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IMBS SPECIAL PUBLICATION 330

NIST

PUBLICATIONS

U.S. DEPARTMENT

OF

COMMERCE

National

- QC

The International

System of Units (SI)

UNITED STATES DEPARTMENT OF COMMERCE

Maubice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • LEWIS M. BRANSCOMB, Director

The International System

of Units (SI)

Editors

Chester H. Page

and

Paul Vigoureux

(Translation approved by the

International Bureau of Weights and Measures

of its publication "Le Systeme International

d'Unites")

-6,

U. 5, National Bureau of Standards Special Publication 330

Nat, Bur. Stand. (U.S.), Spec. Publ. 330, 42 pages (Jan. 1971)

CODEN: XNBSA

Issued January 1971

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D. C. 20402 (Order by SD Catalog No. C 13.10:330) Price 50 cents.
Library of Congress Catalog Card Number: 73-608985

ii
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 uLe 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 only difference between the English and

American versions lies in the spelling of "caesium" and "black body"

in the UK publication and "cesium" and "blackbody" in the USA

publication. 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 secure uniformity of

nomenclature throughout the English-speaking world.

J. Terrien

Director

BIPM

* "Le Systeme International d'UniUs," 1970, OFFILIB, 48 rue Gay-Lussac, F 75

Paris 5.

Ill
Preface

The International Bureau of Weights and Measures (BIPM), in

response to frequent requests, publishes this document containing

Resolutions and Recommendations of the General Conference of

Weights and Measures (CGPM) on the International System of

Units. Explanations have been added as well as relevant extracts from the Recommendations of the International Organization for

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

The Consultative Committee for Units (CCU) of the International

Committee of 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.

J. TERRIEN

Director, BIPM

J. de BOER

President, CCU

IV
The International System of Units

Contents

Page

Foreword Ill

Preface IV

I. Introduction 1

1.1 Historical note 1

1.2 The three classes of SI units 2

II. SI Units 3

11.1 Base units 3

1. Definitions 3

2. Symbols 6

11.2 Derived units 6

1. Expressions 6

2. Recommendations 10

11.3 Supplementary units 11

III. Decimal multiples and sub-multiples of SI units 12

111.1 SI prefixes 12

111.2 Recommendations 12

111.3 The kilogram 12

IV. Units outside the International System 13

IV.l Units used with the International System 13

IV.2 Units accepted temporarily 15

IV.3 CGS units 16

IV.4 Other units 17

Appendix I. Decisions of the CGPM and the CIPM 18

Appendix II. Practical realization of the definitions of some

important units 35

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 Metre 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, adopted as base units

of this "practical system of units", the units of the following six

quantities: length, mass, time, electric current, thermodynamic

temperature, and luminous intensity (see II.l, page 3).

The 11th CGPM (1960), by its Resolution 12, finally 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 12), the derived and supplementary units (see II.2.2, page 10 and II.3, page 11) 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.

Improvements and extensions of this specification have already

become necessary ; some of them have reached a sufficiently advanced

stage to be incorporated in this document, although the CGPM has

not yet given its final approval; in particular, in accordance with

the proposed Resolution approved by the CIPM in October 1969, the

mole is here treated as a base unit.

For the meaning of these abbreviations, see the preface.

1
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 six well-defined units : the metre, the kilogram,

the second, the ampere, the kelvin, and the candela (see II.l, page 3)

.

These SI units are called base units. 2 ' 3 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 derived 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 11).

The SI units of these three classes form a coherent set in the sense normally 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 The 13th CGPM (1967) considered the introduction of the mole into the International System and instructed the CIPM to prepare a draft accordingly. In 1969 the CIPM

approved a draft resolution for submission to the 14th CGPM (1971) to the effect that

the mole should be declared a base unit (See Il.l.l.g, page 5).

3 Translators' note. The spellings "metre" and "kilogram" are used in this USA/UK

translation in the hope of securing worldwide uniformity in the English spelling of the names of the units of the International System. 2
II. SI UNITS

II.l Base units

1. Definitions

a) Unit of length.—-The 11th CGPM (1960) replaced the definition

of the metre based on the international prototype of platinumiridium, in force since 1889 and amplified in 1927, by the following

definition

:

The metre is the length equal to 1 650 763.73 wavelengths in vacuum of the radiation corresponding to the transition between

the levels 2p10 and 5d5 of the krypton-86 atom. (11th CGPM

(1960), Eesolution 6).

The old international prototype of the metre 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.

b) Unit of mass.—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. With the object of removing the ambiguity which still occurred in

the common use of the word "weight", the 3rd CGPM (1901) declared: the kilogram is the unit of mass [and not of weight or of

force] ; it is equal to the mass of the international prototype of the

kilogram.

