| |
| |
| |
| Mass and Mass Standards | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Definition of Mass | |
| |
| |
| |
| The Mass Unit | |
| |
| |
| |
| Mass Artifacts, Mass Standards | |
| |
| |
| References | |
| |
| |
| |
| The Roles of Mass Metrology in Civilization, Paul E. Pontius | |
| |
| |
| |
| The Role of Mass Measurement in Commerce | |
| |
| |
| |
| The Role of Measurement in Technology | |
| |
| |
| |
| The Role of Measurement in Science | |
| |
| |
| References | |
| |
| |
| |
| Report by John Quincy Adams | |
| |
| |
| |
| Recalibration of Mass Standards | |
| |
| |
| |
| Recalibration of the U.S. National Prototype Kilogram | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Experimental | |
| |
| |
| |
| 1984 BIPM Measurements | |
| |
| |
| |
| 1984 NBS Measurements | |
| |
| |
| |
| Recommendations | |
| |
| |
| |
| Third Periodic Verification of National Prototypes of the Kilogram | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Preliminary Comparisons | |
| |
| |
| |
| Comparisons with the International Prototype | |
| |
| |
| |
| Verification of the National Prototypes | |
| |
| |
| |
| Conclusions Drawn from the Third Verification | |
| |
| |
| References | |
| |
| |
| |
| Contamination of Mass Standards | |
| |
| |
| |
| Platinum-Iridium Mass Standards | |
| |
| |
| |
| Growth of Carbonaceous Contamination on Platinum-Iridium Alloy Surfaces, and Cleaning by Ultraviolet-Ozone Treatment | |
| |
| |
| |
| Progress of Contamination and Cleaning Effects | |
| |
| |
| |
| Effects of Changes in Ambient Humidity, Temperature, and Pressure on "Apparent Mass" of Platinum-Iridium Prototype Mass Standards | |
| |
| |
| |
| Evidence of Variations in Mass of Reference Kilograms Due to Mercury Contamination | |
| |
| |
| |
| Mechanism and Long-Term Effects of Mercury Contamination | |
| |
| |
| |
| Water Adsorption Layers on Metal Surfaces | |
| |
| |
| |
| Stainless Steel Mass Standards | |
| |
| |
| |
| Precision Determination of Adsorption Layers on Stainless Steel Mass Standards--Introduction | |
| |
| |
| |
| Adsorption Measurements in Air | |
| |
| |
| |
| Sorption Measurements in Vacuum | |
| |
| |
| |
| Effect of Environment and Cleaning Methods on Surfaces of Stainless Steel and Allied Materials | |
| |
| |
| |
| Studies of Influence of Cleaning on Stability of XSH Alacrite Mass Standards | |
| |
| |
| References | |
| |
| |
| |
| Cleaning of Mass Standards | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Solvent Cleaning and Steam Washing (Nettoyage-Lavage) | |
| |
| |
| |
| Solvent Cleaning | |
| |
| |
| |
| Steam Washing | |
| |
| |
| |
| Effect of Solvent Cleaning and Steam Washing | |
| |
| |
| |
| Summaries of National Laboratory Studies Related to Cleaning | |
| |
| |
| |
| Cleaning at National Physical Laboratory, United Kingdom (NPL) | |
| |
| |
| |
| Cleaning at Institut National de Metrologie, France (INM) | |
| |
| |
| |
| Cleaning at National Research Laboratory of Metrology, Japan (NRLM) | |
| |
| |
| |
| Cleaning of Stainless Steel Mass Standards | |
| |
| |
| |
| Cleaning Procedures Investigated by Weighing and Ellipsometry | |
| |
| |
| |
| Cleaning of Stainless Steel Mass Standards at BIPM | |
| |
| |
| |
| Cleaning of Stainless Steel Mass Standards at NIST | |
| |
| |
| References | |
| |
| |
| |
| From Balance Observations to Mass Differences | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Determination of Mass Difference | |
| |
| |
| References | |
| |
| |
| |
| Glossary of Statistical Terms | |
| |
| |
| References | |
| |
| |
| |
| Measurement Uncertainty | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| NIST Guidlines | |
| |
| |
| |
| Classification of Components of Uncertainty | |
| |
