![17
Chapter one: Fundamentals of measurement
Planck’s blackbody radiation formula
u
h
c
v e
hv
kT
= −
−
8
1
3
3
1
π
(1.12)
In studying the energy density of radiation in a cavity, Max Planck compared two
approximate formulas, one for low frequency and another for high frequency. In 1900,
using an ingenious extrapolation, he found his equation for the energy density of black-
body radiation, which reproduced experimental results. Seeking to understand the signifi-
cance of his formula, he discovered the relation between energy and frequency known as
Planck–Einstein equation.
Hawking equation for black hole temperature
T
hc
GMk
BH =
3
8π
(1.13)
Using insights from thermodynamics, relativist quantum mechanics, and Einstein’s
gravitational theory, Stephen Hawking predicted in 1974 the surprising result that gravita-
tional black holes, which are predicted by general relativity, would radiate energy. His for-
mula for the temperature of the radiating black hole depends on the gravitational constant,
Planck’s constant, the speed of light, and Boltzmann’s constant. While Hawking radiation
remains to be observed, his formula provides a tempting glimpse of the insights that will
be uncovered in a unified theory combining quantum mechanics and gravity.
Navier–Stokes equation for a fluid
ρ ρ µ λ µ ρ
∂
∂
+ ⋅ ∇ = −∇ + ∇ + + ∇ ∇ ⋅ +
v
t
v v p v v g
( ) ( ) ( )
2
(1.14)
The Navier–Stokes equation was derived in the nineteenth century from Newtonian
mechanics to model viscous fluid flow. Its nonlinear properties make it extremely difficult
to solve, even with modern analytic and computational technique. However, its solutions
describe a rich variety of phenomena including turbulence.
Lagrangian for quantum chromodynamics
L F F i gA t m
QDC a
v
a v f
f
a a f f
= − ⋅ + ∇ − −
∑
1
4
µ
µ Ψ Ψ
[ ] (1.15)
Relativistic quantum field theory had its first great success with quantum electro-
dynamics, which explains the interaction of charged particles with the quantized elec-
tromagnetic field. Exploration of non-Abelian gauge theories led next to the spectacular
unification of the electromagnetic and weak interactions. Then, with insights developed
from the quark model, quantum chromodynamics was developed to explain the strong
interactions. This theory predicts that quarks are bound more tightly together as their
separation increases, which explains why individual quarks are not seen directly in exper-
iments. The standard model, which incorporates strong, weak, and electromagnetic inter-
actions into a single quantum field theory, describes the interaction of quarks, gluons,
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T i t l e: Notes and Queries, Vol. V, Number 120, February 14,
1852
A u t h o r: Various
E d i t o r: George Bell
R e l e a s e d a t e: September 13, 2012 [eBook #40743]
Most recently updated: October 23, 2024
L a n g u a g e: English
C r e d i t s: Produced by Charlene Taylor, Jonathan Ingram and
the Online
Distributed Proofreading Team at http://www.pgdp.net
(This
file was produced from images generously made
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by The Internet Library of Early Journals.)
*** START OF THE PROJECT GUTENBERG EBOOK NOTES AND
QUERIES, VOL. V, NUMBER 120, FEBRUARY 14, 1852 ***](https://image.slidesharecdn.com/2635274-250522065112-5cdddb83/85/Handbook-Of-Measurements-Benchmarks-For-Systems-Accuracy-And-Precision-Badiru-60-320.jpg)
![St. John, xviii. 27., where the ἀλεκτοροφωνία of the original is the
cantus galli of the Vulgate, and where Petrus represents the pope,
who is aroused to resipiscere by the example of his predecessor St.
Peter.
This incident in the memorable assembly is adverted to in the
French contemporary letters and memoirs, but more particularly in
the subsequent publication of a learned member of Danes's family,
La Vie, Eloges et Opuscules de Pierre Danes, par P. Hilaire Danes,
Paris, 1731, 4to., with the the portrait of the Tridentine deputy, who
became Bishop of Lavaur, in Languedoc (now département du
Saone), and preceptor to Francis, the short-lived husband of Mary
Stuart, before that prince's ascent to the throne. So high altogether
was he held in public estimation, that he was supposed well entitled
to the laudatory anagram formed of his name (Petrus Danesius), De
superis natus.
In the Council of Trent there only appeared two Englishmen,
Cardinal Pole and Francis Gadwell,[1]
Bishop of St. Asaph, with three
Irish prelates, (1) Thomas Herliky, Bishop of Ross, called Thomas
Overlaithe in the records of the Council; (2) Eugenius O'Harte, there
named Ohairte, a Dominican friar, Bishop of Ardagh; and (3) Donagh
MacCongal, Bishop of Raphoe: Sir James Ware adds a fourth, Robert
Waucup, or Vincentius, of whom, however, I find no mention in the
official catalogue of the assisting prelates. Deprived of sight,
according to Ware, from his childhood, he yet made such proficiency
in learning, that, after attaining the high degree of Doctor of
Sorbonne in France, he was appointed Archbishop of Armagh, or
Primate of Ireland; but of this arch-see he never took possession, it
being held by a reformed occupant, Dr. George Dowdall, appointed
by Henry VIII. in 1543.
[1]
[Query, Thomas Goldwell.]
J. R. (Cork.)
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- 5. Handbook of Measurements Benchmarks for Systems Accuracy and Precision © 2016 by Taylor & Francis Group, LLC
- 6. Industrial Innovation Series Series Editor Adedeji B. Badiru Air Force Institute of Technology (AFIT) – Dayton, Ohio PUBLISHED TITLES Carbon Footprint Analysis: Concepts, Methods, Implementation, and Case Studies, Matthew John Franchetti & Defne Apul Cellular Manufacturing: Mitigating Risk and Uncertainty, John X. Wang Communication for Continuous Improvement Projects, Tina Agustiady Computational Economic Analysis for Engineering and Industry, Adedeji B. Badiru & Olufemi A. Omitaomu Conveyors: Applications, Selection, and Integration, Patrick M. McGuire Culture and Trust in Technology-Driven Organizations, Frances Alston Global Engineering: Design, Decision Making, and Communication, Carlos Acosta, V. Jorge Leon, Charles Conrad, & Cesar O. Malave Handbook of Emergency Response: A Human Factors and Systems Engineering Approach, Adedeji B. Badiru & LeeAnn Racz Handbook of Industrial Engineering Equations, Formulas, and Calculations, Adedeji B. Badiru & Olufemi A. Omitaomu Handbook of Industrial and Systems Engineering, Second Edition Adedeji B. Badiru Handbook of Military Industrial Engineering, Adedeji B. Badiru & Marlin U. Thomas Industrial Control Systems: Mathematical and Statistical Models and Techniques, Adedeji B. Badiru, Oye Ibidapo-Obe, & Babatunde J. Ayeni Industrial Project Management: Concepts, Tools, and Techniques, Adedeji B. Badiru, Abidemi Badiru, & Adetokunboh Badiru Inventory Management: Non-Classical Views, Mohamad Y. Jaber Global Manufacturing Technology Transfer: Africa-USA Strategies, Adaptations, and Management, Adedeji B. Badiru Kansei Engineering - 2-volume set • Innovations of Kansei Engineering, Mitsuo Nagamachi & Anitawati Mohd Lokman • Kansei/Affective Engineering, Mitsuo Nagamachi Kansei Innovation: Practical Design Applications for Product and Service Development, Mitsuo Nagamachi & Anitawati Mohd Lokman Knowledge Discovery from Sensor Data, Auroop R. Ganguly, João Gama, Olufemi A. Omitaomu, Mohamed Medhat Gaber, & Ranga Raju Vatsavai Learning Curves: Theory, Models, and Applications, Mohamad Y. Jaber Managing Projects as Investments: Earned Value to Business Value, Stephen A. Devaux Modern Construction: Lean Project Delivery and Integrated Practices, Lincoln Harding Forbes & Syed M. Ahmed Moving from Project Management to Project Leadership: A Practical Guide to Leading Groups, R. Camper Bull Project Management: Systems, Principles, and Applications, Adedeji B. Badiru Project Management for the Oil and Gas Industry: A World System Approach, Adedeji B. Badiru & Samuel O. Osisanya © 2016 by Taylor & Francis Group, LLC
- 7. Quality Management in Construction Projects, Abdul Razzak Rumane Quality Tools for Managing Construction Projects, Abdul Razzak Rumane Social Responsibility: Failure Mode Effects and Analysis, Holly Alison Duckworth & Rosemond Ann Moore Statistical Techniques for Project Control, Adedeji B. Badiru & Tina Agustiady STEP Project Management: Guide for Science, Technology, and Engineering Projects, Adedeji B. Badiru Sustainability: Utilizing Lean Six Sigma Techniques, Tina Agustiady & Adedeji B. Badiru Systems Thinking: Coping with 21st Century Problems, John Turner Boardman & Brian J. Sauser Techonomics: The Theory of Industrial Evolution, H. Lee Martin Total Project Control: A Practitioner’s Guide to Managing Projects as Investments, Second Edition, Stephen A. Devaux Triple C Model of Project Management: Communication, Cooperation, Coordination, Adedeji B. Badiru FORTHCOMING TITLES 3D Printing Handbook: Product Development for the Defense Industry, Adedeji B. Badiru & Vhance V. Valencia Company Success in Manufacturing Organizations: A Holistic Systems Approach, Ana M. Ferreras & Lesia L. Crumpton-Young Design for Profitability: Guidelines to Cost Effectively Management the Development Process of Complex Products, Salah Ahmed Mohamed Elmoselhy Essentials of Engineering Leadership and Innovation, Pamela McCauley-Bush & Lesia L. Crumpton-Young Global Manufacturing Technology Transfer: Africa-USA Strategies, Adaptations, and Management, Adedeji B. Badiru Guide to Environment Safety and Health Management: Developing, Implementing, and Maintaining a Continuous Improvement Program, Frances Alston & Emily J. Millikin Handbook of Construction Management: Scope, Schedule, and Cost Control, Abdul Razzak Rumane Handbook of Measurements: Benchmarks for Systems Accuracy and Precision, Adedeji B. Badiru & LeeAnn Racz Introduction to Industrial Engineering, Second Edition, Avraham Shtub & Yuval Cohen Manufacturing and Enterprise: An Integrated Systems Approach, Adedeji B. Badiru, Oye Ibidapo-Obe & Babatunde J. Ayeni Project Management for Research: Tools and Techniques for Science and Technology, Adedeji B. Badiru, Vhance V. Valencia & Christina Rusnock Project Management Simplified: A Step-by-Step Process, Barbara Karten A Six Sigma Approach to Sustainability: Continual Improvement for Social Responsibility, Holly Allison Duckworth & Andrea Hoffmeier Zimmerman Total Productive Maintenance: Strategies and Implementation Guide, Tina Agustiady & Elizabeth A. Cudney PUBLISHED TITLES © 2016 by Taylor & Francis Group, LLC
- 8. © 2016 by Taylor & Francis Group, LLC
- 9. Handbook of Measurements Benchmarks for Systems Accuracy and Precision Edited by Adedeji B. Badiru and LeeAnn Racz © 2016 by Taylor & Francis Group, LLC
- 10. CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2016 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20150501 International Standard Book Number-13: 978-1-4822-2523-5 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid- ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or uti- lized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopy- ing, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
- 11. To Deleeville, for the inspiration and motivation for this work © 2016 by Taylor & Francis Group, LLC
- 12. © 2016 by Taylor & Francis Group, LLC
- 13. ix Contents Preface............................................................................................................................................ xiii Acknowledgments.........................................................................................................................xv Editors...........................................................................................................................................xvii Contributors.................................................................................................................................. xix Chapter 1 Fundamentals of measurement..............................................................................1 Adedeji B. Badiru Chapter 2 Human factors measurement................................................................................41 Farman A. Moayed Chapter 3 Measurements of environmental health............................................................79 LeeAnn Racz and Dirk Yamamoto Chapter 4 Measurement of environmental contamination...............................................93 Stuart A. Willison, Matthew L. Magnuson, Adrian S. Hanley, and David W. Nehrkorn Chapter 5 Measurement of land............................................................................................117 Justin D. Delorit Chapter 6 Measuring building performance.....................................................................133 Steven J. Schuldt Chapter 7 Energy systems measurements..........................................................................151 Olufemi A. Omitaomu Chapter 8 Economic systems measurement........................................................................181 LeeAnn Racz Chapter 9 Measurement and quantum mechanics...........................................................189 David E. Weeks Chapter 10 Social science measurement................................................................................203 John J. Elshaw Chapter 11 Systems interoperability measurement............................................................217 Thomas C. Ford © 2016 by Taylor & Francis Group, LLC
- 14. x Contents Chapter 12 A generalized measurement model to quantify health: The multiattribute preference response model......................................................239 Paul F. M. Krabbe Chapter 13 Evolution of large-scale dimensional metrology from the viewpoint of scientific articles and patents.....................................................261 Fiorenzo Franceschini, Domenico Maisano, and Paola Pedone Chapter 14 Gaussian-smoothed Wigner function and its application to precision analysis.................................................................................................277 Hai-Woong Lee Chapter 15 Measurement issues in performance-based logistics....................................287 Kenneth Doerr, Donald R. Eaton, and Ira A. Lewis Chapter 16 Data processing and acquisition systems........................................................303 Livio Conti, Vittorio Sgrigna, David Zilpimiani, and Dario Assante Chapter 17 Part A: Visualization of big data: Current trends..........................................315 Isaac J. Donaldson, Sandra C. Hom, Thomas Housel, Johnathan Mun, and Trent Silkey Chapter 18 Part B: Visualization of big data: Ship maintenance metrics analysis......331 Isaac J. Donaldson, Sandra C. Hom, Thomas Housel, Johnathan Mun, and Trent Silkey Chapter 19 Defining and measuring the success of services contracts...........................371 Patrick Hagan, Joseph Spede, and Trisha Sutton Chapter 20 Measurement of personnel productivity: During government furlough programs...............................................................................................403 Adedeji B. Badiru Chapter 21 Measurement risk analysis.................................................................................421 Adedeji B. Badiru Chapter 22 Data modeling for forecasting............................................................................447 Adedeji B. Badiru Chapter 23 Mathematical measurement of project parameters for multiresource control......................................................................................................................471 Adedeji B. Badiru Chapter 24 Measurement and control of imprecision in engineering design...............491 Ronald E. Giachetti Chapter 25 Fuzzy measurements in systems modeling.....................................................511 Adedeji B. Badiru © 2016 by Taylor & Francis Group, LLC
- 15. xi Contents Chapter 26 Using metrics to manage contractor performance..........................................527 R. Marshall Engelbeck Chapter 27 Low-clutter method for bistatic RCS measurement.......................................543 Peter J. Collins Appendix A: Measurement references and conversion factors............................................551 Appendix B: Measurement equations and formulas.............................................................. 561 Appendix C: Slides of statistics for measurement...................................................................587 Index..............................................................................................................................................687 © 2016 by Taylor & Francis Group, LLC
- 16. © 2016 by Taylor & Francis Group, LLC
- 17. xiii Preface Planning, measurement, and attention to detail form the basis for success in engineering operations. Measurements pervade everything we do and must be viewed from a systems perspective. Using a systems framework, The Handbook of Measurements: Benchmarks for Systems Accuracy, presents a comprehensive guide to everything about measurement. Its technically rigorous approach to systems linking of measurements sets it apart from other handbooks. The broad approach of the handbook covers both qualitative and quantitative topics of measurement. Of particular benefit is the inclusion of human-centric measure- ments such as measurement of personnel productivity and contractor performance. The handbook opens with a chapter on the fundamentals of measurement. It is well understood that humans cannot manage anything that cannot be measured. All elements involved in our day-to-day decision making involve some forms of measurement. Measuring an attri- bute of a system and then analyzing it against some standard, specification, best practice, or benchmark empowers a decision maker to take appropriate and timely actions. Fundamentally, measurement is the act, or the result of a quantitative comparison between a predefined standard and an unknown magnitude. This handbook uses a sys- tems view of measurement to link all aspects. For example, one chapter in the handbook addresses systems interoperability measurement, which further illustrates how the ele- ments of any large complex system interoperate to accomplish a desired end goal. Other chapters in the handbook include human factors measurements for work system analysis, measurements of environmental health, measurement of environmental contamination, measurements of land, measuring building performance, energy systems measurements, economic systems measurements, measurement and quantum mechanics, social science measurement, a measurement model to quantify health, large-scale dimensional metrol- ogy, performance-based logistics, data processing, visualization of big data, maintenance metrics analysis, measuring success of services contracts, measurement of personnel pro- ductivity, measurement risk analysis, data modeling for forecasting, measurements from archival observational data, reduction of measurement imprecision, measurements in ergonomics studies, metrics to manage contractor performance, and a low-clutter method for bistatic radar cross-section measurements. The handbook concludes with three appen- dices on measurement references, conversion factors, equations, formulas, and statistics for measurement. Adedeji B. Badiru and LeeAnn Racz © 2016 by Taylor & Francis Group, LLC