This international prototype made of platinum-iridium is kept at the BIPM under conditions specified by the 1st CGPM in 1889.

c) Unit of time.—Originally the unit of time, the second, was defined as the fraction 1/86 400 of the mean solar day. The exact

definition of "mean solar day" was left to astronomers, but their

measurements have shown that on account of irregularities in the

rotation of the Earth the mean solar day does not guarantee the desired accuracy. In order to define the unit of time more precisely the

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

Astronomical Union which was based on the tropical year. Experimental work had however already shown that an atomic standard

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

accurately. Considering that a very precise definition of the unit of

time of the International System, the second, is indispensable for the

needs of advanced metrology, the 13th CGPM (1967) decided to replace the definition of the second by the following

:

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

corresponding to the transition betioeen the two hyperfine levels of

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

3
d) Unit of electric current.—Electric units, called "international",

for current and resistance, had been introduced by the International

Electrical Congress held in Chicago in 1893, and the definitions of

the "international" ampere and the "international" ohm were con- firmed by the International Conference of London in 1908. Although it was already obvious on the occasion of the 8th CGPM

(1933) that there was a unanimous desire to replace those "international" units by so-called "absolute" units, the official decision to abolish them was only taken by the 9th 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 metre apart in vacuum, would produce

between these conductors a force equal to 2 Y 10~7 newton per metre

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 thermodynamic temperature.—The definition of the unit

of thermodynamic temperature was given in substance by the 10th

CGPM (1954, Resolution 3) which selected the triple point of water

as fundamental fixed point and assigned to it the temperature 273.16

°K by definition. The 13th CGPM (1967, Resolution 3) adopted the name kelvin (symbol K) instead of "degree Kelvin" (symbol °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),

expressed 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 Celsius temperature is in

general expressed in degrees Celsius (symbol °C). The unit "degree

Celsius" is thus equal to the unit "kelvin" and an interval or a differ- ence of Celsius temperature may also be expressed in degrees Celsius.

f) Unit of luminous intensity.—The units of luminous intensity

based on flame or incandescent filament standards in use in various

countries were replaced in 1948 by the "new candle". This decision
had been prepared by the International Commission 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 metre of a blackbody at the

temperature of freezing platinum under a pressure of 101 325 newtons per square metre. (13th CGPM (1967), Resolution 5).

g) Unit of amount of substance.—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".

"Atomic weights" were originally referred to the atomic weight of

oxygen (by general agreement taken as 16). But whereas physicists

separated isotopes in the mass spectrograph and attributed the value

16 to one of the isotopes of oxygen, chemists attributed that same

value to the (slightly variable) mixture of isotopes 16, 17, and 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". The mass corresponding to the unit of amount of carbon 12

still remained to be fixed; by international agreement it has been

fixed at 0.012 kg and the unit of the quantity "amount of substance"

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, unit of amount of substance:

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.

In 1969 the CIPM decided to propose to the 14th CGPM (1971)

to introduce the mole as base unit in the International System of

Units, with the definition given above. Note that this definition

5
specifies at the same time the nature of the quantity whose unit is the mole.4

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; CIPM (1967 and 1969)).

Table 1

jSI base units

Quantity Name Symbol

length ... metre m

mass ... kilogram kg

time second s electric current ampere A

thermodynamic temperature kelvin K

luminous intensity .. candela cd

amount of substance mole mol

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 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.

4 The name of this quantity, adopted by IUPAP, IUPAC, and ISO is in French

"quantitere de matigre", and in English "amount of substance" ; (the German and Russian

translations are "Stoffmenge" and "KOJIHHeCTBO BCmeCTBa"). 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. 6
Table 2

Examples of SI derived units

expressed in terms of base units

Quantity

SI unit

Name Symbol

area square metre mz volume cubic metre m

speed, velocity metre per second m/s

acceleration metre per second squared m/s2 wave number 1 per metre m-1 density, mass density kilogram per cubic metre kg/m3 concentration

(of amount of

substance) mole per cubic metre mol/m3 activity (radioactive) 1 per second S"1 specific volume cubic metre per kilogram m3 /kg

luminance candela per square metre cd/m2

7
Table 3

SI derived units with special names

Quantity

SI unit

Name Symbol

Expression

in terms

of other

units

Expression

in terms

of SI base

units frequency hertz Hz S"1 force newton N m# kg»s-2 pressure pascal(0) Pa N/m2 m"1# kg# s2 energy, work, quantity

of heat joule J N«m m2# kg- s

-2 power, radiant flux watt W J/s m2, kg»s-3 quantity of electricity, electric charge coulomb C A«s s

