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PUBLICATIONS

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NATL INST OF STANDARDS & TECH R.I.C. NBS SPECIAL PUBLICATION 330

1981 EDITION

A1 11 01 780873

/The International system of units (SI) QC100 .U57 NO.330 V1981 C.1 NBS-PUB-R ATIONAL SYSTEM OF UNITS (SI)

r
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act ot Congress on March 3, 1901. The 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 per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essential services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities2 — Radiation Research — Thermodynamics and

Molecular Science — Analytical Chemistry — Materials Science.

THE NATIONAL ENGINEERING LABORATORY provides technology and technical ser- vices to the public and private sectors to address national needs and to solve national

problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement capabilities;

provides engineering measurement traceability services; develops test methods and proposes

engineering standards and code changes; develops and proposes new engineering practices;

and develops and improves mechanisms to transfer results of its research to the ultimate user. The Laboratory consists of the following centers:

Applied Mathematics — Electronics and Electrical Engineering2 — Mechanical

Engineering and Process Technology2 — Building Technology — Fire Research —

Consumer Product Technology — Field Methods.

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal agencies in the selection,

acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759),

relevant Executive Orders, and other directives; carries out this mission by managing the

Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following centers:

Programming Science and Technology — Computer Systems Engineering.

'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Washington, DC 20234.

2 Some divisions within the center are located at Boulder, CO 80303.
OF STANDAAU8

LIBEART

JAN 8 1982

(XcibO

THE INTERNATIONAL SYSTEM OF UNITS (SI)

National Physical Laboratory

United Kingdom

(Translation approved by the

International Bureau of Weights and

Measures of its publication "Le Systeme

International d'Unites")

(Supersedes NBS Special Publication 330

1977 Edition)

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued December 1981

Edited by

David T. Goldman

National Bureau of Standards

United States of America

R. J. Bell
National Bureau of Standards Special Publication 330

Nat. Bur. Stand. (U.S.), Spec. Publ. 330, 53pages (Dec. 1981)

CODEN: NBSMA6

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1981

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

Price $3.25

(Add 25 percent for other than U.S. mailing)
Foreword

Le Bureau International des Poids et Mesures welcomes with pleasure the appearance of this

booklet, an English translation of the new edition of the brochure, "Le Systeme International

d'Unites (SI)," published in French by the BIPM. * The translation was a joint effort by the

National Bureau of Standards (USA) and the National Physical Laboratory (UK). It was checked

by the BIPM, found to conform with the original both in letter and spirit, and approved.

SI, the present-day descendant of the Metric System, has become the universal language of

scientists. It is becoming the universal language of measurement in all industrial, technical, and

commercial areas; in all branches of human activity; and in all countries.

This publication provides for all English-speaking users a complete documentation and a careful

updating of the foundations and fundamental principles of SI. It will contribute to a better

understanding, to a better dissemination, and to a more uniformly correct utilization of SI. It is one

more step towards a mutual understanding between peoples.

P. Giacomo, Director, BIPM

* "Le Systeme Internationa] d'Unites," 4th edition (1981), agent: OFFILIB, 48 rue Gay-Lussac, F-75005 Paris. Complete or

partial translations (of this and/or former editions) have been published in Bulgarian, Chinese, Czechoslovakian, English,

German, Japanese, Romanian, Portuguese, and Spanish. Numerous countries have also published guides for the utilization of SI units.

iii
Preface to the 4th Edition

The International Bureau of Weights and Measures (BIPM), in response to frequent requests,

publishes this document containing Resolutions and Recommendations of the General Conference

on Weights and Measures (CGPM) and the International Committee for Weights and Measures

(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 (CCU) of the International Committee for Weights and

Measures (CIPM) helped to draft the document and has approved the final 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 precision material

standards.

This 4th edition is a revision of the 3d edition (1977); it takes into consideration the decisions of

the 16th General Conference on Weights and Measures (1979) and of the International Committee

for Weights and Measures (1977, 1978, 1980), and the amendments made by the Consultative

Committee for Units (1978, 1980).

January 1981

P. GIACOMO J. de BOER

Director, BIPM Chairman, CCU

iv
The International System of Units

Contents

Foreword

Preface to the 4th Edition

I. Introduction

1.1 Historical note

1.2 Three classes of SI units

1.3 SI prefixes

1.4 System of quantities

1.5 Legislation on units

II. SI units

II. 1 SI base units

II. 1.1. Definitions

II. 1.2. Symbols

11. 2 SI derived units

11. 3 SI supplementary units ,

11.4 Rules for writing and using SI unit symbols

III. Decimal multiples and sub-multiples of SI units

III. 1 SI prefixes

HI. 2 Rules for using SI prefixes

III. 3 The kilogram

IV. Units outside the International System

IV. 1 Units used with the International System

IV. 2 Units in use temporarily

IV.3 CGS units

IV.4 Other units

Appendix I. Decisions of the CGPM and the CIPM

Appendix II. Practical realization of the definitions of some important units

Appendix III. Organs of the Meter Convention

Index

I. INTRODUCTION

I.l Historical note

In 1948 the 9th CGPM\ by its Resolution 6, instructed the CIPM:f "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 recommendations 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.

I. 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 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 linking 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 11th CGPM (1960) admitted a third class of SI units, called supplementary

units, whose nature was not stated exactly (see II. 3, p. 9).

