Handbook of
MASS
MEASUREMENT
© 2002 by CRC Press LLC
CRC PRESS
Boca Raton London New York Washington, D.C.
Handbook of
MASS
MEASUREMENT
FRANK E. JONES
RANDALL M. SCHOONOVER
© 2002 by CRC Press LLC
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In addition, he was mentor to each of us and positively affected our careers.
Chapter 1 introduces mass and mass standards. Historical background material in Section 1.2 is an
excerpt from NBS monograph, “Mass and Mass Values,” by Paul E. Pontius, then chief of the U.S. NBS
section responsible for mass measurements.
Chapter 2 presents recalibration of the U.S. National Prototype Kilogram and the Third Periodic
Verification of National Prototypes of the Kilogram.
Chapter 3 discusses contamination of platinum-iridium mass standards and stainless steel mass stan-
dards. The literature is reviewed and summarized. Carbonaceous contamination, mercury contamina-
tion, water adsorption, and changes in ambient environmental conditions are studied, as are various
methods of analysis.
Cleaning of platinum-iridium mass standards and stainless steel mass standards are discussed in
Chapter 4, including the BIPM (Bureau International des Poids et Mesures) Solvent Cleaning and Steam
Washing procedure. Results of various cleaning methods are presented.
In Chapter 5, the determination of mass differences from balance observations is treated in detail.
In Chapter 6, a glossary of statistical terms that appear throughout the book is provided.
The U.S. National Institute of Standards and Technology (NIST) guidelines for evaluating and express-
ing the uncertainty of measurement results are presented in Chapter 7. The Type A and Type B evaluations
of standard uncertainty are illustrated.
In Chapter 8, weighing designs are discussed in detail. Actual data are used for making calculations.
© 2002 by CRC Press LLC
Calibration of the screen and the built-in weights of direct-reading analytical balances is described in
Chapter 9.
Chapter 10 takes a detailed look at the electronic balance. The two dominant types of electronic balance
in use are the hybrid balance and the electromagnetic force balance. Features and idiosyncrasies of the
balance are discussed.
In Chapter 11, buoyancy corrections and the application of buoyancy corrections to mass determina-
tion are discussed in detail. For illustration, the application of buoyancy corrections to weighings of
titanium dioxide powder in a weighing bottle on a balance is demonstrated.
The development of the air density equation for use in calculation of values of air density to be used
in making buoyancy corrections is presented in detail in Chapter 12. The development of the air density

In Chapter 20, magnetic errors in mass metrology, that is, unsuspected vertical forces that are magnetic
in origin, are discussed.
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The “gravitational configuration effect,” which arises because for weights of nominally equal mass the
distance of the center of gravity above the base of each weight depends on the size and shape of the
weight, is examined in Chapter 21.
In Chapter 22, the “between-time” component of error in mass measurements is examined. The
between-time component manifests itself between groups of measurements made at different times, on
different days, for example.
Chapter 23 illustrates the key elements for the most rigorous mass measurements.
In Chapter 24, control charts are developed and used to demonstrate attainment of statistical control
of a mass calibration process.
Tolerance testing of mass standards is discussed in Chapter 25. Procedures to be followed for deter-
mining whether or not mass standards are within the tolerances specified for a particular class of weights
are reviewed.
Surveillance testing of weights is discussed in Chapter 26. Surveillance looks for signs that one or more
members of a weight set may have changed since the latest calibration.
Chapter 27 describes a project to disseminate the mass unit to surrogate laboratories using the NIST
portable mass calibration package. A surrogate laboratories project began with the premise that a NIST-
certified calibration could be performed by the user in the user’s laboratory. The very informal, low-
budget project was undertaken to expose the technical difficulties that lay in the way.
In Chapter 28, the concept that the mass of an object can be adequately determined (for most
applications) by direct weighing on an electronic balance
without the use of external mass standards is
examined.
A piggyback balance experiment, an illustration of Archimedes’ principle and Newton’s third law, is
described in Chapter 29.
In Chapter 30, the application of the electronic balance in high-precision pycnometry is discussed and
illustrated.
The Appendices are Buoyancy Corrections in Weighing (a course); Examination for Buoyancy Cor-