- 18. © 2016 by Taylor & Francis Group, LLC
- 19. xv Acknowledgments We gratefully acknowledge the contributions and support of all those who played a part in the writing of this book. Special thanks go to Ms. Annabelle Sharp for her responsiveness and dedication to the needs and challenges of typing and organizing the complex manu- script. We also appreciate the editorial and organizational support provided by Richard D. Cook and Thomas M. Dickey in the initial draft of the book. We gratefully acknowledge the extraordinary contributions of Ms. Anna E. Maloney, who pored over the galley proofs to ensure that all final t’s are crossed and all final i’s are dotted. Her keen sense of technical review positively impacted the overall quality of the handbook. © 2016 by Taylor & Francis Group, LLC
- 20. © 2016 by Taylor & Francis Group, LLC
- 21. xvii Editors Adedeji B. Badiru is the dean and senior academic officer for the Graduate School of Engineering and Management at the Air Force Institute of Technology (AFIT). He is responsible for planning, directing, and controlling all operations related to granting doctoral and master’s degrees, professional continuing cyber education, and research and development programs. Previously, Deji Badiru was professor and head of Systems Engineering and Management at AFIT (Air Force Institute of Technology), professor and head of the Department of Industrial & Information Engineering at the University of Tennessee in Knoxville, and professor of industrial engineering and dean of University College at the University of Oklahoma, Norman. He is a registered professional engi- neer (PE), a certified project management professional (PMP), a Fellow of the Institute of Industrial Engineers, and a Fellow of the Nigerian Academy of Engineering. He holds a BS in industrial engineering, an MS in mathematics, and an MS in industrial engineering from Tennessee Technological University, and a PhD in industrial engineering from the University of Central Florida. His areas of interest include mathematical modeling, sys- tems efficiency analysis, and high-tech product development. He is the author of over 30 books, 35 book chapters, 75 technical journal articles, and 115 conference proceedings and presentations. He has also published 30 magazine articles and 20 editorials and periodi- cals to his credit. He is a member of several professional associations and scholastic honor societies. Dr. Badiru has won several awards for his teaching, research, and professional accomplishments. LeeAnn Racz is a bioenvironmental engineering flight commander at RAF Lakenheath, United Kingdom. She previously served as an assistant professor of environmental engi- neering and director of the Graduate Environmental Engineering and Science Program in the Systems & Engineering Management at the Air Force Institute of Technology. She currently holds the rank of Lieutenant Colonel in the US Air Force. Her other assignments have taken her to the US Air Force School of Aerospace Medicine, San Antonio, Texas; the US Air Force Academy, Colorado Springs, Colorado; Peterson Air Force Base, Colorado Springs, Colorado; Osan Air Base, South Korea; and Cannon Air Force Base, Clovis, New Mexico. She is a registered professional engineer (PE), certified industrial hygienist, and board-certified environmental engineer. She holds a BS in environmental engineering from California Polytechnic State University (San Luis Obispo), an MS in biological and agricultural engineering from the University of Idaho, and a PhD in civil and environmen- tal engineering from the University of Utah. Her areas of interest include characterizing the fate of chemical warfare agents and pollutants of emerging concern in the natural and engineered environments, environmental health issues, and using biological reactors to treat industrial waste. Dr. Racz has authored dozens of refereed journal articles, conference proceedings, magazine articles, and presentations, and one handbook. She is a member © 2016 by Taylor & Francis Group, LLC
- 22. xviii Editors of several professional associations and honor societies. Dr. Racz has received numerous awards such as the 2014 Air Education and Training Command Military Educator of the Year Award, the 2014 Military Officers Association of America Educator of the Year Award, the 2012 Southwestern Ohio Council for Higher Education Teaching Excellence Award, and was the 2011 Faculty Scholar of the Year for the Department of Systems and Engineering Management. She is also the 2014 recipient of the Air Force Meritorious Service Medal (one oak leaf cluster) and Air Force Commendation Medal (three oak leaf clusters). © 2016 by Taylor & Francis Group, LLC
- 23. xix Dario Assante University Uninettuno Rome, Italy Adedeji B. Badiru Department of Systems Engineering and Management Air Force Institute of Technology Dayton, Ohio Peter J. Collins Department of Electrical and Computer Engineering Air Force Institute of Technology Dayton, Ohio Livio Conti University Uninettuno Rome, Italy Justin D. Delorit Civil Engineer School Air Force Institute of Technology Dayton, Ohio Kenneth Doerr Graduate School of Business and Public Policy Naval Postgraduate School Monterey, California Isaac J. Donaldson U.S. Navy Naval Computer and Telecommunications Station Naples Naples, Italy Donald R. Eaton Graduate School of Business and Public Policy Naval Postgraduate School Monterey, California John J. Elshaw Department of Systems Engineering and Management Air Force Institute of Technology Dayton, Ohio R. Marshall Engelbeck Graduate School of Business and Public Policy Naval Postgraduate School Monterey, California Thomas C. Ford Department of Systems Engineering and Management Air Force Institute of Technology Dayton, Ohio Fiorenzo Franceschini Politecnico di Torino Department of Management and Production Engineering University of Turin Turin, Italy Ronald E. Giachetti Department of Systems Engineering Naval Postgraduate School Monterey, California Contributors © 2016 by Taylor & Francis Group, LLC
- 24. xx Contributors Patrick Hagan Graduate School of Business and Public Policy Naval Postgraduate School Monterey, California Adrian S. Hanley U.S. Environmental Protection Agency Office of Water Washington, DC Sandra C. Hom Department of Information Science Naval Postgraduate School Monterey, California Thomas Housel Department of Information Science Graduate School of Operational and Information Sciences Naval Postgraduate School Monterey, California Paul F. M. Krabbe Department of Epidemiology University of Groningen Groningen, the Netherlands Hai-Woong Lee Department of Physics Korea Advanced Institute of Science and Technology (KAIST) Daejeon, Korea Ira A. Lewis Graduate School of Business and Public Policy Naval Postgraduate School Monterey, California Matthew L. Magnuson U.S. Environmental Protection Agency Washington, DC Domenico Maisano Politecnico di Torino Department of Management and Production Engineering University of Turin Turin, Italy Farman A. Moayed Department of the Built Environment Indiana State University Terre Haute, Indiana Johnathan Mun Department of Information Science Naval Postgraduate School Monterey, California David W. Nehrkorn Redwood City, California Olufemi A. Omitaomu Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak Ridge, Tennessee Paola Pedone Department of Calibration Laboratories Accredia Turin, Italy LeeAnn Racz Department of Systems Engineering and Management Air Force Institute of Technology Dayton, Ohio Steven J. Schuldt Department of Systems Engineering and Management Air Force Institute of Technology Dayton, Ohio Vittorio Sgrigna Department of Mathematics and Physics University of Rome Tre Rome, Italy Trent Silkey Graduate School of Business and Public Policy Naval Postgraduate School Monterey, California © 2016 by Taylor & Francis Group, LLC
- 25. xxi Contributors Joseph Spede Graduate School of Business and Public Policy Naval Postgraduate School Monterey, California Trisha Sutton Graduate School of Business and Public Policy Naval Postgraduate School Monterey, California David E. Weeks Department of Engineering Physics Air Force Institute of Technology Dayton, Ohio Stuart A. Willison U.S. Environmental Protection Agency Washington, DC Dirk Yamamoto Department of Systems Engineering and Management Air Force Institute of Technology Dayton, Ohio David Zilpimiani National Institute of Geophysics Georgian Academy Sciences Tbilisi, Georgia © 2016 by Taylor & Francis Group, LLC
- 26. 1 chapter one Fundamentals of measurement Adedeji B. Badiru Contents 1.1 Introduction.............................................................................................................................2 1.2 What is measurement?...........................................................................................................3 1.3 The dawn and present of measurement..............................................................................3 1.3.1 The English system...................................................................................................4 1.3.2 The metric system.....................................................................................................5 1.3.3 The SI system.............................................................................................................6 1.3.4 Length.........................................................................................................................7 1.3.5 Weight.........................................................................................................................7 1.3.6 Volume........................................................................................................................7 1.3.7 Time............................................................................................................................7 1.3.7.1 Sundial and water clock............................................................................8 1.3.7.2 Origin of the hour......................................................................................8 1.3.7.3 Minutes and seconds: Fourteenth to sixteenth century.......................9 1.3.8 Hero’s Dioptra............................................................................................................9 1.3.9 Barometer and atmospheric pressure....................................................................9 1.3.10 Mercury thermometer............................................................................................ 10 1.3.11 The chronometer..................................................................................................... 11 1.3.12 Sextant...................................................................................................................... 11 1.3.13 Ancient measurement systems in Africa............................................................12 1.3.13.1 Lebombo bone (35,000 bc).......................................................................12 1.3.13.2 Ishango bone (20,000 bc)..........................................................................13 1.3.13.3 Gebet’a or “Mancala” game (700 bc-present).......................................13 1.3.14 “Moscow” papyrus (2000 bc)................................................................................ 14 1.3.15 “Rhind” mathematical papyrus (1650 bc)........................................................... 14 1.3.16 Timbuktu mathematical manuscripts (1200s ad).............................................. 14 1.3.17 Fundamental scientific equations......................................................................... 14 1.4 Fundamental methods of measurement...........................................................................19 1.4.1 Direct comparison..................................................................................................19 1.4.2 Indirect comparison...............................................................................................19 1.5 Generalized mechanical measuring system.....................................................................20 1.6 Data types and measurement scales..................................................................................21 1.6.1 Nominal scale of measurement............................................................................21 1.6.2 Ordinal scale of measurement..............................................................................21 1.6.3 Interval scale of measurement..............................................................................21 1.6.4 Ratio scale measurement.......................................................................................21 1.7 Common units of measurements.......................................................................................22 1.7.1 Common constants.................................................................................................23 © 2016 by Taylor & Francis Group, LLC
- 27. 2 Handbook of Measurements 1.1 Introduction Throughout history, humans have strived to come up with better tools, techniques, and instruments for measurement. From the very ancient times to the present fast-paced soci- ety, our search for more precise, more convenient, and more accessible measuring devices has led to new developments over the years. The following quotes confirm the importance and efficacy of measurements in our lives. Appendix A presents the most common mea- surement conversion factors. Measure twice, cut once English Proverb Where there is no Standard there can be no Kaizen (improvement) Taiichi Ohno Where there is no measurement, there can be no standard Adedeji Badiru Measurement mitigates mess-ups Adedeji Badiru Measurement pervades everything we do; this applies to technical, management, and social activities and requirements. Even in innocuous situations such as human lei- sure, the importance of measurement comes to the surface; for example, how much, how far, how good, how fast, and how long are typical expressions of some sort of measure- ment. Consider a possible newspaper-classified advertisement that provides the following measurement disclaimer: The acceptable units of measure for all firewood advertisement are cord or fraction of a cord. The units of measurements for a cord are 4″ by 4″ by 8″. The terms face cord, rack, pile, rick, truckload or simi- lar terms are not acceptable. 1.7.2 Measurement numbers and exponents...............................................................24 1.8 Patterns of numbers in measurements..............................................................................24 1.9 Statistics in measurement....................................................................................................26 1.10 Data determination and collection.....................................................................................26 1.11 Data analysis and presentation...........................................................................................29 1.11.1 Raw data...................................................................................................................29 1.11.2 Total revenue...........................................................................................................30 1.11.3 Average revenue......................................................................................................31 1.11.4 Median revenue......................................................................................................33 1.11.5 Quartiles and percentiles......................................................................................34 1.11.6 The mode..................................................................................................................35 1.11.7 Range of revenue....................................................................................................35 1.11.8 Average deviation...................................................................................................35 1.11.9 Sample variance......................................................................................................36 1.11.10 Standard deviation.................................................................................................37 1.12 Conclusion.............................................................................................................................38 References........................................................................................................................................40 © 2016 by Taylor & Francis Group, LLC
