visions

For Joanna, Daniel, Benjamin and Susanna With thanks to Marilyn for her help and encouragement

Visions that Shaped the Universe Copyright ©1994 by Joseph L. Spradley. All rights reserved. Previously published by Wm. C. Brown, 1994-97 and by McGraw-Hill, 1997-2007 ISBN 0-697-26512-9 Reprinted with some revisions in 2007 for Wheaton College Wheaton, IL 60187

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Extended Contents page vi List of Figures ix Preface xi

Introduction: A Changing Universe 1 1. Science and History 1 2. Science and Religion 2 3. Science and Creation 3

1. A Religious Universe 6 1. Prehistoric Cultures 6 2. Ancient Egyptian Science 7 3. Babylonian Science 12 4. Phoenician & Hebrew Influences 17

2. A Rational Universe 22 1. The Greek Miracle 22 2. Pre-Socratic Science 23 3. Athenian Science 30 4. Alexandrian Science 40 3. A Purposeful Universe 49 1. Roman Science 49 2. Early Christian & Byzantine Views 51 3. Islamic Science 56 4. Medieval Christian Science 63 4. An Infinite Universe 71 1. The Copernian System 71 2. Copernican Responses & Parallels 76 3. Reactions to Infinity: Brahe & Kepler 79 4. Visions of Infinity: Galileo & Followers 86 5. A Mechanical Universe 95 1. Galileo & Mechanical Ideas 95 2. Scientific Philosophies & Societies 99 3. Mechanical Instruments & Ideas 104 4. Triumph of Mechanistic Science 109

6. An Energistic Universe 125 1. Origins of the Energy Concept 125 2. The Chemical Revolution 129 3. Heat and Thermodynamics 136 4. Energy Propagation: Waves 143 7. An Evolving Universe 152 1. Early Evolutionary Ideas 152 2. Design & Development in Biology 157 3. Earth History & Geology 162 4. The Theory of Evolution 167 8. An Electromagnetic Universe 176 1. Electric Charge & Current 176 2. Electromagnetism 185 3. Electromagnetic Fields & Waves 191 4. Electromagnetic Applications 200 9. A Relational Universe 206 1. Ether & Relativity Theories 206 2. Radioactivity & Atomic Models 215 3. Quantum Theory & the Atom 221 4. Quantum Wave Theory 228

10. An Expanding Universe 235 1. Evidences of an Expanding Universe 235 2. Nuclear Particles & Energy 240 3. Birth of Stars & the Universe 248 4. Elementary Particles & Forces 252 Conclusion: A Living Universe 262 1. The Secret of Life 263 2. The Miracle of Life 264 3. The Value of Life 266

Index 268

Visions that Shaped the Universe TABLE OF CONTENTS

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List of Figures page ix Preface xi Introduction: A Changing Universe 1 Shifting Views of Science and the Universe

1. SCIENCE AND HISTORY 1 2. SCIENCE AND RELIGION 2 3. SCIENCE AND CREATION 3 Chapter 1. A Religious Universe 6 Origins of Science in the Earliest Civilizations

1. PREHISTORIC CULTURES 6 Paleolithic Hominids 6 Neolithic Cultures 7

2. ANCIENT EGYPTIAN SCIENCE 7 Religious Background 7 Egyptian Technology 8 Egyptian Science 9 Egyptian Mathematics 10

3. BABYLONIAN SCIENCE 12 Cultural Background 12 Babylonian Mathematics 13 Babylonian Astronomy and Mythology 14 Late Babylonian Astrology 16

4. PHOENICIAN & HEBREW INFLUENCES 17 Phoenician Contributions 17 The Hebrew View of Nature 18 The Biblical Idea of Creation 18 The Importance of the Idea of Creation 19 Chapter 2. A Rational Universe 22 Foundations of Science in Ancient Greece

1. THE GREEK MIRACLE 22 The Cultural Setting 22 The Homeric Background 23

2. PRE-SOCRATIC SCIENCE (600-400 BC) 23 Ionian Science: Matter & Change 23 Pythagorean Science: Mystics & Mathematics 26 Eleatics & Atomists: Permanence & Motion 29 3. ATHENIAN SCIENCE (450-323 BC) 30 Early Syntheses of Pre-Socratic Science 30 Plato and the Academy 32 Aristotle and the Lyceum 36 4. ALEXANDRIAN SCIENCE (323-415 BC) 40 Hellenistic Trends 40 Alexandrian Mathematics 40 Alexandrian Astronomy & Geography 43 Chapter 3. A Purposeful Universe 49 Transmission and Transformation of Greek Science

1. ROMAN SCIENCE 49 Encyclopedia Tradition 49 Medicine 50 Astrology and Alchemy 50

2. EARLY CHRISTIAN & BYZANTINE VIEWS 51 The Birth of Christianity 51 Early Christian Views 51 The Augustinian Synthesis 52 Decline of Science in the West 54 Byzantine Science 55 3. ISLAMIC SCIENCE 56 Origins of Islam 56 Islamic Science before AD 1000 57 Islamic Science after AD 1000 59

4. MEDIEVAL CHRISTIAN SCIENCE 63 The Translators 63 Medieval Universities 63 The Medieval Synthesis 65 Reactions to Thomism 66 Renaissance Awakenings 68

Visions that Shaped the Universe EXTENDED CONTENTS

Extended Contents vii

Chapter 4. An Infinite Universe 71 The Copernican Revolution and its Reception

1. THE COPERNICAN SYSTEM 71 Background and Sources 71 Objections and Innovations 72 Advantages and Problems 75

2. COPERNICAN RESPONSES & PARALLELS 76 Early Lutheran Responses to Copernicus 76 Developments in Other Sciences 77 Catholic and Protestant Reactions 79 3. COPERNICAN MODIFICATIONS 79 The Work of Tycho Brahe 79 The Tychonic System 81 Early Work of Johannes Kepler 82 Breaking of the Circle 83 Harmony of the Universe 84 4. COPERNICAN APPLICATIONS 86 Galileo and the Telescope 86 Galileo's Telescopic Discoveries 88 Galileo and the Church 89 Responses & Reactions to Galileo's Work 92 Chapter 5. A Mechanical Universe 95 The Scientific Revolution and Newtonian Synthesis

1. GALILEO AND MECHANICAL IDEAS 95 Free Fall and Gravity 95 Projectile Motion and Inertia 97 Gassendi's Revival of Atomism 98 Borelli's Development of Mechanics 99 2. SCIENTIFIC PHILOSOPHIES & SOCIETIES 99 Bacon's Empiricist Philosophy 99 Descartes and Mechanistic Philosophy 100 Boyle and Corpuscular Philosophy 102 Scientific Societies & the Puritan Ethic 103 3. MECHANICAL INSTRUMENTS & IDEAS 104 Huygens' Clock & other Contributions 104 New Mechanical Ideas 105 The Air Pump and Other Machines 107 The Microscope 108 4. TRIUMPH OF MECHANISTIC SCIENCE 109 Early Newtonian Ideas 109 The Newtonian Synthesis 112 Newton's Fluxions and Optics 117 The Influence of Newtonian Ideas 119

Chapter 6. An Energistic Universe 125 Chemical & Industrial Revolutions, Heat & Light

1. ORIGINS OF THE ENERGY CONCEPT 125 The Vis Viva Concept 125 The Phlogiston Theory 126 New Gases and Experimental Methods 127

2. THE CHEMICAL REVOLUTION 129 Lavoisier and the Elements 129 Dalton's Atomic Theory 131 Avogadro's Molecular Theory 132 Organic and Structural Chemistry 133 Mendeléev's Periodic Table 135

3. HEAT AND THERMODYNAMICS 136 Heat and the Steam Engine 136 Dissipation of Heat 139 Conservation of Energy 140 Thermodynamics and Kinetic Energy 142

4. ENERGY PROPAGATION 143 Waves and Sound 143 Revival of the Wave Theory of Light 146 Development of the Wave Theory of Light 147 Radiation and Spectroscopy 149 Chapter 7. An Evolving Universe 152 Developmental Concepts and Evolutionary Theories

1. EARLY EVOLUTIONARY IDEAS 152 Temporalizing the Chain of Being 152 Evolutionary Speculations 153 Lamarck's Theory: Acquired Characteristics 154 Early Evolution Debates 156 2. DESIGN & DEVELOPMENT IN BIOLOGY 157 Natural Theology & Nature Philosophy 157 Epigenesis and Embryology 158 The Cell Theory 159 The Decline of Vitalism 160 3. EARTH HISTORY AND GEOLOGY 162 Early Theories of the Earth 162 Vulcanism and Neptunism 163 Uniformitarianism and Catastrophism 164 Fossils and Stratification 166 4. THE THEORY OF EVOLUTION 167 The Darwinian Synthesis 167 The Origin of Species 169 Reception and Reaction to Darwinism 170 Genetics and Neo-Darwinism 172

viii Extended Contents

Chapter 8. An Electromagnetic Universe 176 Electric Charge and Field Concepts

1. ELECTRIC CHARGE AND CURRENT 176 The Concept of Electric Charge 177 Electric Conduction and Fluids 178 Electric Force and Quantity of Charge 181 Electric Current and the Battery 183

2. ELECTROMAGNETISM 185 Magnetic Effects of Electric Current 185 Electromagnetic Force & Electric Motor 187 Electromagnetic Induction & the Generator 189 Mutual and Self-Induction 190

3. ELECTROMAGNETIC FIELDS & WAVES 191 The Field Concept and Electrolysis 191 Electric Circuits and Oscillations 194 Maxwell's Electromagnetic Field Theory 196 Prediction of Electromagnetic Waves 197

4. ELECTROMAGNETIC APPLICATIONS 200 Reception of Maxwell's Theory 200 Hertz and the Discovery of Radio Waves 201 Applications of Radio Waves 202 Extensions of the Electromagnetic Spectrum 203 Chapter 9. A Relational Universe 206 Relativity and Quantum Theories

1. ETHER AND RELATIVITY THEORIES 206 The Michelson-Morley Experiment 207 The Lorentz-Fitzgerald Contraction 208 Einstein's Special Theory of Relativity 209 The General Theory of Relativity 212

2. RADIOACTIVITY & ATOMIC MODELS 215 Discovery of Radioactivity & the Electron 215 The Analysis of Radioactivity 218 Radioactive Decay and Isotopes 219 The Nuclear Model of the Atom 220

3. QUANTUM THEORY AND THE ATOM 221 Planck's Analysis of Thermal Radiation 221 Einstein and the Photoelectric Effect 223 Bohr Theory of the Hydrogen Atom 224 Extensions of the Bohr Theory 227

4. QUANTUM WAVE THEORY 228 Wave-Particle Dualities 228 The New Quantum Mechanics 229 Interpretations of Quantum Wave Theory 231 Extensions of Quantum Mechanics 232 Chapter 10. An Expanding Universe 235 The Big Bang Theory and Elementary Particles 1. EVIDENCES OF UNIVERSAL EXPANSION 235 Galaxies and the Red Shift 235 Relativistic Cosmologies 237 Hubble's Law of Expansion 238 The Exploding Universe 239 2. NUCLEAR PARTICLES AND ENERGY 240 Discovery of the Neutron and Neutrino 240 Nuclear Forces and the Meson 242 Discovery of Nuclear Fission 243 The Development of Nuclear Energy 245 3. BIRTH OF STARS AND THE UNIVERSE 248 Energy Processes in the Stars 248 Steady-State Theory & Continuous Creation 249 The Big Bang Theory and Nucleosynthesis 250 Successes of the Big Bang Theory 251 4. ELEMENTARY PARTICLES & FORCES 252 Strange Particles and Particle Families 252 Quarks and Leptons 253 Unified Force Theories 255 Creation of the Universe 257

Conclusion: A Living Universe 262 New Evidence for Design and Human Significance 1. THE SECRET OF LIFE 263

2. THE MIRACLE OF LIFE 264

3. THE VALUE OF LIFE 266 Index 26

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1. A Religious Universe 6 1.1 Ancient Egyptian Geometric Concepts 11 1.2 Babylonian Astronomical Concepts 15

2. A Rational Universe 22 2.1 Thales' Right-Triangle Theorem 24 2.2 Anaximander's Unsupported Earth 25 2.3 The Pythagorean Theorem 27 2.4 Pythagorean Cosmology of Philolaus 28 2.5 The Phases & Eclipses of the Moon 31 2.6 Five Regular Solids of Pythagoras 33 2.7 Concentric Spheres of Eudoxus 35 2.8 Aristotle's Antiperistasis Concept 37 2.9 Aristotle's Geocentric Cosmology 39 2.10 Archimedes' Method of Limits 41 2.11 Conic Sections of Apollonius 42 2.12 The Epicycle of Apollonius 43 2.13 Aristarchus on the Size of the Sun 44 2.14 Eratosthenes' on the Size of the Earth 45 2.15 Ptolemy's Epicycle Model 47

3. A Purposeful Universe 49 3.1 Al-Farghani's Planetary Distances 58 3.2 Al-Haytham's Atmospheric Refraction 60 3.3 Al-Haytham's Crystalline Spheres 61 3.4 Oresme's Graph & Mean-Speed Rule 68

4. An Infinite Universe 71

4.1 Heliocentric Earth Motions 73 4.2 Planetary Distances & Stellar Parallax 74 4.3 Copernicus' Use of Circles for Orbits 75 4.4 Tycho Brahe's Measurements 80 4.5 The Tychonic System 81 4.6 Kepler's Theory of Planetary Distances 83 4.7 Kepler's Three Laws of the Planets 85 4.8 Galileo's Discovery Jupiter's Moons 88 4.9 The Phases of Venus in Three Systems 90 4.10 Torricelli's "Sea of Air" Hypothesis 93

5. A Mechanical Universe 95 5.1 Galileo's Analysis of Motion on an Inclined

Plane 96 5.2 Galileo's Concept of Projectile Motion 97 5.3 Huygen's Centrifugal Force Idea 105 5.4 Conservation Laws in Collisions 106 5.5 Roemer's Measurement of the Speed of Light 107 5.6 Newton's Demonstration of the Composite

Nature of White Light 110 5.7 Inverse-Square Law for the Moon 111 5.8 Newton's Law of Universal Gravitation 114 5.9 Equatorial Bulge and its Effects 115 5.10 Newton's Explanation of the Tides 116 5.11 Comet Orbit & Planet Perturbations 117 5.12 Measurement of Universal Gravitation 123

6. An Energistic Universe 125

6.1 Dalton's Atomic Symbols 132 6.2 Kekulé's Structure for Benzene 135 6.3 Watt's Steam Engine 138 6.4 Rumford's Idea of Heat as Motion 139 6.5 Joule's Measurement of the Mechanical

Equivalence of Heat 141 6.6 Transverse & Longitudinal Waves 144 6.7 Interference & Standing Waves 145 6.8 Young's Double-Slit Experiment 147 6.9 Infrared, Ultraviolet & Line Spectra 149

7. An Evolving Universe 152

7.1 Modern Biological Classification 157 7.2 Stages in Cell Mitosis 160 7.3 Steno's Diagrams of Strata Changes 162 7.4 Hutton's Geological Processes 165 7.5 Smith's Correlation of Fossils & Strata 166 7.6 Wegener's Theory of Continental Drift 172 7.7 Diagram of Mendel's Pea Plants 173

LIST OF FIGURES

x List of Figures

8. An Electromagnetic Universe 176 8.1 Franklin's Lightning Experiment 181 8.2 Volta's Electric Battery 184 8.3 Oersted's Electromagnetic Effect 185 8.4 Ampère's Current Measurement 186 8.5 Ampère's Electrical Theory of Magnetism 187 8.6 Direct-Current Electric Motor 191 8.7 Faraday's Field Concept 192 8.8 Alternating-Current Generator/Motor 193 8.9 Mutual Induction & Transformer 194 8.10 Henry's Electric Oscillator 195 8.11 Maxwell's Electromagnetic Wave Concept 199 8.12 Hertz's Discovery of Radio Waves 201

9. A Relational Universe 206 9.1 Michelson-Morley Experiment 207 9.2 Invariance of the Speed of Light 211 9.3 Principle of Equivalence 213 9.4 Gravitational Bending of Light 215 9.5 Thomson's Identification of Electrons 216 9.6 Millikan's Oil-drop Experiment 217

9.7 Separation of Radioactivity by a Magnetic Field 218 9.8 Rutherford's Scattering Experiment 221 9.9 Thermal Blackbody Radiation 222 9.10 Photoelectric Effect & Photon Concept 224 9.11 Bohr's Model of the Hydrogen Atom 226 9.12 Stimulated Emission and the Laser 227 9.13 Compton's X-ray Experiment 228 9.14 DeBroglie Wavelength for an Orbiting Electron 229 9.15 Free Particle Wave Function 231

10. An Expanding Universe 235 10.1 Friedmann Universes 238 10.2 Hubble's Law of Expansion 239 10.3 Lemaître's Hesitation Universe 240 10.4 Quantum Fields and Exchange Forces 242 10.5 Liquid-drop Model of Nuclear Fission 245 10.6 Nuclear Reactor for Generating Electric Power 246 10.7 Critical Mass Concept 247 10.8 Quark Model of the Proton 254 10.9 Creation & Expansion of the Universe 258

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Most books on the history of science make little effort to describe the concepts of sci-ence in any detail, and few books on the natural sciences attempt a comprehensive historical per-spective. In order to achieve both of these empha-ses on the conceptual and historical within a rea-sonable length, it is necessary to combine both brevity and a clear focus on a basic unifying theme. The broadest possible theme is the universe itself, and the scientific visions that have shaped various views of the universe over the course of history in Western civilization. Although the methodology of science involves the search for natural causes and expla-nations, its history shows that the concepts and theories that guide this search have been heavily influenced by aesthetic, cultural, philosophical and religious values and ideas. Thus an emphasis on history can help to establish connections and show relationships between science and various world views that have dominated different historical periods. The historical approach means that some blind alleys and historically limited perspectives must be explored, but these can reveal the human dimensions of science and the often tortuous proc-ess of scientific discovery. It also should provide an enhanced appreciation for our cultural heritage in regard to many things we often take for granted. Humanities students can especially benefit from the historical approach to science since it allows them to see the relationship between science and culture, and to recognize the relevance of scientific ideas to their disciplines. Such an approach is often more accessible and interesting to the liberal

arts student than the more traditional emphasis on scientific methodology and applications in technology. Science students can also benefit from the historical foundations of their disciplines in order to appreciate how basic scientific concepts were discovered and developed. They should also recognize the connection between their special field of interest and other fields of science, and gain a more critical understanding of scientific theories as human creations. The broader implications of science and its influence on world views are also important for science students to know. The history of science can reveal both the multicultural roots and the societal fruits of scientific knowledge. To clarify scientific ideas in their histori-cal context, some use of mathematics is unavoid-able. Simple geometry and basic algebra are used to express some of the more important scientific relationships and to reveal their quantitative and predictive potential. In a few cases, more advanced equations that express fundamental laws are included to reveal basic connections and sym-metries, even though their operational meaning is too advanced for many readers. A minimum of algebraic manipulation is used to demonstrate the development of scientific laws, but no emphasis is given to problem solving. Most college students should have enough knowledge from high school mathematics to appreciate the simple equations that are used, but even these are not essential to follow most of the discussion of the basic concepts and their historical development from the narrative alone.

PREFACE

xii Preface

To clarify some of the most important concepts, about 100 diagrams appear in conjunc-tion with the text. Although the narrative can be read without reference to these figures, they are intended to provide a graphic representation of ideas that might otherwise be difficult to visualize. Captions should also make the figures intelligible apart from the text. Most of the diagrams relate to important historical contributions. They have been developed and tested for their pedagogical value over several years of teaching. They were designed and produced by the author with the aid of a simple computer graphics program (Microsoft Draw). In many cases, they borrow ideas from other sources, but all are original in their overall conception and design. Much of the material presented here was developed over several years for a general science requirement for nonscience majors at Wheaton College. It has also been used for similar courses abroad at Ahmadu Bello University (Nigeria), at Daystar University College (Kenya), and at the American University in Cairo (Egypt). A good start on the first draft was made possible by a sab-batical leave at the American University in Cairo, where a convenient teaching schedule permitted large blocks of time for writing. The opportunity to travel in Egypt stimulated my interest in both

ancient Egyptian and Islamic science. I would like to express special appreciation to Dr. Fadel Assabghy, Dr. Gregg DeYoung, and Dr. Cynthia Nelson for helping to make my year in Egypt both enjoyable and productive. I would also like to acknowledge the en-couragement of administrators and colleagues at Wheaton College. Dr. Arthur Holmes has been especially helpful in my own liberal arts education ever since I participated in his History of Philoso-phy class early in my teaching career, and since then in various seminars he led. Several genera-tions of students have also provided stimulation and encouragement by their participation in courses I have taught. I especially appreciate the assistance of Dr. Douglas Penney in reviewing some of my manuscript on ancient science, and Dr. William Wharton for making helpful suggestions for the last two chapters on modern science. Any grammatical or spelling errors should be attributed to Microsoft Word, since that program was used to check the grammar and spelling in each chapter. Finally, I am deeply indebted to my wife Marilyn, who provided constant support and encouragement both at home and while living and traveling abroad.

Joseph L. Spradley Physics Department

Wheaton College (IL)

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Science is ever changing. The history of science reveals many ways of viewing the uni-verse. The long tradition of Western science has explored the world from a variety of perspectives, using many different metaphors and models to try to capture its essence. These ideas about the universe have contributed to the shape and meaning of existence within various cultural expressions. They have helped to structure social experience. They have guided the cycles of life and opened up new vistas of understanding and appreciation. They have tried to answer fundamental questions about God and the world, and have offered new ways to benefit from the resources around us. However, every answer has raised new questions and mysteries, and growing knowledge has shifted ideas and values. Every attempt to understand the universe bases its approach on different values and assumptions that affect the very language of observation and the definition of what is factual. Each deserves our appreciation on its own merits. 1. SCIENCE AND HISTORY Any adequate definition of science must be broad enough to account for its changing ideas and historical development. Science is more than just an effort to control nature, which gave rise to

both magic and the craft tradition. It is more than the accumulation of information, whatever accu-racy that may have, since such information is meaningless without interpretation. It is not just any theory about nature without a solid empirical basis, lest it becomes mere speculation. It is important to distinguish science from technology, although they often overlap. Science is more than just a method for gaining systematic knowledge, no matter how precise and objective that knowledge may be. Above all, science is a creative human effort to explain and understand natural phenomena, and thus is continually changing as it interacts with new ideas and observations. What can we learn from the antiquated ideas of the past? Should we only trace those theories and discoveries that have contributed to our modern view of the universe, or can we benefit by learning from the mistakes of the past as well? Awareness of the intellectual roots of con-temporary knowledge and the stages in its development is an important aspect of learning and a safeguard against false or misleading opinions. Some knowledge of the scientific basis of modern technology can help to keep it from becoming a new form of magic or even idolatry. Often, the best way to understand science is to trace the process of discovery and see how scientific ideas have developed historically.

INTRODUCTION

A Changing Universe

Shifting Views of Science and the Universe

Introduction • A Changing Universe 2

The history of science also teaches us that scientific ideas are always changing and that our view of the universe is not the last word. Perhaps there are lessons to learn from other ways of seeing the world that will help us to understand both the importance and the limits of our own intellectual heritage. Every historical period has built its view of the universe on different aspira-tions and assumptions, and ours is no exception. The relationship between science and culture, and the underlying presuppositions of each, are often more evident in the world views of the past. It is necessary to study them in terms of their own goals and values if they are to make sense. Here the emphasis will be on the history of scientific ideas that have influenced various views of the universe and thus shaped world views more generally. The earliest scientific ideas grew out of religious practices that led to careful records of celestial regularities, especially in the ancient Egyptian and Babylonian civilizations (Chapter 1). In an attempt to explain these regularities, the Greeks gave birth to a rational view of the universe. This included the idea of a spherical Earth at the center of the celestial spheres (Chapter 2). The medieval cultures that inherited these ideas developed them into hierarchical systems with a purposeful relationship between God, humans and the Earth (Chapter 3). In the Renaissance revival of Greek knowledge, the new Copernican system of the planets circling the Sun led to the idea of an infi-nite universe (Chapter 4). Development of this heliocentric system in the seventeenth century pro-duced a new emphasis on a mechanical universe of inert matter in motion, culminating in the New-tonian synthesis as the basis for the eighteenth century Enlightenment (Chapter 5). During the Industrial Revolution of the eighteenth century, the energy concept gave rise to the more active view of an energistic universe, supporting a chemical rev-olution (Chapter 6). By the nineteenth century a new idea of progress helped to introduce de-velopmental concepts in geology and biology, leading to the evolving universe of the Darwinian revolution (Chapter 7). Perhaps the most important scientific idea of the nineteenth century was the field concept,

revealing the interdependence of an electro-magnetic universe (Chapter 8). The two major theories of the physical sciences in the twentieth century, quantum and relativity theory, extended the field concept from the smallest atomic system to the largest galactic cluster in an increasingly relational universe (Chapter 9). Most of the ideas of modern science culminate in the vision of an expanding universe based on the big-bang theory, leading to a unified view of cosmology and parti-cle physics (Chapter 10). These concepts correlate with biology through the vision of a living universe, especially in the anthropic principle of recent cosmology (Conclusion). 2. SCIENCE AND RELIGION Religious sensibilities motivated much of the development of science throughout history, and science, in turn, has contributed much to religious insights. The actual history of science largely contradicts the nineteenth century idea of warfare between science and religion. When such conflicts have occurred, historical perspective often shows them, in retrospect, to be the source of new religious conceptions, or corrections that help to purify and enlarge older religious ideas. In the history of Western culture, science and religion have been the two main factors in how we view the universe and our place in it. Our understanding of the universe and our ideas about God are mutually related. All the major religions in Western civili-zation have contributed to and benefited from the development of science and associated views of the universe. The polytheism of the ancient civilizations stimulated the search for regular patterns in the behavior of their celestial deities, leading to the development of descriptive astron-omy. Jewish monotheism and the idea of a uni-verse created by one God provided the basis for a break with polytheism and an understanding of nature governed by universal laws rather than the whims of the gods. Greek rationalism, in spite of its focus on natural phenomena, sought to discover the har-monies of the heavens and the inner soul that animated the world. Islamic scholars developed


Greek science in a monotheistic tradition and kept it alive for eventual transmission to Western Europe. Medieval Christian thinkers supported and developed the doctrine of creation with an emphasis on the goodness and intelligibility of the created order, and the human responsibility to understand and use it wisely. Beginning in the sixteenth century, the Protestant Reformation continued these themes with a further emphasis on individual interpretation of scripture and nature as revelations of God and his creation. The scientific revolution of the sixteenth and seventeenth centuries was largely the product of Christian investigators, who mostly viewed their work as revealing the greater glory of God and contributing to human welfare. This attitude continued through much of the eighteenth and nineteenth centuries and is not without its adherents in the twentieth century. Perhaps the strongest effort to break the ties between science and religion was the positiv-ism of the last half of the nineteenth century and the first half of the twentieth century. Positivists combined the claim that science should limit itself to descriptions of observable phenomena with the assertion that science is the only valid knowledge. They not only excluded religion from science, but also classified it as meaningless because they could not verify it by observational evidence. However, on the basis of this verification criterion, scientific laws are also meaningless since as universal statements it is impossible to verify them conclusively. Furthermore, the positivistic claim that only empirically verified knowledge was valid could not itself be empirically verified, thus invalidating positivism and its narrow view of science. In the second half of the twentieth cen-tury, positivism came under direct attack with a new emphasis on the history of science, notably by writers such as N. R. Hanson, Thomas Kuhn, Stephen Toulmin and Paul Feyerabend. They showed that science changes continually and that many nonscientific factors influence it. Their analysis revealed that “all data is theory laden,” and that no scientific idea is completely separate from prevailing world views and cultural values.

The human dimensions of science, such as creativity, mystery and fallibility, became clear from its history, linking it more closely with a variety of cultural and religious traditions. The end of the myth of scientific objectivity opens up new possibilities for relating science and religion, each benefiting from the other. Unfortunately, in some circles a narrow view of creation hinders this prospect of mutual benefit. 3. SCIENCE AND CREATION In much of recent scientific discussion, the ideas of science and creation have appeared to be in conflict. This is especially true in the reemergence of “creationism” as an alternative approach to science. Ironically, creationists have followed a positivistic approach in insisting on a literal and factual interpretation of the creation narrative in Genesis, as though it were a scientific account of origins. They give little attention to the historical and cultural setting of the narrative, nor to evidence in the text of natural processes, anthropomorphic language, pictorial images or its polemical emphasis against idolatry. This positivistic approach led to the idea that all of creation occurred in six literal days and that the Earth is relatively young, perhaps as recent as 6000 years if there is no allowance made for gaps in the genealogies of the Genesis record. It requires a rejection of much of modern science, especially evidence from astronomy, biology and geology. Three creationist theories are typical of those introduced in the nineteenth century. The gap theory, given notoriety by the notes appended to the 1909 Scofield Reference Bible, separated a creation “in the beginning” from a much later catastrophic ruination and six-day restoration, culminating in the creation of Adam and Eve (at 4004 BC in the Scofield marginal reference). This view relegates fossils to the “primitive creation,” but there is little if any empirical or Biblical basis for such an interpretation. The apparent-age theory proposed that the fossil evidence of ancient life forms resulted from a recent creation of the Earth, but with the appearance of great age. Developed by the British


biologist Philip Henry Gosse (1810-1888), the Greek word Omphalos (navel) in the title of his 1857 book referred to the idea that Adam had a navel even though his direct creation required no umbilical cord, just as the creation of trees would have rings of apparent age. Such a view denies both the reality of all aspects of creation and the validity of empirical observations. Flood geology tried to explain away evi-dence for an ancient Earth by insisting that Noah’s Flood was a universal deluge that buried fossils and reshaped the Earth. Ellen G. White (1827-1915), the charismatic founder of the Seventh-Day Adventist church, used this idea to strengthen her emphasis on Sabbath worship as a memorial to a literal six-day creation. In the 1930s, George McCready Price developed this flood-geology approach in the Seventh-Day Adventist tradition. Henry Morris and John Whitcomb revived it in the 1960s. Flood geology rejects much of the established evidence and scientific inferences of the geological sciences. The Biblical tradition views both the word of God in scripture and the works of God in nature as revelations of God given for human understanding, and thus sees both as intelligible and reliable. Several options for interpreting the Biblical account of creation in the light of modern science are worthy of brief mention. As early as the fifth century, Saint Augustine suggested that the “days” of Genesis were “ineffable” and should be interpreted as God-divided days of indefinite length, rather than Sun-divided days of only 24 hours. Some nineteenth century theologians correlated the “creation days” with geological epochs in the day-age theory. They viewed the diversity of living species as the result of special acts of creation separated by long periods of time. In some versions, this kind of progressive creation tried to partially accom-modate the theory of evolution by allowing for limited evolutionary development of species be-tween creative events. Another nineteenth century suggestion, sometimes called the revelatory-day theory, was that God revealed creation to Moses in six 24-hour days, rather than completing it in six days. This would reflect the Babylonian tradition of recording

their creation accounts on six clay tablets, giving a day of revelation for each tablet. In this view, the Genesis account did not intend to give scientific information about creation, but instead it seeks to evoke worship of God, affirm the dependence of the created order on God’s power, prohibit idolatry, and prevent superstitious views of the universe. It is then the God-given task of humans to employ the usual methods of observation and reason to work out the details of God’s creative activity in bringing the universe to its present state of development. After Charles Darwin introduced the theory of organic evolution, most nineteenth century Biblical theologians (Charles Hodge, Benjamin Warfield, James Orr, Augustus Strong, et al.) accepted various versions of a view called theistic evolution. They maintained that God created the natural order and its laws, and con-tinually guides the evolutionary processes of nature through his immanent activity in the world to achieve his purposes. In this view, the theories of science are the best efforts of humans to de-scribe and explain these processes, but should not be absolutized to exclude the idea of a God who creates and sustains the universe. These theo-logians distinguished between “evolution” as a natural process guided by God, and an “evolu-tionism” that was completely naturalistic and denied the existence of God. Some Christians take exception to the idea of limiting God’s activity to only immanent (internal) processes in nature, suggesting that God is also transcendent and sometimes acts directly to change the course of natural events for special purposes. Thus they suggest that such events as the beginning of life and the appearance of the first humans required direct acts of God to overcome the extreme improbability (see Conclusion) that such events might have occurred spontaneously by purely natural processes. A mediating view concerning the first humans is that God acted directly on preexisting hominids whose bodies developed through evolu-tionary processes. By breathing into them “the breath of life,” God created truly human beings of sufficient intelligence to be morally responsible for their actions and capable of responding to their


creator. In the Biblical tradition, Adam’s disobedience and rejection of God introduced moral evil into the world. Since Adam represented the new humanity, his sin was imputed to all other humans, “For as through the one man’s dis-obedience the many were made sinners” (Romans 5:19). REFERENCES Barbour, Ian G. Religion in an Age of Science. San

Francisco: HarperCollins, 1990. Hanson, N. R. Patterns of Discovery. Cambridge:

Cambridge University Press, 1958.

