A111D3 3flfiD33

o REFERENCE

i NIST

PUBLICATIONS

NBS SPECIAL PUBLICATION 330

1986 EDITION

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

THE UNTERNAllOMAL

SYSTEM OF UMTS (SD
K he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

Jy Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

basis for the nation's physical measurement system, (2) scientific and technological services for industry and

government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety.

The Bureau's technical work is performed by the National Measurement Laboratory, the National

Engineering Laboratory, the Institute for Computer Sciences and Technology, and the Institute for Materials

Science and Engineering

.

The National Measurement Laboratory

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Conducts research and provides measurements, data, standards, reference

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addresses the scientific basis for new advanced materials technologies; plans

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'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Gaithersburg, MD 20899. ^Some divisions within the center are located at Boulder, CO 80303. 'Located at Boulder, CO, with some elements at Gaithersburg, MD.
THE INTERNATIONAL SYSTEM OF UNITS (SD

Edited by

David T. Goldman

National Bureau of Standards

United States of America

R. J. Bell

National Physical Laboratory

United Kingdom

This translation has been approved by

the International Bureau of Weights

and Measures.

(Supersedes NBS Special Publication

330 1981 Edition)

Issued July 1986

1

*<">E«U 0»

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
National Bureau of Standards Special Publication 330, 1986 Edition

Natl. Bur. Stand. (U.S.), Spec. Publ. 330, 1986 Edition, 56 pages (July 1986)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1986

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402
Foreword

This booklet is the United States edition of the English translation of the fifth edition of "Le

Systeme International d'Unites (SI)," the definitive publication in the French language issued in

1985 by the International Bureau of Weights and Measures (BIPM). This U.S. edition, which con- forms in substance with the British edition that follows the French text in the BIPM document is the

result of a joint effort by the National Bureau of Standards (NBS) of the United States and the

National Physical Laboratory (NPL) in the United Kingdom. In order to make this booklet acceptable to the broadest community of users in the USA, it was necessary to recognize present U.S.

practices and standards as they are found in the literature of our domestic voluntary standards

organizations such as the ASTM and the IEEE, and to use American spelling of certain words. This

American version differs from the British one in the following details: (1) it uses the dot instead of

the comma as the decimal marker; (2) the American spellings "meter," "liter," and "deka" are used

rather than the British "metre," "litre," and "deca"; (3) six footnotes are added to identify U.S.

practices that differ from those of the British; and (4) it contains a few instances of common words

in which the American spelling or usage differs from the British.

The British version will be available from the National Physical Laboratories; the American version can be. ordered from the Superintendent of Documents, U.S. Government Printing Office,

Washington, DC 20402.

Both the U.S. and the British versions represent the best efforts to render an authoritative translation; however, in case of a dispute the French text represents the official position of the BIPM.

SI, the present-day descendant of the Metric System, has become the universal language of scientists. It is the universal language of measurement in most countries.

I am pleased to present this updated translation of the official French text to the U.S. scientific and

technical community. It provides a complete documentation and current updating of the foundation

and fundamental principles of SI. I sincerely hope that it will contribute to a better understanding,

better dissemination, and to a more uniformly correct utilization of SI.

Ernest Ambler,

Director,

National Bureau of Standards

iii
Preface to the 5th Edition

Since 1970, the International Bureau of Weights and Measures (Bureau International des Poids et Mesures, BIPM) has regularly published this document containing Resolutions and Recommendations of the General Conference on Weights and Measures (Conference General des Poids et Mesures, CGPM) and the International Committee for Weights and Measures (Comite International

des Poids et Mesures, CIPM) on the International System of Units. Explanations have been added

as well as relevant extracts from the International Standards of the International Organization for

Standardization (ISO) for the practical use of the System.

The Consultative Committee for Units (Comite Consultatif des Unites, CCU) of the CIPM helped

to draft the document and has approved the fmal text.

Appendix I reproduces in chronological order the decisions (Resolutions, Recommendations,

Declarations, etc.) promulgated since 1889 by the CGPM and the CIPM on units of measurement

and on the International System of Units.

Appendix II outlines the measurements, consistent with the theoretical definitions given here, which

metrological laboratories can make to realize the units and to calibrate highest-quality material

standards.

This 5th edition is a revision of the 4th edition (1981); it takes into consideration the decisions of the

17th General Conference on Weights and Measures (1983) and of the International Committee for

Weights and Measures (1981, 1982, 1983, 1984), and the amendments made by the Consultative

Committee for Units (1982, 1984).

(text omitted here not relevant to U.S. edition)

October 1985

P. GIACOMO

Director, BIPM

J. de BOER

Chairman, CCU

iv
The International System of Units

Contents

Page

Foreword iii Preface to the 5th Edition iv

I. Introduction 1

1.1 Historical note 1

1.2 The three classes of SI units 1

1.3 The SI prefixes 2

1.4 System of quantities 2

1.5 Legislation on units 2

II. SI units 3

II. 1 SI base units 3

II. 1.1 Definitions 3

II. 1.2 Symbols 5

II.2 SI derived units 6

II. 3 SI supplementary units 8

II.4 Rules for writing and using SI unit symbols 9

III. Decimal multiples and sub-multiples of SI units 10

III. l SI prefixes 10

III.2 Rules for using SI prefixes 10

III. 3 The kilogram 11

IV. Units outside the International System 12

IV. 1 Units used with the International System 12

IV.2 Units in use temporarily 13

IV.3 CGS units 14

IV.4 Other units 15

Appendix I. Decisions of the CGPM and the CIPM 16

Appendix II. Practical Realization of the Definitions of Some Important Units 40

Appendix III. Organs of the Meter Convention 47

Index 50

V

I. INTRODUCTION

1.1 Historical note

In 1948 the 9th CGPM', by its Resolution 6, instructed the CIPM:* "to study the

establishment of a complete set of rules for units of measurement"; "to find out for

this purpose, by official inquiry, the opinion prevailing in scientific, technical, and

educational circles in all countries" and "to make reconmiendations on the establishment of a practical system of units of measurement suitable for adoption by all signatories to the Meter Convention."

The same General Conference also laid down, by its Resolution 7, general principles for unit symbols and also gave a list of units with special names.

The 10th CGPM (1954), by its Resolution 6, and the 14th CGPM (1971) by its Resolution 3, adopted as base units of this "practical system of units," the units of

the following seven quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity.

The 11th CGPM (1960), by its Resolution 12, adopted the name International System of Units, with the international abbreviation SI, for this practical system of

units of measurement, and laid down rules for the prefixes, the derived and supplementary units, and other matters, thus establishing a comprehensive specification

for units of measurement.

1.2 The three classes of SI units

SI units are divided into three classes: base units, derived units, and supplementary

units.

From the scientific point of view, division of SI units into these three classes is to a certain extent arbitrary, because it is not essential to the physics of the subject.

Nevertheless, the General Conference, considering the advantages of a single,

practical worldwide system of units for international relations, for teaching, and for

scientific work, decided to base the International System on a choice of seven

well-defined units which by convention are regarded as dimensionally independent: the meter, the kilogram, the second, the ampere, the kelvin, the mole, and the

candela (see II. 1, p. 3). These SI units are called base units.

The second class of SI units contains derived units; i.e., units that can be formed by

combining base units according to the algebraic relations Hnking the corresponding

quantities. The names and symbols of some units thus formed in terms of base units can be replaced by special names and symbols which can themselves be used to

form expressions and symbols of other derived units (see II.2, p. 6).

The 1 1th CGPM (1960) admitted a third class of SI units, called supplementary units

and containing the SI units of plane and solid angle (see II. 3, p. 8).

The SI units of these three classes form a coherent set of units in the sense normally

attributed to the word "coherent"; i.e., a system of units mutually related by rules

of multiplication and division without any numerical factor. Following CIPM Reconunendation 1 (1969), the units of this coherent set of units are designated by the

name SI units.

For the meaning of these abbreviations, see the preface.

1
It is important to emphasize that each physical quantity has only one SI unit, even

if the name of this unit can be expressed in different forms, but the inverse is not

true: the same SI unit name can correspond to several different quantities (see p. 7).

1.3 The SI prefixes

The General Conference has adopted a series of prefixes to be used in forming the

decimal multiples and submultiples of SI units (see III.l, p. 10). Following CIPM

Recommendation 1 (1969), the set of prefixes is designated by the name SIprefixes.

The multiples and submultiples of SI units, which are formed by using the SI

prefixes, should be designated by their complete name, multiples and submultiples of

SI units, in order to make a distinction between them and the coherent set of SI

units proper.

1.4 System of quantities

This book does not deal with the system of quantities used with the SI units, an area handled by Technical Committee 12 of the International Organization for Standardization (ISO) which, since 1955, has published a series of International Standards on

quantities and their units, and which strongly recommends the use of the International System of Units.'

In these International Standards, ISO has adopted a system of physical quantities

based on the seven base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. The other quantities—the derived quantities—are defined in terms of these seven base quantities; the

relationships between the derived quantities and the base quantities are expressed

by a system of equations. It is this system of quantities and equations that is properly used with the SI units.

1.5 Legislation on units

Countries have established, through legislation, rules concerning the use of units on

a national basis, either for general use, or for specific areas such as commerce,

health or public safety, education, etc. In a growing number of countries this legislation is based on the use of the International System of Units.

The International Organization ofLegal Metrology (OIML), founded in 1955, is con- cerned with the international harmonization of this legislation.

' ISO 31, in "Units of measurement", ISO Standards Handbook 2, 2nd Edition, ISO, Geneva, 1982, pp. 19-238.

2
II. SI UNITS

II.l SI base units

Ob) unit of mass

Gdlogram)

II.l.l Definitions

(a) unit of The definition of the meter based upon the interaational prototype of platinum-iridlength ium, in force since 1889, had been replaced by the 11th CGPM (1960) by a defini-

(meter) tion based upon the wavelength of a krypton-86 radiation. In order to increase the

precision of realization of the meter, the 17th CGPM (1983) replaced this latter

definition by the following:

The meter is the length of the path travelled by light in vacuum during a time interval

0/1/299 792 458 of a second (17th CGPM (1983), Resolution 1).

The old international prototype of the meter which was legalized by the 1st CGPM

in 1889 is still kept at the International Bureau of Weights and Measures under the

conditions specified in 1889.

The 1st CGPM (1889) sanctioned the international prototype of the kilogram and

declared: this prototype shall henceforth be considered to be the unit of mass.

The 3d CGPM (1901), in a declaration intended to end the ambiguity which existed as to the meaning of the word "weight" in popular usage, confirmed that the

kilogram is the unit of mass; it is equal to the mass ofthe international prototype of the

kilogram (see the complete declaration, p. 17).

This international prototype made of platinum-iridium is kept at the BIPM under

conditions specified by the 1st CGPM in 1889.

unit of The unit of time, the second, was defined originally as the fraction 1/86 400 of the

time mean solar day. The exact definition of "mean solar day" was left to astronomers,

(second) but their measurements have shown that on account of irregularities in the rotation

of Earth, the mean solar day does not guarantee the desired accuracy. In order to

define the unit of time more precisely the 11th CGPM (1960) adopted a definition

given by the International Astronomical Union which was based on the tropical

year. Experimental work had, however, already shown that an atomic standard of

time-interval, based on a transition between two energy levels of an atom or a molecule, could be realized and reproduced much more accurately. Considering

that a very precise definition of the unit of time of the International System, the

second, is indispensable for the needs of advanced metrology, the 13th CGPM

(1967) decided to replace the definition of the second by the following:

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133

atom. (13th CGPM (1967), Resolution 1).

unit of Electric units, called "international," for current and resistance, had been introelectric duced by the International Electrical Congress held in Chicago in 1893, and the

current definitions of the "international" ampere and the "international" ohm were con-

(ampere) firmed by the International Conference of London in 1908.

Although it was already obvious on the occasion of the 8th CGPM (1933) that

there was a unanimous desire to replace those "international" units by so-called

"absolute" units, the official decision to abolish them was only taken by the 9th

(c)

(d)

3
CGPM (1948), which adopted for the unit of electric current, the ampere, the

following definition:

The ampere is that constant current which, if maintained in two straight parallel con- ductors of infinite length, of negligible circular cross section, and placed 1 meter apart

in vacuum, would produce between these conductors a force equal to 2xl0~^ newton

per meter oflength. (CIPM (1946), Resolution 2 approved by the 9th CGPM, 1948).

The expression "MKS unit of force" which occurs in the original text has been replaced here

by "newton," the name adopted for this unit by the 9th CGPM (1948, Resolution 7).

(e) unit of The definition of the unit of thermodynamic temperature was given in substance by

thermo- the 10th CGPM (1954, Resolution 3) which selected the triple point of water as the

dynamic fundamental fixed point and assigned to it the temperature 273.16 K by definition,

temper- The 13th CGPM (1967, Resolution 3) adopted the name kelvin (symbol K) instead

ature of "degree Kelvin" (symbol °K) and in its Resolution 4 defined the unit of thermo-

(kelyin) dynamic temperature as follows:

The kelvin, unit ofthermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. (13th CGPM (1967), Resolution 4).