- 28. 3 Chapter one: Fundamentals of measurement Who would have thought that firewood had such a serious measurement constraint and guideline? Social, psychological, physical, economic, cognitive, and metabolic attri- butes, as well as other human characteristics, are all amenable to measurement systems just as the mechanical devices around us. 1.2 What is measurement? It is well understood that we cannot manage anything if we cannot measure it. All elements involved in our day-to-day decision making involve some form of measurement. Measuring an attribute of a system and then analyzing it against some standard, some best practice, or some benchmark empowers a decision maker to take appropriate and timely actions. Fundamentally, measurement is the act or the result of a quantitative comparison between a predefined standard and an unknown magnitude. Beckwith and Buck (1965), Shillito and De Marle (1992), Morris (1997), Badiru et al. (2012), and Badiru and Kovach (2012) all address concepts, tools, and techniques of measurement systems. If the result is to be generally meaningful, two requirements must be met in the act of measurement: 1. The standard, which is used for comparison, must be accurately known and com- monly accepted. 2. The procedure and instrument employed for obtaining the comparison must be provable and repeatable. The first requirement is that there should be an accepted standard of comparison. A weight cannot simply be heavy. It can only be proportionately as heavy as something else, namely the standard. A comparison must be made, and unless it is made relative to something generally recognized as standard, the measurement can only have a limited meaning; this holds for any quantitative measurement we may wish to make. In general, the comparison is of magnitude, and a numerical result is presupposed. The quantity in question may be twice or 1.4 times as large as the standard, or in some other ratio, but a numerical comparison must be made for it to be meaningful. The typical characteristics of a measurement process include the following • Precision • Accuracy • Correlation • Stability • Linearity • Type of data 1.3 The dawn and present of measurement Weights and measures may be ranked among the necessaries of life to every individual of human society. They enter into the economical arrangements and daily concerns of every family. They are necessary to every occupation of human industry; to the distribution and secu- rity of every species of property; to every transaction of trade and com- merce; to the labors of the husbandman; to the ingenuity of the artificer; to the studies of the philosopher; to the researches of the antiquarian; to the navigation of the mariner, and the marches of the soldier; to all © 2016 by Taylor & Francis Group, LLC
- 29. 4 Handbook of Measurements the exchanges of peace, and all the operations of war. The knowledge 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 the employments of men throughout life. John Quincy Adams Report to the Congress, 1821 The historical accounts of measurements presented in this section are based mostly on NIST (1974), HistoryWorld (2014), and TANF (2014). Weights and measures were among the earliest tools invented by man. Primitive societies needed rudimentary measures for many tasks, such as house and road construction and commerce of raw materials. Man, in early years, used parts of the human body and the natural surroundings as device-measuring standards. Early Babylonian and Egyptian records and the Bible indicate that length was first measured with the foot, forearm, hand, or finger; time was measured by the periods of the sun, moon, and other heavenly bodies. When it was necessary to compare the capaci- ties of containers such as gourds, clay, or metal vessels, they were filled with plant seeds that were then counted to measure volumes. With the development of scales as a means of weighing, seeds and stones served as standards. For instance, the “carat,” still used as a mass unit for gems, is derived from the carob seed. As societies evolved, measurements became more complex. The invention of number- ing systems and the science of mathematics made it possible to create whole systems of measurement units suitable for trade and commerce, land division, taxation, and scientific research. For these more sophisticated uses, it was necessary to not only weigh and mea- sure more complex items, but it was also necessary to do it accurately and repeatedly at different locations. With the limited international exchange of goods and communication of ideas in ancient times, different measuring systems evolved for the same measures and became established in different parts of the world. In ancient times, different parts of the same country might use different measuring systems for the same purpose. Historical records indicate that early measurement systems evolved locally in Africa to take advan- tage of the African natural environment. For example, common early units of measure, in some parts of Africa relied on standardizations based on the cocoa bean sizes and weights. 1.3.1 The English system The measurement system commonly used in the United States today is nearly the same as that brought by the American colony settlers from England. These measures had their origins in a variety of cultures, including Babylonian, Egyptian, Roman, Anglo-Saxon, and Nordic French. The ancient “digit,” “palm,” “span,” and “cubic” units of length slowly lost preference to the length units, “inch,” “foot,” and “yard.” Roman contributions include the use of 12 as a base number and the words from which we derive many of the modern names of measurement units. For example, the 12 divisions of the Roman “pes,” or foot were called “unciae.” The “foot,” as a unit of measuring length is divided into 12 in. The common words “inch” and “ounce” are both derived from Latin words. The “yard” as a measure of length can be traced back to early Saxon kings. They wore a sash or girdle around the waist that could be removed and used as a convenient measuring device. Thus, the word “yard” comes from the Saxon word “gird,” which represents the circumference of a person’s waist, preferably a “standard person,” such as a king. © 2016 by Taylor & Francis Group, LLC
- 30. 5 Chapter one: Fundamentals of measurement Evolution and standardization of measurement units often had interesting origins. For example, it was recorded that King Henry I decreed that a yard should be the distance from the tip of his nose to the end of his outstretched thumb. The length of a furlong (or furrow- long) was established by early Tudor rulers as 220 yards, this led Queen Elizabeth I to declare in the sixteenth century that the traditional Roman mile of 5000 ft would be replaced by one of the 5280 ft, making the mile exactly 8 furlongs and providing a convenient relationship between the furlong and the mile. To this day, there are 5280 ft in 1 mile, which is 1760 yards. Thus, through royal edicts, England by the eighteenth century had achieved a greater degree of standardization than other European countries. The English units were well suited to com- merce and trade because they had been developed and refined to meet commercial needs. Through English colonization and its dominance of world commerce during the seventeenth, eighteenth, and nineteenth centuries, the English system of measurement units became estab- lished in many parts of the world, including the American colonies. The early 13 American colonies, however, had undesirable differences with respect to measurement standards for commerce. The need for a greater uniformity led to clauses in the Articles of Confederation (ratified by the original colonies in 1781) and the Constitution of the United States (ratified in 1788) that gave Congress the power to fix uniform standards for weights and measures across the colonies. Today, standards provided by the U.S. National Institute of Standards and Technology (NIST) ensure uniformity of measurement units throughout the country. 1.3.2 The metric system The need for a single worldwide coordinated measurement system was recognized over 300 years ago. In 1670, Gabriel Mouton, vicar of St. Paul’s Church in Lyons, France, and an astrono- mer, proposed a comprehensive decimal measurement system based on the length of 1 arc- min of a great circle of the Earth. Mouton also proposed the swing length of a pendulum with a frequency of 1 beat/s as the unit of length. A pendulum with this beat would have been fairly easily reproducible, thus facilitating the widespread distribution of uniform standards. In 1790, in the midst of the French Revolution, the National Assembly of France requested the French Academy of Sciences to “deduce an invariable standard for all the measures and all the weights.” The Commission appointed by the Academy created a system that was, at once, simple and scientific. The unit of length was to be a portion of the Earth’s circumfer- ence. Measures for capacity (volume) and mass were to be derived from the unit of length, thus relating the basic units of the system to each other and nature. Furthermore, larger and smaller multiples of each unit were to be created by multiplying or dividing the basic units by 10 and powers of 10. This feature provided a great convenience to users of the system by elimi- nating the need for such calculations as dividing by 16 (to convert ounces to pounds) or by 12 (to convert inches to feet). Similar calculations in the metric system could be performed simply by shifting the decimal point. Thus, the metric system is a “base-10” or “decimal” system. The Commission assigned the name metre (i.e., meter in English) to the unit of length. This name was derived from the Greek word metron, meaning “a measure.” The physical standard representing the meter was to be constructed so that it would equal one 10 mil- lionth of the distance from the North Pole to the equator along the meridian running near Dunkirk in France and Barcelona in Spain. The initial metric unit of mass, the “gram,” was defined as the mass of 1 cm3 (a cube that is 0.01 m on each side) of water at its tem- perature of maximum density. The cubic decimeter (a cube 0.1 m on each side) was chosen as the unit of capacity. The fluid volume measurement for the cubic decimeter was given the name “liter.” Although the metric system was not accepted with much enthusiasm at first, adoption by other nations occurred steadily after France made its use compulsory © 2016 by Taylor & Francis Group, LLC
- 31. 6 Handbook of Measurements in 1840. The standardized structure and decimal features of the metric system made it well suited for scientific and engineering work. Consequently, it is not surprising that the rapid spread of the system coincided with an age of rapid technological development. In the United States, by Act of Congress in 1866, it became “lawful throughout the United States of America to employ the weights and measures of the metric system in all contracts, dealings or court proceedings.” However, the United States has remained a hold-out with respect to a widespread adoption of the metric system. Previous attempts to standardize to the metric system in the United States have failed. Even today, in some localities of the United States, both English and metric systems are used side by side. As an illustration of dual usage of measuring systems, a widespread news report in late September 1999 reported how the National Aeronautics and Space Administration (NASA) lost a $125 million Mars orbiter in a crash onto the surface of Mars because a Lockheed Martin engineering team used the English units of measurement while the agency’s team used the more conventional metric system for a key operation of the space- craft. The unit’s mismatch prevented navigation information from transferring between the Mars Climate Orbiter spacecraft team at Lockheed Martin in Denver and the flight team at NASA’s Jet Propulsion Laboratory in Pasadena, California. Therefore, even at such a high-stakes scientific endeavor, nonstandardization of measuring units can create havoc. Getting back to history, the late 1860s saw the need for even better metric standards to keep pace with scientific advances. In 1875, an international agreement, known as the Meter Convention, set up well-defined metric standards for length and mass and estab- lished permanent mechanisms to recommend and adopt further refinements in the metric system. This agreement, commonly called the “Treaty of the Meter” in the United States, was signed by 17 countries, including the United States. As a result of the treaty, metric standards were constructed and distributed to each nation that ratified the Convention. Since 1893, the internationally adopted metric standards have served as the fundamental measurement standards of the United States, at least, in theory if not in practice. By 1900, a total of 35 nations, including the major nations of continental Europe and most of South America, had officially accepted the metric system. In 1960, the General Conference on Weights and Measures, the diplomatic organization made up of the signa- tory nations to the Meter Convention, adopted an extensive revision and simplification of the system. The following seven units were adopted as the base units for the metric system: 1. Meter (for length) 2. Kilogram (for mass) 3. Second (for time) 4. Ampere (for electric current) 5. Kelvin (for thermodynamic temperature) 6. Mole (for amount of substance) 7. Candela (for luminous intensity) 1.3.3 The SI system Based on the general standardization described above, the name Système International d’Unités (International SystemofUnits),withtheinternationalabbreviationSI,wasadopted for the modern metric system. Throughout the world, measurement science research and development continue to develop more precise and easily reproducible ways of defining measurement units. The working organizations of the General Conference on Weights and Measures coordinate the exchange of information about the use and refinement of the © 2016 by Taylor & Francis Group, LLC
- 32. 7 Chapter one: Fundamentals of measurement metric system and make recommendations concerning improvements in the system and its related standards. Our daily lives are mostly ruled or governed by the measurements of length, weight, volume, and time. These are briefly described in the following sections. 1.3.4 Length The measurement of distance, signified as length, is the most ubiquitous measurement in our world. The units of length represent how we conduct everyday activities and transactions. The two basic units of length measurement are the British units (inch, foot, yard, and mile) and the metric system (meters, kilometers). In its origin, anatomically, the inch is a thumb. The foot logically references the human foot. The yard relates closely to a human pace, but also derives from two cubits (the measure of the forearm). The mile originates from the Roman mille passus, which means a thousand paces. The ancient Romans defined a pace as two steps. Therefore, approximately, a human takes two paces within one yard. The average human walking speed is about 5 kilometers per hour (km/h), or about 3.1 miles per hour (mph). For the complex measuring problems of ancient civilization—surveying the land to register property rights, or selling a commodity by length—a more precise unit was required. The solution was a rod or bar of an exact length, which was kept in a central public place. From this “standard” other identical rods could be copied and distributed through the community. In Egypt and Mesopotamia, these standards were kept in tem- ples. The basic unit of length in both civilizations was the cubit, based on the measurement of a forearm from the elbow to the tip of the middle finger. When a length such as this is standardized, it is usually the king’s dimension, which is first taken as the norm. 1.3.5 Weight For measurements of weight, the human body does not provide convenient approxima- tions as for length. Compared to other grains, grains of wheat are reasonably standard in size. Weight can be expressed with some degree of accuracy in terms of a number of grains of wheat. The use of grains to convey weight is still used today in the measurement of precious metals, such as gold, by jewelers. As with measurements of length, a block of metal was kept in the temples as an official standard for a given number of grains. Copies of this were cast and weighed in the balance for perfect accuracy. However, imperfect human integrity in using scales made it necessary to have an inspectorate of weights and measures for practical adjudication of measurements in the olden days. 1.3.6 Volume From the ancient time of trade and commerce to the present day, a reliable standard of volume is one of the hardest to accomplish. However, we improvise by using items from nature and art. Items such as animal skins, baskets, sacks, or pottery jars could be made to approximately consistent sizes, such that they were sufficient for measurements in ancient measurement transactions. Where the exact amount of any commodity needs to be known, weight is the measure more likely to be used instead of volume. 1.3.7 Time Time is a central aspect of human life. Throughout human history, time has been appreci- ated in very precise terms. Owing to the celestial preciseness of day and night, the day © 2016 by Taylor & Francis Group, LLC
