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E-grāmata: Units of Measurement: History, Fundamentals and Redefining the SI Base Units

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Units of Measurement: History, Fundamentals and Redefining the SI Base UnitsPalielināt
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This book provides comprehensive coverage of the units in physics and engineering and the international system of units. It serves as a useful reference to researchers and engineers.



This book delivers a comprehensive overview of units of measurement. Beginning with a historical look at metrology in Ancient India, the book explains fundamental concepts in metrology such as basic, derived and dimensionless quantities, and introduces the concept of quantity calculus. It discusses and critically examines various three and four-dimensional systems of units used both presently and in the past, while explaining why only four base units are needed for a system of measurement. It discusses the Metre Convention as well as the creation of the International Bureau of Weights and Measures, and gives a detailed look at the evolution of the current SI base units of time, length, mass, electric current, temperature, intensity of illumination and substance.

This updated second edition is extended with timely new chapters discussing past efforts to redefine the SI base units as well as the most recent 2019 redefinitions based entirely on the speed of light and other fundamental physical constants. Additionally, it provides biographical presentations of many of the historical figures behind commonly used units of measurements, such as Newton, Joule and Ohm,   With its accessible and comprehensive treatment of the field, together with its unique presentation of the underlying history, this book is well suited to any student and researcher interested in the practical and historical aspects of the field of metrology.

1 Old Units of Measurement in India
1(60)
1.1 Time Intervals
1(18)
1.1.1 Introduction
1(2)
1.1.2 Time Intervals
3(6)
1.1.3 Sidereal Metrics
9(1)
1.1.4 Time Intervals in Chanakiya Arthsashtra
9(1)
1.1.5 Multiplicity in Smaller Time Intervals
10(1)
1.1.6 Realization of Naadika: A Standard of a Time Interval
10(1)
1.1.7 Lunar Metrics
11(1)
1.1.8 Adjustment in Calendars
12(1)
1.1.9 Middle-Level Time Intervals
12(1)
1.1.10 Bigger Time Intervals
13(2)
1.1.11 Names of 14 Manvantar
15(1)
1.1.12 Time Intervals in Terms of Kalp
15(1)
1.1.13 Summary of Bigger Time Intervals
16(1)
1.1.14 The Time Elapsed Since Creation of Universe
17(1)
1.1.15 Date of Commencement of the Present Kaliyug
18(1)
1.2 Length Intervals
19(16)
1.2.1 Introduction
19(1)
1.2.2 Sets of Smaller Length Intervals
19(1)
1.2.3 Units of Length in Multiples of Angul
20(5)
1.2.4 Two Kinds of Danush
25(1)
1.2.5 Scale of Mohenjo-Daro
26(1)
1.2.6 Supportive Evidences for Taking 1 Angul Equal to 16.764 mm
27(1)
1.2.7 Various Yojan
28(1)
1.2.8 Length in Terms of Latitude
29(2)
1.2.9 Pre-Akbar Length Measures
31(1)
1.2.10 Weights and Measures in Akbar Time
32(1)
1.2.11 Length Units Used by Tailors
33(1)
1.2.12 Length Units in Dependent India
34(1)
1.3 Units of Weight and Volume
35(22)
1.3.1 Introduction
35(1)
1.3.2 Weights Nomenclature from Manusmriti
36(3)
1.3.3 Weights in Terms of Tresarenu
39(1)