The 13th CGPM (1967, Resolution 3) also decided that the unit kelvin and its symbol K should be used to express an interval or a difference of temperature.

Note : In addition to the thermodynamic temperatiu-e (symbol 7^, expressed in kelvins, use

is also made of Celsius temperature (symbol 0 defined by the equation

t = T-To

(f) unit of

amount of

substance

(mole)

where 7o=273.15 K by definition. To express Celsius temperature, the unit "degree Celsius"

which is equal to the unit "kelvin" is used; in this case, "degree Celsius" is a special name

used in place of "kelvin." An interval or difference of Celsius temperature can, however, be

expressed in kelvins as well as in degrees Celsius.

Since the discovery of the fundamental laws of chemistry, units of amount of

substance called, for instance, "gram-atom" and "gram-molecule," have been used

to specify amounts of chemical elements or compounds. These units had a direct

connection with "atomic weights" and "molecular weights," which were in fact

relative masses. "Atomic weights" were originally referred to the atomic weight of

oxygen (by general agreement taken as 16). But whereas physicists separated isotopes in the mass spectrograph and attributed the value 16 to one of the isotopes of

oxygen, chemists attributed that same value to the (slightly variable) mixture of

isotopes 16, 17, 18, which was for them the naturally occurring element oxygen.

Finally an agreement between the International Union of Pure and Applied Physics

(lUPAP) and the International Union of Pure and Applied Chemistry (lUPAC)

brought this duality to an end in 1959/60. Physicists and chemists have ever since

agreed to assign the value 12 to the isotope 12 of carbon. The unified scale thus

obtained gives values of "relative atomic mass."

It remained to define the unit of amount of substance by fixing the corresponding

mass of carbon 12; by international agreement, this mass has been fixed at 0.012 kg,

and the unit of the quantity, "amount of substance," ^ has been given the name mole

(symbol mol).

^ The name of this quantity, adopted by lUPAP, lUPAC, and ISO is in French "quantite de matiere"

and in EngHsh "amount of substance"; (the German and Russian translations are "Stoffmenge" and

« KOJnieCTBOBeincCTBaw. The French name recalls "quantitas materiae" by which in the past the quantity now called "mass" used to be known; we must forget this old meaning, for mass and amount of

substance are entirely different quantities.

4
(g) unit of

luminous

intensity

(candeia)

Following proposals of lUPAP, lUPAC, and ISO, the CIPM gave in 1967, and

confirmed in 1969, the following definition of the mole, adopted by the 14th

CGPM (1971, Resolution 3):

1. The mole is the amount ofsubstance ofa system that contains as many elementary

entities as there are atoms in 0.012 kilogram of carbon 12.

2. When the mole is used, the elementary entities must be specified and may be atoms,

molecules, ions, electrons, other particles, or specified groups ofsuch particles.

In the definition of the mole, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to.

Note that this definition specifies at the same time the nature of the quantity whose

unit is the mole.

The units of luminous intensity based on flame or incandescent filament standards

in use in various countries before 1948 were replaced initially by the "new candle"

based on the luminance of a Planckian radiator (a blackbody) at the temperature of

freezing platinum. This decision had been prepared by the International Commission on Illumination (CIE) and by the International Committee for Weights and

Measures before 1937, and was promulgated by the CIPM in 1946, and then ratified

in 1948 by the 9th CGPM which adopted a new international name for this unit, the

candeia (symbol cd); in 1967 the 13th CGPM gave an amended version of the 1946

definition.

Because of the experimental difficulties in realizing a Planck radiator at high temperatures and the new possibilities offered by radiometry, i.e., the measurement of

optical radiation power, the 16th CGPM adopted in 1979 the following new definition:

The candeia is the luminous intensity, in a given direction, of a source that emits

monochromatic radiation offrequency 540 X 10'^ hertz and that has a radiant intensity

in that direction of (1/683) watt per steradian. (16th CGPM (1979), Resolution 3).

U.1.2 Symbols

The base units of the International System are collected in table 1 with their names

and their symbols (10th CGPM (1954), Resolution 6; 11th CGPM (1960), Resolution 12; 13th CGPM (1967), Resolution 3; 14th CGPM (1971), Resolution 3).

Table 1

SI base units

SI Unit

Quantity' Name Symbol

length meter m

mass kilogram kg

time second s

electric current ampere A

thermodynamic temperature kelvin K

amount of substance mole mol

luminous intensity candeia cd

Translator's note: "Quantity" is the technical word for measurable attributes of phenomena or matter.

5
11.2 SI derived units

Derived units are expressed algebraically in terms of base units by means of the

mathematical symbols of multiplication and division (see table 2 for some examples).

Table 2

Examples of SI derived units expressed in terms of base units

SI Unit

Quantity Name Symbol

area square meter volume cubic meter m'

speed, velocity meter per second m/s

acceleration meter per second squared m/s^ wave number reciprocal meter m-'

density, mass density kilogram per cubic meter kg/m'

speciflc volume cubic meter per kilogram m'Ag

current density ampere per square meter A/m^

magnetic field strength ampere per meter A/m

concentration

(of amount of substance) mole per cubic meter mol/m'

luminance candela per square meter cd/m^

Certain derived units have been given special names and symbols. These names and

symbols are given in tables 3 and 3'; they may themselves be used to express other

derived units (see table 4 for some examples).

In Tables 3, 3', 4, and 5, the final column gives expressions for the SI units con- cerned in terms of SI base units. In this column, factors such as m°, kg", etc. that are equal to 1 are not generally shown explicitly.

Table 3

SI derived units with special names

SI Unit

Quantity Name Symbol

Expression

in terms of other

units

Expression

in terms

of SI base

units

frequency hertz Hz S-' force newton N m • kg • s~^

pressure, stress pascal Pa N/m^ m"' • kg • s~^ energy, work, quantity

of heat joule J N-m m^ • kg • s"^

power, radiant flux watt W J/s m^ • kg • s~'

electric charge.

quantity of electricity coulomb C s-A

electric potential.

potential difference. electromotive force volt V W/A m^-kg-s-5- A-'

capacitance farad F C/V m-^-kg-'-s*-A^

electric resistance ohm a V/A m^ • kg • S-' • A-'

electric conductance Siemens s A/V m-2-kg-' -s'- A^

magnetic flux weber Wb V-s m^-kg-s-^- A-'

magnetic flux density tesla T Wb/m^ kg -8-2 -A-'

inductance henry H Wb/A m^ • kg . S-' • A-2

Celsius temperature*"* degree Celsius °C K

luminous flux lumen Im cd • sr<*' illuminance lux Ix Im/m^ m-^ • cd • sr<*'

See page 4, e. Note.

In photometry, the symbol sr is maintained in expressions for units {see II.3., p. 8).

6
Table 3'

SI derived units with special names admitted for reasons of safeguarding human health

SI Unit

Quantity Name Symbol Expression in terms Expression in terms of other units of SI base units

activity (of a radionuclide) becquerel Bq S-'

absorbed dose,

specific energy

imparted, kerma.

absorbed dose

index gray Gy JAg m^ . s-^

dose equivalent.

dose equivalent

index sievert Sv JAg 2 —2 m' • s

Table 4

Examples of SI derived units expressed by means of special names

SI Unit

Expression

Quantity Name Symbol in terms of

SI base units

dynamic viscosity pascal second Pas — 1 1, „ — 1 m • kg • s moment of force newton meter N-m 2 1 -—2 m • kg • s surface tension newton per meter N/m 1 «-2 kg • s heat flux density.

irradiance watt per square meter kg • s

'

heat capacity, entropy joule per kelvin J/K m • kg • s • K

'

specific heat capacity. joule per kilogram

specific entropy kelvin J/(kg • K) 2 —2 V — I m^ • s • K '

specific energy joule per kilogram JAg 2 —2 m • s thermal conductivity watt per meter kelvin W/(m • K) m kg s • K

energy density joule per cubic meter J/m' m • kg • s electric field strength volt per meter V/m 1 —3 A — I m • kg • s -A '

electric charge density coulomb per cubic meter C/m' — 3 A m • s • A

electric flux density coulomb per square meter C/m^ m

—2 A ' • s • A

permittivity farad per meter F/m m-'-kg-' -s*- A^

permeability henry per meter H/m m • kg • s~^ • A~^

molar energy joule per mole J/mol m^ • kg • s~^ • mol~'

molar entropy, molar

heat capacity joule per mole kelvin J/(mol • K) m^-kg-s-'-K-' -mol-'

exposure (x and y rays) coulomb per kilogram CAg kg~' • s •

A

absorbed dose rate gray per second Gy/s m^-s-'

A single SI unit name may correspond to several different quantities, as has been

mentioned in paragraph 1.2 (p. 2). In the above tables, where the list of quantities is not exhaustive, one finds several examples. Thus the joule per kelvin (J/K) is the SI

unit for the quantity heat capacity as well as for the quantity entropy; also the

ampere (A) is the SI unit for the base quantity electric current as well as for the

derived quantity magnetomotive force. The name of the unit is thus not sufficient

to define the quantity measured; in particular, measuring instruments should indicate not only the unit but also the measured quantity concerned.

7
A derived unit can often be expressed in several different ways by using names of

base units and special names of derived units: for example, in place of joule one

may write newton meter or even kilogram meter squared per second squared.

However, this algebraic freedom is governed by common-sense physical considerations.

In practice, with certain quantities one gives preference to using certain special unit

names, or certain combinations of units, in order to facilitate the distinction between quantities having the same dimension. For example, one designates the SI

unit of frequency as the hertz rather than the reciprocal second, and one designates

the SI unit of moment of force as the newton meter rather than the joule.

In the field of ionizing radiation, in the same way one designates the SI unit of

activity as the becquerel rather than the reciprocal second and the SI units of

absorbed dose and dose equivalent as gray and sievert, respectively, rather than

the joule per kilogram.^

Note: Dimensionless quantities. —The values of certain so-called dimensionless

quantities, as for example refractive index, relative permeability, or relative permittivity, are defined as the ratio of two comparable quantities. These dimensionless

quantities are expressed by pure numbers. The coherent SI unit is then the ratio of

two identical SI units and may be expressed by the number 1.

II.3 SI supplementary units

This class contains two units: the SI unit of plane angle, the radian, and the SI unit

of solid angle, the steradian (11th CGPM (1960), Resolution 12).

Considering that plane angle is generally expressed as the ratio between two

lengths and solid angle as the ratio between an area and the square of a length, and

in order to maintain the internal coherence of the International System based on

only seven base units, the CIPM (1980) specified that, in the International System,

the supplementary units radian and steradian are dimensionless derived units. This

implies that the quantities plane angle and solid angle are considered as dimensionless derived quantities.

Table 5

SI supplementary units

SI Unit

Expression

Quantity Name Symbol in terms of

SI base units

plane angle radian rad m-m"' = 1

solid angle steradian sr

These supplementary units may be used in expressions for derived units to facilitate

distinguishing between quantities of different nature but the same dimension. Some

examples of the use of supplementary units in forming derived units are given in

table 6.

^ See page 39 Recommendation 1 (CI- 1984) adopted by the CIPM.

8
Table 6

Examples of SI derived units formed by using supplementary units

Quantity

SI Unit

Name Symbol

angular velocity radian per second rad/s

angular acceleration radian per second squared rad/s^ radiant intensity watt per steradian W/sr

radiance watt per square meter steradian W-m-^-sr-'

II.4 Rules for writing and using SI unit symbols

The general principles concerning writing the unit symbols were adopted by the

9th CGPM (1948, Resolution 7):

1. Roman (upright) type, in general lower case, is used for the unit symbols. If however,

the name of the unit is derived from a proper name, the first letter of the symbol is in upper case.

2. Unit symbols are unaltered in the plural.

3. Unit symbols are not followed by a period.

To insure uniformity in the use of the SI unit symbols, ISO International Standards give certain recommendations. Following these recommendations:

a) The product of two or more units may be indicated in any of the following

ways,*

for example : N • m, N . m, or N m.

b) A solidus (oblique stroke, /), a horizontal line, or negative exponents may be

used to express a derived unit formed from two others by division,

for example : m/s, TM, or m • s~'

c) The solidus must not be repeated on the same line unless ambiguity is avoided

by parentheses. In complicated cases negative exponents or parentheses should be

used,

for example : m/s^ or m-s~^ but not: m/s/s

m-kg/(s^-A) or m-kg-s~''A~' m-kg/sVA

USA Editors' note: See American National Standard ANSI/IEEE Std 260-1978, which states that in USA practice only the raised dot of these three ways is used.