- 33. 8 Handbook of Measurements and the week are easily recognized and recorded. However, an accurate calendar for a year is more complicated to achieve universally. The morning time before midday (fore- noon) is easily distinguishable from the time after midday (afternoon), provided the sun is shining, and the position of the sun in the landscape can reveal roughly how much of the day has passed. In contrast, the smaller units of time, such as hours, minutes, and seconds, were initially (in ancient times) unmeasurable and unneeded. Unneeded because the ancient man had big blocks of time to accomplish whatever was needed to be done. Microallocation of time was, thus, not essential. However, in our modern society, the min- ute (tiny) time measurements of seconds and minutes are very essential. The following reprinted poem by the coeditor conveys the modern appreciation of the passage of time: The Flight of Time What is the speed and direction of Time? Time flies; but it has no wings. Time goes fast; but it has no speed. Where has time gone? But it has no destination. Time goes here and there; but it has no direction. Time has no embodiment. It neither flies, walks, nor goes anywhere. Yet, the passage of time is constant. Adedeji Badiru 2006 1.3.7.1 Sundial and water clock The sundial and water clock originated in the second millennium bc. The movement of the sun through the sky makes possible a simple estimate of time, from the length and posi- tion of a shadow cast by a vertical stick. If marks were made where the sun’s shadow fell, the time of day could be recorded in a consistent manner. The result was the invention of sundial. An Egyptian example survives from about 800 bc, but records indicate that the principle was familiar to astronomers of earlier times. Practically, it is difficult to measure time precisely on a sundial because the sun’s path through the sky changes with the sea- sons. Early attempts at precision in timekeeping, relied on a different principle known as the water clock. The water clock, known from a Greek word as the clepsydra, attempted to measure time by the amount of water that dripped from a tank. This would have been a reliable form of the clock if the flow of water could be controlled perfectly. In practice, at that time, it could not. The hourglass, using sand on the same principle, had an even longer history and utility. It was a standard feature used in the eighteenth-century pulpits in Britain to ensure a sermon of standard and sufficient duration. 1.3.7.2 Origin of the hour The hour, as a unit of time measurement, originated in the fourteenth century. Until the arrival of clockwork, in the fourteenth century ad, an hour was a variable concept. It is a practical division of the day into 12 segments (12 being the most convenient number for dividing into fractions, since it is divisible by 2, 3, and 4). For the same reason 60, divisible by 2, 3, 4, and 5, has been a larger framework of measurement ever since the Babylonian times. The traditional concept of the hour, as one-twelfth of the time between dawn and dusk, was useful in terms of everyday timekeeping. Approximate appointments could be made easily, at times that could be easily sensed. Noon is always the sixth hour. Half way through the afternoon is the ninth hour. This is famous as the time of the death of Jesus on © 2016 by Taylor & Francis Group, LLC
- 34. 9 Chapter one: Fundamentals of measurement the Cross. The trouble with the traditional hour is that it differs in length from day to day. In addition, a daytime hour is different from one in the night (also divided into 12 equal hours). A clock cannot reflect this variation, but it can offer something more useful. It can provide every day something, which occurs naturally only twice a year, at the spring and autumn equinox, when the 12 h of the day and the 12 h of the night are of the same lengths. In the fourteenth century, coinciding with the first practical clocks, the meaning of an hour gradually changed. It became a specific amount of time, one twenty-fourth of a full solar cycle from dawn to dawn. Today, the day is recognized as 24 h, although it still features on clock faces as two twelves. 1.3.7.3 Minutes and seconds: Fourteenth to sixteenth century Minutes and seconds, as we know them today, originated in the fourteenth to the sixteenth centuries. Even the first clocks could measure periods less than an hour, but soon striking the quarter-hours seemed insufficient. With the arrival of dials for the faces of clocks, in the fourteenth century, something like a minute was required. The Middle Ages inherited a scale of scientific measurement based on 60 from Babylon. In Medieval Latin, the unit of one-sixtieth is pars minuta prima (“first very small part”), and a sixtieth of that is pars minute secunda (“second very small part”). Thus, based on a principle that is 3000 years old, min- utes and seconds find their way into our modern time. Minutes were mentioned from the fourteenth century onward, but clocks were not precise enough for “seconds” of time to be needed until two centuries later. 1.3.8 Hero’s Dioptra Hero’s Dioptra was written in the first century ad. One of the surviving books of Hero of Alexandria, titled On the Dioptra, describes a sophisticated technique, which he had developed for surveying land. Plotting the relative position of features in a landscape, essential for any accurate map, is a more complex task than simply measuring distances. It is necessary to discover accurate angles in both the horizontal and vertical planes. To make this possible, a surveying instrument must somehow maintain both planes consistently in different places, to take readings of the deviation in each plane between one location and another. This is what Hero achieved with the instrument mentioned in his title, the dioptra, which approximately means, the “spyhole,” through which the surveyor looks when pin- pointing the target in order to read the angles. For his device, Hero adapted an instrument long used by Greek astronomers (e.g., Hipparchus) for measuring the angle of stars in the sky. In his days, Hero achieved his device without the convenience of two modern inven- tions, the compass and the telescope. 1.3.9 Barometer and atmospheric pressure Barometer and atmospheric pressure originated between 1643 and 1646. Like many sig- nificant discoveries, the principle of the barometer was observed by accident. Evangelista Torricelli, assistant to Galileo at the end of his life, was interested in knowing why it is more difficult to pump water from a well in which the water lies far below ground level. He suspected that the reason might be the weight of the extra column of air above the water, and he devised a way of testing this theory. He filled a glass tube with mercury; submerging it in a bath of mercury and raising the sealed end to a vertical position, he found that the mercury slipped a little way down the tube. He reasoned that the weight of air on the mercury in the bath was supporting the weight of the column of mercury in © 2016 by Taylor & Francis Group, LLC
- 35. 10 Handbook of Measurements the tube. If this was true, then the space in the glass tube above the mercury column must be a vacuum. This rushed him into controversy with traditional scientists of the day, who believed nature abhorred a vacuum. However, it also encouraged von Guericke, in the next decade, to develop the vacuum pump. The concept of variable atmospheric pressure occurred to Torricelli when he noticed, in 1643, that the height of his column of mercury sometimes varied slightly from its normal level, which was 760 mm above the mercury level in the bath. Observation suggested that these variations related closely to changes in the weather. This was the origin of the barometer. With the concept thus establishing that the air had weight, Torricelli was able to predict that there must be less atmospheric pressure at higher altitudes. In 1646, Blaise Pascal, aided by his brother-in-law, carried a barometer to different levels of the 4000-feet mountain Puy de Dôme, near Clermont, to take readings. The confirmation was that atmospheric pressure varied with altitude. 1.3.10 Mercury thermometer The mercury thermometer originated ca. between 1714 and 1742. Gabriel Daniel Fahrenheit, a German glass blower and instrument maker working in Holland, was interested in improving the design of thermometer that had been in use for half a century. Known as the Florentine thermometer, because it was developed in the 1650s in Florence’s Accademia del Cimento, this pioneering instrument depended on the expansion and contraction of alcohol within a glass tube. Alcohol expands rapidly with a rise in temperature but not at an entirely regular speed of expansion. This made accurate readings difficult, as also did the sheer technical problem of blowing glass tubes with very narrow and entirely consis- tent bores. By 1714, Fahrenheit had made great progress on the technical front, creating two separate alcohol thermometers, which agreed precisely in their reading of tempera- ture. In that year, he heard about the research of a French physicist, Guillaume Amontons, into the thermal properties of mercury. Mercury expands less than alcohol (about 7 times less for the same rise in temperature), but it does so in a more regular manner. Fahrenheit saw the advantage of this regularity, and he had the glass-making skills to accommodate the smaller rate of expansion. He constructed the first mercury thermometer that, sub- sequently, became a standard. There remained the problem of how to calibrate the ther- mometer to show degrees of temperature. The only practical method was to choose two temperatures, which could be established independently, mark them on the thermometer, and divide the intervening length of tube into a number of equal degrees. In 1701, Sir Isaac Newton had proposed the freezing point of water for the bottom of the scale and the temperature of the human body for the top end. Fahrenheit, accustomed to Holland’s cold winters, wanted to include temperatures below the freezing point of water. He, therefore, accepted blood temperature for the top of his scale but adopted the freezing point of salt water for the lower extreme. Measurement is conventionally done in multiples of 2, 3, and 4, therefore, Fahrenheit split his scale into 12 sections, each of them divided into 8 equal parts. This gave him a total of 96°, zero being the freezing point of brine and 96° as an inaccurate estimate of the average temperature of the human blood. Actual human body temperature is 98.6°. With his ther- mometer calibrated on these two points, Fahrenheit could take a reading for the freezing point (32°) and boiling point (212°) of water. In 1742, a Swede, Anders Celsius, proposed an early example of decimalization. His centigrade scale took the freezing and boiling temper- atures of water as 0° and 100°, respectively. In English-speaking countries, this less compli- cated system took more than two centuries to be embraced. Yet even today, the Fahrenheit unit of temperature is more prevalent in some countries, such as the United States. © 2016 by Taylor & Francis Group, LLC
- 36. 11 Chapter one: Fundamentals of measurement 1.3.11 The chronometer The chronometer was developed ca. 1714–1766. Two centuries of ocean travel made it important for ships on naval or merchant business to be able to calculate their positions accurately in any of the oceans in the world. With the help of the simple and ancient astro- labe, the stars would reveal latitude. However, on a revolving planet, longitude is harder. It was essential to know what time it was before it could be determined what place it was. The importance of this was made evident in 1714 when the British government set up a Board of Longitude and offered a massive prize of £20,000, at that time, to any inventor who could produce a clock capable of keeping accurate time at sea. The terms were demanding. To win the prize, a chronometer must be sufficiently accurate to calculate longitude within thirty nautical miles at the end of a journey to the West Indies. This meant that in rough seas, damp salty conditions, and sudden changes of temperature, the instrument must lose or gain not more than three seconds a day. This was a level of accuracy unmatched at the time by the best clocks. The challenge appealed to John Harrison, who was at the time a 21-year-old Lincolnshire carpenter with an interest in clocks. It was nearly 60 years before he could win the money. Luckily, he lived long enough to collect it. By 1735, Harrison had built the first chronometer, which he believed approached the necessary standard. Over the next quarter-century, he replaced it with three improved models before formally undergoing the government’s test. His innovations included bearings that reduce friction, weighted balances interconnected by coiled springs to minimize the effects of movement, and the use of two metals in the balance spring to cope with expansion and contraction caused by changes of temperature. Harrison’s first “sea clock,” in 1735, weighed 72 lb and was 3 ft in all dimensions. His fourth, in 1759, was more like a watch, being circular and 5 in. in diameter. It was this version that underwent the sea trials. Harrison was at that time 67 years old. Therefore, his son, took the chronometer on its test journey to Jamaica in 1761. It was 5 s slow at the end of the voyage. The government argued that this might be a fluke and offered Harrison only £2500. After further trials and the successful building of a Harrison chronometer by another craftsman (at the huge cost of £450), the inventor was finally paid the full prize money in 1773. Harrison had proved in 1761 what was possible, but his chronometer was an elaborate and expensive way of achieving the purpose. It was in France, where a large prize was also on offer from the Académie des Sciences, that the practical chronometer of the future was developed. The French trial, open to all comers, took place in 1766 on a voyage from Le Havre in a specially commissioned yacht, the Aurore. The only chronometer ready for the test was designed by Pierre Le Roy. At the end of 46 days, his machine was accurate to within 8 s. Le Roy’s timepiece was larger than Harrison’s final model, but it was much easier to construct. It provided the pattern of the future. With further modifications from various sources over the next two decades, the marine chronometer emerged before the end of the eighteenth century. Using it in combination with the sextant, explorers traveling the world’s oceans could then bring back accurate information of immense value to the makers of maps and charts of the world. 1.3.12 Sextant The sextant originated between 1731 and 1757. The eighteenth-century search for a way of discovering longitude was accompanied by refinements in the ancient method of estab- lishing latitude. This had been possible since the second century bc by means of the astrolabe. From the beginning of the European voyages in the fifteenth century, practical © 2016 by Taylor & Francis Group, LLC
- 37. 12 Handbook of Measurements improvements had been made to the astrolabe, mainly by providing more convenient cali- brated arcs on which the user could read the number of degrees of the sun or a star above the horizon. The size of these arcs was defined in relation to the full circle. A quadrant (a quarter of the circle) showed 90°, a sextant 60°, and an octant 45°. The use of such arcs in conjunction with the traditional astrolabe is evident from a text dating back to 1555 that reported about voyaging to the West Indies. The author wrote on “quadrant and astro- labe, instruments of astronomy.” The important development during the eighteenth cen- tury was the application of optical devices (mirrors and lenses) to the task of working out angles above the horizon. Slightly differing solutions, by instrument makers in Europe and America, competed during the early decades of the century. The one that prevailed, mainly because it was more convenient at sea, was designed as an octant in 1731 by John Hadley, an established English maker of reflecting telescopes. Hadley’s instrument, like others designed by his contemporaries, used mirrors to bring any two points into align- ment in the observer’s sight line. For the navigator at that time, these two points would usually be the sun and the horizon. To read the angle of the sun, the observer looked through the octant’s eyepiece at the horizon and then turned an adjusting knob until the reflected sphere of the sun (through a darkened glass) was brought down to the same level. The double reflection meant that the actual angle of the sun above the horizon was twice that on the octant’s arc of 45°. Therefore, Hadley’s instrument could read angles up to 90°. In 1734, Hadley added an improvement, which became the standard, by installing an additional level so that the horizontal could be found even if the horizon was not visible. In 1757, after Hadley’s death, a naval captain proposed that the arc in the instrument can be extended from 45° to 60°, making a reading up to 120° possible. With this, Hadley’s octant became a sextant, and the instrument has been in general use since then. 1.3.13 Ancient measurement systems in Africa Africa is home to the world’s earliest known use of measuring and calculation, confirming the continent as the origin of both basic and advanced mathematics. Thousands of years ago, while parallel developments were going on in Europe, Africans were using rudimen- tary numerals, algebra, and geometry in daily life. This knowledge spread throughout the entire world after a series of migrations out of Africa, beginning around 30,000 bc and later following a series of invasions of Africa by Europeans and Asians (1700 bc-present). It is historically documented that early man migrated out of Africa to Europe and Asia. This feat of early travel and navigation could have been facilitated by the indigenous measure- ment systems of ancient Africa. The following sections recount measuring and counting in ancient Africa. 1.3.13.1 Lebombo bone (35,000 bc) The oldest known mathematical instrument is the Lebombo bone, a baboon fibula used as a measuring device and so named after its location of discovery in the Lebombo moun- tains of Swaziland. The device is at least 35,000 years old. Judging from its 29 distinct markings, it could have been either used to track lunar cycles or used as a measuring stick. It is rather interesting to note the significance of the 29 markings (roughly the same num- ber as lunar cycle, i.e., 29.531 days) on the baboon fibula because it is the oldest indication that the baboon, a primate indigenous to Africa, was symbolically linked to Khonsu, who was also associated with time. The Kemetic god, Djehuty (“Tehuti” or “Toth”), was later depicted as a baboon or an ibis, which is a large tropical wading bird with a long neck and long legs. This animal symbolism is usually associated with the moon, math, writing, © 2016 by Taylor & Francis Group, LLC