was closely associated with mass and density metrology.
Since his retirement in 1995 he has continued to work
as a consultant and to publish scientific work. He
attended many schools and has a diploma for electronics
from Devry. During his career he authored and coau-
thored more than 50 scientific papers. His most notable
work was the development, along with his colleague
Horace A. Bowman, of the silicon density standard as
part of the determination of Avogadro’s constant; the
silicon density standard is now in use throughout the
world. He has several inventions and patents to his credit,
among them are the immersed electronic density balance and a unique high-precision load cell mass
comparator.
© 2002 by CRC Press LLC
We are pleased to dedicate this handbook to our wives
Virginia B. Jones and Caryl A. Schoonover.
© 2002 by CRC Press LLC
Contents
1
Mass and Mass Standards
1.1Introduction
1.1.1Definition of Mass
1.1.2The Mass Unit
1.1.3Mass Artifacts, Mass Standards
References
1.2The Roles of Mass Metrology in Civilization,
Paul E. Pontius
1.2.1The Role of Mass Measurement in Commerce
1.2.1.1Prior to the Metric System of Measurement Units
1.2.1.2The Kilogram and the Pound

3.1.1.4Conclusions
3.1.1.5Recommendations
3.1.2Progress of Contamination and Cleaning Effects
3.1.2.1Introduction
3.1.2.2Problems with Steam-Jet Cleaning
3.1.2.3Steam-Jet Cleaning Procedure
3.1.2.4Ultrasonic Cleaning with Solvents Procedure
3.1.2.5Results
3.1.3Effects of Changes in Ambient Humidity, Temperature, and Pressure on
“Apparent Mass” of Platinum-Iridium Prototype Mass Standards
3.1.3.1Introduction
3.1.3.2Experimental Procedures and Results
3.1.3.2.1Surface Effects in Ambient Conditions
3.1.3.2.2Reproducibility of Mass between Ambient Conditions
and Vacuum
3.1.4Evidence of Variations in Mass of Reference Kilograms Due to Mercury
Contamination
3.1.4.1Introduction
3.1.4.2Results
3.1.5Mechanism and Long-Term Effects of Mercury Contamination
3.1.5.1Introduction
3.1.5.2Results and Conclusions
3.1.5.3Recommendations
3.1.6Water Adsorption Layers on Metal Surfaces
3.1.6.1Introduction
3.1.6.2Experimental Procedures
3.1.6.3Results
3.2Stainless Steel Mass Standards
3.2.1Precision Determination of Adsorption Layers on Stainless Steel Mass
Standards— Introduction

4.2Solvent Cleaning and Steam Washing (
Nettoyage-Lavage)
4.2.1Solvent Cleaning
4.2.2Steam Washing
4.2.3Effect of Solvent Cleaning and Steam Washing
4.3Summaries of National Laboratory Studies Related to Cleaning
4.3.1Cleaning at National Physical Laboratory, United Kingdom (NPL)
4.3.2Cleaning at Institut National de Metrologie, France (INM)
4.3.3Cleaning at National Research Laboratory of Metrology, Japan (NRLM)
4.4Cleaning of Stainless Steel Mass Standards
4.4.1Cleaning Procedures Investigated by Weighing and Ellipsometry
4.4.1.1Cleaning Procedures
4.4.1.2Results
4.4.1.3Conclusions
4.4.2Cleaning of Stainless Steel Mass Standards at BIPM
4.4.3Cleaning of Stainless Steel Mass Standards at NIST
References
5
From Balance Observations to Mass Differences
5.1Introduction
5.2Determination of Mass Difference
References
6
Glossary of Statistical Terms
References
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7
Measurement Uncertainty
7.1Introduction
7.2NIST Guidlines

8.6.1Design A.1.2
8.6.2Design C.10
8.6.3Design 16
8.7Calculations of Various Values Associated with Design 16 and the 5-kg, 2-kg
1
, 2-kg
2
,
and 1-kg Weights
8.8Calculations of Various Values Associated with the A.1.2 Design Solution for the 1-kg
and
Σ1-kg Weights and 500 g through Σ100 g
8.8.150 g – 10 g NIST Data
8.8.25 g – 1 g NIST Data
8.8.30.5 g – 0.1 g NIST Data
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8.8.40.05 g – 0.01 g NIST Data
8.8.50.005 g – 0.001 g NIST Data
8.9Commentary
References
9
Calibration of the Screen and the Built-in Weights of a Direct-Reading
Analytical Balance
9.1Calibration of the Screen
9.2Calibration of the Built-in Weights
References
10
A Look at the Electronic Balance
10.1Introduction
10.2The Analytical Balance and the Mass Unit

