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

Preface to the Second Edition
Preface to the First Edition
Contents
Acronyms
1 Old Units of Measurement in India
	1.1 Time Intervals
		1.1.1 Introduction
			1.1.1.1 Source of Information
			1.1.1.2 Concept of Time
			1.1.1.3 Types of Time Scales
				Terrestrial Day
				Sidereal Day
				Solar Day
				Lunar Day
		1.1.2 Time Intervals
			1.1.2.1 Mention of Permanu, Anu and Treserenu in Shrimad Bhagwad Puran
			1.1.2.2 Time Intervals as Fraction of a Day
			1.1.2.3 Time Intervals in Terms of Nimesh
				Time Interval from Vishnu Puran
				Time Intervals from Bhavishya Puran
			1.1.2.4 Smaller Time Intervals in Steps of 60
				Time Intervals Given in Steps of 60
				Time Intervals from Surya Siddhant
				Time Intervals with Multiple Names
				Time Interval in Steps of 30
		1.1.3 Sidereal Metrics
		1.1.4 Time Intervals in Chanakiya Arthsashtra
		1.1.5 Multiplicity in Smaller Time Intervals
		1.1.6 Realization of Naadika: A Standard of a Time Interval
		1.1.7 Lunar Metrics
			1.1.7.1 Tithi
			1.1.7.2 Paksh
			1.1.7.3 Lunar Month
			1.1.7.4 Lunar Ritu, Ayan
		1.1.8 Adjustment in Calendars
			1.1.8.1 Gregorian Calendar
			1.1.8.2 Lunar Calendar
		1.1.9 Middle-Level Time Intervals
		1.1.10 Bigger Time Intervals
			1.1.10.1 Charan
			1.1.10.2 Yug
			1.1.10.3 Duration of Each Yug in Human Years
			1.1.10.4 Durations of Each Yug in Divine Years
			1.1.10.5 Mahayug
			1.1.10.6 Manvantar
			1.1.10.7 Kalp
				In Terms of Manvantar
				In Terms of Mahayug
				Equivalence of Two Definitions
			1.1.10.8 Age of the Sun
			1.1.10.9 Night of Brahma
		1.1.11 Names of 14 Manvantar
		1.1.12 Time Intervals in Terms of Kalp
		1.1.13 Summary of Bigger Time Intervals
		1.1.14 The Time Elapsed Since Creation of Universe
		1.1.15 Date of Commencement of the Present Kaliyug
	1.2 Length Intervals
		1.2.1 Introduction
		1.2.2 Sets of Smaller Length Intervals
			1.2.2.1 Set of Smaller Units of Length as Given in Agni Puran
			1.2.2.2 Set of Smaller Units of Length in Chanakiya Arthsashtra
		1.2.3 Units of Length in Multiples of Angul
			1.2.3.1 Length Units with Different Names But of the Same Value
			1.2.3.2 Smaller Units of Length in Times of Bhoja
				Sub-multiples and Multiples of Angul (Raja Bhoja)