- A

potential difference, volt V W/A m2, kg, s

_3, A-1 electromotive force

capacitance farad F C/V m-2.kg-i. S4.A2 electric resistance ohm o V/A m2 *kg»s_3 »A-2 conductance siemens(0) S A/V m-2.]jg-l. s3.A2

ma cm fitir, flux weber Wb V-s m2 »kg-s-2»A-1 magnetic flux density tesla T Wb/m2 kg-s^'A"1 inductance henry H Wb/A m2 «kg»s-2 «A-2 luminous flux lumen lm cd*sr (6) illuminance lux lx nr2 »cd»sr (6)

(a) In 1969 the CIPM decided to seek approval of the 14th CGPM for this special name

and its symbol.

(6) In this expression the steradian (sr) is treated as a base unit.

8
Table 4

Examples of SI derived waits

expressed by means of special names SI unit

(Quantity Expression

Name Symbol in terms of

SI base units

dynamic

viscosity pascal second Pa*s m~1# kg# s

_1 moment of

force metre newton N# m m2, kg, s

-2 surface tension newton per

metre N/m kg»s"2 heat flux density, watt per square

irradiance metre W/m2 kg# s~

3 heat capacity,

entropy joule per kelvin J/K m2 -kg»s-2 »K-1 specific heat

capacity, joule per

specific kilogram

entropy kelvin J/(kg-K) m^s-^K-1 specific energy joule per

kilogram J/kg m2 «s2 thermal watt per metre

conductivity kelvin W/(m-K) m-kg's^'K-1 energy density joule per cubic

metre J/m3 m-i«kg«s~2 electric field strength volt per metre V/m m^kg^s'^A-1 electric charge coulomb per

density cubic metre C/m3 m_3, s»A

electric flux coulomb per

densitv square metre C/m2 nr^A

permittivity farad per metre F/m m-3# kg_1 *s4# A2 current densitv ampere per

square metre A/m2 magnetic field ampere per

strength metre A/m

permeability, henry per metre H/m m'kg's^A-2 molar energy joule per mole J/mol m2, kg, s~

2# mol"1 molar entropy, joule per mole

molar heat kelvin

capacity J/(mol«K) m^kg-s^-K-^mol-1

i 9
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 corres- ponding SI unit is the ratio of the same two SI units and may be

expressed by the number 1.

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 Recommendations R 31 and Recommendation R 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 is preferably indicated by

a dot. The dot may be dispensed with when there is no risk of con- fusion with another unit symbol

for example: N# m or N m hut not: mN

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

for example: m/s,-^1 or m*s_1 c) The solidus must not be repeated on the same line unless ambiguity is avoided by parentheses. In complicated cases negative

powers or parentheses should be used

for example: m/s2 or m»s~2 but not: m/s/s

m*kg/(s3, A) or m^kg'S'^A-1 m*kg/s3 /A

10
II.3 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), Kesolution 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 ivhich, 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.

(ISO Recommendation R 31, part 1, second edition, December

1965).

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 units

Quantity

SI unit

Name Symbol

angular velocity radian per second rad/s

angular acceleration radian per second

squared rad/s2 radiant intensity watt per steradian W/sr

radiance watt per square metre

steradian W# nra*sr"x

11
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).

Table 7

SI prefixes

Factor Prefix Symbol Factor Prefix Symbol

1012 tera T 10-1 deci d

109 G io-2 centi c 106 mega M io-3 milli m

103 kilo k io-6 micro /* 102 hecto h io-9 nano n

101 deka da io-12 pico P

10-15 femto f io-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 affixed 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: 1 cm3 = 10~6 m3 1 cm"1 = 102 m"1 c) Compound prefixes are to be avoided,

for example: 1 nm but not: 1 m/xm

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).

12
IV. UNITS OUTSIDE THE INTERNATIONAL

SYSTEM

IV.l Units used with the International System

The CIPM (1969) recognized that users of SI will also wish to employ certain units which, although not part of it, are in widespread use. These units play such an important part that they must

be retained for general use with the International System of Units.

They are given in table 8. Table 8 Units in use with the International System

Name Symbol Value in SI unit

minute min 1 min i= 60s

hour(0) h lh = 60 min = 3 600 s day d 1 d = 24 h = 86 400 s degree o 1° = (tt/180) rad

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

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

litre(0)

1 1 1 = 1 dm3 = 10"3 m3 tonne* 0> t 1

1

= 103 kg

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

litre is defined in Resolution 6 of the 12th CGPM (1964).

