![naturally turned his thoughts to his former speculations. Was there
really no way of explaining the discrepancy which this law gave,
when he attempted to reduce the moon’s motion to the action of
gravity? A scientific operation then recently completed, gave the
explanation at once. He had been mistaken in the magnitude of the
earth, and consequently in the distance of the moon, which is
determined by measurements of which the earth’s radius is the base.
He had taken the common estimate, current among geographers
and seamen, that sixty English miles are contained in one degree of
latitude. But Picard, in 1670, had measured the length of a certain
portion of the meridian in France, with far greater accuracy than had
yet been attained and this measure enabled Newton to repeat his
calculations with these amended data. We may imagine the strong
curiosity which he must have felt as to the result of these
calculations. His former conjecture was now found to agree with the
phenomena to a remarkable degree of precision. This conclusion,
thus coming after long doubts and delays, and falling in with the
other results of mechanical calculation for the solar system, gave a
stamp from that moment to his opinions, and through him to those of
the whole philosophical world.
[2d Ed.] [Dr. Robison (Mechanical Philosophy, p. 288) says that
Newton having become a member of the Royal Society, there
learned the accurate measurement of the earth by Picard, differing
very much from the estimation by which he had made his
calculations in 1666. And M. Biot, in his Life of Newton, published in
the Biographie Universelle, says, “According to conjecture, about the
month of June, 1682, Newton being in London at a meeting of the
Royal Society, mention was made of the new measure of a degree of
the earth’s surface, recently executed in France by Picard; and great](https://image.slidesharecdn.com/65737-250222155720-9dae3f0a/85/Immediate-download-Concise-Guide-to-Software-Engineering-From-Fundamentals-to-Application-Methods-2nd-Edition-Gerard-O-Regan-ebooks-2025-27-320.jpg)
![praise was given to the care which had been employed in making
this measure exact.”
I had adopted this conjecture as a fact in my first edition; but it has
been pointed out by Prof. Rigaud (Historical Essay on the First
Publication of the Principia, 1838), that Picard’s measurement was
probably well known to the Fellows of the Royal Society as early as
1675, there being an account of the results of it given in the
Philosophical Transactions for that year. Newton appears to have
discovered the method of determining that a body might describe an
ellipse when acted upon by a force residing in the focus, and varying
405 inversely as the square of the distance, in 1679, upon occasion
of his correspondence with Hooke. In 1684, at Halley’s request, he
returned to the subject, and in February, 1685, there was inserted in
the Register of the Royal Society a paper of Newton’s (Isaaci
Newtoni Propositiones de Motu) which contained some of the
principal Propositions of the first two Books of the Principia. This
paper, however, does not contain the Proposition “Lunam gravitare in
terram,” nor any of the other propositions of the third Book. The
Principia was printed in 1686 and 7, apparently at the expense of
Halley. On the 6th of April, 1687, the third Book was presented to the
Royal Society.]
It does not appear, I think, that before Newton, philosophers in
general had supposed that terrestrial gravity was the very force by
which the moon’s motions are produced. Men had, as we have seen,
taken up the conception of such forces, and had probably called
them gravity: but this was done only to explain, by analogy, what
kind of forces they were, just as at other times they compared them
with magnetism; and it did not imply that terrestrial gravity was a
force which acted in the celestial spaces. After Newton had](https://image.slidesharecdn.com/65737-250222155720-9dae3f0a/85/Immediate-download-Concise-Guide-to-Software-Engineering-From-Fundamentals-to-Application-Methods-2nd-Edition-Gerard-O-Regan-ebooks-2025-28-320.jpg)
Immediate download Concise Guide to Software Engineering: From Fundamentals to Application Methods, 2nd Edition Gerard O'Regan ebooks 2025
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- 3. Undergraduate Topics in Computer Science Series Editor Ian Mackie, University of Sussex, Brighton, UK Advisory Editors Samson Abramsky , Department of Computer Science, University of Oxford, Oxford, UK Chris Hankin , Department of Computing, Imperial College London, London, UK Mike Hinchey , Lero – The Irish Software Research Centre, University of Limerick, Limerick, Ireland Joseph Migga Kizza, The University of Tennessee–Chattanooga, College of Engineering and Computer Science, Chattanooga, Tennessee, USA Dexter C. Kozen, Department of Computer Science, Cornell University, Ithaca, NY, USA Andrew Pitts , Department of Computer Science and Technology, University of Cambridge, Cambridge, UK Hanne Riis Nielson , Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark Steven S. Skiena, Department of Computer Science, Stony Brook University, Stony Brook, NY, USA Iain Stewart , Department of Computer Science, Durham University, Durham, UK
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- 6. Gerard O’Regan University of Central Asia Naryn, Kyrgyzstan ISSN 1863-7310 ISSN 2197-1781 (electronic) Undergraduate Topics in Computer Science ISBN 978-3-031-07815-6 ISBN 978-3-031-07816-3 (eBook) https://doi.org/10.1007/978-3-031-07816-3 1st edition: © Springer International Publishing AG 2017 2nd edition: © Springer Nature Switzerland AG 2022 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
- 7. To Past and present members of the Formal Methods Group (Foundations and Methods Group) at Trinity College Dublin, Ireland.
- 8. vii Preface Overview The objective of this book is to provide a concise introduction to the software engineering field to students and practitioners. The principles of software engi- neering are discussed, and the goal is to give the reader a grasp of the fundamentals of the software engineering field, as well as guidance on how to apply the theory in an industrial environment. Organization and Features Chapter 1 presents a broad overview of software engineering and discusses various software lifecycles and the activities in software development. We discuss requirements gathering and specification, software design, implementation, testing and maintenance. The lightweight Agile methodology is introduced, and it has become very popular in industry. Chapter 2 discusses the professional responsibilities of software engineers. Engineers have a responsibility to ensure that the products that they design and develop are built to the highest possible standards and are safe for the public to use. Engineers must behave ethically in their dealings with their clients, and they need to adhere to the code of ethics of the professional engineering body. Chapter 3 discusses ethical software engineering where the ethical software engineer needs to examine both the technical and the ethical dimensions of deci- sions that affect wider society. We discuss the Volkswagen emissions scandal where engineers installed a “defeat device” to enable cars to pass an emissions test. Chapter 4 introduces project management for traditional software engineering, and we discuss project estimation, project planning and scheduling, project moni- toring and control, risk management, managing communication and change, and managing project quality. Chapter 5 discusses requirements engineering and discusses activities such as requirements gathering, requirements elicitation, requirements analysis, require- ments management, and requirements verification and validation.
