teferenc© A111D1 7flDflt,S

a TECH R.I.C.

« C.1 NBS-PUB-R JBLICATIONS NBS SPECIAL PUBLICATION 330

1977 Edition

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards —QC

100

• U57

No. 330

1977
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress 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

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jjstkHtti Bureau ot Standard

DEC 1 J> t9sr?

00 The International System

(Translation approved by the

International Bureau of Weights and

Measures of its publication "Le Systeme

International d'Unites")

(Supersedes NBS Special Publication 330

1974 Edition)

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

S NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued August 1977

usr of Units

1*77
National Bureau of Standards Special Publication 330

Nat. Bur. Stand. (U.S.), Spec. Publ. 330, 46 pages (Aug. 1977)

CODEN: NBSMA6

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1977

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

(Order by SD Catalog No. CI 3.10:330/4). Stock No. 003-003-01784-1. Price $1.60.

(Add 25 percent additional for other than U.S. mailing).
The International System of Units

Foreword

This document, now published independently by the National Bureau of Standards,

USA, and Her Majesty's Stationery Office, UK, is a translation of the French "Le Systeme

International d' Unites" published by the International Bureau of Weights and Measures.* It was prepared jointly by the National Physical Laboratory, UK, and the National

Bureau of Standards, USA. The International Bureau of Weights and Measures has compared this translation with the French text and finds that it agrees with the intention and

the letter of the original. The International Bureau hopes that wide dissemination of this

approved translation will promote knowledge and understanding of the International System of Units, encourage its use in all realms of science, industry, and commerce, and se- cure uniformity of nomenclature throughout the English-speaking world.

* "Le Systeme International cCUnites," 1970, OFFILIB, 84 rue Gay-Lussac, F. 75005 Paris (Revised edition 1977). Complete or partial translations of this brochure (or of its earlier editions) have been published in other languages, notably Bulgarian, Czech, German, Japanese, Portuguese, and Spanish. Several countries have also published guides for the use

of SI units.

J. Terrien

Director

BIPM

in
Preface of the 3d 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) 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 3d edition is the second edition brought up to date with the decisions of the 15th

CGPM (1975) and the amendments made by the CCU at its 4th and 5th sessions (1974

and 1976) and by the CIPM at its session of September 1976.

January 1977

J. TERRIEN

Director, BIPM

J. de BOER

President, CCU

IV
The International System of Units

Contents

Page

Foreword iii Preface of the 3d Edition iv

I. Introduction 1

1.1 Historical note 1

1.2 The three classes of SI units 1

II. SI units 3

11. 1 SI base units 3

1. Definitions 3

2. Symbols 6

11.2 SI derived units 6

1. Expressions 6

2. Recommendations 8

11.3 SI supplementary units 9

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

111.1 SI prefixes 10

111. 2 Recommendations 10

111.3 The kilogram 10

IV. Units outside the International System 11

IV.l Units used with the International System 11

IV.2 Units accepted temporarily 12

IV.3 CGS units 13

IV.4 Other units 14

Appendix I. Decisions of the CGPM and the CIPM 15

Appendix II. Practical realization of the definitions of some important

units 32

Appendix III. Organs of the Meter Convention 37

V

I. INTRODUCTION

1.1 Historical note

In 1948 the 9th CGPM1

, by its Resolution 6, instructed the CIPM1

: "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 (see II. 1.2, page 6) 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 (see II.l, page 3).

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 (see III.l, page 10), the derived and supplementary units (see

II.2, page 6 and II. 3, page 9) and other matters, thus establishing a

comprehensive specification for units of measurement.

In the present document the expressions "SI units", "SI prefixes", "supplementary units" are used in accordance with Recommendation 1(1969)

of the CIPM.

1.2 The three classes of SI units

SI units are divided into three classes

:

base units,

derived units,

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.l, page 3). These SI

units are called base units.

1 For the meaning of these abbreviations, see the preface.

1
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. Several of these algebraic expressions

in terms of base units can be replaced by special names and symbols which

can themselves be used to form other derivd units (see II.2, page 6).

Although it might be thought that SI units can only be base units or derived units, the 11th CGPM (1960) admitted a third class of SI units,

called supplementary units, for which it declined to state whether they

were base units or derived units (see II.3, page 9)

.

The SI units of these three classes form a coherent set in the sense nor- mally attributed to the expression "coherent system of units".

The decimal multiples and sub-multiples of SI units formed by means of

SI prefixes must be given their full name multiples and sub-multiples of

SI units when it is desired to make a distinction between them and the

coherent set of SI units.

2
II. SI UNITS

b) Unit of

mass

(kilogram)

II.l SI base units

1. Definitions

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

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

(meter) 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 2pi0 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. 16).

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

BIPM under conditions specified by the 1st CGPM in 1889.

c) Unit of Originally the unit of time, the second, was defined as the fraction

time 1/86 400 of the mean solar day. The exact definition of "mean solar day"

(second) was left to astronomers, but their measurements have shown that on ac- count of irregularities in the rotation of Earth, the mean solar day does

not guarantee the desired accuracy. In order to define the unit of time

more precisely the 11th CGPM (1960) adopted a definition given by the

International Astronomical Union which was based on the tropical year.