1.3.4 Charak System of Weights
39(2)
1.3.5 Weight Measurement in Ancient India
41(2)
1.3.6 Weights in Terms of Grain of Rice (chawal)
43(3)
1.3.7 Weights Used in Pre-Akbar Period
46(1)
1.3.8 Weights in Colonial (Pre-Independence) Years
46(2)
1.3.9 Conventions Followed by Public for Weights
48(1)
1.3.10 Weights and Volume Measures by Chanakiya
49(7)
1.3.11 Conversion Factors
56(1)
References
57(4)
2 System of Quantities and Units
61(20)
2.1 Quantities
61(1)
2.2 System of Quantities
62(2)
2.2.1 Quantity
62(1)
2.2.2 Base Quantity
62(1)
2.2.3 System of Base Quantities
62(1)
2.2.4 Derived Quantity
62(1)
2.2.5 Quantity Equation
63(1)
2.2.6 Quantity Value Equation
63(1)
2.2.7 Dimension of Derived Unit
64(1)
2.3 Measurement Unit
64(4)
2.3.1 System of Measurement Units
64(1)
2.3.2 System of Base Units
65(1)
2.3.3 Derived Unit
65(1)
2.3.4 Unit Equation
66(1)
2.3.5 Properties of Units of Measurement
66(1)
2.3.6 Coherent Derived Unit
67(1)
2.4 Quantity of Dimension 1 or Dimensionless Quantity
68(3)
2.4.1 Dimension of a Quantity
68(1)
2.4.2 Quantities of Dimension 1 or Dimensionless Quantities
69(1)
2.4.3 Ordinal Quantity
70(1)
2.4.4 Quantity Scale, Measurement Scale
70(1)
2.4.5 Ordinal Quantity Scale, Ordinal Scale
71(1)
2.4.6 Nominal Property
71(1)
2.5 Conversion Factor Between Units
71(1)
2.6 Quantity Relations
72(1)
2.6.1 Quantity Value
72(1)
2.6.2 Numerical Quantity Value
72(1)
2.6.3 Quantity Calculus
73(1)
2.7 Units Used in Biology, Biochemistry, Molecular Biology, Forensic Science Biological Effects
73(5)
2.7.1 Photochemical or Photo-Biological Quantities and Their Units
74(1)
2.7.2 Conversion of Radiometric to Photometric Quantities
75(1)
2.7.3 Photometry and Photon-Number-Based Quantities
76(1)
2.7.4 Units Used in Photometry
76(1)
2.7.5 Actinic Action Spectrum
77(1)
2.7.6 Types of Visions
77(1)
2.7.7 Unit in the Field of Sound
78(1)
2.7.8 Units in the Field of Ionizing Radiations
78(1)
2.8 SI Units in the Framework of General Relativity
78(1)
References
79(2)
3 Various Systems of Units
81(16)
3.1 Introduction
81(1)
3.2 Relations Between the Quantities
81(5)
3.2.1 Derived Quantities by Definition
82(2)
3.2.2 Derived Quantities by a Phenomenon
84(2)
3.3 Three-Dimensional System of Units
86(2)
3.3.1 Gauss System
86(1)
3.3.2 CGS System
86(1)
3.3.3 FPS System
87(1)
3.4 Four-Dimensional Systems of Units
88(6)
3.4.1 Giorgi System of Units
89(1)
3.4.2 Maxwell System
89(1)
3.4.3 Hartree System
89(1)
3.4.4 Units for Atomic and Molecular Measurements
89(1)
3.4.5 McWeeny System of Units
90(1)
3.4.6 Ohm, Ampere, Second and Metre System
90(1)
3.4.7 Force, Length and Time System
90(1)
3.4.8 System in Terms of Universal Constants (G, H, E and Q)
91(1)
3.4.9 System in Terms of Electric Charge, Flux, Length and Time
92(2)
3.4.10 System in Terms of L, M, T and R
94(1)
3.5 Derived Quantities in Terms of L, M, T and R--An Example
94(2)
3.6 Measurement System in Terms of Length Time Flux and Charge
96(1)
References
96(1)
4 Metre Convention and Evolution of Base Units
97(22)
4.1 BIPM and Metre Convention
97(5)
4.1.1 General Conference on Weights and Measures (CGPM)
98(1)
4.1.2 International Committee for Weights and Measures (CIPM)
98(1)
4.1.3 Consultative Committees
98(2)
4.1.4 International Bureau of Weights and Measures (BIPM)
100(2)
4.1.5 Linkages of Various Organs of Metre Convention
102(1)
