise.

References[1] Thomson, William (October 1848). "On an Absolute Thermometric Scale" (http:/ / zapatopi. net/ kelvin/ papers/

on_an_absolute_thermometric_scale. html). Philosophical Magazine. . Retrieved 2008-02-06.[2] "Resolution 3: Definition of the thermodynamic temperature scale" (http:/ / www. bipm. fr/ en/ CGPM/ db/ 10/ 3/ ). Resolutions of the 10th

CGPM. Bureau International des Poids et Mesures. 1954. . Retrieved 2008-02-06.[3] "Resolution 3: SI unit of thermodynamic temperature (kelvin)" (http:/ / www. bipm. fr/ en/ CGPM/ db/ 13/ 3/ ). Resolutions of the 13th

CGPM. Bureau International des Poids et Mesures. 1967. . Retrieved 2008-02-06.[4] "Resolution 4: Definition of the SI unit of thermodynamic temperature (kelvin)" (http:/ / www. bipm. fr/ en/ CGPM/ db/ 13/ 4/ ). Resolutions

of the 13th CGPM. Bureau International des Poids et Mesures. 1967. . Retrieved 2008-02-06.[5] "Unit of thermodynamic temperature (kelvin)" (http:/ / www1. bipm. org/ en/ si/ si_brochure/ chapter2/ 2-1/ 2-1-1/ kelvin. html). SI Brochure,

8th edition. Bureau International des Poids et Mesures. 1967. pp. Section 2.1.1.5. . Retrieved 2008-02-06.[6] BIPM: SI brochure, Section 5.2 (http:/ / www1. bipm. org/ en/ si/ si_brochure/ chapter5/ 5-2. html)[7] Barry N. Taylor (2008) (.PDF). Guide for the Use of the International System of Units (SI) (http:/ / physics. nist. gov/ Document/ sp811. pdf).

Special Publication 811. National Institute of Standards and Technology. . Retrieved 2009-06-24.[8] http:/ / www. bipm. org/ en/ si/ si_brochure/ chapter5/ 5-2. html[9] "SI Unit rules and style conventions" (http:/ / physics. nist. gov/ cuu/ Units/ checklist. html). National Institute of Standards and Technology.

September 2004. . Retrieved 2008-02-06.[10] "Rules and style conventions for expressing values of quantities" (http:/ / www. bipm. org/ en/ si/ si_brochure/ chapter5/ 5-3-2. html#5-3-3).

SI Brochure, 8th edition. Bureau International des Poids et Mesures. 1967. pp. Section 5.3.3. . Retrieved 2008-02-06.[11] "Units with special names and symbols; units that incorporate special names and symbols" (http:/ / www. bipm. org/ en/ si/ si_brochure/

chapter2/ 2-2/ table3. html). SI Brochure, 8th edition. Bureau International des Poids et Mesures. 2006. pp. Section 2.2.2, Table 3. . Retrieved2008-02-06.

[12] J. Fischer1 et al. "Report to the CIPM on the implications of changing the definition of the base unit Kelvin" (http:/ / www. bipm. org/ wg/CCT/ TG-SI/ Allowed/ Documents/ Report_to_CIPM_2. pdf). International Committee for Weights and Measures (CIPM). . Retrieved2010-02-23.

[13] Ian Mills (29 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units" (http:/ / www. bipm. org/ utils/en/ pdf/ si_brochure_draft_ch2. pdf). CCU. . Retrieved 2011-01-01.

[14] "Updating the definition of the kelvin" (http:/ / www. bipm. org/ wg/ CCT/ TG-SI/ Allowed/ Documents/Updating_the_definition_of_the_kelvin2. pdf). International Bureau for Weights and Measures (BIPM). . Retrieved 2010-02-23.

External links• Bureau International des Poids et Mesures (2006). The International System of Units (SI) Brochure (http:/ / www.

bipm. org/ utils/ common/ pdf/ si_brochure_8_en. pdf). 8th Edition. International Committee for Weights andMeasures. Retrieved 2008-02-06.

• Convert Kelvin to Fahrenheit and Celsius Instantly, Kelvin to Fahrenheit Conversion (http:/ / www. tampile. com/)

Mole 56

MoleThe mole is a unit of measurement for the amount of substance or chemical amount. It is one of the base units in theInternational System of Units, and has the unit symbol mol.[1]

The name mole is an 1897 translation[2] [3] of the German unit Mol, coined by the chemist Wilhelm Ostwald in1893,[4] although the related concept of equivalent mass had been in use at least a century earlier. The name isderived[5] from the German word Molekül (molecule).The mole is defined as the amount of substance that contains as many elementary entities (e.g., atoms, molecules,ions, electrons) as there are atoms in 12 g of the isotope carbon-12 (12C).[1] Thus, by definition, one mole of pure12C has a mass of exactly 12 g. The experimentally determined value of a mole is 6.02214179(30) × 1023.[6] Recentmeasurements give the value 6.02214078(3) × 1023 [7] Therefore the Avogadro constant is6.02214179(30) × 1023 /mol.By this definition, a mole of any pure substance has a mass in grams exactly equal to that substance's molecular oratomic mass; e.g., 1mol of calcium-40 is approximately equal to 40g, because the Ca-40 isotope has a mass of39.9625906 amu on the C-12 scale. In other words, the numerical value of a substance's molecular or atomic mass inatomic mass units is the same as that of its molar mass—the mass of one mole of that substance—in grams.The most common method of determining the amount, expressed in moles, of pure substance the value of whosemolar mass is known, is to measure its mass in grams and then to divide by its molar mass (expressed in g/mol).[8]

Molar masses may be easily calculated from tabulated values of atomic weights and the molar mass constant (whichhas a convenient defined value of 1 g/mol). Other methods include the use of the molar volume or the measurementof electric charge.[8]

The current definition of the mole was approved during the 1960s.[1] [9] Earlier definitions had been based on theatomic mass of hydrogen (about one gram of hydrogen-1 gas, excluding its heavy isotopes), the atomic weight ofoxygen, and the relative atomic mass of oxygen-16; the four different definitions were equivalent to within 1%.The names gram-atom (abbreviated gat.) and gram-molecule have also been used in the same sense as "mole".[1]

However, modern conventions define the gram-atom and the mole differently. While the elementary entity defining amole will vary depending on the substance, the elementary entity for the gram-atom is always the atom. Forexample, 1 mole of He is equivalent to 1 gram-atom of He, but 1 mole of MgB2 is equivalent to 3 gram-atoms ofMgB2.[10] [11]

HistoryThe first table of atomic weights was published by John Dalton (1766–1844) in 1805, based on a system in whichthe atomic weight of hydrogen was defined as 1. These atomic weights were based on the stoichiometric proportionsof chemical reactions and compounds, a fact which greatly aided their acceptance: it was not necessary for a chemistto subscribe to atomic theory (an unproven hypothesis at the time) to make practical use of the tables. This wouldlead to some confusion between atomic weights (promoted by proponents of atomic theory) and equivalent weights(promoted by its opponents and which sometimes differed from atomic weights by an integer factor), which wouldlast throughout much of the nineteenth century.Jöns Jacob Berzelius (1779–1848) was instrumental in the determination of atomic weights to ever increasingaccuracy. He was also the first chemist to use oxygen as the standard to which other weights were referred. Oxygenis a useful standard, as, unlike hydrogen, it forms compounds with most other elements, especially metals. Howeverhe chose to fix the atomic weight of oxygen as 100, an innovation which did not catch on.Charles Frédéric Gerhardt (1816–56), Henri Victor Regnault (1810–78) and Stanislao Cannizzaro (1826–1910) expanded on Berzelius' works, resolving many of the problems of unknown stoichiometry of compounds, and the use of atomic weights attracted a large consensus by the time of the Karlsruhe Congress (1860). The convention had

Mole 57

reverted to defining the atomic weight of hydrogen as 1, although at the level of precision of measurements at thattime—relative uncertainties of around 1%—this was numerically equivalent to the later standard of oxygen = 16.However the chemical convenience of having oxygen as the primary atomic weight standard became ever moreevident with advances in analytical chemistry and the need for ever more accurate atomic weight determinations.