| |
| |
| Standard Uncertainty | |
| |
| |
| |
| Type A Evaluation of Standard Uncertainty | |
| |
| |
| |
| Type B Evaluation of Standard Uncertainty | |
| |
| |
| |
| Combined Standard Uncertainty | |
| |
| |
| |
| Expanded Uncertainty | |
| |
| |
| |
| Relative Uncertainties | |
| |
| |
| |
| Example of Determination of Uncertainty | |
| |
| |
| References | |
| |
| |
| |
| Weighing Designs | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Least Squares | |
| |
| |
| |
| Best Fit | |
| |
| |
| |
| Simplest Example | |
| |
| |
| |
| Equation of a Line | |
| |
| |
| |
| Sequences | |
| |
| |
| |
| Design A.1.2 | |
| |
| |
| |
| Design C.10 | |
| |
| |
| |
| Design 16 | |
| |
| |
| |
| Observation Multipliers for Determining Mass Values and Deviations | |
| |
| |
| |
| Design A.1.2 | |
| |
| |
| |
| Design C.10 | |
| |
| |
| |
| Design 16 | |
| |
| |
| |
| Factors for Computing Weight Standard Deviations Needed for Uncertainty Calculations | |
| |
| |
| |
| Design A.1.2 | |
| |
| |
| |
| Design C.10 | |
| |
| |
| |
| Design 16 | |
| |
| |
| |
| Sample Data Sets and Intermediate Calculations | |
| |
| |
| |
| Design A.1.2 | |
| |
| |
| |
| Design C.10 | |
| |
| |
| |
| Design 16 | |
| |
| |
| |
Calculations of Various Values Associated with Design 16. and the 5-kg, 2-kg[subscript 1], 2-kg[subscript 2], and 1-kg Weights | |
| |
| |
| |
| Calculations of Various Values Associated with the A.1.2 Design Solution for the 1-kg and [Sigma]1-kg Weights and 500 g through [Sigma]100 g | |
| |
| |
| |
50 g - 10. g NIST Data | |
| |
| |
| |
5 g - 1. g NIST Data | |
| |
| |
| |
| 0.5 g - 0.1 g NIST Data | |
| |
| |
| |
| 0.05 g - 0.01 g NIST Data | |
| |
| |
| |
| 0.005 g - 0.001 g NIST Data | |
| |
| |
| |
| Commentary | |
| |
| |
| References | |
| |
| |
| |
| Calibration of the Screen and the Built-in Weights of a Direct-Reading Analytical Balance | |
| |
| |
| |
| Calibration of the Screen | |
| |
| |
| |
| Calibration of the Built-in Weights | |
| |
| |
| References | |
| |
| |
| |
| A Look at the Electronic Balance | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| The Analytical Balance and the Mass Unit | |
| |
| |
| |
| Balance Principles | |
| |
| |
| |
| The Mechanical Balance | |
| |
| |
| |
| The Hybrid Balance | |
| |
| |
| |
| The Electromotive Force Balance | |
| |
| |
| |
| The Servo System | |
| |
| |
| |
| A Closer Look at Electronic Balances | |
| |
| |
| |
| The Hybrid Balance | |
| |
| |
| |
| The Force Balance | |
| |
| |
| |
| Benefits and Idiosyncrasies of Electronic Balances | |
| |
| |
| |
| Benefit | |
| |
| |
| |
| Idiosyncrasies | |
| |
| |
| |
| Black Box Comparison | |
| |
| |
| |
| The Future | |
| |
| |
| References | |
| |
| |
| |
| Examples of Buoyancy Corrections in Weighing | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Buoyant Force and Buoyancy Correction | |
| |
| |
| |
| Application of the Simple Buoyancy Correction Factor to Weighing on a Single-Pan Two-Knife Analytical Balance | |
| |
| |
| |
| The Electronic Analytical Balance | |
| |
| |
| |
| Electronic Balance Calibration and Use | |
| |
| |
| |
| Usual Case for Which the Air Density Is Not the Reference Value | |
| |
| |
| |
| Examples of Effects of Failure to Make Buoyancy Corrections | |
| |
| |
| |
| Other Examples of Buoyancy Correction | |
| |
| |
| |
| Weighing of Syringes | |
| |
| |
| |
| Buoyancy Applied to Weighing in Weighing Bottles | |
| |
| |
| References | |
| |
| |
| |
| Air Density Equation | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Development of the Jones Air Density Equation | |
| |
| |
| |
| Parameters in the Jones Air Density Equation | |
| |
| |
| |
| The Jones Air Density Equation | |
| |
| |
| |
| Uncertainties in Air Density Calculations | |