4.2 International System of Units SI
102(2)
4.2.1 Base Units
104(1)
4.2.2 Latest Definitions of SI Base Units
104(1)
4.3 Evolution of Base Units
104(14)
4.3.1 Unit of Time
106(1)
4.3.2 Unit of Length
107(3)
4.3.3 Unit of Mass
110(2)
4.3.4 Unit of Electric Current
112(1)
4.3.5 Unit of Temperature
113(1)
4.3.6 Unit of Amount of Substance (Mole)
114(2)
4.3.7 Unit of Luminous Intensity
116(1)
4.3.8 Dependence of Base Units
117(1)
References
118(1)
5 New Definitions of SI Base Units
119(14)
5.1 Seven Defining Constants and SI Base Units
119(1)
5.2 Importance of Defining Constants
120(1)
5.2.1 Caesium Frequency
120(1)
5.2.2 Velocity of Light
120(1)
5.2.3 Planck's Constant
120(1)
5.2.4 Elementary Charge
120(1)
5.2.5 Boltzmann Constant
120(1)
5.2.6 Avogadro Constant
121(1)
5.2.7 Luminous Efficacy
121(1)
5.3 Magnitude of Defining Constant in SI Units
121(1)
5.4 Formal Definitions of SI Units
121(2)
5.4.1 The Second
122(1)
5.4.2 The Metre
122(1)
5.4.3 The Kilogram
122(1)
5.4.4 The Ampere
122(1)
5.4.5 The Kelvin
122(1)
5.4.6 The Mole
123(1)
5.4.7 TheCandela
123(1)
5.5 Effect of the New Definition
123(3)
5.5.1 Second
123(1)
5.5.2 Metre
124(1)
5.5.3 Kilogram
124(1)
5.5.4 Ampere
124(1)
5.5.5 The Kelvin
125(1)
5.5.6 The Mole
125(1)
5.5.7 The Candela
126(1)
5.6 Expressing SI Base Units in Denning Constants
126(2)
5.6.1 The Second in Terms of AvCs
126(1)
5.6.2 The Metre in Terms of C and S
127(1)
5.6.3 The Kilogram in Terms of H
127(1)
5.6.4 The Ampere in Terms of E and S
127(1)
5.6.5 The Kelvin in Terms of K
127(1)
5.6.6 Mole in Terms of NA
128(1)
5.6.7 Candela in Terms of Kcd
128(1)
5.7 Relationship Matrix
128(1)
5.7.1 Defining Constants in Terms of Base Units
129(1)
5.7.2 Base Units in Terms of Defining Constants
129(1)
5.7.3 Use of the Matrix
129(1)
5.8 Inter-Dependence of Base Units
129(4)
5.8.1 New SI Units
130(1)
5.8.2 Old SI Units
130(3)
6 Realization of the SI Base Units (S, M, Kilogram)
133(46)
6.1 Practical Realization of the Unit of Time
133(3)
6.1.1 Atomic Clocks
133(1)
6.1.2 Primary Frequency Standards
133(1)
6.1.3 Secondary Representations of the Second
134(1)
6.1.4 International Atomic Time (TAI)
134(1)
6.1.5 Terrestrial Time (TT), Geocentric Coordinate Time(TCG)
135(1)
6.1.6 Coordinated Universal Time (UTC)
136(1)
6.2 Practical Realization of the Metre
136(2)
6.2.1 Standard Radiations
138(1)
6.3 Practical Realization of the Kilogram (via Kibble Balance)
138(24)
6.3.1 Electromechanical (Kibble) Balances
138(7)
6.3.2 Constant Magnetic Field (Generation)
145(5)
6.3.3 Change of the Reluctance of the Yoke
150(1)
6.3.4 Temperature Change of the Rare Earth Magnet
150(1)
6.3.5 Temperature Change of the Yoke Material
151(1)
6.3.6 Engineering of Magnets with Smaller Temperature Coefficients
151(1)
6.3.7 Actively Controlling the Temperature
152(1)
6.3.8 Voltage Measurements
152(2)
6.3.9 Voltmeter
154(2)
6.3.10 Current Generation and Measurement
156(5)
6.3.11 Results
161(1)
6.4 Practical Realization of the Kilogram (via XRCD Method)----
162(12)
6.4.1 Principle
162(2)
6.4.2 Sphere
164(1)
6.4.3 Obtaining 28Si-Enriched Polycrystal
164(1)
6.4.4 Single Crystal Growth
165(1)
6.4.5 Isotopic Composition of Silicon
166(1)
6.4.6 Crystal Perfection: Evaluation of Point Defects
166(2)
6.4.7 MSL Layers
168(2)
6.4.8 Molar Mass
170(1)
6.4.9 Lattice Parameter
171(3)
References (Kibble Balance)
174(2)
References (XRCD)
176(3)