- 9. viii Preface Chapter 6 discusses software design and development, where software design is the blueprint of the solution to be developed. It is concerned with the high-level architecture of the system, as well as the detailed design that describes the algo- rithms and functionality of the individual programs. The detailed design is then implemented in a programming language such as C++ or Java. We discuss software development topics such as software reuse, customized-off-the-shelf software (COTS), and open-source software development. Chapter 7 discusses software inspections, which play an important role in building quality into a product. The well-known Fagan inspection process that was developed at IBM in the 1970s is discussed, as well as lighter review and walk- through methodologies. Chapter 8 is concerned with software testing and discusses the various types of testing that may be carried out during the project. We discuss test planning, test case definition, test environment set-up, test execution, test tracking, test metrics, test reporting, and testing in an e-commerce environment. Chapter 9 discusses ethics and privacy where professional ethics are a code of conduct that governs how members of a profession deal with each other and with third parties. It expresses ideals of human behaviour, and the fundamental values of the organization, and is an indication of its professionalism. Privacy is defined as “the right to be left alone,” and specifies there should be no intrusion upon seclusion, and no public disclosure of private facts or false information. Chapter 10 is concerned with metrics and problem-solving, and this includes a discussion of the balanced score card which assists in identifying appropriate metrics for the organization. The goal, question, metrics (GQM) approach is dis- cussed, and this allows appropriate metrics related to the organization goals to be defined. A selection of sample metrics for an organization is presented, and problem-solving tools such as fishbone diagrams, Pareto charts, trend charts are discussed. Chapter 11 is concerned with the selection and management of a software supplier. It discusses how candidate suppliers may be identified, formally evaluated against defined selection criteria, and how the appropriate supplier is selected. We discuss how the selected supplier is managed during the project. Chapter 12 discusses software configuration management and discusses the fundamental concept of a baseline. Configuration management is concerned with identifying those deliverables that must be subject to change control and controlling changes to them. Chapter 13 discusses software quality assurance and the importance of process quality. It is a premise in the quality field that good processes and conformance to them is essential for the delivery of high-quality product, and this chapter discusses audits, and describes how they are carried out. Chapter 14 discusses the Agile methodology which is a popular lightweight approach to software development. Agile provides opportunities to assess the direction of a project throughout the development lifecycle and ongoing changes to requirements are considered normal in the Agile world. It has a strong collaborative style of working, and it advocates adaptive planning and evolutionary development.
- 10. Preface ix Chapter 15discusses software reliability and dependability and covers topics suchas software reliability and software reliability models; the cleanroom methodology, sys- tem availability; safety and security critical systems; and dependability engineering. Chapter 16 discusses formal methods, which consist of a set of mathematical techniques to specify and derive a program from its specification. Formal methods may be employed to rigorously state the requirements of the proposed system. They may be employed to derive a program from its mathematical specification, and they may be used to provide a rigorous proof that the implemented program satisfies its specification. They have been mainly applied to the safety critical field. Chapter 17 presents the Z specification language, which is one of the more popular formal methods. It was developed at the Programming Research Group at Oxford University in the early 1980s. Z specifications are mathematical, and the use of mathematics ensures precision and allows inconsistencies and gaps in the specification to be identified. Theorem provers may be employed to demonstrate that the software implementation meets its specification. Chapter 18 presents the unified modelling language (UML), which is a visual modelling language for software systems, and I used to present several views of the system architecture. It was developed at Rational Corporation as a notation for modelling object-oriented systems. We present various UML diagrams such as use case diagrams, sequence diagrams, and activity diagrams. Chapter 19 discusses software process improvement. It begins with a discussion of a software process and discusses the benefits that may be gained from a software process improvement initiative. Various models that support software process improvement are discussed, and these include the Capability Maturity Model Integration (CMMI), ISO 9000, Personal Software Process (PSP), and Team Software Process (TSP). Chapter 20 gives an overview of the CMMI model and discusses its five maturity levels and their constituent process areas. We discuss both the staged and continuous representations of the CMMI and SCAMPI appraisals that indicate the extent to which the CMMI has been implemented in the organization, as well as identifying opportunities for improvement. Chapter 21 discusses various tools to support the various software engineering activities. The focus is first to define the process, and then to find tools to support the process. Tools to support project management are discussed as well as tools to support requirements engineering, configuration management, design and devel- opment activities, and software testing. Chapter 22 discusses innovation in the software field including miscellaneous topics such as distributed systems, service-oriented architecture, software as a service, cloud computing and embedded systems. We discuss the need for inno- vation in software engineering and discuss some recent innovations such as aspect-oriented software engineering. Chapter 23 is concerned with the application of the legal system to the com- puting field. This includes the protection of intellectual property such as patents, copyright, trademarks and trade secrets, and the resolution of disputes between parties.