Scale basis Scale basisrelative to 12C = 12

Relative deviationfrom the 12C = 12 scale

Atomic weight of hydrogen = 1 1.00794(7) −0.788%

Atomic weight of oxygen = 16 15.9994(3) +0.00375%

Relative atomic mass of 16O = 16 15.9949146221(15) +0.0318%

The mole as a unitSince its adoption into the International System of Units, there have been a number of criticisms of the concept of themole as a unit like the meter or the second:• the number of molecules etc. in a given lump of material is a fixed dimensionless quantity which can be expressed

simply as a number, so does not require its own base unit[9] ;• the SI thermodynamic mole is irrelevant to analytical chemistry and is causing avoidable costs to advanced

economies[12] ;• the concepts of the SI quantity 'amount of substance' and unit 'mole' are confusing and difficult to teach[13] .In chemistry, it has been known since Proust's law of definite proportions (1794) that knowledge of the mass of eachof the components in a chemical system is not sufficient to define the system. Amount of substance can be describedas mass divided by Proust's "definite proportions", and contains information which is missing from the measurementof mass alone. As demonstrated by Dalton's law of partial pressures (1803), a measurement of mass is not evennecessary to measure the amount of substance (although in practice it is usual). There are many physicalrelationships between amount of substance and other physical quantities, most notably the ideal gas law (where therelationship was first demonstrated in 1857). The term "mole" was first used in a textbook describing thesecolligative properties.

Other units called "mole"Chemical engineers use the concept extensively, but the unit is rather small for industrial use. For convenience inavoiding conversions, some American engineers adopted the pound-mole (noted lb-mol or lbmol), which is definedas the number of entities in 12 lb of 12C. One lb-mol is equal to 453.59237 mol.[14] In the metric system, chemicalengineers once used the kilogram-mole (noted kg-mol), which is defined as the number of entities in 12 kg of 12C,and often referred to the mole as the gram-mole (noted g-mol), when dealing with laboratory data.[14] Howevermodern chemical engineering practice is to use the kilomole (kmol), which is identical to the kilogram-mole, butwhose name and symbol adopt the SI convention for standard multiples of metric units.

Mole 58

Proposed future definition

KilogramAs with other SI base units, there have been proposals to redefine the kilogram in such a way as to define somecurrently measured physical constants to fixed values. One proposed definition of the kilogram is:[15]

The kilogram is the mass of exactly (6.0221415 × 1023⁄0.012) unbound carbon-12 atoms at rest and in theirground state.

This would have the effect of defining the Avogadro constant to be precisely 6.0221415 × 1023 elementary entitiesper mole.A decision on this proposal is expected by the CGPM in October 2011.[16]

Related unitsThe SI units for molar concentration are mol/m3. However, most chemical literature traditionally uses mol/dm3, ormol dm−3, which is the same as mol/L. These traditional units are often denoted by a capital letter M (pronounced"molar"), sometimes preceded by an SI prefix, for example millimoles per litre (mmol/L) or millimolar (mM),micromoles/litre (µmol/L) or micromolar (µM), or nanomoles/L (nmol/L) or nanomolar (nM).

The unit's holidayOctober 23 is called Mole Day.[17] It is an informal holiday in honor of the unit among chemists in North America.The date is derived from Avogadro's number, which is approximately 6.02×1023. It officially starts at 6:02 A.M. andends at 6:02 P.M.

See also• Einstein (unit)• Faraday (unit)• Stoichiometry• Molar concentration• Molarity• Molar volume

References[1] International Bureau of Weights and Measures (2006), The International System of Units (SI) (http:/ / www. bipm. org/ utils/ common/ pdf/

si_brochure_8_en. pdf) (8th ed.), pp. 114–15, ISBN 92-822-2213-6,[2] Helm, Georg (1897). The Principles of Mathematical Chemistry: The Energetics of Chemical Phenomena. transl. by Livingston, J.; Morgan,

R.. New York: Wiley. p. 6.[3] Some sources place the date of first usage in English as 1902. Merriam–Webster proposes (http:/ / www. merriam-webster. com/ dictionary/

mole[5]) an etymology from Molekulärgewicht (molecular weight).[4] Ostwald, Wilhelm (1893). Hand- und Hilfsbuch zur Ausführung Physiko-Chemischer Messungen. Leipzig. p. 119.[5] mole, n.8, Oxford English Dictionary, Draft Revision Dec. 2008[6] Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006"

(http:/ / physics. nist. gov/ cuu/ Constants/ codata. pdf). Rev. Mod. Phys. 80: 633–730. doi:10.1103/RevModPhys.80.633. . Direct link to value(http:/ / physics. nist. gov/ cgi-bin/ cuu/ Value?na).

[7] (http:/ / physics. aps. org/ synopsis-for/ 10. 1103/ PhysRevLett. 106. 030801)B. Andreas et al., Phys. Rev. Lett. 106, 030801 (2011)[8] International Bureau of Weights and Measures. " Realising the mole (http:/ / www. bipm. org/ utils/ en/ pdf/ SIApp2_mol_en. pdf)."

Retrieved 25 September 2008.[9] de Bièvre, P.; Peiser, H.S. (1992). "'Atomic Weight'—The Name, Its History, Definition, and Units" (http:/ / www. iupac. org/ publications/

pac/ 1992/ pdf/ 6410x1535. pdf). Pure Appl. Chem. 64 (10): 1535–43. doi:10.1351/pac199264101535.

Mole 59

[10] Wang, Yuxing et al.; Bouquet, Fr d ric; Sheikin, Ilya; Toulemonde, Pierre; Revaz, Bernard; Eisterer, Michael; Weber, Harald W; Hinderer,Joerg et al. (2003). "Specific heat of MgB2 after irradiation". Journal of Physics: Condensed Matter 15: 883–893.doi:10.1088/0953-8984/15/6/315.

[11] Lortz, R. et al.; Wang, Y.; Abe, S.; Meingast, C.; Paderno, Yu.; Filippov, V.; Junod, A. (2005). "Specific heat, magnetic susceptibility,resistivity and thermal expansion of the superconductor ZrB12" (http:/ / arxiv. org/ abs/ cond-mat/ 0502193). Phys. Rev. B 72: 024547.doi:10.1103/PhysRevB.72.024547. .

[12] Price, Gary (2010). "Failures of the global measurement system. Part 1: the case of chemistry" (http:/ / www. springerlink. com/ content/p63w663v127t5g0q/ ). Accreditation and Quality Assurance 15 (7): 421–427. doi:10.1007/s00769-010-0655-z. ..

[13] Furio, C; Azcona, R;Guisasola, J. (2002). "The learning and teaching of the concepts 'amount of substance' and mole - a review of theliterature" (http:/ / www. uoi. gr/ cerp/ 2002_October/ pdf/ 02Furio. pdf). Chemistry Education: Research and Practice in Europe 3 (3):277–292. .