7 Realization of SI Base Unit Ampere and Other Electric Units
179(10)
7.1 Introduction
179(1)
7.2 Definition of the Electrical/Magnetic Units
179(6)
7.2.1 Practical Realization of Ampere, SI Base Unit of Electric Current
179(1)
7.2.2 Derived Units
180(5)
7.3 Mole
185(1)
7.4 Realization of Mole
186(2)
7.4.1 Pure Sample
186(1)
7.4.2 Pure Gas
187(1)
7.4.3 Chemical Electrolysis
187(1)
7.5 Primary Method
188(1)
References
188(1)
8 Boltzmann Constant Denning Kelvin K
189(24)
8.1 Introduction to Boltzmann Constant
189(1)
8.2 Acoustic Gas Thermometry AGT
190(4)
8.2.1 Measurement at NPL, UK
191(2)
8.2.2 Main Uncertainty Components
193(1)
8.3 Radiation Thermometry
194(3)
8.3.1 Total Radiation Thermometry TRT (Stefan-Boltzmann Measurement)
195(1)
8.3.2 Spectral-Band-Limited Radiation Thermometry
196(1)
8.4 Thermal-Equation-of-State Methods
197(3)
8.4.1 Constant-Volume Gas Thermometry (CVGT)
197(1)
8.4.2 Dielectric-Constant Gas Thermometry
197(2)
8.4.3 Results
199(1)
8.5 Refractive-Index Gas Thermometry RIGT
200(2)
8.6 Doppler-Broadening Thermometry
202(2)
8.7 Noise Thermometry
204(2)
8.8 Realization of K (Hierarchy of Temperature)
206(2)
8.8.1 Temperature Scale
207(1)
8.8.2 Different Temperature Scales
207(1)
8.8.3 Hierarchy in Temperature Measurement
208(1)
References
208(5)
9 Radiometry, Photometry and Realization of Candela and Mole
213(6)
9.1 SI Units Used in Radiometry and Photometry
213(1)
9.2 Traceability and Realization of Photometric Units
214(1)
9.2.1 Traceability Routes for the Practical Realization of Photometric Units
214(1)
9.3 Realizationof the Candela (Cd)
215(2)
9.4 Realization of the Lumen (Lm), SI Derived Unit of Luminous Flux φ v
217(1)
9.5 Realization of the Lux (Lx), SI Derived Unit of Illuminance Ev
218(1)
References
218(1)
10 Derived Quantities and Their Units
219(18)
10.1 Derived Quantities
219(1)
10.2 Units of Derived Quantities
219(1)
10.3 SI Derived Units
220(8)
10.3.1 Units Expressed in Terms of Base Units
220(1)
10.3.2 Derived Units with Special Names
221(3)
10.3.3 Derived Units Formed from the Derived Units with Special Names
224(3)
10.3.4 Derived Quantities of Dimension 1
227(1)
10.4 Units Outside the SI
228(7)
10.4.1 Units Accepted for Use with the SI
229(4)
10.4.2 Non-SI Units with Experimentally Obtained Values
233(1)
10.4.3 Non-SI Units Used by Special Groups
234(1)
10.4.4 Other Non-SI Units with Special Names
235(1)
10.4.5 Other Non-SI Units Found in Old Literature
235(1)
References
235(2)
11 Expressing SI Units
237(24)
11.1 Introduction
237(1)
11.2 SI Prefixes
237(2)
11.2.1 Rules for Using SI Prefixes
237(2)
11.2.2 Prefix About the Kilogram
239(1)
11.3 Writing of SI Unit Symbols
239(6)
11.3.1 Unit Symbols and Their Combinations
239(1)
11.3.2 Names of Units
240(1)
11.3.3 Quantity Calculus
241(3)
11.3.4 Stating Values of Quantities of Dimension One
244(1)
11.4 Expression of Numbers
245(2)
11.4.1 Formatting Numbers and the Decimal Marker
246(1)
11.4.2 Expressing the Measurement Uncertainty
246(1)
11.5 Advantages of SI Units
247(6)
11.5.1 Harmonization of Units
247(2)
11.5.2 Expressing the Values of p0 and e0 in Terms of SI Units
249(1)
11.5.3 Magnetic Flux Density/Magnetizing Force
250(1)
11.5.4 Intensity of Magnetization
251(1)
11.5.5 Homogenizing of Units of Energy in Heat
252(1)
11.5.6 Coherent System
252(1)
11.5.7 Coherent Derived Unit
252(1)