Jaki, Stanley. Science and Creation. Edinburgh: Scottish Academic Press, 1974.

Kuhn, Thomas. The Structure of Scientific Revo-lutions. Chicago: University of Chicago Press, 1962.

Livingstone, David N. Darwin’s Forgotten De-fenders. Grand Rapids, MI: Eerdmans, 1987.

Numbers, Ronald L. The Creationists. New York: Alfred Knopf, 1992.

Ramm, Bernard. The Christian View of Science and Scripture. Grand Rapids, Michigan: Eerdmans, 1955.

Whitcomb, John C. and Henry M. Morris. The Genesis Flood. Philadelphia: Presbyterian and Reformed Publishing Co., 1961.

6

1. PREHISTORIC CULTURES Nowhere is the relationship between sci-ence and religion more evident than in the ancient civilizations where science had its origins. Since the earliest civilizations deified natural creatures and celestial objects, the priests of their religions were diligent to observe the behavior of their gods and record their regularities. This led to considerable knowledge about the heavens and the ability to predict many celestial phenomena. The religious world view of these civili-zations led to the development of practical tech-niques in other fields such as agriculture, architec-ture, writing and mathematics, which were eventu-ally rationalized into early scientific traditions. A survey of early contributions to science by the ancient Egyptian and Babylonian civilizations will show how much these religious concerns motivated the origins of science. First, however, it will be helpful to trace the origin of these religious con-cerns in the earliest human cultures, where they appear to be of the very essence of what it means to be human. Paleolithic Hominids The general stages in the development of cultures are nomadic food gathering, settled

agriculture, and the urban dwelling that initiated the great civilizations of the world. The earliest evidence of hominid (human-like) creatures comes from East Africa, stretching back some two million years into the Old Stone Age or Paleolithic period. In the Lower Paleolithic cultures, evidence points to nomadic hunters and gatherers who sheltered in caves, made stone tools, and used fire, probably kindled from the sparks flying from the chipping of flints. From about one million to about 15 thousand years ago, large glacial sheets per-iodically covered the northern continents in a series of ice ages. By the Middle Paleolithic period about 80,000 years ago, the appearance of Neanderthal hominids includes evidence of burial as well as stone tools and fire. Fossil remains from Europe to the Middle East and Northern Africa, but first found in Neanderthal, Germany, in 1856, give no evidence to indicate whether they became extinct or interbred with more modern types of humans. By the Upper Paleolithic period, there is evidence of a sudden flowering of more distinc-tively human culture, including communal hunting, man-made shelters, and religious belief systems suggested by burial practices and cave paintings. Skeletal remains of the first biologically

CHAPTER 1

A Religious Universe

Origins of Science in the Earliest Civilizations

Chapter 1 • A Religious Universe 7

modern human beings were first found in France in 1868. These so-called Crô-Magnon men appeared about 40,000 years ago, leaving cultural artifacts such as flint and bone tools, shell and ivory jewelry, and naturalistic cave paintings of considerable elegance and vitality. The Upper Paleolithic was also a time of rapid population expansion and migration to all parts of the globe. In this period the use of markings begins, perhaps to keep track of time. The first evidence of musical instruments also appears together with the first indications of the use of magic and language. Magic is an attempt to alter the course of nature by controlling super-natural forces through ritual and incantations. Although it recognizes causal and associational relationships, its utilitarian and superstitious emphases prevent it from being considered as science. Neolithic Cultures About 10,000 years ago, after the end of the last ice age, the formation of settled commu-nities near bodies of water began to appear. These give evidence of a number of new techniques, including sophisticated stone tools and small flint implements, gradual domestication of plants and animals, and the development of pottery. The New Stone Age or Neolithic period, began about 8000 to 6000 BC in the Middle East with polished stone tools, settled villages, cultivated grains, domesticated animals, developed pottery, and weaving. The smelting of ores may have developed out of experience with cooking, leading to the Bronze Age when alloys of copper appear with tin or lead to produce stronger metals. These were first introduced for making tools, weapons, and castings after about 4000 BC. In this period the first urban civilizations made their appearance in the Fertile Crescent, extending from the Nile Delta and the eastern Mediterranean coast to the Tigris and Euphrates River valleys as far as the Persian Gulf. Megalithic monuments consisting of huge stone slabs up to 20 meters in length and 100 tons appeared in Western Europe and the British Isles in the third millennium BC, probably serving

religious functions. The most famous of these is the Stonehenge group of megaliths on the Salisbury Plain in southern England, consisting of four series of giant stones. The two outermost series form circles surrounding a horseshoe shaped series and an ovoid series, within which lies an altar stone. These appear to have combined religion with accurate observations of the Sun and Moon, but lack any written records to confirm this. Similar activities had already begun in Egypt, with the added advantage of some of the earliest written records, leading eventually to the development of science. Egypt would also initiate the Iron Age in about the fifteenth century BC.

2. ANCIENT EGYPTIAN SCIENCE

Religious Background The earliest civilizations emerged in great river valleys that could support extensive agricultural practices. The Nile River valley pro-vided one of the best such environments because of its isolation by deserts from outside attack, its comfortable climate, and its regular pattern of flooding that provided predictable agricultural conditions and annual renewal of fresh topsoil. The invention of hieroglyphic writing (Greek: sacred carvings) and papyrus made it possible for the priests of Egypt to keep extensive records over long periods of time. They made papyrus from interwoven strips of pressed pith from the stem of a tall Nile sedge plant. Hieroglyphic pictograms were eventually adapted into an alphabet of 24 phonetic symbols and an abbreviated script called “hieratic.” The unification in about 3100 BC of Upper Egypt in the south with Lower Egypt in the north (delta region of the Nile) established the First Dynasty of the Old Kingdom, or Pyramid Age, leading to about a thousand years of relative peace and stability along some 1000 kilometers of the Nile Valley. The great pyramid building projects near the beginning of the delta region helped to weld the nation together. The pyramid tombs reveal two features of Egyptian religion: concern for the pharaoh’s afterlife; and the impor-tance of the Sun in their worship, with the rays of the Sun represented by the pyramid shape. They


built them on the western bank of the Nile where the Sun seemed to die each night. Some 80 pyramids still stand in various states of preserva-tion, most in the vicinity of the ancient capital of Memphis near modern Cairo. By the end of this period, the capital was shifted to Upper Egypt to a city that the Greeks called Thebes, which became the dominant city of Egypt for about 1500 years. Here they built the great temples of Luxor and Karnak on the east bank of the Nile, and they dug royal tombs in the Valley of the Kings on the west bank. In addition to their recognizable geo-graphic boundaries, the ancient Egyptians believed that mountain peaks or pillars held up the sky at the four cardinal points. The sky was the goddess Nut who supported the heavenly bodies and across which the Sun-god Atum-Ra sailed each day in a barge like the papyrus boats on the Nile. Two of the earliest religious cults were the Upper Egyptian solar cult of Atum-Ra at Heliopolis (later Amon-Ra at Thebes) and the Lower Egyptian nature cult of Osiris. The solar and nature cults were eventu-ally combined and elaborated in a myth of creation from an eternal ocean. This ocean then subsided to leave the Nile flowing between two oceans in the south and north and a primeval hill from which Atum-Ra created himself. Egyptians viewed Atum as the creator, who thus became joined with the Sun-god Ra, symbolized by the pyramid, giving birth to the sky-goddess Nut and the Earth-god Geb. The children of Nut and Geb were the gods of the nature cult, Set, Nepthys, Osiris and Isis, and their son Horus. The importance of the Sun is evident in many ancient Egyptian texts, such as the following hymn:

Thanks to you, O Sun of the day, You who rise each morning without fail, The brilliance of your light exceeds that of

gold, You who are inspired, great, and creative, Who contain the universe and enfold it at a

glance. Creatures see you as you traverse the sky, Failing to understand how you move. You travel the universe without haste,

Making the people’s day unfold beneath. When you walk toward the west, It hastens the night to bow to your will. When you complete your journey and

return, The universe surges forth to receive your

light, That all creatures may pursue life once

more. The religious world view of the Egyptians took a more definite shape with the identification of the pharaoh with the Sun-god Ra, believed to be the direct ancestor of the pharaohs. They came to associate life with the eastern bank of the Nile where the Sun rose with new life each morning. Cities of the dead, with their monumental tombs in the form of pyramids at Memphis and under-ground chambers at Thebes, were usually built on the western bank where the setting Sun began its journey through the underworld. Pyramid building reenacted the creation of Atum-Ra from the primeval hill. Elaborate funerary preparations for the pharaohs provided a corporate basis for their most deeply rooted concept, the belief in life after death. Priests mummified the dead in a process requiring from 40 to 90 days, depending on family wealth, to provide a home for the soul. Egyptian Technology Religious ideas were a large factor in motivating the technical abilities of the ancient Egyptians, as is especially evident in the con-struction of the great pyramids of Sakkara and Giza near the ancient city of Memphis and the modern city of Cairo. The largest of these, built for King Khufu (Greek: Cheops) in the 27th century BC, was originally 140 meters high with each side measuring 230 meters at the base. It contains about 2.3 million stones averaging 2.5 tons each. Some of its stones weigh as much as 50 tons, apparently moved by no more than ropes, levers, rollers and pulleys. Measurements show that the sides differed by less than 2 centimeters, and their corners form 90-degree angles within 2 minutes of a degree. It was oriented toward the true north with nearly the same degree of accuracy, indicating a high level of astronomical skill.


Construction of the first pyramid, the Step Pyramid at Sakkara, was a century before the Giza pyramids in the 28th century BC during the Third Dynasty for King Zoser, believed to have been the first monarch imputed with divinity. It rises in six steps on each of four sides, peaking at a height of more than sixty meters, and is believed to represent a staircase to heaven. Zoser’s chief advisor, the legendary Imhotep, apparently de-signed the step pyramid. He is also reputed to be the first physician whose name has been recorded. In later times, Egyptians worshiped him as the god of medicine.

Egyptian Science. Although the earliest of about 20 medical papyri that have survived come from about the 17th century BC, they seem to reflect knowledge going back to the earliest dynasties of the Old Kingdom. They are unusual in their emphasis on practical medicine in addition to the usual magical incantations that suggest a “demon theory” of dis-ease. The Edwin Smith Surgical Papyrus, dating from about 1700 BC, was purchased by the American Edwin Smith in 1862 at Luxor, Egypt, but not translated until 1930. It describes 48 sur-gical cases of wounds and fractures throughout the body, giving practical instructions for treatment. It is unique among ancient medical texts in class-ifying some cases as incurable, and thus “not to be treated.” The Ebers Medical Papyrus, dating from about 1600 BC, purchased at Luxor in 1873 by German Egyptologist Georg Ebers, describes some 47 diseases, including symptoms, diagnoses, and prescriptions. These earliest medical texts recog-nized the healing power of nature in many cases, and are impressive in their factual detail. Other texts are more magical, describing the identi-fication of demons from various omens and how to draw them off into an animal, ointment or amulet. One of the most important contributions of ancient Egypt was the invention of the solar cal-endar. The annual flooding of the Nile determined the pattern of agriculture for the Egyptians over a period of a few days more than 12 lunar months (29.5×12=354 days), making a lunar calendar awk-ward for an agricultural civilization. The Egyptians recognized three seasons, which they

called inundation, emergence and harvest. Careful obser-vations revealed that the star Sirius, the brightest star in the heavens, followed this same pattern on a more regular basis. Priestly observers noted that Sirius set earlier every evening as its position shifted closer to the Sun until it finally disappeared in the light of the Sun. About 70 days later, they observed that it reappeared in the morning just before sunrise. This so called heliacal rising of Sirius (the Dog Star in the constellation Canis Major) occurred each year at about the same time that the Nile flooding began, still referred to as the “dog days” of July. The earliest recorded calendar in Egypt consisted of the three seasons, each of four lunar months, but priests added a thirteenth month every two or, more often, three years to synchronize the heliacal rising of Sirius with the year. As Egypt became a better organized kingdom, it supplemented this fluctuating “luni-stellar” calendar of 12- and 13-month years by a “civil calendar” with a constant 365 days, corresponding to the successive reappearances of Sirius. This celestial confirmation established the civil year with 12 months of 30 days each, followed by 5 feast days at the end of the year to celebrate the 5 children of the sky-goddess Nut. This civil calendar, breaking the bonds of the lunar month, served for administrative purposes alongside the older seasonal calendar used for agricultural and religious functions. Eventually the Egyptians noticed that every four years the first day of their civil calendar shifted one more day earlier than the reappearance of Sirius (Egyptian: Sothis), leading them to rec-ognize that the actual solar year is 365 + 1/4 days. A period of 1460 years (4×365) became the so called Sothic cycle, during which the beginning of their civil year shifted by 365 days before it again coincided with the reappearance of Sirius. The Roman author Censorinus noted that this coin-ciding of Sirius with the Egyptian new year occurred in AD 139, leading to speculation that the Egyptians discovered the solar year two or three Sothic cycles earlier at about 2781 BC or even 4241 BC. When Julius Caesar introduced his calendar reforms in 46 BC, he took the advice of the Egyptian astronomer Sosigenes and included a


366-day leap year once every four years, bringing the Julian calendar into closer correspondence with the solar year. The Egyptians developed the Sun dial and other kinds of shadow clocks for measuring time during the day. They also developed the water clock for measuring time at night by making a small opening in the bottom of a conical vessel shaped to allow water to escape at a uniform rate. They grouped stars over a wide equatorial band into 36 constellations, now called “decans” because each occupies ten degrees. Each decan contained a particular star, beginning with Sirius, whose heliacal risings followed each other every ten days to mark the beginning of 10-day weeks. The decans formed a star clock that made it possible to determine the “hour” of the night from the rising of any given constellation. In mid-summer when the night is shortest, only 12 decans rise during darkness, leading to the 12-hour division of night with the length of night-time hours shorter in the summer and longer in the winter. The Egyptians divided the 30-day month into three ten-day weeks corresponding to the decans. They divided the day into ten hours, with one hour added at either end for twilight, giving a total of 12 daytime hours. By about the 14th century BC the concept of 24 equal hours emerged. Religious ideas and astrological concerns strongly influenced both astronomy and the measurement of time. The primary goal as re-vealed by their texts was to determine the correct hour and season of their religious festivals. As each decan shifts nearer the Sun, it disappears for a period of about 70 days. An inscription on a monument of Seti I (ca. 1300 BC) describes how one decan after another “dies” and is then “purified” in the embalming house of the nether world during 70 days of invisibility before being reborn. This matched the traditional 70-day em-balming period in the preparation of mummies. The Egyptians designed even the astronomical inscriptions on coffin lids and tombs to inform the dead when they needed incantations on their nocturnal journeys.

Egyptian Mathematics Practical and religious concerns associated with agriculture, architecture and record keeping also gave rise to Egyptian mathematics. They used a decimal system based on addition, with different symbols for units, tens, and multiples of tens, similar to Roman numerals. A number like 365 then appeared as ρρρΛΛΛΛΛΛ11111, with ρ re-presenting hundreds, Λ for tens, and 1 for units. Multiplication involved an additive process of consecutive duplication. Thus multiplying a number by 16 requires four duplications (24) of the number. Multiplication of 35 by 21 requires adding the results for 1, 4, and 16 as shown:

\ 1 35 2 70 \ 4 140 8 280 \ 16 560

so 1 + 4 + 16 = 21 and 21 x 35 = 35 + 140 + 560 = 735.

Division involved a similar method. Thus dividing 735 by 35 would look like the above example, but the scribe would first find which products add up to 735 and then sum the corresponding multipliers to find the answer 21. Division does not always give a whole number. Thus dividing 25 by 4 involves duplicating 4 until it is the largest number equal to or less than 25. The result would be:

1 4 \ 2 8 \ 4 16

since 8 + 16 = 24 is 1 less than 25 and 2 + 4 = 6, the answer is 6 + 1/4

The Egyptians used only unit fractions, so they did not reduce a sum such as 1/3 plus 1/15 to its simpler equivalent of 2/5, and they expressed higher fractions in terms of various combinations of unit fractions. Apparently the Egyptians developed geo-metry (literally “Earth measurement”) from its association with the need for surveying land


boundaries each year after the Nile floods receded. The concept of area may have grown out of the need for a quantitative measure of a given piece of land as a basis for taxation, as suggested by the Greek historian Herodotus, leading to some of the first geometric formulas. The Egyptians defined the area of a rectangle of base b and height h (see Figure 1.1a) by the product of the lengths of its sides, A = bh, and is thus a measure of the number of square units (s²) it contains. Similarly, they gave the area of a triangle of base b and height h as half of their product, A = bh/2, which follows in the case of a right triangle from dividing a rectangle with its diagonal into two equal triangles (Figure 1.1b). Such formulas appear as practical computa-tional procedures without any attempt to give an explanation or proof. The Egyptian formula for the area of a circle reveals the practical character of their ge-

ometry, in contrast to the theoretical approach of the Greeks. The oldest known mathematical treat-ise, the Rhind Papyrus dating from about the 20th century BC (purchased by the Scotsman Henry Rhind at Luxor in 1858, now in the British Mu-seum), gives a procedure for measuring the area of a circular piece of ground. Probably obtained by trial and error, it involved subtracting from the diameter d of the circle 1/9 of its value (d - d/9) and squaring the result (Figure 1.1c). Since the di-ameter d is twice the radius r, this is equivalent to:

Area = (8d/9)2 = (16r/9)2 = (256/81)r2 = 3.1605r2,

indicating a value of π (circumference/diameter) of about 3.16 as compared with the Greek formula:

Area = πr2 where π = 3.14159....

This is an excellent approximation with an error of less than 1%, but it is a practical rule with no

b = 4m

h=3m

b

h d = 2r

(e) Pyramid

(a) Rectangle (b) Triangle(c) Circle

UnitArea

(d) Cube

s

s

(f) Cylinder

UnitVolume s = 3m

A = bh = 12 m² A = bh/2A=(d - d/9)²=(8d/9)²

= 256 r²/81 = 3.16 r²

V = (8d/9)²hV=s²s=s³ =27m³

b

b

V = b²h/3 Figure 1.1 Ancient Egyptian Area and Volume Concepts and Formulas The Egyptian invention of area and volume concepts involved practical considerations of surveying land and building structures for grain storage or monuments based on the ideas of a unit area s² and a unit volume s³.


theoretical basis, rather than a precise result as derived by the Greeks from mathematical princi-ples. Egyptian scribes also developed the concept of volume (Figure 1.1d), including formu-las for simple geometric solids. In one papyrus, they gave the volume of a cylindrical storage granary (Figure 1.1f) by the product of the area of the circular base times the height. One of the highest achievements of ancient Egyptian mathe-matics, probably found by careful measurement methods, was the formula for the volume V of a truncated pyramid with a square top of sides a, square base of sides b, and height h. Their result is equivalent to the formula:

V = (a2 + ab + b2)h/3 , which reduces to V = b2h/3 when a = 0 for a regular pyramid (Figure 1.1e). This was especially useful in the planning and construction of the pyramids, revealing again the practical and religious sources of Egyptian knowledge. Such a practical application, however, does not disqualify it as being unscientific. In fact, these religious motivations contributed to their concern for accuracy and all the other achievements that the Greeks would later admire so much. 3. BABYLONIAN SCIENCE Cultural Background Science also developed in the river val-leys of the Tigris and Euphrates Rivers, a region known as Mesopotamia (Greek: land between the rivers) where the modern country of Iraq is located. This was also a fertile area like the Nile River valley, but with much more chaotic condi-tions of weather and geography. A greater annual rainfall some-times produced unpredictable flood-ing that would wipe out entire villages. Several Sumerian and Babylonian accounts describe vast floods in this region. An ancient Babylonian flood story from about the 18th century BC appears in a longer work known as the Epic of Gilgamesh, written on twelve tablets. Tablet eleven tells of a flood planned by the gods to destroy all human life. The story is similar to the Biblical account of

Noah’s flood, including the building of an ark, but the rains end on the seventh day and the setting is polytheistic in which the gods personify the forces of nature. Building materials in Mesopotamia were mostly bricks obtained from mud, which have almost completely weathered away over the cen-turies, in contrast to the stone monuments of Egypt. Fewer archaeological monuments remain to reveal the glories of the past and the patterns of life. Invaders had easier access to this region than to Egypt, leading to more warfare and linguistic confusion. In spite of these conditions, there is evidence that early civilizations in Mesopotamia developed a high level of mathematical and astro-nomical skill, largely motivated by religious concerns similar to the Egyptians. The earliest records from this region were written on clay tablets from as early as about 3500 BC by the ancient Sumerian civilization, near where the two rivers join before flowing into the Gulf. They developed a method of writing known as cuneiform (Latin: wedge shaped) by making indentations in clay tablets with pointed reeds and then leaving them in the Sun to bake. Eventually the Akkadians (Assyro-Babylonian) conquered the Sumerians and they mixed with other Semitic peoples, but their culture persisted and reached its intellectual heights about 2000 BC with its center in the ancient city of Babylon on the Tigris River. Most of what we know about the Sumerians and the Babylonians who followed them comes from large quantities of cuneiform tablets recovered over the last century. Unlike the papyrus rolls of Egypt, scribes never assembled these tablets into book form but kept them in large library collections. The golden age of Babylonian culture came under the Amorite King, Hammurabi, in the 18th century BC. The Babylonian language was Semitic in origin and was the language of diplo-macy with Egypt and other nations. However, the Babylonian priests did not forget Sumerian, and it became their sacred language. Hammurabi is best known for the first complete code of laws, which was discovered in 1901 in the form of an engraving on a large block of polished black diorite nearly two and one half meters high, and is


now preserved in the Louvre Museum in Paris. The top shows in low relief the Sun-god Shamash presenting the code to King Hammurabi. Hammurabi’s code includes 282 articles with laws concerning property, business, family, injuries and labor. Perhaps the chaotic conditions in the region led to a greater emphasis on organ-ized information about legal procedures as well as religious practices and scientific knowledge. Available Babylonian scientific texts consist almost exclusively of lists of objects, tables of information, practical hints and worked examples without explanations. In these early Mesopotamian cultures, naming things was synonymous with creating them, providing knowledge of the external world. Babylonian Mathematics About one hundred tablets have been found representing early Babylonian mathematics. Their most important contribution appears to be the invention of the positional number system, which was much more efficient than the Egyptian numeral system and was probably the original source of our modern decimal system. They used a sexigesimal system based on multiples of 60 as well as 10. Only two separate signs appear in their numbers, with wedge shapes like a Y for 1 and < for 10, but the first sign also represented powers of 60 depending on its position. Thus a number like 365 has three positions in the decimal system representing 3 hundreds, 6 tens and 5 units. However, it requires only two positions in base 60, with 6,5 meaning six sixties and 5 units and written as YYYYYY YYYYY. A number such as 32 appears as <<< YY, while a change in positions gives YY <<< equivalent to 2 × 60 + 30 or 150. Since a symbol for zero was not added for several centuries, scribes indicated a missing power of 60 by a space. The many factors in 60 (2, 3, 4, 5, 6, 10, 12, 15, 20, 30) made fractions easy for the Sum-erian computer to manipulate, since their position could designate a negative power of 60 similar to the decimal use of negative powers of 10. Thus a fraction such as 2/15 (.0833...) is 8/60, which they would write in the sexigesimal system as 8 in the next position after units. We still use this system

today in our division of the hour and the degree into 60 minutes, and each minute into 60 seconds. The Sumerians also gave us the division of the circle into 360 degrees, matching their belief that there were 360 days in the year corresponding to a shift in the Sun of about one degree each day relative to the stars. Although the Sumerians had no symbolic equations, they had considerable algebraic ingenu-ity, including the use of negative numbers. They were able to solve the equivalent of linear and quadratic equations, and even simple exponential equations involving compound interest. By 2000 BC the Babylonians could calculate the area of triangles and recorded long lists of different lengths of the sides of right triangles (later gen-eralized in the theorem of Pythagoras). These included not only the more obvious Pythagorean triplets like 3, 4, 5 (3² + 4² = 5²) and 5, 12, 13, but also some less obvious ones like 4961, 6480, 8161. On one tablet the diagonal of a square is marked with a value giving the square root of 2 as

2 = 1;24,51,10 = 1 + 24/60 + 51/60² + 10/60³. Expressed as a decimal, this is equal to 1.414213... instead of the actual value 1.414214.... In general, Babylonian geometry fell somewhat short of the Egyptians. Their usual de-termination of the circumference of a circle was the simple approximation of three times its diame-ter (3d), equivalent to taking π = 3 compared to the Egyptian value of 3.16. The Old Testament of the Bible reflects a possible Babylonian cultural influence in using the same approximate value of 3 in discussing circular measures (I Kings 7:23 and II Chronicles 4:2). One Babylonian tablet dealing with the perimeters and areas of polygons appears to imply the approximate value of

π = 3;7,30 = 3 + 7/60 + 30/60² = 3.125,

but this result is not explicit and must be inferred from the mathematical context. The Babylonians also used a simplified approximation for the volume of a truncated square pyramid, V = (a2+b2)h/2, which suffered by comparison with the correct formula found by the Egyptians and later derived by the Greeks.


Babylonian Astronomy and Mythology The influence of religion is especially clear in Babylonian astronomy. They worshipped celestial objects as gods, especially the Sun, Moon, and the five visible planets. Careful observation of the sacred heavens was the duty of the priest-astronomers. The motions of the heavens were the basis for both the divination of future affairs of state and the determination of the calendar for religious and civil observances. This was a kind of judicial astrology in contrast with the personal as-trology that appeared later. With the mathematical foundations they had established, the Babylonians began the long series of observations over many centuries that would eventually provide the basis for the astronomical generalizations of the Greeks. From about 2000 BC the Sumerians had developed the building of monumental brick towers, called ziggurats, which served both as religious temples and as platforms for astrological observations. They consisted of a series of edifices of decreasing size built on top of each other with an encircling stairway for the priests to reach the top. Though similar to Egyptian pyramids, the Babylonians did not use ziggurats as tombs and their mud bricks were more vulnerable to deterioration from weathering. Only the foundation ruins remain, including one of the best examples at Ur near the Arabian Gulf, where excavations were completed in 1933. It has been suggested that the Biblical account of the Tower of Babel (Genesis 11:1-9) may be related to the ziggurat tradition and the attempt of Babylonian priests to reach their celestial gods. By the time of Hammurabi (ca. 1750 BC), star catalogs and planetary records were regularly prepared. Since Babylon was the center of a large land empire, commerce, religion and agriculture required a predictable and uniform calendar. Along with his other reforms, Hammurabi ordered the establishment of a common calendar to operate throughout his empire. Since the original lunar calendar alternated 29 and 30 day months, 12 months contained 354 days instead of the 365 days of the seasonal cycle. To compensate for this deficiency, the priests occasionally inserted (intercalated) an extra (thirteenth) lunar month so that the legal year would more closely match the

solar year. Eventually they established a 19-year luni-solar calendar (235 lunar months), during which they added an intercalary month in 7 out of every 19 years to nearly match lunar months to the solar year (later called the Metonic cycle after its revival by Meton of Athens in 432 BC). The Babylonians mapped the heavens into groupings of stars that formed recognizable patterns called constellations, named in honor of mythological figures. They divided 36 of these constellations into three bands of 12 each, and the Greeks later added a fourth band of 12 more. Mod-ern astronomy still uses these 48 constellations, together with 40 more seen only from the southern hemisphere, making a total of 88 over the entire sky. The most important of these bands for the Babylonians was a continuous sequence of 12 constellations in a great circle around the sky, about 20 degrees wide, in which the planets always appear. Since these constellations were mostly named after animals, the Greeks called this band the zodiac from the same word as zoology, a kind of celestial zoo. The path of the Sun through the zodiac, approximately one degree per day relative to the stars, is called the ecliptic. One way to map it is to observe the pattern of stars on the western horizon just after sunset, noting the position of the Sun in relation to the zodiacal constellation that appears on the horizon at that time. During one month the Sun advances through one constellation of the zodiac, completing its journey through all 12 in one year, which may have been the basis for dividing the zodiac into 12 constellations. A Babylonian tablet a few centuries after Hammurabi shows each sign of the zodiac marked with 30 vertical lines, and by the 6th century BC the constellations of the zodiac were each divided into 30 equal degrees. After this, astronomers used more mathematics and maintained increasingly detailed records. About the third century BC, the Greeks introduced the zodiac into Egypt and combined it with decans. One star, about 32º above the northern horizon from Babylon (corresponding to the lati-tude of Babylon), appeared to remain almost stationary while all the other stars seemed to rotate around it. This North Star, Polaris, acted as


a kind of polar axis, with a corresponding celestial equator at right angles to it, parallel to the daily motions of the stars and about 58º above the southern horizon at Babylon. The annual shifting of the Sun on the ecliptic (see Figure 1.2) carried it about 23º above the celestial equator in the constellation Cancer, and 23º below the equator in Capricornus. Three of the principal gods of the Baby-lonians governed the “celestial roads” running, respectively, along the celestial equator (Anu), the Tropic of Cancer (Enlil), and the Tropic of Capri-corn (Ea). The summer solstice (Latin: Sun standing) occurred on the longest day of the year when the Sun stood at its highest point on the ecliptic (58º + 23º = 81º above the horizon at Babylon). At the winter solstice, the shortest day of the year, the Sun was at its lowest point on the

ecliptic (58º - 23º = 35º above the horizon). The equinoxes (equal day and night) occurred halfway between the solstices when the Sun crossed the celestial equator. The Babylonian cosmological poem known as the Enuma Elish (from its first two words: When Above) describes the behavior of the celestial gods. The earliest versions of this epic date from the time of Hammurabi and were largely reconstructed from fragments discovered at Nineveh in the nineteenth century. It includes about one thousand lines of text on seven clay tablets covering the following topics, tablet by tablet: (1) Apsu (male personification of fresh water ocean) and Tiamat (female personification of primeval salt water ocean) beget a company of gods, who so try Apsu’s patience that he tries to slay them all. Ea binds and slays Apsu and then

Figure 1.2 Babylonian Concepts of the Daily and Annual Motions of the Sun The Babylonians mapped the constellations of the stars and noted the motions of the planets through the 12 constellations of the zodiac (five shown above). They also charted the annual motion of the Sun along the ecliptic and noted the daily motion of the heavens from east to west about the north star, Polaris. They observed the shift in the angle of the Sun’s path as it moves along the ecliptic above and below the celestial equator, giving the longest and shortest days of the year at the summer and winter solstices, respectively, and the vernal and autumnal equinoxes when the Sun crosses the celestial equator and the day and night are of equal length.


begets Marduk, patron god of Babylon. To avenge her husband, Tiamat creates terrible monsters with Kingu as their head. (2) Ea counter plots against Tiamat and appoints Marduk to oppose her. (3) A banquet is held to prepare for Marduk’s entrance into battle. (4) Marduk (god of light) slays Tiamat, signifying the final victory of order over chaos, and from her body creates the heavens. Later he creates the Earth and appoints residences for the gods of the sky, air, and subterranean waters. (5) Marduk appoints the Moon to rule over the night and to indicate the days and months of the year, and he forms the constellations in the heavens. (6) Marduk creates man from the blood of Kingu and assigns him to serve the gods. (7) Marduk is advanced from chief god of Babylon to head over all the gods. This account of creation from the original watery chaos is also a political claim to the supremacy of Babylon. It is a hymn to Marduk after his defeat of the primal goddess Tiamat. Her defeat by Marduk established world order, which was viewed as inseparably connected to order in the heavens:

Then Marduk created places for the great gods.