- 11. x Preface Chapter 24 discusses cybersecurity and cybercrime. Cybercrime is a crime that involves a computer and a network. The computer may be the vehicle by which the crime was conducted, or it may be the target of the crime. Cybersecurity is con- cerned with the ability of a computer system to protect itself from attacks, and there are several characteristics of security such as confidentiality, integrity, and availability. Chapter 25 is the concluding chapter in which we summarize the journey that we have travelled in this book. Audience The main audience of this book is computer science students who are interested in learning about software engineering and in learning on how to build high-quality and reliable software on time and on budget. It will also be of interest to indus- trialists including software engineers, quality professionals and software managers, as well as the motivated general reader. Acknowledgments I am deeply indebted to family and friends who supported my efforts in this endeavour, and my thanks, as always, to the team at Springer. This book is dedi- cated to present and past members of the Formal Methods Group (Foundations and Methods Group) at Trinity College Dublin where the author spent several happy years. I would especially like to thank Dr. Mícheál Mac An Airchinnigh, Dr. Andrew Butterfield, Dr. Hugh Gibbons, Dr. Arthur Hughes, Alexis Donnelly, Dara Gallagher, Eoin McDonnell, Gradamir Starovic, and Glenn Strong. Cork, Ireland Gerard O’Regan
- 12. xi Contents 1 Fundamentals of Software Engineering. . . . . . . . . . . . . . . . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 What is Software Engineering? . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Challenges in Software Engineering . . . . . . . . . . . . . . . . . . . . 7 1.4 Software Processes and Lifecycles . . . . . . . . . . . . . . . . . . . . . 8 1.4.1 Waterfall Lifecycle . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4.2 Spiral Lifecycles . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4.3 Rational Unified Process . . . . . . . . . . . . . . . . . . . . . 11 1.4.4 Agile Development . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4.5 Continuous Software Development . . . . . . . . . . . . . 14 1.5 Activities in Software Development . . . . . . . . . . . . . . . . . . . . 15 1.5.1 Requirements Definition . . . . . . . . . . . . . . . . . . . . . 15 1.5.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.5.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.5.4 Software Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5.5 Support and Maintenance . . . . . . . . . . . . . . . . . . . . 20 1.6 Software Inspections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.7 Software Project Management . . . . . . . . . . . . . . . . . . . . . . . . 21 1.8 CMMI Maturity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.9 Formal Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.10 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2 Professional Responsibility of Software Engineers . . . . . . . . . . . . . 27 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2 What is a Code of Ethics? . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2.1 Role of a Whistle Blower . . . . . . . . . . . . . . . . . . . . 31 2.3 IEEE Code of Ethics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.4 British Computer Society Code of Conduct . . . . . . . . . . . . . . 34 2.5 ACM Code of Professional Conduct and Ethics . . . . . . . . . . . 35 2.6 Precautionary Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
- 13. xii Contents 2.7 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3 Ethical Software Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2 Safety and Ethics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1 Therac-25 Disaster . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2.2 Space Shuttle Challenger Disaster . . . . . . . . . . . . . . 45 3.3 Ethical Project Management. . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.4 Ethical Software Design and Development . . . . . . . . . . . . . . . 48 3.4.1 Volkswagen Emissions Scandal . . . . . . . . . . . . . . . . 52 3.5 Ethical Software Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.6 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4 Software Project Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 Project Start Up and Initiation . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.3.1 Estimation Techniques . . . . . . . . . . . . . . . . . . . . . . 61 4.3.2 Work Breakdown Structure . . . . . . . . . . . . . . . . . . . 61 4.4 Project Planning and Scheduling . . . . . . . . . . . . . . . . . . . . . . 63 4.5 Risk Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.6 People Management in Projects . . . . . . . . . . . . . . . . . . . . . . . 67 4.7 Quality Management in Projects. . . . . . . . . . . . . . . . . . . . . . . 68 4.8 Project Monitoring and Control . . . . . . . . . . . . . . . . . . . . . . . 69 4.9 Managing Issues and Change Requests. . . . . . . . . . . . . . . . . . 71 4.10 Remote Project Management . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.11 Outsourcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.12 Project Board and Governance . . . . . . . . . . . . . . . . . . . . . . . . 73 4.13 Project Reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.14 Project Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.15 Prince 2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.16 Project Manager Professional . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.17 Project Management Office . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.18 Program Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.19 Project Portfolio Management . . . . . . . . . . . . . . . . . . . . . . . . 80 4.20 Project Management in the Agile World . . . . . . . . . . . . . . . . . 81 4.21 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.22 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
- 14. Contents xiii 5 Requirements Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.2 Requirements Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.2.1 Requirements Elicitation and Specification . . . . . . . . 89 5.2.2 Requirements Analysis . . . . . . . . . . . . . . . . . . . . . . 92 5.2.3 Requirements Verification and Validation. . . . . . . . . 92 5.2.4 Requirements Management . . . . . . . . . . . . . . . . . . . 93 5.2.5 Requirements Traceability . . . . . . . . . . . . . . . . . . . . 94 5.3 System Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.4 Requirements Definition in the Agile World . . . . . . . . . . . . . . 97 5.5 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6 Software Design and Development . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.2 Architecture Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.3 Low-Level Design and Development . . . . . . . . . . . . . . . . . . . 106 6.3.1 Function-Oriented Design . . . . . . . . . . . . . . . . . . . . 107 6.3.2 Object-Oriented Design . . . . . . . . . . . . . . . . . . . . . . 107 6.3.3 User-Interface Design . . . . . . . . . . . . . . . . . . . . . . . 109 6.3.4 Open-Source Development . . . . . . . . . . . . . . . . . . . 109 6.3.5 Customized-off-the-Shelf Software . . . . . . . . . . . . . . 110 6.3.6 Software Reuse. . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.3.7 Design Patterns. . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.3.8 Object-Oriented Programming . . . . . . . . . . . . . . . . . 111 6.4 Software Maintenance and Evolution . . . . . . . . . . . . . . . . . . . 112 6.5 Software Design and Development in the Agile World . . . . . . 113 6.6 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 7 Software Inspections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.2 Economic Benefits of Software Inspections. . . . . . . . . . . . . . . 119 7.3 Informal Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.4 Structured Walkthrough . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.5 Semi-formal Review Meeting. . . . . . . . . . . . . . . . . . . . . . . . . 121 7.6 Fagan Inspections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7.6.1 Fagan Inspection Guidelines . . . . . . . . . . . . . . . . . . 125 7.6.2 Inspectors and Roles . . . . . . . . . . . . . . . . . . . . . . . . 126 7.6.3 Inspection Entry Criteria . . . . . . . . . . . . . . . . . . . . . 126 7.6.4 Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7.6.5 The Inspection Meeting. . . . . . . . . . . . . . . . . . . . . . 128