Experimental work had however already shown that an atomic standard

of time-interval, based on a transition between two energy levels of an

atom or a molecule, could be realized and reproduced much more accurately. Considering that a very precise definition of the unit of time of the International System, the second, is indispensable for the needs of advanced

metrology, the 13th CGPM (1967) decided to replace the definition of the

second by the following

The second is the duration of 9 192 631 770 periods of the radiation cor- responding to the transition between the two hyperfine levels of the ground

state of the cesium-133 atom. (13th CGPM (1967) , Resolution 1)

.

d) Unit of Electric units, called "international", for current and resistance, had

electric been introduced by the International Electrical Congress held in Chicago

current in 1893, and the definitions of the "international" ampere and the "inter-

(ampere) national" ohm were confirmed by the International Conference of London

in 1908.

3
Although it was already obvious on the occasion of the 8th CGPM (1933)

that there was a unanimous desire to replace those "international" units

by so-called "absolute" units, the official decision to abolish them was only

taken by the 9th 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 2 x 10-7 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" adopted by the 9th CGPM (1948, Resolution 7).

e) Unit of The definition of the unit of thermodynamic temperature was given in

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

dynamic point of water as the fundamental fixed point and assigned to it the temtemper- perature 273.16 K by definition. The 13th CGPM (1967, Resolution 3)

ature adopted the name kelvin (symbol K) instead of "degree Kelvin" (symbol

(kelvin) °K) and in its Resolution 4 defined the unit 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 T), ex- pressed in kelvins, use is also made of Celsius temperature (symbol t) defined by the equation

t = T - T0 where T0 = 273.15 K by definition. The unit "degree Celsius" is equal to

the unit "kelvin," but "degree Celsius" is a special name in place of "kelvin" for expressing Celsius temperature. A temperature interval or a

Celsius temperature difference can be expressed in degrees Celsius as well as in kelvins.

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

4
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".

It remained to define the unit of amount of substance by fixing the cor- responding 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) :

The mole is the amount of substance of a system which contains as many

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

Note. 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.

Note that this definition specifies at the same time the nature of the quantity whose unit is the mole. 2

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

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

intensity candle". This decision had been prepared by the International Commission

(candela) on Illumination (CIE) and by the CIPM before 1937, and was promulgated

by the CIPM at its meeting in 1946 in virtue of powers conferred on it in

1933 by the 8th CGPM. The 9th CGPM (1948) ratified the decision of the

CIPM and gave a new international name, candela (symbol cd), to the

unit of luminous intensity. The text of the definition of the candela, as amended in 1967, is 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.

(13th CGPM (1967) . Resolution 5)

.

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

KOJlHHeCTBO 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
2. Symbols

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

their names and their symbols (10th CGPM (1954), Resolution 6; 11th

CGPM (1960), Resolution 12; 13th CGPM (1967), Resolution 3; 14th

CGPM (1971), Resolution 3).

Table 1 SI base units

Quantity t Name Symbol

length ______________ m

mass _ _ _ kg

time __ _ __ __ _ _ s electric current A

thermodynamic temperature _ __. kelvin K

amount of substance _ ' mole mol

luminous intensity _ candela cd

t Translators' note: "Quantity" is the technical word for measurable attributes of phenomena or matter. The general principle governing the writing of unit symbols had already

been adopted by the 9th CGPM (1948), Resolution 7, according to which:

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 [for the first letter]. These symbols are not followed

by a full stop (period)

.

Unit symbols do not change in the plural.

II.2 SI derived units

1. Expressions

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

of the mathematical symbols of multiplication and division. Several derived units have been given special names and symbols which may themselves be used to express other derived units in a simpler way than in

terms of the base units.

Derived units may therefore be classified under three headings. Some of

them are given in tables 2, 3, and 4.

Table 2

Examples of SI derived units expressed in terms of base units

SI unit

Quantity Name Symbol

area square meter m2 volume cubic meter m3 speed, velocity meter per second m/s

acceleration meter per second squared m/s2 nr1 wave number 1 per meter

density, mass density kilogram per cubic meter kg/m3 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"

specific volume cubic meter per kilogram m3/kg

cd/m2 luminance candela per square meter

6
Table 3

SI derived units with special names

SI unit

Quantity SymExpression Expression

Name in terms in terms

bol of other

units

of SI base

units

l "V* f\ /"t 1 1 AVI rtTT jli etjuency hertz TTHz s~

l force newton N m-kg-s-2 m-1

• kg • s~ pressure, 2 stress pascal Pa N/nr

energy, work, quantity

joule T

J

XT —

nr-kg- s~

2 puvvci, iduiant nux watt W T fr, J/s m

2 -kg-s~3 tjudnxity oi electricity,

tiifcrciiiL cnarge coulomb As A s- A

eiectric potential,

potential cunerence,

electromotive force volt V

XXT W/Af A m-- kg- s

' • A

m^-kg-1

* s

4- A

2 cdpdcixance farad r w V

electric resistance ohm o V/A m2- kg-s~3- A

-2 conductance siemens b A/V —2 1 1 _3 A

° m -kg -s •

A

magnetic flux weber Wb V -S m2 'kg , s

-2

- A

-1 magnetic fiux density tesla T W b/m Kg- S -A

inductance henry TTJl Wb/A m2- kg- s

-2- A~2 oeisius temperature degree

Celsius °C K

luminous flux lumen lm cd-sr<M illuminance lux lx lm/m2 m

_2 -cd-sr(b) activity (of a radionuclide) f becquerel Bq s"

1 absorbed dose, specific

energy imparted, kerma,

absorbed dose index gray Gy J/kg m2 -s~

2

<0) See page 4.