He set up their likeness in the constella-tions.

He fixed the year and defined its divisions; Setting up three constellations for each of

the twelve months. He set up the station of Nebiru (Zodiac) as

a measure of them all, That none might be too long or too short, And set up the stations of Enlil and Ea.

By the Assyrian period in the seventh century BC, when King Sargon II ruled both Babylon and Ninevah, eclipse predictions were being made on the basis of Babylonian records over many centuries. They observed the Moon to shift some 5º above and below the ecliptic in a zigzag motion during its 27-day circuit of the zodiac. Records of these zigzag motions made it possible to relate the motion of the Moon to its phases. Since the priests were aware that lunar eclipses only occurred at the full Moon (in oppo-sition with the Sun) when it was near the ecliptic,

they could make predictions by projecting when these occurrences would happen simultaneously. Solar eclipses occur when the new Moon (in conjunction with the Sun) crosses the ecliptic. However, since solar eclipses can only be seen within a narrow band at differing locations on the Earth, the likelihood of being at the right location was very small. By the fourth century BC, the late Babylonian (Persian) astronomer Kidinnu was able to use the centuries of careful and continuous records of his predecessors to account for small fluctuations in the positions of the Sun and Moon. He was able to make more accurate predictions than all but the last of the Greek astronomers, who finally had access to Babylonian records. The Babylonians kept careful records of the motions of all the visible planets (Greek: wan-derer) since they viewed them as gods, including the Sun and Moon among the seven celestial bodies that moved through the zodiac. However, the other five planets had especially irregular motions, carefully recorded since they were thought to reveal the will of the gods. In addition to their daily motion from east to west and their slow eastward progression through the zodiac, they differ from the Sun and Moon in periodically reversing their motion in the zodiac for several weeks before resuming their normal motion. Although the Babylonians recorded this retrograde motion, and could even predict it, there is no evidence that they ever attempted to explain it apart from their religious views.

Late Babylonian Astrology At first, the priests applied Babylonian astrology only to matters of state. They derived the more usual methods of individual divination from the examination of animal entrails and from other terrestrial omens, rather than from observations of the stars. The Babylonians used the sky as a stage for their mythological imagination. By about the third century BC, however, the Chaldeans (New Babylonian Empire from about 625 BC) developed a more personalized form of astrology based on the idea that celestial influences predetermine all events. This included the casting of individual horoscopes, eventually influencing the Roman and medieval world.


Another Chaldean influence, growing out of earlier Babylonian and Jewish traditions, was related to the invention of the seven-day week. The lunar calendar can be divided into quarters of approximately seven days by the phases of the Moon. The Babylonians set aside the seventh day of the month as a feast to Marduk and offered sacrifices to their gods on the 7th, 14th, 21st, and 28th days of the month, placing restrictions on certain activities on those days. However, these Babylonian “weeks” were not continuous like our weeks, and the first day of each lunar month was the first day of a week. The Babylonians called the fifteenth day of the month shabattum, ety-mologically equivalent to the Hebrew Shabbat (Sabbath). By the time of the Chaldeans around the seventh century BC, continuous weeks that followed each other without regard to month and year had been introduced. Mutual influences between Babylonian and Jewish cultures might date from the time of the Jewish captivity in Babylon beginning in 586 BC. Ideas of Chaldean astrology led to the dominance of each day of the week by one of the seven planetary deities, influencing the Romans to name the days of their week after the planets. Ironically, the Roman Catholic Church preserved this pagan astrological basis for the names of the days of the week in Western European languages. The survival of planetary names is obvious in the names for Sunday (Sun), Monday (Moon), and Saturday (Saturn), but not as obvious in the English names for the other days of the week, which were named for the equivalent Anglo-Saxon gods Tiw, Woden, Thor and Frigg. In a language like French, the planetary names are more obvious in the names for Tuesday (Mardi for Mars), Wednesday (Mercredi for Mercury), Thursday (Jeudi for Jupiter), and Friday (Vendredi for Venus). The order of the days of the week is not the usual order according to their relative speeds through the zodiac (Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn). Instead, it is based on a cycle in which each hour of the day is dominated by a planet in their natural order and with each day named after the planet dominating its first hour. Thus the lure of the skies for the Babylonians has

yielded a fertile lore of the skies ever since. Arabs in the Islamic tradition suppressed this astrological basis for the names of the week by naming most of them numerically in Arabic, beginning with Sunday. 4. PHOENICIAN & HEBREW INFLUENCES Phoenician Contributions The Fertile Crescent of the Tigris and Euphrates river valleys extends northwest up the Euphrates before curving south along the Jordan valley and Mediterranean coast, providing a land bridge with Egypt. This region of Palestine and the Phoenician coast developed during the third millennium BC into a unique culture called Ca-naanite, from the name used in the Bible. Canaanite civilization borrowed from Egyptian, Mesopotamian and Aegean influences, among others, including the Hebrews after their migration into the region from their Babylonian origins. Although neither the Phoenicians nor the Hebrews developed strong scientific traditions, both con-tributed important ideas for later work in science. The Phoenicians usually wrote on papy-rus, which in their language led to the Greek word byblos and hence our word Bible. Little of their writing would have survived except that the people of the town of Ugarit in Northern Canaan (now Ras-Shamra in Syria) had shifted to clay tablets before the middle of the second millennium BC. The discovery of Ugarit in 1928 yielded a large number of such clay tablets, some written in a form of Babylonian, but others were written in a Ugaritic (proto-Phoenician) script using an alphabet of only thirty letters. This remarkable invention of an alphabet greatly simplified writing, especially when com-pared to the Babylonian script with some 600 cuneiform signs and the Egyptian use of about 700 hieroglyphic symbols. These earlier complicated forms of writing were a virtual monopoly of the scribal and priestly classes. The alphabet eventually supplanted these earlier forms of writing, making it readily available for more widespread use. The Romans derived their alphabet from the Greeks, who in turn had imitated the Phoenicians.


Although both Sumerians and Egyptians used alphabetic or syllabic scripts along with ideographic symbols, the Phoenicians seem to have been the first to invent the exclusive use of such phonetic symbols. This resulted in a radical simplification of writing by representing the sounds of a language with as few signs as possible. The Phoenician alphabet was especially econ-omical in omitting most vowel signs, leading to some ambiguity for anyone not familiar with the language. After the Israelites settled in Palestine, they adopted a Canaanite dialect and later de-veloped the ancient Hebrew script from the consonantal alphabet of the Phoenicians. Even-tually the Greeks imitated the Phoenician alphabet and improved it by adding vowel symbols, which became the basis for alphabetic writing in most other languages and the foundation for modern science and literature.

The Hebrew View of Nature Most of what is known about ancient Hebrew civilization is based on the Bible. Many aspects of Hebrew culture borrowed from the surrounding civilizations of the Canaanites, Egyp-tians and Mesopotamians. For example, they employed a decimal system with traces of the Babylonian sexigesimal system, especially in their weights and measures. Astronomical knowledge in common with the Babylonians included such constellations as the Great Bear (Ursa Major), Orion and the Pleiades (Job 38:31-32). Most of the language of the Bible about nature is phenomenal, from the perspective of the observer, rather than theoretical. Thus an observer sees the Sun moving around the Earth, and no references are made to the more complicated planetary motions other than perhaps such metaphors as the morning stars (Venus and Mercury?) singing together (Job 38:7). Although the Old Testament reflects and even shares certain aspects of Babylonian cos-mologies, it also presents a fundamentally differ-ent world view that was especially important for the development of science after the Greeks. The radical contrast between the polytheistic gods of nature and the monotheistic God of creation and

history has far reaching implications. Most ancient religions viewed the world as a closed system where good and evil coexisted and deterministic principles influenced both gods and humans. This contrasts sharply with the open Biblical view of a transcendent God who rules over a good creation, in which evil is a subsequent intruder. The participation of God with His people in history and the uniqueness of His covenant with them leads to a break down of the cyclical view of time and its fatalistic attitudes. The Biblical teaching about creation introduced new values and attitudes toward nature that had important implications for the later development of science.

The Biblical Idea of Creation Much of the Biblical creation account ap-pears to be a polemic against the polytheistic and idolatrous cosmogonies and cosmologies of the ancient world. Thus in the Genesis creation nar-rative, God created light before the starry heavens, and he created the Earth and plants before the Sun and Moon (Gen. 1:3-19). Rather than a purely chronological sequence, it appears that this order-ing serves as a polemical rejection of the celestial idolatry of the Babylonians, Egyptians, and Canaanites. The Old Testament directs a number of attacks against astrology (Dan. 2:10-19; Isa. 47:13). The Babylonians deified nature, and the Sun, Moon and planets were among the chief deities. Eventually they named the seven days of the week after the planets and designated each day for worship of the corresponding planetary deity. The Biblical account of creation avoids the usual names of the Sun and Moon, negating their identification with gods by referring to them as the “greater” and “lesser” lights (Gen. 1:16) and giving them a reduced priority in the order of their description. This approach separates the seven-day week from Babylonian idolatry and gives it a new significance, symbolizing the control and ordering of creation by the one God who created and sustains all things. Thus the days of creation appear to provide a ritual order for celebrating God’s creation, rather than a purely historical chronology. It is intended to call God’s people away from idolatry to worship the Creator rather than his creation. This distinction between nature


and God was an important prerequisite to a mature development of science. The literary structure of the first chapter of Genesis also suggests that the “days of creation” are not necessarily chronological. The first three verses emphasize the basic theme of order out of chaos:

In the beginning God created the heavens and the Earth. Now the Earth was form-less and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters. And God said, “Let there be light,” and there was light.

The rest of the chapter describes the ordering process from “formless and empty” chaos to an ordered cosmos by a parallel development of forming and filling:

Forming (Days 1-3) Filling (Days 4-6)

1. Creation of light 4. Creation of Sun Separation from Creation of Moon darkness (1:3-6) and stars (1:14-19)

2. Creation of expanse 5. Creation of birds Separation of waters Creation of fish (1:6-8) (1:20-23)

3. Creation of vegetation 6. Creation of animals Separation of dry Creation of humans ground (1:9-13) (1:24-31).

These verses use forming verbs like “separate” and “gather” in the first three days, and filling verbs like “teem,” “fill,” and “increase” in the last three days. This literary structure clearly emphasizes God’s control over nature and His preparation of an ordered cosmos for human habitation, rather than a chronological account of the stages in creation. The latter idea is reinforced by English translations that read “the first day,” “the second day,” rather than “a first day,” “a second day,” which is more consistent with the lack of a definite article in the original. The inability of Babylonian and Egyptian civilizations to think theoretically in spite of their magnificent technical abilities may correlate with their basic attitudes toward nature. Since both humans and gods were part of nature, history and

society had integral connections to cosmologies that related humanity with the cosmos. Celestial motions and annual floods combined with myth-ological and religious traditions to provide the framework for societal cohesion. Nature exercised control over humans so long as they perceived it as an extension of social relationships and an embodiment of deities to be placated. Scientific curiosity and creativity require the disenchantment of the physical world and the removal of its terror. The Biblical view of creation initiated such a result, which for the first time established a separation of nature from God and made it a matter of human responsibility to exercise stewardship in caring for the Earth and its creatures (Gen. 2:15).

The Importance of the Idea of Creation The importance of creation is not con-fined to the early chapters of Genesis, nor to a mere explanation of origins. The idea that God is the Maker of heaven and Earth permeates the Bible, and this idea has important theological implications. In contrast with mythological cos-mogonies, God is not generated out of some kind of primal chaos, but he is prior to every part of his creation. All things came into being by his will, rather than through cosmic struggle. The world is not bound by conflicting forces of immanent gods to be placated, but is under the control of one God who created it by his power and for his purposes. The attitudes and values contained in the Biblical idea of creation correlate with three basic aspects of science. First, the reality and goodness of creation provide a basis and motivation for experimental science. Second, the order and in-telligibility of nature are essential for theoretical science. Third, the purpose and meaning of creation encourage the development of applied science. These ideas began to permeate Western culture during the medieval period, eventually superseding the limitations of ancient and Greek science. The Bible explicitly proclaims the good-ness and reality of nature. Experimental and observational science, in both laboratory and field work, depends on an affirmative attitude toward the physical world. The first verse of the Bible establishes the existence of the basic categories of


physical reality: “In the beginning God created the heavens and the Earth” (Genesis 1:1). Thus, in the Biblical view, the reality of time (beginning), space (heavens), and matter (Earth) are grounded in creation. The goodness of nature is affirmed six times in the first chapter of Genesis, being repeated for each addition to the created order. The chapter concludes with a seventh affirmation that “God saw everything that he had made, and behold it was very good” (Genesis 1:31). Because the physical world is good, it is worthy of detailed and devoted study. Because it is real, such efforts will not be irrelevant or illusory. However, in the Biblical view, the goodness of creation does not imply a realm of perfection. It sees the world as a place of human probation and judgment (Genesis 3:16-19). The Earth with its thorns and thistles is not evil in itself, but it does not function for humanity as God originally intended. Evil appears as an intruder in a world that is otherwise by nature good. The order and intelligibility of nature follow from the idea of creation through the wisdom of God. This validation of the rational and logical dimensions of the physical world is an essential ingredient in theoretical science, both mathematical and descriptive. In the Biblical view, the regularity of nature is based on more than experience of past events and an inductive assumption about the future. It is grounded in the faithfulness of God who created and sustains the universe. The laws of nature have their source in the nature of God. Order in the physical world is the product of divine wisdom: “O Lord how mani-fold are thy works! In wisdom hast thou made them all” (Psalm 104:24). Numerous Biblical references explicitly affirm the regularity and uniformity of creation. God promised Noah the regularity of “seedtime and harvest, cold and heat, summer and winter, day and night” after the chaos of the flood (Genesis 8:22). Job refers to a “decree for the rain, and a way for the lightning” (Job 28:26) and Jeremiah speaks of the “fixed order of the Moon and stars” (Jeremiah 31:35). Biblical monotheism also implies the unity of the created order in which natural laws apply uniformly throughout a universe governed by one God.

The concept of creation also provides assurance that the created order will be intelligible to human reason. It reveals that the universe has a design in which patterns can be discovered. The Biblical affirmation that “God created man in his own image, in the image of God he created him” (Genesis 1:27) suggests that human creativity and intelligence reflect the order and intelligibility of creation and the laws of logic. The Bible recognizes that we are a part of nature (Genesis 2:7) and thus finite as well as fallen creatures (Genesis 3:6-7). However, the psalmist reaffirms the ability to think God’s thoughts about the universe in spite of our fallen nature: “Great are the works of the Lord, studied by all who have pleasure in them” (Psalm 111:2). The prophet Isaiah invites us to reason even about our sins (Isaiah 1:18). Creation also implies that history and culture have meaning and purpose, providing support for applied science and technology. The Biblical faith that human progress is both possible and important is based on the first command given by God to Adam and Eve: “And God blessed them, and God said to them, ‘Be fruitful and multiply, and fill the Earth and subdue it’” (Genesis 1:28). Being created in the image of God ensures the creative and rational powers to exer-cise this responsibility. Despite our fallen nature, this creation mandate is reaffirmed by the psalmist who declares: “Thou hast given him dominion over the works of thy hands” (Psalm. 8:6). The Biblical idea of creation teaches that nature is not divine, but is God’s handiwork as-signed to human responsibility for its care and protection: “The Lord God took the man and put him in the Garden of Eden to work it and take care of it” (Genesis 2:15). Though we are seen as a part of nature, we are also set apart from nature and can live in the world free from enslavement to nature but responsible for it. The exercise of dominion is clearly distinguished from selfish exploitation by the call to responsible stewardship consistent with the intentions of the Creator. In this view, our distinction from nature and acceptance of dominion are what make us human and is the basis for culture and civilization even though corrupted by sin.


The purpose and meaning of historical existence within the natural order provide moti-vation and significance for science and technol-ogy. The cyclical view of time in the ancient civilizations was antithetical to human purposes since no goals can be achieved without vanishing again. If history is just an endless process of repetition, then no vocation can have lasting significance, and real progress is not possible. God created time with a beginning and end, so its moments are unrepeatable and meaningful as they move toward a final goal. The Biblical view sees the world as good and beautiful and worthy of the efforts of experi-mental science to try to observe and appreciate it. It also believes that the Creator has ordered the universe and reveals it to patient inquiry, confirm-ing the vision of theoretical science in seeking to understand and explain the world. And it gives motivation and purpose for applied science to seek the advancement of human welfare with respon-sibility and wisdom. Although these Biblical attitudes were not applied to science for many

centuries, they eventually permeated western culture, providing the basis for transforming ancient science.

REFERENCES Alioto, Anthony M. A History of Western Science.

Englewood Cliffs, N. J.: Prentice-Hall, 1987. Harris, J. R., ed. The Legacy of Egypt, Second ed.

London: Oxford University Press, 1971. Hatem, M. Abdel-Kader, Life in Ancient Egypt.

Cairo: Al Ahram Commercial Press, 1982. Neugebauer, O. The Exact Sciences in Antiquity,

2nd ed. New York: Dover, 1969. Sarton, George. A History of Science, Cambridge,

Mass.: Harvard University Press, 1952-59. Taton, Rene. Ancient and Medieval Science, Trans.

A. J. Pomerans. New York: Basic Books Inc., 1963.

Toulmin, Stephen and June Goodfield. The Fabric of the Heavens. New York: Harper Row, 1961.

Westermann, Claus. The Genesis Account of Creation. Philadelphia: Fortress, 1964.

22

1. THE GREEK MIRACLE The Greek “miracle” refers to both the wonder one feels for the achievements of ancient Greece and our inability to adequately account for them. Early Greek speculations seem to open up a new universe in contrast to the static ideas of the other ancient civilizations. Although the first Greek attempts at understanding the universe around them resembled science little more than did the Egyptian and Babylonian techniques, each con-tributed in different ways to the development of the scientific tradition. The goal of the ancient civilizations to predict and divine the future is in sharp contrast with the Greek aim to make sense out of natural phenomena. The Greeks were convinced that eternal principles lay behind the flux of changing events, and that a rational explanation was possible. The Cultural Setting The Greek experience around the Aegean Sea differed sharply from that of the Egyptians and Babylonians. Although dynasties might rise and fall in these ancient civilizations, centralized empires remained with stable social organizations. Religious rituals continued in their traditional cycles, and ancient mythologies passed from generation to generation with little change. As-tronomy developed with the demand for accurate

calendars and skillful divination. However, the Aegean lands seldom experienced such order and stability. After the breakdown of the Minoan Empire based in Crete and of the Mycenaean civilization on the Greek mainland by about 1000 BC, the Greek cities were mostly independent except for loose confederacies until Philip of Macedon united them in 338 BC. Most of the Greek port cities depended for their livelihood on maritime trade with the empires of the Eastern Mediterranean and their own colonies along the Ionian coast in the east and the Italian coast in the west. They were well placed to learn from the surrounding civilizations, but they also had to try to reconcile their traditions about Zeus and Apollo with the Egyptian stories of Isis and Osiris or the Babylonian myths about Ea and Marduk. Lacking traditions of their own in astronomy and mathematics, they had to assimilate the ancient knowledge they learned about on a more intellectual level. Happily, Greek social life was structured loosely enough to permit lively discussion of new ideas. The Greeks pursued a variety of ap-proaches in their attempt to understand the universe, including some borrowed from their neighbors, some adaptations, and some original ideas. In spite of debates and disagreements, they were confident that there were unchanging prin-ciples behind the flux of phenomena. Although

CHAPTER 2

A Rational Universe

Foundations of Science in Ancient Greece

Chapter 2 • A Rational Universe 23

their leading thinkers were philosophers rather than prophets or priests, their belief in the exis-tence of such principles was as much a matter of faith as the Egyptian confidence in the regularity of the cycles of nature or the Babylonian belief in the predictability of eclipses. However, this faith gave rise to a new curiosity that led to a search for different kinds of answers and new possibilities. The Homeric Background The first and greatest gift of the emerging Greek culture was Homer’s Iliad, dating from about the ninth century BC. This earliest monu-ment of European literature, perhaps the best of all Western epics, was the herald and teacher of a new way of looking at the world. In spite of its mythological contents, it was remarkably free of religious constraints, magical formulas, and su-perstitions. Together with the Odyssey, it cele-brated the adventuresome spirit of Greek warriors and travelers. Although Herodotus (fl. 450 BC) suggests that the Greeks assimilated Egyptian gods, identifying Amon with Zeus, Isis with Demeter, and Osiris with Dionysus for example, they humanized their gods and heroes, sometimes referring to them as though they were mortals. In many respects the world of Homer is similar to that of the Babylonians. The sky is a solid hemisphere covering the flat Earth, around the rim of which flows the primordial river Okeanos. The eighth century BC poet Hesiod also echoes the Babylonians in his Theogony when he states: “Verily first of all did Chaos come into being, and then broad-bosomed Gaia (Earth)...” Zeus leads the gods against the titanic forces of nature, much like Marduk fought Tiamat, in order to es-tablish their rule. However, the more per-sonal gods of Greece live closer at hand on Mount Olympus in Thessaly, and eventually were seen as subject to the more remote power of fate or des-tiny. Faith in such an unchanging principle in nature was a first step toward a more rational world view. The Homeric age was the literary prepa-ration for another Greek miracle, the sudden ap-pearance of Greek science in the sixth century. As merchants and traders, the Greeks came into contact with the older Egyptian and Babylonian

civilizations. They were able to learn about their techniques and traditions without being bound by them. This was especially true of the Ionian region east of the Greek mainland along the Asiatic coast of the Aegean Sea. Even closer to Ionia was the land of Canaan, or Palestine, where Hebrew prophets by the seventh century had already composed many of the books of the Bible. How-ever, the contrast between the capricious gods and heroes of the Greek poet and storyteller, and the prophetic God of eternal justice, was so great as to probably reduce communication between the Hebrews and Ionians to a minimum. Ionian colonists were an adventurous people whose new location brought them into closer contact with Asians by land and Egyptians by sea. As they learned from these ancient civili-zations, they felt free to raise questions and seek explanations beyond the limits of their original religious sources. Unfortunately, our knowledge of this important step toward a more generalized and theoretical science depends only on fragments from pre-Socratic philosophers (Socrates died in 399 BC), mostly as quotations in the writings of Plato, Aristotle and other Greek writers. 2. PRE-SOCRATIC SCIENCE: RATIONAL BEGINNINGS (600-400 BC) Ionian Science: Matter and Change The first-mentioned of the Greek thinkers in this new tradition was Thales (about 640-546 BC) of Miletus, the main harbor on the Ionian coast. Every listing of the Seven Wise Men of ancient Greece includes him, usually heading the list. As a youth he traveled to Egypt where he learned about astronomy and mathematics, measuring objects like the pyramids from their shadows. Plato says that he was once so intent on observing the stars that he fell into a well. Aristotle portrays a man of more practical potential, who earned a large sum of money by cornering the olive market after leasing all the olive-presses in the region. Herodotus says that Thales’ mother was Phoenician, and he probably also came into con-tact with Babylonians. Herodotus also claims that he predicted the solar eclipse that led the warring


kings of Lydia and Persia to end their fighting. Modern astronomy can date this event since the only solar eclipse to cross Asia Minor at the time of Thales was May 28, 585 BC. Although it may have been possible for him to use Babylonian eclipse tables to predict the time of such an event, its location could only have been by sheer luck since solar eclipses, when they do occur, follow a narrow path on the Earth. Thales initiated the traditions of Greek geometry and cosmology. He is credited with a number of geometric pro-positions, including the generalizations that any angle inscribed in a semi-circle is a right angle (see Figure 2.1), and the sides of similar triangles are proportional. Although he gave no proofs, he began the process of generaliz-ing geometry that culmi-nated 300 years later with Euclid. Thales’ cosmol-ogy seems to borrow from Babylonian mythology in claiming that “all is water.” This somewhat primitive idea of a mate-rial unity in nature seems to be an attempt to account for the basic forms of liquid, solid and gaseous matter in terms of an unchanging ele-mental substance. He taught that the Earth was a flat disk floating on water, as in Homer’s view of the Earth surrounded by the primordial ocean. He seems to rationalize Homer in suggesting that the world was full of gods, as exemplified in his observation of the magnetic effect of a lodestone animated by a soul. The ideas of Thales were modified and extended by Anaximander (ca. 610-546 BC), his younger companion and fellow citizen of Miletus. Anaximander taught that the ultimate basis of

matter was beyond ordinary perception, a sub-stance he called apeiron (unlimited or indefinite), out of which an infinite sequence of worlds has come into being and then been reabsorbed accord-ing to a single law of cosmic justice or necessity. Animals emerged from inanimate matter through the action of the Sun and water, and humans de-veloped from fish. According to Anaximander, our world formed in a process of separation that left the Earth suspended at the center of space, since it had

no preferred direction to move away from the center. The Sun, Moon, and planets consisted of openings in hollow rings or wheels of fire circling the Earth, sug-gesting for the first time the con-tinuity of their motions around the Earth and the idea of a complete celes-tial sphere of stars surrounding the Earth (Figure 2.2), although it was inside the planetary rings. Some later ac-counts of Anaximander indicate that his ideas included quantitative speculations. The solar ring had a diameter some 27 times the Earth’s diameter, and the Sun appears through a hole in its rim equal in size to the Earth (giving the Sun an angular size

of about 4°, which is 8 times too large). The diameter of the lunar ring was 19 times that of the Earth. Eclipses and the phases of the Moon involved changes in the openings in the rings. The orientation of these rings may correspond to simple measurements of sundial shadows, attributed by some sources to Anaximander. He assumed that Earth was a cylinder with a diameter three times its depth. He probably thought of the surface of

α

α

β

β

A B

C

D

O

Figure 2.1 Thales’ Right-Triangle Theorem Thales might have used the following informal proof that a triangle ABC inscribed in a circle on a diameter AB is a right triangle: The diagonals of a rectangle are equal and bisect one another, so a rectangle ABCD can be inscribed in a circle with center O and diameters AB = CD, and thus the angle α+β is a right angle. (Note that the angles of triangle ABC must be 180° = 2α+2β, so α+β = 90°.)


the Earth as corresponding to the flat top of the cylinder (Figure 2.2); but some say he conceived of it as oriented with a convex side on top to account for the changing elevation of the stars when traveling north or south. Anaximander also produced the first primitive map of the world that included Europe and Asia. The last Milesian to speculate about a primary substance or material unity was Anaximenes. Probably a student of Anaximander, he returned to a more physical approach with air as the universal principle, which he also related to the breath of life to account for the human soul and organic processes. Air is indeterminate in itself, but it undergoes observable processes such as conden-sation and rarefaction with their associated temperature changes. The airy exhalation of the Earth rises to form the fiery objects of the heavens, which like the Earth are disks supported by the air. According to Theophrastus, a student of Aristotle, Anaximenes taught that “The heavenly bodies do not move under the Earth, as some suppose (Anaximander?), but round it; like a cap turned round on one’s head.” He suggests that the stars “are fixed like nails in the crystalline vault of the heavens.” This seems to be a clear distinction between stars and planets, but the stars appear to spread over only a hemisphere. In the writings of Heraclitus (ca. 540-475) of Ephesus, chief of the 12 Ionian cities, the problem of permanence and unity amidst diversity gave way to an emphasis on change. His choice of fire as the primordial substance symbolized the conflict and change that ruled the world. Thus he claimed that “Fire governs the universe,” and that “All things are changed by fire and fire by all

things.” However, he also taught that beneath the apparent flux and disharmony of the world there is a profound harmony of universal law that governs change. He despaired because few people listen to what he called the logos (or logic) of divine reason that permeates the universe and reveals its harmony. Heraclitus reconciled the conflict of opposites as the general scheme of nature: “God is day and night, winter and summer, war and peace, surfeit and hunger.” It is the invisible harmony that matters. This principle of rationality in science was a necessary ingredient to transcend the flux of experience. Xenophanes (ca. 570-478) of Colophon in Ionia carried this principle of rationality one step further. He ridiculed the many gods of Homer and went beyond the search for a single material substance by suggesting that unity in diversity could only be found in one invisible God that fills the universe: “The all is one and the one is God.” He taught that all material things come from earth

EarthHorizon

Axis ofRotation

Polaris Circumpolar

stars thatnever rise

Celestial

stars thatnever set Celestial

Sphere

Equator

daily

of celestial sphere

Figure 2.2 Anaximander’s Idea of an Unsupported Earth Anaximander proposed that the Earth is suspended in space, without any support, at the center of a celestial sphere. The celestial sphere provided a mechanism to carry the stars in their daily rotation about a polar axis pointing toward the North Star Polaris, with the celestial equator in a plane perpendicular to this axis of rotation. Circumpolar stars are near enough the polar axes that those between the North Pole and the horizon never set, and those between the South Pole and the horizon never rise.


and water in recurring cycles of flooding, as evidenced by the discovery of seashells in the mountains and fossils in the midst of the Earth. These observations came from a lifetime of traveling after Cyrus the Persian had conquered his homeland. Xenophanes settled for a time in Elea in southern Italy where he may have influenced Parmenides in the same region that the Pytha-goreans settled. Pythagorean Science: Mystics and Mathematics As we have seen, religion played an im-portant role in the development of Greek science in spite of its rationality. This is especially true of the Pythagorean school that began in the Greek colony at Croton in southern Italy, which attracted Ionians because of the Persian menace in the east. Pythagoras (ca. 570-497) was born on the island of Samos in Ionia and may have met Thales before leaving the region to escape the Samian tyrant Polycrates. Some accounts say that Pythagoras traveled to the eastern Mediterranean and lived for several years in Egypt and Babylon, where he learned oriental knowledge before finally settling in Croton. Following a common religious practice of the time, Pythagoras and his disciples formed an ascetic community that abstained from certain foods and lived simply in order to contemplate intellectual pursuits and mystical ideas, such as reincarnation and the relation between music and mathematics. Their practice of secrecy seems to have raised suspicions in Croton that forced Py-thagoras to flee to Metapontum where he died. Apparently women played an important part in the early community. Some accounts indicate that his student Theano, variously described as his wife or daughter, may have helped to keep the school going after his death. The Pythagoreans rejected the Ionian concept of a single material substance and replaced it with the pluralistic idea that numbers are the basis for a universal harmony of opposites, such as odd-even, limited-unlimited, one-many, and straight-curved. They had no symbols for numbers, but represented them by dots in the symmetrical geometric forms of triangles, squares and

rectangles. For example, the sum of the triangular numbers 3 and 6 give the square number 9: o o o o o o o + o o = o o o o o o o o o leading to the discovery that the sum of any two consecutive triangular numbers is a square number. The so called tetractys represented their perfect number 10, o o o o o o o o o o consisting of the numbers 1 + 2 + 3 + 4. The number 1 is a mathematical point, 2 points form a line, 3 produce a plane, and 4 are required for a solid. Thus the tetractys symbolized the structure of the universe and their religious faith in its mathematical harmony. Pythagoras demonstrated his ideas about the mathematical structure of the world with simple experiments on the harmonious sounds produced by the strings of musical instruments. He showed that two strings whose lengths differ by a ratio of 1:2 produce sounds one octave apart (8 tones in diatonic scale), while a ratio of 2:3 gives the har-monic interval called a “fifth” (5 diatonic tones) and a 3:4 ratio is an interval of a “fourth” (4 dia-tonic tones). Thus the harmonic intervals of classical Greek music depend on whole number ratios (root of the word “rational”). The cube re-vealed a “geometric harmony” because its 6 faces, 8 corners and 12 edges form the ratios 1:2:3:4. The Pythagoreans thought that musical intervals determined even the motions of the seven planets, emitting sounds that depended perhaps on their spacing or relative speeds through the zodiac. According to some accounts, only Pythagoras sensed the vibrations of the universe sufficiently to hear this “music of the spheres.” Some also say that he was the first to recognize that the morning and evening stars, Phosphorus and Hesperus, were one and the same, the planet Venus. Various accounts credit either him or his disciple Alcmaion (ca. 500 BC) with the idea that the planets move


slowly backward from west to east relative to the stars along circular paths, rather than erratic wandering. Some sources also claim Alcmaion dis-covered the optic nerves from the eyes to the brain, and the air tubes linking the ears with the mouth. Several Greek writers attribute to Py-thagoras the idea of a spherical Earth, probably based on the perfect symmetry of the sphere and the spherical form of the heavens, rather than on empirical evidence. In fact, most scientific hy-potheses begin as an act of faith that lead to test-able theories, as in this supposition of the spheric-ity of the Earth, which led to a number of confir-mations as later summarized by Aristotle. The idea of spherical perfection became the basis for a new kind of dualism that associated perfection with the celestial world, the abode of the gods, and imper-fection with the sublunar terrestrial world for the next two thousand years. The name of Pythagoras is particularly associated with the theorem giving the square of the hypotenuse of a right triangle as the sum of the squares of the other two sides (c² = a² + b²).