[14] Himmelblau, David (1996). Basic Principles and Calculations in Chemical Engineering (6 ed.). pp. 17–20. ISBN 0-13-305798-4.[15] Mills, Ian M.; Mohr, Peter J.; Quinn, Terry J.; Taylor, Barry N.; Williams, Edwin R. (2005). "Redefinition of the kilogram: a decision whose

time has come" (http:/ / www. iop. org/ EJ/ article/ 0026-1394/ 42/ 2/ 001/ met5_2_001. pdf). Metrologia 42: 71–80.doi:10.1088/0026-1394/42/2/001. . Abstract (http:/ / www. iop. org/ EJ/ abstract/ 0026-1394/ 42/ 2/ 001/ ).

[16] Ian Mills (29 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units" (http:/ / www. bipm. org/ utils/en/ pdf/ si_brochure_draft_ch2. pdf). CCU. . Retrieved 2011-01-01.

[17] History of National Mole Day Foundation, Inc (http:/ / www. moleday. org/ htdocs/ history. html)

External links• ChemTeam: The Origin of the Word 'Mole' (http:/ / web. archive. org/ web/ 20071222072256/ http:/ / dbhs.

wvusd. k12. ca. us/ webdocs/ Mole/ Origin-of-Mole. html) at the Wayback Machine (archived December 22,2007).

Candela

Photopic (black) and scotopic[1] (green) luminosity functions. The photopic includes theCIE 1931 standard [2] (solid), the Judd-Vos 1978 modified data [3] (dashed), and the

Sharpe, Stockman, Jagla & Jägle 2005 data [4] (dotted). The horizontal axis iswavelength in nm.

The candela (pronounced /kænˈdɛlə/or /kænˈdiːlə/, symbol: cd) is the SIbase unit of luminous intensity; that is,power emitted by a light source in aparticular direction, weighted by theluminosity function (a standardizedmodel of the sensitivity of the humaneye to different wavelengths, alsoknown as the luminous efficiencyfunction[4] [5] ). A common candleemits light with a luminous intensity ofroughly one candela. If emission insome directions is blocked by anopaque barrier, the emission wouldstill be approximately one candela inthe directions that are not obscured.

The word candela means candle inLatin, Spanish and Italian.

Candela 60

DefinitionLike other SI base units, the candela has an operational definition—it is defined by a description of a physicalprocess that will produce one candela of luminous intensity. Since the 16th General Conference on Weights andMeasures (CGPM) in 1979, the candela has been defined as:[6]

The candela is the luminous intensity, in a given direction, of a source that emits monochromaticradiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1⁄683 watt persteradian.

The definition describes how to produce a light source that (by definition) emits one candela. Such a source couldthen be used to calibrate instruments designed to measure luminous intensity.The candela is sometimes still called by the old name candle,[7] such as in foot-candle and the modern definition ofcandlepower.

ExplanationThe frequency chosen is in the visible spectrum near green, corresponding to a wavelength of about 555 nanometers.The human eye is most sensitive to this frequency, when adapted for bright conditions. At other frequencies, moreradiant intensity is required to achieve the same luminous intensity, according to the frequency response of thehuman eye. The luminous intensity for light of a particular wavelength is given by

where is the luminous intensity in candelas, is the radiant intensity in W/sr and is the standardluminosity function. If more than one wavelength is present (as is usually the case), one must sum or integrate overthe spectrum of wavelengths present to get the total luminous intensity.A common candle emits roughly 1 cd. A 100 W incandescent lightbulb emits about 120 cd.[8]

OriginPrior to 1948, various standards for luminous intensity were in use in a number of countries. These were typicallybased on the brightness of the flame from a "standard candle" of defined composition, or the brightness of anincandescent filament of specific design. One of the best-known of these was the English standard of candlepower.One candlepower was the light produced by a pure spermaceti candle weighing one sixth of a pound and burning at arate of 120 grains per hour. Germany, Austria and Scandinavia used the hefnerkerze, a unit based on the output of aHefner lamp.[9]

It became clear that a better-defined unit was needed. The Commission Internationale de l'Éclairage (InternationalCommission on Illumination) and the CIPM proposed a “new candle” based on the luminance of a Planck radiator (ablack body) at the temperature of freezing platinum. The value of the new unit was chosen to make it similar to theearlier unit candlepower. The decision was promulgated by the CIPM in 1946:

The value of the new candle is such that the brightness of the full radiator at the temperature ofsolidification of platinum is 60 new candles per square centimetre.[10]

It was then ratified in 1948 by the 9th CGPM which adopted a new name for this unit, the candela. In 1967 the 13thCGPM removed the term "new candle" and gave an amended version of the candela definition, specifying theatmospheric pressure applied to the freezing platinum:

The candela is the luminous intensity, in the perpendicular direction, of a surface of 1/600 000 squaremetre of a black body at the temperature of freezing platinum under a pressure of 101 325 newtons persquare metre.[11]

In 1979, because of the difficulties in realizing a Planck radiator at high temperatures and the new possibilities offered by radiometry, the 16th CGPM adopted the modern definition of the candela.[12] The arbitrary (1/683) term

Candela 61

was chosen so that the new definition would exactly match the old definition. Although the candela is now defined interms of the second (an SI base unit) and the watt (a derived SI unit), the candela remains a base unit of the SIsystem, by definition.[13]

SI photometric light units

Quantity Symbol SI unit Abbr. Notes

Luminous energy Qv lumen second lm·s units are sometimes called talbots

Luminous flux F lumen (= cd·sr) lm also called luminous power

Luminous intensity Iv candela (= lm/sr) cd an SI base unit

Luminance Lv candela per square metre cd/m2 units are sometimes called "nits"

Illuminance Ev lux (= lm/m2) lx Used for light incident on a surface

Luminous emittance Mv lux (= lm/m2) lx Used for light emitted from a surface

Luminous efficacy lumen per watt lm/W ratio of luminous flux to radiant flux

See also SI · Photometry · Radiometry

Relationship between luminous intensity and luminous fluxIf a source emits a known luminous intensity Iv (in candelas) in a well-defined cone, the total luminous flux F inlumens is given by

F = Iv × 2π × (1 - cos(A/2)),where A is the radiation angle of the lamp—the full vertex angle of the emission cone. For example, a lamp thatemits 590 cd with a radiation angle of 40° emits about 223 lumens. See MR16 for emission angles of some commonlamps.[14] [15] [16]

If the source emits light uniformly in all directions, the flux can be found by multiplying the intensity by 4π: auniform 1 candela source emits 12.6 lumens.

References[1] CIE Scotopic luminosity curve (1951) (http:/ / www. cvrl. org/ database/ text/ lum/ scvl. htm)[2] CIE (1931) 2-deg color matching functions (http:/ / www. cvrl. org/ database/ text/ cmfs/ ciexyz31. htm)[3] Judd-Vos modified CIE 2-deg photopic luminosity curve (1978) (http:/ / www. cvrl. org/ database/ text/ lum/ vljv. htm)[4] Sharpe, Stockman, Jagla & Jägle (2005) 2-deg V*(l) luminous efficiency function (http:/ / www. cvrl. org/ database/ text/ lum/ ssvl2. htm)[5] Wyzecki, G.; Stiles, W.S. (1982). Color Science: Concepts and Methods, Quantitative Data and Formulae (2nd ed. ed.). Wiley-Interscience.