For the meaning of these abbreviations, see the preface.

1
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 Recommendation 1 (1969), the units of this coherent set of units are designated by the name SI units.

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

if this unit can be expressed in different forms, but the inverse is not true: the same

SI unit can correspond to several different quantities (see p. 8).

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. 1 , p. 11). Following CIPM

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

prefixes.

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 booklet 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. 1

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, and education. In a growing number of countries this

legislation is based on the use of the International System of Units.

The International Organization of Legal Metrology (OIML), founded in 1955, is concerned with the international harmonization of this legislation.

1 Units of measurement, ISO Standards Handbook 2, ISO, Geneva, 1979, 235 pages.

2
II. SI UNITS

II. 1 SI base units

(a) unit of

length

(meter)

(b) unit of mass

(kilogram)

(c) unit of

time

(second)

(d) unit of

electric

current

(ampere)

II. 1.1. Definitions

The 11th CGPM (1960) replaced the definition of the meter based on the

international prototype of platinum-iridium, in force since 1889 and amplified in

1927, by the following definition:

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

radiation corresponding to the transition between the levels 2p 10 and 5d5 of the

krypton-86 atom. (11th CGPM (1960), Resolution 6).

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) legalized 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 of the international prototype

of the kilogram (see the complete declaration, p. 1 8).

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

conditions specified by the 1st CGPM in 1889.

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

the mean solar day. The exact definition of "mean solar day" was left to as- tronomers, 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 1 1th 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).

Electric units, called "international," for current and resistance, had been

introduced by the International Electrical Congress held in Chicago in 1893, and

the definitions of the "international" ampere and the "international" ohm were

confirmed 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

3
"absolute" units, the official decision to abolish them was only taken by the 9th

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

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 2xlOr?

newton per meter of length. (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

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

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

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

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

(kelvin) of thermodynamic temperature as follows:

The kelvin, unit of thermodynamic 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 temperature (symbol 7), expressed in

kelvins, use is also made of Celsius temperature (symbol /) defined by the equation

t = T - T0

where 7^=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.

(f) unit of

amount of

substance

(mole)

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 (IUPAP) and the International Union of Pure and Applied

Chemistry (IUPAC) 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."

4
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,"2 has been given the name

mole (symbol mol).

Following proposals of IUPAP, IUPAC, 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 of substance of a 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 mole.

(g) unit of The units of luminous intensity based on flame or incandescent filament standards

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

intensity candle" based on the luminance of a Planckian radiator (a blackbody) at the

(candela) temperature of freezing platinum. This decision had been prepared by the Inter- national 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 candela (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 candela is the luminous intensity, in a given direction, of a source that emits

monochromatic radiation of frequency 540x1 0'2 hertz and that has a radiant

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

Resolution 3).

2 The name of this quantity, adopted by IUPAP, IUPAC, and ISO is in French "quantite de matiere"

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

"KojiHiecTBo BemecTBa"). 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.

5
II. 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

5/ 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 candela cd

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

II. 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 m

volume cubic meter _3m

speed, velocity meter per second m/s

acceleration meter per second squared m/s2 wave number 1 per meter

~-i m

density, mass density kilogram per cubic meter kg/m3

specific volume cubic meter per kilogram mVkg

current density ampere per square meter A/m2

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/m2

6
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).

Table 3

5/ derived units with special names

SI Unit

Expression Expression

Quantity Name Symbol in terms in terms

of other of SI base

units units

freauencv hertz Hz s"

1

force newton N m*kg*s 2

pressure, stress pascal Pa N/m2 m~'-kg-s~2

energy, work, quantity

of heat joule J N-m m

2 -kg-s~2

power, radiant flux watt W J/s m

2 -kg-s~3

electric charge,

quantity of electricity coulomb C sA

electric potential,

potential difference,

electromotive force volt V W/A m

2 -kg-s3 -A-' capacitance farad F C/V m2 -kg-'.s

4-A2

electric resistance ohm fi V/A m

2 -kg-s~3 -A~2

electric conductance Siemens S A/V m2 -kg-'.s

3 .A2

magnetic flux weber Wb V-s m

2-kg-s2-A-' magnetic flux density tesla T Wb/m2 kg-s-'-A" 1

inductance henry H Wb/A m

2 .kg-s'2 -A2

Celsius temperature'"' degree Celsius °C K

luminous flux lumen lm cd-sr(4)

illuminance lux lx lm/m2 m^-cd-sr""

< °) See page 4, e, Note.

(W See II.3, page 9 , and CIPM, 1980, Recommendation 1, page 38.

