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Mass and Mass Standards | |

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Introduction | |

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Definition of Mass | |

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The Mass Unit | |

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Mass Artifacts, Mass Standards | |

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References | |

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The Roles of Mass Metrology in Civilization, Paul E. Pontius | |

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The Role of Mass Measurement in Commerce | |

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The Role of Measurement in Technology | |

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The Role of Measurement in Science | |

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References | |

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Report by John Quincy Adams | |

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Recalibration of Mass Standards | |

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Recalibration of the U.S. National Prototype Kilogram | |

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Introduction | |

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Experimental | |

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1984 BIPM Measurements | |

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1984 NBS Measurements | |

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Recommendations | |

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Third Periodic Verification of National Prototypes of the Kilogram | |

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Introduction | |

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Preliminary Comparisons | |

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Comparisons with the International Prototype | |

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Verification of the National Prototypes | |

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Conclusions Drawn from the Third Verification | |

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References | |

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Contamination of Mass Standards | |

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Platinum-Iridium Mass Standards | |

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Growth of Carbonaceous Contamination on Platinum-Iridium Alloy Surfaces, and Cleaning by Ultraviolet-Ozone Treatment | |

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Progress of Contamination and Cleaning Effects | |

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Effects of Changes in Ambient Humidity, Temperature, and Pressure on "Apparent Mass" of Platinum-Iridium Prototype Mass Standards | |

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Evidence of Variations in Mass of Reference Kilograms Due to Mercury Contamination | |

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Mechanism and Long-Term Effects of Mercury Contamination | |

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Water Adsorption Layers on Metal Surfaces | |

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Stainless Steel Mass Standards | |

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Precision Determination of Adsorption Layers on Stainless Steel Mass Standards--Introduction | |

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Adsorption Measurements in Air | |

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Sorption Measurements in Vacuum | |

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Effect of Environment and Cleaning Methods on Surfaces of Stainless Steel and Allied Materials | |

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Studies of Influence of Cleaning on Stability of XSH Alacrite Mass Standards | |

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References | |

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Cleaning of Mass Standards | |

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Introduction | |

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Solvent Cleaning and Steam Washing (Nettoyage-Lavage) | |

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Solvent Cleaning | |

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Steam Washing | |

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Effect of Solvent Cleaning and Steam Washing | |

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Summaries of National Laboratory Studies Related to Cleaning | |

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Cleaning at National Physical Laboratory, United Kingdom (NPL) | |

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Cleaning at Institut National de Metrologie, France (INM) | |

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Cleaning at National Research Laboratory of Metrology, Japan (NRLM) | |

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Cleaning of Stainless Steel Mass Standards | |

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Cleaning Procedures Investigated by Weighing and Ellipsometry | |

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Cleaning of Stainless Steel Mass Standards at BIPM | |

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Cleaning of Stainless Steel Mass Standards at NIST | |

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References | |

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From Balance Observations to Mass Differences | |

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Introduction | |

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Determination of Mass Difference | |

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References | |

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Glossary of Statistical Terms | |

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References | |

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Measurement Uncertainty | |

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Introduction | |

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NIST Guidlines | |

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Classification of Components of Uncertainty | |

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Standard Uncertainty | |

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Type A Evaluation of Standard Uncertainty | |

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Type B Evaluation of Standard Uncertainty | |

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Combined Standard Uncertainty | |

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Expanded Uncertainty | |

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Relative Uncertainties | |

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Example of Determination of Uncertainty | |

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References | |

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Weighing Designs | |

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Introduction | |

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Least Squares | |

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Best Fit | |

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Simplest Example | |

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Equation of a Line | |

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Sequences | |

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Design A.1.2 | |

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Design C.10 | |

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Design 16 | |

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Observation Multipliers for Determining Mass Values and Deviations | |

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Design A.1.2 | |

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Design C.10 | |

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Design 16 | |

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Factors for Computing Weight Standard Deviations Needed for Uncertainty Calculations | |

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Design A.1.2 | |

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Design C.10 | |

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Design 16 | |

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Sample Data Sets and Intermediate Calculations | |

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Design A.1.2 | |

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Design C.10 | |

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Design 16 | |

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Calculations of Various Values Associated with Design 16 and the 5-kg, 2-kg[subscript 1], 2-kg[subscript 2], and 1-kg Weights | |

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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 | |

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50 g - 10 g NIST Data | |

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5 g - 1 g NIST Data | |

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0.5 g - 0.1 g NIST Data | |

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0.05 g - 0.01 g NIST Data | |

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0.005 g - 0.001 g NIST Data | |

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Commentary | |

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References | |

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Calibration of the Screen and the Built-in Weights of a Direct-Reading Analytical Balance | |

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Calibration of the Screen | |

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Calibration of the Built-in Weights | |

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References | |

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A Look at the Electronic Balance | |

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Introduction | |

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The Analytical Balance and the Mass Unit | |