- 15. xiv Contents 7.6.6 Inspection Exit Criteria . . . . . . . . . . . . . . . . . . . . . . 130 7.6.7 Issue Severity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 7.6.8 Defect Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 7.7 Automated Software Inspections . . . . . . . . . . . . . . . . . . . . . . 133 7.8 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 7.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 8 Software Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 8.2 Test Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 8.3 Test Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 8.4 Test Case Design and Definition . . . . . . . . . . . . . . . . . . . . . . 144 8.5 Test Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 8.6 Test Reporting and Project Sign-Off . . . . . . . . . . . . . . . . . . . . 146 8.7 Testing and Quality Improvement . . . . . . . . . . . . . . . . . . . . . 147 8.8 Traceability of Requirements . . . . . . . . . . . . . . . . . . . . . . . . . 148 8.9 Test Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 8.10 E-Commerce Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 8.11 Testing in the Agile World . . . . . . . . . . . . . . . . . . . . . . . . . . 151 8.12 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 8.13 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 9 Ethics and Privacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 9.2 Business Ethics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 9.3 What is Computer Ethics? . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 9.3.1 Ethical Problems in Computing . . . . . . . . . . . . . . . . 160 9.3.2 The Ethical Software Engineer . . . . . . . . . . . . . . . . 161 9.3.3 Ethics in Data Science . . . . . . . . . . . . . . . . . . . . . . 162 9.4 Privacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 9.4.1 Social Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 9.4.2 Internet of Things . . . . . . . . . . . . . . . . . . . . . . . . . . 175 9.4.3 AI and Facial Recognition. . . . . . . . . . . . . . . . . . . . 176 9.4.4 Privacy and the Law . . . . . . . . . . . . . . . . . . . . . . . . 177 9.4.5 EU GDPR Privacy Law . . . . . . . . . . . . . . . . . . . . . 178 9.5 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 9.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 10 Software Metrics and Problem Solving . . . . . . . . . . . . . . . . . . . . . . 181 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 10.2 The Goal Question Metric Paradigm . . . . . . . . . . . . . . . . . . . 182 10.3 The Balanced Scorecard . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
- 16. Contents xv 10.4 Metrics for an Organization . . . . . . . . . . . . . . . . . . . . . . . . . . 187 10.4.1 Customer Satisfaction Metrics . . . . . . . . . . . . . . . . . 187 10.4.2 Process Improvement Metrics . . . . . . . . . . . . . . . . . 188 10.4.3 Human Resources and Training Metrics . . . . . . . . . . 190 10.4.4 Project Management Metrics . . . . . . . . . . . . . . . . . . 191 10.4.5 Development Quality Metrics . . . . . . . . . . . . . . . . . 193 10.4.6 Quality Audit Metrics . . . . . . . . . . . . . . . . . . . . . . . 195 10.4.7 Customer Care Metrics . . . . . . . . . . . . . . . . . . . . . . 197 10.4.8 Miscellaneous Metrics . . . . . . . . . . . . . . . . . . . . . . . 199 10.5 Implementing a Metrics Program . . . . . . . . . . . . . . . . . . . . . . 201 10.5.1 Data Gathering for Metrics . . . . . . . . . . . . . . . . . . . 202 10.6 Problem-Solving Techniques . . . . . . . . . . . . . . . . . . . . . . . . . 203 10.6.1 Fishbone Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . 205 10.6.2 Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 10.6.3 Pareto Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 10.6.4 Trend Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 10.6.5 Scatter Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 10.6.6 Metrics and Statistical Process Control . . . . . . . . . . . 210 10.7 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 10.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 11 Supplier Selection and Management . . . . . . . . . . . . . . . . . . . . . . . . 213 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 11.2 Planning and Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . 216 11.3 Identifying Suppliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 11.4 Prepare and Issue RFP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 11.5 Evaluate Proposals and Select Supplier. . . . . . . . . . . . . . . . . . 217 11.6 Formal Agreement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 11.7 Managing the Supplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 11.8 Acceptance of Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 11.9 Rollout and Customer Support . . . . . . . . . . . . . . . . . . . . . . . . 220 11.10 Ethical Software Outsourcing . . . . . . . . . . . . . . . . . . . . . . . . . 220 11.11 Legal Breach of Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 11.12 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 11.13 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 12 Configuration Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 12.2 Configuration Management System . . . . . . . . . . . . . . . . . . . . 231 12.2.1 Identify Configuration Items . . . . . . . . . . . . . . . . . . 232 12.2.2 Document Control Management . . . . . . . . . . . . . . . 232 12.2.3 Source Code Control Management. . . . . . . . . . . . . . 233 12.2.4 Configuration Management Plan . . . . . . . . . . . . . . . 233
- 17. Another Random Document on Scribd Without Any Related Topics
- 18. He says, moreover, “I am almost confident by circumstances, that Sir Christopher Wren knew the duplicate proportion when I gave him a visit; and then Mr. Hooke, by his book Cometa, will prove the last of us three that knew it.” Hooke’s Cometa was published in 1678. These inferences were all connected with Kepler’s law, that the times are in the sesquiplicate ratio of the major axes of the orbits. But Halley had also been led to the duplicate proportion by another train of reasoning, namely, by considering the force of the sun as an emanation, which must become more feeble in proportion to the increased spherical surface over which it is diffused, and therefore in the inverse proportion of the square of the distances.24 In this view of the matter, however, the difficulty was to determine what would be the motion of a body acted on by such a force, when the orbit is not circular but oblong. The investigation of this case was a problem which, we can 398 easily conceive, must have appeared of very formidable complexity while it was unsolved, and the first of its kind. Accordingly Halley, as his biographer says, “finding himself unable to make it out in any geometrical way, first applied to Mr. Hooke and Sir Christopher Wren, and meeting with no assistance from either of them, he went to Cambridge in August (1684), to Mr. Newton, who supplied him fully with what he had so ardently sought.” 23 Biog. Brit., art. Hooke. 24 Bullialdus, in 1645, had asserted that the force by which the sun “prehendit et harpagat,” takes hold of and grapples the planets, must be as the inverse square of the distance. A paper of Halley’s in the Philosophical Transactions for January, 1686, professedly inserted as a preparation for Newton’s work, contains some arguments against the Cartesian hypothesis of gravity, which seem to imply that Cartesian opinions had some
- 19. footing among English philosophers; and we are told by Whiston, Newton’s successor in his professorship at Cambridge, that Cartesianism formed a part of the studies of that place. Indeed, Rohault’s Physics was used as a classbook at that University long after the time of which we are speaking; but the peculiar Cartesian doctrines which it contained were soon superseded by others. With regard, then, to this part of the discovery, that the force of the sun follows the inverse duplicate proportion of the distances, we see that several other persons were on the verge of it at the same time with Newton; though he alone possessed that combination of distinctness of thought and power of mathematical invention, which enabled him to force his way across the barrier. But another, and so far as we know, an earlier train of thought, led by a different path to the same result; and it was the convergence of these two lines of reasoning that brought the conclusion to men’s minds with irresistible force. I speak now of the identification of the force which retains the moon in her orbit with the force of gravity by which bodies fall at the earth’s surface. In this comparison Newton had, so far as I am aware, no forerunner. We are now, therefore, arrived at the point at which the history of Newton’s great discovery properly begins. ~Additional material in the 3rd edition.~ 399
- 20. I CHAPTER II. The Inductive Epoch of Newton.—Discovery of the Universal Gravitation of Matter, according to the Law of the Inverse Square of the Distance. N order that we may the more clearly consider the bearing of this, the greatest scientific discovery ever made, we shall resolve it into the partial propositions of which it consists. Of these we may enumerate five. The doctrine of universal gravitation asserts, 1. That the force by which the different planets are attracted to the sun is in the inverse proportion of the squares of their distances; 2. That the force by which the same planet is attracted to the sun, in different parts of its orbit, is also in the inverse proportion of the squares of the distances; 3. That the earth also exerts such a force on the moon, and that this force is identical with the force of gravity; 4. That bodies thus act on other bodies, besides those which revolve round them; thus, that the sun exerts such a force on the moon and satellites, and that the planets exert such forces on one another; 5. That this force, thus exerted by the general masses of the sun, earth, and planets, arises from the attraction of each particle of these masses; which attraction follows the above law, and belongs to all matter alike.