Table 3'

5/ 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 mV2

dose equivalent,

dose equivalent

index sievert Sv JAg m

2 -s2

7
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

Hvnamip U vi^r*OQitv y llallll^ V I^LAJ.MIV Pq.c m -kg-s

UH'llltlll Ul HM LL IICWIUU IIICLCI Min •mm m

2 -kg-s2

c 1

Millt* I qdCtr* tpncirtn ItllSKMl ncwion per meter iN/m kg-s HCal I1UA Lltll>ll\ , lrmHianff* 11 1 tlU luNL L Wall JJCI SUUalC lilt It 1 WAn2 W / III Kg-S

m2 Urr o~2 If -1 m -Kg-S -is. 1 1 t o. >. t si j 'ai> 1 1 y t 1 1 1 1 KJijy ion If1 npr tf*l\/in JvJUlC |"tl v Ci V Ml J/ IV

<snf*f*ifif* hpat" rnnaoitv JCIU1C }'tl MlUgl alii cnApi fir* /=> M'ttlJIt C1ILI r-» f f-f"">r djjy r\v )'*-» 1 t;in m -s *lv

't 1 1 cut i piy i on I/1 npr Vil^fTfQm JUU1C JJCI PwlitJ^,! alii J /Kg m2 <T2 m -s thermal ronrliirtivitv w/ntt Wail npr tnf^ti^r Ir^lvin JJCI 11ICIC1 fit! VIM VV / ^IIl'IV) m-Kg-s -IV viiLig y uviiiMLy iniilf1 fif^r fiiKir* tn ptpr juuic |jci c uuit nitit I j / m m '-kg-s

2

electric field strength volt per meter V/m m-kg-s^-A-1

electric charge density coulomb per cubic meter C/m3 m~

3 -s-A

electric flux density coulomb per square meter C/m2 m"2 -s-A permittivity farad per meter F/m m3 -kg-'-s

4-A2

permeability henry per meter H/m m-kg-s"2 -A"

2 molar energy joule per mole J/mol m

2 -kg-s

2 -mol"' molar entropy, molar

heat capacity joule per mole kelvin J/(mol-K) m

2 -kg-s2 .K1 -mor' exposure (x and y rays) coulomb per kilogram C/kg kg'-s-A

absorbed dose rate gray per second Gy/s m

2 -s3

As mentioned at the end of section 1.2 (p. 2), the same SI unit can correspond to

several different quantities; some examples are given in the tables above, where

the enumeration of the cited quantities should not be considered exhaustive. 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.

Although a derived unit can be expressed in several equivalent ways by using

names of base units and special names of derived units, the CIPM sees no

objection to the use of certain combinations or of certain special names in order to

distinguish more easily between quantities of the same dimension. For example,

the hertz is used, instead of the reciprocal second, for frequency; and the newton

meter, instead of the joule, for moment of force.

In the field of ionizing radiation, the becquerel is similarly used, instead of the

reciprocal second, for activity; and the gray or the sievert, instead of the joule per

kilogram, for their respective quantities.

Note: The values of certain so-called dimensionless quantities, as for example

refractive index, relative permeability, or relative permittivity, are expressed by

pure numbers. The corresponding SI unit is then the ratio of two identical

SI units and may be expressed by the number 1.

8
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).

Table 5

5/ supplementary units

SI unit

Quantity Name Symbol

plane angle radian rad

solid angle steradian sr

At the time of the introduction of the International System, the 11th CGPM left open the question of the nature of these supplementary units. 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, the CIPM (1980)

specified that in the International System the quantities plane angle and solid

angle should be considered as dimensionless derived quantities. Therefore, the supplementary units radian and steradian are to be regarded as dimensionless derived

units which may be used or omitted in the expressions for derived units.

Some examples of the use of supplementary units in forming derived units are given in table 6.

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/s2

radiant intensity watt per steradian W/sr

radiance watt per square meter steradian W-m-2 -sr-'

9
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"

1

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/s2 or m-s"

2 but not: m/s/s

m-kg/(s3 -A) or m-kg-s"3 -A

_1 m-kg/s^A

' USA Editors' note: For USA practice, see American National Standard ANSI/IEEE Std 260-1978.

10
III. DECIMAL MULTIPLES AND

SUB-MULTIPLES OF SI UNITS

III.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" 15 and 10" 18 were added by the 12th

CGPM (1964, Resolution 8) and those for 10

15 and 10 18 by the 15th CGPM (1975,

Resolution 10).

Table 7

SI prefixes

Factor Prefix Symbol Factor Prefix Symbol

10

18 exa E 10"' deci d

10 15 peta P io-2 centi c

10' 2 tera T io3 milli m

109 giga G icr6 micro

10" mega M IO"

9 nano n

10

3 kilo k 10" 12 pico P

102 hecto h IO"

15 femto f

10' deka da IO"'

8 atto a

III. 2 Rules for using SI prefixes

Following 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 cm3 = (10"2 m)3 = 10"6 m

3

1 cm"1 = (10

2 m)"1 = 102 m"1

1 U.S"

1 = (10'6 s)"1 = 106 s"

1

1 V/cm = (1 V)/(10"2 m) = 10

2 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 mjam

4. A prefix should never be used alone

for example: 106 /m3 but not: M/m3

11
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"6 kg = 1 milligram (1 mg) but not: 1 microkilogram (1 ukg).

12
IV. UNITS OUTSIDE THE INTERNATIONAL SYSTEM

IV. 1 Units used with the International 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 uses 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 unit

minute min 1 min = 60s

hour'01 h 1 h = 60 min = 3 600 s day d 1 d = 24 h = 86 400 s degree 1° = (7j7180)rad

minute r = (1/60)° = (tt/10 800) rad second « r = (1/60)' = (tt/648 000) rad

liter(w 1,L 1 L = 1 dm3 = 10"3 m

3

metric ton

(c"

t i t = 103 kg

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

(4) 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).

(c| This unit and its symbol were adopted by the International Committee in 1879 {Proces-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 Definition

electronvolt eV (a)

unified atomic mass unit u

<b)

{a) The electronvolt is the kinetic energy acquired by an electron in passing through a potential difference of 1 volt in vacuum; 1 eV= 1.602 19 X 10" 19 J approximately.