<b> In this expression the steradian (sr) is treated as a base unit.

f Translators' note: this term is more appropriate than the direct translation 'ionizing radiations' of the present French text.

Table 4

Examples of SI derived units expressed by means of special names

SI unit

Quantity Name Symbol

Expression

in terms of

SI base units

dynamic viscosity pascal second Pas m'-kg-s"1 moment of force newton meter N-m nr-kg-s-2 surface tension newton per meter N/m kg-s-2 power density, heat flux

density, irradiance watt per square meter W/m2 kg-s-3 heat capacity, entropy joule per kelvin J/K m2 -kg-s~2 -K~'

specific heat capacity, joule per kilogram

specific entropy kelvin J/(kg-K) m

2 -s2 -K-'

specific energy joule per kilogram J/kg m2 -s"

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

J/m3 m-kg-s^-K"1 nr'-kg-s-2 energy density joule per cubic meter

electric field strength volt per meter V/m

C/m3 m-kg-s~3

- A"1

electric charge density coulomb per cubic meter m~3 -sA

electric flux density coulomb per square

meter C/m3 m~2 -sA

permittivity farad per meter F/m m-n. kg-i. s

4. A2

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

-

A

-2 molar energy joule per mole J/mol m2 -kg-s"2 -mol-1 molar entropy, molar heat

capacity joule per mole kelvin J/(mol-K) m2

• kg • s~

2

• K"1• mol"1 kg"1 exposure (x and y rays) coulomb per kilogram C/kg • s • A

absorbed dose rate gray per second Gy/s m2 -s~

3

7
Note—The values of certain so-called dimensionless quantities, as for

example refractive index, relative permeability or relative permittivity, are expressed by pure numbers. In this case the corresponding SI unit is

the ratio of the same two SI units and may be expressed by the number 1. 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 the

moment of a force.

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

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

per kilogram, for specific energy imparted, kerma, absorbed dose, and absorbed dose index.

2. Recommendations

The International Organization for Standardization (ISO) has issued

additional recommendations with the aim of securing uniformity in the use of units, in particular those of the International System (see the series

of International Standards ISO 31 and International Standard ISO 1000

of Technical Committee ISO/TC 12 "Quantities, units, symbols, conversion

factors and conversion tables")

.

According to these recommendations

:

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

following ways,1

"

for example: N-m, N.m, or N m.

b) A solidus (oblique stroke, /), a horizontal line, or negative powers

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

, m

for example: m/s, — or m-s-1

s

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

avoided by parentheses. In complicated cases negative powers or parentheses should be used

for example: m/s2 or m-s -2 but not: m/s/s

nvkg/(s3 -A) or m-kg-s- 8

- A- 1 m-kg/s3 /A

t USA Editors' note : For USA practice, see American National Standard Y 10.19.

8
II.3 SI supplementary units

The General Conference has not yet classified certain units of the International System under either base units or derived units. These SI units are assigned to the third class called "supplementary units", and may be

regarded either as base units or as derived units.

For the time being this class contains only two, purely geometrical, 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 SI supplementary units

SI unit

Quantity Name Symbol

plane angle radian rad

solid angle steradian sr

The radian is the plane angle between two radii of a circle which cut off on the circumference an arc equal in length to the radius.

The steradian is the solid angle which, having its vertex in the center of a sphere,

cuts off an area of the surface of the sphere equal to that of a square with sides of length

equal to the radius of the sphere.

(International Standard ISO 31/1)

.

Supplementary units may be used to form derived units. Examples are given in table 6.

Table 6

Examples of SI derived units formed by using supplementary writs

Quantity

SI units

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-nf'-sr-1

9
III. DECIMAL MULTIPLES AND

SUB-MULTIPLES OF SI UNITS

III.l SI prefixes

The 11th CGPM (1960, Resolution 12) adopted a first series of names

and symbols of prefixes to form 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 1018 by the 15th CGPM (1975, Resolution 10).

Table 7 SI prefixes

Factor Prefix Symbol Factor Prefix Symbol

10,s exa E 10 1 deci d

10,n peta P lo-- centi c 1012 tera T 10"* milli m

10° eiRa G lO"8 micro

10° mega M io-° nano n

103 kilo k 10 12 pico P

102 hecto h io-lc femto f

10 1 deka da 10 18 atto a

111.2 Recommendations

ISO recommends the following rules for the use of SI prefixes

a) Prefix symbols are printed in roman (upright) type without spacing

between the prefix symbol and the unit symbol.

b) An exponent attached to a symbol containing a prefix indicates that

the multiple or sub-multiple of the unit is raised to the power expressed

by the exponent,

for example: 1cm3 = (10_2 m) 3 = 10_G nr

1 cm-1 = (10-2 m)"1 = 102 m-1

1 fis1 ^ (10-6 s)'1 = 10° s"

1

c) Compound prefixes, formed by the juxtaposition of two or more SI

prefixes, are not to be used.

for example: 1 nm but not: 1 m^m

111.3 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).

