Units of Measurement (eBook)

Preface 7
Contents 9
Acronyms 15
1 Metrology Through Ages 18
1.1 Introduction 18
1.2 History of Metrology in India 19
1.2.1 Legal Metrology 19
1.2.2 Town Planning 19
1.2.3 Length Measurements 19
1.2.4 Time Measurements 20
Time Intervals 20
Sidereal Metrics 22
Smaller Units of Time Used in the Vedas 22
Lunar Metrics 22
Tropical Metrics 23
Reckoning of Time Among Other Entities 23
Counting of Time 25
Time Scale in Seconds 26
1.2.5 Units of Time and Angle 27
1.2.6 Mass Measurement 27
For Trade in Food Grains and Similar Items 27
For Gold Trade 27
For Silver Trade 28
1.2.7 Volume Measurements 28
1.2.8 Numeration 29
References 30
Further Readings 30
2 System of Quantities and Units 32
2.1 Quantities 32
2.2 System of Quantities 33
2.2.1 Quantity 33
2.2.2 Base Quantity 33
2.2.3 System of Base Quantities 33
2.2.4 Derived Quantity 33
2.2.5 Quantity Equation 34
2.3 Measurement Unit 34
2.3.1 System of Measurement Units 35
2.3.2 System of Base Units 35
Properties of Base Units 35
Minimum Number of Base Units 35
2.3.3 Derived Unit 36
2.3.4 Unit Equation 36
2.3.5 Properties of Units of Measurement 37
2.3.6 Coherent Derived Unit 37
2.4 Quantity of Dimension 1 or Dimensionless Quantity 38
2.4.1 Dimension of a Quantity 38
2.4.2 Quantities of Dimension 1 or Dimensionless Quantities 39
2.4.3 Ordinal Quantity 40
2.4.4 Quantity Scale, Measurement Scale 40
2.4.5 Ordinal Quantity Scale, Ordinal Scale 40
2.4.6 Nominal Property 41
2.5 Conversion Factor Between Units 41
2.6 Quantity Relations 41
2.6.1 Quantity Value 41
2.6.2 Numerical Quantity Value 42
2.6.3 Quantity Calculus 43
2.7 Units Used in Biology Biochemistry, Molecular Biology, Forensic Science for Biological Effects 43
2.7.1 Photochemical or Photo-biological Quantitiesand Their Units 43
2.8 Units Used in Photometry 44
2.8.1 Photometry 44
2.8.2 Actinic Action Spectrum 45
2.8.3 Types of Visions 45
2.9 Unit in the Field of Sound 45
2.10 Units in the Field of Ionizing Radiations 46
2.11 SI Units in the Framework of General Relativity 46
References 46
3 Various Systems of Units 48
3.1 Introduction 48
3.2 Relations Between the Quantities 48
3.2.1 Derived Quantities by Definition 49
3.2.2 Derived Quantities by a Phenomenon 51
3.3 Three-Dimensional Systems of Units 53
3.3.1 Gauss System 53
3.3.2 CGS System 53
3.3.3 FPS System 54
3.4 Four-Dimensional Systems of Units 56
3.4.1 Giorgi System 56
3.4.2 Maxwell System 56
3.4.3 Hartree System 56
3.4.4 Units for Atomic and Molecular Measurements 57
3.4.5 McWeeny System 57
3.4.6 Ohm, Ampere, Second and Metre System 57
3.4.7 Force, Length and Time System 57
3.4.8 System in Terms of Universal Constants (G, H, E and Q) 58
3.4.9 System in Terms of Electric Charge, Flux,Length and Time 59
3.4.10 System in Terms of L, M, T and R 59
3.5 Derived Quantities in Terms of L, M, T and R: An Example 61
References 62
4 Metre Convention and Evolution of Base Units 63
4.1 BIPM and Metre Convention 63
4.1.1 General Conference on Weights and Measures (CGPM) 63
4.1.2 International Committee for Weightsand Measures (CIPM) 64
4.1.3 Consultative Committees 64
Consultative Committee for Electricity and Magnetism (CCEM) 64
Consultative Committee for Photometry and Radiometry (CCPR) 65
Consultative Committee for Thermometry (CCT) 65
Consultative Committee for Length (CCL) 65
Consultative Committee for Time and Frequency (CCTF) 65
Consultative Committee for Ionizing Radiation (CCRI) 65
Consultative Committee for Units (CCU) 65
Consultative Committee for Mass and Related Quantities (CCM) 65
Consultative Committee for Amount of Substance: Metrology in Chemistry (CCQM) 66
Consultative Committee for Acoustics, Ultrasound and Vibration(CCAUV) 66
4.1.4 International Bureau of Weights and Measures (BIPM) 66
Scientific Activities 66
Objects of BIPM 66
Staff at BIPM 67
Publications 67
Metrologia 67
4.1.5 Linkages of Various Organs of Metre Convention 67
4.2 International System of Units (SI) 68
4.2.1 Base Units 69
4.3 Evolution of Base Units 69
4.3.1 Unit of Length 71
4.3.2 Unit of Mass 74
International Prototype of Kilogram 74
4.3.3 Unit of Time 76
4.3.4 Unit of Electric Current 77
4.3.5 Unit of Luminous Intensity 77
4.3.6 Unit of Temperature 78
Unit of Thermodynamic Temperature (Kelvin) 79
4.3.7 Unit of Amount of Substance (Mole) 80
4.3.8 Dependence of Base Units 81
References 81
5 Realization of Base Units 82