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

1 u = 1.660 57 X 10"27 kg approximately.

Translators' note: In some English-speaking countries this unit is called "tonne." USA Editors' note: In the USA, the recommended symbol for liter is L.

13
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 10 m

arew a 1 a = 1 dam2 = 102 m

2

hectare"" ha 1 ha = 1 hm2 = 104 m

2

barn(c> b 1 b = 100 fm2 = 10"28 m

2

bar"* bar 1 bar = 0.1 MPa = 105 Pa

gal w Gal 1 Gal = 1 cm/s2 = 10"2 m/s2

curie1" Ci 1 Ci = 3.7 X 1010 Bq

roentgen1 *' R 1 R = 2.58 X 10~4 C/kg

radw rad 1 rad = 1 cGy = 10 2 Gy

rem01 rem 1 rem = 1 cSv = 10"2 Sv

(

'' , The nautical mile is a special unit employed for marine and aerial navigation to express distances. The conventional value given above was adopted by the First International Extraordinary

Hydrographic Conference, Monaco, 1929, under the name "International nautical mile." m This unit' and its symbol were adopted by the CIPM in 1879 {Proces-Verbaux CIPM, 1879, p. 41).

(c) Ther barn is a special unit employed in nuclear physics to express effective cross sections.

{d) This unit and its symbol are included in Resolution 7 of the 9th CGPM (1948). w The gal is a special unit employed in geodesy and geophysics to express the acceleration due to gravity. w The curie is a special unit employed in nuclear physics to express activity of radionuclides (12th

CGPM (1964), Resolution 7).

tg) 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. w 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.

14
IV.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.

3 Such units are

listed in table 11. Table 11 CGS units with special names

Name Symbol Value in SI unit

erg'

0 ' erg 1 erg = 10"7 J dyne'01 dyn 1 dyn = 10 5 N

poise"" P 1 P = 1 dyn-s/cm2 = 0.1 Pas

stokes St 1 St = 1 cmVs = 10"4 m

2/s gauss

(W Gs, G 1 Gs corresponds to 10"4 T

oersted(4) Oe 1 Oe corresponds to . A/m

maxwell"'' Mx 1 Mx corresponds to 10"8 Wb

stilb

(a) sb 1 sb = 1 cd/cm2 = 10" cd/m2

phot ph 1 ph = 10" lx

{a) 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 corresponding unit of the International System, which has four dimensions when only mechanical and electric quantities are considered.

1 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.

15
IV.4 Other units

As regards units outside the International System which do not come under

sections 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

fermi 1 fermi = 1 fm = 10 15 m

metric carat<0) 1 metric carat = 200 mg = 2 X 10"4 kg

101 325

torr 1 torr = Pa

760

standard atmosphere (atm)(i>) 1 atm = 101 325 Pa

kilogram-force (kgf) 1 kgf = 9.806 65 N

calorie (cal)

,,r)

micron (u,)'^ 1 ju, = 1 /im = 10"6 m

x unit w

stere (st)w 1 st = 1 m

3 gamma (y) 1 y = 1 nT = 10~9 T

1 y = 1 /j,g = lO"

9 kg

1 \ = 1 /aL = 10"6 L = 10 m

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

pearls, and precious stones.

(W Resolution 4 of the 10th CGPM (1954). The designation "standard atmosphere" for a reference

pressure of 101 325 Pa is still acceptable.

{c) Several "calories" have been in use: — calorie labeled "at 15 "C": 1 cal ]5 = 4.185 5 J (value adopted by the CIPM in 1950 (ProcesVerbaux CIPM, 22, 1950, pp. 79-80)); — a calorie labeled "IT" (International Table): 1 cal IT = 4.186 8 J (5th International Conference on

the Properties of Steam, London, 1956); — a calorie labeled "thermochemical": 1 cal lh = 4.184 J. M The name of this unit and its symbol, adopted by the CIPM in 1879 (Proces-Verbaux CIPM, 1879, p. 41) and retained in Resolution 7 of the 9th CGPM (1948) were abolished by the 13th CGPM (1967,

Resolution 7).

<el This special unit was employed to express wavelengths of x rays; 1 x unit = 1.002x10 4 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."

fe) This symbol is mentioned in Proces- Verbaux CIPM, 1 880, p. 56.

"" This symbol is mentioned in Proces-Verbaux CIPM, 1880, p. 30.

16
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 Generate des Pojds et Mesures

(CGPM)

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

(CIPM)

1st CGPM, 1889

meter Sanction of the international prototypes of the meter and the kilogram (CR, 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

fulfil 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.*

* Definition abrogated in 1960 (see p. 25: 11th CGPM, Resolution 6).

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

henceforth be considered as the unit of mass.

17
3 The hydrogen thermometer centigrade scale in terms of which the equations

of the prototype Meters have been established.

B. As regards national prototypes:

3d CGPM, 1901

liter Declaration concerning the definition of the liter (CR, 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. 29: 12th CGPM, Resolution 6)

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

gn (CR, 70)

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

to which the kilogram has been defined as a unit of mass;

4

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

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

1889;

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

practice still subsists 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;

1 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 everyday use, weight is often used in the sense of mass for which the SI unit is the kilogram.