				Specific Fields of Use of Prasaya, Sadharan or Saya
					Prasaya
					Sadharan
					Saya
			1.2.3.3 Yojan in Bhoja Time
			1.2.3.4 Units of Length in Multiples of Angul
			1.2.3.5 Units Used for Distance Measurements
			1.2.3.6 Units of Length by Cardarelli
		1.2.4 Two Kinds of Danush
		1.2.5 Scale of Mohenjo-Daro
			1.2.5.1 Situation of Mohenjo-Daro
			1.2.5.2 Scale of Mohenjo-Daro
			1.2.5.3 Decoding the Mohenjo-Daro Scale
		1.2.6 Supportive Evidences for Taking 1 Angul Equal to 16.764 mm
			1.2.6.1 The Indus Inch
			1.2.6.2 Temple Wall Engravings Related to Dhanush
			1.2.6.3 Mohenjo-daro’s Great Bath
		1.2.7 Various Yojan
			1.2.7.1 Yojan in Valmiki Ramayan
			1.2.7.2 British Yojan
			1.2.7.3 Indian Yojan
			1.2.7.4 Units in Terms of Human Limbs
		1.2.8 Length in Terms of Latitude
			1.2.8.1 Change in Distance with Latitude and Longitude
				Distance Due to Change in Latitude Only
				Distance Due to Change in Longitude Only
			1.2.8.2 Variation of Latitude from Equator to Pole
			1.2.8.3 Definition of Metre
		1.2.9 Pre-Akbar Length Measures
			1.2.9.1 Linear Units in Terms of Angul
		1.2.10 Weights and Measures in Akbar Time
			1.2.10.1 System of Weights and Measures by Akbar
			1.2.10.2 Akbar IIahi Gaz
				Administration and Standardization of Land Measurement in Akbar’s Period
			1.2.10.3 Smaller Units of Length in Akbar Period (1556–1605)
		1.2.11 Length Units Used by Tailors
		1.2.12 Length Units in Dependent India
			1.2.12.1 Base Unit 1 in.
			1.2.12.2 Imperial Length Units
	1.3 Units of Weight and Volume
		1.3.1 Introduction
			1.3.1.1 Mass and Weight
			1.3.1.2 Grain
			1.3.1.3 Measurement of Weights Per Grain of a Cereals
			1.3.1.4 Value of Troy Grain
		1.3.2 Weights Nomenclature from Manusmriti
			1.3.2.1 Verses of Manusmriti Pertaining to Weights
			1.3.2.2 Weights in Terms of Grains
			1.3.2.3 Weights in Multiples of Ratti
				Silver Trade
				Gold Trade
		1.3.3 Weights in Terms of Tresarenu
		1.3.4 Charak System of Weights
			1.3.4.1 Weights Used in Ayurveda
			1.3.4.2 Pal Tolaa Relationship
		1.3.5 Weight Measurement in Ancient India
			1.3.5.1 Weight Units in Narad Puran
			1.3.5.2 Weights Used for Food Grains
			1.3.5.3 Volume of Granular Materials
		1.3.6 Weights in Terms of Grain of Rice (chawal)
			1.3.6.1 Weights in Terms of Rice (Chawal)
			1.3.6.2 Weights in Multiples of Rice with Husk (Dhaan)
			1.3.6.3 Bullion Weights in Terms of Chawal (Rice)
			1.3.6.4 Weights System Used in Southern Part of India
		1.3.7 Weights Used in Pre-Akbar Period
			1.3.7.1 Weights in Terms of chawal, ratti, maashaa, Etc
			1.3.7.2 Weights in Terms of Siki
		1.3.8 Weights in Colonial (Pre-Independence) Years
			1.3.8.1 Weights in Terms of Khaskas
			1.3.8.2 Variety of Weights Before Independence
			1.3.8.3 Weights in Terms of Gunja
		1.3.9 Conventions Followed by Public for Weights
			1.3.9.1 Urban Area
			1.3.9.2 Rural Area
			1.3.9.3 Present Situation
		1.3.10 Weights and Volume Measures by Chanakiya
			1.3.10.1 Weights
				Smaller Units of Weights
					Gold Trade
					Silver Trade
					Diamond Trade
				Bigger Units of Weights
				Miscellaneous Weight Units
				Denominations of Weights
					Gold Trade
					Silver Trade
					General Trade
				Material of Weights
			1.3.10.2 Balances
				Balances in Gold Trade
				Balances for Other Commodities
					Samavritta Balance
					Parimani Balance
					Commercial Balances
			1.3.10.3 Volume Measurements
				Types of Drona
				Other Units of Volume
