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MASS AND MASS STANDARDSDefinition of MassThe Mass UnitMass Artifacts, Mass StandardsReferencesHistorical BackgroundRole of Measurement in ScienceFootnotesReferencesRECALIBRATION OF MASS STANDARDSRecalibration of the U.S. National Prototype KilogramThird Periodic Verification of National Prototypes of the KilogramCONTAMINATION OF MASS STANDARDSIntroductionPlatinum-Iridium StandardsStainless Steel Mass StandardsMass StandardsStainless Steel and Allied MaterialsStudies of Influence of Cleaning on Stability of XSH Alacrite Mass StandardsReferencesCLEANING OF MASS STANDARDSIntroductionSolvent Cleaning and Steam Washing (Nettoyage-Lavage)Summaries of National Laboratory Studies Related to CleaningCleaning of Stainless Steel Mass StandardsReferencesFROM BALANCE OBSERVATIONS TO MASS DIFFERENCESIntroductionDetermination of Mass DifferenceReferencesIntroductionMeasurementMean, Arithmetic Mean, AverageDeviationStandard Deviation, SDDegrees of Freedom, DFPopulationSamplePopulation Standard DeviationVarianceRandom SampleNormal Distribution of MeasurementsConcept of a Limiting MeanCentral Limit TheoremStudent's tF TestOther Pertinent TermsBibliographyReferenceMEASUREMENT UNCERTAINTYIntroductionNIST GuidelinesExample of Determination of UncertaintyReferencesWEIGHING DESIGNSIntroductionLeast SquaresSequencesObservation Multipliers for Determining Mass Values and DeviationsFactors for Computing Weight Standard Deviation Needed for Uncertainty CalculationsCalculations of Various Values Associated with Design 16 and the 5-kg, 2-kg, 2-kg2, and 1-kg WeightsCalculations of Various Values Associated with the A.1.2 Design Solution for the 1-kg and ?1-kg WeightsCommentaryReferencesCALIBRATION OF THE SCREEN AND THE BUILT-IN WEIGHTS OF A DIRECT-READING ANALYTICAL BALANCECalibration of the ScreenCalibration of the Built-In WeightsReferencesA LOOK AT THE ELECTRONIC BALANCEIntroductionThe Analytical Balance and the Mass UnitBalance PrinciplesA Closer Look at Electronic BalancesBenefits and Idiosyncrasies of Electronic BalancesBlack Box ComparisonThe FutureReferencesBUOYANCY CORRECTIONS IN WEIGHINGIntroductionBuoyant Force and Buoyancy CorrectionApplication of the Simple Buoyancy Correction Factor to Weighing on a Single-Pan Analytical BalanceThe Electronic Analytical BalanceUsual Case for Which the Air Density Is Not the Reference ValueExamples of Effects of Failure to Make Buoyancy CorrectionsOther Examples of Buoyancy CorrectionReferencesAIR DENSITY EQUATIONIntroductionDevelopment of the Jones Air Density EquationWeight of Dry AirCIPM-81 Air Density EquationCIPM 1981/1991 EquationRecommendationDirect Determination of Air DensityExperimental Determination of Air Density in Weighing on a 1- Kilogram Balance in Air and in VacuumA Practical Approach to Air Density DeterminationTest of Air Density Equation at Differing AltitudeReferencesDENSITY OF SOLID OBJECTSDevelopment of a Density Scale Based on the Density of a Solid ObjectPrinciples of Use of the Submersible BalanceDetermination of Density of Mass Standards; Requirement and MethodThe Density of a Solid Object by Hydrostatic WeighingAn Efficient Method for Measuring the Density (or Volume) of Similar ObjectsReferencesCALCULATION OF THE DENSITY OF WATERIntroductionFormulations of Wagenbreth and BlankeKell's FormulationsConversion of IPTS-68 to ITS-90Redeterminations of Water DensityChange in Density of Water with Air SaturationDensity of Air-Saturated