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

the standard acceleration due to gravity is 980.665 cm/s2

, value already stated in

the laws of some countries."5

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

and Measures" (PV, 1887, 88).

'This conventional reference "standard value" (g„ = 9.806 65 m/s2 ) was confirmed in 1913 by the 5th CGPM (CR, 44). This value should be used for reduction to standard gravity of measurements made

in any location on Earth.

mass and

weight

£n

18
7th CGPM, 1927

meter Definition of the meter by the international Prototype (CR, 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 standard 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. 25: 11th CGPM, Resolution 6).

CIPM, 1946

Definitions ofphotometric units (PV, 20, 1 19)

Resolution6

photometric

units

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. 31': 13th CGPM, Resolution 5).

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

and Resolution 2

7

electric

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.

6 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, 54). For the lumen the qualifier "new"

was later abandoned.

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

19
Watt (unit of power). —The watt is the power which in one second gives rise to

energy of 1 joule.

B) Definitions of electric 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 2xlCT7 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 electric 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

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

of heat (joule) (CR, 55 and 63)

Resolution 3

8

1. With present-day technique, 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 Consultative Committee [for Thermometry and Calorimetry]

considers that the zero of the centesimal thermodynamic scale must be defined as the temperature 0.010 0 degree below that of the triple point of pure water.

thermodynamic

scale

unit of

quantity of

heat

The three propositions contained in this Resolution 3 have been adopted by the General Conference.

20
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.

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.

9

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, 88).

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

practical

system of

units of

measurement

Proposal for establishing a practical system of units of measurement (CR, 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;

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

22, 92).

21
to make recommendations for a single practical system of units of measurement,

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

symbols and Writing and printing of unit symbols and of numbers (CR, 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 m volt V

•cubic meter _3m watt w

•micron* 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 lx

calorie cal lumen lm

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. 32, 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. 30: 13th CGPM, Resolution 3).

**** Decision abrogated in 1967 (see p. 30: 13th CGPM, Resolution 3).

22
10th CGPM, 1954

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

dynamic

scsilc 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.*

* See p. 3 1 , Resolution 4 of the 13th CGPM, 1967, which explicitly defines the kelvin.

standard Definition ofstandard atmosphere (CR, 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 Practical system of units (CR, 80)

system

of units 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 (sec p. 30: 13th CGPM. Resolution 3).

23
CIPM, 1956

second Definition of the unit of time (PV, 25, 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 —12 960 276 813

... ._, X 10"9 of the tropical year for 1900 January 0 at 12 h ET,

4Uo yso 4yt>

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. 30: 13th CGPM, Resolution 1).

SI International System of Units (PV, 25, 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

requested 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:

[here follows the list of the six base units with their symbols, reproduced in Resolution 1 2 of the 1 1th CGPM

(I960)]

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

might be added later:

[here follows the table of units reproduced in paragraph 4 of Resolution 12 of the I Ith CGPM (I960)]

24
11th CGPM, 1960

meter Definition of the meter (CR, 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,

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

decides

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 p 10 and 5 d5 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.

Resolution 7

The 11th CGPM

requests the CIPM

1 to prepare specifications for the realization of the new definition of the

meter;

10

2 to select secondary wavelength standards for measurement of length by

interferometry, and to prepare specifications for their use;

3 to continue the work in progress on improvement of length standards.

second Definition of the unit of time (CR, 86)

Resolution 9

The 11th CGPM

considering

the powers given to the CIPM by the 10th CGPM, to define 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. 30: 13th CGPM, Resolution 1).

10 See Appendix II, p. 39, for the relevant Recommendation adopted by the CIPM.

25
International System of Units (CR, 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

1 000 000 106 mega M

1 000 103 kilo k

100 102 hecto h

10 10' deka da

0.1 io-' deci d

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

0.000 001 10"6 micro

0.000 000 001 IO"

9 nano n

0.000 000 000 001 10 12 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. 30: 13th CGPM, Resolution 3).

** A seventh base unit, the mole, was adopted in 1971 by the 14th CGPM (Resolution 3, see p. 34).

*** See pages 29 and 36 for the four new prefixes adopted by the 12th CGPM (1964), Resolution 8, and the 15th CGPM (1975), Resolution 10.

26
DERIVED UNITS****

area square meter

2 m

volume cubic meter m

frequency * hertz Hz 1/s ma« Hensitv ^densitv^ kilogram per cubic meter kg/m3

IV to' "* speed, velocity meter per second m/s

ancriilar vplnpitv radian per second rad/s

acceleration meter per second squared m/s2

angular acceleration radian per second squared rad/s2

force newton N kg-m/s 2

pressure (mechanical stress) newton per square meter N/m2

kinematic viscosity square meter per second m

2/s

dynamic viscosity newton-second per square meter N-s/m2

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

power watt W J/s

quantity of electricity coulomb c As

nntpntial L7UIL1I L lul Hiffprpnpp Ulllvl Wll^<^) electromotive force volt V W/A

electric field strength volt per meter V/m

electric resistance ohm n V/A

capacitance farad F A-s/V

magnetic flux weber Wb V-s

inductance henry H V-s/A

mapnf*tic* flux densitv tesla T Wb/m2

macrnptip fiplH strpnirth ampere per meter A/m

magnetomotive force ampere A

luminous flux lumen lm cd-sr luminance candela per square meter cd/m2

illuminance lux lx lm/m2

**** See page 32 for the other units added by the 13th CGPM (1967), Resolution 6.

Cubic decimeter and liter (CR, 88)

Resolution 13

The 11th CGPM,

considering

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

106

,

that determinations 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.