				Construction of Volumetric Measures
					Volumetric Measures for Granular Material
					Volumetric Measures for Liquids
			1.3.10.4 Administrative Measures
				Price Control on Weight and Measure
				Verification Period and Fee Chargeable
				Taptavyaji
				Smaller Standard Measures
		1.3.11 Conversion Factors
	References
2 System of Quantities and Units
	2.1 Quantities
	2.2 System of Quantities
		2.2.1 Quantity
		2.2.2 Base Quantity
		2.2.3 System of Base Quantities
		2.2.4 Derived Quantity
		2.2.5 Quantity Equation
		2.2.6 Quantity Value Equation
		2.2.7 Dimension of Derived Unit
	2.3 Measurement Unit
		2.3.1 System of Measurement Units
		2.3.2 System of Base Units
			2.3.2.1 Properties of Base Units
			2.3.2.2 Minimum Number of Base Units
		2.3.3 Derived Unit
		2.3.4 Unit Equation
		2.3.5 Properties of Units of Measurement
		2.3.6 Coherent Derived Unit
	2.4 Quantity of Dimension 1 or Dimensionless Quantity
		2.4.1 Dimension of a Quantity
		2.4.2 Quantities of Dimension 1 or Dimensionless Quantities
		2.4.3 Ordinal Quantity
		2.4.4 Quantity Scale, Measurement Scale
		2.4.5 Ordinal Quantity Scale, Ordinal Scale
		2.4.6 Nominal Property
	2.5 Conversion Factor Between Units
	2.6 Quantity Relations
		2.6.1 Quantity Value
		2.6.2 Numerical Quantity Value
		2.6.3 Quantity Calculus
	2.7 Units Used in Biology, Biochemistry, Molecular Biology, Forensic Science Biological Effects
		2.7.1 Photochemical or Photo-Biological Quantities and Their Units
		2.7.2 Conversion of Radiometric to Photometric Quantities
		2.7.3 Photometry and Photon-Number-Based Quantities
		2.7.4 Units Used in Photometry
		2.7.5 Actinic Action Spectrum
		2.7.6 Types of Visions
		2.7.7 Unit in the Field of Sound
		2.7.8 Units in the Field of Ionizing Radiations
	2.8 SI Units in the Framework of General Relativity
	References
3 Various Systems of Units
	3.1 Introduction
	3.2 Relations Between the Quantities
		3.2.1 Derived Quantities by Definition
		3.2.2 Derived Quantities by a Phenomenon
	3.3 Three-Dimensional System of Units
		3.3.1 Gauss System
		3.3.2 CGS System
		3.3.3 FPS System
	3.4 Four-Dimensional Systems of Units
		3.4.1 Giorgi System of Units
		3.4.2 Maxwell System
		3.4.3 Hartree System
		3.4.4 Units for Atomic and Molecular Measurements
		3.4.5 McWeeny System of Units
		3.4.6 Ohm, Ampere, Second and Metre System
		3.4.7 Force, Length and Time System
		3.4.8 System in Terms of Universal Constants (G, H, E and Q)
		3.4.9 System in Terms of Electric Charge, Flux, Length and Time
		3.4.10 System in Terms of L, M, T and R
	3.5 Derived Quantities in Terms of L, M, T and R—An Example
	3.6 Measurement System in Terms of Length Time Flux and Charge
	References
4 Metre Convention and Evolution of Base Units
	4.1 BIPM and Metre Convention
		4.1.1 General Conference on Weights and Measures (CGPM)
		4.1.2 International Committee for Weights and Measures (CIPM)
		4.1.3 Consultative Committees
			4.1.3.1 Consultative Committee for Electricity and Magnetism (CCEM)
			4.1.3.2 Consultative Committee for Photometry and Radiometry (CCPR)
			4.1.3.3 Consultative Committee for Thermometry (CCT)
			4.1.3.4 Consultative Committee for Length (CCL)
			4.1.3.5 Consultative Committee for Time and Frequency (CCTF)
			4.1.3.6 Consultative Committee for Ionizing Radiation (CCRI)
			4.1.3.7 Consultative Committee for Units (CCU)
			4.1.3.8 Consultative Committee for Mass and Related Quantities (CCM)
			4.1.3.9 Consultative Committee for Amount of Substance: Metrology in Chemistry (CCQM)