Water on ITS-90Compressibility-Corrected Water Density EquationEffect of Isotopic ConcentrationsEstimation of Uncertainty in Water Density Due to Variation in Isotopic ConcentrationsSummaryReferencesCONVENTIONAL MASS; CONCEPT, INTENT, BENEFITS, AND LIMITATIONSIntroductionConventional Value of Weighing in AirExamples of ComputationDiscussionExample 1Example 2Example 3Example 4ConclusionsReferencesA COMPARISON OF ERROR PROPAGATIONS FOR MASS AND CONVENTIONAL MASSIntroductionSteel Standard of Mass S and Density 7.950 g/cm3g/cm3 with a Stainless Steel Standard of Mass SMaximum Permissible Errors on VerificationUncertainty Trade-OffsSummary ReferencesEXAMINATION OF PARAMETERS THAT CAN CAUSE ERROR IN MASS DETERMINATIONSIntroductionMass ComparisonThe Fundamental Mass Comparison RelationshipUncertainties in the Determination of X Due to Uncertainties in the Parameters in Equation (17.2)Buoyancy Thermal EquilibiumAtmospheric EffectsMagnetic EffectsInstability of IPKCleaningConclusionsDiscussion ReferencesDETERMINATION OF THE MASS OF A PISTON-GAGE WEIGHT, PRACTICAL UNCERTAINTY LIMITSIntroductionAssignment of MassReferencesRESPONSE OF APPARENT MASS TO THERMAL GRADIENTS AND FREE CONVECTIVE CURRENTSThermal GradientsFree Convective CurrentsReferencesMAGNETIC ERRORS IN MASS METROLOGYIntroductionMagnetic ForceReferencesEFFECT OF GRAVITATIONAL CONFIGURATION OF WEIGHTS ON PRECISION OF MASS MEASUREMENTSIntroductionMagnitude of the Gravitational Configuration EffectSignificance of the Gravitational Configuration CorrectionReferencesBETWEEN-TIME COMPONENT OF ERROR IN MASS MEASUREMENTSIntroductionReferencesLABORATORY STANDARD OPERATING PROCEDURESIntroductionEnvironmental ControlsBalancesMass StandardsWeight CleaningWeighingStatistical SurveillanceRoutine BookkeepingReferenceCONTROL CHARTSIntroductionProcedureTypes of Control ChartsUpdating Control ChartsInterpretation of Control Chart TestsReference TOLERANCE TESTING OF MASS STANDARDSIntroductionPrerequisitesMethodologyProcedure--Option A, Use of Single-Pan BalanceProcedure--Option B, Use of Full Electronic BalanceProcedure--Option C, Use of Equal Arm BalanceTolerance EvaluationReferenceSURVEILLANCE TESTINGIntroduction Types of Surveillance TestsSurveillance LimitsSurveillance ChartsIdentification of Weights the Mass of Which Has ChangedReferencesTHE MASS UNIT DISSEMINATED TO SURROGATE LABORATORIES USING THE NIST PORTABLE MASS CALIBRATION PACKAGEIntroductionReviewThe Third PackageHardware and SoftwareThe MeasurementsDataAnalysisConclusionsReferencesHIGHLY ACCURATE DIRECT MASS MEASUREMENTS WITHOUT THE USE OF EXTERNAL STANDARDS IntroductionThe Force DetectorDiscussion of the MethodUncertaintiesBalance SelectionBalanceDiscussionDirection of Future Developments in Electronic Balances and Their UsesReferencesTHE PIGGYBACK BALANCE EXPERIMENT; AN ILLUSTRATION OF ARCHIMEDES' PRINCIPLE AND NEWTON'S THIRD LAWIntroductionThe Piggyback Thought Balance ExperimentThe Laboratory ExperimentConclusionReferencesTHE APPLICATION OF THE ELECTRONIC BALANCE IN HIGH PRECISION PYCNOMETRYIntroductionPycnometer CalibrationApparatusAnalysisDataDiscussionReferencesAPPENDICESBuoyancy Corrections in Weighing CourseExamination for Buoyancy Corrections in Weighing CourseAnswers for Examination for Buoyancy Corrections in Weighing CourseMaximum Permissible Errors (MPE)Minimum and Maximum Limits for Density of Weights Density and Coefficient of Linear Expansion for Pure Metals, Commercial Metals, and AlloysLinearity Test