27

cubic

decimeter

and liter
CIPM, 1961

cubic decimeter and liter (PV, 29, 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.

12th CGPM, 1964

frequency Atomic standard offrequency (CR, 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

standards, 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, 26, and CR, 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

2 S1/2 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.

28
liter Liter (CR, 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.

curie Curie (CR, 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

-1 ),*

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

3.7 x 1010 s"

1

. The symbol for this unit is Ci.

* In 1975 the name "becquerel" (Bq) was adopted for the SI unit of activity (see p. 35: 15th

CGPM, Resolution 8); 1 Ci = 3.7x 10

10 Bq.

femto SI prefixes fern to and atto (CR, 94)

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

lCT

15 femto f

1(T

18 atto a

29
13th CGPM, 1967-1968

second SI unit of time (second) (CR, 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 definition now in force of the unit of

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

standard,

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 5/ unit of thermodynamic temperature (kelvin) (CR, 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,

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";

30
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.

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 1/273.16 of the

thermodynamic temperature of the triple point of water."

candela SI unit of luminous intensity (candela) (CR, 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, 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. 36: 16th CGPM, Resolution 3).

31
SI derived SI derived units (CR, 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 rrf' 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"

1 *

* I he unit ol acti\iu received a special name and symbol in 1975 (see p. 35: 15th CCil'M. Resolution S).

micron (/x) Abrogation of earlier decisions (micron, new candle) (CR, 105)

new candle

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 "u," 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, 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 11th 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."

32
CIPM, 1969

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

CGPM (1960) (PV, 37,30)

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";

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. 38: Recommendation 1 (CI-1980) of the CIPM.

14th CGPM, 1971

Pascal; 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, 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,

pascal;

Siemens

33
that several international organizations have ensured and are still successfully

ensuring the establishment of time scales based on astronomical motions,

particularly thanks to the permanent services of the Bureau International de

l'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,

requests CIPM

1 to give a definition of International Atomic Time; 11

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 ofsubstance (mole) (CR, 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

'

' In anticipation of this request, 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 l'Heure on the basis of the readings of atomic clocks operating in various establishments in accordance with the definition of the second, the unit of time of the International System of Units."

34
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

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

15th CGPM, 1975

UTC Universal Coordinated Time (CR, 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

International 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.

SI units for ionizing radiation (CR, 105)

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,

adopts the following special name for the SI unit oi activity: 1 becquerel. symbol Bq, equal to one reciprocal second. > RESOLUTION 8

35

bequerel

gray
adopts the following special name for an SI unit in the field of

j ionizing radiation: gray, symbol Gy, equal to one joule per > RESOLUTION 9

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 in joules

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

studying this matter in collaboration with the competent international

organizations.*

' Translators' note: It has since been agreed (CCU, 1976; CIPM, 1977) that the gray may be used

to express the four quantities absorbed dose, specific energy imparted, kerma, and absorbed dose

index.

peta SI prefixes peta and exa (CR, 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

1016 peta P

1018 exa E

16th CGPM, 1979

candela SI unit of luminous intensity (candela) (CR, 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 540 XlO12 hertz, has been

adopted by the International Committee for Weights and Measures in 1977,

36
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,

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 XlO12 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.

sievert Special name for the SI unit of dose equivalent (CR, 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 matter 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.

1 Translators' note: It should be noted that the quantity dose equivalent, H, is the product of the absorbed dose, D, of ionizing radiation, and the dimensionless factors Q (quality factor) and N

(product of any other multiplying factors) stipulated by the International Commission on Radiological

Protection. Thus, for a given irradiation, the numerical value in joules per kilogram of these two

quantities D and H may differ, depending on the values of Q and TV. To avoid any risk of confusion,

the special names for the respective units should be used; i.e., D should be expressed in grays, and H

should be expressed in sieverts.

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),

37
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

'I SI supplementary units (radian and steradian) (PV, 48)

supplementary

units Recommendation 1 (CI- 1980)

The CIPM,

taking into consideration Resolution 3 adopted by ISO/TCI 2 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 field 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 11th CGPM in 1960 allows the freedom

of treating the radian and the steradian as SI base units,

that such a possibility 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.

38
APPENDIX II

Practical realization of the definitions

of some important units

1. Length

The following recommendation was adopted by the CIPM in 1960 to specify the

characteristics of the discharge lamp radiating the standard line of krypton 86:

In accordance with paragraph 1 of Resolution 7 adopted by the 11th CGPM (October

1960) the CIPM recommends that the line of krypton 86 adopted as primary standard of

length be realized by means of a hot cathode discharge lamp containing krypton 86 of

purity not less than 99% in sufficient quantity to ensure the presence of solid krypton at a temperature of 64 °K. The lamp shall have a capillary of internal diameter 2 to 4

millimeters, and wall thickness approximately 1 millimeter.