10
IV. UNITS OUTSIDE THE INTERNATIONAL

SYSTEM

IV.l 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 to not 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 = 60 s hour'"' h 1 h -: 60 min : = 3 600 s day d 1 d = 24 h = 86 400 s degree 0 1° = (tt/180) rad

minute / 1' = (1/60)° = (tt/10 800) rad

second // 1" = (1/60)' = (tt/648 000) rad

liter(b> 1 1 1 = 1 dm1 = 10"3 m3 metric ton t t 1 t = 103 kg

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

.

(""This unit and its symbol were adopted by CIPM in 1879 ( Proces-Verbaux CIPM,

1879, p. 41). For the symbol for liter,t when there is a risk of confusion between the

letter 1 and the number 1, one may use the abbreviation "ltr" or write "liter" in full (CIPM, 1976). The present definition of the liter is in Resolution 6 of the 12th CGPM

(1964).

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

some other units which 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 («)

(6) unified atomic mass unit u

astronomical unit (0) parsec pc

Id) m 1 electronvolt is the kinetic energy acquired by on electron in passing through a

potential difference of 1 volt in vacuum; 1 eV = 1.602 19 X 10~19 J approximately.

(M The unified atomic mass unit is equal to the fraction a/i2 of the mass of an atom of

the nuclide "C; 1 u=1.660 57 x 10 2' kg approximately.

<0) This unit does not have an international symbol ; abbreviations are used, for ex- ample, AU in English, UA in French, AE in German, a.e.JJin Russian, etc. The astro- nomical unit of distance is the length of the radius of the unperturbed circular orbit of a body of negligible mass moving round the Sun with a sidereal angular velocity of

0.017 202 098 950 radian per day of 86 400 ephemeris seconds. In the system of astronomical constants of the International Astronomical Union (1976), the value adopted is 1 AU = 149 597.870 X 10" m.

,4) 1 parsec is the distance at which 1 astronomical unit subtends an angle of 1 second

of arc; we thus have approximately, 1 pc = 206 265 AU = 30 857 X 10 12 m.

t Translators' note : In some English-speaking countries, this unit is called "tonne."

X USA Editors' note : In the USA, the recommended symbol for liter is L instead of 1 to avoid confusion between the letter 1 and the number 1.

11
IV.2 Units accepted temporarily

In view of existing practice the CIPM (1969) considered it was preferable to keep temporarily, for use with those of the International System,

the units listed in table 10.

Table 10

Units to be used temporarily with the

International System

Name Symbol Value in SI unit

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

knot 1 nautical mile per hour =

(1852/3600) m/s

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

are' 6' a 1 a = 1 dam2 = 102 m2 hectare'6' ha 1 ha = 1 hm2 = 10* ma barn"" b 1 b = 100 fm2 = 10-28 m2 bar"1 ' bar 1 bar = 0.1 MPa = 105 Pa

standard atmosphere'"' atm 1 atm = 101 325 Pa

gal"> Gal 1 Gal = 1 cm/s3 = 10"2 m/s2 curie"" Ci 1 Ci = 3.7 X 1010 Bq

R = 2.58 X 10-4 C/kg

rad = 1 cGy = 10"2 Gy

rontgen"" R 1 rad"' rad 1

'"' 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 Inter- national Extraordinary Hydrographic Conference, Monaco, 1929, under the name "Inter- national nautical mile".

m This unit and its symbol were adopted by the CIPM in 1879 (Proces-Verbaux CIPM,

1879, p. 41). USA Editors' note: In recommended USA practice, hectare would appear in table 8.

<c) The barn is a special unit employed in nuclear physics to express effective cross

96CtlOTlS w> This unit and its symbol are included in Resolution 7 of the 9th CGPM (1948).

(e ' Resolution 4 of 10th CGPM (1954).

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

"" The curie is a special unit employed in nuclear physics to express activity of

radionuclides (12th CGPM (1964), Resolution 7).

cw The rontgen 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.

12
IV.3 CGS units

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

units of the International System, CGS units which 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<0) dyn 1 dyn = 10"5 N

poise(a) P 1 P = l dyn-s/cma = 0.1 Pas

stokes St 1 St = 1 crnVs = 10-* m2/s

gauss"" Gs, G 1 Gs corresponds to 10-4 T

oersted'" Oe 1 Oe corresponds to A/m

maxwell"" Mx 1 Mx corresponds to 10~s Wb

stilb(a) sb 1 sb = 1 cd/cm3 = 104 cd/m2 phot ph 1 ph = 104 lx

w This unit and its symbol were included in Resolution 7 of the 9th CGPM (1948).

<w 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 electric quantities are considered.

3 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.

13
IV.4 Other units

As regards units outside the International System which do not come

under sections IV.l, 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

in ame v aiuc in 01 unit

fermi 1 fermi = 1 fm = 10"15 m

metric carat'"* 1 metric carat = ^uu mg — & X 10 Kg

torr 1

. 101 325 ~

t0rr=

760

Pa

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

calorie (cal) 1 cal = 4.186 8 J

<b> micron (m)

(c> 1 H= lfim = lO^m

x unit""

stere (st) 00

1 st = 1 m3 gamma (7) 1 7 = 1 nT = 10-9 T

7

<f> 1 7 = l^g = 10-8 kg

x

<#> 1 X - 1 HI = 10 ° 1 = lO"0 m3

<0) This name was adopted by the 4th CGPM (1907, pp. 89-91) for commercial dealings

in diamonds, pearls, and precious stones.