According to legend, he sacrificed a hundred oxen to celebrate the discovery of this general relation, or perhaps even its proof. He could have obtained a proof from consideration of a small square with sides of length c inscribed at an angle in a larger square so as to divide its sides into lengths a and b, forming four triangles of sides a, b, and c and of area ab/2 each (Figure 2.3a). The area of the large square then takes two equal forms:

c² + 4(ab/2) = (a + b)² = a² + 2ab + b²,

which reduce to the Pythagorean theorem,

c² = a² + b². However, when this result is applied to the simplest right isosceles triangle with sides one unit long, it gives 2 for the hypotenuse (Figure 2.3b), which was found to have no rational repre-sentation, as later shown by Euclid. If the hypote-nuse is assumed to have a rational representation with integers m and n of 2 = m/n, then m² = 2n² so m² must be even. Thus m must also be even and

ab/2

b a

b

a

c

c

1

12√

(a) Pythagorean Theorem (b) Discovery of Irrationals Figure 2.3 Proof of the Pythagorean Theorem and the Discovery of Irrationals (a) The Pythagorean theorem for any right triangle can be proved by equating the small square of area c² plus the four triangles each of area ab/2 to the area of the large square (a + b)². (b) A right triangle of sides a = b = 1 has hypotenuse c given by c² = 1² + 1² = 2 or c = 2. The Pythagoreans discovered that this number was irrational by assuming that it was rational and then showing that this assumption led to a contradiction.


n must be odd for any ratio reduced to its lowest terms. But if m is even then m = 2p (p is an integer), so m² = 4p² = 2n² and n must be even. Since no number can be both odd and even, 2 cannot be a ratio of whole numbers. This dis-covery of irrational numbers challenged the basic assumptions of the Pythagoreans and seemed a threat to their view of the universe. They aban-doned their effort to identify number with geome-try, and the two remained largely separate until af-ter the development of algebra and analytic ge-ometry. The new emphasis was on form and qual-ity, instead of the quantitative use of numbers. More than a century after Pythagoras died, his followers were still developing his ideas, including the proposal of an unusual cosmology. Philolaus (ca 480-400 BC) was born at or near Croton. He was the first to propose the motion of

the Earth (and by implication its rotation as well). Recognizing the orbital motion of the planets, he was able to eliminate their daily westward revolutions and have only eastward motions by having the Earth revolve once every 24 hours around a postulated Central Fire, or “Hearth of the Universe,” which acts as a central force or motor (Figure 2.4). Observers on Earth do not see the central fire because the inhabited side of the Earth always faces outward. Thus the Earth also rotates about its own axis (though Philolaus was probably not aware of this). According to Philolaus, a Counter Earth always moves directly between the Central Fire and the Earth, shading the Earth from the Central Fire. Thus there are ten revolving bodies spaced ac-cording to a musical progression in the fol-lowing order: Counter Earth, Earth, Moon, Sun, the five

Saturn (30-year revolution)

Sun (1-year revolution)Moon (27 days)Earth (daily revolution)

Counter Earth (daily)

Central Fire (stationary)

Celestial Sphere (stationary stars)

10 planets with moving earth,counter earth and central fire

Venus (revolves near sun)Mercury (revolves near sun)

Jupiter (12-year revolution)Mars (2-year revolution)

Figure 2.4 Pythagorean Cosmology of Philolaus with a Moving Earth In the cosmology of Philolaus, the Earth revolves around the Central Fire every day, making it un-necessary for the stars and planets to have a daily revolution. The idea of a Counter Earth may have been introduced to shield the Earth from the Central Fire by always moving between them. The Earth is inhabited on the side away from the Counter Earth and thus it is never seen. Aristotle sug-gested that the unobservable Counter Earth may have been added to the idea of a moving Earth to give 10 celestial bodies, since 10 was the number of perfection for the Pythagoreans.


planets and finally the celestial sphere. Actually, with a rotating Earth the stars could have remained stationary. However, Philolaus gave the celestial sphere a very slow rotation, perhaps to generate the lowest pitch in the music of the spheres. Aristotle suggests that Philolaus added the Counter Earth to make the number of moving objects equal to the perfect number ten. According to some accounts, the younger Pythagorean Ecphantos (ca. 350 BC) and perhaps his teacher Hicetas (ca. 400-335BC), both from Syracuse, suggested that the Earth was at the center of the universe and rotated daily on its axis instead of a rotating celestial sphere. Eleatics and Atomists: Permanence and Motion A more metaphysical approach to reality developed on the southwest coast of Italy at Elea, established by Ionians fleeing the Persians. The founder of the Eleatic school was Parmenides (ca. 515-450 BC), who had some association with the Pythagoreans, but appears to have more influence from Xenophanes. He tried to develop Ionian monism as an alternative to Pythagorean dualism and pluralism by the use of pure logic regardless of appearances. Instead of a primordial substance, however, he postulated an ultimate reality of Being (the One) beyond all phenomena. By the law of contradiction, the opposite of Being is not-Being, which cannot exist even though it can be thought. The same argument applies to the void, and if the void does not exist motion is not possible. Contrary to Heraclitus, change is not possible since it implies that Being comes from its opposite, not-Being, which does not exist. The infinite is also impossible, since thinking of it is to set a limit in thought. Multiplicity is really unity, and reality is beyond appearances. Logic seems to have displaced science. In actuality, Parmenides did not deny that phenomena followed laws that science could study, only that there is an unchanging reality behind all phenomena. His cosmology was quite similar to that of the Pythagoreans, except that the unity of being replaced the multiplicity of num-bers. Being completely fills space without any void in a finite spherical universe, since the sphere is continuous yet finite. He was the only non-Pythagorean to accept the spherical form of the

Earth until Plato. He was the first to divide the Earth into five zones, but he thought the tropic zones were about twice their actual width and uninhabited. He was also the first to use a series of concentric spheres to account for the different mo-tions of the planets, with the Earth at the center, but he located the celestial sphere below the Sun similar to Anaximander. In the midst of the Earth was a divinity ruling over all, and she generated all the gods. Parmenides’ disciple Zeno (ca. 490-430 BC), who came from Elea, defended his master’s ideas. He developed several paradoxes to show the logical absurdity of motion. In the first, called the “dichotomy” by Aristotle, Zeno claims that you cannot travel between two points in a finite time since you first must go half the distance, then half the remaining distance, ad infinitum, through an infinite number of points. A second, called the “Achilles,” asserts that Achilles cannot pass a tortoise because he first must reach the place from which the tortoise started. By then the tortoise will have gained some ground that Achilles must again make up, and so on, making it impossible to catch up. Thus motion is inconceivable on the pluralistic basis of space as the sum of points and time as the sum of instants. The Eleatic school made it nec-essary to reconcile perception with reason. Atomism in ancient Greece reacted to both Ionian monism and the Eleatic denial of mo-tion. The atomists introduced a radical pluralism in which the world consists of an infinite number of imperceptible atoms moving in an infinite void. Aristotle and other Greek authors agree that Leucippus invented the atomic theory, but seem to know very little about him. He flourished about 430 BC, and was probably from Miletus. He may have once been a student of Zeno, but probably reacted against the fantastic ideas of Parmenides. In the one statement credited to him, he seems to be the first to clearly state the principle of causality: “Nothing happens in vain (without reason), everything has a cause and is the result of necessity.” Leucippus’ student Democritus (ca. 460-371 BC), who came from Abdera in the north of Greece, developed and described his ideas. He used an inheritance to study for several years in Egypt, and may have traveled as far as Persia and


India. Known as the “Laughing Philosopher,” all branches of philosophy and science interested him. He defined the atom as the smallest conceivable unit of matter, and thus indivisible or literally “uncuttable.” They are alike in quality but differ in “shape, order and position,” according to Aristotle’s description. Different combinations of the atoms make up all things, and apparent changes in matter result from their separation and rejoining in different patterns. But what is the cause of motion among the atoms? Apparently motion is their natural state, so it is not necessary to account for it. Both the atoms and their motion in the void are eternal, a kind of anticipation of the principles of conser-vation of matter and momentum. The ideas of causation and necessity had been reduced to a mechanical determinism in which human freedom and choice are only an illusion resulting from ig-norance and the infinite complexity of combining atoms. Worlds are formed and then vanish from the blind swirling of the atoms throughout infinite space. While Parmenides denied change and the evidence of the senses, basing everything on the mind, the atomists used their theory to explain the phenomena, but in the process they lost the mind. The soul was not distinct from matter, but con-sisted of more subtle and mobile atoms and there-fore superior to the grosser atoms of the body. Sensations result from the impact of atoms on the body and are due to their size, shape and ar-rangements. In a purely atomistic theory, devoid of any organizing principle, life and thought remain a mystery. The Greeks resisted this thoroughgoing materialism, partly because of ideas like the void and self-moving bodies, and partly because it seemed to lack any basis for values like freedom and responsibility. The comic dramatist Aristo-phanes (fl. 400 BC) summarized their reaction in the couplet, “Whirl is King, Zeus is dead.” About a century after Democritus, Epicu-rus (341-270 BC) of Samos revived atomism and established a popular school in Athens. He tried to escape from its determinism by allowing the atoms to have a random tendency to “swerve” as they fall through space, but the Epicureans could still find nothing of higher value than human pleasure with

moderation; thus their motto was “Eat, drink and be merry, for tomorrow we die.” Their ideas were the basis for an epic Latin poem by Lucretius (ca. 95-55 BC), which became quite influential in the revival of atomistic ideas after its rediscovery in AD 1417. 3. ATHENIAN SCIENCE: RATIONAL SYNTHESES (450-323 BC) Early Syntheses of Pre-Socratic Science Athens had reached its pinnacle of suc-cess after the defeat of the Persians in the fifth century BC. Even after the Peloponnesian Wars and the fall of Athens to Sparta in 404 BC, it remained the crossroads and intellectual center of Greece. Ideas from the far corners of Greek culture converged in Athens, where they stimulated lively debate and discussion. But the proliferation of scientific theories had given rise to a group of teachers known as sophists who taught that all theories are equally true and false and only practi-cal expediency is possible. Socrates (ca. 470-399 BC) countered this growing idea that “man is the measure of all things” by pointing out that their principle of relativism must also submit to having no sure basis in truth, and therefore invalidates itself. His intellectual heirs, especially Plato and Aristotle, attempted to synthesize differing scientific ideas in order to “save the appearances” and reveal the underlying reality. To some extent, Anaxagoras, Empedocles and others had already begun to combine Ionian and Pythagorean ideas reaching Athens. With Anaxagoras (ca. 500-428 BC), the last of the Ionian philosophers, a more scientific approach is evident, He moved to Athens soon after the Persian wars, where he became the first teacher of natural philosophy in that city and a friend of Pericles. His solution to the problem of change was to postulate that matter is a mixture of countless “seeds” (spermata), differing from elements since each is as complex as the whole, and from atoms since there is no limit to their subdivision. Going beyond Pythagorean numbers as an organizing principle, Anaxagoras asserted that Mind (nous) orders the seeds apart from matter and is the source of its motion. Mind


produces a cosmos out of chaos through a process of rotation. Anaxagoras extended Ionian materialism to suggest that the Moon was a material object like the Earth, and the Sun was incandescent iron like a meteorite that fell in 467 BC. He also applied Py-thagorean geometric ideas to the Sun and Moon to explain lunar phases in terms of reflected light from the Sun (Figure 2.5). Thus, according to Plato, he was the first to clearly recognize that the Moon reflects light from the Sun in differing geo-metric relationships to produce its phases. He may have also recognized that eclipses are alignments of Earth, Moon and Sun, though this could not have been entirely clear due to his belief that the Earth was disk shaped. A few years before his

death, enemies of Pericles charged him with im-pious rationalism and banished him from Athens. Empedocles (ca. 492-432 BC) of Agri-gentum, on the south coast of Sicily, traveled in Italy and the Peloponnesian Peninsula, perhaps even as far as Athens, as a rhapsodist, healer and preacher. He suggested a compromise between Ionian monism and complete pluralism by postu-lating four distinct and unchangeable substances: earth, water, air and fire. These substances were first called elements by Plato, and appear to sym-bolize solids, liquids, gases and heat. Empedocles also introduced a primitive concept of attractive and repulsive forces that he called love and strife, distinct from matter, by which the four elements unite or separate to pro-

SUN NEWMOON

CRESCENTGIBBOUS

EARTHSolareclipse

Lunareclipse

Rays of sun

Orbit of moon

Phases of moon as seen from earth

FULLMOON

Actualillumination

of moon

WAXINGCRESCENT

WANINGWANING

WAXINGGIBBOUS

FIRSTQUARTER

THIRDQUARTER

Figure 2.5 Greek Rational Explanation for Phases and Eclipses of the Moon Anaxagoras believed that the Sun was a ball of fire, that the Moon was made from Earth, and that the phases of the Moon resulted from the light of the Sun reflected from the Moon as viewed from the Earth. Thus when the Moon is between the Sun and the Earth, no reflected light can be seen from the new Moon; and as the angle between the Moon and the Sun increases, the phases of the Moon wax to crescent, half, gibbous, and full. The orbit of the Moon is inclined 5° from the plane of the Sun’s apparent motion (ecliptic), so that eclipses only occur when the Moon is crossing the ecliptic plane at the new Moon (solar eclipse) when it comes in front of the Sun at conjunction, or at the full Moon (lunar eclipse) when it passes through the shadow of the Earth at opposition.


duce the various forms of matter. Some accounts suggest that he chose four based on the Pythago-rean tetrad, and others because of a presumed relation with four of the five regular solids as de-veloped later by Plato. He conceived of the stars as attached to an egg-shaped crystalline surface and speculated about the finite speed of light. His theory of vision was a compromise between light emitted and light received by the eye. His idea of health was a condition of equilibrium between the four elements. Hippocrates (ca. 450-370 BC) of Cos, an island off the Ionian coast, extended the ap-plication of Pythagorean and Ionian ideas to medicine. He came from a family of medical practitioners in the tradition of Asclepius (Greek god of medicine), which had begun to embrace the emerging rational spirit in Greece. He traveled widely in Greece, and by some accounts he studied in Egypt and taught in Athens before establishing a school of medicine in Cos. The Hippocratic corpus of more than 50 books in Alexandria by 300 BC represents this rational and empirical tradition that led to the reputation of Hippocrates as the “father of medicine.” Hippocratic physiology associated four humors (bodily secretions) with the four elements of Empedocles, as well as the four seasons and the four major organs of the body. Thus he connected blood with air, the heart, and spring; yellow bile with fire, the liver, and summer; the mysterious black bile with earth, the spleen, and autumn; and phlegm with water, the brain, and winter. By the second century AD, the Roman physician Galen related the four humors (blood, yellow bile, black bile and phlegm) to four qualities in pairs (moist-hot, hot-dry, dry-cold and cold-moist), and even to four temperaments (sanguine, choleric, melan-cholic and phlegmatic). In the Hippocratic tradition, good health meant to achieve a Pythagorean harmony through a balance of the humors in their ideal proportions. The physician was to aid nature in restoring equi-librium, especially through “diet,” which included sleep, rest and exercise. The famous Hippocratic Oath for acceptance into the physician’s guild an-nunciates the professional attitudes and ethical obligations of physicians.

Not to be confused with Hippocrates of Cos was his older contemporary, Hippocrates of Chios, from another island on the Ionian coast. He taught mathematics in Athens about the middle of the fifth century BC and wrote what was probably the first textbook in geometry. He began the process, later completed by Euclid, of putting the increasing number of geometric theorems from Ionian, Pythagorean, and other sources into a systematic order, and thus might qualify as the “father of geometry.” His most famous discovery was how to find the area (squaring) of certain crescent-shaped lunes formed by the intersection of two circular arcs with different radii, showing for the first time the possibility of squaring curvi-linear figures. His younger contemporary and fel-low citizen, Oinopides of Chios, used Pythagorean astronomy to obtain the first meaningful measure-ment of the angle of the ecliptic (obliquity: 24 degrees) relative to the celestial equator. Plato and the Academy Plato (427-347 BC), like his teacher Socrates, concerned himself more directly with moral and political philosophy than natural science, but his Pythagorean emphasis on the importance of mathematics led to the first truly universal synthesis of Greek thought. After eight years as a disciple of Socrates, ending with his death, Plato spent twelve years traveling as far as Egypt and Italy. At about age 40 he began a school in Athens called the Academy (at an oak grove originally owned by the Greek hero Academos), which lasted for nearly a thousand years. His famous theory of Ideas encompassed all knowledge, including cosmology. It greatly influ-enced scientific thinking, even though it demoted the world of observable phenomena to mere ap-pearance and opinion in contrast with the realm of pure Ideas, which was the source of true knowl-edge about reality. Plato attempted to resolve the conflict be-tween permanence and change by separating true knowledge about reality from opinion based on appearances. Science, like knowledge in general, is to ascertain eternal Ideas or universal Forms through their changing appearances to our senses. The idea of equality, for example, is not the same


as its appearance in the material world, where two objects may appear the same, but when examined more closely are found to be different. Like mathematical concepts, rational contemplation reveals the eternal Ideas, rather than sense experience. If we do not use our reason to separate these eternal Ideas from ever changing phenom-ena, what Plato called “saving the appearances,” we are like prisoners chained in a cave so that they can only see flickering shadows on its walls. If we can break our chains, we will see that these shadows are only reflections of eternal Ideas in the real world outside. Tradition says that over the gate of Plato’s Academy was a sign saying “Let no man ignorant of geometry en-ter.” His later dialogues became more and more mathematical, and his Timaeus reveals a dis-tinctively Pythagorean cosmology. As a rational account of the harmony of the universe, he bases it on the Forms; but since these can only be imper-fectly realized in the world, he calls it only a “likely story.” Thus there can be no exact science of nature, and God is not a creator but a “Demiurge” who injects reason and order into ma-terial chaos. Plato’s real contribution to science is not any particular discovery, but the idea that mathematics can reveal and model the world around us and yet be apart from it. In Plato’s “likely story,” the universe is a living body whose rational soul reveals itself in the regularity of the heavens. Both the universe and the Earth at its center are spherical and consist of a harmony of the four elements structured by the

geometry of the regular solids. Theaetetus (d. 369 BC), a Pythagorean mathematician and con-temporary of Plato, studied these solids formed by identical polygons on each face meeting at equal angles. He was probably the first to show that only five regular solids can exist (Figure 2.6).

Plato associated fire with the tetrahedron (4 triangular faces), having the sharpest corners. The structure of water depends on the icosahedron (20 equilateral triangles), closest to the smoothness of a sphere. Air has the form of the octahedron (8 triangles), whose faces could break up and reform as fire or water. Earth relates to the cube (6 squares), the most immobile and also, with its square sides, incapable of combining with the other elements. Since there are five solids, Plato associated the entire universe with the dodecahe-dron (12 pentagons), and later with a fifth element called ether.

dodecahedron icosahedron(ether) (water)

tetrahedron cube octahedron(fire) (earth) (air)

Figure 2.6 Five Regular Solids of Pythagoras (Platonic Solids) A regular solid, or polyhedron, has congruent faces, each a regular polygon and meeting at equal angles. The Pythagorean fascination with the four of these solids previously known led to their discovery of the dodecahedron. Plato speculated that these solids determined the structure and properties of the four elements.


Although Plato did not work out the ce-lestial motions in detail, he felt that a theory of the heavens must go beyond mere description by seeking to make sense out of their motions. He viewed the circle as the eternal Idea for explaining the apparent irregularities of planetary motion, which became the leading idea in astronomy for the next two thousand years. He divided the heavens into two kinds of motion: the Circle of the Same for the daily rotations of all celestial bodies from east to west parallel to the celestial equator; and the Circle of the Diverse, which was divided into seven unequal and slower motions for the planets from west to east through the constel-lations of the zodiac. Plato claimed that the planetary circles are also of unequal diameters proportional to the arbitrary sequence 1, 2, 3, 4, 8, 9, 27, in the order of Moon, Sun, Mercury, Venus, Mars, Jupiter and Saturn. He also noted “opposite tendencies” in the motions of the planets, and in the case of Mars “the appearance of turning back on itself.” This may be an implicit reference to its occasional westward retrograde motion. According to Plato, the daily rotation of the Circle of the Same corresponds to the motion of the World Soul, and God is further identified with the Idea of the Good. The same rational principle is found in humans, whose immortal soul perceives the operation of reason in nature. Time is defined as the “moving image of eternity,” which came into being with this world and the motion of the heavenly spheres. The details of Plato’s system were left for his students to work out, who tended to form into two groups called the “gods” and the “giants.” The gods, such as Eu-doxus, favored mathematics and the Forms, while the giants, especially Aristotle, tried to bring sci-ence down to the visible world. Eudoxus (ca 400-347 BC) was born in Cnidus on the Ionian coast. He studied geometry and medicine before entering Plato’s Academy, and is credited with proving the formulas for the volumes of the cone and pyramid. After a few months in Athens, he went to Egypt and studied for more than a year with a priest of Heliopolis, where he probably gained his knowledge of plane-tary motions. He eventually returned to Athens as a teacher with his own students. He was the first to

go beyond the Egyptians in proposing a four-year cycle of solar years that included a leap year, some 300 years before Julius Caesar introduced it into his Julian calendar. He was the greatest math-ematician and astronomer of his age, far surpassing Plato in his scientific achievements. In mathematics Eudoxus is best known for his theory of proportions and his method of exhaustion (Books V and VI in Euclid’s Ele-ments), building on the work of Theaetetus. The discovery of irrationals was disturbing to Plato as a source of instability in mathematics. In his general theory of proportions, Eudoxus extended the ideas of number and length to include irrationals by introducing the concept of magnitudes with no particular quantitative values, but reducible to proportions based on a definition of equal ratios. He also showed how the continued division of a given magnitude can “exhaust” the continuum of a curve in order to compute the areas and volumes of curved figures. Archimedes later developed this method of exhaustion, which appeared in the 17th century AD as the limit of an infinite sequence in the calculus. Eudoxus pioneered in the first of several attempts to solve Plato’s problem of the planets. As quoted from his younger contemporary, Eude-mos of Rhodes, Plato wanted to know “which uni-form and ordered movements must be assumed to account for the apparent movements of the plan-ets.” The elegant solution of Eudoxus combined the circular motions of a series of concentric spheres, each inside the other, with the Earth as their common center. To explain the various planetary motions, he used a total of 26 spheres: four for each planet and three each for the Sun and Moon. Nineteenth century analyses, especially by the Italian astronomer Giovanni Schiaparelli, showed the validity and limits of his scheme. The outermost sphere of the four spheres for each planet produced its daily westward rota-tion about the Earth. The second with its poles oriented at an angle of about 24° from those of the first, corresonding to the angle between the ecliptic and the celestial equator, gave its eastward sidereal motion (relative to the stars) through the zodiac. The third sphere rotated with the synodic period of the planet (time between successive conjunctions


with the Sun), with its poles attached at right angles to those of the second sphere and carried around by it. The third and fourth spheres rotated with the same period but in op-posite directions about poles oriented at dif-ferent angles for each planet relative to each other (see Figure 2.7 for Saturn). The planet itself remained on the fourth sphere, which together with the third produced a figure eight motion that altered the speed and position of the planet as a possible fit to its actual retro-grade motion. This system was adequate for three of the planets, but apparently fails to account very well for the retrograde motions of Mars and Venus. It also failed to account for the changing brightness of the planets since their distances from the Earth at the center remained constant for each planet on its given sphere. Of the three spheres for the Moon, the first provided its daily westward rotation and the third its 27-day eastward motion through the zo-diac. The second intervening sphere revolved westward once every 18.5 years to account for the retrograde motion of the lunar nodes (intersections of its orbit with the ecliptic) associated with eclipse cycles. Only two spheres are needed for the daily motion of the Sun and its annual motions around the ecliptic; but Eudoxus added a third sphere to account for a possible inclination of the Sun’s orbit relative to the ecliptic, which he viewed as the great circle through the middle of the zodiac. No attempt was made to account for the inequality of the seasons discovered 60 years

earlier by Meton of Athens, who also introduced the 19-year luni-solar cycle of the Babylonians to the Greeks. Thus with the celestial sphere included, Eudoxus ended with a total of 27 con-centric (or homocentric) spheres in the first serious attempt to match the actual planetary motions. A considerable simplification of the sys-tem of Eudoxus could have been realized if the ideas of another student of Plato, Heraclides (ca. 388-315 BC) of Pontus (on the Black Sea), had been accepted. His reputation is indicated by a story that says he was placed in charge of the Academy during Plato’s ill-fated attempt to train a philosopher-king in Sicily. Heraclides taught a form of atomic theory in which the particles were held together by a kind of Empedoclean attraction in an infinite universe. Several accounts mention that Heraclides suggested the daily rotation of the Earth on

Polaris

Polar axis

Ecliptic axis

23.5°

Celestial sphere

EarthN

S

30 year eclipticrevolution axis of Saturn

Saturn

Equator

Retrogradeaxes

One retrogradeper year

Daily rotation ofstars & Saturn

Figure 2.7 Concentric Spheres of Eudoxus for Planetary Motions The concentric sphere model of Eudoxus required four spheres for each of the planets to show all their motions about the Earth. In the case of Saturn, the outermost sphere revolves once every 30 years parallel to the ecliptic to account for motion around the zodiac; the next sphere rotates once each day to carry Saturn in its daily motion; and the two innermost spheres give a smaller variation within the zodiac to reproduce Saturn’s retrograde motion about once each year.


its axis. For example, in the first century AD Aetius of Antioch wrote that “Heraclides of Pontus and Ecphantos the Pythagorean let the Earth move, not progressively but in a turning manner like a wheel fitted with an axis, from west to east round its own center.” According to some sources, he also suggested that the motions of Mercury and Venus could be accounted for by having them revolve around the Sun as it moves around the Earth, an idea mistakenly referred to for centuries as the Egyptian system. These ideas could have eliminated nearly half of the spheres of Eudoxus, but instead it became much more complicated with the additions of Callippus and Aristotle. Aristotle and the Lyceum Aristotle (384-322 BC) was the greatest scientist of antiquity, both in the breadth of his synthesis of Greek knowledge and in the depth of his focus on natural phenomena. He was born in the city of Stagira on the northern coast of the Aegean Sea, near the border between Ionia and Macedonia. His father Nichomachus belonged to an Asclepiad family in the Ionian tradition of empirical medicine and was physician to Amyntas II, king of the semi-Greek region of Macedonia and grandfather of Alexander the Great. After the death of his parents, his guardian sent him to Athens at the age of seventeen to study at the Academy, where Plato called him “the intelligence of the school.” Aristotle remained in Athens for twenty years and his early writings were in the Platonic tradition. After the death of Plato in 347 BC, Aristotle joined a school at Assos in Ionia, where he also studied marine life around the island of Lesbos and married Pythias, adopted daughter of the director of the school. In 343 BC Philip of Macedonia invited him to become tutor for his son Alexander. After Philip defeated his adversaries, he established the Hellenic League of Greek states in 338 BC. Alexander succeeded him two years later, after his assassination. Aristotle then returned to Athens and established his own school east of the city walls, calling it the Lyceum since it was at the sacred grove of the wolf-god Apollon Lyceios. Alexander provided support for the school, including many kinds of natural specimens

for its museum, brought back from his far-flung conquests. These were especially important for Aristotle’s empirical emphasis as compared to the idealistic emphasis of the Academy. Although Aristotle agreed with Plato that sense experience does not give unchangeable knowledge, he preferred to accept the evidence of the senses and the complexity of nature as the starting point of any explanation. Since form never appears without matter, the two should not be separated. Thus Aristotle viewed forms as immanent in matter, rather than existing in a transcendent realm of eternal Ideas beyond the senses. Although the forms are fully real, they serve more as abstract categories that aid in the process of defining and classifying. This led to the first truly systematic study of logic in his Organon as the proper method of rational science, based on the faith that nature conforms to logical analysis. It also led to a qualitative emphasis on classification rather than a quantitative emphasis on math-ematics, which Aristotle thought could be too easily separated from the changing world of physical things. He didn’t even give speed a quantitative definition, since dividing distance by time would not be a commensurable ratio. To account for change, Aristotle identi-fies matter with potentiality and form with actual-ity. An acorn has the potential within it to become an actual tree. It grows toward the goal or telos of its form or essence. This kind of purposeful change from potential to actual is called teleology and pervades all of Aristotelian science. In his treatise entitled Physics, Aristotle divided the causes of change into four classes, reflecting a synthesis of Greek thought. The material cause of any change was its elemental substance (Ionian contribution); formal cause was its ideal essence (Pythagorean-Platonic approach); efficient cause was its source of motion (atomist emphasis); and the final cause was its goal (religious tradition). The material cause of a statue is the marble used to make it; the formal cause is the figure it portrays; the efficient cause is the action of the sculptor; and most important is the final cause or purpose, perhaps to serve as an idol to honor a god.