It is considered that, provided the conditions listed below are satisfied, the wavelength

of the radiation emitted by the positive column is equal to the wavelength corresponding

to the transition between the unperturbed levels to within 1 in 10

8

:

1. the capillary is observed end-on in a direction such that the light rays used travel

from the cathode end to the anode end;

2. the lower part of the lamp including the capillary is immersed in a bath maintained

to within 1 degree of the temperature of the triple point of nitrogen;

3. the current density in the capillary is 0.3+0.1 ampere per square centimeter.

{Proces-Verbaux CIPM, 28, 1960, 71; Comptes rendus 11th CGPM, 1960, 85)

The ancillary apparatus comprises the stabilized current supply for the lamp, a vacuum-tight cryostat, a thermometer for use in the region of 63 K, a vacuum

pump, and either a monochromator, to isolate the line, or special interference

filters.

Other lines of krypton 86 and several lines of mercury 198 and of cadmium 114

are recommended as secondary standards {Proces-Verbaux CIPM, 31, 1963,

Recommendation 1, 26 and Comptes rendus 12th CGPM, 1964, 18).

Two monochromatic radiations, one in the visible the other in the infrared

spectral region, produced by helium-neon lasers stabilized on a saturated absorption line of iodine or of methane, are recommended as wavelength standards

with the following values (PV CIPM, 41, 1973, 112)

component i

These lines are reproducible with an uncertainty of the order of 1 in 10

10

; the

value of their wavelength in meters is subject to the uncertainty of the standard

(the wavelength of the 86Kr line) estimated to be 4 in 109. By measuring the beat

frequencies of neighboring lines (for example various components of the hyperfine

multiplet of iodine), very exact values of the wavelength differences are obtained.

The wavelengths of all these lines vary with pressure, temperature, and

composition of the air in which the light travels; the refractive index of the air

must therefore in general be measured in situ.

Line Wavelength in vacuum

3 392 231.40 X 10" 12 m

632 991.399 X 10" 12 m

Methane, P(7), band v3 Iodine 127, R(127), band 11-5

39
To measure end or line standards these radiations are used in an interference

comparator, a complicated instrument with mechanical, optical interference, and

thermometric components.

The wavelength of the methane line mentioned above multiplied by its frequency

(measured by comparison with the l33Cs transition of the definition of the second)

yields the speed of propagation of electromagnetic waves in vacuum

t = 299 792 458 m/s, recommended by the 15th CGPM (Resolution 2).

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 platinumiridium or of stainless steel is compared with the mass of the prototype by means

of balances whose precision can reach 1 in 108 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 standardized 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

cesium time standards are also commercially available.

In the best equipment, the accuracy corresponds to an uncertainty of a part in 10 13

or even in 10

14

.

Radio stations broadcast waves whose frequencies are known with an uncertainty

of a part in 10" or 1012.

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 TAI12

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 previously 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.

13 Furthermore, the legal times of most countries are

offset by a whole number of hours (time zones and "daylight saving" time).

12 See Appendix I, page 34 (footnote 11), for the definition of TAI given by CIPM at the request of the

14th CGPM (1971, Resolution 1).

13 The difference UTC-TAI was -19 s on 1 Jan. 1981.

40
4. Electric quantities

So-called "absolute" electrical measurements, i.e., those that realize the unit

according 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

measurements 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 ThompsonLampard).

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

8

; for

the ampere, it is a few parts in 10

6

.

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 sulphate electrolyte for standards of

electromotive force;

3. capacitors (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'

p for the ampere, measurement of the ratio h/e

by the Josephson effect for the volt.

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

6

, 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 Comite Consultatif de Thermometrie, 10th

session, 1974, Annexe T31, and Comptes Rendus, 15th CGPM, 1975, Annexe 2; the English translation is published in Metrologia, 12, No. 1, 7, 1976.

The instruments employed to measure temperatures in 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 Temperature Scale between 0.5 K and 30 K" (EPT-76). This provisional practical scale was published in Comite Consultatif de Thermometrie, 12th

41
session, 1978, p. T 7 and Proces-Verbaux CIPM, 46, 1978, p. T 7; 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 explained 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

12 C atoms in 0.012 kilogram of

carbon 12. As neither the mass m(12C) 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('2 C), which can be accurately determined.'4 The mass corresponding to 1 mole of X is then [m(X)/m( 12 C)]X 0.012 kg, which is expressed by saying that the

molar mass M(X) of X (quotient of mass by amount of substance) is M(X) = [m(X)/m(n

C)] X 0.012 kg/mol.

For example, the atom of fluorine l9 F and the atom of carbon 12 C have masses

that are in the ratio 18.9984/12. The molar mass of the molecular gas F2 is

2X 18.9984

M(F2) - x 0.012 kg/mol = 0.037 996 8 kg/mol.

The amount of substance corresponding to a given mass of gas F2

, 0.05 kg for

example, is:

0.05 kg

0.037 996 8 kg-mol" = 1.315 90 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/3 the mass of one molecule is m(B) = am(X) +fim(Y) + ...

This mass is not known with accuracy, but the ratio m(B)/m(12 C) can be

determined accurately. The molar mass of a molecular substance B is then

m(B) / m(X) m(Y) \

M(B) = ^E) X 0 012 kg/n,°' =

\ m(!3Q

+ ^ mf^Q+

"/

X 0 012 k8/m01'

The same procedure is used in the more general case when the composition of the

substance B is specified as X0Y£ ... even if a, (3, ... are not integers. If we denote

the mass ratios m(X)/m(n

C), m(Y)/w('2 C), ... by r(X), r(Y), the molar mass

of the substance B is given by the formula:

M(B) = [ar(X) + /3r(Y) + ...] X 0.012 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.