- 21. The history of the establishment of these five truths will be given in order. 1. Sun’s Force on Different Planets.—With regard to the first of the above five propositions, that the different planets are attracted to the sun by a force which is inversely as the square of the distance, Newton had so far been anticipated, that several persons had discovered it to be true, or nearly true; that is, they had discovered that if the orbits of the planets were circles, the proportions of the central force to the inverse square of the distance would follow from Kepler’s third law, of the sesquiplicate proportion of the periodic times. As we have seen, Huyghens’ theorems would have proved this, if they had been so applied; Wren knew it; Hooke not only knew it, but claimed a prior knowledge to Newton; and Halley had satisfied himself that it was at 400 least nearly true, before he visited Newton. Hooke was reported to Newton at Cambridge, as having applied to the Royal Society to do him justice with regard to his claims; but when Halley wrote and informed Newton (in a letter dated June 29, 1686), that Hooke’s conduct “had been represented in worse colors than it ought,” Newton inserted in his book a notice of these his predecessors, in order, as he said, “to compose the dispute.”25 This notice appears in a Scholium to the fourth Proposition of the Principia, which states the general law of revolutions in circles. “The case of the sixth corollary,” Newton there says, “obtains in the celestial bodies, as has been separately inferred by our countrymen, Wren, Hooke, and Halley;” he soon after names Huyghens, “who, in his excellent treatise De Horologio Oscillatorio, compares the force of gravity with the centrifugal forces of revolving bodies.” 25 Biog. Brit. folio, art. Hooke.
- 22. The two steps requisite for this discovery were, to propose the motions of the planets as simply a mechanical problem, and to apply mathematical reasoning so as to solve this problem, with reference to Kepler’s third law considered as a fact. The former step was a consequence of the mechanical discoveries of Galileo and his school; the result of the firm and clear place which these gradually obtained in men’s mind, and of the utter abolition of all the notions of solid spheres by Kepler. The mathematical step required no small mathematical powers; as appears, when we consider that this was the first example of such a problem, and that the method of limits, under all its forms, was at this time in its infancy, or rather, at its birth. Accordingly, even this step, though much the easiest in the path of deduction, no one before Newton completely executed. 2. Force in different Points of an Orbit.—The inference of the law of the force from Kepler’s two laws concerning the elliptical motion, was a problem quite different from the preceding, and much more difficult; but the dispute with respect to priority in the two propositions was intermingled. Borelli, in 1666, had, as we have seen, endeavored to reconcile the general form of the orbit with the notion of a central attractive force, by taking centrifugal force into the account; and Hooke, in 1679, had asserted that the result of the law of the inverse square in the force of the earth would be an ellipse,26 or a curve like an ellipse.27 But it does not appear that this was any thing more than 401 a conjecture. Halley says28 that “Hooke, in 1683, told him he had demonstrated all the laws of the celestial motions by the reciprocally duplicate proportion of the force of gravity; but that, being offered forty shillings by Sir Christopher Wren to produce such a demonstration, his answer was, that he had it, but would conceal it for some time, that others, trying and failing, might know how to value it when he should make it public.” Halley, however, truly
- 23. observes, that after the publication of the demonstration in the Principia, this reason no longer held; and adds, “I have plainly told him, that unless he produce another differing demonstration, and let the world judge of it, neither I nor any one else can believe it.” 26 Newton’s Letter, Biog. Brit., Hooke, p. 2660. 27 Birch’s Hist. R. S., Wallis’s Life. 28 Enc. Brit., Hooke, p. 2660. Newton allows that Hooke’s assertions in 1679 gave occasion to his investigation on this point of the theory. His demonstration is contained in the second and third Sections of the Principia. He first treats of the general law of central forces in any curve; and then, on account, as he states, of the application to the motion of the heavenly bodies, he treats of the case of force varying inversely as the square of the distance, in a more diffuse manner. In this, as in the former portion of his discovery, the two steps were, the proposing the heavenly motions as a mechanical problem, and the solving this problem. Borelli and Hooke had certainly made the former step, with considerable distinctness; but the mathematical solution required no common inventive power. Newton seems to have been much ruffled by Hooke’s speaking slightly of the value of this second step; and is moved in return to deny Hooke’s pretensions with some asperity, and to assert his own. He says, in a letter to Halley, “Borelli did something in it, and wrote modestly; he (Hooke) has done nothing; and yet written in such a way as if he knew, and had sufficiently hinted all but what remained to be determined by the drudgery of calculations and observations; excusing himself from that labor by reason of his other business;
- 24. whereas he should rather have excused himself by reason of his inability; for it is very plain, by his words, he knew not how to go about it. Now is not this very fine? Mathematicians that find out, settle, and do all the business, must content themselves with being nothing but dry calculators and drudges; and another that does nothing but pretend and grasp at all things, must carry away all the inventions, as well of those that were to follow him as of those that 402 went before.” This was written, however, under the influence of some degree of mistake; and in a subsequent letter, Newton says, “Now I understand he was in some respects misrepresented to me, I wish I had spared the postscript to my last,” in which is the passage just quoted. We see, by the melting away of rival claims, the undivided honor which belongs to Newton, as the real discoverer of the proposition now under notice. We may add, that in the sequel of the third Section of the Principia, he has traced its consequences, and solved various problems flowing from it with his usual fertility and beauty of mathematical resource; and has there shown the necessary connection of Kepler’s third law with his first and second. 3. Moon’s Gravity to the Earth.—Though others had considered cosmical forces as governed by the general laws of motion, it does not appear that they had identified such forces with the force of terrestrial gravity. This step in Newton’s discoveries has generally been the most spoken of by superficial thinkers; and a false kind of interest has been attached to it, from the story of its being suggested by the fall of an apple. The popular mind is caught by the character of an eventful narrative which the anecdote gives to this occurrence; and by the antithesis which makes a profound theory appear the result of a trivial accident. How inappropriate is such a view of the matter we shall soon see. The narrative of the progress of Newton’s thoughts, is given by Pemberton (who had it from Newton himself) in