- 38. 13 Chapter one: Fundamentals of measurement and science. The use of baboon bones as measuring devices had continued throughout Africa, suggesting that Africans always held the baboon as sacred and associated it with the moon, math, and time. 1.3.13.2 Ishango bone (20,000 bc) The world’s oldest evidence of advanced mathematics was also a baboon fibula that was discovered in the present-day Democratic Republic of Congo and dates to at least 20,000 bc. The bone is now housed in the Museum of Natural Sciences in Brussels. The Ishango bone is not merely a measuring device or tally stick as some people erroneously suggest. The bone’s inscriptions are clearly separated into clusters of markings that represent various quantities. When the markings are counted, they are all odd numbers with the left column containing all prime numbers between 10 and 20 and the right column containing added and subtracted numbers. When both columns are calculated, they add up to 60 (nearly double the length of the lunar cycle). We recall that the number 60 also featured promi- nently in the development of early measuring devices in Europe. 1.3.13.3 Gebet’a or “Mancala” game (700 bc-present) Although the oldest known evidence of the ancient counting board game, Gebet’a or “Mancala” as it is more popularly known, comes from Yeha (700 bc) in Ethiopia, it was probably used in Central Africa many years prior to that. The game forced players to strategically capture a greater number of stones than one’s opponent. The game usually consists of a wooden board with two rows of six holes each and two larger holes at either end. However, in antiquity, the holes were more likely to be carved into stone, clay, or mud. More advanced versions found in Central and East Africa, such as the Omweso, Igisoro, and Bao, usually involve four rows of eight holes each. A variant of this counting game still exists today in the Yoruba culture of Nigeria. It is called “Ayo” game, which tests the counting and tracking ability of players. A photograph of a modern Yoruba Ayo game board from coeditor Adedeji Badiru’s household is shown in Figure 1.1. Notice the row of six holes on each player’s side, with a master counting hole above the row. Figure 1.1 Nigerian Yoruba Ayo game board (for counting). (Photo courtesy of Adedeji Badiru family, 2014.) © 2016 by Taylor & Francis Group, LLC
- 39. 14 Handbook of Measurements This example and other similar artifacts demonstrated the handed-down legacy of ancient counting in Africa. 1.3.14 “Moscow” papyrus (2000 bc) Housed in Moscow’s Pushkin State Museum of Fine Arts, what is known as “Moscow” papyrus was purchased by Vladimir Golenishchev sometime in the 1890s. Written in hier- atic from perhaps the 13th dynasty in Kemet, the name of ancient Egypt, the papyrus is one of the world’s oldest examples of the use of geometry and algebra. The document con- tains approximately 25 mathematical problems, including how to calculate the length of a ship’s rudder, the surface area of a basket, the volume of a frustum (a truncated pyramid), and various ways of solving for unknowns. 1.3.15 “Rhind” mathematical papyrus (1650 bc) Purchased by Alexander Rhind in 1858 ad, the so-called “Rhind” Mathematical Papyrus dates to approximately 1650 bc and is presently housed in the British Museum. Although some Egyptologists link this to the foreign Hyksos, this text was found during excavations at the Ramesseum in Waset (Thebes) in Southern Egypt, which never came under Hyksos’ rule. The first page contains 20 arithmetic problems, including addition and multiplication of fractions, and 20 algebraic problems, including linear equations. The second page shows how to calculate the volume of rectangular and cylindrical granaries, with pi (Π) esti- mated at 3.1605. There are also calculations for the area of triangles (slopes of a pyramid) and an octagon. The third page continues with 24 problems, including the multiplication of algebraic fractions, among others. 1.3.16 Timbuktu mathematical manuscripts (1200s ad) Timbuktu in Mali is well known as a hub of commerce in ancient times. Timbuktu is home to one of the world’s oldest universities, Sankore, which had libraries full of manuscripts mainly written in Ajami (African languages, such as Hausa in this case, written in a script similar to “Arabic”) in the 1200s ad. When Europeans and Western Asians began visiting and colonizing Mali from the 1300s to 1800s ad, Malians began to hide the manuscripts. Many of the scripts were mathematical and astronomical in nature. In recent years, as many as 700,000 scripts have been rediscovered and attest to the continuous knowledge of advanced mathematics, science, and measurements in Africa, well before European colonization. 1.3.17 Fundamental scientific equations This section presents some of the seminal and fundamental theoretical scientific equations that have emerged over the centuries. Perhaps the most quoted and recognized in the modern scientific literature is Einstein’s equation. Einstein’s equation E mc = 2 (1.1) The fundamental relationship connecting energy, mass, and the speed of light emerges from Einstein’s theory of special relativity, published in 1905. Showing the equivalence of mass and energy, it may be the most famous and beautiful equation in all of modern © 2016 by Taylor & Francis Group, LLC
- 40. 15 Chapter one: Fundamentals of measurement science. Its power was graphically demonstrated less than four decades later with the dis- covery of nuclear fission, a process in which a small amount of mass is converted to a very large amount of energy, precisely in accord with this equation. Einstein’s field equation R g R g GT v v v v µ µ µ µ π − + = 1 2 8 Λ (1.2) Einstein’s elegant equation published in 1916 is the foundation of his theory of gravity, the theory of general relativity. The equation relates the geometrical curvature of space− time with the energy density of matter. The theory constructs an entirely new picture of space and time, out of which gravity emerges in the form of geometry and from which Newton’s theory of gravity emerges as a limiting case. Einstein’s field equation explains many features of modern cosmology, including the expansion of the universe and the bending of star light by matter, and it predicts black holes and gravitational waves. He introduced a cosmological constant in the equation, which he called his greatest blunder, but that quantity may be needed if, as recent observations suggest, the expansion of the universe is accelerating. A remaining challenge for physicists in the twenty-first century is to produce a fundamental theory uniting gravitation and quantum mechanics. Heisenberg’s uncertainty principle ∆ ∆ ≥ x p h 2 (1.3) In 1927, Werner Heisenberg’s matrix formulation of quantum mechanics led him to discover that an irreducible uncertainty exists when measuring the position and momen- tum of an object simultaneously. Unlike classical mechanics, quantum mechanics requires that the more accurately the position of an object is known, the less accurately its momen- tum is known, and vice versa. The magnitude of that irreducible uncertainty is propor- tional to Planck’s constant. Schrödinger equation i t H ∂ ∂ = Ψ Ψ (1.4) In 1926, Erwin Schrödinger derived his nonrelativistic wave equation for the quan- tum mechanical motion of particles such as electrons in atoms. The probability density of finding a particle at a particular position in space is the square of the absolute value of the complex wave function, which is calculated from Schrödinger’s equation. This equation accurately predicts the allowed energy levels for the electron in the hydrogen atom. With the use of modern computers, generalizations of this equation predict the properties of larger molecules and the behavior of electrons in complex materials. Dirac equation i t c p mc e ∂ ∂ = ⋅ − + + Ψ Α Φ Ψ α β ( ) 2 (1.5) In 1928, Paul Dirac derived a relativistic generalization of Schrödinger’s wave equa- tion for the quantum mechanical motion of a charged particle in an electromagnetic field. © 2016 by Taylor Francis Group, LLC
- 41. 16 Handbook of Measurements His marvelous equation predicts the magnetic moment of the electron and the existence of antimatter. Maxwell’s equations ∇ ⋅ = D p (1.6) ∇ × = + ∂ ∂ H J D t (1.7) ∇ × + ∂ ∂ = E B t 0 (1.8) ∇ ⋅ = B 0 (1.9) The fundamental equations explaining classical electromagnetism were developed over many years by James Clerk Maxwell and were completed in his famous treatise pub- lished in 1873. His classical field theory provides an elegant framework for understanding electricity, magnetism, and propagation of light. Maxwell’s theory was a major achieve- ment of nineteenth-century physics, and it contained one of the clues that was used years later by Einstein to develop special relativity. Classical field theory was also the spring- board for the development of quantum filed theory. Boltzmann’s equation for entropy S k W = ln (1.10) Ludwig Boltzmann, one of the founders of statistical mechanics in the late nineteenth century, proposed that the probability for any physical state of macroscopic system is pro- portional to the number of ways in which the internal state of that system can be rear- ranged without changing the system’s external properties. When more arrangements are possible, the system is more disordered. Boltzmann showed that the logarithm of the mul- tiplicity of states of a system, or its disorder, is proportional to its entropy, and the constant of proportionality is Boltzmann’s constant k. The second law of thermodynamics states that the total entropy of a system and its surroundings always increase as time elapses. Boltzmann’s equation for entropy is carved on his grave. Planck–Einstein equation E hv = (1.11) The simple relation between the energy of a light quantum and the frequency of the associated light wave first emerged in a formula discovered in 1900 by Max Planck. He was examining the intensity of electromagnetic radiation emitted by the atoms in the walls of an enclosed cavity (a blackbody) at fixed temperature. He found that he could fit the experimental data by assuming that the energy associated with each mode of the electro- magnetic field is an integral multiple of some minimum energy that is proportional to the frequency. The constant of proportionality, h, is known as Planck’s constant. It is one of the most important fundamental numbers in physics. In 1905, Albert Einstein recognized that Planck’s equation implies that light is absorbed or emitted in discrete quanta, explaining the photoelectric effect and igniting the quantum mechanical revolution. © 2016 by Taylor Francis Group, LLC
- 42. 17 Chapter one: Fundamentals of measurement Planck’s blackbody radiation formula u h c v e hv kT = − − 8 1 3 3 1 π (1.12) In studying the energy density of radiation in a cavity, Max Planck compared two approximate formulas, one for low frequency and another for high frequency. In 1900, using an ingenious extrapolation, he found his equation for the energy density of black- body radiation, which reproduced experimental results. Seeking to understand the signifi- cance of his formula, he discovered the relation between energy and frequency known as Planck–Einstein equation. Hawking equation for black hole temperature T hc GMk BH = 3 8π (1.13) Using insights from thermodynamics, relativist quantum mechanics, and Einstein’s gravitational theory, Stephen Hawking predicted in 1974 the surprising result that gravita- tional black holes, which are predicted by general relativity, would radiate energy. His for- mula for the temperature of the radiating black hole depends on the gravitational constant, Planck’s constant, the speed of light, and Boltzmann’s constant. While Hawking radiation remains to be observed, his formula provides a tempting glimpse of the insights that will be uncovered in a unified theory combining quantum mechanics and gravity. Navier–Stokes equation for a fluid ρ ρ µ λ µ ρ ∂ ∂ + ⋅ ∇ = −∇ + ∇ + + ∇ ∇ ⋅ + v t v v p v v g ( ) ( ) ( ) 2 (1.14) The Navier–Stokes equation was derived in the nineteenth century from Newtonian mechanics to model viscous fluid flow. Its nonlinear properties make it extremely difficult to solve, even with modern analytic and computational technique. However, its solutions describe a rich variety of phenomena including turbulence. Lagrangian for quantum chromodynamics L F F i gA t m QDC a v a v f f a a f f = − ⋅ + ∇ − − ∑ 1 4 µ µ Ψ Ψ [ ] (1.15) Relativistic quantum field theory had its first great success with quantum electro- dynamics, which explains the interaction of charged particles with the quantized elec- tromagnetic field. Exploration of non-Abelian gauge theories led next to the spectacular unification of the electromagnetic and weak interactions. Then, with insights developed from the quark model, quantum chromodynamics was developed to explain the strong interactions. This theory predicts that quarks are bound more tightly together as their separation increases, which explains why individual quarks are not seen directly in exper- iments. The standard model, which incorporates strong, weak, and electromagnetic inter- actions into a single quantum field theory, describes the interaction of quarks, gluons, © 2016 by Taylor Francis Group, LLC
- 43. 18 Handbook of Measurements and leptons and has achieved remarkable success in predicting experimental results in elementary particle physics. Bardeen–Cooper–Schrieffer equation for superconductivity T e c N V = − 1 13 1 0 . ( ) Θ (1.16) Superconductors are materials that exhibit no electrical resistance at low tempera- tures. In 1957, John Bardeen, Leon N. Cooper, and J. Robert Schrieffer applied quantum field theory with an approximate effective potential to explain this unique behavior of electrons in a superconductor. The electrons were paired and move collectively without resistance in the crystal lattice of the superconducting material. The BCS theory and its later generalizations predict a wide variety of phenomena that agree with experimental observations and have many practical applications. John Bardeen’s contributions to solid- state physics also include inventing the transistor, made from semiconductors, with Walter Brattain and William Shockley in 1947. Josephson effect d dt eV h ( ) ∆ = ϕ 2 (1.17) In 1962, Brian Josephson made the remarkable prediction that electric current could flow between two thin pieces of superconducting material separated by a thin piece of insulating material without application of a voltage. Using the BCS theory of superconduc- tivity, he also predicted that if a voltage difference were maintained across the junction, there would be an alternating current with a frequency related to the voltage and Planck’s constant. The presence of magnetic fields influences the Josephson effect, allowing it to be used to measure very weak magnetic fields approaching the microscopic limit set by quantum mechanics. Fermat’s last theorem x y z n n n + = (1.18) While studying the properties of whole numbers, or integers, the French mathemati- cian Pierre de Fermat wrote in 1637 that it is impossible for the cube of an integer to be written as the sum of the cubes of two other integers. More generally, he stated that it is impossible to find such a relation between three integers for any integral power greater than two. He went on to write a tantalizing statement in the margin of his copy of a Latin translation of Diophantus’s Arithemetica: “I have a truly marvelous demonstration of this proposition, which this margin is too narrow to contain.” It took over 350 years to prove Fermat’s simple conjecture. The feat was achieved by Andrew Wiles in 1994 with a “tour de force” proof of many pages using newly developed techniques in number theory. It is noteworthy that many researchers, mathematicians, and scholars toiled for almost four centuries before a credible proof of Fermat’s last theorem was found. Indeed, the lead edi- tor of this handbook, as a mathematics graduate student in the early 1980s, was introduced to the problem during his advanced calculus studies under Professor Reginald Mazeres at Tennessee Technological University in 1980. Like many naïve researchers before him, he struggled with the problem as a potential thesis topic for 6 months before abandoning it to pursue a more doable topic in predictive time series modeling. © 2016 by Taylor Francis Group, LLC
- 44. 19 Chapter one: Fundamentals of measurement 1.4 Fundamental methods of measurement There are two basic methods of measurement: 1. Direct comparison with either a primary or a secondary standard. 2. Indirect comparison with a standard with the use of a calibrated system. 1.4.1 Direct comparison How do you measure the length of a cold-rolled bar? You probably use a steel tape. You compare the bar’s length with a standard. The bar is so many feet long because that many units on your standard have the same length as the bar. You have determined this by mak- ing a direct comparison. Although you do not have access to the primary standard defin- ing the unit, you manage very well with a secondary standard. Primary measurement standards have the least amount of uncertainty compared to the certified value and are traceable directly to the SI. Secondary standards, on the other hand, are derived by assign- ing value by comparison to a primary standard. In some respect, measurement by direct comparison is quite common. Many length measurements are made in this way. In addition, time of the day is usually determined by comparison, with a watch used as a secondary standard. The watch goes through its dou- ble-cycle, in synchronization with the earth’s rotation. Although, in this case, the primary standard is available to everyone, the watch is more convenient because it works on cloudy days, indoors, outdoors, in daylight, and in the dark (at night). It is also more precise. That is, its resolution is better. In addition, if well regulated, the watch is more accurate because the earth does not rotate at a uniform speed. It is seen, therefore, that in some cases, a sec- ondary standard is actually more useful than the primary standard. Measuring by direct comparison implies stripping the measurement problem to its bare essentials. However, the method is not always the most accurate or the best. The human senses are not equipped to make direct comparisons of all quantities with equal facility. In many cases, they are not sensitive enough. We can make direct length comparisons using a steel rule with a level of precision of about 0.01 in. Often we wish for a greater accuracy, in which case we must call for additional assistance from some calibrated measuring system. 1.4.2 Indirect comparison While we can do a reasonable job through direct comparison of length, how well can we compare masses, for example? Our senses enable us to make rough comparisons. We can lift a pound of meat and compare its effect with that of some unknown mass. If the unknown is about the same weight, we may be able to say that it is slightly heavier, or perhaps, not quite as heavy as our “standard” pound, but we could never be certain that the two masses were the same, even say within one ounce. Our ability to make this com- parison is not as good as it is for the displacement of the mass. Our effectiveness in coming close to the standard is related to our ability to “gage” the relative impacts of mass on our ability to displace the mass. This brings to mind the common riddle, “Which weighs more? A pound of feathers or a pound of stones?” Of course, both weigh the same with respect to the standard weight of “pound.” In making most engineering measurements, we require the assistance of some form of the measuring system, and measurement by direct comparison is less general than mea- surement by indirect comparison. © 2016 by Taylor Francis Group, LLC
