### Summary

"How much does it weigh?" seems a simple question. To scientists and engineers, however, the answer is far from simple, and determining the answer demands consideration of an almost overwhelming number of factors.

With an intriguing blend of history, fundamentals, and technical details, the Handbook of Mass Measurement sets forth the details of achieving the highest precision in mass measurements. It covers the whole field, from the development, calibration, and maintenance of mass standards to detailed accounts of weighing designs, balances, and uncertainty. It addresses the entire measurement process and provides in-depth examinations of the various factors that introduce error.

Much of the material is the authors' own work and some of it is published here for the first time. Jones and Schoonover are both highly regarded veterans of the U.S. National Institute of Standards and Technology. With this handbook, they have provided a service and resource vital to anyone involved not only in the determination of mass, but also to the entire field of precision measurement.

### Table of Contents

MASS AND MASS STANDARDS

Definition of Mass

The Mass Unit

Mass Artifacts, Mass Standards

References

Historical Background

Role of Measurement in Science

Footnotes

References

RECALIBRATION OF MASS STANDARDS

Recalibration of the U.S. National Prototype Kilogram

Third Periodic Verification of National Prototypes of the Kilogram

CONTAMINATION OF MASS STANDARDS

Introduction

Platinum-Iridium Standards

Stainless Steel Mass Standards

Mass Standards

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)

Summaries of National Laboratory Studies Related to Cleaning

Cleaning of Stainless Steel Mass Standards

References

FROM BALANCE OBSERVATIONS TO MASS DIFFERENCES

Introduction

Determination of Mass Difference

References

Introduction

Measurement

Mean, Arithmetic Mean, Average

Deviation

Standard Deviation, SD

Degrees of Freedom, DF

Population

Sample

Population Standard Deviation

Variance

Random Sample

Normal Distribution of Measurements

Concept of a Limiting Mean

Central Limit Theorem

Student's t

F Test

Other Pertinent Terms

Bibliography

Reference

MEASUREMENT UNCERTAINTY

Introduction

NIST Guidelines

Example of Determination of Uncertainty

References

WEIGHING DESIGNS

Introduction

Least Squares

Sequences

Observation Multipliers for Determining Mass Values and Deviations

Factors for Computing Weight Standard Deviation Needed for Uncertainty Calculations

Calculations of Various Values Associated with Design 16 and the 5-kg, 2-kg, 2-kg2, and 1-kg Weights

Calculations of Various Values Associated with the A.1.2 Design Solution for the 1-kg and ?1-kg Weights

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

A Closer Look at Electronic Balances

Benefits and Idiosyncrasies of Electronic Balances

Black Box Comparison

The Future

References

BUOYANCY CORRECTIONS IN WEIGHING

Introduction

Buoyant Force and Buoyancy Correction

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

The Electronic Analytical Balance

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

References

AIR DENSITY EQUATION

Introduction

Development of the Jones Air Density Equation

Weight of Dry Air

CIPM-81 Air Density Equation

CIPM 1981/1991 Equation

Recommendation

Direct Determination of Air Density

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

A Practical Approach to Air Density Determination

Test of Air Density Equation at Differing Altitude

References

DENSITY OF SOLID OBJECTS

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

Principles of Use of the Submersible Balance

Determination of Density of Mass Standards; Requirement and Method

The Density of a Solid Object by Hydrostatic Weighing

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

References

CALCULATION OF THE DENSITY OF WATER

Introduction

Formulations of Wagenbreth and Blanke

Kell's Formulations

Conversion of IPTS-68 to ITS-90

Redeterminations of Water Density

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 MASS; CONCEPT, INTENT, BENEFITS, AND LIMITATIONS

Introduction

Conventional Value of Weighing in Air

Examples of Computation

Discussion

Example 1

Example 2

Example 3

Example 4

Conclusions

References

A COMPARISON OF ERROR PROPAGATIONS FOR MASS AND CONVENTIONAL MASS

Introduction

Steel Standard of Mass S and Density 7.950 g/cm3

g/cm3 with a Stainless Steel Standard of Mass S

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 Equation (17.2)

Buoyancy

Thermal Equilibium

Atmospheric Effects

Magnetic Effects

Instability of IPK

Cleaning

Conclusions

Discussion

References

DETERMINATION OF THE MASS OF A PISTON-GAGE WEIGHT, PRACTICAL UNCERTAINTY LIMITS

Introduction

Assignment of Mass

References

RESPONSE OF APPARENT MASS TO THERMAL GRADIENTS AND FREE CONVECTIVE CURRENTS

Thermal Gradients

Free Convective Currents

References

MAGNETIC ERRORS IN MASS METROLOGY

Introduction

Magnetic Force

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

References

LABORATORY STANDARD OPERATING PROCEDURES

Introduction

Environmental Controls

Balances

Mass Standards

Weight Cleaning

Weighing

Statistical Surveillance

Routine Bookkeeping

Reference

CONTROL CHARTS

Introduction

Procedure

Types of Control Charts

Updating Control Charts

Interpretation of Control Chart Tests

Reference

TOLERANCE TESTING OF MASS STANDARDS

Introduction

Prerequisites

Methodology

Procedure--Option A, Use of Single-Pan 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

Surveillance Limits

Surveillance Charts

Identification of Weights the Mass of Which 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

Balance

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

Conclusion

References

THE APPLICATION OF THE ELECTRONIC BALANCE IN HIGH PRECISION PYCNOMETRY

Introduction

Pycnometer Calibration

Apparatus

Analysis

Data

Discussion

References

APPENDICES

Buoyancy Corrections in Weighing Course

Examination for Buoyancy Corrections in Weighing Course

Answers for Examination for Buoyancy Corrections in Weighing Course

Maximum Permissible Errors (MPE)

Minimum and Maximum Limits for Density of Weights

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

Linearity Test

### Reviews

"This book will clearly become the definitive reference source for all those concerned with measurement of mass, whether in basic science, engineering, or commerce. It encapsulates a unique range of practical experience that has not been recorded before."

-David R. Lide, Former Director, Standard Reference data, NIST and Editor-in-Chief of the CRC Handbook of Chemistry and Physics

From David Lide, Former Director, NIST and Editor-in-Chief of the CRC Handbook of Chemistry and Physics:

"Weights and measures may be ranked among the necessaries of life … They are necessary to every occupation of human industry; to the distribution and security of every species of property … The kn

owledge of them, as in established use, is among the first elements of education, and is often learned by those who learn nothing else, not even to read and write. This knowledge is riveted in the memory by the habitual application of it to employments of men throughout life."

-John Quincy Adams, 1821