- 25. his preface to his View of Newton’s Philosophy, and by Voltaire, who had it from Mrs. Conduit, Newton’s niece.29 “The first thoughts,” we are told, “which gave rise to his Principia, he had when he retired from Cambridge, in 1666, on account of the plague (he was then twenty-four years of age). As he sat alone in a garden, he fell into a speculation on the power of gravity; that as this power is not found sensibly diminished at the remotest distance from the centre of the earth to which we can rise, neither at the tops of the loftiest buildings, nor even on the summits of the highest mountains, it appeared to him reasonable to conclude that this power must extend much further than was usually thought: Why not as high as the moon? said he to himself; and if so, her motion must be influenced by it; perhaps she is retained in her orbit thereby.” 29 Elémens de Phil. de Newton, 3me partie, chap. iii. The thought of cosmical gravitation was thus distinctly brought into being; and Newton’s superiority here was, that he conceived the 403 celestial motions as distinctly as the motions which took place close to him;—considered them as of the same kind, and applied the same rules to each, without hesitation or obscurity. But so far, this thought was merely a guess: its occurrence showed the activity of the thinker; but to give it any value, it required much more than a “why not?”—a “perhaps.” Accordingly, Newton’s “why not?” was immediately succeeded by his “if so, what then?” His reasoning was, that if gravity reach to the moon, it is probably of the same kind as the central force of the sun, and follows the same rule with respect to the distance. What is this rule? We have already seen that, by calculating from Kepler’s laws, and supposing the orbits to be circles, the rule of the force appears to be the inverse duplicate proportion of the distance; and this, which had been current as a conjecture
- 26. among the previous generation of mathematicians, Newton had already proved by indisputable reasonings, and was thus prepared to proceed in his train of inquiry. If, then, he went on, pursuing his train of thought, the earth’s gravity extend to the moon, diminishing according to the inverse square of the distance, will it, at the moon’s orbit, be of the proper magnitude for retaining her in her path? Here again came in calculation, and a calculation of extreme interest; for how important and how critical was the decision which depended on the resulting numbers? According to Newton’s calculations, made at this time, the moon by her motion in her orbit, was deflected from the tangent every minute through a space of thirteen feet. But by noticing the space through which bodies would fall in one minute at the earth’s surface, and supposing this to be diminished in the ratio of the inverse square, it appeared that gravity would, at the moon’s orbit, draw a body through more than fifteen feet. The difference seems small, the approximation encouraging, the theory plausible; a man in love with his own fancies would readily have discovered or invented some probable cause of this difference. But Newton acquiesced in it as a disproof of his conjecture, and “laid aside at that time any further thoughts of this matter;” thus resigning a favorite hypothesis, with a candor and openness to conviction not inferior to Kepler, though his notion had been taken up on far stronger and sounder grounds than Kepler dealt in; and without even, so far as we know, Kepler’s regrets and struggles. Nor was this levity or indifference; the idea, though thus laid aside, was not finally condemned and abandoned. When Hooke, in 1679, contradicted Newton on the subject of the curve described by a falling body, and asserted it to be an ellipse, Newton 404 was led to investigate the subject, and was then again conducted, by another road, to the same law of the inverse square of the distance. This
- 27. naturally turned his thoughts to his former speculations. Was there really no way of explaining the discrepancy which this law gave, when he attempted to reduce the moon’s motion to the action of gravity? A scientific operation then recently completed, gave the explanation at once. He had been mistaken in the magnitude of the earth, and consequently in the distance of the moon, which is determined by measurements of which the earth’s radius is the base. He had taken the common estimate, current among geographers and seamen, that sixty English miles are contained in one degree of latitude. But Picard, in 1670, had measured the length of a certain portion of the meridian in France, with far greater accuracy than had yet been attained and this measure enabled Newton to repeat his calculations with these amended data. We may imagine the strong curiosity which he must have felt as to the result of these calculations. His former conjecture was now found to agree with the phenomena to a remarkable degree of precision. This conclusion, thus coming after long doubts and delays, and falling in with the other results of mechanical calculation for the solar system, gave a stamp from that moment to his opinions, and through him to those of the whole philosophical world. [2d Ed.] [Dr. Robison (Mechanical Philosophy, p. 288) says that Newton having become a member of the Royal Society, there learned the accurate measurement of the earth by Picard, differing very much from the estimation by which he had made his calculations in 1666. And M. Biot, in his Life of Newton, published in the Biographie Universelle, says, “According to conjecture, about the month of June, 1682, Newton being in London at a meeting of the Royal Society, mention was made of the new measure of a degree of the earth’s surface, recently executed in France by Picard; and great
- 28. praise was given to the care which had been employed in making this measure exact.” I had adopted this conjecture as a fact in my first edition; but it has been pointed out by Prof. Rigaud (Historical Essay on the First Publication of the Principia, 1838), that Picard’s measurement was probably well known to the Fellows of the Royal Society as early as 1675, there being an account of the results of it given in the Philosophical Transactions for that year. Newton appears to have discovered the method of determining that a body might describe an ellipse when acted upon by a force residing in the focus, and varying 405 inversely as the square of the distance, in 1679, upon occasion of his correspondence with Hooke. In 1684, at Halley’s request, he returned to the subject, and in February, 1685, there was inserted in the Register of the Royal Society a paper of Newton’s (Isaaci Newtoni Propositiones de Motu) which contained some of the principal Propositions of the first two Books of the Principia. This paper, however, does not contain the Proposition “Lunam gravitare in terram,” nor any of the other propositions of the third Book. The Principia was printed in 1686 and 7, apparently at the expense of Halley. On the 6th of April, 1687, the third Book was presented to the Royal Society.] It does not appear, I think, that before Newton, philosophers in general had supposed that terrestrial gravity was the very force by which the moon’s motions are produced. Men had, as we have seen, taken up the conception of such forces, and had probably called them gravity: but this was done only to explain, by analogy, what kind of forces they were, just as at other times they compared them with magnetism; and it did not imply that terrestrial gravity was a force which acted in the celestial spaces. After Newton had
- 29. discovered that this was so, the application of the term “gravity” did undoubtedly convey such a suggestion; but we should err if we inferred from this coincidence of expression that the notion was commonly entertained before him. Thus Huyghens appears to use language which may be mistaken, when he says,30 that Borelli was of opinion that the primary planets were urged by “gravity” towards the sun, and the satellites towards the primaries. The notion of terrestrial gravity, as being actually a cosmical force, is foreign to all Borelli’s speculations.31 But Horrox, as early as 1635, appears to have entertained the true view on this subject, although vitiated by Keplerian errors concerning the connection between the rotation of the central body and its effect on the body which revolves about it. Thus he says,32 that the emanation of the earth carries a projected stone along with the motion of the earth, just in the same way as it carries the moon in her orbit; and that this force is greater on the stone than on the moon, because the distance is less. 30 Cosmotheoros, l. 2. p. 720. 31 I have found no instance in which the word is so used by him. 32 Astronomia Kepleriana defensa et promota, cap. 2. See further on this subject in the Additions to this volume. The Proposition in which Newton has stated the discovery of which we are now speaking, is the fourth of his third Book: “That the moon gravitates to the earth, and by the force of gravity is perpetually 406 deflected from a rectilinear motion, and retained in her orbit.” The proof consists in the numerical calculation, of which he only gives the elements, and points out the method; but we may observe, that no small degree of knowledge of the way in which astronomers had obtained these elements, and judgment in