13
It is likewise necessary to recognize, outside the International System, some others units which are useful in specialized fields of scientific research, 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

in specialized fields Name Symbol Definition

electronvolt eV <o) unified atomic mass unit u

(ft) astronomical unit AU (e) parsec pc «*)

(a) 1 electronvolt is the energy acquired by an electron in passing through a potential

difference of 1 volt in vacuum ; 1 eV — 1.602 19 X 10-19 J approximately.

(6) The unified atomic mass unit is equal to the fraction 1/12 of the mass of an atom

of the nuclide 12C ; 1 u = 1.660 53 > 10-27 kg approximately.

(c) The astronomical 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 the value adopted

for it is : 1 AU = 149 600 X 10« m.

In French, the symbol UA is used.

(d) 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 1012 m.

14
IV.2 Units accepted temporarily

In view of existing practice the CIPM (1969) considered it was

preferable to keep for the time being, for use with those of the International System, the units listed in table 10.

Table 10

Units to be used with the

International System for a limited time

Name Symbol Value in SI units

nautical mile(0) 1 nautical mile = 1 852 m

knot 1 nautical mile per hour ~

0 ^1852/3600) m/s

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

are(M a 1 a = 1 dam2 = 102 m2 hectare* 6

> ha 1 ha = 1 hm2 = 104 m2 barn(c) b 1 b = 100 fm2 = 10-28 m2 bar(d) bar 1 bar =z 0.1 MPa — 105 Pa

standard atmosphere* e

)

atm 1 atm = 101 325 Pa

gal (/) Gal 1 Gal = 1 cm/s2 = 10"2 m/s2 curie*'* Ci 1 Ci = 3.7 X 1010 s1 rontgenU) E 1 R = 2.58 X lO"4 C/kg

rad(i) rad 1 rad = 10-2 J/kg

(a) 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".

(6) This unit and its symbol were adopted by the CIPM in 1879 (Proc&s-V erbaux CIPM,

1879, p. 41).

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

sections.

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

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

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

(a) The curie is a special unit employed in nuclear physics to express activity of radionuclides (12th CGPM (1964), Resolution 7).

(h) The rontgen is a special unit employed to express exposure of X or 7 radiations.

(i) 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 symbol

for rad.

15
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 names5

. Such units are listed in table 11. Table 11

CGS units with special names

i> ame iaymooi v aiue m iaJL units

er

g(a) erg 1 erg = 10-7 J

dyne(a) dyn 1 dyn = 10-5 N

poise(0) P 1 P = 1 dyn-s/cm2 = 0.1 Pa- s stokes St 1 St = 1 cm2 /s = 10-4 m2/s

gaussm Gs, G 1 Gs corresponds to 10-4 T

oersted* 6

}

Oe 1 ^ A * 1000 A / 1 Oe corresponds to ^ A/m

maxwell* 6 > Mx 1 Mx corresponds to 10-8 Wb

stilb (a) sb 1 stilb = 1 cd/cm2 = 104 cd/m2 phot ph 1 ph = 104 lx

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

(6) 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 4-dimensional

International System.

5 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 under- standing 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. 16
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

JName v aiue in ui units

fermi 1 fermi = 1 fm = 10-15 m

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

101 325 „ torr ltorr=

760

Pa

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

calorie (cal) 1 cal = 4.186 8 J

(6) micron (/x)

(c) 1 fx

! = 1 fxm = 10-6 m

X unit(d) stere (st) (e) 1 st = 1 m3 gamma (y) 1 y = 1 nT = 10-9 T

1 y = 1 pg = 10-9 kg

1 A = 1 fil = 10-6 1

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

in diamonds, pearls, and precious stones.

f 6) This value is that of the so-called "IT" calorie (5th International Conference

on Properties of Steam, London, 1956).

(c) The name of this unit and its symbol, adopted by the CIPM in 1879 (Proc&s- Verbaux CIPM, 1879, p. 41) and retained in Resolution 7 of the 9th CGPM (1948) were

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

(d) This special unit was employed to express wavelengths of X rays; 1 X unit =

1.002 X 10-4 nm approximately.

(e) This special unit employed to measure firewood was adopted by the CIPM in 1879

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

(/) This symbol is mentioned in ProcH-Verbaux CIPM, 1880, p. 56.