			4.1.3.10 Consultative Committee for Acoustics, Ultrasound and Vibration (CCAUV)
		4.1.4 International Bureau of Weights and Measures (BIPM)
			4.1.4.1 Scientific Activities
			4.1.4.2 Objects of BIPM
			4.1.4.3 Staff at BIPM
			4.1.4.4 Publications
			4.1.4.5 Metrologia
		4.1.5 Linkages of Various Organs of Metre Convention
	4.2 International System of Units SI
		4.2.1 Base Units
		4.2.2 Latest Definitions of SI Base Units
	4.3 Evolution of Base Units
		4.3.1 Unit of Time
		4.3.2 Unit of Length
		4.3.3 Unit of Mass
			4.3.3.1 International Prototype of Kilogram
		4.3.4 Unit of Electric Current
		4.3.5 Unit of Temperature
			4.3.5.1 Unit of Thermodynamic Temperature (Kelvin)
		4.3.6 Unit of Amount of Substance (Mole)
		4.3.7 Unit of Luminous Intensity
		4.3.8 Dependence of Base Units
	References
5 New Definitions of SI Base Units
	5.1 Seven Defining Constants and SI Base Units
	5.2 Importance of Defining Constants
		5.2.1 Caesium Frequency
		5.2.2 Velocity of Light
		5.2.3 Planck’s Constant
		5.2.4 Elementary Charge
		5.2.5 Boltzmann Constant
		5.2.6 Avogadro Constant
		5.2.7 Luminous Efficacy
	5.3 Magnitude of Defining Constant in SI Units
	5.4 Formal Definitions of SI Units
		5.4.1 The Second
		5.4.2 The Metre
		5.4.3 The Kilogram
		5.4.4 The Ampere
		5.4.5 The Kelvin
		5.4.6 The Mole
		5.4.7 The Candela
	5.5 Effect of the New Definition
		5.5.1 Second
		5.5.2 Metre
		5.5.3 Kilogram
		5.5.4 Ampere
			5.5.4.1 Effect of Taking H and E as Exact Value
		5.5.5 The Kelvin
		5.5.6 The Mole
		5.5.7 The Candela
	5.6 Expressing SI Base Units in Defining Constants
		5.6.1 The Second in Terms of ΔνCs
		5.6.2 The Metre in Terms of C and S
		5.6.3 The Kilogram in Terms of H
		5.6.4 The Ampere in Terms of E and S
		5.6.5 The Kelvin in Terms of K
		5.6.6 Mole in Terms of NA
		5.6.7 Candela in Terms of Kcd
	5.7 Relationship Matrix
		5.7.1 Defining Constants in Terms of Base Units
		5.7.2 Base Units in Terms of Defining Constants
		5.7.3 Use of the Matrix
	5.8 Inter-Dependence of Base Units
		5.8.1 New SI Units
		5.8.2 Old SI Units
6 Realization of the SI Base Units (S, M, Kilogram)
	6.1 Practical Realization of the Unit of Time
		6.1.1 Atomic Clocks
		6.1.2 Primary Frequency Standards
		6.1.3 Secondary Representations of the Second
		6.1.4 International Atomic Time (TAI)
		6.1.5 Terrestrial Time (TT), Geocentric Coordinate Time (TCG)
		6.1.6 Coordinated Universal Time (UTC)
	6.2 Practical Realization of the Metre
		6.2.1 Standard Radiations
	6.3 Practical Realization of the Kilogram (via Kibble Balance)
		6.3.1 Electromechanical (Kibble) Balances
			6.3.1.1 Measurement of Velocity (U)
			6.3.1.2 Measurement of Mass
			6.3.1.3 Measurement of g
			6.3.1.4 Corrections
		6.3.2 Constant Magnetic Field (Generation)
			6.3.2.1 Magnets
			6.3.2.2 Design for the Magnet System
			6.3.2.3 Effect of the Weighing Current on the Magnetic Flux Density
			6.3.2.4 Demagnetization of the Rare Earth Magnets
		6.3.3 Change of the Reluctance of the Yoke
			6.3.3.1 The Reluctance Force
		6.3.4 Temperature Change of the Rare Earth Magnet
		6.3.5 Temperature Change of the Yoke Material
		6.3.6 Engineering of Magnets with Smaller Temperature Coefficients
		6.3.7 Actively Controlling the Temperature
		6.3.8 Voltage Measurements
			6.3.8.1 Measurement Techniques
			6.3.8.2 Josephson Reference
			6.3.8.3 Hysteretic Arrays
			6.3.8.4 Programmable Arrays
		6.3.9 Voltmeter
			6.3.9.1 Amplifiers
			6.3.9.2 Synchronization of the Voltmeter and Counter