<w This value is that of the so-called "IT" calorie (5th International Conference on

Properties of Steam, London, 1956).

<<0 The name of this unit and its symbol, adopted by the CIPM in 1879 (ProcesVerbaux CIPM, 1879, p. 41) and retained in Resolution 7 of the 9th CGPM (1948) were

abolished by the 13th CGPM (1967, Resolution 7)

.

4 This special unit was employed to express wavelengths of x rays; 1 x unit =

1.002x10"* 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".

(f) This symbol is mentioned in Proces-Verbaux CIPM, 1880, p. 56.

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

14
APPENDIX I

Decisions of the CGPM and the CIPM

(The more important decisions abrogated, modified, or added to, are

indicated by an asterisk.*)

CR: Comptes rendus des seances de la Conference Generate des Poids

etMesures (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

kilogram (CR, 34-38)

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

which 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 per cent 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. 22: 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.

3 The hydrogen thermometer centigrade scale in terms of which the

equations of the prototype Meters have been established.

B. As regards national prototypes

15
liter

3rd CGPM, 1901

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. 26: 12th CGPM, Resolution 6)

mass and Declaration on the unit of mass and on the definition of weight; convenweight tional value of g» (CR, 70)

ffn 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 weighV 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

;

t USA Editors' note : In the USA weight is the commonly used term for mass. Because of

the dual use of the term weight as a quantity, this term should be avoided in technical practice. (Ameri- can National Standard Z210.1.) "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

7th CGPM, 1927

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. 22: 11th CGPM, Resolution 6).

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

and Measures" (PV, 1887, 88).

s Note of BIPM. This conventional reference "standard value" (gn = 9.806 65 m/s2

) to be used in the reduction to standard gravity of measurements made in some place on Earth has been reconfirmed in 1913 by the 5th CGPM (CR, 44).

16
photometric

units

CIPM, 1946

Definitions of photometric units (PV, 20, 119)

Resolution "

mechanical

and

electric

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.*

* Definition modified in 1967 (see p. 27: 13th CGPM, Resolution 5).

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

flux emitted in unit solid angle (steradian) by a uniform point source having a luminous intensity of 1 new candle.

5

Definitions of electric units (PV, 20, 131)

Resolution 2

~

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

electric units

Unit of force.—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*.

* The name "newton" was adopted in 1948 for the MKS unit of force (see

note 7 ).

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

point of application of 1 MKS unit of force [newton] moves a distance of 1

meter in the direction of the force.

Watt (unit of power).—The watt is that 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 2 X 10-7 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.

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).

17
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

thermodynamic

scale

unit of

heat

degree

Celsius

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.

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.

Adoption of "degree 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)

.

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

18
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

;

to make recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Meter Convention.

19
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

•meter

• square meter

•cubic meter

• micron * •liter

• gram

•tonne

second

erg

dyne

degree Celsius

•degree absolute**

calorie

bar

hour

Symbol Unit Symbol

m ampere __ _ A

m

2 volt V

m

3 watt _____ W

M ohm _ _ J2

1 coulomb __ __ C

g farad __ F

t henry _ H

S hertz _ _ _ Hz

erg poise __ . P

dyn newton _ _ _. N

°C •candela ("new candle") cd

°K lux _ _ _ _ lx

cal lumen _ _ . lm

bar stilb - —_ sb

h

* Unit and symbol abrogated in 1967 (see p. 28: 13th CGPM, Resolution 7). ** Name and symbol changed in 1967 (see p. 27: 13th CGPM, Resolution 3).

Notes

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

had already been adopted by a decision of the CIPM.

2. 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.

3. To indicate a temperature interval or difference, rather than a temperature, the word "degree" in full, or the abbreviation "deg", must be

used.*

* See p. 27, Resolution 3 of the 13th CGPM, 1967.

10th CGPM, 1954

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

dynamic Resolution 3

scale

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. 27, Resolution 4 of the 13th CGPM, 1967.

20
standard

atmosphere

practical

system

of units

Definition of standard atmosphere (CR, 79)

Resolution 4 The 10th CGPM, having noted that the definition of the standard atmosphere given by the 9th CGPM when defining the International Temperature Scale, led some physicists to believe that this definition of the standard atmosphere was valid only for accurate work in thermometry,

declares that it adopts, for general use, the definition

1 standard atmosphere = 1 013 250 dynes per square centimeter, i.e.,

101 325 newtons per square meter.

Practical system of units (CR, 80)

Resolution 6

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

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

length meter

mass kilogram

time second

electric current ampere

thermodynamic temperature degree Kelvin*

luminous intensity candela

* Name changed to "kelvin" in 1967 (see p. 27 : 13th CGPM, Resolution 3).

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

12 960 276 813

time (ET) is the fraction x 10 9 of the tropical year for

408 986 496

1900 January 0 at 12 h ET,

decides

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

1900 January 0 at 12 hours ephemeris time".*

* Definition abrogated in 1967 (see p. 26: 13th CGPM, Resolution 1).