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Balance Principles | |

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The Mechanical Balance | |

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The Hybrid Balance | |

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The Electromotive Force Balance | |

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The Servo System | |

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A Closer Look at Electronic Balances | |

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The Hybrid Balance | |

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The Force Balance | |

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Benefits and Idiosyncrasies of Electronic Balances | |

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Benefit | |

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Idiosyncrasies | |

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Black Box Comparison | |

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The Future | |

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References | |

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Examples of Buoyancy Corrections in Weighing | |

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Introduction | |

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Buoyant Force and Buoyancy Correction | |

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Application of the Simple Buoyancy Correction Factor to Weighing on a Single-Pan Two-Knife Analytical Balance | |

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The Electronic Analytical Balance | |

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Electronic Balance Calibration and Use | |

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Usual Case for Which the Air Density Is Not the Reference Value | |

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Examples of Effects of Failure to Make Buoyancy Corrections | |

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Other Examples of Buoyancy Correction | |

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Weighing of Syringes | |

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Buoyancy Applied to Weighing in Weighing Bottles | |

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References | |

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Air Density Equation | |

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Introduction | |

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Development of the Jones Air Density Equation | |

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Parameters in the Jones Air Density Equation | |

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The Jones Air Density Equation | |

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Uncertainties in Air Density Calculations | |

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Use of Constant Values of F, Z, and M[subscript a] in the Air Density Equation | |

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CIPM-81 Air Density Equation | |

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CIPM 1981/1991 Equation | |

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Recommendation | |

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Direct Determination of Air Density | |

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Introduction | |

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Experimental Procedure | |

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Results and Conclusions | |

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Experimental Determination of Air Density in Weighing on a 1-kg Balance in Air and in Vacuum | |

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Introduction | |

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Results and Conclusions | |

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A Practical Approach to Air Density Determination | |

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Introduction | |

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Air Density | |

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Test of Air Density Equation at Differing Altitudes | |

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Introduction | |

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Experimental Details | |

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Calculation of Air Density for Buoyancy Correction | |

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Measurements of Parameters in the Air Density Equation | |

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Weighings | |

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Conclusions | |

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References | |

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Density of Solid Objects | |

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Development of a Density Scale Based on the Density of a Solid Object | |

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Introduction | |

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Apparatus | |

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Principles of Use of the Submersible Balance | |

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Measurements | |

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Summary | |

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Discussion | |

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Determination of Density of Mass Standards; Requirement and Method | |

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Introduction | |

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Requirements | |

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Principles and Applications | |

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The Density of a Solid by Hydrostatic Weighing | |

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The Force Detector | |

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Air Density | |

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Water Density | |

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A General Algorithm for Hydrostatic Weighing | |

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The General Hydrostatic Weighing Equations | |

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Linearity Test and Correction | |

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Analysis | |

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Balance Selection | |

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Data Results | |

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Conclusions | |

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Appendix 1--Liquid Density by Hydrostatic Weighing | |

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Appendix 2--Glassware Calibration | |

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An Efficient Method for Measuring the Density (or Volume) of Similar Objects | |

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Introduction | |

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The Requirement | |

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The Method | |

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The Measurement of Liquid Density | |

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Error Analysis | |

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Apparatus | |

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Data | |

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Conclusion | |

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References | |

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Calculation of the Density of Water | |

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Introduction | |

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Formulations of Wagenbreth and Blanke | |

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Kell's Formulations | |

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Density of Standard Mean Ocean Water | |

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Isothermal Compressibility of Water | |

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Conversion of IPTS-68 to ITS-90 | |

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Redeterminations of Water Density | |

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Measurements of Patterson and Morris | |

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Measurements of Watanabe | |

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Measurements of Takenaka and Masui | |

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Comparison of the Results for the Three Recent Formulations | |

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Change in Density of Water with Air Saturation | |

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Density of Air-Saturated Water on ITS-90 | |

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Compressibility-Corrected Water Density Equation | |

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Effect of Isotopic Concentrations | |

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Estimation of Uncertainty in Water Density Due to Variation in Isotopic Concentrations | |

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Summary | |

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References | |

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Conventional Value of the Result of Weighing in Air | |

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Introduction | |

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Conventional Value of Weighing in Air | |

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Examples of Computation | |

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Discussion | |

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Conclusions | |

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References | |

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A Comparison of Error Propagations for Mass and Conventional Mass | |

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Conventional Value of the Result of Weighing in Air | |

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Uncertainties in Mass Determinations | |

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Uncertainties in the Determination of m Due to Uncertainties in the Parameters in Eq. (16.2) | |

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Balance Standard Deviation | |

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Application to R111 | |

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Comparisons of Weights | |

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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] | |

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Error Propagation for Conventional Value of Weighing in Air | |

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Comparison of E[subscript 2] Weights with E[subscript 1] Weights | |

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Maximum Permissible Errors on Verification | |