| |
| |
| |
| Use of Constant Values of F, Z, and M[subscript a] in the Air Density Equation | |
| |
| |
| |
| CIPM-81 Air Density Equation | |
| |
| |
| |
| CIPM 1981/1991 Equation | |
| |
| |
| |
| Recommendation | |
| |
| |
| |
| Direct Determination of Air Density | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Experimental Procedure | |
| |
| |
| |
| Results and Conclusions | |
| |
| |
| |
| Experimental Determination of Air Density in Weighing on a 1-kg Balance in Air and in Vacuum | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Results and Conclusions | |
| |
| |
| |
| A Practical Approach to Air Density Determination | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Air Density | |
| |
| |
| |
| Test of Air Density Equation at Differing Altitudes | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Experimental Details | |
| |
| |
| |
| Calculation of Air Density for Buoyancy Correction | |
| |
| |
| |
| Measurements of Parameters in the Air Density Equation | |
| |
| |
| |
| Weighings | |
| |
| |
| |
| Conclusions | |
| |
| |
| References | |
| |
| |
| |
| Density of Solid Objects | |
| |
| |
| |
| Development of a Density Scale Based on the Density of a Solid Object | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Apparatus | |
| |
| |
| |
| Principles of Use of the Submersible Balance | |
| |
| |
| |
| Measurements | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Discussion | |
| |
| |
| |
| Determination of Density of Mass Standards; Requirement and Method | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Requirements | |
| |
| |
| |
| Principles and Applications | |
| |
| |
| |
| The Density of a Solid by Hydrostatic Weighing | |
| |
| |
| |
| The Force Detector | |
| |
| |
| |
| Air Density | |
| |
| |
| |
| Water Density | |
| |
| |
| |
| A General Algorithm for Hydrostatic Weighing | |
| |
| |
| |
| The General Hydrostatic Weighing Equations | |
| |
| |
| |
| Linearity Test and Correction | |
| |
| |
| |
| Analysis | |
| |
| |
| |
| Balance Selection | |
| |
| |
| |
| Data Results | |
| |
| |
| |
| Conclusions | |
| |
| |
| |
| Appendix 1--Liquid Density by Hydrostatic Weighing | |
| |
| |
| |
| Appendix 2--Glassware Calibration | |
| |
| |
| |
| An Efficient Method for Measuring the Density (or Volume) of Similar Objects | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| The Requirement | |
| |
| |
| |
| The Method | |
| |
| |
| |
| The Measurement of Liquid Density | |
| |
| |
| |
| Error Analysis | |
| |
| |
| |
| Apparatus | |
| |
| |
| |
| Data | |
| |
| |
| |
| Conclusion | |
| |
| |
| References | |
| |
| |
| |
| Calculation of the Density of Water | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Formulations of Wagenbreth and Blanke | |
| |
| |
| |
| Kell's Formulations | |
| |
| |
| |
| Density of Standard Mean Ocean Water | |
| |
| |
| |
| Isothermal Compressibility of Water | |
| |
| |
| |
| Conversion of IPTS-68 to ITS-90 | |
| |
| |
| |
| Redeterminations of Water Density | |
| |
| |
| |
| Measurements of Patterson and Morris | |
| |
| |
| |
| Measurements of Watanabe | |
| |
| |
| |
| Measurements of Takenaka and Masui | |
| |
| |
| |
| Comparison of the Results for the Three Recent Formulations | |
| |
| |
| |
| Change in Density of Water with Air Saturation | |
| |
| |
| |
| Density of Air-Saturated Water on ITS-90 | |
| |
| |
| |
| Compressibility-Corrected Water Density Equation | |
| |
| |
| |
| Effect of Isotopic Concentrations | |
| |
| |
| |
| Estimation of Uncertainty in Water Density Due to Variation in Isotopic Concentrations | |
| |
| |
| |
| Summary | |
| |
| |
| References | |
| |
| |
| |