ISBN 0471021067.[6] "Base unit definitions: Candela" (http:/ / physics. nist. gov/ cuu/ Units/ candela. html). The NIST Reference on Constants, Units, and

Uncertainty. . Retrieved Sept. 27, 2010.[7] Merriam-Webster (http:/ / m-w. com/ dictionary/ candela)[8] "What is a Candela?" (http:/ / www. wisegeek. com/ what-is-a-candela. htm). WiseGeek. . Retrieved Aug. 24, 2008.[9] "Hefner unit, or Hefner candle" (http:/ / www. sizes. com/ units/ hefner. htm). Sizes.com. 30 May 2007. . Retrieved 25 Feb. 2009.[10] Barry N. Taylor (1992). The Metric System: The International System of Units (SI) (http:/ / books. google. com/

books?id=y2-BDaoBVnwC& pg=PA18& dq="value+ of+ the+ new+ candle+ is+ such+ that+ the+ brightness+ of+ the+ full+ radiator"&as_brr=3& ei=elatR_S1FofgswPvu430BQ& sig=yl2AU7A-R1O9e5ZuEzuLwekiM2E). U. S. Department of Commerce. p. 18.ISBN 0941375749. . (NIST Special Publication 330, 1991 ed.)

[11] 13th CGPM Resolution 5, CR, 104 (1967), and Metrologia, 4, 43–44 (1968).[12] 16th CGPM Resolution 3, CR, 100 (1979), and Metrologia, 16, 56 (1980).[13] http:/ / www1. bipm. org/ en/ si/ si_brochure/ appendix2/ photometric. html#history[14] Theory (http:/ / www. theledlight. com/ lumens. html)

Candela 62

[15] Formulas (http:/ / forums. linear1. org/ index. php/ topic,113. 0. html)[16] Online converter (http:/ / led. linear1. org/ lumen. wiz)

63

Apprendix

SI derived unitThe International System of Units (SI) specifies a set of seven base units from which all other units of measurementare formed. These other units are called SI derived units and are also considered part of the standard. SI units wasafter the French Le Système International d'Unités which opted for a universal, unified and self-consistent system ofmeasurement units based on the MKS (metre-kilogram-second) system.The names of SI units are always written in lowercase. The unit symbols of units named after persons, however, arealways spelled with an initial capital letter (e.g., the symbol of hertz is Hz; but metre becomes m).

Derived units with special namesBase units can be combined to derive units of measurement for other quantities. In addition to the two dimensionlessderived units radian (rad) and steradian (sr), 20 other derived units have special names.

Named units derived from SI base units

Name Symbol Quantity Expression in terms of otherunits

Expression in terms of SI baseunits

hertz Hz frequency 1/s s-1

radian rad angle m·m-1 dimensionless

steradian sr solid angle m2·m-2 dimensionless

newton N force, weight kg·m/s2 kg·m·s−2

pascal Pa pressure, stress N/m2 m−1·kg·s−2

joule J energy, work, heat N·m = C·V = W·s m2·kg·s−2

watt W power, radiant flux J/s = V·A m2·kg·s−3

coulomb C electric charge or quantity of electricity s·A s·A

volt V voltage, electrical potential difference,electromotive force

W/A = J/C m2·kg·s−3·A−1

farad F electric capacitance C/V m−2·kg−1·s4·A2

ohm Ω electric resistance, impedance, reactance V/A m2·kg·s−3·A−2

siemens S electrical conductance 1/Ω m−2·kg−1·s3·A2

weber Wb magnetic flux J/A m2·kg·s−2·A−1

tesla T magnetic field strength, magnetic flux density V·s/m2 = Wb/m2 = N/(A·m) kg·s−2·A−1

henry H inductance V·s/A = Wb/A m2·kg·s−2·A−2

Celsius °C Celsius temperature K − 273.15 K − 273.15

lumen lm luminous flux lx·m2 cd·sr

SI derived unit 64

lux lx illuminance lm/m2 m−2·cd·sr

becquerel Bq radioactivity (decays per unit time) 1/s s−1

gray Gy absorbed dose (of ionizing radiation) J/kg m2·s−2

sievert Sv equivalent dose (of ionizing radiation) J/kg m2·s−2

katal kat catalytic activity mol/s s−1·mol

Other common units, such as the litre, are not SI units, but are accepted for use with SI (cf. non-SI units accepted foruse with SI).

Supplementary unitsUntil 1995, the SI classified the radian and the steradian as supplementary units, but this designation was abandonedand the units were grouped as derived units.

Other quantities and units

Compound units derived from SI units Name Symbol Quantity Expression in

termsof SI base units

square metre m2 area m2

cubic metre m3 volume m3

metre per second m/s speed, velocity m·s−1

cubic metre per second m3/s volumetric flow m3·s−1

metre per second squared m/s2 acceleration m·s−2

metre per second cubed m/s3 jerk, jolt m·s−3

metre per quartic second m/s4 snap, jounce m·s−4

radian per second rad/s angular velocity s−1

newton second N·s momentum, impulse m·kg·s−1

newton metre second N·m·s angular momentum m2·kg·s−1

newton metre N·m = J/rad torque, moment of force m2·kg·s−2

newton per second N/s yank m·kg·s−3

reciprocal metre m−1 wavenumber m−1

kilogram per square metre kg/m2 area density m−2·kg

kilogram per cubic metre kg/m3 density, mass density m−3·kg

cubic metre per kilogram m3/kg specific volume m3·kg−1

mole per cubic metre mol/m3 amount (-of-substance) concentration m−3·mol

SI derived unit 65

cubic metre per mole m3/mol molar volume m3·mol−1

joule second J·s action m2·kg·s−1

joule per kelvin J/K heat capacity, entropy m2·kg·s−2·K−1

joule per kelvin mole J/(K·mol) molar heat capacity, molar entropy m2·kg·s−2·K−1·mol−1

joule per kilogram kelvin J/(K·kg) specific heat capacity, specific entropy m2·s−2·K−1

joule per mole J/mol molar energy m2·kg·s−2·mol−1

joule per kilogram J/kg specific energy m2·s−2

joule per cubic metre J/m3 energy density m−1·kg·s−2

newton per metre N/m = J/m2 surface tension kg·s−2

watt per square metre W/m2 heat flux density, irradiance kg·s−3

watt per metre kelvin W/(m·K) thermal conductivity m·kg·s−3·K−1

square metre per second m2/s kinematic viscosity, diffusion coefficient m2·s−1

pascal second Pa·s = N·s/m2 dynamic viscosity m−1·kg·s−1

coulomb per square metre C/m2 electric displacement field m−2·s·A

coulomb per cubic metre C/m3 electric charge density m−3·s·A

ampere per square metre A/m2 electric current density A·m−2

siemens per metre S/m conductivity m−3·kg−1·s3·A2

siemens square metre per mole S·m2/mol molar conductivity kg-1·s3·mol−1·A2

farad per metre F/m permittivity m−3·kg−1·s4·A2

henry per metre H/m permeability m·kg·s−2·A−2

volt per metre V/m electric field strength m·kg·s−3·A−1

ampere per metre A/m magnetic field strength A·m−1

candela per square metre cd/m2 luminance cd·m−2

coulomb per kilogram C/kg exposure (X and gamma rays) kg−1·s·A

gray per second Gy/s absorbed dose rate m2·s−3

ohm metre Ω·m resistivity m3·kg·s−3·A−2

References• I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC: Quantities, Units and Symbols in Physical

Chemistry, 2nd edition (June 1993), Blackwell Science Inc (p. 72)

Units accepted for use with SI 66

Units accepted for use with SIThis is a list of units that are not defined as part of the International System of Units (SI), but are otherwisementioned in the SI[1] [2] , because either the SI accepts their use as being multiples or submultiples of SI-units, orthey have important contemporary application, or are otherwise commonly encountered.