9
III. DECIMAL MULTIPLES AND

SUB-MULTIPLES OF SI UNITS

in.l SI prefixes

The 11th CGPM (1960, Resolution 12) adopted a first series of prefixes and symbols of prefixes to form the names and symbols of the decimal multiples and submultiples of SI units. Prefixes for 10"" and 10"'* were added by the 12th CGPM

(1964, Resolution 8) and those for 10" and 10'* by the 15th CGPM (1975, Resolution 10).

Table 7

SI prefixes

Factor Prefix Symbol Factor Prefix Symbol

10" exa E 10-' deci d

10" peta P 10-^ centi c

10 tera T 10-' milli m

10' giga G 10-* micro

10* mega M io-» nano n

10' kUo k

10-'^ pico P

10^ hecto h 10-" femto f 10' deka* da 10-18 atto a

ni.2 Rules for using SI prefixes

In accord with the general principles adopted by the ISO, the CIPM recommends

that the following rules for using the SI prefixes be observed:

1. Prefix symbols are printed in roman (upright) type without spacing between

the prefix symbol and the unit symbol.

2. The grouping formed by the prefix symbol attached to the unit symbol constitutes a new inseparable symbol (of a multiple or submultiple of the unit concerned)

which can be raised to a positive or negative power and which can be combined

with other unit symbols to form compound unit symbols,

for example: 1 cm^=(10-^ m)'= 10"' m^

1 cm-'=(10-^ m)-' = 10'

m-'

1 /Lis-'=(10-S)-' = 10'

S-'

1 V/cm=(l V)/(10-' m)= 10^ V/m

3. Compound prefixes, i.e., prefixes formed by the juxtaposition of two or more

SI prefixes, are not to be used,

for example: 1 nm but not: 1 mjiim

4. A prefix should never be used alone

for example: lOVm^ but not: M/m^

* USA Editors' note: Outside the USA, the spelling "deca" is extensively used.

10
III.3 The kilogram

Among the base units of the International System, the unit of mass is the only one

whose name, for historical reasons, contains a prefix. Names of decimal multiples

and sub-multiples of the unit of mass are formed by attaching prefixes to the word

"gram" (CIPM (1967), Recommendation 2),

for example: 10~* kg= 1 milligram (1 mg) but not: 1 microkilogram (1 jiikg).

11
IV. UNITS OUTSIDE THE INTERNATIONAL SYSTEM

IV.l Units used with the Internatioiial System

The CIPM (1969) recognized that users of SI will wish to employ with it certain

units not part of it, but which are important and are widely used. These units are given in table 8. The combination of units of this table with SI units to form

compound units should be restricted to special cases in order not to lose the advantage of the coherence of SI units.

Table 8

Units in use with the International System

Name Symbol Value in SI units

minute min 1 min = 60s

hour*"' h 1 h = 60min = 3 600s

day d 1 d = 24h = 86 400s

degree o1 = (fl-/180)rad

minute t 1

'

= (1/60)° =(ir/10 800) rad

second m1 • = (1/60)' =(ir/648 000) rad

liter<*> 1.L 1 L = ldm'=10-'m'

metric ton*'*' t 1

1

= 10' kg

<'"The symbol of this unit is included in Resolution 7 of the 9th CGPM (1948).

<*' This unit and the symbol 1 were adopted by CIPM in 1879 (Proces-Verbaux CIPM, 1879, p. 41). The

alternative symbol, L, was adopted by the 16th CGPM (1979, Resolution 6) in order to avoid the risk of

confusion between the letter 1 and the number 1.' The present definition of the liter is in Resolution 6 of

the 12th CGPM (1964).

'"•This unit and its symbol were adopted by the International Committee in 1879 {Procis-Verbaux CIPM,

1879, p. 41).

It is likewise necessary to recognize, outside the International System, some other

units that are useful in specialized fields, because their values expressed in SI units

must be obtained by experiment, and are therefore not known exactly (table 9).

Table 9

Units used with the International System whose values

in SI units are obtained experimentally

Name Symbol Defmition

electronvolt eV (a)

unified atomic mass unit u

(b)

The electronvolt is the kinetic energy acquired by an electron in passing through a potential differ- ence of 1 volt in vacuum; 1 eV= 1.602 19 x 10"" J approximately.

***The unified atomic mass unit is equal to (1/12) of the mass of an atom of the nuclide '^C;

1 u= 1.660 57 X

10"^' kg approximately.

' USA Editors' note: In some English-speaking countries this unit is called "tonne."

' USA Editors' note: In the USA, the recommended symbol for liter is L.

12
IV.2 Units in use temporarily

In view of existing practice in certain fields or countries, the CIPM (1978) considered that it was acceptable for those units listed in table 10 to continue to be used

with SI units until the CIPM considers their use no longer necessary. However,

these units should not be introduced where they are not used at present.

Table 10

Units in use temporarily with the International System

Name Symbol Value in SI unit

nautical mile'"' 1 nautical mile = 1 852 m

knot

A

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

angstrom 1 A=0.1 nm=10-"'m

are<" a 1 a=l dam^=10^m^

hectare**" ha 1 ha=l hm^=10''m2

bam*'^' b 1 b=100fm^=10-^' m^

bar<* bar lbar=0.1 MPa=100kPa=1000hPa=10' Pa

gal<'> Gal 1 Gal=l cm/s^=10-Ws2

curie^ Ci 1 0=3.7X10'° Bq

roentgen**' R 1 R =2.58X10-' CAg

rad<*' rad 1 rad=l cGy=10-2 Gy

rem<'' rem 1 rem=l cSv=10-^ Sv

*"* The nautical mUe is a special unit employed for marine and aerial navigation to express distances. TTie conventional value given above was adopted by the First International Extraordinary Hydrographic Conference, Monaco, 1929, under the name "International nautical mile."

<*>This unit and its symbol were adopted by the CIPM in 1879 (Proces-Verbaux CIPM, 1879, p. 41) and

are used to express agrarian areas. '"'The bam is a special unit employed in nuclear physics to express effective cross sections.

'^ This unit and its symbol are included in Resolution 7 of the 9th CGPM (1948).

The gal is a special unit employed in geodesy and geophysics to express the acceleration due to gravity.

^The curie is a special unit employed in nuclear physics to express activity of radionuclides (12th

CGPM (1964), Resolution 7). The roentgen is a special unit employed to express exposure of x or y radiations.

'** The rad is a special unit employed to express absorbed dose of ionizing radiations. When there is risk of confusion with the symbol for radian, rd may be used as the symbol for rad. The rem is a special unit used in radioprotection to express dose equivalent.

* USA Editors* note: In recommended USA practice, hectare would appear in table 8. See Federal

Register Notice of February 26, 1982, "Metric System of Measurement."

13
rv.3 CGS units

In the field of mechanics, the CGS system of units was based upon three base

units: the centimeter, the gram, and the second. In the field of electricity and

magnetism, units were expressed in terms of these three base units; this led to the

establishment of several different systems, for example the CGS Electrostatic System, the CGS Electromagnetic System, and the CGS Gaussian System. In these

three last-mentioned systems, the system of quantities and the corresponding system of equations are often different from those used with SI units.

The CIPM considers that it is in general preferable not to use, with the units of the

International System, CGS units that have special names.* Such units are listed in

table 11.

Table 11

CGS units with special names

Name Symbol Value in SI unit

erg*") erg 1 erg=10-'J

dyne*"' dyn 1 dyn=10-'N

poise'"* P 1 P=l dyn-s/cm^=0.1 Pa-s stokes St 1 St=l cmVs=10-''mVs

gauss'*' Gs,G 1 Gs corresponds to 10~* T

oersted'** Oe 1 Oe corresponds to (1000/4i7-)A/m

maxwell*** Mx 1 Mx corresponds to 10~' Wb

stilb'** sb 1 sb=l cd/cm2=l(ycd/m2

phot ph 1 ph=10''lx

'''*This unit and its symbol were included in Resolution 7 of the 9th CGPM (1948). ***This unit is part of the so-called "electromagnetic" 3-dimensional CGS system and cannot strictly

speaking be compared to the correspionding unit of the International System, which has foiu" dimensions

when only mechanical and electric quantities are considered.

* The aim of the International System of Units and of the recommendations contained in this document

is to secure a greater degree of uniformity, hence a better mutual understanding of the general use of

units. Nevertheless in certain specialized fields of scientific research, in particular in theoretical physics, there may sometimes be very good reasons for using other systems or other units. Whichever units are used, it is important that the symbols employed for them follow current international recommendations.

14
IV.4 Other units

As regards units outside the International System which do not come under sec- tions IV. 1, 2, and 3, the CIPM considers that it is in general preferable to avoid

them, and to use instead units of the International System. Some of those units are

listed in table 12.

Table 12

Other units generally deprecated

Name Value in SI unit

fenni 1 fermi=l fni=10~"m

metric carat'"* 1 metric carat=200 mg=2x 10"'' kg

torr 1 torr=(101 325/760) Pa

standard atmosphere (atm)'*' 1 atm= 101 325 Pa

kilogram-force (kgO 1 kgf=9.806 65 N

calorie (cal)*"' micron (fi.)'''* 1 /i= 1 fim= 10~'

m

X unit*''

stereCst)*" 1 st=l m'

gamma (y) 1 7=1 nT=10~'T

y<«> 1 7=1 )ng=10-'kg

X<*' 1 X= 1 /xL= 10-' L= 10-» m'

'"'This name was adopted by the 4th CGPM (1907, pp. 89-91) for commercial dealings in diamonds,

pearls, and precious stones.

<*' Resolution 4 of the 10th CGPM (1954). The designation "standard atmosphere" for a reference pressure of 101 325 Pa is still acceptable.

Several "calories" have been in use: — calorie labeled "at 15 °C": 1 cali5=4.185 5 J (value adopted by the CIPM in 1950 (Proces-Verbaux

CIPM. 22, 1950, pp. 79-80)); — a calorie labeled "IT" (International Table): 1 calrr=4.186 8 J (5th International Conference on

the Properties of Steam, London, 1956); — a calorie labeled "thermochemical": 1 calth=4.184 J. <*The name of this unit and its symbol, adopted by the CIPM in 1879 (Proces-Verbaux CIPM, 1879,

p. 41) and repeated in Resolution 7 of the 9th CGPM (1948) were abolished by the 13th CGPM (1967,

Resolution 7). This special unit was employed to express wavelengths of x rays; 1 x unit= 1.002 X 10"* nm approximately.

'"This special unit employed to measure firewood was adopted by the CIPM in 1879 with the symbol

"s" (Proces-Verbaux CIPM, 1879, p. 41). The 9th CGPM (1948, Resolution 7) changed the symbol to

"St." '^'This symbol is mentioned in Proces-Verbaux CIPM, 1880, p. 56. **'This symbol is mentioned in Proces-Verbaux CIPM, 1880, p. 30.

15
APPENDIX I

Decisions of the CGPM and the CIPM

The more important decisions abrogated, modified, or added to, are indicated by an

asterisk (*). These references and the footnotes have been added by the BIPM to

make understanding of the text easier.

CR: Comptes rendus des seances de la Conference Generale des Poids et Mesures

(CGPM)

PV: Proces-Verbaux des seances du Comite International des Poids et Mesures

(CIPM)

1st CGPM, 1889

gjgj. Sanction ofthe international prototypes ofthe meter and the kilogram (CR, pp. 34-38)

kilogram

The General Conference

considering

the "Compte rendu of the President of the CIPM" and the "Report of the CIPM,"

which show that, by the collaboration of the French section of the international

Meter Commission and of the CIPM, the fundamental measurements of the international and national prototypes of the meter and of the kilogram have been made

with all the accuracy and reliability that the present state of science permits; that

the international and national prototypes of the meter and the kilogram are made of an alloy of platinum with 10 percent iridium, to within 0.000 1; the equality in

length of the international Meter and the equality in mass of the international

Kilogram with the length of the Meter and the mass of the Kilogram kept in the

Archives of France;

that the differences between the national Meters and the international Meter lie within 0.01 millimeter and that these differences are based on a hydrogen thermometer scale which can always be reproduced thanks to the stability of hydrogen,

provided identical conditions are secured;

that the differences between the national Kilograms and the international Kilogram

lie within 1 milligram;

that the international Meter and Kilogram and the national Meters and Kilograms

fulfill the requirements of the Meter Convention,

sanctions

A, As regards international prototypes:

1. The Prototype of the meter chosen by the CIPM. This prototype, at the

temperature of melting ice, shall henceforth represent the metric unit of length.*

2. The Prototype of the kilogram adopted by the CIPM. This prototype shall

henceforth be considered as the unit of mass.

3. The hydrogen thermometer centigrade scale in terms of which the equations of

the prototype Meters have been established.

Definition abrogated in 1960 (see p. 24: 11th CGPM, Resolution 6).