21
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 en- quiry 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 12 of the 11th CGPM (1960) ] 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 Resoluton 12 of the

11th CGPM (I960)]

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 ac- curacy 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 Pi0 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 9

;

9 See Appendix II, p. 32, for the relevant Recommendation adopted by the CIPM.

22
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. 26: 13th CGPM, Resolution 1).

SI 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

* Name and symbol of unit modified in 1967 (see p. 27: 13th CGPM,

Resolution 3)

.

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 submultiples of the units,

decides

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

System of Units"*

;

* A seventh base unit, the mole, was adopted in 1971 by the 14th CGPM

(Resolution 3, see p. 30)

.

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

;

23
3 names of multiples and sub-multiples of the units are formed by means

of the following prefixes * :

Multiplying factor Prefix Symbol

l UUU UUU UUU UUU —1U tera 1 1 UUU UUU UUU = 1U griga G

I UUU UUU—1U mega i\/r

1 UUU — 1U KliO i_K

100=10" 11 10=10' deka da

0.1=10"' deci d

0.01=10-= centi c 0.001=10-'' milli m

0.000 001=10^ micro f- 0.000 000 001=10-' nano n

0.000 000 000 001 =10 12 pico P

*See pages 26 and 31 for the four new prefixes adopted by the 12th CGPM (1964),

Resolution 8, and the 15th CGPM (1975), Resolution 10.

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 angles steradian sr Dfrtvpti TTwttq *

area _ square meter m~

volume _ cubic meter m3 frequency _ _ hertz Hz 1/s mass density (density) kilogram per cubic meter kg/m3 speed, velocity meter par second m/s

angular velocity _ _ 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: pressure (mechanical

stress) - _ newton per square meter N/m2 kinematic viscosity square meter per second mVs

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 A-s

potential difference,

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 webar Wb V-s

inductance _ _ __ henry H V-s/A

magnetic flux density tesla T Wb/m2 magnetic field strength 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 28 for the other units added by the 13th CGPM (1967) , Resolution 6.

24
cubic Cubic decimeter and liter (CR, 88)

decimeter

and liter

Resolution 13

The 11th CGPM,

considering

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

parts in 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.

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

Atomic standard of frequency (CR, 93)

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 S,, 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.

frequency

standard

25
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 3rd 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 re- sults 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 r1

. The symbol for this unit is Ci.

* In 1975 the name "becquerel" (Bq) was adopted for the SI unit of activity (see p. 31: 15th CGPM, Resolution 8) ; 1 Ci = 3.7 X 1010 Bq.

femto SI prefixes femto and atto (CR, 94)

atto

i 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

:

Multipying factor Prefix Symbol

1(T15 femto f

10-,s atto a

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 fulfil 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,

26
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 unit of time of the International System of Units 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.

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

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) 10

, that the unit of thermodynamic temperature

and the unit of temperature interval are one and the same unit, which

ought to be denoted by a single name and single symbol,

decides

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

;

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

interval

;

3 a temperature interval may also be expressed in degrees Celsius

;

4 the decisions mentioned in the opening paragraph concerning the

name of the unit of thermodynamic temperature, its symbol and the designation of the unit to express an interval or a difference of temperatures

are abrogated, but the usages which derive from these decisions remain

permissible for the time being.

Resolution 4

kelvin 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

10 "1. The unit degree Kelvin (symbol °K) may be employed for a difference of two thermodynamic temperatures as well as for thermodynamic temperature itself. "2. If it is found necessary to suppress the name Kelvin, the international symbol "deg" is recommended

for the unit of difference of temperature. (The symbol "deg" is read, for example: "degre" in French,

"degree" in English, "gradous" (rpajiyc) in Russian, "Grad" in German, "graad" in Dutch").

kelvin

(degree

Celsius)

27
SI derived

units

micron (^)

new candle

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."

SI derived units (CR, 105)

Resolution 6

The 13th CGPM

considering that it is useful to add some derived units to the list of paragraph 4 of Resolution 12 of the 11th CGPM (1960)

,

decides to add

wave number 1 per meter m"1 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"' *

* Name and symbol of the unit changed in 1975 (see p. 31 ; 15th

CGPM, Resolution 8)

.

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

Resolution 7 The 13th CGPM,

considering that subsequent decisions of the General Conference con- cerning 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 'V 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".

28
CIPM, 1969

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.

14th CGPM, 1971

Pascal; Siemens (CR, 77)

The 14th CGPM 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)

.

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 conse- quence of the atomic definition of the second,

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,

29
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.

mole SI unit of amount of substance (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 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 which 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.

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.

11 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 time unit of the International System of Units'.

30
becquerel SI units for ionizing radiation (CR, 105)

*» ray 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 non-specialists, —taking into consideration also the grave risk of errors in therapeutic

work,

adopts the following special name for the SI unit of}

activity: becquerel, symbol Bq, equal to one reciprocal^ Resolution 8

second. )

adopts the following special name for an SI unit in]

the field of ionizing radiation : gray, symbol Gy, equal to } Resolution 9

one joule per kilogram.12

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

101G peta P

1018 exa E

13 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 or- ganizations.

31
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 con- taining 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 milli- meter.