Units officially accepted for use with the SI

Name Symbol Quantity Equivalent SI unit

Widely used units expected to be used indefinitely

minute min time (SI unit multiple) 1 min = 60 s

hour h time (SI unit multiple) 1 h = 60 min = 3600 s

day d time (SI unit multiple) 1 d = 24 h = 1440 min = 86400 s

degree of arc ° angle (dimensionless unit) 1° = (π/180) rad

minute of arc ′ angle (dimensionless unit) 1′ = (1/60)° = (π/10800) rad

second of arc ″ angle (dimensionless unit) 1″ = (1/60)′ = (1/3600)° = (π/648000) rad

hectare ha area (decimal unit multiple) 1 ha = 100 a = 10000 m2 = 1 hm2

litre l or L volume (decimal unit multiple) 1 l = 1 dm3 = 0.001 m3

tonne t mass (decimal unit multiple) 1 t = 103 kg = 1 Mg

Logarithmic units

neper Np dimensionless ratio of field quantities LF = ln(F/F0) Np

dimensionless ratio of power quantities LP = 1⁄2ln(P/P0) Np

bel, decibel B, dB dimensionless ratio of field quantities LF = 2 log10(F/F0) B

dimensionless ratio of power quantities LP = log10(P/P0) B

Units with experimentally determined values

electronvolt eV energy 1 eV = 1.60217653(14) × 10−19 J

atomic mass unitdalton

uDa

mass 1 u = 1 Da = 1.66053886(28) × 10−27 kg

astronomical unit AU length 1 AU = 1.49597870691(6) × 1011 m

Natural units (n.u.)

n.u. of speed c0

speed 299792458 m/s (exact)[3]

n.u. of action ħ action 1.05457168(18) × 10−34 J·s

n.u. of mass me

mass of electron 9.1093826(16) × 10−31 kg

n.u. of time time 1.2880886677(86) × 10−21 s

Atomic units (a.u.)

a.u. elementary charge e elementary charge 1.60217653(14) × 10−19 C

a.u. of length (bohr) a0

Bohr radius 0.5291772108(18) × 10−10 m

a.u. of energy (hartree) Eh

Hartree energy 4.35974417(75) × 10−18 J

Units accepted for use with SI 67

a.u. of time ħ/Eh

time 2.418884326505(16) × 10−17 s

Common units not officially sanctioned

Name Symbol Quantity

Equivalent SI unit

Ångström,angstrom

Å length 1 Å = 0.1 nm = 10−10 m

nautical mile nm length 1 nautical mile = 1852 m

knot kt speed 1 knot = 1 nautical mile per hour = (1852/3600) m/s

are a area 1 a = 1 dam2 = 100 m2

barn b area 1 b = 10−28 m2

bar bar pressure 1 bar = 105 Pa

millibar mbar pressure 1 mbar = 1 hPa = 100 Pa (was used in atmospheric meteorology, the preferred unit is now the hectopascal)

atmosphere atm pressure 1 atm = 1013.25 mbar = 1013.25 hPa = 1.01325 × 105 Pa (commonly used in atmospheric meteorology, inoceanology and for pressures within liquids, or in the industry for pressures within containers of liquifiedgas)

References[1] "Non-SI units accepted for use with the SI, and units based on fundamental constants" (http:/ / www. bipm. org/ en/ si/ si_brochure/ chapter4/

4-1. html) (PDF). SI brochure (8th edition). BIPM. . Retrieved 2010-08-28.[2] Taylor, Barry N. (ed.) (2001). "The International System of Units (SI)" (http:/ / physics. nist. gov/ Pubs/ SP330/ sp330. pdf). Special

Publication 330. Gaithersburg, Maryland: National Institute of Standards and Technology (NIST). .[3] In this case it is not the speed of light, but the length of the meter, which is obtained by experiment

Article Sources and Contributors 68

Article Sources and ContributorsInternational System of Units  Source: http://en.wikipedia.org/w/index.php?oldid=409155669  Contributors: (3ucky(3all, 28bytes, A bit iffy, A ghost, A-giau, AEMoreira042281, AaronSw,Accurizer, Adamstevenson, Adamtester, Aeons, Aexus, Ahoerstemeier, Aitias, Ajscilingo, AlefZet, Alexwcovington, Alkari, Allan McInnes, Alpha Quadrant, Altenmann, Andre Engels,AndrewHowse, Andros 1337, Andyabides, Antiedman, Ap, Aquilina, Aquilosion, Argonaut999, Armando82, ArnoldReinhold, Ashishbhatnagar72, AugPi, Aulis Eskola, Auyongjin, AxelBoldt,BD2412, BW95, Bart133, Bcrowell, Bdesham, Beetstra, Beland, Belg4mit, Ben-Zin, Benhoyt, BertSen, Bgpaulus, Blainster, BlaiseFEgan, Blaze Labs Research, BlueMoonlet, Bobblewik,Bobo192, Boivie, Boson, BozMo, BrainMagMo, Brett4u6, Brews ohare, Bryan Derksen, Bsoft, C.Fred, C777, CPCHEM, Caltas, Cameronc, Can't sleep, clown will eat me, Canadianism,Capricorn42, Carlj7, Carnildo, Carthage, Cdang, Centrx, Charles Matthews, ChazYork, Chris Page, Christian Kaese, Chzz, CiudadanoGlobal, Click23, Colsmeghead, Conversion script,Coolhandscot, CosineKitty, Cosva, Cpl Syx, Creidieki, Crissov, Cwlq, Cybercobra, CyclePat, DARTH SIDIOUS 2, Dainamo, Dan kelley90, DannyDaWriter, Dante Alighieri, DarkFalls,Darrenhusted, DarthParadox, DarthSilk, Daveyg21, David Latapie, David from Downunder, David.Monniaux, Davidmaxwaterman, Davipo, DeadEyeArrow, Delirium, Devinlee, Dger, Dhollm,Diberri, DirkvdM, Discospinster, Diti, Djr32, DmitryKo, Docu, Dod1, Doktor Drakken, Dr Dec, DrBob, Dreish, Driax, Drphilharmonic, Drumguy8800, Dungodung, Dutchguy, Dyslexik,Eadmund, Ebear422, EdH, Egil, Ehrenkater, Elektron, Elium2, Elyada, EnOreg, Englishnerd, Enquire, Enzo Aquarius, Epbr123, Eric119, Eridani, Espoo, Eszett, Euric, Facts707, Fakedeeps,Falconpimp, Fatkat61, Favonian, Felix Dance, Femto, Fibula, Finell, Firefox333, Fishal, Flauto Dolce, Flávio Paiva F1, Fnlayson, Fp.monkey, Freak in the bunnysuit, FrstFrs, Fstorino,GTBacchus, Gabbe, Gaius Cornelius, Galoubet, Gameking3002, Gandalf44, Gatto, Gene Nygaard, Gennaro Prota, Gerry Ashton, Gertie, Giftlite, Gimmetrow, Glenn L, Gogo Dodo, GoldFlower,Goodnightmush, Graham87, Grammarmonger, Granucci, Greg L, Gulliveig, Gurch, HJ Mitchell, HTait, Hairy Dude, Haverton, Head, Headbomb, Hektor, Henrygb, Henrywizard, Heron, Holon,Hongooi, HorsePunchKid, Humanoidmanticore, Huseyx2, Hypnoticcow, IE, II MusLiM HyBRiD II, Icairns, Ichwan Palongengi, Ike9898, Ikiwi, Imnotminkus, Indefatigable, Indon, Inferno,Lord of Penguins, Intelati, Invenio, Inwind, Itai, Ixfd64, J4V4, JPH-FM, JWB, Jacob Brower, Jacobolus, Jagginess, Jargoon, Java13690, Jc3s5h, Jcmonteiro42, Jcw69, Jdpipe, Jeepien, Jeffreyn,Jeodesic, Jeronimo, Jerry, JimWae, Jimfbleak, Jimp, Jl.mendieta, Joe Kress, Joeblakesley, Joen235, Joetaras, John David Wright, John Quincy Adding Machine, JohnGeering, Johndarrington,Jojit fb, Jonahgreenthal, Jonathunder, Joseolgon, Jovianeye, Jruderman, Julesd, Juliancolton, Jusdafax, Jusjih, Kaihsu, Kan8eDie, Katydidit, Keilana, KelleyCook, King of Hearts, Klausok, Koyn,Kr5t, Kraftlos, Krauss, Kvng, Kwamikagami, Kwekubo, KyleP, L Kensington, LanceHelsten, Laudaka, Laurusnobilis, Lawrence Cohen, LeadSongDog, Lee S. 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Waggers, Wakuran, Warpflyght, Wavelength, Wayward, Wcp07, Wdl1961, Weregerbil, Wereon, Wernher, WhisperToMe, Whispering, Wiff&Hoos, WikHead, Wikievil666, Wikinist,Wikipedian06, Wile E. Heresiarch, Wisq, Wtmitchell, Wtshymanski, X3210, XJamRastafire, Yama, Youandme, Youssefsan, Yurell, Yyy, Zginder, Ziggymarley01, ΚΕΚΡΩΨ, आशीष भटनागर, 官翁,635 anonymous edits