- 30. selecting among them, were necessary: thus, the mean distance of the moon had been made as little as fifty-six and a half semidiameters of the earth by Tycho, and as much as sixty-two and a half by Kircher: Newton gives good reasons for adopting sixty-one. The term “gravity,” and the expression “to gravitate,” which, as we have just seen, Newton uses of the moon, were to receive a still wider application in consequence of his discoveries; but in order to make this extension clearer, we consider it as a separate step. ~Additional material in the 3rd edition.~ 4. Mutual Attraction of all the Celestial Bodies.—If the preceding parts of the discovery of gravitation were comparatively easy to conjecture, and difficult to prove, this was much more the case with the part of which we have now to speak, the attraction of other bodies, besides the central ones, upon the planets and satellites. If the mathematical calculation of the unmixed effect of a central force required transcendent talents, how much must the difficulty be increased, when other influences prevented those first results from being accurately verified, while the deviations from accuracy were far more complex than the original action! If it had not been that these deviations, though surprisingly numerous and complicated in their nature, were very small in their quantity, it would have been impossible for the intellect of man to deal with the subject; as it was, the struggle with its difficulties is even now a matter of wonder. The conjecture that there is some mutual action of the planets, had been put forth by Hooke in his Attempt to prove the Motion of the Earth (1674). It followed, he said, from his doctrine, that not only the sun and moon act upon the course and motion of the earth, but that Mercury, Venus, Mars, Jupiter, and Saturn, have also, by their
- 31. attractive power, a considerable influence upon the motion of the earth, and the earth in like manner powerfully affects the motions of those bodies. And Borelli, in attempting to form “theories” of the satellites of Jupiter, had seen, though dimly and confusedly, the probability that the sun would disturb the motions of these bodies. Thus he says (cap. 14), “How can we believe that the Medicean globes are not, like other planets, impelled with a greater velocity when they approach the sun: and thus they are acted upon by two moving forces, one of 407 which produces their proper revolution about Jupiter, the other regulates their motion round the sun.” And in another place (cap. 20), he attempts to show an effect of this principle upon the inclination of the orbit; though, as might be expected, without any real result. The case which most obviously suggests the notion that the sun exerts a power to disturb the motions of secondary planets about primary ones, might seem to be our own moon; for the great inequalities which had hitherto been discovered, had all, except the first, or elliptical anomaly, a reference to the position of the sun. Nevertheless, I do not know that any one had attempted thus to explain the curiously irregular course of the earth’s attendant. To calculate, from the disturbing agency, the amount of the irregularities, was a problem which could not, at any former period, have been dreamt of as likely to be at any time within the verge of human power. Newton both made the step of inferring that there were such forces, and, to a very great extent, calculated the effects of them. The inference is made on mechanical principles, in the sixth Theorem of the third Book of the Principia;—that the moon is attracted by the sun, as the earth is;—that the satellites of Jupiter
- 32. and Saturn are attracted as the primaries are; in the same manner, and with the same forces. If this were not so, it is shown that these attendant bodies could not accompany the principal ones in the regular manner in which they do. All those bodies at equal distances from the sun would be equally attracted. But the complexity which must occur in tracing the results of this principle will easily be seen. The satellite and the primary, though nearly at the same distance, and in the same direction, from the sun, are not exactly so. Moreover the difference of the distances and of the directions is perpetually changing; and if the motion of the satellite be elliptical, the cycle of change is long and intricate: on this account alone the effects of the sun’s action will inevitably follow cycles as long and as perplexed as those of the positions. But on another account they will be still more complicated; for in the continued action of a force, the effect which takes place at first, modifies and alters the effect afterwards. The result at any moment is the sum of the results in preceding instants: and since the terms, in this series of instantaneous effects, follow very complex rules, the sums of such series will be, it might be expected, utterly incapable of being reduced to any manageable degree of simplicity. It certainly does not appear that any one but Newton could make 408 any impression on this problem, or course of problems. No one for sixty years after the publication of the Principia, and, with Newton’s methods, no one up to the present day, had added any thing of any value to his deductions. We know that he calculated all the principal lunar inequalities; in many of the cases, he has given us his processes; in others, only his results. But who has presented, in his beautiful geometry, or deduced from his simple principles, any of the inequalities which he left untouched? The ponderous instrument
- 33. of synthesis, so effective in his hands, has never since been grasped by one who could use it for such purposes; and we gaze at it with admiring curiosity, as on some gigantic implement of war, which stands idle among the memorials of ancient days, and makes us wonder what manner of man he was who could wield as a weapon what we can hardly lift as a burden. It is not necessary to point out in detail the sagacity and skill which mark this part of the Principia. The mode in which the author obtains the effect of a disturbing force in producing a motion of the apse of an elliptical orbit (the ninth Section of the first Book), has always been admired for its ingenuity and elegance. The general statement of the nature of the principal inequalities produced by the sun in the motion of a satellite, given in the sixty-sixth Proposition, is, even yet, one of the best explanations of such action; and the calculations of the quantity of the effects in the third Book, for instance, the variation of the moon, the motion of the nodes and its inequalities, the change of inclination of the orbit,—are full of beautiful and efficacious artifices. But Newton’s inventive faculty was exercised to an extent greater than these published investigations show. In several cases he has suppressed the demonstration of his method, and given us the result only; either from haste or from mere weariness, which might well overtake one who, while he was struggling with facts and numbers, with difficulties of conception and practice, was aiming also at that geometrical elegance of exposition, which he considered as alone fit for the public eye. Thus, in stating the effect of the eccentricity of the moon’s orbit upon the motion of the apogee, he says,33 “The computations, as too intricate and embarrassed with approximations, I do not choose to introduce.” 33 Schol. to Prop. 35, first edit.
