Precise Dimensions: A History of Units from 1791-2018

179 Pages·2017·36.306 MB·English

by  Malcolm Cooper, Jim Grozier

Precise Dimensions
A history of units from 1791–2018

Precise Dimensions
A history of units from 1791–2018
Malcolm Cooper
The History of Physics Group of the IOP
Jim Grozier
The History of Physics Group of the IOP
IOP Publishing, Bristol, UK
ªIOPPublishingLtd2017
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MalcolmCooperandJimGrozierhaveassertedtheirrighttobeidentifiedastheeditorsofthis
workinaccordancewithsections77and78oftheCopyright,DesignsandPatentsAct1988.
MediacontentforthisbookisavailablefromBookinformationathttps://doi.org/10.1088/978-0-
7503-1487-9.
ISBN 978-0-7503-1487-9(ebook)
ISBN 978-0-7503-1485-5(print)
ISBN 978-0-7503-1486-2(mobi)
DOI 10.1088/978-0-7503-1487-9
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ThisbookisdedicatedtothememoryofDrBryanPeterKibble(1938–2016)Hewas
an excellent physicist who spent most of his life working in the area of precision
measurementsandmademanymajorcontributionstothisfield.Hemeasuredthehigh-
field gyromagnetic ratio of the proton, which led to the invention of the watt balance,
now renamed the Kibble balance in his honour.
He also spent time measuring the unit of capacitance, the Farad, in terms of the base
units of the SI using a device called a calculable capacitor. This process is referredto
as ‘realising’ the unit of capacitance and by a conceptually simple extension to the
process it was also possible to realise the SI ohm. This work introduced him to ac
coaxialbridges,thebeautyofwhichstayedwithhimforallhislifeandinspiredhimto
write two books: Coaxial AC Bridges with G H Rayner and Coaxial Electrical
Circuits for Interference-free Measurements with Shakil Awan and Jürgen Schurr.
He continued to work in this field after his retirement and played a major part in
elucidating the present understanding of the ac Quantum Hall Effect.
Hewasbestknownforhisinventionofthemovingcoilwatt(orKibble)balanceandI
hadtheprivilegeofworkingwithhimonthisalmostfromitsinception.Thisdiscovery,
and the subsequent global effects resulting from the invention, is the subject of a talk
thathegavein2016.Thetranscriptofthistalkisreproducedinthisbook,andediting
hasbeenkepttoaminimumtoallowhisstyleandsenseofhumourtoberetainedinthe
text. I hope that it will allow you to make the journey with him from his initial
invention to its consequence—the redefinition of the kilogram, which is now less than
twoyearsaway.Everyonewhoknewhimwishedthathecouldhavebeentheretoseeit.
Ian Robinson, June 2017

Contents
The Editors x
Preface xi
Acknowledgments xii
Author biographies xiii
Introduction xvii
Glimpses in brief xviii
1 The metre and the metric system 1-1
Part 1: The making of the metre 1-1
1.1 Introduction 1-1
1.2 The birth of the metric system 1-1
1.3 The Meridian Expedition 1-3
1.4 How the Meridian was measured 1-4
1.5 From angles to metres 1-7
1.6 Measuring the base lines 1-8
1.7 Crunching the numbers 1-10
1.8 Extrapolation to the quadrant 1-12
1.9 Conclusion 1-13
Part 2: The metre convention and the BIPM 1-15
1.10 The archive metre shows its age 1-15
1.11 The international consensus: 1864–1875 1-15
1.12 The metre convention: 1 March to 20 May 1875 1-16
1.13 The metric system in the 20th and 21st centuries 1-18
References 1-19
2 From notion to precision: the SI second 2-1
2.1 Ancient times 2-1
2.2 The mechanical clock 2-3
2.3 The pendulum 2-5
2.4 Pursuing precision 2-7
2.5 Earth abandoned? 2-10
2.6 Electronics appear 2-11
2.7 Independent standards 2-12
2.8 Conclusions 2-13
References 2-14
vii
PreciseDimensions
3 Lord Rayleigh’s determination of the ohm 3-1
3.1 Introduction 3-1
3.2 The rotating coil method 3-3
3.3 Value of the BA unit of resistance as determined by Rayleigh 3-7
3.4 The Lorenz method 3-7
3.5 The mercury standard 3-10
3.6 Subsequent developments and modern resistance standards 3-11
References 3-15
4 Temperature scales: past, present and future: 1700–2050 4-1
4.1 Introduction 4-1
4.2 de facto temperature scales: 1700–1900 4-2
4.3 Towards defined temperature scales 4-8
4.4 The demise of defined temperature scales? 4-12
4.5 Summary 4-15
References 4-16
5 Kelvin’s absolute temperature and its measurement 5-1
5.1 Thomson’s motivations for absolute temperature 5-1
5.2 The absolute as the abstract 5-3
5.3 The operationalization of Thomson’s first absolute temperature 5-4
5.4 Thomson’s second concept of absolute temperature 5-9
5.5 The operationalization of the second concept 5-13
5.5.1 The ideal gas thermometer as an indicator of absolute 5-13
temperature
5.5.2 Checking the behaviour of actual gases against the ideal 5-15
5.6 Iterative operationalization 5-16
5.6.1 The problem of circularity 5-16
5.6.2 An iterative solution to the circularity problem 5-18
5.6.3 Implications of the iterative solution 5-21
References 5-22
6 A brief history of the unit of chemical amount 6-1
6.1 Comparative measurements 6-2
6.2 Quantitative measurements 6-2
6.3 The mass unit of the chemist: the gram-molecule 6-4
6.4 The many atomic weight scales 6-5
6.5 The name: mole 6-7
viii
PreciseDimensions
6.6 Molar measurements in practice 6-9
6.7 Amount of substance as a dimensional quantity 6-13
6.8 The Avogadro number 6-13
6.9 Proposed new definition of the mole 6-14
6.10 Consequences of the entity-based definition 6-15
6.11 Outlook 6-16
References 6-17
7 The history of the SI unit of light, the candela 7-1
7.1 Introduction: light and vision 7-1
7.2 Artefact-based standards and units for measurement of ‘light’ 7-2
7.2.1 The evolution of artificial lighting 7-2
7.2.2 Flame standards 7-3
7.2.3 The black-body standard, the ‘new candle’ and the ‘candela’ 7-5
7.3 A radiometric approach to photometry 7-6
7.3.1 The relationship between photometry and radiometry 7-7
7.3.2 Luminous efficacy 7-9
7.3.3 The 1979 radiometric definition of the candela 7-9
7.3.4 Practical photometry using the 1979 radiometric definition 7-14
7.3.5 The use of photometric quantities and units 7-14
7.3.6 Quantifying other photobiological and photochemical effects 7-15
7.4 A look to the future 7-16
References 7-19
8 The story of mass standards 1791–2018 8-1
8.1 Introduction 8-1
8.2 Construction of the kilogram of the archives 8-1
8.3 William Hallowes Miller and the New Imperial Standard Pound 8-7
8.4 The metre convention, the BIPM and the international prototype 8-11
of the kilogram
8.5 Relative stability of national and international prototypes 8-12
8.6 The new definition of the kilogram 8-13
8.7 Realisation of the kilogram using the silicon x-ray crystal density 8-14
method: Si→SI
8.8 Conclusion 8-15
References 8-15
9 Mass from energy—a unit for a quantum world 9-1
ix