14 There are many methods of measuring this ratio, the most direct one being by the mass

spectrograph.

42
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

3 at T=273.15 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 {Proces-Verbaux CIPM, 18, 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(X). By its Recommendation 1 (CI- 1972), CIPM recommends the use of the V(\) values adopted by the

International Commission on Illumination (CIE) in 1971.

15 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'(A) gives the spectral luminous

efficiency for scotopic vision (CIE 1951); this function V'(X) was ratified by the

CIPM in September 1976.

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 function 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(A)

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

luminous intensity.

IS CIE Publications No. 18 (1970), page 43, and No. 15 (1971), page 93; Proces-Verbaux CIPM, 40,

1972, Annexe 1. The V(\) \=y(K)] 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.

43
APPENDIX HI

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.

BIPM has its headquarters near Paris, in the grounds 43 520 m

2 ) 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 BIPM is to ensure worldwide unification of physical measurements; it

is responsible for: —establishing the fundamental 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 co-ordination of corresponding measuring techniques; —carrying out and co-ordinating determinations relating to the fundamental

physical constants that are involved in the above mentioned activities.

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 receives 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 modern

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 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 BIPM to the

Governments of the Member States of the Meter Convention.

* As of 31 December 1980 forty-five States were members of this Convention: Argentina (Rep. o0,

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. oQ, Hungary, India, Indonesia, Iran, Ireland, Italy, Japan, Korea (Rep. of), Mexico, Netherlands, Norway, Pakistan, Poland, Portugal, Romania, Spain, South Africa, Sweden,

Switzerland, Thailand, Turkey, U.S.S.R., United Kingdom, U.S.A., Uruguay, Venezuela, Yugoslavia.

44
The activities of BIPM, which in the beginning were limited to the measurements

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 (1960). 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 work in the laboratories of BIPM. They do metrological research, and

also undertake measurement and certification of material standards of the abovementioned quantities. BIPM's annual appropriation is of the order of 8 600 000

gold francs, approximately 3 400 000 U.S. dollars (in 1981).

In view of the extension of the work entrusted to BIPM, CIPM has set up since

1927, under 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 co-ordinating 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 (Proces-Verbaux CIPM,

1963, 31, 97). Each Consultative Committee, the chairman of which is normally a member of CIPM, is composed of delegates from the major Metrology

Laboratories and specialized Institutes, a list of which is drawn up by CIPM, as well as individual members also appointed by 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), 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 of Measurement of Ionizing

Radiations (CCEMRI), set up in 1958.

In 1969 this Consultative Committee established four sections: Section I (Measurement of x and y 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.

45
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 Generate 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.

46
The International System of Units (SI) 4th Edition 1981

Index

(Numbers in boldface indicate the pages w

Page

acceleration due to gravity, standard

value of fe n ) IX amount of substance 42 ampere t 4,20.41

atmosphere, standard 23

atto 29

becquerel 35 Bureau, International, of Weights and

Measures (BIPM) 44-46

candela 5, 31, 36

candle, new 19. 32 Committee, International, for Weights

and Measures (C1PM) 44-46 Committees, Consultative 45 Conference, General, on Weights and Measures (CGPM) 44-46 Convention, Meter 44 coulomb 20

cubic decimeter 27

curie 29

definitions of units, practical realization of the 39-43 degree Celsius 4. 21, 30

electric quantities 4

exa 36

farad 20 femto 29 frequency standard ('-^Cs) 28

gray 35

henry 20

the definitions of the units are to be found)

Page

joule 19

kelvin 4, 30,3

kilogram 3, 12. 17 kilogram, multiples of 32

legislation on units 2 length 39

liter 18. 27. 29. 37

liter (symbols) 37 lumen 19

mass 40 mass and weight 18 meter 3, 17. 19. 25 micron 32 mole 4, 34

newton 19 numbers, writing and printing of 22

ohm 20

pascal 33

peta 36 photometric quantities 43

prefixes, SI 11.26.29.36

prefixes, SI, rules for use of I 1

quantities, system of 2 quantity, meaning of 6

radian 9. 26

realization, practical, of the definitions of some important units 39-43

47
Page

second

SI units and multiples thereof Siemens

sievert steradian substance, amount of symbols, for base units symbols, for derived units with

special names

s\ mbols. for the liter symbols, writing & use of system of quantities

system of units, international system of units, proposal for establishing a practical

3, 24. 25. 30

26. 33

33

37

9. 26

4. 34

6

1

13. 37

6. 10. 22

226

2 1 . 23. 24

unit of quantity of heat (joule) units in use temporarily

units, CGS, with special names

units, electric units generally deprecated

units in use with SI

units, legislation on

units, photometric

units, SI base

units. SI base, sy mbols

units, SI derived

units, SI derived, with special names

units, SI, multiples and submultiples

units, SI supplementary

units, SI, the three classes of, UTC

TAI

temperature

temperature, Celsius temperature, thermodynamic

thermodynamic scale time

time, international atomic

time, universal coordinated

334 1 volt 4

4. 30

20, 2340

33-34 watt

15 weber

weight (see mass)

J£U.S. GOVERNMENT PRINTING OFFICE: 1981-360-997/1878

48


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