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 10s

:

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 capillarv is 0.3±0.1 ampere per square centimeter.

(Proces-Verbaux CIPM, 1960, 28, 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 kryton 86 and several lines of mercury 198 and of

cadmium 114 are recommended as secondary standards (Proces-Verbaux

CIPM, 1963, 31, 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, 112, 1973)

component i

These lines are reproducible with an uncertainty of the order of 1 in 1010

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

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

measuring the beat frequencies of neighbouring 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.

To measure end or line standards these radiations are used in an interference comparator, a complicated instrument with mechanical, optical

interference, and thermometric components.

Line

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

Wavelength in vacuum

3 392 231.40 X 10"12 m

632 991.399 X 10~12 m

32
The wavelength of the methane line mentioned above multiplied by its

frequency (measured by comparison with the 133 Cs transition of the definition of the second) yields the speed of propagation of electro-magnetic

waves in vacuum c = 299 792 458 m/s, recommended by the 15th CGPM

(Resolution 2). This value of c will probably be kept unaltered in the

future.

2. Mass

The primary standard of the unit of mass is the international prototype

of the kilogram kept at the BIPM. The mass of 1-kg secondary standards

of platinum-iridium or of stainless steel is compared with the mass of the

prototype by means of balances whose precision can reach 1 in 108 or better.

By an easy operation a series of masses can be standardized to obtain

multiples and sub-multiples of the kilogram.

3. Time

Some laboratories are able to make the equipment required to produce

electric oscillations at the frequency of vibration of the atom of cesium-133

which defines the second. This equipment includes a quartz oscillator, frequency multipliers and synthesizers, a klystron, phase-sensitive detectors,

an apparatus for producing an atomic beam of cesium in vacuum, cavity

resonators, uniform and non-uniform magnetic fields, and an ion detector.

Complete assemblies to produce this frequency are also commercially

available.

By division it is possible to obtain pulses at the desired frequencies, for

instance 1 Hz, 1 kHz, etc. In the best equipments, the stability and accuracy correspond to an

uncertainty of 1 in 10 12 or even 1 in 1013

. Radio stations broadcast waves whose frequencies are known to about

the same accuracy.

There are other standards besides the cesium beam, among them the

hydrogen maser, rubidium clocks, quartz frequency standards and clocks,

etc. Their frequency is controlled by comparison with a cesium standard,

either directly, or by means of radio transmissions.

Most 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 TAP3 by an exact 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 and of June, and in the

second instance at the end of March and of September, to keep UTC in

agreement with the time denned by the rotation of Earth with an approximation better than 0.9 s.

14 Furthermore, the legal times of most countries are offset by a whole number of hours (time zones and 'summer' time)

.

13 See Appendix I, page 29, for the definition of TAI given by CIPM at the request of the 14th CGPM

(1971, Resolution 1).

14 The difference UTC-TAI became — 16 s on 1 Jan. 1977.

33
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 en- joying 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 Thompson-Lampard)

.

The volt is deduced from the ampere and the ohm.

The uncertainty in the absolute determination of the farad is a few parts

in 10s

; for the ampere, it is a few parts in 10°.

The results of absolute measurements are obtained by means of secondary standards which are, for instance

1. coils of manganin wire for resistance standards

;

2. galvanic cells with cadmium 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 which maintain the electric units:

measurement of the gyromagnetic ratio of the proton yp

' 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 106

, 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.

34
6. Amount of substance

All quantitative results of chemical analysis or of dosages can be ex- pressed in moles, in other words in units of amount of substance of the

constituent particles. 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( 12 C) of an atom of

carbon 12 nor the mass m(X) of an atom X can be measured accurately,

we use the ratio of these masses, m(X)/m(12 C), which can be ac- curately determined.15 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) = [w(X)/m( 12 C)] X 0.012 kg/mol.

For example, the atom of fluorine 19 F and the atom of carbon 12 C have

masses which are in the ratio 18.9984/12. The molar mass of the molecular

gas F2 is

2 X 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 8kg-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 = XaYjS . . ., the mass of one molecule is m(B) = «m(X) +

/8m (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) n

( m(X) m(Y) ) Af (B) = ^—X0.012 kg/mol = a —

+p !—_+...

m(12 C) ( m(12 C) m(12 C) j x 0.012 kg/mol.

The same procedure is used in the more general case when the composition of the substance B is specified as XaY^ . . . even if a, (3, . . . are not

integers. If we denote the mass ratios m(X)/m(12 C), ra(Y)/m( 12 C), . . . by r(X), r(Y), . . ., the molar mass of the substance B is given by the

formula

M(B) = [«r(X) + /?r(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.

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

35
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 m3 at

T = 273.15 K and p = 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 mole of (1/2) 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

Absolute photometric measurements by comparison with the luminance

of a blackbody at the temperature of freezing platinum can only be undertaken by a few well-equipped laboratories. The accuracy of these measurements is somewhat better than 1 %

.

The results of these measurements are maintained by means of incandescent lamps fed with d.c. in a specified manner. These lamps constitute

standards of luminous intensity and of luminous flux.