16
B. As regards national prototypes:

3d CGPM, 1901

liter Declaration concerning the definition of the liter (CR, p. 38)*

The Conference declares:

1. The unit of volume, for high accuracy determinations, is the volume occupied

by a mass of 1 kilogram of pure water, at its maximum density and at standard

atmospheric pressure; this volume is called "liter."*

2

* Definition abrogated in 1964 (see p. 27: 12th CGPM, Resolution 6)

mass Declaration on the unit ofmass and on the definition of weight; conventional value ofg„

and weight (CR, p. 70)

Taking into account the decision of the CIPM of 15 October 1887, according to

which the kilogram has been defmed as a unit of mass;

Taking into account the decision contained in the sanction of the prototypes of the

Metric System, unanimously accepted by the CGPM on 26 September 1889;

Considering the necessity to put an end to the ambiguity which in current practice

still exists on the meaning of the word weight, used sometimes for mass, sometimes

for mechanical force;

The Conference declares:

"1. The kilogram is the unit of mass; it is equal to the mass of the international

prototype of the kilogram;

"2. The word weight* denotes a quantity of the same nature as a force; the weight

of a body is the product of its mass and the acceleration due to gravity; in particular, the standard weight of a body is the product of its mass and the standard

acceleration due to gravity;

"3. The value adopted in the international Service of Weights and Measures for

the standard acceleration due to gravity is 980.665 cm/s^ value already stated in

the laws of some countries."^

' "The mass of the international Kilogram is taken as the unit for the international Service of Weights

and Measures" (PV, 1887, p. 88). ^This conventional reference "standard value" (g„ = 9.806 65 m/s^) was confirmed in 1913 by the 5th CGPM (CR, p. 44). This value should be used for reduction to standard gravity of measurements made

in any location on Earth. USA Editors' note: In the USA, ambiguity exists in the use of the term weight as a quantity to mean

either force or mass. In science and technology this declaration (CGPM (1901)) is usually followed,

with the newton the corresponding unit. In commercial and everday use, weight is often used in the

sense of mass for which the SI unit is the kilogram.

17
7th CGPM, 1927

meter Definition of the meter by the international Prototype (CR, p. 49)*

The unit of length is the meter, defined by the distance, at 0°, between the axes of

the two central lines marked on the bar of platinum-iridium kept at the BIPM, and

declared Prototype of the meter by the 1st CGPM, this bar being subject to stan- dard atmospheric pressure and supported on two cylinders of at least one centimeter diameter, symmetrically placed in the same horizontal plane at a distance of 571

mm from each other.*

• Definition abrogated in 1960 (see p. 24; 11th CGPM, Resolution 6).

CIPM, 1946

photometric Definitions ofphotometric units (PV, 20, p. 119)

units

Resolution '

4. The photometric units may be defined as follows:

New candle (unit of luminous intensity).—The value of the new candle is such that

the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per square centimeter.*

New lumen (unit of luminous flux).—The new lumen is the luminous flux emitted in

unit solid angle (steradian) by an isotropic point source having a luminous intensity

of 1 new candle.

5

* Definition modified in 1967 (see p. 30: 13th CGPM, Resolution 5).

mechanical Definitions of electric units (PV, 20, 131)

and

electric Resolution 2

units

4. A) Definitions of the mechanical units which enter the definitions of electric

units:

Unit offorce. —The unit of force [in the MKS (Meter, Kilogram, Second) system]

is that force which gives to a mass of 1 kilogram an acceleration of 1 meter per

second, per second.

Joule (unit of energy or work).—The joule is the work done when the point of

application of 1 MKS unit of force [newton] moves a distance of 1 meter in the

direction of the force.

Watt (Unit of power).—The watt is the power which in one second gives rise to

energy of 1 joule.

^ The two definitions contained in this Resolution were ratified by the 9th CGPM (1948), which also approved the name candela given to the "new candle" (CR, p. 54). For the lumen the qualifier "new"

was later abandoned.

The definitions contained in this Resolution 2 were approved by the 9th CGPM (1948), (CR, p. 49), which moreover adopted the name newton (Resolution 7) for the MKS unit of force.

18
B) Definitions of electrical units. The CIPM accepts the following propositions

which define the theoretical value of the electric units:

Ampere (unit of electric current).—The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between

these conductors a force equal to 2X 10~^ MKS unit of force [newton] per meter of

length.

Volt (unit of potential difference and of electromotive force).—The volt is the

difference of electric potential between two points of a conducting wire carrying a constant current of 1 ampere, when the power dissipated between these points is equal to 1 watt.

Ohm (unit of electric resistance).—The ohm is the electric resistance between two

points of a conductor when a constant potential difference of 1 volt, applied to

these points, produces in the conductor a current of 1 ampere, the conductor not

being the seat of any electromotive force.

Coulomb (unit of quantity of electricity).—The coulomb is the quantity of electricity carried in 1 second by a current of 1 ampere.

Farad (unit of capacitance).—The farad is the capacitance of a capacitor between

the plates of which there appears a potential difference of 1 volt when it is charged

by a quantity of electricity of 1 coulomb.

Henry (unit of electric inductance).—The henry is the inductance of a closed circuit

in which an electromotive force of 1 volt is produced when the electric current in

the circuit varies uniformly at the rate of 1 ampere per second.

Weber (unit of magnetic flux). —The weber is that magnetic flux which, linking a

circuit of one turn, would produce in it an electromotive force of 1 volt if it were

reduced to zero at a uniform rate in 1 second.

9th CGPM, 1948

thermodynamic Triple point of water; thermodynamic scale with a single fixed point; unit of quantity of

scale heat (joule) (CR, pp. 55 and 63).

unit of

quantity of heat

Resolution 3

1. With present-day techniques, the triple point of water is capable of providing a thermometric reference point with an accuracy higher than can be obtained from

the melting point of ice.

In consequence the CCTC [Consultative Committee for Thermometry and

Calorimetry] considers that the zero of the centesimal thermodynamic scale must

be defined as the temperature 0.0 10 0 degree below that of the triple point of water.

2. The CCTC accepts the principle of an absolute thermodynamic scale with a

single fundamental fixed point, at present provided by the triple point of pure

water, the absolute temperature of which will be fixed at a later date.

The introduction of this new scale does not affect in any way the use of the

International Scale, which remains the recommended practical scale.

' The three propositions contained in this Resolution 3 were adopted by the General Conference.

19
3. The unit of quantity of heat is the joule.

Note: It is requested that the results of calorimetric experiments be as far as possible expressed in joules.

If the experiments are made by comparison with the rise of temperature of water

(and that, for some reason, it is not possible to avoid using the calorie) the information necessary for conversion to joules must be provided.

The CIPM, advised by the CCTC, should prepare a table giving, in joules per

degree, the most accurate values that can be obtained from experiments on the

specific heat of water.*

degree Adoption of "degree Celsius"

Celsius

From three names ("degree centigrade," "centesimal degree," "degree Celsius")

proposed to denote the degree of temperature, the CIPM has chosen "degree Celsius" (PV, 21, 1948, p. 88).

This name is also adopted by the General Conference (CR, p. 64).

Proposal for establishing a practical system of units of measurement (CR, p. 64).

Resolution 6

The General Conference,

considering

that the CIPM has been requested by the International Union of Physics to adopt

for international use a practical international system of units; that the International

Union of Physics recommends the MKS system and one electric unit of the absolute practical system, but does not recommend that the CGS system be abandoned

by physicists;

that the CGPM has itself received from the French Government a similar request,

accompanied by a draft to be used as basis of discussion for the establishment of a complete specification of units of measurement;

instructs the CIPM:

to seek by an energetic, active, official enquiry the opinion of scientific, technical,

and educational circles of all countries (offering them in effect the French document as basis);

to gather and study the answers;

to make recommendations for a single practical system of units of measurement,

suitable for adoption by all countries adhering to the Meter Convention.

practical

system of

units of

measurement

' A table, prepared in response to this request, was approved and published by the CIPM in 1950 (PV,

22, p. 92).

20
symbols and Writing and printing of unit symbols and of numbers (CR, p. 70)

numbers

Resolution 7

Principles

Roman (upright) type, in general lower case, is used for symbols of units; if however the symbols are derived from proper names, capital roman type is used. These

symbols are not followed by a full stop.

In numbers, the comma (French practice) or the dot (British practice) is used only

to separate the integral part of numbers from the decimal part. Numbers may be

divided in groups of three in order to facilitate reading; neither dots nor commas

are ever inserted in the spaces between groups.

Unit Symbol Unit Symbol

• meter m ampere A

• square meter volt V

• cubic meter m' watt W

• micron* J* ohm n

• liter** 1 coulomb C

• gram g farad F

• metric ton t henry H

second s hertz Hz

erg erg poise P

dyne dyn newton N

degree Celsius °C • candela (new candle*) cd

• degree absolute*** "K lux Ix calorie cal lumen Im

bar bar stilb sb hour h

Notes

I. The symbols whose unit names are preceded by dots are those which had

already been adopted by a decision of the CIPM.

II. The symbol for the stere, the unit of volume for firewood, shall be "st" and

not "s," which had been previously assigned to it by the CIPM.

III. To indicate a temperature interval or difference, rather than temperature, the

word "degree" in full, or the abbreviation "deg," must be used.****

See p. 31, Resolution 7 of the 13th CGPM (1967).

*• An alternative symbol, L, was adopted in 1979 (see p. 37: 16th CGPM, Resolution 6).

•*• Name and symbol changed in 1967 (see p. 29: 13th CGPM, Resolution 3).

*••• Decision abrogated in 1967 (see p. 29: 13th CGPM, Resolution 3).

21
10th CGPM, 1954

thermo- Definition of the thermodynamic temperature scale (CR, p. 79)

dynamic

scale

Resolution 3

The 10th CGPM decides to define the thermodynamic temperature scale by

choosing the triple point of water as the fundamental fixed point, and assigning to

it the temperature 273.16 degrees Kelvin, exactly.^

standard Definition ofstandard atmosphere (CR, p. 79)

atmosphere

Resolution 4

The 10th CGPM, having noted that the definition of the standard atmosphere

given by the 9th CGPM when defining the International Temperature Scale led

some physicists to believe that this definition of the standard atmosphere was valid

only for accurate work in thermometry,

declares that it adopts, for general use, the definition:

1 standard atmosphere = 1 013 250 dynes per square centimeter, i.e., 101 325 newtons per square meter.

practical

system

of units

Practical system of units (CR, p. 80)

Resolution 6

In accordance with the wish expressed by the 9th CGPM in its Resolution 6 concerning the establishment of a practical system of units of measurement for international use, the 10th CGPM

decides to adopt as base units of the system, the following units:

length mass

time

electric current thermodynamic temperature

luminous intensity

meter

kilogram

second

ampere

degree Kelvin*

candela

* Name changed to "kelvin" in 1967 (see p. 29: 13th CGPM, Resolution 3).

' See p. 29, Resolution 4 of the 13th CGPM (1967) which explicity defines the kelvin.

22
CIPM, 1956

Definition of the unit of time (PV, 25, p. 77)*

Resolution 1

In virtue of the powers invested in it by Resolution 5 of the 10th CGPM, the CIPM

considering

1. that the 9th General Assembly of the International Astronomical Union

(Dublin, 1955) declared itself in favor of linking the second to the tropical year;

2. that, according to the decisions of the 8th General Assembly of the International Astronomical Union (Rome, 1952), the second of ephemeris time (ET) is the

fraction

^408986 496^ ^ ' °^ tropical year for 1900 January 0 at 12 h ET,

decides

"The second is the fraction 1/31 556 925.974 7 of the tropical year for

1900 January 0 at 12 hours ephemeris time."*

Definition abrogated in 1967 (see p. 28: 13th CGPM, Resolution 1).

International System of Units (PV, 25, p. 83)

Resolution 3

The CIPM

considering

the task entrusted to it by Resolution 6 of the 9th CGPM concerning the establishment of a practical system of units of measurement suitable for adoption by all countries adhering to the Meter Convention.

the documents received from twenty-one countries in reply to the enquiry re- quested by the 9th CGPM,

Resolution 6 of the 10th CGPM, fixing the base units of the system to be

established,

recommends

1. that the name "International System of Units" be given to the system founded

on the base units adopted by the 10th CGPM, viz:

[There follows the list of the six base units with their symbols, reproduced in Resolution 12 of the 11th CGPM (I960)]

2. that the units listed in the table below be used, without excluding others which

might be added later:

[There follows the table of units reproduced in paragraph 4 of Resolution 12 of the 1 1th CGPM (I960)]

23
11th CGPM, 1960

Definition of the meter (CR, p. 85)*

Resolution 6

The 11th CGPM

considering

that the international Prototype does not define the meter with an accuracy adequate for the present needs of metrology.

decides

that it is moreover desirable to adopt a natural and indestructible standard,

1. The meter is the length equal to 1 650 763.73 wavelengths in vacuum of the

radiation corresponding to the transition between the levels 2 pio and 5 ds of the

krypton 86 atom.*

2. The definition of the meter in force since 1889, based on the international

Prototype of platinum-iridium, is abrogated.