- 45. 20 Handbook of Measurements 1.5 Generalized mechanical measuring system Most mechanical measurement systems (Beckwith and Buck, 1965) fall within the frame- work of a generalized arrangement consisting of three stages, as follows: Stage I: A detector–transducer stage Stage II: An intermediate modifying stage Stage III: The terminating stage, consisting of one or a combination of an indicator, a recorder, or some form of the controller. Each stage is made up of a distinct component or grouping of components, which per- form required and definite steps in the measurement. These may be termed basic elements, whose scope is determined by their functioning rather than their construction. First stage detector–transducer: The prime function of the first stage is to detect or to sense the input signal. This primary device must be sensitive to the input quantity. At the same time, ide- ally it should be insensitive to every other possible input. For instance, if it is a pressure pickup, it should not be sensitive to, say, acceleration; if it is a strain gauge, it should be insensitive to temperature; or if a linear accelerometer, it should be insensitive to angular acceleration, and so on. Unfortunately, it is very rare indeed to find a detecting device that is completely selective. As an example of a simple detector–transducer device, consider an automobile tire pressure gauge. It consists of a cylinder and a piston, a spring resisting the piston movement, and a stem with scale divisions. As the air pressure bears against the piston, the resulting force compresses the spring until the spring and air forces are balanced. The calibrated stem, which remains in place after the spring returns the piston, indicates the applied pressure. In this case, the piston–cylinder combination along with the spring makes up the detector–transducer. The piston and cylinder form one basic ele- ment, while the spring is another basic element. The piston–cylinder combination, serving as a force-summing device, senses the pressure effect, and the spring transduces it into the displacement. Realistically, not all measurements we encounter in theory and practice are of transduceable mechanical settings. Measurements, thus, can take more generic paths of actualization. Figure 1.2 shows a generic measurement loop revolving around variable Analyze M e a s u r e I n t e r p r e t Communicate Identify variable I m p l e m e n t Figure 1.2 Generic measurement loop. © 2016 by Taylor Francis Group, LLC
- 46. 21 Chapter one: Fundamentals of measurement identification, actual measurement, analyzing the measurement result, interpreting the measuring in the context of the prevailing practical application, and implementing the measurement for actionable decisions. In each stage of the loop, communication is a central requirement. Communication can be in the form of a pictorial display, a verbal announce- ment, or a written dissemination. A measurement is not usable unless it is communicated in an appropriate form and at the appropriate time. 1.6 Data types and measurement scales Every decision requires data collection, measurement, and analysis. In practice, we encoun- ter different types of measurement scales depending on the particular items of interest. Data may need to be collected on decision factors, costs, performance levels, outputs, and so on. The different types of data measurement scales that are applicable are presented below. 1.6.1 Nominal scale of measurement The nominal scale is the lowest level of measurement scales. It classifies items into cat- egories. The categories are mutually exclusive and collectively exhaustive. That is, the cat- egories do not overlap, and they cover all possible categories of the characteristics being observed. For example, in the analysis of the critical path in a project network, each job is classified as either critical or not critical. Gender, type of industry, job classification, and color are examples of measurements on a nominal scale. 1.6.2 Ordinal scale of measurement An ordinal scale is distinguished from a nominal scale by the property of order among the categories. An example is the process of prioritizing project tasks for resource allocation. We know that first is above second, but we do not know how far above. Similarly, we know that better is preferred to good, but we do not know by how much. In quality control, the ABC classification of items based on the Pareto distribution is an example of a measure- ment on an ordinal scale. 1.6.3 Interval scale of measurement An interval scale is distinguished from an ordinal scale by having equal intervals between the units of measurement. The assignment of priority ratings to project objectives on a scale of 0–10 is an example of a measurement on an interval scale. Even though an objec- tive may have a priority rating of zero, it does not mean that the objective has absolutely no significance to the project team. Similarly, the scoring of zero on an examination does not imply that a student knows absolutely nothing about the materials covered by the examination. Temperature is a good example of an item that is measured on an interval scale. Even though there is a zero point on the temperature scale, it is an arbitrary relative measure. Other examples of interval scale are IQ measurements and aptitude ratings. 1.6.4 Ratio scale measurement A ratio scale has the same properties of an interval scale, but with a true zero point. For example, an estimate of zero time units for the duration of a task is a ratio scale measure- ment. Other examples of items measured on a ratio scale are cost, time, volume, length, © 2016 by Taylor Francis Group, LLC
- 47. 22 Handbook of Measurements height, weight, and inventory level. Many of the items measured in engineering systems will be on a ratio scale. Another important aspect of measurement involves the classification scheme used. Most systems will have both quantitative and qualitative data. Quantitative data require that we describe the characteristics of the items being studied numerically. Qualitative data, on the other hand, are associated with attributes that are not measured numerically. Most items measured on the nominal and ordinal scales will normally be classified into the qualitative data category while those measured on the interval and ratio scales will normally be classified into the quantitative data category. The implication for engineering system control is that qualitative data can lead to bias in the control mechanism because qualitative data are subjected to the personal views and interpretations of the person using the data. As much as possible, data for an engineering systems control should be based on a quantitative measurement. Figure 1.3 illustrates the four different types of data classification. Notice that the temperature is included in the “relative” category rather the “true zero” category. Even though there are zero temperature points on the common tem- perature scales (i.e., Fahrenheit, Celsius, and Kelvin), those points are experimentally or theoretically established. They are not true points as one might find in a counting system. 1.7 Common units of measurements Some common units of measurement include the following: Acre: An area of 43,560 ft2. Agate: 1/14 in. (used in printing for measuring column length). Ampere: Unit of electric current. Astronomical (A.U.): 93,000,000 miles; the average distance of the earth from the sun (used in astronomy). Bale: A large bundle of goods. In the United States, approximate weight of a bale of cot- ton is 500 lbs. The weight of a bale may vary from country to country. Board foot: 144 in.3 (12 × 12 × 1 used for lumber). Bolt: 40 yards (used for measuring cloth). Cost IQ First, second Color Gender Design type Low, high Good, better Grade point average Temperature True zero Ratio Relative Interval Order Ordinal Classification Nominal Attribute Type of data Examples Voltage level Electric current Figure 1.3 Four primary types of data. © 2016 by Taylor Francis Group, LLC
- 48. 23 Chapter one: Fundamentals of measurement Btu: British thermal unit; the amount of heat needed to increase the temperature of 1 lb of water by 1°F (252 cal). Carat: 200 mg or 3086 troy; used for weighing precious stones (originally the weight of a seed of the carob tree in the Mediterranean region). See also Karat. Chain: 66 ft; used in surveying (1 mile = 80 chains). Cubit: 18 in. (derived from the distance between elbow and tip of the middle finger). Decibel: Unit of relative loudness. Freight Ton: 40 ft3 of merchandise (used for cargo freight). Gross: 12 dozen (144). Hertz: Unit of measurement of electromagnetic wave frequencies (measures cycles per second). Hogshead: Two liquid barrels or 14,653 in.3 Horsepower: The power needed to lift 33,000 lbs a distance of 1 ft in 1 min (about 1 1/2 times the power an average horse can exert); used for measuring the power of mechanical engines. Karat: A measure of the purity of gold. It indicates how many parts out of 24 are pure. 18-karat gold is 3/4 pure gold. Knot: Rate of the speed of 1 nautical mile/h; used for measuring the speed of ships (not distance). League: Approximately 3 miles. Light-year: 5,880,000,000,000 miles; distance traveled by light in 1 year at the rate of 186,281.7 miles/s; used for measurement of interstellar space. Magnum: Two-quart bottle; used for measuring wine. Ohm: Unit of electrical resistance. Parsec: Approximately 3.26 light-years of 19.2 trillion miles; used for measuring inter- stellar distances. Pi (π): 3.14159265+; the ratio of the circumference of a circle to its diameter. Pica: 1/6 in. or 12 points; used in printing for measuring column width. Pipe: Two hogsheads; used for measuring wine and other liquids. Point: 0.013837 (~1/72 in. or 1/12 pica); used in printing for measuring type size. Quintal: 100,000 g or 220.46 lbs avoirdupois. Quire: 24 or 25 sheets; used for measuring paper (20 quires is one ream). Ream: 480 or 500 sheets; used for measuring paper. Roentgen: Dosage unit of radiation exposure produced by x-rays. Score: 20 units. Span: 9 in. or 22.86 cm; derived from the distance between the end of the thumb and the end of the little finger when both are outstretched. Square: 100 ft2; used in building. Stone: 14 lbs avoirdupois in Great Britain. Therm: 100,000 Btus. Township: U.S. land measurement of almost 36 square miles; used in surveying. Tun: 252 gallons (sometimes larger); used for measuring wine and other liquids. Watt: Unit of power. 1.7.1 Common constants Speed of light: 2.997,925 × 1010 cm/s (983.6 × 106 ft/s; 186,284 miles/s) Velocity of sound: 340.3 m/s (1116 ft/s) Gravity (acceleration): 9.80665 m/s2 (32.174 ft/s2; 386.089 in./s2) © 2016 by Taylor Francis Group, LLC
- 49. 24 Handbook of Measurements 1.7.2 Measurement numbers and exponents Exponentiation is essential in measurements both small and large numbers. The standard exponentiation numbers and prefixes are presented as follows: yotta (1024): 1 000 000 000 000 000 000 000 000 zetta (1021): 1 000 000 000 000 000 000 000 exa (1018): 1 000 000 000 000 000 000 peta (1015): 1 000 000 000 000 000 tera (1012): 1 000 000 000 000 giga (109): 1 000 000 000 mega (106): 1 000 000 kilo (103): 1 000 hecto (102): 100 deca (101): 10 deci (10−1): 0.1 centi (10−2): 0.01 milli (10−3): 0.001 micro (10−6): 0.000 001 nano (10−9): 0.000 000 001 pico (10−12): 0.000 000 000 001 femto (10−15): 0.000 000 000 000 001 atto (10−18): 0.000 000 000 000 000 001 zepto (10−21): 0.000 000 000 000 000 000 001 yocto (10−24): 0.000 000 000 000 000 000 000 001 1.8 Patterns of numbers in measurements Numbers are the basis for any measurement. They have many inherent properties that are fascinating and these should be leveraged in measurement systems. Some interesting number patterns relevant to measurement systems are shown as follows: 1 × 8 + 1 = 9 12 × 8 + 2 = 98 123 × 8 + 3 = 987 1234 × 8 + 4 = 9876 12,345 × 8 + 5 = 98,765 123,456 × 8 + 6 = 987,654 1,234,567 × 8 + 7 = 9,876,543 12,345,678 × 8 + 8 = 98,765,432 123,456,789 × 8 + 9 = 987,654,321 1 × 9 + 2 = 11 12 × 9 + 3 = 111 123 × 9 + 4 = 1111 1234 × 9 + 5 = 11,111 12,345 × 9 + 6 = 111,111 123,456 × 9 + 7 = 1,111,111 1,234,567 × 9 + 8 = 11,111,111 12,345,678 × 9 + 9 = 111,111,111 123,456,789 × 9 + 10 = 1,111,111,111 © 2016 by Taylor Francis Group, LLC
- 50. 25 Chapter one: Fundamentals of measurement 9 × 9 + 7 = 88 98 × 9 + 6 = 888 987 × 9 + 5 = 8888 9876 × 9 + 4 = 88,888 98,765 × 9 + 3 = 888,888 987,654 × 9 + 2 = 8,888,888 9,876,543 × 9 + 1 = 88,888,888 98,765,432 × 9 + 0 = 888,888,888 1 × 1 = 1 11 × 11 = 121 111 × 111 = 12,321 1111 × 1111 = 1,234,321 11,111 × 11,111 = 123,454,321 111,111 × 111111 = 12,345,654,321 1,111,111 × 1,111,111 = 1,234,567,654,321 11,111,111 × 11,111,111 = 123,456,787,654,321 111,111,111 × 111,111,111 = 12,345,678,987,654,321 111,111,111 × 111,111,111 = 12,345,678,987,654,321 1 × 8 + 1 = 9 12 × 8 + 2 = 98 123 × 8 + 3 = 987 1234 × 8 + 4 = 9876 12,345 × 8 + 5 = 98,765 123,456 × 8 + 6 = 987,654 1,234,567 × 8 + 7 = 9,876,543 12,345,678 × 8 + 8 = 98,765,432 123,456,789 × 8 + 9 = 987,654,321 1 × 9 + 2 = 11 12 × 9 + 3 = 111 123 × 9 + 4 = 1111 1234 × 9 + 5 = 11,111 12,345 × 9 + 6 = 111,111 123,456 × 9 + 7 = 1,111,111 1,234,567 × 9 + 8 = 11,111,111 12,345,678 × 9 + 9 = 111,111,111 123,456,789 × 9 + 10 = 1,111,111,111 9 × 9 + 7 = 88 98 × 9 + 6 = 888 987 × 9 + 5 = 8888 9876 × 9 + 4 = 88,888 98,765 × 9 + 3 = 888,888 987,654 × 9 + 2 = 8,888,888 9,876,543 × 9 + 1 = 88,888,888 98,765,432 × 9 + 0 = 888,888,888 © 2016 by Taylor Francis Group, LLC
- 51. 26 Handbook of Measurements 1 × 1 = 1 11 × 11 = 121 111 × 111 = 12,321 1111 × 1111 = 1,234,321 11,111 × 11111 = 123,454,321 111,111 × 111,111 = 12,345,654,321 1,111,111 × 1,111,111 = 1,234,567,654,321 11,111,111 × 11,111,111 = 123,456,787,654,321 111,111,111 × 111,111,111 = 12,345,678,987,654,321 1.9 Statistics in measurement Statistical data management is essential for measurement with respect to analyzing and interpreting measurement outputs. In this section, a project control scenario is used to illustrate data management for measurement of project performance. Transient data is defined as a volatile set of data that is used for one-time decision mak- ing and is not needed again. As an example, the number of operators that show up at a job site on a given day; unless there is some correlation between the day-to-day attendance records of operators, this piece of information will be relevant only for that given day. The project manager can make his decision for that day based on that day’s attendance record. Transient data need not be stored in a permanent database unless it may be needed for future analysis or uses (e.g., forecasting, incentive programs, and performance review). Recurring data refers to the data that is encountered frequently enough to necessitate storage on a permanent basis. An example is a file containing contract due dates. This file will need to be kept at least through the project life cycle. Recurring data may be further categorized into static data and dynamic data. A recurring data that is static will retain its original parameters and values each time it is retrieved and used. A recurring data that is dynamic has the potential for taking on different parameters and values each time it is retrieved and used. Storage and retrieval considerations for project control should address the following questions: 1. What is the origin of the data? 2. How long will the data be maintained? 3. Who needs access to the data? 4. What will the data be used for? 5. How often will the data be needed? 6. Is the data for reference purposes only (i.e., no printouts)? 7. Is the data for reporting purposes (i.e., generate reports)? 8. In what format is the data needed? 9. How fast will the data need to be retrieved? 10. What security measures are needed for the data? 1.10 Data determination and collection It is essential to determine what data to collect for project control purposes. Data collec- tion and analysis are basic components of generating information for project control. The requirements for data collection are discussed next. Choosing the data. This involves selecting data based on their relevance, the level of likelihood that they will be needed for future decisions, and whether or not they © 2016 by Taylor Francis Group, LLC