		6.3.10 Current Generation and Measurement
			6.3.10.1 Current Sources
			6.3.10.2 The Measurement Resistor
			6.3.10.3 Measurement of Resistance in Terms of QHE
		6.3.11 Results
	6.4 Practical Realization of the Kilogram (via XRCD Method)
		6.4.1 Principle
		6.4.2 Sphere
			6.4.2.1 Volume of Sphere
		6.4.3 Obtaining 28Si-Enriched Polycrystal
		6.4.4 Single Crystal Growth
		6.4.5 Isotopic Composition of Silicon
		6.4.6 Crystal Perfection: Evaluation of Point Defects
		6.4.7 MSL Layers
		6.4.8 Molar Mass
		6.4.9 Lattice Parameter
			6.4.9.1 Experimental Apparatus
			6.4.9.2 Measurement Procedure
			6.4.9.3 Results
			6.4.9.4 Uncertainty in XRCD Method
	References (Kibble Balance)
7 Realization of SI Base Unit Ampere and Other Electric Units
	7.1 Introduction
	7.2 Definition of the Electrical/Magnetic Units
		7.2.1 Practical Realization of Ampere, SI Base Unit of Electric Current
		7.2.2 Derived Units
			7.2.2.1 Practical Realization of the Volt, V, SI Derived Unit of Electric Potential Difference (Voltage) and Electromotive Force
			7.2.2.2 Practical Realization of the Ohm, Ω, SI Derived Unit of Electric Resistance and Impedance
			7.2.2.3 Practical Realization of the Siemens, S, SI Derived Unit of Electric Conductance
			7.2.2.4 Practical Realization of the Coulomb, C, SI Derived Unit of Electric Charge
			7.2.2.5 Practical Realization of the Farad, F, SI Derived Unit of Capacitance
			7.2.2.6 Practical Realization of the Henry, H, SI Derived Unit of Inductance
			7.2.2.7 Practical Realization of the Watt, W, SI Derived Unit of Power
			7.2.2.8 Practical Realization of the Tesla, T, SI Derived Unit of Magnetic Flux Density
			7.2.2.9 Practical Realization of the Weber, Wb, SI Derived Unit of Magnetic Flux
			7.2.2.10 Magnetic Constant μ0 and Related Quantities
	7.3 Mole
	7.4 Realization of Mole
		7.4.1 Pure Sample
		7.4.2 Pure Gas
		7.4.3 Chemical Electrolysis
	7.5 Primary Method
	References
8 Boltzmann Constant Defining Kelvin K
	8.1 Introduction to Boltzmann Constant
	8.2 Acoustic Gas Thermometry AGT
		8.2.1 Measurement at NPL, UK
		8.2.2 Main Uncertainty Components
	8.3 Radiation Thermometry
		8.3.1 Total Radiation Thermometry TRT (Stefan–Boltzmann Measurement)
		8.3.2 Spectral-Band-Limited Radiation Thermometry
	8.4 Thermal-Equation-of-State Methods
		8.4.1 Constant-Volume Gas Thermometry (CVGT)
		8.4.2 Dielectric-Constant Gas Thermometry
		8.4.3 Results
	8.5 Refractive-Index Gas Thermometry RIGT
	8.6 Doppler-Broadening Thermometry
	8.7 Noise Thermometry
	8.8 Realization of K (Hierarchy of Temperature)
		8.8.1 Temperature Scale
		8.8.2 Different Temperature Scales
		8.8.3 Hierarchy in Temperature Measurement
	References
9 Radiometry, Photometry and Realization of Candela and Mole
	9.1 SI Units Used in Radiometry and Photometry
	9.2 Traceability and Realization of Photometric Units
		9.2.1 Traceability Routes for the Practical Realization of Photometric Units
			9.2.1.1 Detector-Based Photometric Traceability
			9.2.1.2 Source-Based Photometric Traceability
	9.3 Realizationof the Candela (Cd)
	9.4 Realization of the Lumen (Lm), SI Derived Unit of Luminous Flux
	9.5 Realization of the Lux (Lx), SI Derived Unit of Illuminance Ev
	References
10 Derived Quantities and Their Units
	10.1 Derived Quantities
	10.2 Units of Derived Quantities
	10.3 SI Derived Units
		10.3.1 Units Expressed in Terms of Base Units
		10.3.2 Derived Units with Special Names
		10.3.3 Derived Units Formed from the Derived Units with Special Names