Kilogram  Source: http://en.wikipedia.org/w/index.php?oldid=409500030  Contributors: A. di M., ACM2, Abdullais4u, Academic Challenger, Acather96, Adrian.benko, Agentilini, Agur barJacé, Ahoerstemeier, AlexiusHoratius, Andrew c, AndrewHowse, Andros 1337, Arch dude, Arkiedragon, Arkuat, Armando82, Army1987, ArnoldReinhold, Atakdoug, Austintruax13, Avoided,AxelBoldt, Bazzargh, Bcjordan, Becuproductions, Bender235, Betterusername, Big Bird, BigNate37, Bilbo1507, BlaiseFEgan, BlckKnght, Bobblewik, Booyabazooka, Brews ohare,Brougham96, Bryan Derksen, CALR, CatherineMunro, Chameleon, Charles Matthews, Chetvorno, Chong shao wei, Chooserr, ChrisCork, Christian List, Claud300000, Cmprince, ColoniesChris, Conversion script, Coopdot, CorvetteZ51, CosineKitty, Cosmic Latte, Courcelles, Crissov, Cyfal, Dabomb87, Dbachmann, Deltawk, Denelson83, DerHexer, Dina, DirkvdM, Dmmaus,Dobermanji, DocWatson42, Docu, Dolphin51, Donarreiskoffer, Doug Bell, Dougjih, DrBob, Dracoreles, DragonHawk, Dragons flight, Duja, Dungodung, Długosz, EVula, Eassin, Ed Poor,Edward, Egil, El buffoono, ElisaEXPLOSiON, Elliotneal, Enuja, Epbr123, Eric Forste, EvanProdromou, Ewlyahoocom, Falcon8765, Fantasy, Faulcon DeLacy, Faxel, Firien, FlamingSilmaril,FlavrSavr, Fram, Fran Rogers, Fredrik, Fropuff, Fuhghettaboutit, Gary King, Gene Nygaard, Generalcp702, Gentleannie7, Giftlite, Gilliam, Glacier Wolf, Gogo Dodo, GraemeL, Grafen,GrahamColm, Greg L, GregRobson, GregorB, GringoCroco, Grouse, Gusmahler, Gzornenplatz, Hankwang, Hans Adler, Headbomb, Henridam, HenryLi, Henryiscool, HereToHelp, Heron,Hobzi, Hoof38, Huey45, HumphreyW, Icairns, IceUnshattered, Indefatigable, Inquisitus, Insanephantom, Int21h, IrishPete, Island, Ixfd64, J.delanoy, JRHorse, Jaardon, Jack Merridew, JacupEllis9, Jannex, Jebba, Jeff G., Jeronimo, JimDunning, JimWae, Jimp, John Vandenberg, JohnG62, Jonathan Grynspan, Jrockley, Jusjih, KDesk, Kbrose, Keber, Keenan Pepper, Kenyon,Kevinskogg, Knowledgebycoop, Koavf, Kww, LeadSongDog, LeaveSleaves, Lee S. Svoboda, Leonard glas, LilHelpa, Lloydic, Lord Emsworth, Lozeldafan, Lupin, Macrakis, Maedac,Mandarax, Manuel Trujillo Berges, Maros, Martinvl, Masky, Mastercampbell, Matbar, Mav, Maximus Rex, Maypigeon of Liberty, Mcgeachy, Mconst, Mejor Los Indios, Michael Devore,Michaelmior, Mikael Häggström, Mike Dill, Mild Bill Hiccup, Mintleaf, Misstessx3, Mlaffs, Modster, Modulatum, Monkbel, Moyogo, Netheril96, Neverquick, NewEnglandYankee, Nike, Nk,Nlonlonlo, Nunquam Dormio, Ohconfucius, Ozkidzez91, Pakaran, Paul Stansifer, PauloColacino, Peak, Petri Krohn, Philip Trueman, Physchim62, PierreAbbat, Pieter Suurmond, Pigman, Pinar,Pinethicket, PrincessofLlyr, Radiant!, Ragib, Random832, Ratika123, Rbj, Reedy, Referos, Rhialto, Richard Taytor, RichiH, Rjwilmsi, Rmhermen, Roadrunner, Ronald20, Ronhjones, Ruakh,SMcCandlish, Saturn star, SaveThePoint, Sbyrnes321, Schnolle, Sdedeo, SeanMack, Selket, Shadow demon, Shastrix, SheffieldSteel, Sjorford, Skater, SkyLined, Slashme, Slowking Man,Smashville, Sobolewski, Spartaz, Spfanstiel, Splarka, Starfarmer, Stephan Leeds, Svdmolen, Swatjester, SweetNeo85, Tarek, Tarquin, Tawker, The Anome, The Thing That Should Not Be,Theroyalweman, Thorwald, Thunderbird2, Tide rolls, Tifoo, TigerShark, Tiki2099, Timb66, Timc, TimothyRias, Timwi, Tolivero, TomTheHand, Tommy2010, Tonsofpcs, Tragh, Travelbird,Trevor MacInnis, Tsogo3, Unyoyega, Urhixidur, Ute Oronto, Vinyanov, Viskonsas, Vlma111, Voyagerfan5761, Wavelength, Wcp07, WereSpielChequers, West.andrew.g, Wik, Wikinger,Wknight94, Wolfkeeper, Wtshymanski, XJamRastafire, Xiner, Yath, ZacBowlingAlt, Zakian49, ZayZayEM, Zfr, Zginder, Zidane tribal, Zinneke, Zocky, आशीष भटनागर, 429 anonymous edits