3. The international Prototype of the meter sanctioned by the 1st CGPM in 1889

shall be kept at the BIPM under the conditions specified in 1889.

* Definition abrogated in 1983 (see p. 38: 17th CGPM, Resolution 1).

Definition of the unit of time (CR, p. 86)*

Resolution 9

The 1 1th CGPM

considering

the powers given to the CIPM by the 10th CGPM, to defme the fundamental unit

of time,

the decision taken by the CIPM in 1956,

ratifies the following definition:

"The second is the fraction 1/31 556 925.974 7 of the tropical year for

1900 January 0 at 12 hours ephemeris time."*

• Definition abrogated in 1967 (see p. 28: 13th CGPM, Resolution 1).

24
International System of Units (CR, p. 87).

Resolution 12

The 11th CGPM

considering

Resolution 6 of the 10th CGPM, by which it adopted six base units on which to

establish a practical system of measurement for international use:

length meter m

mass kilogram kg

time second s

electric current ampere A

thermodynamic temperature degree Kelvin °K*

luminous intensity candela cd

Resolution 3 adopted by the CIPM in 1956,

the recommendations adopted by the CIPM in 1958 concerning an abbreviation for

the name of the system, and prefixes to form multiples and sub-multiples of the

units,

decides

1. the system founded on the six base units above is called "International System

of Units,"**

2. the international abbreviation of the name of the system is: SI,

3. names of multiples and sub-multiples of the units are formed by means of the

following prefixes:***

Multiplying factor Prefix Symbol

1 000 000 000 000 10'2 tera T

1 000 000 000 10' giga G

1 000 000 10' mega M

1 000 10' kilo k

100 102 hecto h

10 10' deka da

0.1 10-' deci d

0.01 10-2 centi c 0.001 10-3 milli m

0.000 001 10-' micro |t 0.000 000 001 10-' nano n

0.000 000 000 001 10-'2 pico P

4. the units listed below are used in the system, without excluding others which

might be added later

SUPPLEMENTARY UNITS

plane angle radian rad

solid angle steradian sr

* Name and symbol of unit modified in 1967 (see p. 29: 13th CGPM, Resolution 3). ** A seventh base unit, the mole, was adopted in 1971 by the 14th CGPM, Resolution 3, see p. 33. •*• See pages 28 and 35 for the four new prefixes adopted by the 12th CGPM (1964), Resolution 8, and

the 15th CGPM (1975), Resolution 10.

25
DERIVED UNITS *

area square meter volume cubic meter m'

frequency hertz Hz 1/s mass density (density) kilogram per cubic meter kg/m'

speed, velocity meter per second m/s

angular velocity radian per second rad/s

acceleration meter per second squared m/s^

angular acceleration radian per second squared rad/s^ force newton N kg • m/s'

pressure (mechanical stress) newton per square meter N/m^

kinematic viscosity square meter per second mVs

dynamic viscosity newton-second per square meter N • s/m'

work, energy, quantity of heat joule J N-m

power watt W J/s

quantity of electricity coulomb C A-s

potential difference. electromotive force volt V W/A

electric field strength volt per meter V/m

electric resistance ohm ft V/A

capacitance farad F A-s/V

magnetic flux weber Wb V -s inductance henry H V-s/A

magnetic flux density tesla T Wb/m'

magnetic field strength ampere per meter A/m

magnetomotive force ampere A

luminous flux lumen Im cd • sr luminance candela per square meter cd/m^

illuminance lux Ix Im/m^

* See page 30 for the other units added by the 13th CGPM (1967), Resolution 6.

cubic Cubic decimeter and liter (CR, p. 88)

decimeter

and liter

Resolution 13

The 11th CGPM,

considering

that the cubic decimeter and the liter are unequal and differ by about 28 parts in

10^

that determination of physical quantities which involve measurements of volume

are being made more and more accurately, thus increasing the risk of confusion

between the cubic decimeter and the liter.

requests the CIPM to study the problem and submit its conclusions to the 12th

CGPM.

CIPM, 1961

cubic decimeter and liter (PV, 29, p. 34)

Recommendation

The CIPM recommends that the results of accurate measurements of volume be

expressed in units of the International System and not in liters.

26
12th CGPM, 1964

firequency Atomic standard offrequency (CR, p. 93)

standard

Resolution 5

The 12th CGPM,

considering

that the 11th CGPM noted in its Resolution 10 the urgency, in the interests of

accurate metrology, of adopting an atomic or molecular standard of time interval,

that in spite of the results already obtained with cesium atomic frequency stan- dards, the time has not yet come for the CGPM to adopt a new definition of the

second, base unit of the International System of Units, because of the new and

considerable improvements likely to be obtained from work now in progress,

considering also that it is not desirable to wait any longer before time measurements

in physics are based on atomic or molecular frequency standards,

empowers the CIPM to name the atomic or molecular frequency standards to be

employed for the time being,

requests the Organizations and Laboratories knowledgeable in this field to pursue

work connected with a new definition of the second.

DECLARATION OF THE CIPM (1964) (PV, 32, p. 26, and CR, p. 93)

The CIPM,

empowered by Resolution 5 of the 12th CGPM to name atomic or molecular frequency standards for temporary use for time measurements in physics,

declares that the standard to be employed is the transition between the hyperfine

levels F=4, M=0 and F=3, M=0 of the ground state of the cesium 133 atom,

unperturbed by external fields, and that the frequency of this transition is assigned

the value 9 192 631 770 hertz.

liter Liter (CR, p. 93)

Resolution 6

The 12th CGPM,

considering Resolution 13 adopted by the 11th CGPM in 1960 and the Recommendation adopted by the CIPM in 1961,

1. abrogates the definition of the liter given in 1901 by the 3d CGPM,

2. declares that the word "liter" may be employed as a special name for the cubic

decimeter,

3. recommends that the name liter should not be employed to give the results of

high accuracy volume measurements.

27
curie Curie (CR, p. 94)

Resolution 7

The 12th CGPM,

considering that the curie has been used for a long time in many countries as a unit

of activity for radionuclides.

recognizing that in the International System of Units (SI), the unit of this activity is the second to the power of minus one (s~'),*

accepts that the curie be still retained, outside SI, as unit of activity, with the value

3.7 X 10'° s-'. The symbol for this unit is Ci.

* In 1975 the name "becquerel" (Bq) was adopted for the SI unit of activity (see p. 34: 15th

CGPM, Resolution 8): 1 Ci=3.7x 10'° Bq.

femto SI prefixes fernto and atto (CR, p. 94)

and atto

Resolution 8

The 12th CGPM,

decides to add to the list of prefixes for the formation of names of multiples and

sub-multiples of units, adopted by the 11th CGPM, Resolution 12, paragraph 3, the

following two new prefixes:

Multiplying factor Prefix Symbol

10-" femto f 10"'* atto a

13th CGPM, 1967-1968

second SI unit of time (second) (CR, p. 103)

Resolution 1

The 13th CGPM,

considering

that the definition of the second adopted by the CIPM in 1956 (Resolution 1) and

ratified by Resolution 9 of the 11th CGPM (1960), later upheld by Resolution 5 of

the 12th CGPM (1964), is inadequate for the present needs of metrology,

that at its meeting of 1964 the CIPM, empowered by Resolution 5 of the 12th

CGPM (1964), recommended, in order to fulfill these requirements, a cesium

atomic frequency standard for temporary use,

that this frequency standard has now been sufficiently tested and found sufficiently

accurate to provide a definition of the second fulfilling present requirements,

that the time has now come to replace the defmition now in force of the unit of

time of the International System of Units by an atomic definition based on that

standard.

28
decides

1. The SI unit of time is the second defined as follows:

"The second is the duration of 9 192 631 770 periods of the radiation corresponding

to the transition between the two hyperfine levels of the ground state of the cesium

133 atom."

2. Resolution 1 adopted by the CIPM at its meeting of 1956 and Resolution 9 of

the 11th CGPM are now abrogated.

kelvin SI unit of thermodynamic temperature (kelvin) (CR, p. 104)

(degree

Celsius) Resolution 3

The 13th CGPM

considering

the names "degree Kelvin" and "degree," the symbols ""K" and "deg," and the

rules for their use given in Resolution 7 of the 9th CGPM (1948), in Resolution 12

of the 11th CGPM (1960), and the decision taken by the CIPM in 1962 (PV, 30,

p. 27), that the unit of thermodynamic temperature and the unit of temperature

interval are one and the same unit, which ought to be denoted by a single name and

single symbol,

decides

1. the unit of thermodynamic temperature is denoted by the name "kelvin" and its symbol is "K";

2. the same name and the same symbol are used to express a temperature interval;

3. a temperature interval may also be expressed in degrees Celsius;

4. the decisions mentioned in the opening paragraph concerning the name of the

unit of thermodynamic temperature, its symbol, and the designation of the unit to

express an interval or a difference of temperatures are abrogated, but the usages

which derive from these decisions remain permissible for the time being.*

* At its 1980 meeting the CIPM approved the report of the 7th meeting of the CCU which

requested that the use of the symbols "°K" and "deg" no longer be permitted.

kelyin Resolution 4

The 13th CGPM,

considering that it is useful to formulate more explicitly the definition of the unit of

thermodynamic temperature contained in Resolution 3 of the 10th CGPM (1954).

decides to express this definition as follows:

"The kelvin, unit of thermodynamic temperature, is the fraction 1/273A6 of the

thermodynamic temperature of the triple point of water."

29
candela SI unit of luminous intensity (candela) (CR, p. 104)*

Resolution 5

The 13th CGPM

considering

the definition of the unit of luminous intensity ratified by the 9th CGPM (1948) and

contained in the "Resolution concerning the change of photometric units" adopted

by CIPM in 1946 (PV, 20, p. 119) in virtue of the powers conferred by the 8th

CGPM (1933).

that this definition fixes satisfactorily the unit of luminous intensity, but that its wording may be open to criticism,

decides to express the definition of the candela as follows:

"The candela is the luminous intensity, in the perpendicular direction, of a surface

of 1/600 000 square meter of a blackbody at the temperature of freezing platinum

under a pressure of 101 325 newtons per square meter."*

* Definition abrogated in 1979 (see p. 35: 16th CGPM, Resolution 3).

SI derived SI derived units (CR, p. 105)

units

Resolution 6

The 13th CGPM

considering that it is useful to add some derived units to the list of paragraph 4 of

Resolution 12 of the 11th CGPM (1960),

decides to add:

wave number 1 per meter m~'

entropy joule per kelvin J/K

specific heat capacity joule per kilogram kelvin J/(kg'K)

thermal conductivity watt per meter kelvin W/(m'K)

radiant intensity watt per steradian W/sr

activity (of a radioactive source) 1 per second s"'*

• The unit of activity received a special name and symbol in 1975 (see p. 34: 15th CGPM, Resolution 8).

30
Abrogation of earlier decisions (micron, new candle) (CR, p. 105)

Resolution 7

The 13th CGPM,

considering that subsequent decisions of the General Conference concerning the

International System of Units are incompatible with parts of Resolution 7 of the 9th

CGPM (1948),

decides accordingly to remove from Resolution 7 of the 9th Conference:

1. the unit name "micron," and the symbol "/x" which had been given to that unit,

but which has now become a prefix;

2. the unit name "new candle."

CIPM, 1967

multiples of Decimal multiples and sub-multiples of the unit of mass (PV, 35, p. 29)

kilogram

Recommendation 2

The CIPM,

considering that the rule for forming names of decimal multiples and sub-multiples

of the units of paragraph 3 of Resolution 12 of the 11th CGPM (1960) might be

interpreted in different ways when applied to the unit of mass,

declares that the rules of Resolution 12 of the 1 1th CGPM apply to the kilogram in

the following manner: the names of decimal multiples and sub-multiples of the unit

of mass are formed by attaching prefixes to the word "gram."

CIPM, 1969

SI International System of Units: Rules for application of Resolution 12 of the 11th

CGPM (1960) (PV, 37, p. 30)

Recommendation 1 (1969)

The CIPM,

considering that Resolution 12 of the 11th CGPM (1960) concerning the International System of Units, has provoked discussions on certain of its aspects,

declares

1. the base units, the supplementary units, and the derived units, of the International System of Units, which form a coherent set, are denoted by the name "SI

units";

2. the prefixes adopted by the CGPM for the formation of decimal multiples and

sub-multiples of SI units are called "SI prefixes";

micron (ju.) new candle

31
and recommends

3. the use of SI units, and of their decimal multiples and sub-multiples whose

names are formed by means of SI prefixes.

Note : The name "supplementary units," appearing in Resolution 12 of the 11th

CGPM (and in the present Recommendation) is given to SI units for which the

General Conference declines to state whether they are base units or derived units.*

See p. 37: Recommendation 1 (CI- 1980) of the CIPM.