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

17
APPENDIX I Decisions of the CGPM and the CIPM

CR : Oomptes rendus des seances de la Conference Generate des

Poids et Mesures (CGPM)

PV: Proces-Yerbaux des seances du Comite International des

Poids et Mesures (CIPM)

1st CGPM, 1889

Sanction of the international prototypes of the metre and the kilo- gram (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 Metre Commission and of the CIPM,

the fundamental measurements of the international and national

prototypes of the metre 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 metre

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

Metre and the equality in mass of the international Kilogram with

the length of the Metre and the mass of the Kilogram kept in the

Archives of France;

that the differences between the national Metres and the international Metre lie within 0.01 millimetre and that these differences are based on a hydrogen thermometer scale which can always be repro- duced thanks to the stability of hydrogen, provided identical conditions are secured

;

that the differences between the national Kilograms and the inter- national Kilogram lie within 1 milligram

;

that the international Metre and Kilogram and the national

Metres and Kilograms fulfil the requirements of the Metre Convention,

sanctions

A. As regards international prototypes

:

1 The Prototype of the metre chosen by the CIPM.

This prototype, at the temperature of melting ice, shall henceforth represent the metric unit of length.

2 The Prototype of the kilogram adopted by the CIPM.

This prototype shall henceforth be considered as the unit of mass.

3 The hydrogen thermometer centigrade scale in terms of which

the equations of the prototype Metres have been established. B. As regards national prototypes:

18
3rd CGPM, 1901

Declaration concerning the definition of the litre (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 "litre". 2

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

conventional value of gn (CR, TO)

Taking into account the decision of the CIPM of the 15 October

1887, according to which the kilogram has been denned as a unit

of mass6

; 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 tveight denotes a quantity of the same nature as a

force; the weight of a body is the product of its mass and the accel- eration due to gravity ; in particular, the standard weight of a body

is the product of its mass and the standard acceleration due to gravity;

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

Measures for the standard acceleration due to gravity is 980.665

cm/s2

, value already stated in the laws of some countries,"7

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

of Weights and Measures" (PV, 1887, 88).

7 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

the Earth has been reconfirmed in 1913 by the 5th CGPM (CR, 44). 19
7th CGPM, 1927

Definition of the metre by the international Prototype (CR, 49)

The unit of length is the metre, 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

metre by the 1st CGPM, this bar being subject to standard atmospheric pressure and supported on two cylinders of at least one centi- metre diameter, symmetrically placed in the same horizontal plane

at a distance of 571 mm from each other. CIPM, 1946

Definitions of photometric units (PV, 20, 119)

Resolution8

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 centi- metre. 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.

5Definitions of electric units (PV, 20, 131)

Resolution 2

9

4. A) Definitions of the mechanical units which enter the defi- nitions of electric units

:

Unit of force.—The unit of force [in the MKS (Metre, Kilogram,

Second) system] is the force which gives to a mass of 1 kilogram an

acceleration of 1 metre per second, per second ( *

)

.

* The name "newton" has been proposed for the MKS unit of force.

8 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.

9 The definitions contained in this Resolution 2 were approved by the 9th CGPM

(1948), (CR, 49), which moreover adopted the name newton (Resolution 7). 20
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 metre in the direction of the force. Watt (unit of power).—The watt is the power which in one sec- ond 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 metre apart in vacuum, would produce between these conductors a

jforce equal to 2 X 10~7 MKS unit of force [newton] per metre 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 resist- ance 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 electro- motive force. Coulomb (unit of quantity of electricity).—The coulomb is the

quantity of electricity carried in 1 second by a current of 1 ampere.

Farad (unit of electric capacitance).—The farad is the capacitance

of a capacitor between the plates of which there appears a potential

difference of 1 volt when it is charged by a quantity of electricity of

1 coulomb.

Henry (unit of electric inductance).—The henry is the induct- ance 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 the magnetic flux

which, linking a circuit of one turn, would produce in it an electro- motive force of 1 volt if it were reduced to zero at a uniform rate in

1 second.

21
9th CGPM, 1948

Triple point of water; thermodynamic scale with a single fixed

point; unit of quantity of heat (joule) (CR, 55 and 63)

Resolution 3

10

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).

10 The three propositions contained in this Resolution 3 have been adopted by the General Conference. 22
Proposal for establishing a practical system of units of measure- ment (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 sys- tem of units; that the International Union of Physics recommends

the MKS system and one electric unit of the absolute practical sys- tem, 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 Metre Convention.

Writing and printing of unit symbols and of 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) are 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.

23
Unit Symbol

.metre m

.square metre m2 .cubic metre m3 .micron ^

.litre 1 .gram g

.tonne t second _ — s erg erg

dyne dyn

degree Celsius °C

.degree absolute °K

calorie cal bar bar

hour h

Unit Symbol

ampere A

volt V

watt W

ohm fi coulomb C

farad F

henry H

hertz Hz

poise P

newton N

.candela ("new

candle") cd

lux lx lumen lm

stilb sb

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 u

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.