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Mole  Source: http://en.wikipedia.org/w/index.php?oldid=409736187  Contributors: 16@r, ABERBOY, Adamtester, Addshore, Afroman092, Alansohn, Alaphent, Aldis90, Alex Frei, AlpacaPrince, AlphaEta, Altoidamadeus, Anaxial, Andre Engels, Andrew Nutter, Angry bee, Angusmclellan, Ankitbhatt, Anonymous Dissident, Antandrus, Anupamsr, ArmadilloFromHell, ArnoldReinhold, Ashishbhatnagar72, Astrochemist, AxelBoldt, B jonas, Babban12, Barts1a, Becky Sayles, Ben Jos, Ben-Zin, Bender235, Bert bertington, BillWSmithJr, Blainster, BlindEagle, Bobblewik, Bobby D. DS., Bobo192, Bomac, Bragr, Brews ohare, Brianga, Bryan Derksen, Bsadowski1, Busha5a5a5, ByroDaMan, CalumH93, Canadacow, Carson18, Carson19, CasperEACClemence, Causesobad, Cenarium, Centrx, Chaojoker, Chemical Engineer, Chovain, Christian75, Ckerr, Cold Phront, Collard, Cometstyles, Conversion script, Corhuva, CoyneT, Cremepuff222, Crispmuncher, Csmallw, DARTH SIDIOUS 2, Danny B-), Danny lost, Darth Panda, Darthgriz98, Dbachmann, Deltabeignet, DerHexer, Dina, Discospinster, Dkgdkg, Dolamite02, Donarreiskoffer, DrBob, Drw25, Dspradau, Duncan.france, Dungodung, DéRahier, Długosz, Ed Poor, Eddy 1000, EdgeOfEpsilon, Edward Z. Yang, Ehrenkater, El C, El T, El'Cypher, Enchanter, Enviroboy, Epbr123, Eric119, Escape Orbit, Evmichel, Excelblue, Exprice, Ezhiki, Facts707, Feinoha, Femto, Fieldday-sunday, Filpaul, Flowright138, Freakofnurture, Frnknstn, Fæ, Gaius Cornelius, Gandalf61, Gauss, Gene Nygaard, Giftlite, Gilliam, Glane23, Glenn, Gogo Dodo, Gonhidi, Gooder69, Graham87, Greg L, Grouse, Grunt, Gurch, HMfan1, Hadal, Hairy Dude, Hamiltondaniel, Hanacy, Headbomb, Herbee, Heron, Husond, Hydrogen Iodide, Icairns, Immunize, Insanity Incarnate, Islander, Itub, J.delanoy, J4mm4, JForget, JackZhou, Jake,

Article Sources and Contributors 70

Jeppesn, Jimp, Jittat, Jj137, Jo grainger, John254, JohnMark, Johnanth, Jokl, Jonathan Rabbitt, Jonathanischoice, Josh the Nerd, Josh1772, Joshlepaknpsa, Jsd, Julesd, Junglecat, KDesk,Kaiserkarl13, Kaldosh, Kbrose, Khalid Mahmood, Killing Vector, Kinu, KittySaturn, Kku, Kubigula, Lambiam, Leongielen, Livitup, Livy15, Llrc, Llywelyn, LoveEncounterFlow, LukeSurl,Luminifer, Luna Santin, Lunchscale, MacAuslan, Madhero88, Manifolded, MarcoTolo, Marj Tiefert, Martin.Budden, Martin451, Martinvl, Mateo SA, Mathmo, MattieTK, Mav, Max 2000,Mbell, Mbeychok, McSly, McVities, Mdd4696, Membender, Meno25, Mervyn, Michael Eriksson, Michael Hardy, Misha Vargas, Miss Madeline, Mobiusone7, Mojomama, Monkeyman,Moulding, Mschlindwein, Mukerjee, Murraay, Müslimix, Nagy, Narayansg, Neckro, Necrobius, Neucleon, Nicho322, Nick Y., NickBush24, Niteman555, Nn123645, Noloop, Nono64,Notinasnaid, NuclearWarfare, Od Mishehu, Ojigiri, OngoingCivilUnrest, Optiguy54, Ospalh, Oxymoron83, P.wormer, Palica, Pandacomics, Patrick, Pdch, Peter Karlsen, PhGustaf, PhilipHermarij, Philip Trueman, Physchim62, Piano non troppo, Pinethicket, Pip2andahalf, Piperh, Pldms, Practicingrationalist, Prophile, Psbsub, Rapigan, Razorflame, Rbj, RedHillian, Referos,Reywas92, Riotrocket8676, Rjwilmsi, Ronhjones, RoyBoy, Ruud Koot, SJP, SWAdair, Sabik, Salsb, Sarbruis, Saucepan, Schentler, Scottiedog15, SeanWillard, Semperf, Shirulashem, Shizhao,SimpsonDG, Sir Nicholas de Mimsy-Porpington, Skinner4251, Skunklover, Slakr, Slashme, Slicky, Slothropslothop, Smurfix, SouthH, Soyseñorsnibbles, SpK, Squids and Chips, Srleffler,Stellmach, Stephenb, Subversive.sound, Sultanofsurreal, SunDragon34, SunsetFlare, Suzumebachisecret, Swestrup, Szajd, Tachyon01, Tarquin, Telex, Tetracube, The Realms of Gold, The ThingThat Should Not Be, Theda, Thegeneralguy, Theislikerice, Thistheman, Thumperward, Thunderbird2, Tide rolls, Tim1988, Tomandlu, Tpruane, Treluckey, Trevor MacInnis, Triona,TrippingTroubadour, Trujaman, Tsemii, Ubuntu2, Uncle Dick, Ungawa555tookie2, Unyoyega, Urhixidur, V8rik, Vaughan Pratt, Vina, Vlmastra, Vsmith, Wayne Slam, Wdflake,WereSpielChequers, Whkoh, Whoosis, Wikipe-tan, William Avery, Willking1979, WinterSpw, Wolfboy567, Wordsmith, Wtshymanski, XJamRastafire, Yamamoto Ichiro, Yarrghman,Yoman82, Yougotdied, Ypark5, Yurell, Zachlipton, Zako234, Zambani, Zamtheuniman, Zephyris, Zginder, Zhengjp, 766 ,لیقع فشاک anonymous edits