| Conventional Value of the Result of Weighing in Air | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Conventional Value of Weighing in Air | |
| |
| |
| |
| Examples of Computation | |
| |
| |
| |
| Discussion | |
| |
| |
| |
| Conclusions | |
| |
| |
| References | |
| |
| |
| |
| A Comparison of Error Propagations for Mass and Conventional Mass | |
| |
| |
| |
| Conventional Value of the Result of Weighing in Air | |
| |
| |
| |
| Uncertainties in Mass Determinations | |
| |
| |
| |
| Uncertainties in the Determination of m Due to Uncertainties in the Parameters in Eq. (16.2) | |
| |
| |
| |
| Balance Standard Deviation | |
| |
| |
| |
| Application to R111 | |
| |
| |
| |
| Comparisons of Weights | |
| |
| |
| |
| Comparison of a Stainless Steel E[subscript 1] Weight with a Stainless Steel Standard of Mass S and Density 7.950 g/cm[superscript 3] | |
| |
| |
| |
| Error Propagation for Conventional Value of Weighing in Air | |
| |
| |
| |
| Comparison of E[subscript 2] Weights with E[subscript 1] Weights | |
| |
| |
| |
| Maximum Permissible Errors on Verification | |
| |
| |
| |
| Uncertainty Trade-Offs | |
| |
| |
| |
| Summary | |
| |
| |
| References | |
| |
| |
| |
| Examination of Parameters That Can Cause Error in Mass Determinations | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Mass Comparison | |
| |
| |
| |
| The Fundamental Mass Comparison Relationship | |
| |
| |
| |
| Uncertainties in the Determination of X Due to Uncertainties in the Parameters in Eq. (17.2) | |
| |
| |
| |
| Buoyancy | |
| |
| |
| |
| Thermal Equilibrium | |
| |
| |
| |
| Atmospheric Effects | |
| |
| |
| |
| Magnetic Effects | |
| |
| |
| |
| Instability of IPK | |
| |
| |
| |
| Cleaning | |
| |
| |
| |
| Conclusions | |
| |
| |
| |
| Discussion | |
| |
| |
| References | |
| |
| |
| |
| Determination of the Mass of a Piston-Gauge Weight, Practical Uncertainty Limits | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Assignment of Mass | |
| |
| |
| References | |
| |
| |
| |
| Response of Apparent Mass to Thermal Gradients and Free Convective Currents | |
| |
| |
| |
| Thermal Gradients | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Conclusions | |
| |
| |
| |
| Free Convective Currents | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Experimental | |
| |
| |
| |
| Results and Discussion | |
| |
| |
| |
| Temperature Differences and Change of Apparent Mass of Weights | |
| |
| |
| References | |
| |
| |
| |
| Magnetic Errors in Mass Metrology | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Magnetic Force | |
| |
| |
| |
| Application of a Magnetic Force Equation | |
| |
| |
| References | |
| |
| |
| |
| Effect of Gravitational Configuration of Weights on Precision of Mass Measurements | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Magnitude of the Gravitational Configuration Effect | |
| |
| |
| |
| Significance of the Gravitational Configuration Correction | |
| |
| |
| References | |
| |
| |
| |
| Between-Time Component of Error in Mass Measurements | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Experimental | |
| |
| |
| |
| Discussion | |
| |
| |
| References | |
| |
| |
| |
| Laboratory Standard Operating Procedure and Weighing Practices | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Environmental Controls and Instrumentation | |
| |
| |
| |
| Balances | |
| |
| |
| |
| Mass Standards | |
| |
| |
| |
| Weight Cleaning | |
| |
| |
| |
| Weighing | |
| |
| |
| |
| Balance Problems | |
| |
| |
| |
| Balance Support | |
| |
| |
| |
| Loading Errors | |
| |
| |
| |
| Electronic Forces | |
| |
| |
| |
| Convection | |
| |
| |
| |
| Unnatural Pressure Variations | |
| |
| |
| |
| External Air Motion | |
| |
| |
| |
| Statistical Surveillance | |
| |
| |
| |
| Routine Bookkeeping | |
| |
| |