10th CGPM, 1954

Definition of the thermodynamic temperature scale (CR, 79)

Resolution 3 The 10th CGPM decides to define the thermodynamic temperature scale by choosing the triple point of water as the fundamental

fixed point, and assigning to it the temperature 273.16 degrees Kelvin,

exactly.

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,

24
declares that it adopts, for general use, the definition

:

1 standard atmosphere = 1 013 250 dynes per square centimetre,

i.e., 101 325 newtons per square metre. 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 metre mass kilogram

time second

electric current ampere

thermodynamic temperature degree Kelvin

luminous intensity candela

CIPM, 1956

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

» -i . /T?rm . , 12 960 276 813 w 1A , , of ephemeris time (ET) is the fraction

... Aexo— X 10~9 of

4Uo yob 4yo

the tropical year for 1900 January 0 at 12 h ET,

decides

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

for 1900 January 0 at 12 hours ephemeris time".

International System of Units (PV, 25, 83)

Resolution 3

The CIPM

considering

the task entrusted to it by Resolution 6 of the 9th CGPM concern- ing the establishment of a practical system of units of measurement

suitable for adoption by all countries adhering to the Metre Convention,

25
the documents received from twenty-one countries in reply to the

enquiry requested by the 9th CGPM,

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

to be established

recommends

1 that the name "International System of Units'' be given to the system founded on the base units adopted by the 10th CGPM, viz

:

[here follows the list of the six base units with their symbols, reproduced in Resolution 12 of the 11th CGPM (I960] 2 that the units listed in the table below be used, without excluding others which might be added later

:

[here follows the table of units reproduced in paragraph 4 of Resolution 12 of the 11th CGPM (I960)] 11th CGPM, 1960

Definition of the metre (CR, 85)

Resolution 6 The 11th CGPM

considering

that the international Prototype does not define the metre with an

accuracy adequate for the present needs of metrology,

that it is moreover desirable to adopt a natural and indestructible

standard,

decides

1 The metre is the length equal to 1 650 763.73 wavelengths in vacuum of the radiation corresponding to the transition between the

levels 2 p10 and 5 d5 of the krypton-86 atom.

2 The definition of the metre in force since 1889, based on the

international Prototype of platinum-iridium, is abrogated.

3 The international Prototype of the metre 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 metre11

; 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.

11 See Appendix 2. p 35, for the relevant Recommendation adopted by the CIPM. 26
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".

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 inter- national use: length metre m

mass kilogram kg

time second s electric current ampere A

thermodynamic temperature degree Kelvin °K

luminous intensity candela cd

Resolution 3 adopted by the CIPM in 1956,

The recommendations adopted by the CIPM in 1958 concerning an abbreviation for the name of the system, and prefixes to form

multiples and sub-multiples of the units,

decides

1 the system founded on the six base units above is called "Inter- national System of Units"

;

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

;

27
3 names of multiples and sub-multiples of the units are formed

by means of the following prefixes

:

Multiplying factor Prefix Symbol

1 aaa aaa aaa aaa 1A12 l uuu uuu uuu uuu = iu * tera

rp 1 UUU UUU UUU = 1U r\Kj

1 AAA AAA 1 A6 l uuu uuu = iu° mega M

1 AAA 1 A3 1

* 1 _ 1 UUU = 1U KllO K

1 AA 1 A2 "U „ iuu = iu necto n

1 A 1 Al An^n iu = iu cteKa aa

0.1 = 10"1 deci d

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

0.000 001 — lO"6 micro /* A AAA AAA AA1 1 A-9 „ „ ^, „ u.uuu uuu uui — iu nano n

0.000 000 000 001 = 10-12 pico P

A.

Tt tl~ip LIJLO iiT>if LIXllUoo lictpri -lloLCvl nplnw UC1UW die fiT*p liQPn llov-Vl inJ.11 trip l/llO civstprn OJ'OLCIll} without excluding

others which might be added later Supplementary Units

plane angle radian rao. solid angles steradian sr Derived Units

area square metre m

volume cubic metre 1 1

1

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

angular velocity radian per second rad/s

acceleration metre per second squared m/s2 angular acceleration radian per second squared rad/s2 force newton N kg«m/s2 pressure (mechanical stress) newton per square metre N/m2 kinematic viscosity square metre per second m2 /s dynamic viscosity newton-second per square metre 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

plpptrio fiplfi strength volt ner metre V/m

electric resistance ohm Q V/A

capacitance farad F A»s/V

magnetic flux weber Wb V»s

inductance henry H Va/A

magnetic flux density tesla T Wb/m2 magnetic field strength ampere per metre A/m

magnetomotive force ampere A

luminous flux lumen lm cd«sr luminance candela per square metre cd/m2 illuminance lux lx lm/m2

28
Cubic decimetre and litre (CR, 88)

Resolution 13

The 11th CGPM,

considering

that the cubic decimetre and the litre are unequal and differ by

about 28 parts in 106

, that determinations of physical quantities which involve measure- ments of volume are being made more and more accurately, thus in- creasing the risk of confusion between the cubic decimetre and the

litre, requests the CIPM to study the problem and submit its conclusions to the 12th CGPM.