14th CGPM, 1971

pascal; Pascal; Siemens

Siemens

The 14th CGPM (CR, p. 59) adopted the special names "pascal" (symbol Pa), for

the SI unit newton per square meter, and "Siemens" (symbol S), for the SI unit of

electric conductance (reciprocal ohm).

TAI International Atomic Time; function of CIPM (CR, p. 77)

Resolution 1 The 14th CGPM

considering

that the second, unit of time of the International System of Units, has since 1967

been defined in terms of a natural atomic frequency; and no longer in terms of the

time scales provided by astronomical motions,

that the need for an International Atomic Time (TAI) scale is a consequence of the

atomic definition of the second,

that several international organizations have ensured and are still successfully en- suring the establishment of time scales based on astronomical motions, particularly

thanks to the permanent services of the Bureau International de I'Heure (BIH),

that BIH has started to establish an atomic time scale of recognized quality and

proven usefulness,

that the atomic frequency standards for realizing the second have been considered

and must continue to be considered by CIPM, helped by a Consultative Committee, and that the unit interval of the International Atomic Time scale must be the

second realized according to its atomic definition,

that all the competent international scientific organizations and the national laboratories active in this field have expressed the wish that CIPM and CGPM should

give a definition of International Atomic Time, and should contribute to the establishment of the International Atomic Time scale,

that the usefulness of International Atomic Time entails close coordination with the

time scales based on astronomical motions,

I

32
requests the CIPM

1. to give a definition of International Atomic Time *

;

2. to take the necessary steps, in agreement with the international organizations

concerned, to ensure that available scientific competence and existing facilities are used in the best possible way to realize the International Atomic Time scale and to

satisfy the requirements of users of International Atomic Time.

SI unit of amount of substance (mole) (CR, p. 78)

Resolution 3

The 14th CGPM

considering the advice of the International Union of Pure and Applied Physics, of

the International Union of Pure and Applied Chemistry, and of the International

Organization for Standardization, concerning the need to define a unit of amount of

substance,

decides

1. The mole is the amount of substance of a system that contains as many elementary entities as there are atoms* in 0.012 kilogram of carbon 12: its symbol is "mol."

2. When the mole is used, the elementary entities must be specified and may be

atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

3. The mole is a base unit of the International System of Units.

• At its 1980 meeting, the CIPM approved the report of the 7th meeting of the CCU (1980)

specifying that "in this definition, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to."

' In anticipation of this request, the CIPM had asked the Consultative Committee for the Definition of

the Second (CCDS), to prepare a definition of International Atomic Time. This definition, approved by

CIPM at its 59th session (October 1970), is as follows:

"International Atomic Time [TAI] is the time reference coordinate established by the Bureau International de VHeure on the basis of the readings ofatomic clocks operating in various establishments in accordance with

the definition of the second, the unit of time of the International System of Units.

33
15th CGPM, 1975

speed Recommended value (CR, p. 103)

of light

Resolution 2

The 15th CGPM,

considering the excellent agreement among the results of wavelength measurements

on the radiations of lasers locked on a molecular absorption line in the visible or

infrared region, with an uncertainty estimated at ±4x10"' which corresponds to

the uncertainty of the realization of the meter,

considering also the concordant measurements of the frequencies of several of these

radiations,

recommends the use of the resulting value for the speed of propagation of electromagnetic waves in vacuum c = 299 792 458 meters per second.

UTC Universal Coordinated Time (CR, p. 104)

Resolution 5

The 15th CGPM

considering that the system called "Coordinated Universal Time" (UTC) is widely

used, that it is broadcast in most radio transmissions of time signals, that this wide

diffusion makes available to the users not only frequency standards but also Inter- national Atomic Time and an approximation to Universal Time (or, if one prefers,

mean solar time),

notes that Coordinated Universal Time provides the basis of civil time, the use of

which is legal in most countries,

judges that this usage can be strongly endorsed.

bequerel SI units for ionizing radiations (CR, p. 105)

gray

Resolutions 8 and 9

The 15th CGPM

by reason of the pressing requirement, expressed by the International Commission

on Radiation Units and Measurements (ICRU), to extend the use of the International System of Units to radiological research and applications,

by reason of the need to make as easy as possible the use of the units for nonspecialists,

taking into consideration also the grave risk of errors in therapeutic work.

34
adopts the following special name for the SI unit of activity:

becquerel, symbol Bq, equal to one reciprocal second

adopts the following special name for the SI unit of ionizing

radiation: gray, symbol Gy, equal to one joule per kilogram

Note: The gray is the SI unit of absorbed dose. In the field of ionizing radiation

the gray may also be used with other physical quantities also expressed joules per

kilogram; the Consultative Committee for Units is made responsible for studying

this matter in collaboration with the competent international organizations.'

peta SI prefixes peta and exa (CR, p. 106) exa

Resolution 10

The 15th CGPM

decides to add to the list of SI prefixes to be used for multiples, which was adopted

by the 11th CGPM, Resolution 12, paragraph 3, the two following prefixes:

Multiplying factor Prefix Symbol

10" peta P

10" exa E

16th CGPM, 1979

candela SI unit of luminous intensity (candela) (CR, p. 100)

Resolution 3

The 16th CGPM

considering

that despite the notable efforts of some laboratories there remain excessive

divergences between the results of realizations of the candela based upon the

present blackbody primary standard,

that radiometric techniques are developing rapidly, allowing precisions that are already equivalent to those of photometry and that these techniques are already in use in national laboratories to realize the candela without having to construct a blackbody,

that the relation between luminous quantities of photometry and radiometric quantities, namely the value of 683 lumens per watt for the spectral luminous efficacy of

monochromatic radiation of frequency 540x10'^ hertz, has been adopted by the

International Committee for Weights and Measures in 1977,

that this value has been accepted as being sufficiently accurate for the system of

luminous photopic quantities, that it implies a change of only about 3% for the

system of luminous scotopic quantities, and that it therefore ensures satisfactory

continuity,

' At its 1976 meeting, the CIPM approved the report of the 5th meeting of the CCU (1976), specifying

that, following the advice of the ICRU, the gray may also be used to express specific energy imparted,

kerma and absorbed dose index.

35

Resolution 8

Resolution 9
that the time has come to give the candela a definition that will allow an improvement in both the ease of realization and precision of photometric standards, and

that applies to both photopic and scotopic photometric quantities and to quantities

yet to be defined in the mesopic field,

decides

1. The candela is the luminous intensity, in a given direction, of a source that

emits monochromatic radiation of frequency 540 X 10'^ hertz and that has a radiant

intensity in that direction of (1/683) watt per steradian.

2. The definition of the candela (at the time called new candle) adopted by the

CIPM in 1946 by reason of the powers conferred by the 8th CGPM in 1933,

ratified by the 9th CGPM in 1948, then amended by the 13th CGPM in 1967, is abrogated.

Special name for the SI unit of dose equivalent (CR, p. 100)

Resolution 5

The 16th CGPM

considering

the effort made to introduce SI units into the field of ionizing radiations,

the risk to human beings of an underestimated radiation dose, a risk that could

result from a confusion between absorbed dose and dose equivalent,

that the proliferation of special names represents a danger for the International

System of Units and must be avoided in every possible way, but that this rule can

be broken when it is a mater of safeguarding human health.

adopts the special name sievert, symbol Sv, for the SI unit of dose equivalent in the

field of radioprotection. The sievert is equal to the joule per kilogram.'"

At its 1984 meeting the CIPM decided to accompany this Resolution with the following explanation

(see Recommendation 1 (CI- 1984), page 39):

"The quantity dose equivalent H is the product of the absorbed dose D of ionizing radiation and

the dimensionless factors Q (quality factor) and (product of any other multiplying factors) stipulated

by the International Commission on Radiological Protection: H=Q'ND.

Thus, for a given radiation, the numerical value of H in joules per kilogram may differ from that of D in joules per kilogram depending upon the values of Q and N. In order to avoid any risk of

confusion between the absorbed dose D and the dose equivalent H, the special names for the respective

units should be used, that is, the name gray should be used instead of joules per kilogram for the unit of

absorbed dose D and the name sievert instead ofjoules per kilogram for the unit of dose equivalent H."

36
liter Symbols for the liter (CR, 101)

Resolution 6

The 16th CGPM

recognizing the general principles adopted for writing the unit symbols in

Resolution 7 of the 9th CGPM (1948),

considering that the symbol 1 for the unit liter was adopted by the CIPM in 1879 and

confirmed in the same Resolution of 1948,

considering also that, in order to avoid the risk of confusion between the letter 1 and

the number 1, several countries have adopted the symbol L instead of 1 for the unit

liter,

considering that the name liter, although not included in the International System of

Units, must be admitted for general use with the System,

decides, as an exception, to adopt the two symbols 1 and L as symbols to be used for

the unit liter,

considering further that in the future only one of these two symbols should be

retained,

invites the CIPM to follow the development of the use of these two symbols and to

give the 18th CGPM its opinion as to the possibility of suppressing one of them.

CIPM, 1980

SI SI supplementary units (radian and steradian) (PV, 48, p. 24)

supplementary

units

Resolution 1 (CI- 1980)

The CIPM,

taking into consideration Resolution 3 adopted by ISO/TC12 in 1978 and Recommendation Ul (1980) adopted by the Consultative Committee for Units (CCU) at

its 7th meeting,

considering that the units radian and steradian are usually introduced into expressions for units when there is need for clarification, especially in photometry where

the steradian plays an important role in distinguishing between units corresponding

to different quantities,

that in the equations used one generally expresses plane angle as the ratio of two

lengths and solid angle as the ratio between an area and the square of a length, and

consequently that these quantities are treated as dimensionless quantities,

that the study of the formalisms in use in the scientific Held shows that none exists

which is at the same time coherent and convenient and in which the quantities

plane angle and solid angle might be considered as base quantities,

considering also

that the interpretation given by the CIPM in 1969 for the class of supplementary

units introduced in Resolution 12 of the 1 1th CGPM in 1960 allows the freedom of

treating the radian and the steradian as SI base units.

37
that such a possibiUty compromises the internal coherence of the SI based on only seven base units,

decides to interpret the class of supplementary units in the International System as a class of dimensionless derived units for which the CGPM allows the freedom of

using or not using them in expressions for SI derived units.

17th CGPM, 1983

meter Definition of the meter (CR, p. 97)

Resolution 1

The 17th CGPM,

considering

that the present definition does not allow a sufficiently precise realization of the

meter for all requirements,

that progress made in the stabilization of lasers allows radiations to be obtained that are more reproducible and easier to use than the standard radiation emitted by a krypton 86 lamp,

that progress made in the measurement of the frequency and wavelength of these

radiations has resulted in concordant determinations of the speed of light whose

accuracy is limited principally by the realization of the present definition of the

meter,

that wavelengths determined from frequency measurements and a given value for

the speed of light have a reproducibility superior to that which can be obtained by

comparison with the wavelength of the standard radiation of krypton 86,

that there is an advantage, notably for astronomy and geodesy, in maintaining

unchanged the value of the speed of light recommended in 1975 by the 15th CGPM

in its Resolution 2 (c =299 792 458 m/s),

that a new definition of the meter has been envisaged in various forms all of which

have the effect of giving the speed of light an exact value, equal to the

recommended value, and that this introduces no appreciable discontinuity into the

unit of length, taking into account the uncertainty of ±4xl0~' of the best

realizations of the present definition of the meter,

that these various forms, making reference either to the path travelled by light in a

specified time interval or to the wavelength of a radiation of measured or specified

frequency, have been the object of consultations and deep discussions, have been

recognized as being equivalent and that a consensus has emerged in favor of the

first form,

that the CCDM is now in a position to give instructions for the practical realization

of such a definition, instructions which could include the use of the orange radiation of krypton 86 used as standard up to now, and which may in due course be

extended or revised.

38
decides

1. The meter is the length of the path travelled by light in vacuum during a time

interval of 1/299 792 458 of a second,

2. The definition of the meter in force since 1960, based upon the transition between the levels 2pio and Sds of the atom of krypton 86, is abrogated.

meter On the realization of the definition of the meter (CR, p. 98)

Resolution 2

The 17th CGPM

invites the CIPM

to draw up instructions for the practical realization of the new definition of the

meter,"

to choose radiations which can be recommended as standards of wavelength for

the interferometric measurement of length and to draw up instructions for their

use,

to pursue studies undertaken to improve these standards.

aPM, 1984

gray Concerning the sievert (FV, 52, p. 31)

sievert

Recommendation 1 (CI- 1984)

The CIPM,

considering the confusion which continues to exist on the subject of Resolution 5,

approved by the 16th CGPM (1979),

decides to introduce the following explanation in the brochure "Le Systeme

International d'Unites (SI)":

"The quantity dose equivalent H is the product of the absorbed dose D of ionizing

radiation and the dimensionless factors Q (quality factor) and (product of any

other multiplying factors) stipulated by the International Commission on

Radiological Protection:

H=QN'D

Thus, for a given radiation, the numerical value of f?^ in joules per kilogram may

differ from that of D in joules per kilogram depending upon the values of Q and N.