| References | |
| |
| |
| |
| Control Charts | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Procedure | |
| |
| |
| |
| System Monitored | |
| |
| |
| |
| Check Standards | |
| |
| |
| |
| Frequency of Measurement | |
| |
| |
| |
| Types of Control Charts | |
| |
| |
| |
| X Control Chart | |
| |
| |
| |
| Initial Control Limits, X Chart | |
| |
| |
| |
| X Control Chart | |
| |
| |
| |
| Initial Control Limits, X Chart | |
| |
| |
| |
| Updating Control Charts | |
| |
| |
| |
| Interpretation of Control Chart Tests | |
| |
| |
| References | |
| |
| |
| |
| Tolerance Testing of Mass Standards | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Prerequisites | |
| |
| |
| |
| Methodology | |
| |
| |
| |
| Scope, Precision, Accuracy | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Apparatus/Equipment | |
| |
| |
| |
| Procedure--Option A, Use of Single-Pan Mechanical Balance | |
| |
| |
| |
| Procedure--Option B, Use of Full-Electronic Balance | |
| |
| |
| |
| Procedure--Option C, Use of Equal-Arm Balance | |
| |
| |
| |
| Tolerance Evaluation | |
| |
| |
| Reference | |
| |
| |
| |
| Surveillance Testing | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Types of Surveillance Tests | |
| |
| |
| |
| Type I Test | |
| |
| |
| |
| Surveillance Limits | |
| |
| |
| |
| Surveillance Charts | |
| |
| |
| |
| Identification of Weights Whose Mass Has Changed | |
| |
| |
| References | |
| |
| |
| |
| The Mass Unit Disseminated to Surrogate Laboratories Using the NIST Portable Mass Calibration Package | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Review | |
| |
| |
| |
| The Third Package | |
| |
| |
| |
| Hardware and Software | |
| |
| |
| |
| The Measurements | |
| |
| |
| |
| Data | |
| |
| |
| |
| Analysis | |
| |
| |
| |
| Conclusions | |
| |
| |
| References | |
| |
| |
| |
| Highly Accurate Direct Mass Measurements without the Use of External Standards | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| The Force Detector | |
| |
| |
| |
| Discussion of the Method | |
| |
| |
| |
| Uncertainties | |
| |
| |
| |
| Balance Selection | |
| |
| |
| |
| Determining the Estimate of Standard Deviation of the Balance | |
| |
| |
| |
| Linearity Test and Correction | |
| |
| |
| |
| Data | |
| |
| |
| |
| Discussion | |
| |
| |
| |
| Direction of Future Developments in Electronic Balances and Their Uses | |
| |
| |
| References | |
| |
| |
| |
| The Piggyback Balance Experiment: An Illustration of Archimedes' Principle and Newton's Third Law | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| The Piggyback Thought Balance Experiment | |
| |
| |
| |
| The Laboratory Experiment | |
| |
| |
| |
| Experimental Results | |
| |
| |
| |
| Conclusion | |
| |
| |
| References | |
| |
| |
| |
| The Application of the Electronic Balance in High-Precision Pycnometry | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Pycnometer Calibration | |
| |
| |
| |
| Experimental Pycnometer Calibration | |
| |
| |
| |
| Apparatus | |
| |
| |
| |
| Air Density and Water Density | |
| |
| |
| |
| Analysis | |
| |
| |
| |
| Data | |
| |
| |
| |
| Discussion | |
| |
| |
| References | |
| |
| |
| |
| Buoyancy Corrections in Weighing Course | |
| |
| |
| |
| Examination for "Buoyancy Corrections in Weighing" Course | |
| |
| |
| |
| Answers for Examination Questions for "Buoyancy Corrections in Weighing" Course | |
| |
| |
| Appendix B | |
| |
| |
| |
| Maximum Permissible Errors (MPE), in mg | |
| |
| |
| |
| Minimum and Maximum Limits for Density of Weights ([rho subscript min], [rho subscript max]) | |
| |
| |
| |
| Density and Coefficient of Linear Expansion of Pure Metals, Commercial Metals and Alloys | |
| |
| |
| |
| Linearity Test | |
| |
| |
| Index | |