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11.4The Electronic Analytical Balance
11.4.1Electronic Balance Calibration and Use
11.4.2Usual Case for Which the Air Density Is Not the Reference Value
11.5Examples of Effects of Failure to Make Buoyancy Corrections
11.6Other Examples of Buoyancy Correction
11.6.1Weighing of Syringes
11.6.2Buoyancy Applied to Weighing in Weighing Bottles
References
12
Air Density Equation
12.1Introduction
12.2Development of the Jones Air Density Equation
12.2.1Parameters in the Jones Air Density Equation
12.2.1.1Universal Gas Constant,
R
12.2.1.2Apparent Molecular Weight of Air, M
a
12.2.1.3Compressibility Factor, Z
12.2.1.4Ratio of the Molecular Weight of Water to the Molecular Weight
of Dry Air,
ε
12.2.1.5Effective Water Vapor Pressure, e
′
12.2.1.6Enhancement Factor, f
12.2.1.7Saturation Vapor Pressure of Water, e
s
12.2.1.8Carbon Dioxide Abundance, x
CO
2

12.2.3.2.3Products of the Partial Derivatives and the Estimates
of Standard Deviation, (∂ρ/∂Y
i
)·(SD
i
), for the
Environmental Quantities
12.2.4Use of Constant Values of F,Z, and M
a
in the Air Density Equation
12.3CIPM-81 Air Density Equation
12.4CIPM 1981/1991 Equation
12.5Recommendation
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12.6Direct Determination of Air Density
12.6.1Introduction
12.6.2Experimental Procedure
12.6.3Results and Conclusions
12.7Experimental Determination of Air Density in Weighing on a 1-kg Balance in Air
and in Vacuum
12.7.1Introduction
12.7.2Results and Conclusions
12.8A Practical Approach to Air Density Determination
12.8.1Introduction
12.8.2Air Density
12.8.2.1Temperature
12.8.2.2Melting Point of Ice
12.8.2.3Triple Point of Water
12.8.2.4Steam Point
12.8.2.5Relative Humidity

13.3Determination of Density of Mass Standards; Requirement and Method
13.3.1Introduction
13.3.2Requirements
13.3.3Principles and Applications
13.4The Density of a Solid by Hydrostatic Weighing
13.4.1The Force Detector
13.4.2Air Density
13.4.3Water Density
13.4.4A General Algorithm for Hydrostatic Weighing
13.4.5The General Hydrostatic Weighing Equations
13.4.5.1Air Weighing
13.4.5.2Water Weighing
13.4.6Linearity Test and Correction
13.4.7Analysis
13.4.8Balance Selection
13.4.9Data Results
13.4.10Conclusions
13.4.11Appendix 1 — Liquid Density by Hydrostatic Weighing
13.4.12Appendix 2 — Glassware Calibration
13.5An Efficient Method for Measuring the Density (or Volume) of Similar Objects
13.5.1Introduction
13.5.2The Requirement
13.5.3The Method
13.5.4The Measurement of Liquid Density
13.5.5Error Analysis
13.5.6Apparatus
13.5.7Data
13.5.8Conclusion
References
14

A Comparison of Error Propagations for Mass and Conventional Mass
16.1Conventional Value of the Result of Weighing in Air
16.2Uncertainties in Mass Determinations
16.3Uncertainties in the Determination of
m Due to Uncertainties in the Parameters
in Eq. (16.2)
16.3.1Balance Standard Deviation
16.3.2Application to R111
16.4Comparisons of Weights
16.4.1Comparison of a Stainless Steel E
1
Weight with a Stainless Steel Standard of
Mass S and Density 7.950 g/cm
3
16.4.2Error Propagation for Conventional Value of Weighing in Air
16.4.3Comparison of E
2
Weights with E
1
Weights
16.5Maximum Permissible Errors on Verification
16.6Uncertainty Trade-Offs
16.7Summary
References
17
Examination of Parameters That Can Cause Error in Mass Determinations
17.1Introduction
17.2Mass Comparison
17.3The Fundamental Mass Comparison Relationship
17.4Uncertainties in the Determination of X Due to Uncertainties in the Parameters

Magnetic Errors in Mass Metrology
20.1Introduction
20.2Magnetic Force
20.3Application of a Magnetic Force Equation
References
21
Effect of Gravitational Configuration of Weights on Precision of Mass
Measurements
21.1Introduction
21.2Magnitude of the Gravitational Configuration Effect
21.3Significance of the Gravitational Configuration Correction
References
22
Between-Time Component of Error in Mass Measurements
22.1Introduction
22.2Experimental
22.3Discussion.
References
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23
Laboratory Standard Operating Procedure and Weighing Practices
23.1Introduction
23.2Environmental Controls and Instrumentation
23.3Balances
23.4Mass Standards
23.5Weight Cleaning
23.6Weighing
23.7Balance Problems
23.7.1Balance Support
23.7.2Loading Errors