In order to avoid any risk of confusion between the absorbed dose D and the dose

equivalent H, the special names for the respective units should be used, that is, the

name gray should be used instead of joules per kilogram for the unit of absorbed

dose D and the name sievert instead of joules per kilogram for the unit of dose

equivalent H. "

" See Appendix II, p. 40 Recommendation 1 (CI-1983) adopted by the CIPM in 1983.

39
APPENDIX II

Practical Realization of the Definitions

of Some Important Units

1. Length

The Recommendation 1 (CI- 1983) was adopted by the CIPM in 1983 to specify the

rules for the practical realization of the definition of the meter:

The CIPM

recommends

that the meter be realized by one of the following methods:

fl) by means of the length / of the path travelled in vacuum by a plane

electromagnetic wave in a time /; this length is obtained from the measured time t, using the relation l=C't and the value of the speed of light in vacuum

c=299 792 458 m/s;

b) hy means of the wavelength in vacuum \ of a plane electromagnetic wave of

frequency /; this wavelength is obtained from the measured frequency /, using the

relation \=c/f- and the value of the speed of light in vacuum c =299 792 458 m/s;

c) by means of one of the radiations from the list below, whose stated wavelength in vacuum or whose stated frequency can be used with the uncertainty

shown, provided that the given specifications and accepted good practice are followed;

and that in all cases any necessary corrections be applied to take account of

actual conditions such as diffraction, gravitation, or imperfection in the vacuum.

List OF RECOMMENDED RADIATIONS, 1983

In this list, the values of the frequency /and of the wavelength \ should be related

exactly by the relation \f=c, with c=299 792 458 m/s but the values of X are rounded.

1. Radiations of Lasers Stabilized by Saturated Absorption *

1.1 Absorbing molecule CH4, transition V3, P(7), component ¥f^.

The values /= 88 376 181 608 kHz

\= 3 392 231 397.0 fm

with an estimated overall relative uncertainty of ±1.3x 10~'° [which results from

an estimated relative standard deviation of 0.44 X 10"'°] apply to the radiation of a He-Ne laser stabilized with a cell of methane, within or external to the laser, subject to the conditions:

methane pressure < 3 Pa

mean one-way axial intracavity surface power density ** < 10* W • m~^

radius of wavefront curvature > 1 m

inequality of power between counter-propagating waves < 5%.

40
1.2. Absorbing molecule '"I2, transition 17-1, P(62), component o.

The values /= 520 206 808.51 MHz

\=576 294 760.27 fm

with an estimated *** overall relative uncertainty of ±6x10^'° [which results

from an estimated relative standard deviation of 2x 10~'°] apply to the radiation of a dye laser (or frequency-doubled He-Ne laser) stabilized with a cell of iodine,

within or external to the laser, having a cold-fmger temperature of 6 °C±2 °C.

1.3. Absorbing molecule '"I2, transition 11-5, R(127), component i.

The values /=473 612 214.8 MHz

\= 632 991 398.1 fm

with an estimated overall relative uncertainty of ±1 X 10"' [which results from an

estimated relative standard deviation of 3.4x10"'°] apply to the radiation of a

stabilized He-Ne laser containing an iodine cell, subject to the conditions:

cell-wall temperature between 16 °C and 50 °C with a cold-fmger temperature

of 15 °C±1 °C

one-way intracavity beam power ** 15 mW±10 mW

frequency modulation amplitude, peak to peak, 6 MHz± 1 MHz.

1.4. Absorbing molecule '"I2, transition 9-2, R(47), component o.

The values /=489 880 355.1 MHz

\=611 970 769.8 fm

with an estimated overall relative uncertainty of ±l.lx 10"' [which results from

an estimated relative standard deviation of 3.7 X 10"'°] apply to the radiation of a He-Ne laser stabilized with a cell of iodine, within or external to the laser, having

a cold-fmger temperature of —5 °C±2 °C.

1.5. Absorbing molecule '^^l2, transition 43-0, P(13), component (sometimes

called component s).

The values /= 582 490 603.6 MHz

\=514 673 466.2 fm

with an estimated overall relative uncertainty of ±1.3x10"' [which results from

an estimated relative standard deviation of 4.3 X 10"'°] apply to the radiation of an

Ar"^ laser stabilized with a cell of iodine, within or external to the laser, having a cold-finger temperature of —5 °C±2 °C.

Notes

* Each of these radiations can be replaced, without degrading the accuracy, by a radiation corresponding to another component of the same transition or by another radiation, when the frequency difference

is known with sufficient accuracy. Details of methods of stabilization are described in numerous scientific and technical publications. References to appropriate articles, illustrating accepted good practice

for a particular radiation, may be obtained by application to a member laboratory of the CCDM, or the BIPM.

*• The one-way intracavity beam power is obtained by dividing the output power by the transmittance

of the output mirror. *•* This uncertainty, and the frequency and wavelength values, are based on the weighted mean of

only two determinations. The more precise of the two, however, was a measurement dependent only on

frequency mixing and multiplication techniques relative to the radiation in 1.1. above.

41
2. Radiations ofSpectral Lamps

2.1. Radiations corresponding to the transition between the levels 2pio and Sdj of

the atom of **Kr.

The value X=605 780 210 fm

with an estimated overall relative uncertainty of ±4X 10~' [which results from an

estimated relative standard deviation of 1.3x 10~'] applies to the radiation emitted

by a lamp operated under the conditions recommended by the CIPM {Proces-Verbaux CIPM, 49th session, 1960, pp. 71-72 and Comptes Rendus, 11th CGPM. 1960,

p. 85).

2.2. Radiations of the atoms *^Kr, "*Hg and "*Cd recommended by the CIPM in

1963 (Comite Consultatifpour la Definition du Metre, 3rd session, 1962, pp. 18-19

and Proces-Verbaux CIPM, 52nd session, 1963, pp. 26-27), with the indicated values

for the wavelengths and the corresponding uncertainties.

2. Mass

The primary standard of the unit of mass is the international prototype of the

kilogram kept at the BIPM. The mass of 1-kg secondary standards of platinum-iridium or of stainless steel is compared with the mass of the prototype by means of

balances whose precision can reach 1 in 10* or better. In the case of stainless steel

standards, the accuracy of the comparison depends upon the accuracy with which

the correction due to air buoyancy is known.

By an easy operation a series of masses can be standaradized to obtain multiples and

sub-multiples of the kilogram.

3. Time

Some research laboratories are able to construct the equipment required to produce

electric oscillations at a frequency whose relationship to the transition frequency of

the atom of cesium 133 which defines the second is known. It is possible thus to

obtain pulses at desired frequencies, 1 Hz, 1 kHz, etc. Some cesiimi time standards

are also commercially available.

In the best equipment, the accuracy corresponds to an uncertainty of a part in 10'^

or even in 10'*.

Radio stations broadcast waves whose frequencies are known with an uncertainty

of a part in 10" or 10'^

There exist very stable clocks and frequency generators besides those using cesium,

including the hydrogen maser, and rubidium and quartz clocks. Their frequency

has to be standardized by comparison with a cesium time standard, either directly, or by means of radio transmissions.

Time signals broadcast by radio waves are given in a time scale called Coordinated

Universal Time (UTC) as recommended by the 15th CGPM (Resolution 5) in 1975.

UTC is defined in such a manner that it differs from TAI' by a whole number of

seconds. The difference UTC—TAI was set equal to —10 s starting the first of

January 1972, the date of application of the reformulation of UTC which previ-

' See Appendix I, page 33 (footnote 8), for the definition of TAI given by CIPM at the request of the 14th CGPM (1971, Resolution 1).

42
ously involved a frequency offset; this difference can be modified by 1 second, by

the use of a positive or negative leap second at the end of a month of UTC,

preferably in the first instance at the end of December or of June, and in the second

instance at the end of March or of September, to keep UTC in agreement with the

time defined by the rotation of Earth with an approximation better than 0.9 s.^ Furthermore, the legal times of most countries are offset from UTC by a whole

number of hours (time zones and "daylight saving" time).

The precision and accuracy of time measurement sometimes justify relativistic corrections. The defijiition of the second must be understood as the definition of the

unit of proper time, i.e., strictly speaking the user must be in the neighborhood of

the clock and at rest with respect to it. In general, within the expanse of a laboratory, only the effects of special relativity are significant, if the clock is in the

laboratory. But, in applications which bring into play distant clocks, it may be

necessary to take general relativity theory into account. In particular, TAI is based

upon a worldwide network of clocks and its definition has been completed as follows (declaration of the CCDS : BIPM Consultative Committee on the Definition

of the Second. 9, 1980, p. S 15):

"TAI is a coordinate time scale defined in a geocentric reference frame with the SI

second as realized on the rotating geoid as the scale unit".

For all clocks fixed in relation to the Earth, situated at sea level, the TAI second is equal to the second realized locally, but at 2 000 m altitude, for example, it appears

to be longer, the difference being 2.2x 10~'^ s.

4. Electrical quantities

So-called "absolute" electrical measurements, i.e., those that realize the unit ac- cording to its definition, can be undertaken only by laboratories enjoying exceptional facilities.

Electric current is obtained in amperes by measuring the force between two coils,

of measurable shape and size, that carry the current.

The ohm, the farad, and the henry are accurately linked by impedance measure- ments at a known frequency, and may be determined in absolute value by calculation (1) of the self-inductance of a coil, or the mutual inductance of two coils, in

terms of their linear dimensions, or (2) of the change in capacitance of a capacitor

in terms of the change in length of its electrodes (method of Thompson-Lampard).

The volt is deduced from the ampere and the ohm.

The uncertainty in the absolute determination of the farad is a few parts in 10*; for

the ampere, it is a few parts in 10*.

The results of absolute measurements are obtained by means of secondary standards which are, for instance:

1. coils of manganin wire for resistance standards;

2. galvanic cells with cadmium sulfate electrolyte (for standards of electromotive

force);

3. capacitors (for standards of capacitance of 10 pF for example).

Application of recent techniques also provides means of checking the stability of

the secondary standards that maintain the electric units: measurement of the gyromagnetic ratio of the proton y'^ for the ampere, measurement of the ratio h/e by the

^The difference UTC-TAI was -22 s on 1 Jan. 1985.

43
Josephson effect for the volt, and measurement of the ratio h/e^ by the quantum

Hall effect for the ohm.

5. Temperature

Absolute measurements of temperature in accordance with the definition of the

unit of thermodynamic temperature, the kelvin, are related to thermodynamics, for

example by the gas thermometer.

At 273.16 K accuracy is of the order of 1 in 10^ but it is not as good at higher and

at lower temperatures.

The International Practical Temperature Scale of 1968, amended edition of 1975,

adopted by the 15th CGPM, agrees with the best thermodynamic results to date.

The text on this scale is published in BIPM Comite Consultatif de Thermometrie,

10th session, 1974, Annexe T31, and BIPM Comptes Rendus, 15th CGPM, 1975,

Annexe 2; the English translation is published in Metrologia, 12, No. 1, 1976, p. 7.

The instruments employed to measure temperatures on the International Scale are the platinum resistance thermometer, the platinum- 10% rhodium/platinum thermocouple, and the monochromatic optical pyrometer. These instruments are calibrated at a number of reproducible temperatures, called "defining fixed points," the

values of which are assigned by agreement.

In 1978, a low temperature scale was established under the name "1976 Provisional

0.5 K to 30 K Temperature Scale " (EPT-76). This provisional practical scale was

published in BIPM Comite Consultatif de Thermometrie, 12th session, 1978, p. T7

and BIPM Proces-Verbaux CIPM, 46, 1978, p. T7; the English translation was published in Metrologia, 15, 1979, p. 65.

6. Amount of substance

All quantitative results of chemical analysis or of dosages can be expressed in

moles, in other words in units of amount of substance of the elementary entities.

The principle of physical measurements based on the definition of this unit is ex- plained below.

The simplest case is that of a sample of a pure substance that is considered to be

formed of atoms; call X the chemical symbol of these atoms. A mole of atoms X

contains by definition as many atoms as there are '^C atoms in 0.012 kilogram of

carbon 12. As neither the mass m('^C) of an atom of carbon 12 nor the mass m(X)

of an atom X can be measured accurately, we use the ratio of these masses, m (X)/

m('^C), which can be accurately determined.^ The mass corresponding to 1 mole of

X is then [m(X)/m('^C)]X 0.012 kg, which is expressed by saying that the molar

mass Af(X) of X (quotient of mass by amount of substance) is

A/(X) = [m (X)/m ('^C)] X 0.012 kg/mol.

For example, the atom of fluorine "F and the atom of carbon '^C have masses that are in the ratio 18.9984/12. The molar mass of the molecular gas F2 is

2 V 1 8 9984

M(F2)=

^ - X0.012 kg/mol =0.037 996 8 kg/mol.