Aristotle’s geocentric cosmology extends from the ever-changing Earth to the unchanging heavens. Each of the four elements has a tendency to occupy its natural place: Earth and water have natural downward motions (gravity), with earth seeking the center of the universe surrounded by water; air and fire move upward (levity), with air surrounding the water and fire extending to the sphere of the Moon. Left to themselves in the sub- lunar world, the elements seek their natural places and their natural state of rest unless disturbed by some outside force. Motion that is not natural requires a mover or efficient cause that produces “violent motion” by direct contact. Qualitative changes occur with mixing of the elements as in heating, which adds fire and causes the upward motion of smoke or steam. When clouds lose heat they change to rain which falls to its natural place. Since comets and meteors involve change, Aris-totle explained them as sublunar exhalations of fire and classified them with meteorology rather than as celestial phenomena. The idea that violent motion requires a mover included the effect of resistance to motion caused by the surrounding medium. Aristotle viewed the speed of an object as proportional to the force of the mover and inversely proportional to the resistance of the medium (v = F/R). The smaller the resistance the faster an object would move, leading to the conclusion that a void or vacuum is impossible since it would have no resis-tance and therefore allow infinite speed. Consid-ering the resistance of media such as air, water, or honey, it is easy to see why Aristotle believed that heavy objects fall faster than light objects. He faced a more difficult problem in the violent motion of a projectile after it leaves the original mover. Here he developed the dubious doctrine of antiperistasis, which taught that air pushed out from the front of a projectile rushes around to the back to prevent a vacuum, and thus acts as a mover (Figure 2.8). As the circulating air diminishes, natural motion takes over causing the projectile to fall to the ground. Aristotle gave several arguments for the spherical shape of the Earth, both theoretical and empirical. Objects fall vertically toward their

natural place at the center, thus forming a sphere. During a lunar eclipse the shadow of the Earth on the Moon always has a convex circular curvature. Traveling north or south changes the elevation of the stars, with new stars appearing on the horizon. He even recognized that this observation implies that the Earth “is of no great size,” but quotes an estimate that is about double the actual size as measured in the following century. This led him to accept the idea of continuous oceans to the west of the Pillars of Hercules (Straits of Gibraltar) all the way to India (Asia). In contrast to the change and imperfection of the sub-lunar region of the four elements, Aristotle viewed the heavens as changeless and perfect, partaking of the “divine nature.” In De Caelo (On the Heavens he argues that “motion in a circle is perfect, having neither beginning nor end, nor ceasing in infinite time,” so the natural motion of the heavens is circular. The corre-sponding perfection of the sphere leads to the spherical shape of the heavens with the Earth at the center. It also implies their finite size, since no infinite body can have a center; so there is “neither body nor space nor vacuum” beyond the outermost sphere. A fifth element (quintessence in Latin) called aether fills the celestial region. It was an incorruptible substance with an intrinsic circular

violentmotion

naturalmotion

air circulation

Figure 2.8 Aristotle’s Antiperistasis Concept Aristotle explained the violent motion of a projectile in terms of the circulation of air pushed from the front of a moving object, rushing to the back to prevent a void behind the object. This air circulation, called antiperi-stasis, pushes the object until it weakens enough to allow natural motion to prevail.


motion. This material conception of the heavens required a more physical construction than that of the abstract geometrical spheres of Eudoxus and Callippus. Callippus (ca. 370-300 BC) was born in Cyzicos (on the Sea of Marmara), where Eudoxus had earlier conducted a school. Some thirty years after Eudoxus published his system, Callippus recognized its limitations and tried to correct them by adding seven more spheres to the 26 of Eudoxus, making a total of 33 planetary spheres. He was able to account for the retrograde motion of Mars, Venus and Mercury by adding one more sphere to each; and he added two more spheres to both the Moon and the Sun to correct for their variable speeds, having made better measurements of the lengths of the seasons (beginning with the vernal equinox: 94, 92, 89, and 90 days). This is one of the first examples of direct interaction be-tween theory and observation. When he went to Athens, he stayed with Aristotle and helped him to correct and complete the system of Eudoxus. In seeking a more physical explanation of planetary motions, Aristotle added unnecessary complications to the elegant mathematical system of Eudoxus and Callippus. By linking all the spheres into a single mechanical system, he had to add “unrolling” spheres between each set of plane-tary spheres to keep them from interfering with each other. Inside the four spheres of Saturn, for instance, he added three spheres with the opposite motions of the inner three of Saturn’s spheres, thus cancelling their motion and leaving only the daily motion of its outer sphere to connect with the outer sphere of Jupiter. He also added three such spheres inside the spheres of Jupiter and four each inside those of Mars, Venus, Mercury and the Sun. The Moon required no new spheres, leaving 22 spheres to be added. This made a total of 55 planetary spheres plus the celestial sphere as the highest of the celestial gods. In his Metaphysics Aristotle introduced an unmoved mover of the spheres and everything else in the universe. This is as close as he comes to a transcendent God, the Prime Mover beyond the celestial sphere who is eternal and incorruptible, pure actuality and form, unencumbered by matter, and of perfect goodness. As pure form God moves

things as a Final Cause rather than by physical contact. He is the object of love and desire toward whom all things strive and whose only action is self contemplation. In Aristotle’s universal system God is at the pinnacle of a hierarchy of being that links every level of nature. Everything below God suffers from a degree of privation so that each species, while having its own form, is inferior to those above it and can be classified by the form to which it strives. This hierarchical cosmology (Figure 2.9), later called the “Great Chain of Being,” had a strong influence on the Medieval world view of both Islam and Christianity. Descending from God and the planets to the sub-lunar region and the inanimate world, everything had its place and purpose in nature, distinguished by different as-pects of its soul (form of its body). In view of their reasoning abilities or rational soul, Aristotle de-fined humans as “rational animals,” linking the celestial and terrestrial realms. All animals have both a sensitive soul and a nutritive soul, but plants have only a nutritive soul. Aristotle classified plants and animals as static species, in which he viewed mutations as failures to realize their form. He gave special attention to biology, classifying over 500 species in categories approximating modern taxonomy, including some discoveries not confirmed until the nineteenth century. He also be-lieved in spontaneous generation, and thought that the heart was the central organ of perception with the brain serving to cool its action. Although Aristotle lacked the concepts of creation and personal immortality, his ideas were still a major influence on Western religions. His conception of immortality, in which only the ac-tive reason is eternal, is bleak and impersonal; but the logic and breadth of his ideas were too power-ful to ignore and his scientific system lasted longer than any other in history. After Alexander the Great died in 323 BC, reaction against Macedonian subjugation led to a charge of impiety against Aristotle, forcing him to leave Athens. He died a year later at the age of 63. Aristotle’s ideas received further devel-opment by his friend and successor in the Lyceum for 35 years, Theophrastus (ca 371-287 BC) of Lesbos. He became famous as the founder of


botany for his work on plant life, including the classification of about 500 species, and he wrote the first treatise on mineralogy. Theophrastus did not hesitate to criticize his master, rejecting final causes in many aspects of nature, questioning the idea of spontaneous generation, and suggesting the brain as the seat of intelligence. He also recognized the nature of sexual reproduction in higher plants. Succeeding Theophrastus in the Lyceum for 19 years was Strato of Lampsacus (ca. 340- 268 BC) known as the physicist, who had earlier helped establish the Museum in Alexandria. Strato developed and criticized Aristotle’s physics. He replaced the concept of levity in the upward tendency of air and fire with the idea of displacement caused by the downward movement of heavy bodies. He also introduced the idea of acceleration for falling objects, their faster motion resulting from closer approach to their natural place,

later referred to as a kind of jubilation as they neared home. After the death of Strato, interest in sci-ence declined at the Lyceum, shifting from Athens to Alexandria in Egypt. In Athens Epicurus revived atomism at his school mainly to combat religion and superstition. For example, understanding the source of light from the Moon was not as important as denying its divinity. Holding an opposing view was Zeno of Cition on the island of Cyprus, (b. ca. 350 BC), who founded the Stoics, so named after the porch (stoa) where he taught in Athens. He em-phasized the divinity of the celestial bodies and their control over the destinies of humans, who are at the mercy of arbitrary fate. The Sun was the ruling power of the universe even as the heart ruled the body. These ideas provided an intellectual basis for divination and astrology, as well as the new imperialisms of the Greeks and Romans.

Earth

Water

FireAir

Ether

55planetaryspheres

Ecliptic axis

Polar axisPrime Mover

Lunarsphere

Celestial sphereGreat Chain of Being

God (Prime Mover)Angels (Planets)

AnimalsPlantsMatter

Lunar SphereHumans

(Rational animals)

Figure 2.9 Aristotle’s Geocentric Cosmology & Great Chain of Being Aristotle replaced the 26 mathematical concentric spheres of Eudoxus with 55 solid planetary spheres to transmit motion from the Prime Mover through the celestial region to the terrestrial region with its four sub-lunar spheres of fire, air, water, and earth at the center. This hierarchical cosmology featured the dualism of an unchanging celestial region of perfection and the imperfect changing terrestrial region, linked by the Great Chain of Being with humans as the central link between the celestial and terrestrial reflected in their rational and animal characteristics.


4. ALEXANDRIAN SCIENCE: RATIONAL APPLICATIONS (323 BC - 415 AD) Hellenistic Trends The main center of Greek science after Aristotle shifted from Athens to Alexandria during the Hellenistic and Greco-Roman periods. After being defeated by the Spartans in 404 BC and subjugated by Philip of Macedon in 338 BC, the Athenians turned increasingly toward superstition or cynicism as developed by the Stoics and Epicu-reans. Alexander the Great founded the city of Alexandria on the Mediterranean coast of Egypt in 332 BC. His subsequent conquest of Mesopotamia provided access to Babylonian astronomy and mathematics, but it also exposed Greece to new inroads of Babylonian astrology. The Alexandrian conquests ended the old Hellenism and inaugurated the Hellenistic age with more of an international character. It was also an age of greater special-ization in the sciences and a retreat from the grander systems of Athenian philosophy. It followed the more realistic emphases of Aristotle, but also led to some of the greatest achievements in Greek mathematics and astronomy. Rational science continued to develop with increasing rigor, but without probing many new questions. Following the death of Alexander at Babylon in 323 BC, his empire fell apart and Egypt came under the rule of one of his generals, Ptolemy I (Soter), who like Alexander was a stu-dent of Aristotle. He founded the Museum and Library at Alexandria about 300 BC with the help of Strato. They were expanded after 285 BC by his son Ptolemy II, who was a student of Strato before his return to Athens to head the Lyceum. The Museum, or Temple to the Muses, the mythical nine daughters of Zeus, was a teaching and research center modeled on the Lyceum, but much larger. More than a hundred state-paid teachers staffed the Museum, which included an astro-nomical observatory, a botanical garden, a zoo and dissecting rooms. The Library of about half a million scrolls was the largest in the ancient world. This new international cosmopolis attracted many mathematicians and scientists by its relative peace and stability and the patronage of the Ptolemies. The Museum was the chief center for Greek

science for about 700 years, though its contri-butions declined in the later centuries. Alexandrian Mathematics One of the earliest and most famous of the Alexandrian mathematicians was Euclid (fl. 300 BC), called “the father of geometry” although little is known about his life. He probably studied at the Academy in Athens and went to Alexandria in the early years of the Museum. Euclid’s Elements of Geometry is the most successful textbook in the history of mathematics and one of the most important mathematical treatises ever written. When asked by King Ptolemy I if there was any easier way to learn mathematics, Euclid replied that “there is no royal road to geometry.” Another story tells of a student who wanted to know what he would get from learning geometry. Euclid called his slave and said, “Give him a coin, since he must gain from what he learns.” Little of the thirteen books in the Elements appears to be original, but his achievement was to gather to-gether the propositions and proofs from widely scattered sources and put them into a strong logical order forming a consistent deductive system. This synthesis of Greek mathematics became the model for mathematical rigor and axiomatic systems for more than two thousand years. Euclid’s Elements begins with 23 defini-tions, such as the intuitive ideas that points have no parts, lines have length without breadth, and parallel lines never meet. Next are five geometric postulates followed by five general notions similar to Aristotle’s logical axioms, such as number three: equals subtracted from equals are equal. The five unproven postulates are: (1) a straight line may be drawn between any two points; (2) a straight line may be continuously extended; (3) a circle may be constructed about any point; (4) all right angles are equal; (5) through a point not on a given line, one and only one line can be drawn parallel to a given line. The fifth is the famous parallel postulate. Euclid recognized that it had no proof and thus treated it as a postulate. Non-Euclidean geometries first appeared in the nineteenth century. These assumed that either no parallel lines or that more than one could be drawn through a point parallel to another line, which later


led to important applications in cosmology such as the concept of space curvature. The Elements contain 467 propositions established by various methods of proof. Most are straight forward, but they also include the method of exhaustion introduced by Eudoxus, and reduc-tion to the absurd. The first six books cover plane geometry, and the last three books deal with solid geometry, including the five regular solids. Books VII-IX cover arithmetic and number theory, in-cluding prime numbers. Book X is Euclid’s masterpiece on irrationals treated geometrically, but practically obsolete in terms of modern algebra. He also wrote a book on Optics, which applied geometry to the Greek theory that vision results from emissions coming out of the eye (extramission theory). Proposition 20 of Book IX is an elegant illustration of reduction to the absurd to show that the number of primes is infinite. Euclid assumes the contrary: a finite series of primes 2, 3, 5, 7, 11,..., k, where k is the largest. Their product plus 1, that is P = 2.3.5.7.11...k+1, is either prime or not. If P is prime it is larger than k. If P is not prime it must be divisible by some prime p, which cannot be 2, 3, 5, 7,..., or k because it would then leave a remainder of 1. In either case there is a new prime greater than any prime k, contrary to the original assumption, and thus there must be an infinite number of primes. Perhaps the greatest mathematician of antiquity was Archimedes (ca. 287-212 BC) of Syracuse in Sicily, although he was best known for his mechanical inventions. He studied in Alexandria and maintained his contacts there after returning to Syracuse. Among his reputed inventions were compound pulleys, the hydraulic screw still used in Egypt for raising water, catapults for defensive purposes, and concave mirrors to deflect rays from the Sun and reputedly set Roman ships on fire. According to Plutarch, however, Ar-chimedes regarded “as ignoble and sordid the business of mechanics and every sort of art that is directed to use and profit,” typical of Greek ra-tionalism. He was killed in the sack of Syracuse under the Roman general Marcellus in 212 BC. Legend says that a soldier came upon him while he

was contemplating geometric figures drawn in the sand, and killed him when Archimedes shouted to keep off. Most of the dozen surviving books by Archimedes are on geometry. These are not as encyclopedic as Euclid, but they are highly origi-nal. In his Measurement of the Circle he shows that the area of a circle is equal to that of a triangle whose base is the circumference and whose height is the radius of the circle (2πr × r/2), equivalent to the formula A = πr² (Figure 2.10). He also uses Eudoxus’ method of exhaustion with polygons of 96 sides inscribed and circumscribed about a circle to estimate the value of π between 3.141 and 3.142. In the Sphere and Cylinder, Archimedes

r

b

b b

Figure 2.10 Archimedes’ Method of Limits Archimedes obtained the formula for the area of a circle by inscribing it in a regular polygon whose area could be calculated by breaking it up into isosceles triangles of area br/2, where b is the length of the sides of the polygon and r is the radius of the circle. Then the area of the circle is found to any desired approximation by increasing the number of sides n on the polygon to any desired limit. In the largest possible limit, the perimeter of the polygon n×b is equal to the circumference of the circle C, giving the area of the circle in the limit as:

A = n×br/2 = C(r/2) = 2πr(r/2) = πr².


uses the method of exhaustion to find the surface of a sphere (4πr²) and its volume (4πr³/3). His book, The Method, discovered at Constantinople in 1906, reveals that he often used a method of mechanical intuition to obtain his results before proving them. His approach anticipated the calcu-lus, but he never passed to the limit of an infinite sequence. Archimedes also created two branches of theoretical mechanics, statics and hydrostatics. In his Equilibrium of Planes and at least one lost treatise, he developed the laws of the lever and calculated centers of gravity for various figures. According to legend he boasted to King Hieron of Syracuse: “Give me a point of support and I shall move the world.” He then demonstrated his claim by moving a fully laden ship with a compound pulley. In his book On Floating Bodies, Ar-chimedes established the principle of buoyancy according to which a body immersed in a fluid loses an amount of weight (or gains a buoyant force opposing its weight) equal to the fluid it displaces. Legend says that he made this discovery when he noticed his loss of weight in water, and that he ran out of the bath shouting Eureka! (I found it!). This enabled him to show that King Hieron’s crown was not pure gold by finding that it weighed less in water than an equal weight of gold, and therefore that its volume was greater than the gold. In a curious book called the Sand Reckoner he developed a method for representing large quantities to estimate the number of grains of sand that would fill the universe as estimated by Aristarchus. The only other Greek mathemetician comparable with Archimedes was Apollonius (ca. 262-190 BC), born in Perga on the southern coast of Asia Minor. He studied in Alexandria about 25 years after Archimedes and flourished there under Ptolemy III and Ptolemy IV. His most famous work was the Conic Sections, analyzing the intersections of a plane and a right circular cone. About half is a systematic survey of earlier results and the other half is a new method of analyzing conics. He showed that the cone generates three kinds of conics (Figure 2.11), and gave the names for them that are still used today: the ellipse,

parabola, and hyperbola, all of which have important applications in science. The Conics comprise eight books with 487 propositions that describe the construction of conics and their prop-erties. Apollonius also developed an analysis of a looping geometric curve known as an epicycle, produced by a point rotating on a small circle as the center of this circle rotates around a large cir-cle. This led to new ways of representing the motions of the planets. He recognized in the sys-tem of Heraclides that the motions of Mercury and Venus around the Sun corresponded to epicycles that traced a series of loops as the Sun moves around the Earth. He developed a generalized theory of planetary motion on an epicycle circle whose center moves around the circumference of another circle (deferent) centered on the Earth

Parabola

Hyperbola

Ellipse

Circle

•

Figure 2.11 Conic Sections of Apollonius Apollonius analyzed the conic sections formed by the intersection of a cone with various planes. A plane parallel to the axis of the cone intersects it in the two branches of the hyperbola. A plane perpendicular to the axis intersects the cone in a circle. A plane oblique to the axis of the cone intersects it in an ellipse. A plane parallel to a side (generator) of the cone intersects it in a parabola.


(Figure 2.12), and showed that it could be applied to Mars, Jupiter and Saturn to account for their ret-rograde motions. He also developed a theory of eccentrics, in which the center of a planet’s motion is displaced from the Earth and allowed to rotate around it to account for apparent planetary motions. Hipparchus and Ptolemy developed these devices further, and applied them as a substitute for concentric spheres to account for the motions and changing brightness of the planets.

Alexandrian Astronomy and Geography The first important astronomer associated with Alexandria was Aristarchus (ca 310-230 BC) of Samos. Little is known about his life, but he probably came to the Alexandrian Museum in his youth and was a student of Strato. He is sometimes called the “Copernicus of Antiquity” for his suggestion of a complete heliocentric theory of the

planets, as reported by Archimedes in his Sand Reckoner:

His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun in the circumference of a circle, the Sun lying in the middle of the orbit, and that the sphere of the fixed stars situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.

Not only is this heliocentric, but it assumes an immense distance to the stars to account for the lack of any apparent shift in the angles of the stars due to the motion of the Earth (stellar parallax). Aristarchus suffered criticism for his ideas from Cleanthes the Stoic, whose ethical zeal led him to suggest a charge of impiety “for moving the hearth of the universe (the Earth) and trying to save the phenomena by the assumption that the heaven is at rest.” About a century later, Seleucus the Babylonian (fl. 150s BC) strongly supported the theory, but Hipparchus and Ptolemy both rejected it. The only surviving book by Aris-tarchus, On the Sizes and Distances of the Sun and Moon, does not mention the theory, but its conclusions on the vast size of the Sun compared to the Moon give a hint of its origin, and Archimedes gives some additional details. Aristarchus recognized that when the Moon is exactly half illuminated by light from the Sun (half Moon), the triangle formed by the Sun, Moon and Earth is a right triangle with its right angle at the Moon. He estimated the angle at the Earth to be 29/30 of a right angle or 87°, giving an angle of 3° at the Sun and an Earth-Sun distance of about 19 times the Earth-Moon distance. Since the apparent sizes of the Sun and Moon are about equal, he concluded that the diameter of the Sun is about 19 times that of the Moon. By timing how long the Moon is in the Earth’s shadow during a lunar eclipse, he estimated its diameter to be that of two Moons, hence the Sun’s diameter would be almost 10 times the diameter of the Earth. Thus it would seem reasonable for the Earth to revolve

•• •

Epicycle

P

Deferent circle

Earth

Figure 2.12 The Epicycle of Apollonius Apollonius analyzed the epicycle formed by a point P rotating on a small circle whose center rotates on a larger circle called the deferent. This looping curve was used to represent the apparent path of a planet (at P) with their periodic retrograde motions.


around the much larger Sun and the immense sphere of the stars to remain stationary as the Earth rotates (Figure 2.13). Modern measurements reinforce this he-liocentric conclusion with an angle at the Earth of about 89°51’, giving an Earth-Sun distance of about 400 times the Earth-Moon distance, an Earth diameter of nearly four Moons, and thus a solar diameter of about 100 times the diameter of the Earth. The difficulty for Aristarchus was in de-termining when the Moon was exactly half illumi-nated and its exact path during an eclipse. Eratosthenes (ca 275-194 BC) of Cyrene (west of Alexandria) used similar geometric rea-soning to measure the size of the Earth. Educated in Athens, he had broader interests than most Hellenistic scholars, including history, poetry, as-tronomy, mathematics and geography. He became the librarian of the Alexandrian Museum and the

founder of mathematical geography. On a visit to Syene (modern Aswan), 500 miles south of Alexandria on the Nile, he observed the reflection of the Sun from the bottom of a deep well at noon on the summer solstice (day when the Sun reaches the extreme of its northward motion). Since the Sun was directly overhead, he knew that Syene was on (or near) the Tropic of Cancer (about 24° latitude). Measurements of the Sun’s shadow at noon on the summer solstice in Alexandria showed that it inclines toward the south about 1/50 of a great circle or about 7° (24° + 7° = 31° latitude). In view of the Sun’s great distance, its rays at Alexandria and Syene may be considered parallel; so perpendiculars to the surface of the Earth from these two locations extended to the center of the Earth will intersect at the same angle, giving their separation as 1/50 of the Earth’s circumference.

SUN

EARTH

HALFMOON

SM

EMES

3°

87°

For a 3° Triangle: ES = 20 EMSo Sun's Diameter: S = 20 M

From Eclipse Timing: M = E/2So Sun's Diameter is: S = 10 E

(Modern values: S = 400 M = 100 E)Moon's Orbit

EarthShadow

Figure 2.13 Aristarchus’ Determination of the Distance and Size of the Sun Aristarchus estimated an angle of 87° between the Sun and the Moon at the time of a half Moon when the Earth-Moon line (EM) is at right angles to the Sun-Moon line. Thus the remaining angle of the Earth-Sun-Moon triangle is only 3°, giving an Earth-Sun distance of about 20 times the Earth-Moon distance (ES = 20 EM). Since the apparent (angular) size of the Sun and Moon are nearly equal (0.5°), the diameter of the Sun must be about 20 times larger than that of the Moon (S = 20 M). By timing a lunar eclipse, Aristarchus estimated that the diameter of the Moon is half that of the Sun (M = E/2). Thus the diameter of the Sun is about 10 times larger than that of the Earth, and he concluded that it is more reasonable that the Earth rotates around the Sun.


The circumference of the Earth then follows by multiplying their separation of 500 miles by 50 to get 25,000 miles (Figure 2.12). This is a fairly accurate result, but Eratosthenes’ value of 250,000 stadia is difficult to compare since the 5000 stadia distance between Alexandria and Syene came from counting paces, and the length of stadia differed among Romans and Egyptians. In his Geographical Memoirs, Eratosth-enes established the five geographic zones: the tropics within 24° of the equator, the polar regions within 24° of the poles, and the temperate zones in between. His map of the known Earth shows lines of latitude and longitude, with an estimate of 78,000 stadia of land (about 8000 miles) from the

Atlantic to the eastern end of the Indian Ocean. He believed that there was a connection between these oceans because of similar tides. About a century after Eratosthenes, the Stoic Posidonius (ca. 135-50 BC) of Apamea (in Syria) was the first to correlate variations in the tides (spring and neap) with the positions of both the Sun and Moon. He attempted a new de-termination of the size of the Earth from the lati-tudes and distances between Rhodes and Alexan-dria. He obtained a value of only 180,000 stadia (18,000 miles) and suggested the possibility of sailing west to reach India. This is the value used by Ptolemy that eventually influenced Columbus to think that India was only about 3000 miles west.

Equator

Syene (Aswan)

AlexandriaNile

Pole

7o24o

7o

Shadow

Sun'srays Zenith

500miles

Summer solstice at noon

of obelisk

at Syene

Figure 2.14 Eratosthenes’ Measurement of the Circumference of the Earth On a visit to Syene at the summer solstice, Eratosthenes observed that the rays of the noonday Sun were reflected from the bottom of a well. He knew that the rays of the noonday Sun on the same day at Alexandria cast a shadow of 7° from the vertical. By assuming that the Sun is far enough away compared to the size of the Earth for its rays to be assumed parallel, it follows that the angle at the center of the Earth between Syene and Alexandria is also 7°. Thus the circumference of the Earth is 360/7 or about 50 times the distance between these cities. Given a distance of 500 miles between them, the circumference of the Earth is given by: C = (360/7) × 500 miles = 50 × 500 miles = 25,000 miles.


The greatest astronomer of antiquity was Hipparchus (ca 190-120 BC) of Nicea in Asia Minor. Most of what is known about him comes from Ptolemy some three centuries later, who mentions his early observations from Alexandria and later ones from the island of Rhodes. Hippar-chus recognized the advantages of using the epi-cycle and eccentric methods of Apollonius to account for both the motions and changing brightness of the planets. He was the first to apply both methods to the planets in a new attempt to solve Plato’s problem of explaining planetary motions by combinations of circles. Hipparchus used a fixed eccentric for the Sun’s orbit (center shifted toward the summer sol-stice) to account for the inequality of the seasons (six days longer for spring and summer). For the larger inequalities of the Moon, he used a deferent inclined at 5° to the ecliptic and an epicycle whose center moved eastward around the deferent. The Moon rotated westward on the epicycle at nearly the same rate to account for its changing speed at syzygies (new and full Moon), faster when closer to the Earth. He also began to apply the eccentrics and epicycles of Apollonius to the planets, which Ptolemy later completed. The mathematical basis for the epicycle system of the planets was an early form of trigo-nometry invented by Hipparchus. He established propositions and relations between arcs and chords of spherical triangles, adopted the Babylonian division of the circle into 360°, and compiled a table of chords to compute positions on the celestial sphere. These mathematical tools com-bined with the most accurate observations of an-tiquity gave measurements to within about 1/6 of a degree (10’). Hipparchus measured the distance of the Moon (orbital radius r) from the fact that its 0.5° angular size through a complete orbit of 360° traverses 720 lunar diameters d, so the circumfer-ence of its orbit 2πr = 720d and r = 115d. By measuring the time of a lunar eclipse more accu-rately than Aristarchus did, he deduced that the diameter of the Earth is about 3.5 lunar diameters d, so the distance of the Moon is about 33 Earth diameters (115/3.5), slightly larger than the actual value of 30.

Drawing on star records of earlier Alex-andrian astronomers and ancient Babylonians, Hipparchus discovered a slow westward shift of the equinox points (where the celestial equator intersects the ecliptic) of about 1.3° per century (46”/year), causing the equinox to arrive slightly earlier each year. The modern value for this “precession of the equinoxes” is about 1.4° per century or 50” per year, resulting in a shift of the equinox points around the entire ecliptic in about 26,000 years (360°/50”), nearly 2000 years in each constellation of the zodiac. Thus the vernal equinox had been in the constellation Taurus in Sumerian times, had shifted to Aries by the time of Greek science, moving on to Pisces in the Christian era (reaching Aquarius in about 2300). Hipparchus also compared his observa-tions of the summer solstice with those of Aristar-chus 145 years earlier and found the tropical year (time between the Sun’s return to the precessing equinox) to be 365 days 5 hours 55 minutes, about 6 minutes in excess of the modern value. His de-termination of the mean lunar month (29.531 days) using ancient Babylonian records was correct within one second, making more accurate eclipse predictions possible. In 134 BC Hipparchus discovered a new star in Scorpio, also recorded by the Chinese. According to Pliny, this led him to compile a catalog of some 850 stars. He was the first to give their ecliptic coordinates of latitude and longitude, and to divide them into six orders of magnitude according to their relative brightness, the 20 brightest being of first order. For 300 years after Hipparchus, little fur-ther work occurred in theoretical astronomy until his work was extended and finished by Claudius Ptolemy (ca AD 100-170). He produced the first complete treatise on astronomical science based on epicycles, and was the last notable astronomer of antiquity. Little is known about Ptolemy, but his recorded observations at Alexandria are from AD 127 to 151, and he may have been Egyptian rather than Greek. Although his observations were less accurate than those of Hipparchus, he estimated the average distance of the Moon more accurately by a parallax method involving the shift in the apparent position of the Moon relative to the stars as they appear to circle the Earth each day.


Ptolemy’s fame rests on his major trea-tise, Mathematike Syntaxis, known as the Almagest from Arab translations that prefixed the article al to the Greek megiste, meaning “The Greatest.” The first nine of thirteen books are a mathematical introduction, since for Ptolemy astronomy is a math-ematical science in which circular motions are proper to the nature of divine things. Book I includes a Table of Chords and Books VII and VIII contain an expanded Star Catalog. The last four books apply the epicycle and eccentric methods of Apollonius and Hipparchus to the planets. Ptolemy discovered a sec-ond inequality in the motion of the Moon near quadratures (half Moon), which he accounted for by a mov-able eccentric with the center of the lunar orbit rotating on a small circle around the center of the Earth. This caused the distance of the Moon from the Earth to vary from as much as 65 to 34 Earth diameters (actual 32 to 28.5), making its apparent di-ameter vary to a maximum of nearly twice the observed value and show-ing his priority of mathematics over physical appearances. By applying epicycles, eccentrics, movable eccentrics, and combinations of these to the planets, Ptolemy was able to account for all their various motions with a total of some 40 cir-cles. These included small circles perpendicular to the deferent circles, revolving with the periods of each planet to account for the inclination of their orbits. Epicycles for Mercury and Venus had their centers fixed on a line from the Earth to the Sun to account for their observed proximity to the Sun. In the spirit of Plato, Ptolemy still had concern about the non-uniform speeds of the plan-ets about either the Earth or the center of their def-erents. Thus he added one more device, the equant, to an already complicated system. This was a point at the same distance as the Earth from the center of

the deferent, but on the opposite side from the center, about which the centers of the planetary epicycles moved uniformly with equal angles in equal times (Figure 2.15).

Ptolemy wrote several other books, but his sole authorship of them raises questions. This is especially true of the Geography, which includes eight books, unprecedented in their scope and influence. Unfortunately his work suffers from the choice of Posidonius’ incorrect value of 180,000 stadia for the circumference of the Earth, and 500 stadia to the degree instead of 600. His book on Optics followed the extramission theory of vision, and states the law of equal angles for incidence and reflection. It included measurements of refraction and the incorrect suggestion that refracted angles are proportional to incident

••

•

Equant Eccentric

Planet

Epicycle

Retrograde

Deferent •

•Earth

Circle

C

α

Figure 2.15 Ptolemy’s Epicycle, Eccentric and Equant Ptolemy followed Hipparchus in using the epicycle to explain retrograde motion, and the eccentric position of the Earth to account for the inequality of the seasons. He introduced the equant to obtain uniform motion of the center of the epicycle as required by Plato. About the equant, he showed that the center of the epicycle moves through equal angles (α) in equal times if it is equi-distant from the center of the deferent circle as the eccentric but on the opposite side.


angles. Unfortunately, one of his most influential books was the Tetrabiblos, a kind of bible of Hel-lenistic astrology. The Museum of Alexandria produced very little original science after Ptolemy. One last contribution in mathematics was a step toward algebra by Diophantus who flourished around AD 250 in Alexandria. Only six of the original 13 books of his Arithmetica have survived, but these are enough to show both his Babylonian indebtedness and his own originality. He worked with rudimentary equations with one unknown of powers up to 6, having only positive rational so-lutions. His best known work is with equations requiring integer solutions, which were often in-determinate with no single set of solutions or even an infinite set, still known as Diophantine equa-tions. One of the last men of science at the Mu-seum was Theon of Alexandria, who wrote several commentaries including a valuable one on Ptolemy. But he was the last to make full use of the Library, since a part of it housed in the Sera-peum (Temple of the bull god Serapis) was largely destroyed in his lifetime by a monk-led Christian mob in AD 390. His daughter Hypatia, the only noted woman scholar of ancient times, lectured at the Museum and wrote useful commentaries on several earlier scholars such as Apollonius, Ptolemy and Diophantus. Although several Christian bishops were among her students, an-other anti-pagan mob of Christian zealots killed her in AD 415, marking the virtual end of Greek science in Alexandria. A thirteenth-century ac-count, and therefore somewhat unreliable, claims that the Museum was destroyed after the Muslim conquest of AD 640. REFERENCES Archimedes. The Works of Archimedes Including

the Method. trans. Thomas L. Heath. Chicago: University of Chicago Press, 1952.

Aristarchus of Samos. Distances of the Sun and Moon. trans. Ivor Thomas. Cambridge, Mass.: Harvard University Press, 1980.

Aristotle. The Complete Works of Aristotle. ed. Jonathan Barnes. Princeton, N.J.: Princeton University Press, 1984.

Clagett, Marshall. Greek Science in Antiquity. New York: Collier, 1963.

Cornford, Francis M. From Religion to Philoso-phy: A Study in the Origins of Western Specu-lation. New York: Longmans, Green, 1912.

Dreyer, J. L. E. A History of Astronomy from Thales to Kepler. New York: Dover, 1953.

Eratosthenes. Measurement of the Earth. trans. Ivor Thomas. Cambridge, Mass.: Harvard University Press, 1980.

Euclid. The Elements. ed. and trans. Thomas L. Heath. 3 vols. New York: Dover, 1956.

Heath, Sir Thomas. Aristarchus of Samos: The Ancient Copernicus. New York: Dover, 1981.

Lindberg, David C. The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious & Institutional Con-text, 600 BC to AD1450. Chicago: University of Chicago Press, 1992.

Lloyd, G. E. R. Early Greek Science: Thales to Aristotle. New York: Norton, 1970.

Lloyd, G. E. R. Greek Science after Aristotle. London: Chatts and Windus, 1973.

Lloyd, G. E. R. Magic, Reason, and Experience: Studies in the Origin and Development of Greek Science. New York: Cambridge Uni-versity Press, 1979.

Lloyd, G. S. and Raven, J. E. The Pre-Socratic Philosophers: A Critical History with Selection of the Texts. Cambridge, Eng.: Cambridge University Press, 1957.