5.1 The Metre 82
5.1.1 Standard Radiations 83
5.2 The Kilogram 84
5.2.1 Method of Cleaning 84
Cleaning with Chamois Leather 84
Cleaning with Steam 85
Efficacy of the Cleaning Procedure 86
5.2.2 Uncertainty in National Standards 86
5.3 The Second 87
5.4 The Ampere 87
5.4.1 Josephson and Klitzing Constants 88
5.4.2 Values of Josephson and Klitzing Constants 88
5.5 The Candela 88
5.6 The Kelvin 89
5.6.1 Triple Point of Water 89
5.6.2 Temperature Scales 90
5.6.3 ITS-90 90
Defining Fixed Points on ITS-90 90
ITS-90 and PLTS-2000 91
Defining Fixed Points on PLTS-2000 92
5.7 The Mole 93
References 94
6 Derived Quantities and Their Units 95
6.1 Derived Quantities 95
6.2 Units of Derived Quantities 95
6.3 SI Derived Units 96
6.3.1 Units Expressed in Terms of Base Units 96
6.3.2 Derived Units with Special Names 97
6.3.3 Derived Units Formed from the Derived Units with Special Names 97
6.3.4 Derived Quantities of Dimension 1 97
6.4 Units Outside the SI 103
6.4.1 Units Accepted for Use with the SI 103
6.4.2 Non-SI Units with Experimentally Obtained Values 103
6.4.3 Non-SI Units Used by Special Groups 104
6.4.4 Other Non-SI Units with Special Names 105
6.4.5 Other Non-SI Units Found in the Old Literature 107
References 108
7 Expressing SI Units 109
7.1 Introduction 109
7.2 SI Prefixes 109
7.2.1 Rules for Using SI Prefixes 109
7.2.2 Prefix About the Kilogram 111
7.3 Writing of SI Unit Symbols 111
7.3.1 Unit Symbols and Their Combinations 111
7.3.2 Names of Units 112
7.3.3 Quantity Calculus 113
Value of Quantity 113
Numerical Value of a Given Quantity 113
Formatting the Value of a Quantity 113
Symbols of Quantities 114
Quantity Symbols and Unit Symbols 114
7.3.4 Stating Values of Quantities of Dimension 1 115
Use of Symbol % 116
7.4 Expression of Numbers 117
7.4.1 Formatting Numbers, and the Decimal Marker 117
7.4.2 Expressing the Measurement Uncertainty 118
7.5 Advantages of SI Units 118
7.5.1 Harmonization of Units 118
General Principle 118
7.5.2 Expressing the Values of o and o in Terms of SI Units 120
7.5.3 Expressing Electrostatic and ElectromagneticQuantities in SI Units 121
Charge and Current 121
Potential 123
Electrical Resistance 124
Electrical Capacitance 124
emu of Magnetic Flux 125
Magnetic field Strength (Flux Density) 125
Electric field 125
Inductance 125
7.5.4 SI Units of Quantities in Magnetic Field 126
SI Unit of Magnetic Pole Strength 126
Magnetic Flux Density/Magnetizing Force 126
Intensity of Magnetization 127
7.5.5 Homogenizing of Units of Energy in Heat 129
7.5.6 Coherent System 129
Coherent Derived Unit 129
7.5.7 Well-Defined Units 130
References 130
8 Future Definitions of SI Units 131
8.1 In Terms of Physical Constants 131
8.1.1 Basis of SI Units 131
8.2 From Single Source 132
8.2.1 In Terms of Hydrogen Atom 132
8.2.2 In Terms of Only One Standard (Frequency) 133
8.2.3 In Terms of Fundamental Constants UsingMaxwell Equations 134
8.2.4 A Consistent Set of Fundamental Constants by BIPM 134
8.3 CIPM Recommendation 1 (CI-2005) 135
8.4 A Proposal to Redefine Kilogram, Ampere, Kelvin and Mole 136
8.4.1 Kilogram 136
8.4.2 Ampere 136
8.4.3 Kelvin 136
8.4.4 Mole 137
8.5 The Values of h, e, k and NA 137
8.5.1 Observations 138
8.6 Practical Standards to Realize Kilogram 138
8.6.1 Other Methods of Redefining Kilogram 138
8.6.2 Conclusion in Regard to the Kilogram 139
8.6.3 Measurement Standards 139
Embodiment of Units of Measurements 139
References 140
9 Scientists Associated with Units of Measurements 141
9.1 Scientists Associated with Base Units 141
9.1.1 Lord Kelvin 141
9.1.2 Anders Celsius 142
9.1.3 Andre Marie Ampere 143
9.2 Scientists Associated with Derived Units 144
9.2.1 Sir Isaac Newton 144
9.2.2 Heinrich Rudolf Hertz 145
9.2.3 Blaise Pascal 146
9.2.4 James Prescott Joule 147
9.2.5 James Watt 148
9.2.6 Charles Augustin Coulomb 149
9.2.7 Alessandro Volta 151
9.2.8 Michael Faraday 152
9.2.9 Wilhelm Eduard Weber 153
9.2.10 Nickola Tesla 154
9.2.11 Joseph Henry 155
9.2.12 Antoine Henri Becquerel 156
9.2.13 Louis Harold Gray 157
9.2.14 Rolf M. Sievert 158
Sievert Chamber 160
9.2.15 Georg Simon Ohm 160
9.2.16 Werner von Siemens 162
9.3 Some Units Not Named After Any Scientist 163
Appendix A: National Physical laboratory 164
A.1 Metre 164
A.2 Kilogram 164
A.3 Second 165
A.4 Ampere 165
A.5 Kelvin 165
A.6 Candela 166
A.7 Mole 166
A.8 Radiation 166
References 166
Index 167