- 52. 27 Chapter one: Fundamentals of measurement contribute to making the decision better. The intended users of the data should also be identified. Collecting the data. This identifies a suitable method of collecting the data as well as the source from which the data will be collected. The collection method depends on the particular operation being addressed. The common methods include manual tabulation, direct keyboard entry, optical character reader, magnetic coding, electronic scanner, and more recently, voice command. An input control may be used to confirm the accuracy of collected data. Examples of items to control when collecting data are the following: Relevance check. This checks if the data are relevant to the prevailing problem. For exam- ple, data collected on personnel productivity may not be relevant for decision-involving marketing strategies. Limit check. This checks to ensure that the data are within known or acceptable limits. For example, an employee overtime claim amounting to over 80 h/week for several weeks in a row is an indication of a record well beyond ordinary limits. Critical value. This identifies a boundary point for data values. Values below or above a critical value fall in different data categories. For example, the lower specification limit for a given characteristic of a product is a critical value that determines whether the product meets quality requirements. Coding the data. This refers to the technique used for representing data in a form useful for generating information. This should be done in a compact and yet meaningful format. The performance of information systems can be greatly improved if effective data formats and coding are designed into the system right from the beginning. Processing the data. Data processing is the manipulation of data to generate useful infor- mation. Different types of information may be generated from a given data set depending on how it is processed. The processing method should consider how the information will be used, who will be using it, and what caliber of system response time is desired. If pos- sible, processing controls should be used. Control total. Check for the completeness of the processing by comparing accumulated results to a known total. An example of this is the comparison of machine throughput to a standard production level or the comparison of cumulative project budget depletion to a cost accounting standard. Consistency check. Check if the processing is producing the same results for similar data. For example, an electronic inspection device that suddenly shows a measurement that is 10 times higher than the norm warrants an investigation of both the input and the processing mechanisms. Scales of measurement. For numeric scales, specify units of measurement, increments, the zero point on the measurement scale, and the range of values. Using the information. Using information involves people. Computers can collect data, manipulate data, and generate information, but the ultimate decision rests with people, and decision making starts when information becomes available. Intuition, experience, training, interest, and ethics are just a few of the factors that determine how people use information. The same piece of information that is positively used to further the progress of a project in one instance may also be used negatively in another instance. To assure that data and information are used appropriately, computer-based security measures can be built into the information system. Project data may be obtained from several sources. Some potential sources are • Formal reports • Interviews and surveys © 2016 by Taylor Francis Group, LLC
- 53. 28 Handbook of Measurements • Regular project meetings • Personnel time cards or work schedules The timing of data is also very important for project control purposes. The contents, level of detail, and frequency of data can affect the control process. An important aspect of project management is the determination of the data required to generate the information needed for project control. The function of keeping track of the vast quantity of rapidly changing and interrelated data about project attributes can be very complicated. The major steps involved in data analysis for project control are • Data collection • Data analysis and presentation • Decision making • Implementation of action Data is processed to generate information. Information is analyzed by the decision maker to make the required decisions. Good decisions are based on timely and relevant information, which in turn is based on reliable data. Data analysis for project control may involve the following functions: • Organizing and printing computer-generated information in a form usable by managers • Integrating different hardware and software systems to communicate in the same project environment • Incorporating new technologies such as expert systems into data analysis • Using graphics and other presentation techniques to convey project information Proper data management will prevent misuse, misinterpretation, or mishandling. Data is needed at every stage in the lifecycle of a project from the problem identification stage through the project phase-out stage. The various items for which data may be needed are project specifications, feasibility study, resource availability, staff size, schedule, project status, performance data, and phase-out plan. The documentation of data requirements should cover the following • Data summary. A data summary is a general summary of the information and deci- sions for which the data is required as well as the form in which the data should be prepared. The summary indicates the impact of the data requirements on the orga- nizational goals. • Data-processing environment. The processing environment identifies the project for which the data is required, the user personnel, and the computer system to be used in processing the data. It refers to the project request or authorization and relation- ship to other projects and specifies the expected data communication needs and mode of transmission. • Data policies and procedures. Data handling policies and procedures describe policies governing data handling, storage, and modification and the specific procedures for implementing changes to the data. Additionally, they provide instructions for data collection and organization. • Static data. A static data description describes that portion of the data that is used mainly for reference purposes and it is rarely updated. © 2016 by Taylor Francis Group, LLC
- 54. 29 Chapter one: Fundamentals of measurement • Dynamic data. A dynamic data description defines the portion of the data that is fre- quently updated based on the prevailing circumstances in the organization. • Data frequency. The frequency of data update specifies the expected frequency of data change for the dynamic portion of the data, for example, quarterly. This data change frequency should be described in relation to the frequency of processing. • Data constraints. Data constraints refer to the limitations on the data requirements. Constraints may be procedural (e.g., based on corporate policy), technical (e.g., based on computer limitations), or imposed (e.g., based on project goals). • Data compatibility. Data compatibility analysis involves ensuring that data collected for project control needs will be compatible with future needs. • Data contingency. A data contingency plan concerns data security measures in case of accidental or deliberate damage or sabotage affecting hardware, software, or personnel. 1.11 Data analysis and presentation Data analysis refers to the various mathematical and graphical operations that can be performed on data to elicit the inherent information contained in the data. The man- ner in which project data is analyzed and presented can affect how the information is perceived by the decision maker. The examples presented in this section illustrate how basic data analysis techniques can be used to convey important information for project control. In many cases, data are represented as the answer to direct questions such as, when is the project deadline? Who are the people assigned to the first task? How many resource units are available? Are enough funds available for the project? What are the quarterly expenditures on the project for the past two years? Is personnel productivity low, aver- age, or high? Who is the person in charge of the project? Answers to these types of ques- tions constitute data of different forms or expressed on different scales. The resulting data may be qualitative or quantitative. Different techniques are available for analyzing the different types of data. This section discusses some of the basic techniques for data analysis. The data presented in Table 1.1 is used to illustrate the data analysis techniques. 1.11.1 Raw data Raw data consists of ordinary observations recorded for a decision variable or factor. Examples of factors for which data may be collected for decision making are revenue, cost, personnel productivity, task duration, project completion time, product quality, and resource availability. Raw data should be organized into a format suitable for visual review and computational analysis. The data in Table 1.1 represents the quarterly revenues from projects A, B, C, and D. For example, the data for quarter 1 indicates that project C yielded Table 1.1 Quarterly revenue from four projects (in $1000s) Project Quarter 1 Quarter 2 Quarter 3 Quarter 4 Row total A 3000 3200 3400 2800 12,400 B 1200 1900 2500 2400 8000 C 4500 3400 4600 4200 16,700 D 2000 2500 3200 2600 10,300 Total 10,700 11,000 13,700 12,000 47,400 © 2016 by Taylor Francis Group, LLC
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- 59. The Project Gutenberg eBook of Notes and Queries, Vol. V, Number 120, February 14, 1852
- 60. This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online at www.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook. T i t l e: Notes and Queries, Vol. V, Number 120, February 14, 1852 A u t h o r: Various E d i t o r: George Bell R e l e a s e d a t e: September 13, 2012 [eBook #40743] Most recently updated: October 23, 2024 L a n g u a g e: English C r e d i t s: Produced by Charlene Taylor, Jonathan Ingram and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Library of Early Journals.) *** START OF THE PROJECT GUTENBERG EBOOK NOTES AND QUERIES, VOL. V, NUMBER 120, FEBRUARY 14, 1852 ***
- 61. Vol. V.—No. 120. NOTES AND QUERIES: A MEDIUM OF INTER-COMMUNICATION FOR LITERARY MEN, ARTISTS, ANTIQUARIES, GENEALOGISTS, ETC. When found, make a note of.—Captain Cuttle. Vol. V.—No. 120. Saturday, February 14. 1852. Price Fourpence. Stamped Edition, 5d. Transcriber's Note: Ϲ (Greek Capital Lunate Sigma Symbol) rather than Σ has been used in some words to reproduce the characters exactly; Hebrew characters have been represented as printed.
- 62. CONTENTS. Notes:— The Old Countess of Desmond 145 The Imperial Eagle of France 147 Folk Lore:—Valentine's Day—Nottingham Hornblowing —Bee Superstitions; Blessing Apple-trees; A Neck! a Neck!—Hooping Cough 148 Note on the Coins of Vabalathus 148 The Agnomen of Brother Jonathan, of Masonic Origin 149 Minor Notes:—Hippopotamus, Behemoth—Curious Inscription—Coins of Edward III. struck at Antwerp in 1337 149 Queries:— Is the Walrus found in the Baltic? 150 English Free Towns, by J. H. Parker 150 Minor Queries:—Bishop Hall's Resolutions—Mother Huff and Mother Damnable—Sir Samuel Garth— German's Lips—Richard Leveridge—Thomas Durfey—Audley Family—Ink—Mistletoe excluded from Churches—Blind taught to read—Hyrne, Meaning of—The fairest Attendant of the Scottish Queen—Soud, soud, soud, soud!—Key Experiments—Shield of Hercules—Sum Liber, et non sum, c. 150
- 63. Minor Queries Answered:—Whipping a Husband; Hudibras—Aldus—The last links are broken— Under Weigh or Way—The Pope's Eye—History is Philosophy 152 Replies:— Coverdale's Bible, by George Offor 153 As Stars with Trains of Fire, c., by Samuel Hickson 154 Dials, Dial Mottoes, c. 155 Can Bishops vacate their Sees? 156 Character of a True Churchman 156 Wearing Gloves in Presence of Royalty 157 Gospel Oaks 157 The Pendulum Demonstration 158 Expurgated Quaker Bible, by Archdeacon Cotton 158 Junius Rumours 159 Wady Mokatteb not mentioned in Num. xi. 26., by Rev. Dr. Todd 159 Replies to Minor Queries:—Rotten Row—Preached from a Pulpit rather than a Tub—Olivarius— Slavery in Scotland—Cibber's Lives of the Poets— Theoloneum—John of Padua—Stoke—Eliza Fenning—Ghost Stories—Autographs of Weever and Fuller—Lines on the Bible—Hell-rake—Family Likenesses—Grimsdyke—Portraits of Wolfe, c. 160 Miscellaneous:— Notes on Books, c. 166 Books and Odd Volumes wanted 166 Notices to Correspondents 167
- 64. Advertisements 167 List of Notes and Queries volumes and pages
- 65. Notes. THE OLD COUNTESS OF DESMOND. (Continued from Vol. iv., p. 426.) I feel much obliged to J. H. M., who writes from Bath, and has directed my attention to Horace Walpole's minute inquiry respecting the Old Countess of Desmond, as also to Pennant's Tours, all which I have had opportunity of examining since I wrote to you last. The references do not incline me to alter one word of the opinion I have ventured as to the identity of this lady; on the contrary, with the utmost respect for his name and services to the cause of antiquarian research, I propose to show that Horace Walpole (whose interest in the question was, by his own confession, but incidental, and ancillary to his historic inquiries into the case of Richard III., and who had no direct data to go on) knew nothing of the matter, and was quite mistaken as to the individual. Before I proceed on this daring undertaking, I beg to say, that an inspection of Pennant's print, called The Old Countess of Desmond, satisfies me that it is not taken from a duplicate picture of that in possession of the Knight of Kerry: though there certainly is a resemblance in the faces of the two portraits, yet the differences are many and decisive. Pennant says that there are four other pictures in Great Britain in the same dress, and without any difference of feature, besides that at Dupplin Castle, from which his print was copied; but that of the Knight of Kerry must be reckoned as a sixth portrait, taken at a much more advanced period of life: in it the wrinkles and features denote extreme old age. The head-dresses are markedly different, that of Pennant being a cloth hood lying back
- 66. from the face in folds; in the Knight of Kerry's, the head-dress is more like a beaver bonnet standing forward from the head, and throwing the face somewhat into shade. In Pennant's, the cloak is plainly fastened by leathern strap, somewhat after the manner of a laced shoe; in the other, the fastening is a single button: but the difference most marked is this, that the persons originally sitting for these pictures, looked opposite ways, and, of course, presented different sides to the painter. So that, in Pennant's plate, the right side-face is forward; and in the other, the left: therefore, these pictures are markedly and manifestly neither the same, nor copies either of the other. It does not concern us, in order to maintain the authority of our Irish picture, to follow up the question at issue between Pennant and Walpole but I may here observe, that either must be wrong in an important matter of fact. Walpole, in a note to his Fugitive Pieces (Lord Orford's Works, vol. i. p. 210-17.), writes thus: Having by permission of the Lord Chamberlain obtained a copy of the picture at Windsor Castle, called The Countess of Desmond, I discovered that it is not her portrait; on the back is written in an old hand, 'The Mother of Rembrandt.' He then proceeds to prove the identity of this picture with one given to King Charles I. by Sir Robert Car, My Lord Ankrom (after Duke of Roxburg), and set down in the Windsor Catalogue as Portrait of an old woman, with a great scarf on her head, by Rembrandt. Pennant's note differs from this in an essential particular; he mentions this picture at Windsor Castle thus: This was a present from Sir Robert Car, Earl of Roxburg, as is signified on the back; above it is written with a pen, 'Rembrandt' (not a word of his mother), which must be a mistake, for Rembrandt was not fourteen years of age in 1614, at a time when it is certain (?) that the Countess was not living, and ... it does not appear that he ever visited England. The discrepancy of these two accounts is obvious—if it be written in an old hand, 'The Mother of Rembrandt,' on the back of the picture, it seems strange that Pennant should omit the first three words; if they be not so written, it seems equally strange that
- 67. Walpole should venture to add them. I presume the picture at Windsor is still extant; and probably some reader of N. Q. having access to it, will be so good as to settle the question of accuracy and veracity between two gentlemen, of whom one must be guilty of suppressio veri, or the other of suggestio falsi. Horace Walpole, or his editor, must have corrected his Fugitive Pieces since the Strawberry Hill edition, to which J. H. M. refers, was printed; for in the edition I have consulted, instead of saying I can make no sense of the word noie, the meaning is correctly given in a foot-note to the inscription; and the passage given by J. H. M. is altogether omitted from the text. I must now proceed in my bold attempt to show that Horace Walpole knew nothing of a matter, into which he made a minute inquiry. This may seem presumptuous in a tyro towards one of the old masters of antiquarian lore and research; but I plead in apology the great advance of the science since Horace Walpole's days, and the greater plenty of materials for forming or correcting a judgement. It has been well said, that a single chapter of Mr. Charles Knight's Old England would full furnish and set up an antiquarian of the last century; and this is true, such and so many are the advantages for obtaining information, which we modern antiquaries possess over those who are gone before us; and lastly, to quote old Fuller's quaintness, I would say that a dwarf on a giant's shoulders can see farther than he who carries him: thus do I explain and excuse my attempt to impugn the conclusion of Horace Walpole. Walpole's first conjectures applied to a Countess of Desmond, whose tomb is at Sligo in Ireland, and who was widow to that Gerald, the sixteenth earl, ingens rebellibus exemplar, who was outlawed, and killed in the wood of Glanagynty, in the county of Kerry, a.d. 1583. Walpole applied to an Irish correspondent for copies of the inscriptions on her tomb; but we need not follow or discuss the supposition of her identity with the old Countess further, for he himself abandons it, and writes to his Irish correspondent thus: —The inscriptions you have sent me have not cleared away the difficulties relating to the Countess of Desmond; on the contrary,