Candela  Source: http://en.wikipedia.org/w/index.php?oldid=409742839  Contributors: *drew, .:Ajvol:., 5 albert square, Altenmann, Anarchivist, Andre Engels, Andrew Pullen, Angela,Ashishbhatnagar72, Ben-Zin, BenFrantzDale, Bender235, Bobblewik, Briantw, Bvbacon, Chasingsol, Chendy, ClickRick, Conversion script, Dicklyon, Dodiad, Dominik, DuKot, Dungodung, EdPoor, Ed!, Eep², Electron9, Femto, Fudoreaper, Gilliam, Grunt, Haham hanuka, Harold f, Hashar, Headbomb, Heron, Hottentot, Icairns, Indefatigable, IntrigueBlue, JForget, Jeltz, Jim.henderson,Jimp, Jóna Þórunn, KDesk, Kerry7374, Kwamikagami, L353a1, Lumos3, MPerel, Mani1, Marj Tiefert, Maximaximax, Merovingian, MimirZero, Mishad7, Modeha, Mtidei, Paolo.dL, Pgabolde,Phil Boswell, Quirk, RL0919, Reddi, Referos, Richiesmit, Rjwilmsi, RoyBoy, Ruakh, ScottAllenRauch, Sheepy, Siber79, SimonP, Snags, Srjsignal, Srleffler, Stephan Leeds, Stevenj, Stijak,Sunny256, Svick, Teles, The snare, Thisismyusernamedon'tuseit, Tobias Hoevekamp, Tommy2010, Urhixidur, Voyajer, Vsmith, Wikicat, Wtshymanski, XJamRastafire, Zginder, 85 anonymousedits

SI derived unit  Source: http://en.wikipedia.org/w/index.php?oldid=407754781  Contributors: 1984, 64.34.161.xxx, ABCD, Adamtester, Albmont, Andre Engels, Andrejj, Andythebrave,Antarctic-adventurer, Ap, Argo Navis, Ashishbhatnagar72, Aulis Eskola, AxelBoldt, Beland, Bkell, Bobblewik, Borgx, Brianjd, Bryan Derksen, CALR, Can't sleep, clown will eat me,CatherineMunro, Conversion script, Deanos, Dhollm, DrBob, DrTorstenHenning, Eclecticology, Eric119, Escape Orbit, Evil saltine, Evilphoenix, Facts707, Fourchannel, Fuhghettaboutit,Galoubet, Gene Nygaard, Giftlite, Glenn, Guanaco, Hangfromthefloor, Headbomb, Heron, Hick ninja, Icairns, Ideyal, Jay, Jbell4combo, Jimp, Jusjih, Kbrose, Khaosworks, Kingsboysarecool,Kjoonlee, Leotohill, Lommer, Mav, Mckaysalisbury, Myria, NOrbeck, P30Carl, Patrick, Pengu, Physchim62, Piotrus, Radagast83, Ram-Man, Rhythm, Roal AT, SEWilco, SGBailey, SJK,SimonP, Snigbrook, Spartin 205, Spike35031, Steel, Swiveler, T, The Rambling Man, Tim Starling, Topory, Troy 07, Ukexpat, Vargenau, WOSlinker, Waffleguy4, Winthrowe, XJamRastafire,Yk Yk Yk, 이형주, 93 anonymous edits

Units accepted for use with SI  Source: http://en.wikipedia.org/w/index.php?oldid=406673058  Contributors: 0x845FED, Adamtester, Bleakcomb, Bobblewik, Dhollm, Facts707, Gerry Ashton,Jc3s5h, Jmk, Kbrose, Martinvl, Mclay1, Metaxis, Micro01, Nnh, Rjwilmsi, Satori Son, StradivariusTV, That-Vela-Fella, Verdy p, 8 anonymous edits

Image Sources, Licenses and Contributors 71

Image Sources, Licenses and ContributorsImage:SI Brochure Cover.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:SI_Brochure_Cover.jpg  License: unknown  Contributors: AEMoreira042281, Benhoyt, Coredesat, Diti,Urhixidur, 3 anonymous editsFile:Metrication by year map.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Metrication_by_year_map.svg  License: Public Domain  Contributors: User:AzaTothImage:Non-Metric User.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Non-Metric_User.svg  License: GNU Free Documentation License  Contributors: User:Ichwan PalongengiImage:Metric seal.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Metric_seal.svg  License: Public Domain  Contributors: Bestiasonica, Egg, ShizhaoFile:BIPM courtyard.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:BIPM_courtyard.jpg  License: Public Domain  Contributors: NISTImage:Dunkerque Belfort.JPG  Source: http://en.wikipedia.org/w/index.php?title=File:Dunkerque_Belfort.JPG  License: Creative Commons Attribution-Sharealike 3.0  Contributors:WelleschikImage:Monjuic's castle in Barcelona.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Monjuic's_castle_in_Barcelona.jpg  License: Creative Commons Attribution-Sharealike 2.5 Contributors: Gepardenforellenfischer, Jordiferrer, Marb, 1 anonymous editsImage:Platinum-Iridium meter bar.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Platinum-Iridium_meter_bar.jpg  License: Public Domain  Contributors: Juiced lemon, Karelj,Rd232, Schekinov Alexey Victorovich, SvdmolenFile:CGKilogram.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:CGKilogram.jpg  License: GNU Free Documentation License  Contributors: EPO, Greg A L, Juiced lemon,Ohconfucius, Orion 8, Rastrelli F, Wutsje, 1 anonymous editsFile:Little girl on swing.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Little_girl_on_swing.jpg  License: Creative Commons Attribution 2.0  Contributors: Luiz CarlosFile:Prototype mass drifts.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Prototype_mass_drifts.jpg  License: GNU Free Documentation License  Contributors: Original uploaderwas Greg L at en.wikipediaFile:Denmark’s K48 Kilogram.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Denmark’s_K48_Kilogram.jpg  License: GNU Free Documentation License  Contributors: User:GregLFile:Lasertests.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Lasertests.jpg  License: Public Domain  Contributors: The Air Force Research Laboratory’s Directed EnergyDirectorateFile:Watt balance, large view.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Watt_balance,_large_view.jpg  License: GNU Free Documentation License  Contributors: Photo byRichard Steiner (Original uploader was Greg L at en.wikipedia)File:Michelson Interferometer Laser Interference Fringes-Red.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Michelson_Interferometer_Laser_Interference_Fringes-Red.jpg License: Creative Commons Attribution-Sharealike 3.0  Contributors: Greg LFile:Silicon sphere for Avogadro project.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Silicon_sphere_for_Avogadro_project.jpg  License: GNU Free Documentation License Contributors: The Commonwealth Scientific and Industrial Research Organisation of AustraliaFile:Meissner effect zoom.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Meissner_effect_zoom.jpg  License: Public Domain  Contributors: Greg L, Monkeybait, Saeed.VeradiFile:Nuvola apps kview.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Nuvola_apps_kview.svg  License: unknown  Contributors: Ch1902Image:Searchtool.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Searchtool.svg  License: GNU Lesser General Public License  Contributors: User:YsangkokFile:Flashingsecond.gif  Source: http://en.wikipedia.org/w/index.php?title=File:Flashingsecond.gif  License: Public Domain  Contributors: User:Sbyrnes321File:FOCS-1.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:FOCS-1.jpg  License: Public Domain  Contributors: METASFile:Galvanometer 1890 drawing.png  Source: http://en.wikipedia.org/w/index.php?title=File:Galvanometer_1890_drawing.png  License: Public Domain  Contributors: QuibikImage:Luminosity.png  Source: http://en.wikipedia.org/w/index.php?title=File:Luminosity.png  License: Public Domain  Contributors: Original uploader was Dicklyon at en.wikipediaImage:Spectrum4websiteEval.png  Source: http://en.wikipedia.org/w/index.php?title=File:Spectrum4websiteEval.png  License: GNU Free Documentation License  Contributors: Adoniscik,AirBa, Duesentrieb, Gringer, Littletung, Sonarpulse, Tano4595, W!B:, 3 anonymous edits

License 72

LicenseCreative Commons Attribution-Share Alike 3.0 Unportedhttp:/ / creativecommons. org/ licenses/ by-sa/ 3. 0/