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Uncertainty Trade-Offs | |

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Summary | |

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References | |

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Examination of Parameters That Can Cause Error in Mass Determinations | |

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Introduction | |

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Mass Comparison | |

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The Fundamental Mass Comparison Relationship | |

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Uncertainties in the Determination of X Due to Uncertainties in the Parameters in Eq. (17.2) | |

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Buoyancy | |

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Thermal Equilibrium | |

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Atmospheric Effects | |

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Magnetic Effects | |

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Instability of IPK | |

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Cleaning | |

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Conclusions | |

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Discussion | |

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References | |

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Determination of the Mass of a Piston-Gauge Weight, Practical Uncertainty Limits | |

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Introduction | |

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Assignment of Mass | |

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References | |

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Response of Apparent Mass to Thermal Gradients and Free Convective Currents | |

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Thermal Gradients | |

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Introduction | |

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Conclusions | |

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Free Convective Currents | |

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Introduction | |

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Experimental | |

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Results and Discussion | |

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Temperature Differences and Change of Apparent Mass of Weights | |

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References | |

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Magnetic Errors in Mass Metrology | |

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Introduction | |

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Magnetic Force | |

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Application of a Magnetic Force Equation | |

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References | |

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Effect of Gravitational Configuration of Weights on Precision of Mass Measurements | |

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Introduction | |

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Magnitude of the Gravitational Configuration Effect | |

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Significance of the Gravitational Configuration Correction | |

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References | |

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Between-Time Component of Error in Mass Measurements | |

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Introduction | |

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Experimental | |

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Discussion | |

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References | |

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Laboratory Standard Operating Procedure and Weighing Practices | |

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Introduction | |

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Environmental Controls and Instrumentation | |

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Balances | |

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Mass Standards | |

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Weight Cleaning | |

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Weighing | |

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Balance Problems | |

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Balance Support | |

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Loading Errors | |

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Electronic Forces | |

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Convection | |

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Unnatural Pressure Variations | |

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External Air Motion | |

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Statistical Surveillance | |

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Routine Bookkeeping | |

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References | |

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Control Charts | |

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Introduction | |

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Procedure | |

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System Monitored | |

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Check Standards | |

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Frequency of Measurement | |

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Types of Control Charts | |

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X Control Chart | |

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Initial Control Limits, X Chart | |

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X Control Chart | |

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Initial Control Limits, X Chart | |

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Updating Control Charts | |

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Interpretation of Control Chart Tests | |

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References | |

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Tolerance Testing of Mass Standards | |

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Introduction | |

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Prerequisites | |

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Methodology | |

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Scope, Precision, Accuracy | |

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Summary | |

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Apparatus/Equipment | |

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Procedure--Option A, Use of Single-Pan Mechanical Balance | |

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Procedure--Option B, Use of Full-Electronic Balance | |

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Procedure--Option C, Use of Equal-Arm Balance | |

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Tolerance Evaluation | |

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Reference | |

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Surveillance Testing | |

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Introduction | |

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Types of Surveillance Tests | |

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Type I Test | |

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Surveillance Limits | |

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Surveillance Charts | |

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Identification of Weights Whose Mass Has Changed | |

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References | |

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The Mass Unit Disseminated to Surrogate Laboratories Using the NIST Portable Mass Calibration Package | |

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Introduction | |

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Review | |

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The Third Package | |

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Hardware and Software | |

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The Measurements | |

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Data | |

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Analysis | |

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Conclusions | |

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References | |

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Highly Accurate Direct Mass Measurements without the Use of External Standards | |

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Introduction | |

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The Force Detector | |

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Discussion of the Method | |

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Uncertainties | |

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Balance Selection | |

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Determining the Estimate of Standard Deviation of the Balance | |

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Linearity Test and Correction | |

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Data | |

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Discussion | |

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Direction of Future Developments in Electronic Balances and Their Uses | |

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References | |

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The Piggyback Balance Experiment: An Illustration of Archimedes' Principle and Newton's Third Law | |

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Introduction | |

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The Piggyback Thought Balance Experiment | |

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The Laboratory Experiment | |

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Experimental Results | |

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Conclusion | |

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References | |

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The Application of the Electronic Balance in High-Precision Pycnometry | |

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Introduction | |

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Pycnometer Calibration | |

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Experimental Pycnometer Calibration | |

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Apparatus | |

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Air Density and Water Density | |

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Analysis | |

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Data | |

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Discussion | |

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References | |

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Buoyancy Corrections in Weighing Course | |

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Examination for "Buoyancy Corrections in Weighing" Course | |

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Answers for Examination Questions for "Buoyancy Corrections in Weighing" Course | |

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Appendix B | |

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Maximum Permissible Errors (MPE), in mg | |

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Minimum and Maximum Limits for Density of Weights ([rho subscript min], [rho subscript max]) | |

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Density and Coefficient of Linear Expansion of Pure Metals, Commercial Metals and Alloys | |

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Linearity Test | |

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Index | |