		10.3.4 Derived Quantities of Dimension 1
	10.4 Units Outside the SI
		10.4.1 Units Accepted for Use with the SI
		10.4.2 Non-SI Units with Experimentally Obtained Values
		10.4.3 Non-SI Units Used by Special Groups
		10.4.4 Other Non-SI Units with Special Names
		10.4.5 Other Non-SI Units Found in Old Literature
	References
11 Expressing SI Units
	11.1 Introduction
	11.2 SI Prefixes
		11.2.1 Rules for Using SI Prefixes
		11.2.2 Prefix About the Kilogram
	11.3 Writing of SI Unit Symbols
		11.3.1 Unit Symbols and Their Combinations
		11.3.2 Names of Units
		11.3.3 Quantity Calculus
			11.3.3.1 Value of Quantity
			11.3.3.2 Numerical Value of a Given Quantity
			11.3.3.3 Formatting the Value of a Quantity
			11.3.3.4 Symbols of Quantities
			11.3.3.5 Quantity Symbols and Unit Symbols
		11.3.4 Stating Values of Quantities of Dimension One
			11.3.4.1 Use of Symbol %
	11.4 Expression of Numbers
		11.4.1 Formatting Numbers and the Decimal Marker
		11.4.2 Expressing the Measurement Uncertainty
	11.5 Advantages of SI Units
		11.5.1 Harmonization of Units
			11.5.1.1 SI Unit of Magnetic Pole Strength
		11.5.2 Expressing the Values of μO and εO in Terms of SI Units
		11.5.3 Magnetic Flux Density/Magnetizing Force
		11.5.4 Intensity of Magnetization
		11.5.5 Homogenizing of Units of Energy in Heat
		11.5.6 Coherent System
		11.5.7 Coherent Derived Unit
		11.5.8 Well-Defined Units
	11.6 Expressing Electrostatic and Electromagnetic Quantities in SI Units
		11.6.1 Charge and Current
			11.6.1.1 Esu of Charge
			11.6.1.2 Emu of Current and Charge
		11.6.2 Potential
			11.6.2.1 esu Potential
			11.6.2.2 Emu Potential
		11.6.3 Electrical Resistance
			11.6.3.1 Esu of Resistance
			11.6.3.2 Emu of Resistance
		11.6.4 Electrical Capacitance
			11.6.4.1 Esu of Capacitance
			11.6.4.2 Emu of Capacitance
		11.6.5 Emu of Magnetic Flux
		11.6.6 Magnetic Field Strength (Flux Density)
		11.6.7 Electric Field
		11.6.8 Inductance
		11.6.9 Oerested
	References
12 Past Efforts in Redefining of SI Units
	12.1 In Terms of Physical Constants
		12.1.1 Basis of SI Units
	12.2 From a Single Source
		12.2.1 In Terms of Hydrogen Atom
		12.2.2 In Terms of Only One Standard (Frequency)
		12.2.3 In Terms of Fundamental Constants Using Maxwell Equations
		12.2.4 A Consistent Set of Fundamental Constants by BIPM
	12.3 CIPM Recommendation 1 (CI-2005)
	12.4 A Proposal to Redefine Kilogram, Ampere, Kelvin and Mole
		12.4.1 Kilogram
		12.4.2 Ampere
		12.4.3 Kelvin
		12.4.4 Mole
	12.5 The Values of h, e, k and NA
		12.5.1 Observations
	12.6 Practical Standards to Realize Kilogram
		12.6.1 Other Methods of Redefining Kilogram
	References
13 Scientists Associated with Units of Measurements
	13.1 Scientists Associated with Base Units
		13.1.1 Anders Celsius
		13.1.2 Andre Marie Ampere
		13.1.3 Avogadro
		13.1.4 Boltzmann Ludwig Eduard
		13.1.5 Lord Kelvin
		13.1.6 Planck, Karl Ernst Ludwig Marx (Max)
	13.2 Scientists Associated with Derived Units
		13.2.1 Sir Isaac Newton
		13.2.2 Heinrich Rudolf Hertz
		13.2.3 Blaise Pascal
		13.2.4 James Prescott Joule
		13.2.5 James Watt
		13.2.6 Charles Augustin Coulomb
		13.2.7 Alessandro Volta
		13.2.8 Michael Faraday
		13.2.9 Wilhelm Eduard Weber
		13.2.10 Nickola Tesla
		13.2.11 Joseph Henry
		13.2.12 Antoine Henri Becquerel
		13.2.13 Louis Harold Gray
		13.2.14 Rolf M. Sievert
		13.2.15 Georg Simon Ohm
		13.2.16 Werner Von Siemens
	13.3 Some Units Not Named After Any Scientist
Index