CIPM, 1961

Cubic decimetre and litre (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 litres. 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.

29
Declaration of The CIPM (1964) (PV, 32, 26 and CR, 93)

The CIPM,

empoivered by Resolution 5 of the 12th CGPM to name atomic or molecular frequency standards for temporary use for time measure- ments 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. Litre (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 litre given in 1901 by the 3rd

CGPM

2 declares that the word "litre" may be employed as a special name for the cubic decimetre,

3 recommends that the name litre should not be employed to give

the results of high accuracy volume measurements.

Curie (CR, 94)

Resolution 7

The 12th CGPM,

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

countries as a unit of activity for radionuclides,

recognizing that in the International System of Units (SI), the

unit of this activity is the second to the power of minus one (s-1

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

with the value 3.7 X 1010 s"1

. The symbol for this unit is Ci. Prefixes femto and atto (CR, 94)

Resolution 8 The 12 CGPM,

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

multiples and sub-multiples of units, adopted by the 11th CGPM,

Resolution 12, paragraph 3, the following two new prefixes

:

Multiplying factor Prefix Symbol

10-15 femto f 10-18 atto a 30
13th CGPM, 1967-1968

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

(I960), 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 re- quirements, a cesium atomic frequency standard for temporary use, that this frequency standard has now been sufficiently tested and

found sufficiently accurate to provide a definition of the second

fulfilling present requirements,

that the time has now come to replace the definition now in force

of the unit of time of the International System of Units by an atomic

definition based on that standard,

decides

1 The 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.

Unit of thermodynamic temperature (helvin) (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) 12

, 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,

12 "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 : "degr6" in French, "degree" in English, "gradous" (rpaflyc)

in Russian, "Grad" in German, "graad" in Dutch"). 31
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

The 13th CGPM,

considering that it is useful to formulate more explicitly the defini- tion 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". Unit of luminous intensity (candela) (CR, 104)

Resolution 5 The 13th CGPM

considering

the definition of the unit of luminous intensity ratified by the 9th

CGPM (1948) and contained in the "Resolution concerning the

change of photometric units" adopted by the 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 di- rection, of a surface of 1/600 000 square metre of a blackbody at the

temperature of freezing platinum under a pressure of 101 325 newtons per square metre."

32
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 metre, nr1 entropy . joule per kelvin J/K

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

thermal conductivity watt per metre kelvin W/(m»K)

radiant intensity watt per steradian W/sr

activity (of a radioactive

source) . 1 per second s-1 Abrogation of earlier decisions (micron, new candle) (CR, 105)

Resolution 7

The 13th CGPM,

considering that subsequent decisions of the General Conference

concerning the International System of Units are incompatible with

parts of Resolution 7 of the 9th CGPM (1948),

decides accordingly to remove from Resolution 7 of the 9th Conference : 1 the unit name "micron", and the symbol 'V which had been

given to that unit, but which has now become a prefix;

2 the unit name "new candle".

CIPM, 1967

Decimal multiples and sub -multiples of the unit of mass (PV 35,

29)

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".

33
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) concern- ing 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 submultiples 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. Unit of amount of substance (mole)

DraftTM

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.

13 The CIPM (October 1969) has agreed to submit to the 14th CGPM in 1971 this draft proposed by the Consultative Committee for Units (CCU, 2nd session, 1969, page U 20). 34
APPENDIX II Practical realization of the definitions

of some important units

1. Length

The following recommendation was adopted by the CIPM in 1960

to specify the characteristics of the discharge lamp radiating the

standard line of krypton 86

:

In accordance with paragraph 1 of Resolution 7 adopted by the 11th CGPM (October 1960) the CIPM recommends that the line of krypton 86 adopted as primary standard of length be realized by means

of a hot cathode discharge lamp containing krypton 86 of purity not

less than 99% in sufficient quantity to ensure the presence of solid krypton at a temperature of 64 °K. The lamp shall have a capillary of internal diameter 2 to 4 millimetres, and wall thickness approximately

1 millimetre.

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 108

: 1. the capillary is observed end-on in a direction such that the

light rays used travel from the cathode end to the anode end

;

2. the lower part of the lamp including the capillary is immersed in a bath maintained to within 1 degree of the temperature of the triple

point of nitrogen

;

3. the current density in the capillary is 0.3 ± 0.1 ampere per square centimetre. (Proc&s-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. The wavelength of the standard line, reproducible to 1 in 108 ac- cording to the above specifications, might be made reproducible to

1 in 109 approximately with more stringent specifications.