Tolerance Testing of Mass Standards
25.1Introduction
25.2Prerequisites
—
X
—
X
—
X
—
—
X
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25.3Methodology
25.3.1 Scope, Precision, Accuracy
25.3.2Summary
25.4Apparatus/Equipment
25.5Procedure — Option A, Use of Single-Pan Mechanical Balance
25.6Procedure — Option B, Use of Full-Electronic Balance
25.7Procedure — Option C, Use of Equal-Arm Balance
25.8Tolerance Evaluation
Reference
26
Surveillance Testing
26.1Introduction
26.2Types of Surveillance Tests
26.3Type I Test
26.4Surveillance Limits
26.5Surveillance Charts
26.6Identification of Weights Whose Mass Has Changed

Principle and Newton’s Third Law
29.1Introduction
29.2The Piggyback Thought Balance Experiment
29.3The Laboratory Experiment
29.4Experimental Results
29.5Conclusion
References
30
The Application of the Electronic Balance in High-Precision
Pycnometry
30.1Introduction
30.2Pycnometer Calibration
30.3Experimental Pycnometer Calibration
30.3.1Apparatus
30.3.1.1The Electronic Balance
30.3.1.2Pycnometer
30.3.1.3Constant-Temperature Water Bath
30.3.1.4Water Bath Temperature
30.3.2Air Density and Water Density
30.3.2.1Air Density
30.3.2.2Water Density
30.4Analysis
30.5Data
30.6Discussion
References
AppendixA
Buoyancy Corrections in Weighing Course
Appendix A.1:Examination for “Buoyancy Corrections in Weighing”
Course
Appendix A.2:Answers for Examination Questions for “Buoyancy

the kilogram is realized as an artifact, i.e., an object. Originally, the artifact was designed to have the mass of
1 cubic decimeter of pure water at the temperature of maximum density of water, 4°C. Subsequent determi-
nation of the density of pure water with the air removed at 4°C under standard atmospheric pressure
(101,325 pascals) yielded the present value of 1.000028 cubic decimeters for the volume of 1 kilogram of water.
1.1.3Mass Artifacts, Mass Standards
The present embodiment of the kilogram is based on the French platinum kilogram of the Archives
constructed in 1792. Several platinmum-iridium (Pt-Ir) cylinders of height equal to diameter and nom-
inal mass of 1 kg were manufactured in England. These cylinders were polished and adjusted and
compared with the kilogram of the Archives. The cylinder with mass closest to that of the kilogram of
the Archives was sent to the International Bureau of Weights and Measures (Bureau International des
Poids et Mesures, BIPM) in Paris and chosen as the International Prototype Kilogram (IPK) in 1883. It
was ratified as the IPK by the first General Conference of Weights and Measures (CPGM) in 1899. Other
prototype kilograms were constructed and distributed as national prototypes. The United States received
prototypes Nos. 4 and 20. All other mass standards in the United States are referred to these. As a matter
of practice, the unit of mass as maintained by the developed nations is interchangeable among them.
Figure 1.1 is a photograph of a building at BIPM, kindly provided by BIPM. Figure 1.2 is U.S. prototype
kilogram K20, Figure 1.3 is a collection of brass weights, Figure 1.4 is a stainless steel weight set, and Figure 1.5
is a collection of large stainless steel weights that, when assembled, become a deadweight force machine.
References
1. Condon, E. U. and Odishaw, H., Handbook of Physics, McGraw-Hill, New York, 1958, 2.
2. The Harper Encyclopedia of Science, Harper & Row, Evanston Sigma, New York, 1967, 223.
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1.2 The Roles of Mass Metrology in Civilization*
Paul E. Pontius
1.2.1 The Role of Mass Measurement in Commerce
1.2.1.1 Prior to the Metric System of Measurement Units
The existence of deliberate alloys of copper with lead for small ornaments and alloys of copper with
varying amounts of tin for a wide variety of bronzes implies an ability to make accurate measurements
with a weighing device ca. 3000
B

Mass Values, 1974, by Paul E. Pontius, who was at that time Head of the NBS Mass Group.
© 2002 by CRC Press LLC
or object used to verify the exactness of comparison could have been accepted by custom. Wealthy families,
early rulers, or governments may have fostered the development of ordered weight sets to account for
and protect their wealth. Measurement practices associated with collecting taxes in kind would likely be
adopted in all other transactions.
FIGURE 1.2 U.S. kilogram No. 20.
FIGURE 1.3 Brass weight set.
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FIGURE 1.4 Stainless steel weight set.
FIGURE 1.5 Large stainless steel weights that when assembled become a deadweight force machine.
© 2002 by CRC Press LLC