11.5.8 Weil-Defined Units
253(1)
11.6 Expressing Electrostatic and Electromagnetic Quantities in SI Units
253(6)
11.6.1 Charge and Current
254(1)
11.6.2 Potential
255(1)
11.6.3 Electrical Resistance
256(1)
11.6.4 Electrical Capacitance
257(1)
11.6.5 Emu of Magnetic Flux
257(1)
11.6.6 Magnetic Field Strength (Flux Density)
257(1)
11.6.7 Electric Field
258(1)
11.6.8 Inductance
258(1)
11.6.9 Oerested
258(1)
References
259(2)
12 Past Efforts in Redefining of SI Units
261(10)
12.1 In Terms of Physical Constants
261(1)
12.1.1 Basis of SI Units
261(1)
12.2 From a Single Source
262(2)
12.2.1 In Terms of Hydrogen Atom
262(1)
12.2.2 In Terms of Only One Standard (Frequency)
263(1)
12.2.3 In Terms of Fundamental Constants Using Maxwell Equations
263(1)
12.2.4 A Consistent Set of Fundamental Constants by BIPM
264(1)
12.3 CIPM Recommendation 1 (CI-2005)
264(2)
12.4 A Proposal to Redefine Kilogram, Ampere, Kelvin and Mole
266(1)
12.4.1 Kilogram
266(1)
12.4.2 Ampere
266(1)
12.4.3 Kelvin
266(1)
12.4.4 Mole
266(1)
12.5 The Values of h, e, k and NA
267(1)
12.5.1 Observations
268(1)
12.6 Practical Standards to Realize Kilogram
268(1)
12.6.1 Other Methods of Redefining Kilogram
268(1)
References
269(2)
13 Scientists Associated with Units of Measurements
271(26)
13.1 Scientists Associated with Base Units
271(8)
13.1.1 Anders Celsius
271(2)
13.1.2 Andre Marie Ampere
273(1)
13.1.3 Avogadro
273(2)
13.1.4 Boltzmann Ludwig Eduard
275(1)
13.1.5 Lord Kelvin
276(1)
13.1.6 Planck, Karl Ernst Ludwig Marx (Max)
277(2)
13.2 Scientists Associated with Derived Units
279(17)
13.2.1 Sir Isaac Newton
279(1)
13.2.2 Heinrich Rudolf Hertz
280(1)
13.2.3 Blaise Pascal
281(1)
13.2.4 James Prescott Joule
282(1)
13.2.5 James Watt
283(1)
13.2.6 Charles Augustin Coulomb
284(1)
13.2.7 Alessandro Volta
285(1)
13.2.8 Michael Faraday
286(1)
13.2.9 Wilhelm Eduard Weber
287(1)
13.2.10 NickolaTesla
288(1)
13.2.11 Joseph Henry
289(1)
13.2.12 Antoine Henri Becquerel
290(1)
13.2.13 Louis Harold Gray
291(1)
13.2.14 Rolf M. Sievert
292(2)
13.2.15 Georg Simon Ohm
294(1)
13.2.16 Werner Von Siemens
295(1)
13.3 Some Units Not Named After Any Scientist
296(1)
Index 297
Dr. S. V. Gupta received masters degrees in physics and mathematics from Allahabad University and Agra University, India, respectively, and holds a PhD from Delhi University. Dr. Gupta subsequently completed advanced training at the International Bureau of Weights and Measures, BIPM, France; International Organisation of Legal Metrology (OIML), Paris France; National Physical Laboratory, UK; and PTB (Physikalisch-Technische Bundesanstalt), Germany. He has been involved in various projects with the National Institute for Standards and Technology, NIST, USA and with the PTB, Germany. Dr. Gupta was recently awarded the title of Mapiki Ratan (a Jewel in Metrology). He is a member of the Institute of Physics UK. He is first Asian whose name has been placed in the Honours and awards list of the International Organisation of Legal Metrology (OIML), Paris, France since 2004. He has worked in the National Physical Laboratory of India for 37 years. He has been UNIDO Expert to various countries. After retirement from the regular service, he has written about 23 books (including editions) on different topics of metrology and legal metrology.
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