Lovejoy, Arthur O. The Great Chain of Being. Cambridge, Mass.: Harvard Univ. Press, 1936.

Newton, Robert. The Crime of Claudius Ptolemy. Baltimore: Johns Hopkins Univ. Press, 1977.

Ptolemy. Almagest. trans. R. Catesby Taliaferro. Chicago: University of Chicago Press, 1948.

Sambursky, S. The Physical World of the Greeks. London: Routledge and Kegan Paul, 1956.

Santillana, Giorgio. The Origins of Scientific Thought. New York: New American Library, 1970.

Toulmin, Stephen and June Goodfield. The Fabric of the Heavens. New York: Harper, 1961.

49

1. ROMAN SCIENCE The Roman, Christian, and Islamic civi-lizations that inherited ancient Greek science inclined more toward practical and religious goals than the Greeks. They valued science more for its usefulness, its moral lessons, or as a “handmaiden” to theology, than for its own sake. With some notable exceptions, this attitude tended to inhibit the development of science, although it did aid in its transmission and eventual resurgence. It also led to a more purposeful view of the universe, in the traditions of Plato and Aristotle, as compared with its “enlightened” modern successors. The Romans came to civilization under the tutelage of the Etruscans, adopting the system of astrology and liver divination the Etruscans brought from their original home in Asia Minor. The Romans became increasingly aware of the su-periority of Greek culture as they subjugated the dynasties that had emerged from the Greek colo-nies established by Alexander the Great. The trans-mission of Greek science to Rome took place during the period that included some of the highest attainments of Hellenistic science, culminating in the work of Ptolemy. Science then slowly declined, with few additional contributions by the Romans, nearly disappearing completely for almost 500 years after the fall of the Roman Empire in the fifth century AD. The seeds of this

decline are apparent in the Roman attitude toward Greek science. Encyclopedia Tradition. The Roman genius was in the field of or-ganization, engineering and law, but they created little original science. They greatly admired Greek learning, but valued its practical applications more than its rational methods of inquiry. This led to an emphasis on encyclopedias and handbooks of Greek knowledge, encompassing content rather than method. An early encyclopedia by Marcus Terentius Varro (116-27 BC) included nine books covering grammar, dialectics, rhetoric, geometry, arithmetic, astronomy, music, medicine and architecture. Martianus Capella in the fifth century and Flavius Cassiodorus (ca AD 490-580) in the sixth century adopted all but the last two of these as the basis for the seven liberal arts studied in the Middle Ages. Pliny the Elder (AD 23-79) compiled a more comprehensive and empirical encyclopedia than that of Varro. Like many Roman writers, Pliny was a Stoic who viewed the Sun as the soul of the universe, which itself was eternal and di-vine. His Natural History consisted of 37 books of facts and fantasies (unicorn, mermaids, phoenix, etc.) derived somewhat uncritically from some 2000 sources written by 146 Roman and 326 Greek authors. He also recorded many of his own

CHAPTER 3

A Purposeful Universe

Transmission and Transformation of Greek Science

Chapter 3 • A Purposeful Universe 50

observations, leading to his death while observing an eruption of Mount Vesuvius. Medicine. The Romans assimilated Greek medicine more successfully than mathematics or astronomy, perhaps because of its obvious utility. Aurelius Celsus wrote an important encyclopedia On Medi-cal Matters about AD 30, which included an excellent compilation of Alexandrian Greek sources. Celsus gave a complete account of the skeleton and many surgical procedures, including removal of cataracts and tonsils. He also summa-rized the work of Herophilus and Erasistratus (3rd Century BC) at Alexandria. Herophilus was the first to perform public dissections, including some on live criminals (vivisection) provided by the state. He recognized the brain as the seat of intelligence and distinguished arteries from veins by their pulsations. Erasistratus followed his teacher Strato in using mechanical concepts and the idea of a vacuum to describe digestion and the operation of the heart valves, but he thought the arteries were filled with air. The last important medical philosopher in the Greek tradition was Galen of Pergamum (AD 129-199) in Asia Minor. Galen served as a surgeon to gladiators in Pergamum and traveled widely in the Roman world. At Rome he became court physician to the emperors Marcus Aurelius and Lucius Verus. He was a prolific writer, including some 131 medical volumes of which 83 have survived. He based his anatomical studies on dissection of Barbary apes, causing some con-fusion due to differences in human anatomy. He demonstrated that the arteries were filled with blood rather than air, but thought that the heart was responsible for respiration. He also failed to recognize the circulation of the blood, leading him to the incorrect idea that blood flows through in-visible pores in the dividing wall (septum) of the heart. Galen’s theories dominated medicine throughout the Middle Ages, partly due to their connection with religious and mystical ideas. He followed Plato and Aristotle in his concern with the cosmic purposes to explain the nature of or-ganisms. He combined Aristotle’s hierarchy of

rational, animal and vegetable souls with the three-fluid theory of Erasistratus by suggesting that the brain was the source of rational spirits distributed by the nervous system, the heart was the source of animal spirits in the respiratory system, and the liver is the central organ of the digestive system, distributing vegetable spirits through the veins. He accepted the Stoic idea that air was the breath and soul of the universe, and that respiration connected humans (the microcosm) with the cosmic spirit (macrocosm) through the pneuma, which was half air and half fire. Astrology and Alchemy. Beginning about the second century BC, several mystery religions entered Rome from the east, offering mysterious methods of purification and the ideas of immortality and union with God. The cult of Isis from Egypt combined with Greek influences to promise moral purification. Chaldean astrology led to the cult of the “Invincible Sun” and the idea that the soul lives after death among the divine stars. Persian Zoroastrianism contributed the cult of Mithra with its perpetual struggle between the spirits of light and darkness. These beliefs combined with Stoicism and the mystical trends of Pythagoreanism and Platonism to support the development of astrology and al-chemy. Both Posidonius (d. 50 BC) and Ptolemy (d. AD 170) embraced astrology and contributed to its grip on the Roman mind. The influence of Posidonius was spread by his widely read handbooks and especially his commentary on Plato’s Timaeus. His lunar theory of the tides demonstrated his Stoic conviction of the sympathy between celestial and terrestrial phenomena. Ptolemy’s astrological convictions were the stimulus for his study of mathematical astronomy, whose results he felt confirmed the power of the stars over Earthly events. Although his Tetrabiblos avoided excesses, it gave scientific support to astrology, which increasingly associated the seven planets with human activities, such as Mars with war and Venus with love. Spiritual concepts also stimulated interest in chemical processes in what the Arabs later called alchemy. Starting about AD 100, the early


alchemists found support in the Stoic idea that all objects in nature were alive and growing in harmony with the universal spirit of nature. They combined this with theories concerning the transformations of the four elements to suggest the possibility of transmuting base metals into silver and gold. Secret knowledge of this type informed the Gnostic sect, who viewed transmutation as a symbol of death and resurrection. Alchemy received further credence from the Neoplatonic philosophy of Plotinus (ca. AD 205-270) in the third century AD, who elaborated the ideas of Plato into a spiritual hierarchy of being that began with God and flowed down through the Forms to the lowest levels of material being. Near the end of the third century at Alexandria, Zosimos combined these Greek theoretical and mystical ideas with Egyptian practical techniques in an encyclopedia consisting of 28 books; but the mystical side prevailed with his successors as the Roman empire crumbled and collapsed. 2. EARLY CHRISTIAN AND BYZANTINE VIEWS OF SCIENCE The Birth of Christianity. The Hellenistic age and the decline of Rome were also the setting in which a new civili-zation began to emerge with new religious aspira-tions that eventually transformed the Greek heri-tage. The birth of Christianity gave rise to a new emphasis on the reality of the transcendent world revealed in the Bible, with the natural world viewed as contingent on the supernatural realm. The first Christians were Jews in Palestine, and Christianity first spread beyond its homeland to Hellenized Jews living in the Roman empire. With its roots in Jewish history and the teachings of Jesus, Christianity became a universal religion through the work of the Apostle Paul, using the Greek language as a vehicle. The Bible recounts Paul’s visit to Athens (Acts 17) where he debated with Epicurean and Stoic philosophers about the Unseen God of the Greek poets. His letters establishing the first churches infused Christianity with Greek reason. Thus the problem of reconciling revelation and reason began with

the birth of Christianity as a world religion, and the question of the relationship between science and Scripture was unavoidable. Even before the spread of Christianity, the relation between revelation and rationalism engaged Hellenized Jews such as Philo (30 BC - AD 50) of Alexandria. Philo recognized that Greek philosophy was not necessarily a threat to Judaism, and that one and the same reason could speak in philosophers like Plato and in the revealed truths of Moses and the Prophets. He was able to reinterpret biblical cosmology in terms of Platonism and Stoicism by means of the allegori-cal method in common use at Alexandria. For example, he interpreted references in Scripture to a first man Adam as symbolizing spirit or mind, and he took Eve to represent sensuality. Philo used the Stoic conception of the Divine Logos (Greek: Word) to describe the wisdom and goodness of God, and the Jewish concept of creation and the fall to account for evil as originating in matter. His goal was not to explain nature, but to use science and philosophy to understand spiritual truth in a manner similar to Plato’s view of mathematics. Early Christian Views. The early Church Fathers of Alexandria accepted the allegorizing of Scripture, but warned against its excesses when divorced from faith. The Gnostic heresy equated the Hebrew God with Plato’s Demiurge, and claimed that special knowl-edge or gnosis was necessary to recognize the true source of Being. Some held that the essential as-pect of humanity was spirit, denying the bodily resurrection of Jesus and even his material exis-tence. They practiced asceticism as a means of escaping the bondage of sensuous matter, which they equated with evil. Clement of Alexandria, who died about AD 215, taught that Greek science could protect true faith from heresy if reasoning was accompa-nied by faith. He accepted the geocentric cosmol-ogy of the Greeks, but related the structure of the world to the Jewish tabernacle. Thus the Ark of God’s Covenant with Israel symbolized the eighth sphere of the fixed stars as the dwelling place of God.


The greatest leader of the Alexandrian catechetical school was the theologian Origen (ca. 185-284), who developed the first systematic ex-position of Christian theology based on the whole of Greek knowledge. He attempted to resolve the classical dualism of form and matter by deriving all reality as an emanation from a transcendent God through the Divine Logos identified with Christ, who “is of the same essence with God, distinct but not separate, like the Sunbeam and the Sun.” Applying similar Neoplatonic ideas to the Christian doctrine of creation led to a distinction between the eternal world of spirit and the temporal world of matter created by God. To avoid conflict with the Greek theory of natural place, Origen used the allegorical method to interpret the Biblical reference to “waters...above the firmament” (super celestial waters) created on the second day of creation (Genesis 1:5-8). Thus he suggested that these waters refer to the power of the angels to which the celestial waters of our spirits should seek to rise. For three centuries, Christianity grew in spite of sporadic persecution, culminating in the conversion of the emperor Constantine early in the fourth century, and the Council of Nicea in AD 325, which helped to establish the official doctrine of the Church. Using a formulation derived from Origen, but free from his Neoplatonic framework, the Nicene Creed defined the relationship between the divine and human natures of Christ. The mystery of the Trinity provided a basis for the source of the intelligibility of all other things. The categories of Greek science no longer seemed so persuasive, and the intelligibility of nature ap-peared to rest on a higher level. Both the universe and history depend on God and derive their intelligibility from the Trinity. Explanation rises above the context to be explained. A freely creating God grants humans the freedom to sin, and only by God becoming man in Christ can he restore fallen human nature. Christian writers now began to deal with pagan science more confidently, even if not very competently. The disagreement of the various schools of Greek philosophy appeared to show the weakness of reason as compared to the unity of

Biblical revelation. Gregory of Nyssa (ca. 331-396) questioned the reality of the material world, suggesting that qualities created by God are con-cepts whose union are perceived as matter. But he believed that the world provided signs and sym-bols that would lead to God. His brother Basil (ca. 330-379), Bishop of Caesarea, defended the Biblical account of creation in his Homilies on the Hexaemeron (six days of creation) by attacking the materialists who failed to see the beauty and purpose of the creation as the work of an intelli-gent Creator. Basil rejected the allegorical interpreta-tion of the super celestial waters and attempted to give a realistic explanation in terms of a spherical Earth surrounded by two heavens, with the waters between them. He held that the inner “firmament” was of a crystalline nature that was capable of supporting the waters. His brother Gregory suggested that the outer convex surface of this sphere contains mountains and valleys that hold the celestial waters. Ambrose of Milan (ca. 337-397) also accepted the spherical heavens, adding that the purpose of the celestial waters was to cool the axis of the celestial spheres to prevent its overheating from perpetual rotation! Basil’s interpretation of these waters eventually led to the medieval scheme of three heavens: the firmament of fixed stars, surrounded by the crystalline heavens composed of crystal-lized water, and finally the empyrean sphere of pure intellect where angels abide. Unfortunately, leaders of the Syrian Church reverted to the flat-Earth theory, including Cyril of Jerusalem (fl. ca. 360) and Diodorus, Bishop of Tarsus (died ca. 394), the latter condemning the Greek system of the world as atheistic. The Augustinian Synthesis. A more reasoned defense of Christianity emanated from Augustine (354-430), Bishop of Hippo in North Africa, who was the greatest thinker and teacher of the early Christian Church. He received a broad education in all the liberal arts before his conversion and discipling by Ambrose. Plato and Neoplatonism were strong influences on Augustine, and he used Greek philosophy more than any of the Church Fathers. After the sacking


of Rome by the Visigoths in AD 410, Pagans widely blamed the disaster on Christians for having abandoned the old gods. In his greatest work, The City of God, Augustine answered Pagan critics by pointing to the contingency of the material world and the fact that all worldly things decay, including Rome and its Empire. Like Plato, Augustine believed that ulti-mate and eternal reality is spiritual, while material nature is temporal and changing. Unlike Plato, however, he rejected the Greek cyclical view of time as antithetical to human purposes and meaning, since the achievement of any goals would only vanish again. He based his linear view of history on both creation and redemption. God created time with a beginning and an end, and sent Christ into the world to save humanity for an eternal destiny. Although he emphasized the spiritual over the natural world, he began the transformation of Western thinking that would eventually free science from the recurring cycles of Greek cosmology. Although Augustine is typical of the en-tire Christian age in viewing knowledge as a search for eternal truth, which is ultimately God, he also recognized the value of natural knowledge for illuminating Christian doctrine, and worked to develop a harmony between reason and faith. Since God created humans in his image, self-knowledge is a reflection of the divine light, and even doubt demonstrates a consciousness of truth. Reason is a divine gift to be cultivated. All truth, scientific and religious, is God’s truth. All sciences have value in so far as they contribute to the knowledge of God, and error results from reasoning without faith in this ultimate goal: “Understand in order that you may believe, believe in order that you may understand.” Augustine often made use of natural knowledge to interpret Scripture. For example, he applied the doctrine of rationes seminales (seed-like principles) to the problem of reconciling the Biblical idea of an immediate creation with the observational evidence of progressive develop-ment of natural forms, especially in biology. This Stoic concept that nature contains the seeds of its own development made it possible to view God’s creation as complete in the beginning without

ignoring developmental evidence. He thus sug-gested that God created all things in the beginning, but some he created potentially as seed-like principles that subsequently develop into mature organisms, an idea that he even applied to the origin of Adam and Eve. It also led to a conception of natural law described by Augustine in his Literal Commentary on Genesis: “The ordinary course of nature in the whole of creation has cer-tain natural laws in accordance with which...The elements of the physical world...have a fixed power and quality determining for each thing what it can do or not do.” In the same book, he warned against using the Bible in a way that would contradict the best science of his day:

Usually, even a non-Christian knows some-thing about the Earth, the heavens, and the other elements of the world, about the mo-tion and orbit of the stars and even their size and relative positions, about the predictable eclipses of the Sun and Moon, the cycles of the years and the seasons, about the kinds of animals, shrubs, stones, and so forth, and this knowledge he holds to as being certain from reason and experience. Now, it is a disgraceful and dangerous thing for an infidel to hear a Christian, presumably giving the meaning of Holy Scripture, talking nonsense on these topics; and we should take all means to prevent such an embarrassing situation, in which people show up vast ignorance in a Christian and laugh it to scorn.

Augustine also used science and reason to argue against false ideas and heresies. In the City of God he attacked Stoic determinism and causal astrology as contradicting reason and experience. He repeatedly argues that twins “conceived in precisely the same moment” often differ dramatically in many aspects of their character and life. Although he admits the possibility of stellar influence on physical things such as the seasons and the tides, such influences do not limit the freedom of the human will. This is an important point in Augustine’s theology, in which moral evil springs from the human will without impugning the goodness of God’s creation. Thus, he defined


evil as the privation or omission of the good, and it has no independent status of its own. The Augustinian view provides a positive basis for the study of nature and an argument against the Greek concept of terrestrial imperfection. Decline of Science in the West. The focus of Christian thought on theo-logical issues combined with the continuing col-lapse of the Roman Empire to accelerate the decline of Greek science in the West. In AD 455 the Vandals sacked Rome again, and the last Ro-man Emperor was deposed in 476, marking the final fall of Rome. Anicius Boethius (ca. 480-524), one of the last Latin Christians to have a thorough knowledge of Greek, prepared translations and commentaries on Aristotle’s logical treatises and summaries of scientific subjects. He wrote manuals on the “quadrivium” of arithmetic, music, geometry and astronomy. His works together with Roman commentaries and translated fragments from Plato were virtually the only sources of Greek science left to the West for over 500 years. Befriended at first by the Ostrogothic ruler Theodoric, he later imprisoned Boethius and finally executed him on suspicion of treason. He wrote his chief work On the Consolation of Phi-losophy while in prison. Two events marked the triumph of Christianity in the year AD 529, the closing of the Academy in Athens and the birth of the Benedictine monastic order at Monte Cassino in Italy. Christian monasticism began as an ascetic movement of hermits in Egypt by Saint Anthony in the third century, and independently as an organized community of discipline and devotion in Southern Egypt by Pachomios in the fourth century. It reached into the Eastern Roman Empire through Basil, Bishop of Caesarea, later in the fourth century and took root in the West from the work of Benedict of Nursia (ca. 480-543) and Cassiodorus in the sixth century. The sisters of Pachomios, Basil and Benedict also established monasteries for women. For about four centuries, monasticism was the greatest civilizing power amidst periodic anarchy and general corruption in Western Europe. Monasteries preserved many of the literary

treasures of antiquity and of Christianity, and were sanctuaries for men and women who transmitted and increased that knowledge. The Benedictine Rule, which became the primary form of monasticism in the West, discouraged excessive asceticism, established law and order, and encour-aged useful work. Monks did both manual labor and scholarly work, and each received equal dig-nity. Thus began the breakdown of the classical elitism that had hindered experimental work in Greek science due to their low esteem for manual work done by slaves and artisans. Unfortunately, the sixth century saw fur-ther revival of the flat-Earth theory from the work of Cosmas of Alexandria, so called because of the fame and influence of his geographic work. After his conversion to Christianity about 548, he be-came a monk at Mount Sinai and wrote his Topographia Christiana, a 12 volume illustrated treatise on geography and a “Christian” defense of the flat-Earth view based on the Mosaic account of the Tabernacle. Part of his defense was an attack on the idea of the Antipodes, a place on the oppo-site side of a spherical Earth where people would be upside down with opposing (anti) feet (podes). Even Augustine had questioned the rationality of a populated Antipodes as contrary to the unity of the human race, but now Cosmas argued that the idea was both absurd and heretical since God made only one “face” of the Earth for the descendants of Adam. Early in the seventh century Isidore (ca. 560-636), Archbishop of Seville in Spain, tried to salvage what was left of Greek learning in a popular encyclopedia called the Etymologies. He based it largely on Pliny, backed by the authority of Scripture where possible. He recorded the Greek theory of a geocentric spherical Earth and suggested that the Antipodes was in Libya. He tended to allegorize the material world for its spiritual significance, especially animals and fabulous creatures such as satyrs, Cyclops and dog-headed men. A century later in northern England, the Venerable Bede (673-735), so called because of his great reputation for learning, wrote a number of scientific books based on Pliny and other Latin authors. He maintained the sphericity of the Earth


and revived the lunar theory of the tides, being the first to recognize the different times for high tides at different locations. He had sufficient astro-nomical skill to calculate the date of Easter from AD 532 to 1063, and probably initiated the Western dating of events from the birth of Christ (Anno Domini). His student Alcuin brought English learning to the court of the Frankish King Charlemagne (Latin: Carolus) in Rome, who had been crowned emperor by the pope in 800. Alcuin later established a school at Tours that provided a glimmer of learning in the Carolingian Renais-sance of the ninth century. Byzantine Science. Although the Fathers of the western Church lost much of Greek science, Eastern Chris-tendom made a greater effort to preserve scientific texts and to Christianize the systems of Aristotle and Ptolemy. Germanic invasions in the West in-creasingly separated the Latin half of the empire from the Greek-speaking East. The Eastern or Byzantine Empire preserved both Greek scientific learning and Roman administrative structures sur-rounding the eastern Mediterranean. At Athens the Byzantine Emperor Justinian closed the Academy of Plato in AD 529 due to its paganism, and many of its scholars fled to Persia. The last notable pagan philosopher of Byzantium, centered at Constantinople, was the Neoplatonist Proclus (ca. 410-485), who received his education in Alexandria and became head of the Academy in Athens. He wrote an introduction to Hipparchus and Ptolemy that combined the mathematical system of Ptolemy with elements of Aristotle’s cosmology, including the seven plane-tary spheres plus the celestial sphere and that of the Prime Mover. Proclus suggested that the separation of the spheres was determined in such a way that the greatest distance of a planet on its epicycle is equal to the smallest distance of the planet immediately above it. Thus the greatest distance of the Moon equalled the smallest distance of Mercury, and so on, making it possible to calculate the assumed dimensions of the universe. He gave a proof of the geometric equivalence of epicycles and eccentrics, but denied the existence of the precession of the equinoxes.

Around the beginning of the sixth century the Christian Neoplatonist Dionysius, perhaps a student of Proclus, proposed in his Celestial Hierarchy that the angelic beings mentioned in Scripture formed a nine-fold hierarchy consistent with the Neoplatonic idea of a hierarchy of spirits in the heavens. He arranged them into three sub-sidiary hierarchies, which subsequently served as the movers of the nine celestial spheres. Starting with the Primum Mobile, these included the Seraphim, Cherubim and Thrones, then Dom-inations, Virtues, and Powers, and finally Prin-cipalities, Archangels, and the Angels who moved the Moon. Dionysius further arranged each order of angelic beings by rank similar to the hierarchy of the church with its Patriarch, bishops, and so on. Above this hierarchy was the abode of God in a tenth empyrean (Greek: fiery) heaven, and below was a descending hierarchy of man, animals, plants and so on down to the inhabitants of hell at the center of the Earth, forming a con-tinuous chain of being. This system had consider-able influence in the later Middle Ages when Dionysius was mistaken for the Athenian convert of the Apostle Paul, Dionysius the Areopagite. The Byzantine Emperor Michael sent a copy of the works of this “pseudo-Dionysius” to the western emperor Louis the Pious in 827. The Irish phil-osopher John Scotus (Erigena) translated them from Greek to Latin before he died about AD 870. In the first half of the sixth century at Al-exandria, John Philoponus (d. ca. 575) opposed many aspects of this view. He was a philosopher, grammarian and professional teacher, who later converted to Christianity and wrote commentaries on the works of Aristotle, criticizing many of his scientific ideas. John’s conversion led to bitter debates with his intellectual rival Simplicius, one of the last Neoplatonists, who later left Alexandria for Athens and then moved on to Persia for four years after the Academy was closed in 529. Phi-loponus rejected Aristotle’s dichotomy between the terrestrial and celestial regions and the immutability of the heavens. However, this important step was not widely accepted, and it prompted the unconverted Simplicius to sarcastically ask how he reconciled that view with his Christian faith.


Philoponus noted the different colors of the stars and argued that this was evidence for differing compositions and thus the possibility of decay. He suggested that the Sun consisted of the terrestrial element fire and that the planets did not move in simple circles about the Earth. These ideas led to the conclusion that the heavens are not divine and that God is separate from his creation and transcends the heavens as well as Earth. This early triumph of Christian doctrine over Ar-istotelian teaching was a major contribution to the later development of cosmology. In support of creation, Philoponus also attacked Aristotle’s doc-trine of the eternity of the world. He distinguished between the heavens created on the first day of creation and the firmament of the stars on the second day, the former constituting a ninth sphere beyond the firmament to account for precession of the equinoxes. He explained the celestial waters of the creation account as being in a solid state to form the transparent crystalline spheres. The ideas of Philoponus on motion were especially significant, anticipating modern views of momentum and free fall. He denied that angelic beings moved the planets, suggesting instead that God gave the celestial bodies a “motive power” of their own, not unlike the natural tendency of terrestrial objects to fall towards the Earth. He refused to accept any limit on God’s ability to produce a void, or that the speed v of an object would be infinite in a void (R = 0), replacing Aristotle’s force ratio v = F/R with v = F – R. Ar-guing purely from reason and experience centuries before Galileo, he denied that bodies fall with speeds proportional to their weights: “For if you let two bodies fall from the same height, one of them being many times as heavy as the other, you will see that...the actual difference in time is very small.” Philoponus also questioned Aristotle’s antiperistasis concept of projectile motion: air pushed from the front of an object and rushing to the rear to keep it moving gives air the conflicting roles of both resisting and causing motion. Instead he suggested that a force could impart an immaterial motive power to a projectile to keep it moving. Simplicius added that when such a motive power dissipates, the body slows and its natural

tendency to fall increases. Initially these ideas in-fluenced the West only indirectly through the Arabs, especially since the Church declared Philoponus a heretic after his death, but they eventually reappeared in the fourteenth-century impetus concept leading to the idea of inertia. His book Physica was transated into Latin in 1535, in-fluencing Galileo as seen in his early notebooks. Unfortunately Byzantium became preoc-cupied with politics and theology, and its treasure of Greek books and manuscripts gathered dust in its libraries. The state became identified with the Eastern Christian Church, turning intellectual de-bates into ideological ones that stifled natural philosophy. However, some scholarship continued in the monasteries of the eastern Byzantine provinces of Armenia and Syria, where Greek sci-ence and philosophy were translated into Syriac. Some of their work spread into Persia, especially at Jundishapur east of the Tigris River, where the Persian king had established a school of astronomy and medicine. Its doctors and teachers were largely Syriac-speaking Jews and Nestorian Christians. After the Arabs conquered this region, many of these Greek works were translated from Syriac versions or directly from Greek into Arabic. Although early Christianity concerned itself primarily with spiritual goals and made few direct contributions to science, it had an important transforming effect on the Greek tradition. It challenged the eternity of the world and the cyclic view of time, replacing it with a linear view of history in which real progress was possible. It introduced a new respect for manual labor and a positive view of the goodness of all of creation. It denied the divinity of the heavens and the Greek dualism between the celestial and terrestrial realms, recognizing unity and purpose in the uni-verse. In the meantime the flame of science was kept alive in the Islamic tradition until it could be revived again in the West. 3. ISLAMIC SCIENCE Origins of Islam. Inspired by Muhammad the Prophet (ca. 570-632) in the seventh century, the inhabitants of Arabia conquered the Middle East and within a


few decades had established an empire that in-cluded all of Persia, Egypt, the North African coast, and Southern Spain. Even before the rise of Islam, Arab tribes bordering the eastern Roman empire had learned something of Byzantine cul-ture, including some converts to Christianity. This together with the religious tolerance of early Islam aided in the Muslim assimilation of Greek science. One of these Hellenized border tribes, the Omayyads, founded the first Muslim Caliphate (“successors” of Muhammad) at Damascus in AD 661 and set up an astronomical observatory there about 700. The Arab Empire fragmented when the Abbasids conquered the Omayyad dynasty of Damascus in 749 and established their own Ca-liphate at Baghdad, assimilating much of Persian culture. The science they produced was a synthesis of Greek science with Persian, Hindu and other influences. The Omayyads continued to rule in Spain and produced an important scientific center at Cordoba, which eventually became one of the main points of contact with the West. These di-verse Muslim cultures were united by their belief in the sacredness and infallibility of the Koran (“Recital”), which established the Arabic language in a permanent form as one of the main vehicles of knowledge and culture. The Koran, with its basic theme of the omnipotence and oneness of God (Allah) and submission (Islam) to His will, encourages the study of nature as an example of the unity and greatness of Allah:

Verily, in the creation of the heavens and of the Earth, and in the succession of the night and of the day, are marvels and signs for men of understanding heart. (Sura III: 190)

As the creation of Allah, nature is the visible sign of the Godhead, stimulating many Muslims to study science as a religious duty. Islamic Science before AD 1000. Starting from AD 754, the great patrons of science were the Caliphs of Baghdad. Al-Mansur, the second Abbasid Caliph and founder of Baghdad, engaged Indian scholars to translate Hindu works into Arabic and brought Nestorian Christians from Jandishapur to translate Greek

scientific works, some already in Syriac versions. Harun Al-Rashid, the fifth Caliph from 786 to 809, hero of the Thousand and One Nights, collected many Greek manuscripts and encouraged original scientific work. The most famous Arabic alchemist worked under his patronage: Jabir ibn Hayyan (ca. AD 720-815), called Geber in the West, who was from the mystical Sufi sect of Islam. He wrote numerous books on alchemy based on his theory that the four Greek elements combined to form mercury and sulfur, which then combine in various proportions to form the metals. Although Jabir based these proportions on a mystical numerology, he did emphasize careful measurements with a balance scale. In about 815 Al-Ma’mun, the seventh and greatest Abbasid Caliph (813-833), set up a study center called the Bayt al-Hikma (House of Wisdom), which included a library and an obser-vatory. He was a Mu’tazil (seceder), who opposed the Sunni Muslim orthodoxy in his emphasis on reason, believing in the relative freedom of the will and that the Koran is not “uncreated and eternal.” He combined free thought with intoler-ance for his Sunni opponents, but welcomed Jews and Christians in his court. Here the Nestorian Christian physician Hunain ibn Ishaq (ca 809-873) translated much of Galen and other Greek scientific works with the assistance of about ninety pupils, including his son Ishaq ibn Hunain, who translated the Elements of Euclid and the Almagest of Ptolemy among others. The greatest scientist of this period was Al-Khwarizmi (ca 800-850), who synthesized Greek and Hindu knowledge. His book on arith-metic made known the Hindu positional system of decimal numbers, including the zero, miscalled “Arabic numerals” by Latin translators, who also distorted his name to “algorithm” for rules of cal-culating. His book on algebra, Al-jabr w’al Muqabala, introduced analytical and geometrical methods of solving linear and quadratic equations (ax² + bx + c = 0). The word Al-jabr refers to “transposition” or “restoration” of an unknown quantity, giving the word “algebra” in Latin transliteration, while muqabala refers to “equalization” or “simplification” of an equation. Al-Khwarizmi also produced astronomical and


trigonometric tables that contained both sine and tangent functions instead of chords. The astronomer Al-Farghani (820-861) was a younger contemporary of Al-Khwarizmi at Baghdad in the ninth century. They probably worked together in trying to improve geographic meas-urements of the degree of latitude, as requested by the Caliph Al-Ma’mun to determine the size of the Earth. Al-Farghani accepted the Ptolemaic system and determined the greatest distances and diameters of the planets based on the as-sumption of Proclus that there is no radial separation between the epicycles of adja-cent planets (Figure 3.1). After persecu-tion in the Orthodox reaction against the Mu’tazila, he moved to Egypt to work on a nilometer to measure Nile flooding. His contemporary, Al-Kindi (ca. 801-866), was an encyclopedic scientist and phi-losopher, who developed a Neoplatonic view of Aristotle and criticized alchemy. He wrote four books on Hindu numerals, and produced an influential treatise on optics based on Euclid and Ptolemy. The leading astronomer of the late ninth and early tenth centuries was Al-Battani (ca. AD 858-929), known by Albategnius in Latin, who extended the work of Al-Farghani at Baghdad. Al-though a Muslim, Al-Battani came from Harran in Mesopotamia, where the Sabian sect had com-bined Babylonian astrology with Neoplatonism. The accuracy of his measurements may have been aided by the work of his father, who by some ac-counts was the inventor of the spherical astrolabe for determining star positions. He accepted the Ptolemaic system, but made more accurate meas-urements of the inclination of the ecliptic as 23°35΄ from the celestial equator, the precession of the equinoxes as 54.5˝ per year (4.5˝ too large), and the time of equinox to within an hour or two. He discovered the motion of the solar apsides: a slow variation of the position of the Sun when it has its smallest apparent size (aphelion), having shifted by 16°47΄ along the ecliptic since Ptolemy.