' There are many methods of measuring this ratio, the most direct one being by the mass spectrograph.

44
The amount of substance corresponding to a given mass of gas F2, 0.05 kg for

example, is:

0.05 kg , 0.037 996 8kg.mol-'=^-^^^^°'°°'-

In the case of a pure substance that is supposed made up of molecules B, which are combinations of atoms X, Y, . . . according to the chemical formula B=XaY^ . .

.

,

the mass of one molecule is m(B)=aw(X)+/3m(Y)+ . .

.

This mass is not known with accuracy, but the ratio m(B)/m('^C) can be determined accurately. The molar mass of a molecular substance B is then

M{^)=^^)X^-^^'2' kg/mol=(a^^ + iS^^ + . . .)x0.012 kg/mol.

The same procedure is used in the more general case when the composition of the

substance B is specified as XgY^ . . . even if a, i8, . . . are not integers. If we denote

the mass ratios m(X)/m('^C), m(Y)/m('^C), ... by r(X), /-(Y), . . ., the molar mass

of the substance B is given by the formula:

M(B)=[ar(X) + i8/-(Y)+ . . .]X0.012 kg/mol.

There are other methods based on the laws of physics and physical chemistry for

measuring amounts of substance; three examples are given below:

With perfect gases, 1 mole of particles of any gas occupies the same volume at a temperature T and a pressure p (approximately 0.022 4 m^ at J =273. 16 K and

/> = 101 325 Pa); hence a method of measuring the ratio of amounts of substance for

any two gases (the corrections to apply if the gases are not perfect are well known).

For quantitative electrolytic reactions the ratio of amounts of substance can be

obtained by measuring quantities of electricity. For example, 1 mole of Ag and 1/2

mole of Cu are deposited on a cathode by the same quantity of electricity (approximately 96 487 C).

Application of the laws of Raoult is yet another method of determining ratios of

amounts of substance in extremely dilute solutions.

7. Photometric quantities

The method approved by CIPM in 1937 (BIPM Proces-Verbaux CIPM, 18, p. 237)

for determining the value of photometric quantities for luminous sources whose

radiation does not have the same spectral composition, utilizes a procedure taking

account of the "spectral luminous efficiencies" V(\). By its Recommendation 1 (CI- 1972), CIPM recommends the use of the V(X) values adopted by the International Commission on Illumination (CIE) in 1971.* The weighting function V(X)

was obtained for photopic vision, i.e., for retinas adapted to light. For retinas

adapted to darkness, another function V'(X) gives the spectral luminous efficiency

for scotopic vision (CIE 1951); this function V'(X) was ratified by the CIPM in

September 1976.

" CIE Publications No. 18 (1970), page 43, and No. 15 (1971), page 93; BIPM Proces-Verbaux CIPM, 40, 1972, Annexe 1. The V{\) {=y{X)\ values are given for wavelengths in 1-nm steps from 360 to 830 nm;

they are an improvement on the values in 10-nm steps adopted by CIPM in 1933, and previously by CIE

in 1924.

45
Photometric quantities are thereby defined in purely physical terms as quantities

proportional to the sum or integral of a spectral power distribution, weighted

according to a specified ftinction of wavelength.

Before 1979, the standard lamps then in use were calibrated by comparison with

the luminance of a Planckian radiator (a blackbody) at the temperature of freezing

platinum. Since the adoption of the new definition of the candela in 1979, this

measurement is carried out by comparison with the monochromatic radiation

specified in the definition, or with some other radiation by taking account of V(X)

or V'(X).

The standard lamps are incandescent lamps powered by a specified direct current;

they provide either a known luminous flux or, in a given direction, a known lumi- nous intensity.

46
APPENDIX III

Note on the Organs of the Meter Convention

BIPM, CIPM, CGPM

The International Bureau of Weights and Measures (BIPM) was set up by the Meter

Convention signed in Paris on 20 May 1875 by seventeen States during the final

session of the Diplomatic Conference of the Meter. This Convention was amended

in 1921.

The BIPM has its headquarters near Paris, in the grounds (43 520 m^) of the Pavilion de Breteuil (Pare de Saint-Cloud), placed at its disposal by the French Government; its upkeep is financed jointly by the Member States of the Meter

Convention.*

The task of the BIPM is to ensure worldwide unification of physical measurements;

it is responsible for: —establishing the fimdamental standards and scales for measurement of the principal physical quantities and maintaining the international prototypes; —carrying out comparisons of national and international standards; —ensuring the coordination of corresponding measuring techniques; —carrying out and coordinating determinations relating to the fundamental physical constants that are involved in the above-mentioned activities.

The BIPM operates under the exclusive supervision of the International Committee

for Weights and Measures (CIPM), which itself comes under the authority of the

General Conference on Weights and Measures (CGPM).

The General Conference consists of delegates from all the Member States of the

Meter Convention and meets at present every four years. At each meeting it re- ceives the Report of the International Committee on the work accomplished, and it

is responsible for: —discussing and instigating the arrangements required to ensure the propagation

and improvement of the International System of Units (SI), which is the modem

form of the metric system; —confirming the results of new fundamental metrological determinations and the

various scientific resolutions of international scope; —adopting the important decisions concerning the organization and development

of the BIPM.

The International Committee consists of eighteen members each belonging to a

different State; it meets at present every year. The officers of this Committee issue an Annual Report on the administrative and financial position of the BIPM to the

Governments of the Member States of the Meter Convention.

* In October 1985 forty-seven States were members of this Convention: Argentina (Rep. oO, Australia,

Austria, Belgium, Brazil, Bulgaria, Cameroon, Canada, Chile, China (People's Rep. of), Czechoslovakia,

Denmark, Dominican Republic, Egypt, Finland, France, German Democratic Rep., Germany (Federal

Rep. oO, Hungary, India, Indonesia, Iran, Ireland, Israel, Italy, Japan, Korea (Dem.

People's Rep.), Korea (Rep. of), Mexico, Netherlands, Norway, Pakistan, Poland, Portugal, Romania,

South Africa, Spain, Sweden, Switzerland, Thailand, Turkey, U.S.S.R., United Kingdom, U.S.A.,

Uruguay, Venezuela, Yugoslavia.

47
The activities of the BIPM, which in the beginning were limited to the measure- ments of length and mass and to metrological studies in relation to these quantities,

have been extended to standards of measurement for electricity (1927), photometry

(1937), and ionizing radiations (196Q). To this end the original laboratories, built in

1876-1878, were enlarged in 1929 and two new buildings were constructed in 1963-

1964 for the ionizing radiation laboratories.

Some thirty physicists or technicians are working in the BIPM laboratories. They

are mainly conducting metrological research, international comparisons of realizations of units, and the checking of standards used in the above-mentioned areas. An

annual report in Procfes-Verbaux [of the International Committee] gives the details

of the work in progress. BIPM's annual appropriation is of the order of 13 144 000

gold francs, approximately 23 850 000 French francs (in 1985).

In view of the extension of the work entrusted to the BIPM, the CIPM has set up

since 1927, imder the name of Consultative Committees, bodies designed to provide

it with information on matters that it refers to them for study and advice. These

Consultative Committees, which may form temporary or permanent "Working

Groups" to study special subjects, are responsible for coordinating the international

work carried out in their respective fields and proposing recommendations concerning the amendments to be made to the definitions and values of units. In order

to ensure worldwide uniformity in units of measurement, the International Committee accordingly acts directly or submits proposals for sanction by the General

Conference.

The Consultative Committees have common regulations (BIPM Pnx^s-Verbaux

CIPM, 31, 1963, p. 97). Each Consultative Committee, the chairman of which is normally a member of the CIPM, is composed of delegates from the major metrology laboratories and specialized institutes, a list of which is drawn up by the CIPM,

as well as individual members also appointed by the CIPM and one representative

of BIPM. These committees hold their meetings at irregular intervals; at present

there are eight of them in existence.

1. The Consultative Committee for Electricity (CCE), set up in 1927.

2. The Consultative Committee for Photometry and Radiometry (CCPR), new name

given in 1971 to the Consultative Committee for Photometry set up in 1933

(between 1930 and 1933 the preceding Committee (CCE) dealt with matters

concerning Photometry).

3. The Consultative Committee for Thermometry (CCT), which for a time was

called Consultative Committee for Thermometry and Calorimetry (CCTC) set

up in 1937.

4. The Consultative Committee for the Definition of the Meter (CCDM), set up in

1952.

5. The Consultative Committee for the Definition of the Second (CCDS), set up in

1956.

6. The Consultative Committee for the Standards ofMeasurement ofIonizing Radiations (CCEMRI), set up in 1958. In 1969 this Consultative Committee established four sections: Section I (Measurement of x and 7 rays, electrons);

Section II (Measurement of radionuclides); Section III (Neutron measurements); Section IV (a-energy standards). In 1975 this last section was dissolved

and Section II made responsible for its field of activity.

7. The Consultative Committee for Units (CCU), set up in 1964 (this Consultative

Committee replaced the "Commission for the System of Units" set up by the

CIPM in 1954).

8. The Consultative Committee for Mass and Related Quantities (CCM), set up in

1980.

48
The proceedings of the General Conference, the International Committee, the

Consultative Committees, and the International Bureau are published under the

auspices of the latter in the following series: — Comptes rendus des seances de la Conference Generale des Poids et Mesures; — Proces-Verbaux des seances du Comite International des Poids et Mesures — Sessions des Comites Consultatifs; — Recueil de Travaux du Bureau International des Poids et Mesures (this collection

for private distribution brings together articles published in scientific and technical

journals and books, as well as certain work published in the form of duplicated

reports).

From time to time BIPM publishes a report on the development of the Metric

System throughout the world, entitled Les recents progres du Systeme Metrique.

The collection of the Travaux et Memoires du Bureau International des Poids et Mesures (22 volumes published between 1881 and 1966) ceased in 1966 by a decision of CIPM.

Since 1965 the international journal Metrologia, edited under the auspices of CIPM,

has published articles on the more important work on scientific metrology carried

out throughout the world, on the improvement in measuring methods and

standards, on units, etc., as well as reports concerning the activities, decisions, and

recommendations of the various bodies created under the Meter Convention.

49
The International System of Units (SI) 5th Edition 1986

Index

(Numbers in boldface indicate the pages where the deflnitions of the units are to be found)

Page

acceleration due to gravity, standard

value of (g„) 17 amount of substance 44

ampere 3, 19

atmosphere, standard 22

atto 28

becquerel 34

Bureau, International, of Weights and

Measures (BIPM) 47-49

candela 5, 30, 35

candle, new 18, 31 Committee, International, for Weights

and Measures (CIPM) 47-49

Committees, Consultative 48

Conference, General, on Weights and

Measures (CGPM) 47-49

Convention, Meter 47

coulomb 19

cubic decimeter 26

curie 28

defmitions of units, practical

realization of the 40-46

degree Celsius 4, 20,29

electrical quantities 43 exa 35

farad 19

femto 28

force 18 frequency standard ('"Cs) 27

gray 34

henry 19

Page

mass 42 mass and weight 17 meter 3, 16, 18, 24, 38, 39

micron 31 mole 33, 44

newton 18 numbers, writing and printing of 21

ohm 19

pascal 32

peta 35

photometric quantities 45

prefixes, SI 10, 25, 28, 35

prefixes, SI, rules for use of 10

quantities, system of 2

quantity, meaning of 5 quantity of heat 19

radian 8, 25

realization, practical, of the definitions of some important units 40-46

second 3, 23, 24, 28

SI units and multiples thereof 25, 31 Siemens 32

sievert 36

steradian 8, 25

substance, amount of 4, 33

symbols, for base units 5 symbols, for derived units with

special names 6 symbols, for the liter 12, 37 symbols, rules for writing and use of 9, 21 system of quantities 2 system of units, international 23, 25 system of units, proposal for

establishing a practical 20, 22, 23

joule

kelvin kilogram

kilogram, multiples of

legislation on units length

liter

liter (symbols)

lumen

18

4, 29

3, 16

11, 31

2

38, 39

17, 26, 27, 37

37

18

TAI

temperature

temperature, Celsius

temperature, thermodynamic

thermodynamic scale time

time, international atomic

time, universal coordinated

32

44

4

4, 29

19, 22

42

32, 34

34, 42

50
Page

unit of force 18

unit of quantity of heat (joule) 19

units in use temporarily 13

units, CGS, with special names 14

units, electric 18

units generally deprecated 15 units in use with SI 12

units, legislation on 2

units, photometric 18

units, SI base 3

units, SI base, symbols 5

units, SI derived 6-8, 26, 30

units, SI derived, with special names 6

imits, SI, multiples and submultiples of 2, 10

units, SI supplementary 8, 9

units, SI, the three classes of, 1 UTC 34

volt 19 watt 18 weber 19

51

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