- 68. they make me doubt whether the lady interred at Sligo was the person reported to have lived to such an immense age. Well might he doubt it, for in no one particular could they be identified: e.g. the lady buried at Sligo made her will in 1636, and survived to 1656,—a date long beyond the latest assigned for the demise of the old Countess. Sir Walter Raleigh expressly says, the old Countess had held her jointure from all the Earls of Desmond since the time of Edward IV., a description which could not apply to the widow of a person who did not die until 1583, in the reign of Elizabeth. There are many other impossibilities in the case, discussed by Walpole, into which it is unnecessary to follow him. Walpole then reverts to the issue of Thomas, the sixth Earl of Desmond, who was compelled to surrender his earldom, a.d. 1418, for making an inferior marriage; and conjectures that the old Countess might have been the wife of a grandson of his born 1452, or thereabouts, who would be, as Walpole states, a titular earl: but this absurd supposition is met by the fact of our old Countess enjoying a jointure from all the earls de facto in another line; a provision which the widow of an adverse claimant to the earldom could hardly have made good. Walpole's last conjecture, following the suggestion of Smith's History of Cork, fixes on the widow of Thomas (the twelfth earl, according to the careful pedigree of Sir William Betham, though Smith erroneously calls him the thirteenth earl), and asserts the identity of the old Countess with a second wife, called Catherine Fitzgerald of Dromana (the Dacres branch of the Geraldines): for this assertion Smith, in a footnote, quotes the Russel MSS., and Walpole calls this the most positive evidence we have. Of the MSS. referred to, I can find no further trace, and this positive evidence is weakened by the silence of Lodge's Peerage as to any second marriage of the earl in question, while, on the contrary, he gives many probabilities against it. Thomas (moyle, or bald), twelfth earl, succeeded to his nephew, James, the eleventh earl, in 1529, being then in extreme age, and died in five years after; he was the second brother of James, ninth earl, murdered in 1587—whose widow I
- 69. affirm the old Countess to have been. Let us not lose sight of the fact, that the old Countess, by general consent, was married in the reign of Edward IV., who died 1483. And I would ask, what probability is there that a younger brother would be already married to a second wife, in the lifetime of his elder brother, who is described as murdered while flourishing in wealth and power at the age of twenty-nine years? The supposition carries improbability on the face of it; none of the genealogies mention this second marriage at all; and Dr. Smith, whose county histories I have had particular occasion to examine, was, though a diligent collector of reports, no antiquarian authority to rely on. Above all, it is to be remembered, that Sir Walter Raleigh calls her The old Countess of Desmond of Inchequin: this is in itself proof, all but positive, that the lady was an O'Bryen, for none other could have part or lot in the hereditary designation of that family: hence I have no hesitation in adhering to the conclusion, which, with slight correction of dates, I have adopted from accurate authorities, that Margaret O'brien, WIFE OF JAMES, NINTH EARL OF DESMOND, WHO WAS MURDERED IN 1587, WAS THE GENUINE AND ONLY 'OLD COUNTESS.' Upon the only point on which I venture to correct my authority, namely, as to the date of the earl's death, I find, on reference to an older authority than any to which we have hitherto referred, that my emendation is confirmed. In the Annals of the Four Masters, compiled from more ancient documents still, in the year 1636, I find, under the date 1487, the following: The Earl of Desmond, James Fitzgerald, was treacherously killed by his own people at Rathgeola (Rathkeale, co. Limerick), at the instigation of his brother John. A. B. R. Belmont. THE IMPERIAL EAGLE OF FRANCE. On reading the Times of the 7th ult. at our city library, in which the following translation of a paragraph in the French journal, Le
- 70. Constitutionnel, appeared, application was made to me for an explanation of that part where the Emperor Napoleon is represented as stating, among other advantages of preferring an eagle to a cock as the national emblem or ensign, which, during the ancient dynasty of France, the latter had been— that it owes its origin to a pun. I will not have the cock, said the Emperor; it lives on the dunghill, and allows itself to have its throat twisted by the fox. I will take the eagle, which bears the thunderbolt, and which can gaze on the sun. The French eagles shall make themselves respected, like the Roman eagles. The cock, besides, has the disadvantage of owing its origin to a pun, c. Premising that the French journalist's object is to authorise the present ruler of France's similar adoption and restoration of the noble bird on the French standard by the example of his uncle, I briefly stated the circumstance to which Napoleon, on this occasion, referred; and as not unsuited, I should think, to your miscellany, I beg leave to repeat it here. In 1545, during the sitting of the Council of Trent, Peter Danes, one of the most eminent ecclesiastics of France, who had been professor of Greek, and filled several other consonant stations, appeared at the memorable council as one of the French representatives. While there, his colleague, Nicholas Pseaume, Bishop of Verdun, in a vehement oration, denounced the relaxed discipline of the Italians, when Sebastian Vancius de Arimino (so named in the Canones et Decreta of the Council), Bishop of Orvietto (Urbevetanus), sneeringly exclaimed Gallus cantat, dwelling on the double sense of the word Gallus—a Frenchman or a cock, and intending to express the cock crows; to which Danes promptly and pointedly responded, Utinam et Galli cantum Petrus resipisceret, which excited, as it deserved, the general applause of the assembly, thus turning the insult into a triumph. The apt allusion will be made clear by a reference to the words of the Gospels: St. Matthew, xxvi. 75.; St. Mark, xiv. 68. 72.; St. Luke, xxii. 61-2.; and
- 71. St. John, xviii. 27., where the ἀλεκτοροφωνία of the original is the cantus galli of the Vulgate, and where Petrus represents the pope, who is aroused to resipiscere by the example of his predecessor St. Peter. This incident in the memorable assembly is adverted to in the French contemporary letters and memoirs, but more particularly in the subsequent publication of a learned member of Danes's family, La Vie, Eloges et Opuscules de Pierre Danes, par P. Hilaire Danes, Paris, 1731, 4to., with the the portrait of the Tridentine deputy, who became Bishop of Lavaur, in Languedoc (now département du Saone), and preceptor to Francis, the short-lived husband of Mary Stuart, before that prince's ascent to the throne. So high altogether was he held in public estimation, that he was supposed well entitled to the laudatory anagram formed of his name (Petrus Danesius), De superis natus. In the Council of Trent there only appeared two Englishmen, Cardinal Pole and Francis Gadwell,[1] Bishop of St. Asaph, with three Irish prelates, (1) Thomas Herliky, Bishop of Ross, called Thomas Overlaithe in the records of the Council; (2) Eugenius O'Harte, there named Ohairte, a Dominican friar, Bishop of Ardagh; and (3) Donagh MacCongal, Bishop of Raphoe: Sir James Ware adds a fourth, Robert Waucup, or Vincentius, of whom, however, I find no mention in the official catalogue of the assisting prelates. Deprived of sight, according to Ware, from his childhood, he yet made such proficiency in learning, that, after attaining the high degree of Doctor of Sorbonne in France, he was appointed Archbishop of Armagh, or Primate of Ireland; but of this arch-see he never took possession, it being held by a reformed occupant, Dr. George Dowdall, appointed by Henry VIII. in 1543. [1] [Query, Thomas Goldwell.] J. R. (Cork.) FOLK LORE.
- 72. Valentine's Day (Vol. v., p. 55.). —Your correspondent J. S. A. will find the following notice of a similar custom to the one he alludes to in Mr. L. Jewitt's paper on the Customs of the County of Derby, in the last number of the Journal of the British Archæological Association: Of the latter (divinations) there is a curious instance at Ashborne, where a young woman who wishes to divine who her future husband is to be, goes into the church-yard at midnight, and as the clock strikes twelve, commences running round the church, repeating without intermission— 'I sow hemp-seed, hemp-seed I sow, He that loves me best Come after me and mow.' Having thus performed the circuit of the church twelve times without stopping, the figure of her lover is supposed to appear and follow her. J. Nottingham Hornblowing. —About the beginning of December the boys in and around Nottingham amuse themselves, to the annoyance of the more peaceable inhabitants, by parading the streets and blowing horns. I have noticed this for several years, and therefore do not think it is any whim or caprice which causes them to act thus; on the contrary, I think it must be the relic of some ancient custom. If any of your correspondents could elucidate this, it would particularly oblige Stomachosus. Bee Superstitions—Blessing Apple-trees—A Neck! a Neck!
- 73. —The superstition concerning the bees is common among the smaller farmers in the rural districts of Devon. I once knew an apprentice boy sent back from the funeral cortège by the nurse, to tell the bees of it, as it had been forgotten. They usually put some wine and honey for them before the hives on that day. A man whose ideas have been confused frequently says his head has been among the bees (buzzing). The custom is still very prevalent in Devonshire of hollowing to the apple-trees on Old Christmas Eve. Toasted bread and sugar is soaked in new cider made hot for the farmer's family, and the boys take some out to pour on the oldest tree, and sing— Here's to thee, Old apple-tree, From every bough Give apples enough, Hat fulls, cap fulls Bushel, bushel boss fulls. Hurrah, hurrah! The village boys go round also for the purpose, and get some halfpence given them for their hollering, as they call it. I believe this to be derived from a Pagan custom of offering to Ceres. The farmer's men have also a custom, on cutting the last sheaf of wheat on the farm, of shouting out A neck! a neck! as they select a handful of the finest ears of corn, which they bind up, and plait the straw of it, often very prettily, which they present to the master, who hangs it up in the farm kitchen till the following harvest. I do not know whence this custom arises. William Collyns, M.R.C.S. Kenton. Hooping Cough.
- 74. —In Cornwall, a slice of bread and butter or cake belonging to a married couple whose Christian names are John and Joan, if eaten by the sufferer under this disorder, is considered an efficacious remedy, though of course not always readily found. W. S. S. NOTE ON THE COINS OF VABALATHUS. (Vol. iv., pp. 255. 427. 491.) Since the publication of my last note on the coins of Vabalathus, I have obtained the Lettres Numismatiques du Baron Marchant, 1850. The original edition being very rare, and I believe only three hundred of this one having been printed, I have thought it might be as well to record some additional information from it in your pages. Marchant reads, Vabalathus Verenda Concessione Romanorum Imperatore Medis datus Rex. It is needless to remark on this, further than on the more ancient interpretations. He points out that the Greek letters, or rather numerals, show the coins to have been struck in a country where Greek, if not the popular language, was that of the government, along with Latin. This country was necessarily an Oriental one, and I think this observation would rather lead to the inference that the word Vcrimdr, occupying the place usually filled by Cæsar, Augustus, ϹΕΒΑϹΩϹ, c., might be an Oriental title, though expressed in Latin letters. Millin, to whom he had communicated his view, thought correctly que ça sentait un peu le père Harduin, and it was only published in the posthumous edition of his works. De Gauley has published coins struck by the Arabs in Africa, which have Latin legends, in some of which the Arabic titles are given in Latin letters. The Emir Musa Ben Nasir appears thus, MυSE. F. NASIR. AMIRA. The coins of Vabalathus offer a more ancient example of the same. I have given what appears to me the clue, and I hope it will be followed out by Orientalists. M. de Longperier, in his annotations to the 28th letter, shows that the name Ἀθηνᾶς is derived from Ἀθηνόδωρος, and appears to think
- 75. ΑΘΗΝΟΥ or ΑΘΗΝΥ the genitive of ΑΘΗΝΑϹ. The difficulty, he says, is, that names in ᾶς have, in the Alexandrian dialect, the genitive ᾶτος. He does not appear to have noticed the reading as ΥΙοϹ (or ΟΥ as Ο ΥΙοϹ?), which appears to me to remove the difficulty, but also to obviate the necessity of the name Ἀθηνᾶς at all. He remarks on the similarity of name between Αθηνας, Αθηνατος, and Odenathus. If, he says, we examine comparatively Vabalath (ΟΥΑΒΑΛΑΘ) and Odenath, or rather Odanath, as in Zosimus, we see an analogous formation; Ou-baalat, Ou-tanat, the feminine of Baal or Bel, and of Tan, Dan, or Zan, preceded by the same syllable. Baalat is a Scripture form (Jos. xix. 44.; 1 Kings ix. 48.; Paral. ii. viii. 6.). De Gauley has found the name of Tanat in a Phœnician inscription, and Lenormant remarks that this feminine form of Zan, or Jupiter, corresponds to Athéné. Thus Ou-tanat is the equivalent of Athenas, consequently of Athenodorus. Vabalathus is thus, if these etymological considerations be correct, the son of Odenathus. Longperier proposes to read ΕΡΩΤΑϹ for ϹΡΩΙΑϹ, and to consider this the equivalent of Herodes, mentioned by Trebellius Pollio. With all deference to M. de Longperier, I venture to oppose the following objections. First, Some coins read ϹΡΙΑϹ, which would read ΕΡΤΑϹ on his principle. Since, in the coins of Zenobia, Vabalathus, and those bearing the name of Athenodorus, whether struck by Vabalathus or not, is not material at present, we find the names at full length, not omitting the vowels, it is natural to suppose that the same would here take place, if the word really were the name of Herodes. To explain, if we found ΖΗΝΟΒΙΑ and ΖΝΟΒΙΑ, ΑΘΗΝΟΔΩΡΟϹ and ΑΘΝΔΡΟϹ, or similar contractions, we might consider ΕΡΩΤΑϹ and ΕΡΤΑϹ identical. Secondly, On my specimens of this coin I find the ι in this word distinctly formed, and the Τ in the next word ΑΥΤ as distinct. All authors have read this letter ι, although varying in the rest. Thirdly, On the obverse of these specimens the Ε is larger and more open than the Ϲ, as may be seen in the conclusion ...ΝΟϹ . ϹΕΒ, where it is preceded by two sigmas,
- 76. and is easy to compare with them. We should naturally expect to find it having the same form on the reverse, if the reading ΕΡΩΤΑϹ were correct. But it is of the same size as the other letters, on my specimens at least. I need not say that there is no trace of the central stroke. W. H. S. Edinburgh. THE AGNOMEN OF BROTHER JONATHAN, OF MASONIC ORIGIN. George Washington, commander-in-chief of the American army in the revolution, was a mason, as were all the other generals, with the solitary exception of Arnold the traitor, who attempted to deliver West Point, a most important position, into the hands of the enemy. It was this treasonable act on the part of Arnold which caused the gallant Andre's death, and ultimately placed a monument over his remains in Westminster Abbey. On one occasion, when the American army had met with some serious reverses, General Washington called his brother officers together, to consult in what manner their effects could be the best counteracted. Differing as they did in opinion, the commander-in-chief postponed any action on the subject, by remarking, Let us consult brother Jonathan, referring to Jonathan Trumbull, who was a well-known mason, and particularly distinguished for his sound judgment, strict morals, and having the tongue of good report. George Washington was initiated a mason in Fredericksburg, Virginia, Lodge No. 4, on the 4th of November, 1752, was passed a fellow craft on the 3rd of March, 1753, and raised to the sublime degree of a master mason on the 4th day of August, 1753. The hundredth anniversary of this distinguished mason's initiation is to be celebrated in America throughout the length and breadth of the land. W. W.
- 77. La Valetta, Malta. Minor Notes. Hippopotamus, Behemoth. —The young animal which has drawn so much attention hitherto, will increase in attractiveness as he acquires his voice, for which the zoologist may now arectis auribus await the development. It has appeared singular to many who knew the Greek name of this animal to signify river-horse, that he should be so unlike a horse. Nevertheless, the Greeks who knew him only at a distance, as we did formerly, named him from his voice and ears after an animal which he so little resembles in other respects. The Egyptian words from which the Behemoth of Job (chap. xl. v. 10.) are derived, more fitly designate him as water-ox, B-ehe-moūt = literatim, the aquatic ox. T. W. B. Lichfield. Curious Inscription (Vol. iv., pp. 88. 182.). —My ecclesiological note-book supplies two additional examples of the curious kind of inscription communicated by your correspondents J. O. B. and Mr. E. S. Taylor (by the way, the one mentioned by J. O. B. was found also at St. Olave's, Hart Street; see Weever, Fun. Mon.). These both occur at Winchester Cathedral: the first near a door in the north aisle, at the south-west angle:— ☜ ILL PREC AC ATOR H VI ☞
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