One of the first Muslim writers on medi-cine was the Persian Al-Razi (ca. 854-925), known in Latin by Rhazes, a contemporary of Al-Battani and chief physician at Baghdad’s largest hospital. He followed the theories of Galen, but applied new techniques and chemical ideas to medicine, such as the use of plaster of Paris to set broken bones. He appears to have been the first to classify substances into animal, vegetable and mineral, and modified Jabir’s mercury and sulfur theory of solids to include salt. He made important contributions to obstetrics and ophthalmic surgery, but is best known as the first to correctly distinguish between measles and smallpox. By the tenth century Muslim science ap-pears to increasingly spread out from Baghdad,

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Earth

SunVenus

Mercury

Moon

Orbit of the sunand outer limit

of epicycle for Venus

Figure 3.1 Al-Farghani’s Planetary Distance Estimate Al-Farghani based his estimate of planetary distances on the assumption that the epicycles of the planets just fit between their respective deferent circles. Thus he assumed that the greatest distance of the Moon from the Earth is equal to the least distance of Mercury. The least distance of Venus is then equal to the least distance of Mercury plus the diameter of its epicycle. In the Ptolemaic system the centers of the epicycles of Mercury and Venus are on the line from the Earth to the Sun to account for the fact that these planets only appear near the Sun.


which was the center of Sunni orthodoxy. Al-Mas’udi was a Mu’tazilite Arab who left Baghdad for Syria and Egypt after writing an encyclopedic work on science and geography in 947, including the first description of windmills. Abu Kamil (fl. 900), the Egyptian calculator (al-hasib al-Misri), improved al-Khwarizmi’s algebra, including meth-ods to find both the roots of quadratic equations. The Turkish philosopher Al-Farabi (ca. 870-950) studied in Baghdad but settled in Damascus where he developed a synthesis of Neoplatonism, Aristotelianism and Sufism, at-tempting to harmonize Islamic and Greek philoso-phy in much the same way as Augustine had done with Christianity. To weaken Aristotle’s idea of an eternal universe, he suggested that creation is an actualization of forms in matter. His encyclopedic works embraced all of science, including an oriental treatise on music that recognized major and minor thirds (ratios of 4:5 and 5:6) as har-monic consonances. Sunni orthodoxy reasserted its position against Mu’tazilite rationalism in the theology of al-Ashari (873-935) at Baghdad . The Asharites opposed the Aristotelian conception of an imper-sonal God and eternal universe. They preferred a modified form of atomism which viewed atoms as a continuous creation of God. They discarded the concepts of causation and the uniformity of nature in favor of the absolute and arbitrary power of God and allowance for His miraculous intervention. Although they established the unity and orthodoxy of Islam, they inhibited the free thought and research required in science. One reaction to Sunni orthodoxy was the formation of a secret association south of Baghdad at Basra in 983 called the “Brethren of Purity” (Ikhwan al-safa). They believed in the purifying power of knowledge and developed a mystical synthesis of various religious and Greek sources, especially Pythagorean, Neoplatonic and Sufi. For them knowledge formed a hierarchy from natural philosophy to theology, but the highest is a knowledge of God and his purposes. They wrote an encyclopedic work of 52 volumes, including 17 books on science that combined the alchemy of Jabir with astrology and numerology. But the orthodox Sunni of Baghdad declared it heretical.

The end of the ninth century witnessed the rise of Islamic centers of science in Cordoba and Cairo. Al-Hakam II, the ninth Omayyad Caliph of Cordoba in Spain, ruled from 961 to 976 in the greatest city of that time after Constan-tinople. He was a great patron of science who built up a university of some 400,000 volumes, the chief Islamic center of learning at the time. Some of the earliest scientific influences on Europe date from this period, such as writings by Gerbert of Aurillac (France, ca 940-1003) on the astrolabe and Arabic numerals (without zero). After studying Arabic mathematics and astronomy in Barcelona, Gerbert returned to Rheims and later became Pope Sylvester II in 999. In 969 the Fatimids conquered Egypt and established the city of Cairo. They were members of the radical Shi’ite sect that believed their leaders were direct descendants of Muhammad through his daughter Fatima. The third Fatimid caliph at Cairo, al-Hakim, ruled from 996 to 1020. Although he was mentally disturbed and issued many out-rageous laws, al-Hakim recognized the value of science and established the Dar al-’ilm (Hall of Knowledge), which lasted until the end of Fatimid rule in 1171, including a library and an observatory similar to the earlier Bayt al-Hikma at Baghdad. Meanwhile, Baghdad continued to decline as the mercenary Seljuk Turks took over increasing control of the Eastern Caliphate. Islamic Science after AD 1000. The greatest astronomer at Cairo, and perhaps of all the Muslims, was the Egyptian Ibn Yunis (died in 1009). He used the well-equipped observatory of al-Hakim’s Dar al’ilm to improve on earlier observations in preparing the Hakemite astronomical tables named after his patron. They contain records of old and new eclipses, conjunc-tions and astronomical constants, including some of the most accurate Muslim measurements, such as a value of 51.2˝ per year for precession of the equinoxes (1˝ off). He was also the leading mathematician of his time, making many contri-butions to spherical trigonometry. Also working at Cairo in the time of al-Hakim was al-Haytham (ca. 965-1039) from Basra, known in Latin as Alhazen. He was the


greatest Muslim physicist, but also an astronomer and mathematician. His Optics showed a great advance in both theory and experimental method, strongly influencing later Western scientists such as Roger Bacon and Kepler. He studied both spherical and parabolic mirrors, and determined the magnifying power of a lens. He showed that Ptolemy was wrong in assuming that the angles of refraction and incidence were proportional, except for small angles. He opposed the Greek extra-mission theory of vision, which taught that the eye emits rays, correctly suggesting the intromission theory that light comes from objects into the eye. However, he wrongly thought that the lens of the eye was its sensitive part where images form. As in his optics, al-Haytham’s contribu-tions in astronomy were both observational and theoretical. He studied the effect of atmospheric refraction on light (Figure 3.2), showing that twilight lasts as long as the Sun is less than 19° below the horizon. This led him to an estimate of the height of the atmosphere of only about 10

miles, in contrast with Aristotle’s belief that it extended to the sphere of the Moon. Al-Haytham rejected the purely geomet-ric view of the Ptolemaic system, and proceeded to solidify the heavens in accordance with the more realistic Muslim emphasis on a created physical universe. Each planet moved between two solid concentric spherical surfaces, eccentric with re-spect to the Earth, with a solid epicycle sphere carrying the planet and revolving like a ball bearing in its casing (Figure 3.3). These eccentric surfaces were between two other concentric spherical surfaces centered on the Earth. Al-Haytham added a ninth sphere to account for daily rotation of the heavens, while the sphere of the stars accounted for precession. Two physicians of note who practiced at the court of al-Hakim in Cairo near the beginning of the eleventh century were Masawaih al-Mardini and ‘Ammar al-Mawsili. Masawaih was a Jacobite (Syriac) Christian who wrote a book on the remedies for various diseases, and a treatise on

Earth

Local horizon

Local zenith

Setting sunApparent

ActualObserver

Sun seenbelow horizon

Atmosphere

Apparent starActual position

Figure 3.2 Al-Haytham’s Consideration of the Effects of Atmospheric Refraction Al-Haytham recognized that light rays from the Sun or a star are bent by atmospheric refraction so that they appear higher than they actually are. The effect is larger when the Sun is near the horizon due to the longer path of light through the atmosphere, allowing the Sun to be seen on the horizon even when it is actually below the horizon.


pharmacology based on Muslim knowledge that became the standard text on pharmacy in the West for several centuries. ‘Ammar was the most origi-nal of Muslim oculists, whose book on treatment of the eye includes six operations for cataract sur-gery, although surgery was only used as a last resort in Islamic medicine. Some of the most important Islamic sci-ence continued east of Baghdad by Arabic speak-ing Persians. Al-Biruni (973-1051) was a Shi’ite Muslim and encyclopedic scientist, who traveled widely in India but settled in Sijistan (Af-ghanistan). He gave the best medieval account of Hindu numerals. His geographical works rec-ognized geological changes even before the crea-tion of Adam, such as the existence of prehistoric seas in the Arabian Steppe and Indus Valley, and fossil evidence for the extinction of species. This suggested a temporal succession in the Great Chain of Being, but it did not lead to any concept of evolution. He made measurements of latitudes and longitudes, and discussed the possibility that the Earth rotates on its axis. The most famous Islamic scientist was the Persian philosopher and physician Ibn Sina

(980-1037), called Avicenna in Latin, who was from near Bukhara in Uzbekistan. He was a prodigy who memorized the Koran by age ten and mastered the science of his day by the age of six-teen. His philosophy was an Islamic synthesis of Aristotle and Neoplatonism that viewed all beings as radiations from the source of Being in God. Ibn Sina’s medical works were a vast compilation of ancient and Muslim sources, based largely on Galen and his own observations, which remained supreme for six centuries. He sometimes differed with Aristotle, as in his development of the ideas of Philoponus on projectile motion to allow for an impressed force that would continue indefinitely in a void. This “inclination” or “tendency” (maiyil) of an object is similar to inertia, but is more closely connected to Aristotle’s final cause, linking motion to the love of God as the Prime Mover in the universe. Two other Persian scientists made impor-tant contributions at the beginning of the twelfth century, a time that marked the beginning of decline in Islamic science. ‘Omar Khayyam (ca 1050-1123) was a tentmaker, astronomer, mathe-matician and poet, best known for his poem the

Inner eccentric sphereOuter eccentric sphere

Inner surrounding sphereOuter surrounding sphere

Center of eccentric sphereCenter of the world

Epicycle sphere

Epicycle channel

Planet revolving on epicycle

••

Figure 3.3 Al-Haytham’s Use of Crystalline Spheres in the Ptolemaic System Al-Haytham developed a physical model of the Ptolemaic System by introducing eccentric crystalline spheres between which a small revolving sphere could carry a planet on its circumference to produce the epicycle path that accounts for its retrograde motion.


Ruba’iyat, paraphrased in English translation by Edward FitzGerald. Known variously as a sufi mystic and an agnostic, he wrote in Persian rather than Arabic. He was one of the greatest of medie-val mathematicians, marking the climax of Muslim algebra. His study of cubic equations classified 13 different forms, including partial geometric solutions of most of them (no negative roots). He prepared improved astronomical tables and devised a highly accurate reform of the Persian calendar. A contemporary of ‘Omar Khayyam, the physicist and astronomer al-Khazini was a Greek slave whose Persian master provided him with a good education. He compiled the Sinjaric astro-nomical tables, named after Sultan Sinjar of Khurasan. His Book of the Balance of Wisdom (1122) summarized and extended Greek and Muslim work on mechanics, including applications of the balance, laws of the lever, a theory of gravity applied even to the atmosphere, and ob-servations on capillary action. He gave the first quantitative definition of average speed as distance divided by time (v = x/t), a ratio the Greeks had thought incommensurable, but it made possible simple algebraic solutions such as distance given by rate times time (x=vt). By the twelfth century, the main center of Islamic science had shifted to the western Cal-iphate at Cordoba. Al-Zarkali (ca. 1029-1087) of Cordoba established astronomy in southern Spain during the eleventh century. The leading observer of his time, he invented an improved astrolabe and edited the Toledan Tables of 1080 based on obser-vations at Toledo with other Muslim and Jewish astronomers. In the twelfth century Jabir ibn Aflah of Seville (known as Geber in Latin, not to be confused with the 8th century alchemist Jabir ibn Hayyan) began a movement against the Ptolemaic system. This was carried on by Ibn Bajja of Saragossa (Avempace in Latin, died ca. 1139), who criticized epicycles for their lack of physical reality. The astronomer al-Bitruji (Alpetrugius in Latin) attempted to work out a planetary system based on the concentric spheres of Eudoxus and Aristotle involving spiral motions, but could not account for the many observational complexities known to the Muslims.

Aristotelian influence on Islamic thought reached its peak with the last great Muslim phi-losopher, the Cordovan physician Ibn Rushd (Averroes in Latin, 1125-1198), who wrote three commentaries on Aristotle’s works in Arabic translations corrupted by Neoplatonism. He tried to reconcile Aristotle with Muslim theology, as in his suggestion that the eternity of the world might be understood as the perpetual creative activity of God, but he denied personal immortality. Jewish scholars also attempted to inte-grate Aristotle with the Old Testament. Their leader was the Jewish philosopher-physician Moses Maimonides (1135-1204), also from Cordoba, who wrote his Guide for the Perplexed in Arabic. In 1165 he settled in Cairo where he became physician to the Ayubbid Sultan Salah al-Din (Saladin), who had restored Sunni orthodoxy in Egypt. The efforts by Ibn Rushd and Maimonides to interpret Aristotle, known as Averroism, caused orthodox revulsions among the Muslims of Spain, and later among Jewish Talmudists and Christian leaders as well. Muslim orthodoxy was established earlier in the twelfth century by the work of the great Islamic theologian al-Ghazzali (died 1111), who was able to reconcile his Sufi tendencies with strict orthodoxy and absolute divine determinism in his Destruction (or Vanity) of Philosophy. Ibn Rushd wrote his chief philosophical work as a reply to al-Ghazzali’s attack on rationalism (Destruction of the Destruction), but the orthodox Muslim reaction was to reaffirm the weakness of human under-standing and the strength of faith, silencing philosophers and burning their books. Some scholars suggest that this orthodox reaction was the beginning of the end of inde-pendent research and scientific inquiry in Islam. Others suggest that Muslim awareness of their intellectual superiority may have led to a lack of initiative, just as Christian awareness of inferiority initiated renewed progress. Whatever the causes, they were reinforced by Christian invasions in Spain plus Turkish and Mongol attacks in the east. By the thirteenth century, European awakenings largely eclipsed Islamic science. Only in the present century did the work of Ibn al-Nafis (1210-88) at the Nasiri hospital in


Cairo come to light. He recognized Galen’s mistake in assuming that blood could pass through the dividing wall (septum) of the heart, and stated the theory of the lesser circulation of the blood from the right ventricle of the heart to the left through the lungs about 300 years before its discovery in Europe. Although the Arabs improved and ex-panded the Greek tradition of science, they seemed to have little motivation to significantly revise it. Their primary concern was to see how existing science could contribute to their goal for all knowledge: a better understanding of the purposes and greatness of God. As with Christianity, their belief in a single divine law governing the universe helped to unify the terrestrial and celestial realms that remained separate in Greek thought, recognizing all of nature as dependent on one God. The rise of Islamic orthodoxy and the decline of Arabic science was evident by the twelfth century, but its transmission to the West was the spark that reignited learning in Europe. 4. MEDIEVAL CHRISTIAN SCIENCE The Translators. Medieval Christian contacts with Islamic culture began with hostile relations. After their conquests in Spain, the Arabs conquered Sicily in 902 where they ruled until the Norman invasions of 1077. In southern Italy at Salerno, an ancient health-resort in a region that still spoke a dialect of Greek, a medical school had slowly emerged independent of ecclesiastical control, which now became an important center of professional learning under Norman influence. About 1077 Constantine the African, a Christian convert from Carthage, began somewhat crude translations into Latin of both Greek and Arabic medical texts he had brought to Salerno. The school received fur-ther stimulus from the first Crusade (1096-99), but it did not receive an official charter as a university until 1231. The western Crusade against the Muslims in Spain led to the fall of Toledo in 1085. Christians then established a school of translators at Toledo with bilingual Muslims and Christians, attracting European scholars there to learn Muslim

science. John of Seville (ca. 1090-1165), a Jewish convert to Christianity, was one of the early translators at Toledo who translated many Arabic works on science and philosophy into Castilian. He was assisted by Domingo Gundisalvo, who translated from Castilian into Latin, including a book on al-Khwarizmi’s arithmetic in about 1140 that helped spread the positional decimal system of “Arabic” numerals, including zero. Gerard of Cremona (ca. 1114-87) was the most important of the early translators at Toledo, completing a Latin version of Ptolemy’s Almagest in 1175, and about ninety additional works by other Greek authors, including medical works by Hippocrates and Galen. Other translators worked outside of Toledo. Adelard of Bath (ca. 1090-1150), after traveling to Salerno, Sicily and the Middle East, returned to England and completed the first translation of Euclid’s Elements and the trigonometric tables of al-Khwarizmi from Arabic to Latin. He also wrote some original works, including an experimental demonstration of the supposed impossibility of a vacuum. Another Englishman, Robert of Chester, completed the first translations of the Koran (1143) and of al-Khwarizmi’s Algebra (1145 at Segovia), marking the beginning of European algebra. He coined the Latin word sinus (sine) for the corresponding Arabic trigonometric function. Because Christian translators showed a preference for Roman and Greek authors already known to them, they tended to overlook some Persian and Arabic works, such as the discovery of the lesser circulation of the blood by Ibn al-Nafis. This tended to augment older sources with their previously unavailable works, and thus were more easily assimilated into the newly emerging university curricula. This was especially true of the works of Aristotle, which now were almost all available and began to replace the earlier emphasis of the Church Fathers on Plato with a Scholastic emphasis on Aristotelian philosophy. Medieval Universities. The translation activity of the twelfth century boosted the universities, which were simultaneously replacing the monasteries and


cathedral schools. Students at the cathedral schools began to form guild associations of masters and students, using the term “university” by the thirteenth century. The universities of Paris, Oxford and Cambridge grew out of ecclesiastical corporations of students and masters led by a chancellor. They formed civic universities at Bologna and Padua with a rector elected by the students. State universities received charters from monarchs such as Frederick II at Naples and Salerno, and Ferdinand III at Salamanca in Spain. As Arabic translations into Latin were becoming available, a new emphasis on applica-tion and even experimentation appeared in thir-teenth century Europe. Leonardo Fibonacci of Pisa (ca. 1170-1250) wrote some of the first original books on Arabic arithmetic and algebra after studying in North Africa where his father was a Pisan commercial agent. His Liber Abaci (Book of the Abacus, 1202) discusses operations and appli-cations with both whole numbers and fractions (using the line for division). In a problem on the number of offspring of a pair of rabbits, he introduces the so-called Fibonacci series 1, 1, 2, 3, 5, 8, 13,..., where each term is the sum of the two preceding ones. Both John of Holywood (Sacro-bosco) at Paris and Jordanus Nemorarius (died 1237), probably a Dominican from Saxony, wrote works on Arabic mathematics. Jordanus used letters to denote known and unknown quantities, and began to apply mathematics to mechanical problems, founding the medieval school of mechanics in his book On Weights. At Oxford University the Franciscan School gave rise to a new emphasis on empiricism, perhaps reflecting the delight of Francis of Assisi in the natural world of God’s creation. Robert Grosseteste (ca. 1168-1253) was a translator from Greek and one of the first to introduce Aristotle at Oxford, where he served as its first chancellor and first reader to the Oxford Franciscans, becoming Bishop of Lincoln in 1235. Although he believed that truth came from divine illumination, he recognized that knowledge of the material world had to begin with the senses. He argued that scientific propositions, in contrast with logic and mathematics, must be verified or falsified from experience. He had a special interest in light and

tried to explain the rainbow by refraction of Sunlight in a cloud. He taught that light was the origin of spatial extension and that the universe originated with light. The most famous student of Grosseteste at Oxford was Roger Bacon (ca. 1219-92). After teaching at Paris for several years, he returned to Oxford about 1250, where he became a Franciscan friar and advocate of experimental science. His most important writings were at the request of Pope Clement IV in 1266-1267. He went beyond Grosseteste in his work in optics, especially his use of mathematics in the tradition of Alhazen. Thus Bacon used geometric diagrams to describe the action of a burning mirror and the magnifying power of a lens, even suggesting combinations of lenses to act as a telescope. He tried to combine Aristotle’s ideas about the effect of light on the surrounding medium with Alhazen’s intromission theory of vision. He held that the Moon was the source of its own light, which caused the tides. Bacon also developed Alhazen’s solid celestial spheres to reconcile Aristotle and Ptolemy, accounting for the unusual motions of the planets by the action of angels. He was one the first to suggest circumnavigation of the Earth and correction of the Julian calendar for the effect of precession of the equinoxes. Even more than Grosseteste, Bacon stressed the use of experiment and observation to correct false authority and to distinguish the true results of alchemy and magic; but his activity with alchemy led to accusations of practicing the “black arts.” Bacon’s concept of the laboratory is close to the original meaning of laboratorium, a combi-nation of labor and prayer (oratorium). His attacks on the pedantry and conceit of academic authorities incurred the wrath of the schoolmen, apparently leading to his imprisonment for some fifteen years and the suppression of his works. He predicted self-propelled ships, horseless carriages, and flying machines, but shared the widespread belief in astrology and that every detail of nature corresponded with the Creator’s special purpose. Bacon speaks of Petrus Peregrinus (Peter the Stranger), a French Crusader from Maricourt, as the greatest experimenter of his time. He wrote a book on magnetism about 1269, in which he


describes magnetic poles, how to magnetize iron, and experiments with a spherical lodestone. He describes both floating and pivoted compasses, probably as developed from Chinese and Muslim sources. He incorrectly believed that the compass points to the pole star rather than the Earth’s pole, and thought that a spherical magnet would rotate spontaneously. He suggested the idea of a mag-netic clock-drive for a planetarium about the time the first mechanical clocks were appearing in Europe. The Medieval Synthesis. After the appearance of Aristotle’s Phys-ics and Metaphysics in Latin with the comments of Averroes (Ibn Rushd), a reaction set in at Paris leading to the forbidding of these works in 1210 and 1215. Although an attempt was made to rein-force this ban in 1231, the work of reconciling Aristotelian natural philosophy with Christian doctrine was begun about 1245 by Albert the Great (Albertus Magnus, ca. 1200-1280). Albert studied medicine in Italy before joining the Dominican Order and taking a theology degree at Paris, where he taught before moving to Cologne. He was the greatest naturalist of the Middle Ages, writing extensive commentaries on Latin versions of Aristotle with many of his own observations added. His best works were on botany and min-eralogy, but he closely followed the theories of Aristotle, except where they clashed with his faith. He insisted on the importance of observation and experiment, and attempted to explain alchemy in terms of natural causes. Thomas Aquinas (ca. 1225-1274) devel-oped the most complete synthesis of Christian thought with Aristotelian science and philosophy. He studied at Monte Cassino and Naples before joining the Dominican Order against the protests of his father. He then studied at Paris and Cologne under Albertus Magnus and recognized the power of Aristotelian thought uncorrupted by Neo-platonism. He taught at Cologne, Paris, Bologna, Rome and Naples, while devoting himself to the construction of his comprehensive system of scholastic philosophy entitled Summa Theologiae. His basic goal was to demonstrate the rationality of the universe as a revelation of God. He accepted

much of Augustinian thought, but adopted Aristotelian methods and cosmology. He distinguished between reason and faith, but sought to show that faith in revealed truth is not contrary to reason. Like Albert, but unlike Averroes who ac-cepted all of Aristotle, Aquinas felt free to criticize specific points in conflict with the Bible. He agreed with Maimonides in accepting the Ptolemaic system as a working hypothesis, but he distinguished three heavens: the Empyrean (abode of God), the crystalline (firmament of Genesis 1), and the sidereal sphere of the stars and planets. The nine orders of angels included three in the outermost Empyrean, three on Earth, and three in the intervening region. God created the world, both matter and form, out of nothing, since as pure spirit matter could not have emanated from Him, as in Neoplatonism. According to Thomas God’s creation is continuous, dependent upon Him for its existence at every moment of time. His purpose in creation is to reveal himself in all possible ways, so he cre-ates all possible grades of being from the lowest creatures on Earth to the highest order of angels. These ideas led to his five “proofs” for the exis-tence of God as inferences from His creation, drawing on earlier ideas from Aristotelian, Augustinian and Islamic thought: (1) Motion requires a mover, so there must ultimately be an Unmoved Mover (Aristotle). (2) Every effect has a cause, so there must ultimately be a First Cause (Augustine). (3) Natural objects are not necessary, but are merely contingent (possible), so there must be a Necessary Being as the ground or basis of the contingent (al-Farabi). (4) The chain of being forms a scale of perfection, so there must be a perfect or Highest Being (Augustine). (5) All things in nature have an end or purpose, implying a design, so there must be an Intelligent Designer. Although Church authorities at first cen-sured the gigantic achievement of Thomas Aqui-nas, it eventually became the basis for much of the late medieval world view. In 1277 Bishop Tempier of Paris, with the backing of the university, condemned many of the views of Aristotle, espe-cially in their more extreme Averroistic form. In spite of this condemnation, Thomism became the


official doctrine of the Dominican Order in 1278, and by 1325 the articles directed specifically against Aquinas were nullified. The theism of Aquinas transformed Aristotle’s Unmoved Mover into the Supreme Good of the universe. Aristotle’s final causes became God’s purposes in a unified hierarchical pattern of order with everything playing its part and striving to achieve its purpose (teleology). The medieval world view based on Thomistic ideas received its most sublime expres-sion by the poet Dante (1265-1321) in The Divine Comedy, the greatest of medieval poems. This epic journey moves down through the circles of Hell and then up again to the Earth and purgatory, and finally through the celestial spheres to the Empyrean. It uses the Aristotelian cosmology as a symbolic structure to convey the importance of spiritual truth, reflecting the Christian drama of existence with human beings on the center stage. Though corrupt, the Earth was a place of possible redemption where meaning and purpose infused all life, and social structures were in accord with the universe. Reactions to Thomism. In spite of the growing influence of the Thomistic synthesis, a skeptical reaction devel-oped at both Oxford and Paris that led to some important scientific ideas. This was partly in re-sponse to the Condemnation of 1277, which attacked any limits on the absolute power of God, such as His ability to make several worlds or to produce a vacuum by moving the world in a straight line. The resulting critique of knowledge led to new possibilities for human imagination. The phenomena of nature began to receive more attention than grand syntheses of knowledge. The nominalist movement of the fourteenth century held that only particular objects of experience are real. Since science can only study such objects, nominalists argued that the general concepts or universals of scholastic philosophy are not real, but mere abstractions. The Oxford Franciscans were generally more inclined toward Augustinian Platonism than Thomistic theology, preferring more specialized studies such as light. John Peckham, who carried

on Roger Bacon’s optical studies at Oxford before becoming Archbishop of Canterbury in 1279, condemned Thomism in 1284 and 1286. One of the most important medieval works on optics was completed in 1304 by Theodoric of Freiberg (ca. 1250-1310), a German Dominican who managed to combine Thomism with Neoplatonism. He used geometry to show how both refraction and reflection of Sunlight inside individual water droplets can form a rainbow, as suggested by Albertus Magnus. He went on to verify his results experimentally by measuring the deviation of light in translucent spherical crystals. One of the leaders in this nominalist reaction was the English Franciscan William of Ockham (ca. 1285-1349), who studied at Oxford and taught at Paris, dying of the plague. Since for him only particulars exist, all our knowledge must begin with them. By a process he called intuition, or perception, we abstract from particular objects the qualities common to them to form universal concepts, which only exist as ideas expressed in words or signs. Since universals have no existence outside the mind, they should be recognized as abstractions and not unnecessarily multiplied, leading to the suggestion that the simplest expla-nation is the best: “It is vain to do with more as-sumptions what can be done with fewer.” This principle is known as Ockham’s razor since it shaves off superfluous universals. Nominalism led to new emphases in the fourteenth century. Since complete certainty was not possible with even the simplest explanation, experience and human reason were inadequate for acquiring knowledge about God and the world apart from faith and revelation. Thirteenth century confidence in reason gave way to a belief in the fourteenth century that only probable knowledge was possible, giving rise to a tendency to formulate problems hypothetically “according to the imagination.” Instead of claiming to know about essences, scientific discussions shifted to an emphasis on changing qualities and intensities, leading to increased analysis and quantification of change and motion. A group of scholastics at Merton College, Oxford, known as the Mertonians, began to apply this new analytical approach to the changing


intensities of motion. In 1328 Thomas Brad-wardine (ca. 1290-1349) criticized Aristotle’s idea of velocity as a ratio of impressed force F to resis-tance R (v = F/R), since this ratio is positive even when R is equal to or greater than F, permitting motion under conditions that should prevent it. Instead he suggested an exponential relationship equivalent to v = log(F/R) in modern notation. He also considered the possibility of a void (R = 0) by suggesting that light elements in a body constitute a quality of “internal resistance” that would prevent infinite speed in a vacuum. He also suggested the possibility of an infinite void space beyond our world. In the course of distinguishing different qualities of motion, the Mertonians developed their most important result, the Mean Speed Rule. They defined motion with uniform intensity as a constant speed with equal distances traversed in equal times. Non-uniform or difform motion has a varying speed, and uniformly difform motion varies at a uniform rate, constantly increasing or decreasing in speed (constant acceleration). Having made these logical distinctions, William Heytesbury in 1335 states that a body with uni-formly increasing speed from 0 to V during a given period of time will travel the same distance as it would have at a constant mean speed of V/2. Although these logical possibilities were “ac-cording to imagination” and not applied to actual events, they later provided the basis for Galileo’s analysis of falling objects. Ideas of motion received further devel-opment in the nominalist tradition at Paris by Jean Buridan (ca. 1295-1358), who became rector of the university in 1327. He applied Ockham’s razor to Aristotle’s doctrine of antiperistasis, which explained projectile motion by the push of air rushing to prevent a void behind a moving object. Buridan attempted to give a simpler explanation that would also account for the motion of a spear pointed at both ends with nothing for air to push against, or the rotation of a top that spins without changing its position. In his theory the initial force on a projectile imparts an internal quality of “impetus” to an object that sustains its motion with an intensity proportional to its speed and quantity of matter.

Buridan’s impetus is similar to the con-cept of motive power suggested by Philoponus in the sixth century, except that the latter was impressed externally on an object rather than an internal quality. However, Philoponus had little influence on scholastic thought except possibley through Arabic sources. Impetus was also similar to Galileo’s later concept of inertia: the natural tendency of an object is to remain at rest or in motion. But unlike inertia, impetus is a continually active cause of projectile motion, only diminished by external resistance, and does not apply to an object at rest. Buridan applied his impetus idea to simplify medieval concepts of celestial motion that introduced intelligences or angels to move the planets. Thus he suggested the possibility that God gave the celestial spheres an impetus that keeps them moving, since there is no resistance in the heavens to slow them. As with the similar ideas of Philoponus, Buridan contributed to a breakdown of the absolute distinction between the celestial and terrestrial regions. The analysis of motion received further development at Paris by Buridan’s student, Nicole Oresme (ca. 1320-1382), who became Bishop of Lisieux in 1377. He recognized that all motion is relative in the sense that the speed of a body will differ with respect to other bodies that have dif-fering speeds. From this relativity of motion, Oresme pointed out that the daily rotation of the heavens is observationally equivalent to daily ro-tation of the Earth on its axis. While not suggest-ing that such rotation of the Earth was a fact, he at least considered it as a rational possibility. He reinforced this idea by his suggestion that the air and objects on the Earth would share in the Earth’s rotation, initiated and sustained by impetus con-ferred at the time of creation. While rejecting the idea of a rotating Earth as a reality, he demon-strated the possibility that two equally rational conclusions can be mutually contradictory, thus showing the inadequacy of reason in contrast with faith. In about 1350, Oresme published the first graphical representation of motion nearly 300 years before Galileo in his treatise On the Con-figurations of Qualities and Motions. He plotted


the intensity of speed vertically against the time of travel horizontally, giving a rec-tangle of constant height for a body with constant speed and a triangle with sloping height for uniformly increasing speed (Figure 3.4). The area of these figures (velocity × time) thus gives the distance travelled. He was then able to use this result to prove the Mertonian Mean Speed Rule for uniformly increasing speed (Figure 3.4). He showed that in a given time t a body travels the same distance at a uniformly increasing speed to a final velocity V (triangle area Vt/2) as the same body travels at a constant speed v (rec-tangle area vt) if v = V/2 (mean speed). Renaissance Awakenings. By the fifteenth century, nominal-ist thought and humanist stirrings began to open up new possibilities in Western Europe. The formation of National monarchies and princely city-states began to challenge the universality of the Church. Commercial wealth was begin-ning to rival feudal power based on own-ership of land. About eight Crusades during the period from about 1090 to 1290 had expanded mental horizons, if not spiritual. The Mongol conquests had opened the East to adventurers like Marco Polo (1254-1324), and the age of exploration was dawning in the West. The artist-engineers of the Renaissance were beginning to assimilate the learning of scholars into the craft tradition. The last great philosopher of the Middle Ages, Nicolas of Cusa (1401-1464), a German Cardinal and Bishop of Brixen in the Tyrol, ex-plored the limits of nominalist thought concerning the incompetence of reason and reached some surprising conclusions. Influenced by Neoplaton-ism and German mysticism, he tried to describe the relation between finite experience and the infinite God in his book Learned Ignorance, pub-lished in 1440. This led to the modern-sounding conclusions that the universe has no unique center nor circumference (except God), and that there is no state of absolute rest. Thus the Earth moves and

cannot be the center of the universe, and other worlds may exist and be inhabited. Unfortunately, his astronomical ideas were too speculative and undeveloped to contribute to scientific progress. Several events in 1453 accelerated the process of change. The fall of Constantinople to Islamic Turks increased the flow of Byzantine scholars to Italy, bringing many original Greek manuscripts with them. Arabic translations could now be corrected, and additional classics of Greek science became available. The French finally drove out the English, ending the Hundred Years War in which cannon had begun to replace the catapult. This led to improvements in mining, metallurgy, and the construction of fortifications, with new challenges for engineers and artisans. About the same year, the appearance of the Gutenberg Bible marked the invention of the printing press, ensuring the preservation, distribution and multiplication of knowledge.