The method approved by CIPM in 1937 (Proces-Verbaux CIPM, 18, 237)

for determining the value of photometric quantities for luminous sources having a color other than that of the primary standard, utilizes a procedure taking account of the "spectral luminous efficiencies" V(\). By its

recommendation CI 1 (1972), CIPM recommends the use of the V(\)

values adopted by the International Commission on Illumination (CIE) in

1971. 16 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"(A) 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.

16 CIE Publications No. 18 (1970), page 43, and No. 15 (1971), page 93: Proces-Verbaux CIPM, 40, 1972, Annexe 1. The V (X) [ = ]/(X)] values are given for wavelengths in 1-nm steps from 360 to 830 nm ; they are an improvement on the values in 10-nm steps adopted by CIPM in 1933, and previously by

CIE in 1924.

36
APPENDIX III

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 m2 ) 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 the determinations relating to the fundamental physical constants.

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 least once every six 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 least once every two years. 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.

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

•As of 31 December 1976 forty-four States were members of this Convention: Argentina (Rep. of), Australia, Austria, Belgium, Brazil, Bulgaria, Cameroon, Canada, Chile, Czechoslovakia, Denmark, Dominican Republic, Egypt, Finland, France, German Democratic Rep., Germany (Federal Rep. of), Hungary,

India, Indonesia, Iran, Ireland, Italy, Japan, Korea, Mexico, the Netherlands, Norway, Pakistan, Poland,

Portugal, Rumania, Spain, South Africa, Sweden, Switzerland, Thailand, Turkey, U.S.S.R., United Kingdom,

U.S.A., Uruguay, Venezuela, Yugoslavia.

37
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 above-mentioned quantities. BIPM's annual budget is of the order of 5 000 000 gold

francs, approximately 2 000 000 U.S. dollars (in 1977)

.

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 which 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 a delegate from each of the

large 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 seven of them in

existence.

1. The Consultative Committee for Electricity (C.C.E.), set up in 1927.

2. The Consultative Committee for Photometry and Radiometry

(C.C.P.R.), new name given in 1971 to the Consultative Committee

for Photometry set up in 1933 (between 1930 and 1933 the preceding

Committee (C.C.E.) dealt with matters concerning Photometry).

3. The Consultative Committee for Thermometry (C.C.T.) , set up in 1937.

4. The Consultative Committee for the Definition of the Meter (C.C.D.M.)

,

set up in 1952.

5. The Consultative Committee for the Definition of the Second (C.C.D.S.),

set up in 1956.

6. The Consultative Committee for the Standards of Measurement of

Ionizing Radiations (C.C.E.M.R.I.) , 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 («-energy

standards) . In 1975 this last section was dissolved and Section II made re- sponsible for its field of activity.

7. The Consultative Committee for Units (C.C.U.), set up in 1964.

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 Consultaltifs;

38
—Recueil de Travaux du Bureau International des Poids et Mesures

(this compilation 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 con- cerning the activities, decisions and recommendations of the various

bodies created under the Metric Convention.

39
The International System of Units (SI) 3d Edition 1977

Index

(Numbers in boldface indicate the pages where the definitions of the units are to be found)

Page

acceleration due to gravity, standard

value of (gn ) 16

ampere 4, 17, 34

atmosphere, standard 21

atto 26

becquerel 31

Bureau, International, of Weights and

Measures (BIPM) 37-39

candela 5, 27

candle, new 17, 28

Committee, International, for Weights

and Measures (CIPM) 37-39

Committees, Consultative 38

Conference, General, on Weights and

Measures (CGPM) 37-39

Convention, Meter 37

coulomb 18

cubic decimeter 25

curie 26

definitions of units, practical

realization of the 32-36

degree Celsius 4, 18, 27

electric quantities 34 exa 31

farad 18

femto 26

frequency standard (

133 Cs) 25

gn 16

gray 31

henry 18

Page

joule 18

kelvin 4, 27

kilogram 3, 15

kilogram, multiples of 10, 28

length 32

liter 16, 25, 26

liter (symbol) 11

lumen 17

mass 33 mass and weight 16

meter 3, 15, 16, 22

micron 28

mole 4, 5, 30

newton 17

numbers, writing and printing of 20

ohm 17

pascal 29

peta 31

photometric quantities 36

prefixes, SI 10, 24, 26, 31

prefixes, SI, rules for use of 10

quantity, meaning of 6

radian 9, 24

realization, practical, of the definitions

of some important units 32-36

second 3, 21, 23, 26

40
Page Page

SI units and multiples thereof 29 unit of quantity of heat (joule) 18

Siemens 29 units accepted temporarily 12

steradian 9, 24 units, CGS, with special names 13

substance, amount of 4-5, 35 units, electric 17

symbol, for the liter 11 units generally deprecated 14

symbols, for base units 6 units in use with SI 11

symbols, for derived units with units, photometric 17

special names 7 units, SI base 3

symbols, writing & printing of 6, 8, 20 units, SI derived 6-8, 24, 28

system of units, international 23 units, SI derived, with special names 7

system of units, proposal for units, SI supplementary 9, 24

establishing a practical 19, 21, 22 units, SI, the three classes of, 1 UTC 30

TAI 29

temperature o4

volt 17

temperature, Celsius 4

thermodynamic scale 18, 20

time 33 watt 17

time, international atomic 29-30 weber 18

time, universal coordinated 30 weight (see mass)

41

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