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

cadmium 114 are recommended as secondary standards (ProcesVerbaux CIPM, 1963, 31, Recommendation 1, 26 and Comptes rendus

12th CGPM, 1964, 18).

The wavelength of these lines varies 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.

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

35
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. The stability and the reproducibility can exceed 1 in 1011

. Eadio stations broadcast waves whose frequencies are known to about the same accuracy. Time signals also are broadcast by radio waves. These signals are

at present given in a time scale called "Coordinated Universal Time

(UTC)", in which the second is larger than that defined by the

CGPM, in order that the day of 86 400 seconds should be approximately equal to the present period of rotation of the Earth (this

period is known to be irregular)

.

Since 1966 for example, the following offset has been agreed upon

:

1 second (UTC) = , .j()0 1()10 1 second (true)

Moreover, the first minute of each month is sometimes increased or decreased by 1 or more tenths of a second, in order to allow for the

change in the period of rotation of the Earth.

The carrier frequency, expressed in hertz, is in general a round

number decreased by the offset above in order to maintain the phase

relation between th carrier and the time signals. Waves without

offset are also broadcast.

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.

36
4. Electric quantities

So-called "absolute" electrical measurements, i.e. those that realize the unit according to its definition, can be undertaken only by

laboratories enjoying exceptional facilities. Electric current is obtained in amperes by measuring the force

between two coils, of measurable shape and size, that carry the

current. The ohm, the farad, and the henry are accurately linked by impedance measurements at a known frequency, and may be determined

in absolute value by calculation (1) of the self-inductance of a coil, or the mutual inductance of two coils, in terms of their linear di- mensions, 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 accuracy of these measurements lies between 1 and 3 in 106

. 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 for 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 adopted by the

CIPM in 1968 agrees with the best thermodynamic results to date. The text on this scale (which replaces the 1948 scale, amended in

1960) is published in Comite Consultatif de Thermometries 8th ses- sion, 1967, Annexe 18, and Oomptes rendu*, 13th CGPM, 1967-1968,

Annexe 2; the English translation is published in Metrologia, 5, 35, 1969. The instruments employed to measure temperatures in the Inter- national Scale are the platinum resistance thermometer, the platinum10% rhodium/platinum thermocouple and the monochromatic optical

37
pyrometer. These instruments are calibrated at a number of repro- ducible temperatures, called "defining fixed points," the values of

which are assigned by agreement.

6. Photometric quantities

Absolute photometric measurements by comparison with the lumi- nance of a blackbody at the temperature of freezing platinum can

only be undertaken by a few well-equipped laboratories. The ac- curacy 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 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 efficien- cies" F(A) adopted by it in 1933. They were at that time known

as "relative visibility (or luminosity) factors", and had been recom- mended by the CIE in 1924. 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.

7. Amount of substance

All quantitative results of chemical analysis or of dosages can be

expressed in moles, in other words in units of amount of substance

of the 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 12C atoms in 0.012 kilogram of carbon 12. As neither the mass m(12C) of an atom of carbon 12 nor the mass m(X) of an atom

X can be measured accurately, we use the ratio of these masses, m(X)/m(12C), which can be accurately determined.14 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 71/ (X) of X

(quotient of mass by amount of substance) is M(X) = [m(X)/m( 12Q] X 0.012 kg/mol.

14 There are many methods of measuring this ratio, the most direct one being by the mass spectrograph. 38
For example, the atom of fluorine 19 F and the atom of carbon 12C

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

molecular gas F2 is

:

9 v 18 QQft 4 M(F2 ) —

12 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 * <YH i* f\f\ i nno*7 rw? o 1 TT = 1-315 90 mol

0.037 996 8 kg-moH

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 = Xa Yp . . ., the mass of one molecule is m(B) — am(X) -f- /3m(Y) + . . . This mass is not known with accuracy, but the ratio m(B)/m( 12C)

can be determined accurately. The molar mass of a molecular sub- stance B is then

mil) *<B> >< °- 012 k^mo1 =| * + mVK3)

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 X« Yp . . . even if a, /?,

. . . are not integers. If we denote the mass ratios m(X)/m(12C),

ra(Y)/m( 12 C), ... by r*(X), ^(Y), . . ., the molar mass of the sub- stance B is given by the formula

:

M(B) = |>(X) + pr(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.

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 — 273.16 K and p = 101 325 N/m2

) ; 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 sub- stance 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.

39

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