- 34. The computations of the theoretical motion of the moon being thus difficult, and its irregularities numerous and complex, we may ask 409 whether Newton’s reasoning was sufficient to establish this part of his theory; namely, that her actual motions arise from her gravitation to the sun. And to this we may reply, that it was sufficient for that purpose,—since it showed that, from Newton’s hypothesis, inequalities must result, following the laws which the moon’s inequalities were known to follow;—since the amount of the inequalities given by the theory agreed nearly with the rules which astronomers had collected from observation;—and since, by the very intricacy of the calculation, it was rendered probable, that the first results might be somewhat inaccurate, and thus might give rise to the still remaining differences between the calculations and the facts. A Progression of the Apogee; a Regression of the Nodes; and, besides the Elliptical, or first Inequality, an inequality, following the law of the Evection, or second inequality discovered by Ptolemy; another, following the law of the Variation discovered by Tycho;— were pointed out in the first edition of the Principia, as the consequences of the theory. Moreover, the quantities of these inequalities were calculated and compared with observation with the utmost confidence, and the agreement in most instances was striking. The Variation agreed with Halley’s recent observations within a minute of a degree.34 The Mean Motion of the Nodes in a year agreed within less than one-hundredth of the whole.35 The Equation of the Motion of the Nodes also agreed well.36 The Inclination of the Plane of the Orbit to the ecliptic, and its changes, according to the different situations of the nodes, likewise agreed.37 The Evection has been already noticed as encumbered with peculiar difficulties: here the accordance was less close. The Difference of the daily progress of the Apogee in syzygy, and its daily Regress in
- 35. Quadratures, is, Newton says, “4¼ minutes by the Tables, 6⅔ by our calculation.” He boldly adds, “I suspect this difference to be due to the fault of the Tables.” In the second edition (1711) he added the calculation of several other inequalities, as the Annual Equation, also discovered by Tycho; and he compared them with more recent observations made by Flamsteed at Greenwich; but even in what has already been stated, it must be allowed that there is a wonderful accordance of theory with phenomena, both being very complex in the rules which they educe. 34 B. iii. Prop. 29. 35 Prop. 32. 36 Prop. 33. 37 Prop. 35. The same theory which gave these Inequalities in the motion of the Moon produced by the disturbing force of the sun, gave also 410 corresponding Inequalities in the motions of the Satellites of other planets, arising from the same cause; and likewise pointed out the necessary existence of irregularities in the motions of the Planets arising from their mutual attraction. Newton gave propositions by which the Irregularities of the motion of Jupiter’s moons might be deduced from those of our own;38 and it was shown that the motions of their nodes would be slow by theory, as Flamsteed had found it to be by observation.39 But Newton did not attempt to calculate the effect of the mutual action of the planets, though he observes, that in the case of Jupiter and Saturn this effect is too considerable to be neglected;40 and he notices in the second edition,41 that it follows from the theory of gravity, that the aphelia of Mercury, Venus, the Earth, and Mars, slightly progress.
- 36. 38 B. i. Prop. 66. 39 B. iii. Prop. 23. 40 B. iii. Prop. 13. 41 Scholium to Prop. 14. B. iii. In one celebrated instance, indeed, the deviation of the theory of the Principia from observation was wider, and more difficult to explain; and as this deviation for a time resisted the analysis of Euler and Clairaut, as it had resisted the synthesis of Newton, it at one period staggered the faith of mathematicians in the exactness of the law of the inverse square of the distance. I speak of the Motion of the Moon’s Apogee, a problem which has already been referred to; and in which Newton’s method, and all the methods which could be devised for some time afterwards, gave only half the observed motion; a circumstance which arose, as was discovered by Clairaut in 1750, from the insufficiency of the method of approximation. Newton does not attempt to conceal this discrepancy. After calculating what the motion of apse would be, upon the assumption of a disturbing force of the same amount as that which the sun exerts on the moon, he simply says,42 “the apse of the moon moves about twice as fast.” 42 B. i. Prop. 44, second edit. There is reason to believe, however, that Newton had, in his unpublished calculations, rectified this discrepancy. The difficulty of doing what Newton did in this branch of the subject, and the powers it must have required, may be judged of from what has already been stated;—that no one, with his methods, has yet been able to add any thing to his labors: few have undertaken to illustrate what he has written, and no great number
- 37. have understood it throughout. The extreme complication of the forces, and of the conditions under which they act, makes the subject by far the most thorny walk of mathematics. It is necessary to resolve the action 411 into many elements, such as can be separated; to invent artifices for dealing with each of these; and then to recompound the laws thus obtained into one common conception. The moon’s motion cannot be conceived without comprehending a scheme more complex than the Ptolemaic epicycles and eccentrics in their worst form; and the component parts of the system are not, in this instance, mere geometrical ideas, requiring only a distinct apprehension of relations of space in order to hold them securely; they are the foundations of mechanical notions, and require to be grasped so that we can apply to them sound mechanical reasonings. Newton’s successors, in the next generation, abandoned the hope of imitating him in this intense mental effort; they gave the subject over to the operation of algebraical reasoning, in which symbols think for us, without our dwelling constantly upon their meaning, and obtain for us the consequences which result from the relations of space and the laws of force, however complicated be the conditions under which they are combined. Even Newton’s countrymen, though they were long before they applied themselves to the method thus opposed to his, did not produce any thing which showed that they had mastered, or could retrace, the Newtonian investigations. Thus the Problem of Three Bodies,43 treated geometrically, belongs exclusively to Newton; and the proofs of the mutual action of the sun, planets, and satellites, which depend upon such reasoning, could not be discovered by any one but him. 43 See the history of the Problem of Three Bodies, ante, in Book vi. Chap. vi. Sect. 7.