Uniformly Increasing Velocity

AverageVelocity

Final Velocity

Time

Velocity

t0

ConstantVelocity v V

Figure 3.4 Oresme’s Velocity Graph and the Mean-Speed Rule Oresme represented a uniformly increasing velocity by a straight line of constantly increasing height, producing a triangle of maximum height equal to the final velocity V attained at a time t. He represented a constant velocity v by a horizontal line of constant height v above zero. The distance travelled in either case is given by the area under the graph (velocity × time). The rectangular area under the constant velocity graph (vt) is equal to the triangular area (Vt/2) if the constant velocity v = V/2. Thus the mean speed of a uniformly increasing velocity is half of its final value.


The practical needs of navigation and calendar reform in the fifteenth century led to the revival of observational and mathematical astron-omy. After working with astronomer George Peurbach (1423-61) at the University of Vienna, John Muller (1436-76), known as Regiomontanus (Latin for Konigsberg in Franconia), studied original Greek versions of Ptolemy’s Syntaxis in Italy before starting his own observations in Nuremberg. Regiomontanus was the first to use the mechanical clock in astronomy and to correct his observations for atmospheric refraction. He made the first scientific study of a comet in 1472, later identified as Halley’s comet. He published his planetary tables in 1475, including a list of predicted eclipses up to 1530. He also published the first complete book on trigonometry, including a table of sines for every minute of arc. On a trip to Rome to help reform the Julian calendar, he died of plague before the project could proceed. The tables and nautical almanacs of Regiomontanus were important in the discovery voyages of Christopher Columbus in 1492 and of Vasco da Gama, who circled Africa to reach India in 1498. Columbus learned of Roger Bacon’s inferences based on Ptolemy’s incorrect estimate of the circumference of the Earth (recorded in Cardinal d’Ailly’s Imago Mundi, written in 1410 and printed in 1490). He was further encouraged in the feasibility of reaching India by sailing west after seeing a map of the Florentine physician-cosmographer Paolo Toscanelli (1397-1482), who had used Marco Polo’s report of the vast eastward extent of Asia to conclude that only about 3000 miles of ocean separated it from Europe. When Portuguese geographers rejected his “Indies Enterprise” on the basis of what they properly considered a gross underestimate, Columbus re-ceived support from Spain. The fortunate coinci-dence of finding unknown continents that were about 3000 miles distant rewarded his ill-founded faith. Although his discoveries showed the insufficiency of ancient knowledge, he died probably unaware of his great discovery. Some shifts away from the ancients and the scholastics appears in the artist-engineers of the Renaissance. Leonardo da Vinci (1452-1519) is noteworthy for his emphasis on experiment and

mathematical empiricism, even though his ideas had little effect on science. As an artist he pene-trated beneath outward appearances to the inner anatomy and mechanics of the body. As an engi-neer he went beyond the impetus theorists in quantitative measurements and experiments, if not in theory. He correlated projectile range with the angle and force (amount of gunpowder) of a can-non and determined the basic laws of friction. His belief in human creativity led to notebooks full of inventive ideas, such as flying machines, subma-rines, and all sorts of mechanical devices. Al-though none of this led to new scientific theories, he symbolizes the beginning of a new way of viewing nature. Although science seemed to make little progress in the medieval period, scholars did establish some important prerequisites for scien-tific advance. They recovered, extended and transformed much of the Greek scientific tradition. Both Arabic translations and original Greek sources became increasingly available, and the all important arithmetic and algebraic achievements of the Arabs began to enter European thought. The Thomistic synthesis and other scholastic move-ments demonstrated the importance of reason and the rational order of the universe, as well as the intelligibility of God’s creation to human rational-ity created in the image of God. Medieval theology altered the Greek heritage and showed the poten-tial of compatibility between scienctific knowledge and Christian faith. Monasticism kept the desire for learning alive, and the emergence of universities expanded knowledge, reinforcing new attitudes and values. The Benedictine order exhibited a new respect for manual labor and the goodness of creation, while the Franciscans led the way in a new appreciation of nature leading to an emphasis on observation and experiment. Even the condemnation of 1277 opened up new possibilities for human imagina-tion, leading to suggestions of a moving Earth, a vacuum in space, and the existence of other worlds. A new analysis of motion emerged, chal-lenging the divinity of the heavens. The linear view of history and the concept of purpose in the universe culminated in a new confidence in human creativity and the possibility of progress. The stage


was set for the emergence of a new view of the universe that historians would call the Scientific Revolution. REFERENCES Aquinas, Thomas. Summa Theologica trans.

Daniel J. Sullivan and the Fathers of the Eng-lish Dominican Province. 2 vols. Chicago, University of Chicago Press, 1952.

Augustine of Hippo. City of God. trans. Henry Bettenson. London: Pelican, 1972.

Clagett, Marshall. The Science of Mechanics in the Middle Ages. Madison: University of Wis-consin Press, 1959.

Crombie, A. C. Medieval and Early Modern Sci-ence, vol. 1 and 2. Garden City, N.Y.: Dou-bleday, 1959.

Grant, Edward, ed. A Sourcebook in Medieval Science. Cambridge, Mass.: Harvard University Press, 1974.

Grant, Edward. Physical Science in the Middle Ages. Cambridge, England: Cambridge Uni-versity Press, 1977.

Grant, Michael. Dawn of the Middle Ages. New York: McGraw-Hill, 1981.

Lindberg, David C. The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious and Institutional Con-text, 600 BC to AD 1450. Chicago: University of Chicago Press, 1992.

Lindberg, David C. Theories of Vision from Al-Kindi to Kepler. Chicago: University of Chi-cago Press, 1976.

Mason, Stephen F. A History of the Sciences. New York: Collier Books, 1962.

Nasr, Seyyed Hassein. An Introduction to Islamic Cosmological Doctrines. Boulder, Colo.: Shambhala, 1978.

Peters, F. E. Aristotle and the Arabs: The Aristo-telian Tradition in Islam. New York: New York University Press, 1968.

71

1. THE COPERNICAN SYSTEM

The heliocentric theory of a moving Earth revolving around the Sun was conceived and developed in a sixteenth century world still domi-nated by Medieval Scholasticism, but being reshaped by the Renaissance and Reformation. The slow reception of this theory suggests that it was a revolution only in the original sense of the word: a return to an earlier position, as in the revolution of the planets to their original places in the zodiac, or the Reformation attempt to return to the purity of the early Church. The Renaissance revival of Plato and other Greek classics was a stimulus to a renewed emphasis on geometry and the harmony of the heavens as an alternative to Aristotelian cosmology and Ptolemaic complex-ities that had dominated Medieval science. One aspect of this Platonic revival was the mathematical mysticism of Pythagoras and the Hermetic tradition. Hermetic literature included some fifteen works of popular Greek philosophy along with Jewish and Persian elements. These were written between A.D. 100 and 300 and as-cribed to the Egyptian god Hermes Trismegistus. The Renaissance viewed Hermes as a real Egyp-tian priest whose teachings were the source of the ideas of Pythagoras, Plato and Neoplatonism. To-gether with astrology and alchemy, Hermeticism saw the universe as filled with a cosmic spirit

which orders and maintains the universe. Humans fit into this cosmology by exercising creative power over nature, unlocking the mysteries of its harmony with the keys of mathematics. The Copernican revolution involved a vast expansion of space that eventually exploded into an infinite universe. This resulted in the de-struction of the medieval cosmos and the dis-placement of humans from their central place in the world, or perhaps more correctly, the loss of the very world in which they were living. Thus the finite and well-ordered world in which the very structure of space embodied a hierarchy of perfection and purpose gave way to an indetermi-nate world of infinite space bound together only by impersonal mathematical laws. But the initial steps in this revolution were of a much more conserva-tive and traditional nature.

Background and Sources Nicolaus Copernicus (1473-1543) was born in the town of Torun on the Vistula in what is now northern Poland. He was the son of a local merchant, but his father died when he was ten years old. His maternal uncle adopted him, and then in 1489 became Bishop of Ermland, a nearly independent principality under the protection of the King of Poland. Through his uncle’s patronage, Copernicus was able to begin study in 1491 at the University of Cracow, where he learned about

CHAPTER 4

An Infinite Universe

The Copernican Revolution and its Reception

Chapter 4 • An Infinite Universe 72

Ptolemaic astronomy. From 1497 to 1506 he studied Greek, canon law, mathematics, and medicine in Italy at the universities of Bologna and Padua. Meanwhile, he continued to pursue his interests in astronomy, assisting the astronomer Domenico Maria da Novara (1454-1504) in making observations. Platonic and Pythagorean influences are evident in 1500 from his presenta-tion of a series of lectures on “mathematics” (probably astronomy) at Rome. When Copernicus returned home to Ermland, he spent six years as secretary, legal advisor and personal physician to his uncle at Heilsberg Castle until he died in 1512. He then assumed the position his uncle had secured for him as canon at the Cathedral of Frauenberg on the Baltic. His administrative duties included finances, politics and ecclesiastical affairs, but he never took holy orders to become a priest and had enough spare time to develop his heliocentric system in detail. His reputation in astronomy was already sufficient to earn him an invitation to give his opinion on calendar reform at a church council in 1514, but he declined due to the lack of accurate enough information. Copernicus was a conservative reformer who insisted on the Platonic principle that the planets move in uniform circular motions or combinations of such motions. His goal was to purify the Ptolemaic System by returning to the original concepts of Pythagorean harmony, much like Martin Luther wanted to return to the original purity of the Church. Most of his astronomical work was of a theoretical nature to develop a heliocentric system of the planets as complete as the geocentric system of Ptolemy, using many of Ptolemy’s methods and observations. His own observations were limited to measurements of the inclination of the ecliptic, and a few conjunctions and oppositions of planets in order to check some of the elements of planetary orbits. His most radical innovation was to allow for the motion of the Earth based on geometric arguments instead of the physical arguments required by the traditional Aristotelian hierarchy of the disciplines.

In 1514 Copernicus circulated among his friends a manuscript called the Commentariolus, giving a short description of his heliocentric system

without mathematical demonstrations. To explain the non-uniform motions of the planets around the Sun in terms of uniform circular motions, Copernicus used 34 circles and claimed that Ptolemy had required some 80 circles (actually about 40 in the Ptolemaic System). By the time his complete system was published, the number of circles had increased to 48 to achieve an accuracy equivalent to that of Ptolemy (see Koestler p. 193). The work was printed shortly before his death in 1543 under the title De Revolutionibus Orbium Coelestium (The Revolutions of the Celestial Orbs). In the preface Copernicus dedicated De Revolutionibus to Pope Paul III and quoted from Plutarch to indicate some of the sources of his new system:

Some say that the Earth is at rest, but Phi-lolaus the Pythagorean says that it is carried in a circle round the fire, slantwise, in the same way as the Sun and Moon. Heraclides of Pontus and Ecphantus the Pythagorean give the Earth motion, not indeed translatory, but like a wheel on its axis, from west to east, about its own centre.

He makes no mention of Aristarchus in connection with the heliocentric idea, but his original manuscript does include a passage struck out by black lines stating that “Philolaus perceived the mobility of the Earth, which also some say was the opinion of Aristarchus of Samos.” Of course, there is no evidence of a complete heliocentric system worked out before Copernicus. Objections and Innovations

Although Copernicus followed many of Ptolemy’s methods and assumptions about uniform circular motions, he objected to the lack of geometric harmony and consistency. In the Commentariolus he wrote that “a system of this sort seemed neither sufficiently absolute nor sufficiently pleasing to the mind.” For example, the centers of the Ptolemaic epicycles for Mercury and Venus were confined on a line from the Earth to the Sun to account for the fact that they only appear in the morning or evening (near the Sun), while the other planets may appear at any time of the night. Most objectionable to Copernicus was Ptolemy’s use of the equant to account for the non-uniform motion of


planets relative to the centers of their circles. Finally, he recognized that he could eliminate three of Ptolemy’s circles for each of the planets by ascribing three motions to the Earth instead. For the three motions of the Earth, Copernicus included the daily rotation of the Earth on its axis, the annual revolution in its orbit, and a conical wobbling of its axis at a rate that accounts for the precession of the equinoxes (Figure 4.1). Instead of impetus or some other physical cause, he argues that the Earth’s rotation is the natural

motion of a sphere. With its annual revolution, the Earth moved in the same direction as all the planets around the Sun, without requiring the dual plane-tary motions of daily rotation plus opposing motion through the zodiac. Precessional wobbling of the Earth avoided the imperfect shifting of the heavens, which was even more problematic due to Copernicus’ belief that the rate of precession had varied since the time of Hipparchus. In arguing for the central position of the Sun, Copernicus draws on the mystical Neopy-

sun

132 4

Mars

EarthVenus

Polaris Vega

* ** *

dailyyearly

26000 y

23°

SS

AE

WS

VE

Pisces (VE)Aquarius

Capricornus

Sagittarius(WS)

Scorpio

LibraVirgo (AE)

Leo

Cancer

Gemini (SS)

Taurus

Aries

retrogrademotion

(15000 AD)

Figure 4.1 Earth Motions and Apparent Motions in the Heliocentric System The heliocentric system requires three motions of the Earth: (1) daily rotation on its axis pointing toward Polaris; (2) annual revolution in its orbit around the Sun; (3) a 26,000 year precession or wobble of the axis of the Earth at about a 23° inclination to account for the precession of the equi-noxes. This inclination of the Earth’s axis explains the seasons, with the axis inclining toward the Sun at the summer solstice (SS) and away from the Sun at the winter solstice (WS) in the northern hemisphere. The apparent motion of the Sun through the constellations of the zodiac is due to the Earth’s annual orbit on the ecliptic plane. Thus the Sun appears to be in the constellation Pisces at the vernal equinox (VE) and in Virgo at the autumnal equinox (AE). After 13,000 years the Earth’s axis will point toward Vega, so the seasons will be shifted in relation to the stars. As the Earth ap-proaches Mars, it appears to move from star 1 to 2, then backward to star 3 as it passes Mars, and finally forward to star 4 as it leaves Mars, causing an apparent retrograde motion.


thagorean language and Hermetic tradition of the late Renaissance:

In the center of all rests the Sun. For who would place this lamp of a very beautiful temple in another or better place than this wherefrom it can illuminate everything at the same time? As a matter of fact, not un-happily do some call it a lantern; others, the mind and still others, the pilot of the world. Tresmegistus calls it a “visible god;” Sophocles’ Electra, “that which gazes upon all things.”

As the source of heat, light and life, the Sun ought to rest in the center of the universe. Stability is more appropriate to a nobler body like the Sun rather than the Earth. He answers Ptolemy’s objection that a rotating Earth would fly apart by suggesting that the Earth, as well as other heavenly bodies, holds together by its own gravity, acting on aggregates of matter rather than across space. Furthermore, it is more likely that gravity would tear apart the immense celestial sphere if the stars rotated around the Earth every day. In short,

Copernicus defies the ancient division between celestial perfection and terrestrial imperfection. The harmony of the Copernican system is especially evident in its ordering of the planets by their distances, which could be correctly calculated for the first time from heliocentric assumptions. The Ptolemaic system arbitrarily based this ordering on uncertain periods, especially for Mer-cury and Venus, and on erroneous distances from the assumption that no space should lie between the epicycles of adjacent planets. Copernicus cal-culated the actual periods of the planets around the Sun from a combination of the Earth’s annual motion and the apparent motion of the planet through the zodiac, giving 88 days for Mercury and 225 days for Venus. For the first time, Copernicus calculated the relative distances of the planets from the Sun correctly by measuring angles in the triangle formed by the Sun, Earth, and a given planet (Figure 4.2), based on the radius of the Earth’s or-bit about the Sun as one astronomical unit (1 AU). This method gave 0.4 AU for Mercury and 0.7 AU for Venus. This reveals that distances increase

eE

V

S * *p p1 2

Figure 4.2 Planet Distances and Stellar Parallax in the Copernican System In the heliocentric system, Copernicus used the orbital radius of the Earth ES = 1 AU (astronom-ical unit) as a base line for calculating the relative distances of the planets. Thus the orbital radius VS of Venus is found from its largest observed angle from the Sun, which is its maximum elongation e = 46°. Since EV is tangent to the orbit of Venus, EVS is a right triangle with VS = 0.72 AU. As the Earth moves in its orbit, the directions of the stars should change. Maximum change should occur over six months, and half of the resulting angle is the stellar parallax angle p. If a star has a parallax p1, then a more distant star would have a smaller parallax p2 < p1. Since Copernicus could detect no parallax, he assumed the stars must be so far away that p is too small to measure.


with increasing period, providing for the first time a definite basis for the order of the planets. Advantages and Problems The Copernican system gives simple ex-planations of several phenomena, rather than mere representations or “saving of appearances.” This is quite evident in regard to the proximity of Mercury and Venus to the Sun, which is simply due to their orbits being nearer the Sun, rather than an accidental restriction of their epicycles on an Earth-Sun line. Copernicus explained seasonal variations more directly as resulting from the in-clination of the Earth’s axis toward Polaris, tilting toward the Sun in summer and away from the Sun in winter instead of the apparent motion of the Sun on the ecliptic (see Figure 4.1). One of the clearest advantages of the Copernican system is in explaining planetary retrograde motion, which turns out to be an optical illusion instead of an actual epicycle looping motion. For example, as the faster-moving Earth passes Mars it appears to stop and retrogress against the back-ground of the fixed stars (see Figure 4.1), much like pedestrians appear to go backward relative to passengers in a moving bus. The moving Earth also accounts for variations in the brightness of the planets, as with Mars, Jupiter and Saturn, which are always nearest the Earth when they rise in the evening since the Earth is then directly between them and the Sun (in opposition). Unfortunately, the harmony revealed by Copernicus did not include an associated simplicity because of his commitment to the Platonic ideal of uniform speed and circular motions. The inequality of the seasons (up to four days) and the varying speeds of the planets required the continued use of eccentrics and epicycles, though not the detested equant. A slowly changing eccentricity in the Earth’s circular orbit even required an eccentric point re-volving on a tiny circle around another

point which in turn revolved around the Sun (Fig-ure 4.3, greatly exaggerated for clarity). In fact, none of the planetary orbits were truly helio-centric. Copernicus did not need epicycles to ac-count for the retrograde motions of the planets, but he did use them to account for varying speeds and inclinations from the ecliptic. He used an in-genious combination of epicycles to avoid large changes in the apparent diameter of the Moon as compared to the Ptolemaic system, in which the lunar diameter changes by a factor of four. Al-though Copernicus reduced the number of epi-cycles by about half and eliminated the equant, the system was still embarrassingly complex. From the perspective of the prevailing Aristotelian cosmology, the Copernican system

••

•

• •

•••

sun

Venus

Mercury

earth

moonC

Figure 4.3 Copernicus’ Use of Circles for Planet Motions Copernicus followed Ptolemy in using combinations of cir-cles to account for observed variations in the orbits and speeds of the planets, even though he reversed the positions of the Earth and the Sun. His system was not truly he--liocentric in that each planet had its own center offset from the Sun, and in the case of the inner planets these centers themselves rotated on tiny circles. He was able to eliminate Ptolemy’s equant by referring the planetary motions to the center (C) of the Earth’s orbit, which itself revolved on two small circles (exaggerated here). Copernicus introduced a unique treatment of Mercury by making it oscillate on the diameter of its epicycle instead of revolving around it.


faced many problems. Falling objects would no longer fall toward their natural place at the center of the universe, and should be quickly displaced to the west by a rapidly moving Earth. Motion of the Earth through space would seem to require the forbidden void. No mover was evident to keep the massive Earth moving. Contrary to Aristotelian principles, which allowed only one proper motion to a simple body, Copernicus assigned three to the Earth. In effect, the Copernican system elevated the lower discipline of geometry above physical and even theological explanations, in violation of the traditional hierarchy of the disciplines. Copernicus made no attempt to address the theological issues involved, especially in rela-tion to Thomistic theology and its Aristotelian basis. The Copernican system seemed to deny the cosmic hierarchy of God and the angels, the cen-trality of the human drama, and the chain-of-being itself. A new set of values allowed the Sun to rule over bodies of more or less equal status, the Earth together with the planets equally possessing gravity and circularity of motion. Moreover, the helio-centric system seems to contradict a literal interpretation of the Bible. For example, Psalm 93:1 states that “The world is firmly established, it cannot be moved,” and Ecclesiastes l:5 reminds us that “The Sun rises and the Sun sets, and hurries back to where it rises.” No wonder that Coperni-cus delayed publication of his work for several years until shortly before he died. Finally, the most important empirical evidence for a moving Earth was missing. On an orbiting Earth, an observer should be able to detect a slight shift of the fixed stars over the course of the six months that it takes to move from one side of its huge orbit to another. Even the polar axis of the Earth’s rotation should not point at the same star over the course of the year. But Copernicus was unable to detect any change in the directions of the stars (stellar parallax), so he offered the following argument:

That there are no such phenomena for the fixed stars proves their immeasurable dis-tance, because of which the outer sphere’s (apparent) annual motion or its (parallactic) image is invisible to the eyes.... So great is

this divine work of the Great and Noble Creator!

Although Copernicus does not assert infinite space, the “immeasurable distance” of the stellar sphere makes it impossible to detect stellar parallax. He goes beyond Ptolemy’s argument that the Earth compared to the skies is “as a point” in suggesting the same for the whole circle of the Earth’s annual motion around the Sun. His response to the lack of this crucial empirical evidence was an act of faith in a greatly expanded view of the universe and its Creator. This faith would not be rewarded until 300 years later when Friedrich Bessel (1764-1846) finally detected a tiny stellar parallax in 1838. 2. COPERNICAN RESPONSES & PARALLELS: THE LEAP TO INFINITY Early Lutheran Responses to Copernicus The first published account of the Copernican system was written in 1540 by Georg Joachim Rheticus (1514-1574) with the permission of Copernicus under the title Narratio Prima (First Report). Rheticus was a Protestant mathematics lecturer from the heart of the Lutheran Reformation at the University of Wittenberg, who learned about the work of Copernicus and became his first major disciple in 1539. When he returned to his teaching duties at Wittenberg in 1542, he was enthusiastic about the new theory and introduced it to many of his students. He es-pecially appreciated the unity and order revealed by its correlation of the distances and periods of the planets about the Sun, ending his book with a passage on the Pythagorean harmony of the soul. It also appears that Rheticus wrote a recently dis-covered (R. Hooykaas, 1984) anonymous treatise published posthumously in 1651, entitled Letter on the Motion of the Earth, arguing for the compatibility of the Bible and heliocentric theory. It was Rheticus who finally persuaded Copernicus to publish his Revolutionibus. Because of other duties, Rheticus lacked the time to over-see the publication of De Revolutionibus and so entrusted it to a fellow Lutheran, Andreas Osiander (1498-1552). Without seeking any permission, Osiander added an unsigned introduc-


tory “Letter to the Reader” (Ad Lectorum), perhaps in an attempt to save Copernicus from a hostile reception. He appealed to the traditional hierarchy of disciplines that Copernicus had defied, sug-gesting that astronomy does not yield truth like philosophy, but only hypotheses that provide “a calculus consistent with the observations.” Such hypotheses are of value if they lead to better calculations even if they lack “the semblance of the truth.” Thus De Revolutionibus was often read as a convenient fiction until the author of the preface was finally identified by Kepler. Protestant reaction in general was some-what ambiguous toward the Copernican theory. In a vague statement recorded in his Table Talks, Martin Luther said, “That fool wants to turn the whole art of astronomy upside down,” but this was in 1539 before the appearance of any published account of the theory. There is no clear evidence that John Calvin knew of the theory, or if he did, he did not consider it important enough for public comment. Luther’s close associate, Philipp Mel-anchthon (1497-1560), was initially hostile to the theory, but later shifted his position to some degree. In his sweeping educational reforms of nearly a dozen German Protestant universities, he gave mathematics a special place in the curricu-lum, helping to give astronomy a greater respect-ability. Although he rejected the Earth’s motion, based on a literal reading of the Bible, Melanch-thon encouraged the use of Copernican calculating mechanisms involving uniformly revolving spheres without the equant. Melanchthon’s followers at Wittenberg developed a strong tradition of mathematical astronomy that spread through northern Europe. Erasmus Reinhold (1511-1553) and his many dis-ciples, with the notable exception of his colleague Rheticus, accepted Melanchthon’s objections to a moving Earth, but made extensive use of Coperni-can calculations. In 1551 Reinhold completed his Prussian Tables, named after his patron Albrecht, Duke of Prussia, which later became the basis for the calendar reform of Pope Gregory XIII in 1582. The Gregorian calendar corrected an error of ten days that had accumulated in the Julian calendar due to an erroneous length of the year that did not

account for precession of the equinoxes. It intro-duced a new tropical year that corrected for pre-cession by omitting centenary leap years divisible by 400. Catholic states accepted it immediately, but most Protestant nations waited for about 150 years before accepting the Gregorian calendar. Developments in Other Sciences The Copernican challenge to Aristotelian and hierarchical views was matched in other sci-ences during the sixteenth century, often with similar mystical and religious overtones. The Swiss physician and alchemist Theophrastus Bombastus von Hohenheim (ca 1493-1541) at-tempted a revolution in medicine and chemistry called “iatrochemistry.” He took the name Paracelsus, meaning “better than Celsus,” the Roman physician whose mostly Hippocratic works (ca A.D. 30) had been discovered and published in 1478. He began his career at the University of Basel in 1527 by burning the books of Galen and Avicenna (Ibn Sina) to show his opposition to ancient authority in science and medicine. Paracelsus emphasized the importance of personal experience and a new view of alchemy as the search for the invisible forces of life and nature. Bodily changes are chemical processes animated by unique spiritual entities, and alchemy should yield medicines to treat specific diseases, including minerals as well as plants. He rejected the four-humor and four-element theories, replac-ing them with the three spiritual essences of mer-cury, sulphur and salt. In spite of these mystical principles, he was a careful experimenter and was the first to describe zinc. He viewed his system as a religious reformation to restore Hippocratic pu-rity, not unlike Luther’s Reformation, and began the transition from alchemy to chemistry. A similar reform of anatomy began with the publication of Humani Corporis Fabrica in 1543 by the Flemish physician Andreas Vesalius (1514-64), correcting Galen in the same year Co-pernicus revised Ptolemy. Vesalius went from Paris to Italy where he was free to do his own dis-sections, and became a professor at Padua. He followed much of Galenic theory, even as Coper-nicus had used Ptolemaic methods; but in rejecting the usual practice of using an uneducated barber


surgeon to do dissections, he was able to correct Galen by showing that he had actually based many of his ideas on animal anatomy rather than human. The most impressive pages of Vesalius’ book were the beautiful woodcut engravings that accurately illustrated the muscles and other struc-tures of the human body. Many of these were done by Jan Stephen van Calcar, a pupil of the artist Titian, and marked an important innovation over the mostly verbal descriptions of earlier ana-tomical books. In his study of the function of the heart, Vesalius could not find evidence for the pores in the septum that Galen claimed in saying that blood flows between the chambers of the heart, but he offered no alternative to his theory. A former colleague of Vesalius at Paris, Michael Servetus (1511-53), suggested the lesser (pulmonary) circulation of the blood from the right to the left chamber of the heart through the lungs, apparently unaware of the similar proposal by Ibn al-Nafis 300 years earlier. As a heretical religious reformer, he based his theory on a Unitarian-type theology that rejected the doctrine of the Trinity, as well as Galen’s triadic hierarchy of brain, heart and liver. In a small section of his book, The Restoration of Christianity (1553), he argued that the Holy Spirit was the all-pervading breath of God, and that the blood contained only one kind of spirit instead of both natural and vital spirits. He claimed that “The soul itself is the blood,” implying that it perished with the body. This was one of the charges against him when he was apprehended by Calvin at Geneva, tried for heresy and burned at the stake. Infinite Conceptions of the Universe Reinhold’s Prussian Tables helped to spread Copernican ideas to England where John Field used them in 1556 as the basis for an alma-nac in which he commends the writings of Copernicus and Reinhold. In a preface to this almanac, the mathematician and astrologer John Dee (1527-1608) also subscribes to the Copernican system. His student, Thomas Digges, joined Dee in an unsuccessful attempt to measure the annual parallax of a new star that appeared in 1572. The

immeasurable distance of the stars implied by this lack of stellar parallax now led Digges to the concept of an infinite universe. The first English account of the Coperni-can system appeared in 1576 by Thomas Digges (ca 1546-1595), who was an Oxford mathemati-cian with strong Puritan tendencies. He gave the first description of an infinite Copernican universe in a brief treatise entitled A Perfit Description of the Celestiall Orbes, appended to an almanac (A Prognostication Euerlasting) published by his father, Leonard Digges. In a diagram Thomas Digges gives a simplified representation of the heliocentric system surrounded by stars spread throughout space, instead of being confined in the usual manner to a celestial sphere. He labeled the spherical gap between the planets and the stars as “the habitacle for the elect” above which “This orbe of starres fixed infinitely up extendeth hit self in altitude sphericallye...with per-petuall shininge glorious lightes innumerable.” He labeled the Earth’s orbit as “The great orbe carreinge this globe of mortalitye” about the Sun. Digges seems to be indicating a deeper symbolic meaning for this new heliocentric view of the world. An even more radical view of the infinite universe was preached by Giordano Bruno (1548-1600), a Dominican monk from Naples. In 1576 he left his order in Naples and went to Geneva, where the Calvinists ejected him. He traveled about Europe teaching Hermetic philosophy until Aristotelians rejected him in Paris. At Oxford in 1583 he defended the Copernican theory before a hostile audience, publishing his ideas a year later in a humanistic dialogue called The Ash Wednes-day Supper. Bruno believed that the power of an infinite God cannot be restricted to a finite world. In De Monade he asserted not only that there was an infinite number of stars in infinite space, but each was a Sun with its own populated planets. For Bruno the infinite presence of God united the universe rather than a hierarchy of beings. Not only did Bruno’s Hermetic tenden-cies border on pantheism, but he also attacked monks, miracles and established religion. After spending some time in Wittenberg, he returned to Italy where the Office of the Inquisition arrested him at Venice in 1592 and charged him with


heresies, though these charges did not relate directly to the Copernican theory. In fact, the Catholic church had not yet taken an official position on the Copernican system. After a seven-year trial, Bruno was burned at the stake in 1600. Catholic and Protestant Reactions Reactions by the Catholic Church to the Copernican system were at first slow, but not always unfavorable. The Council of Trent, meeting from 1545 to 1563, initiated the Counter-Reformation and the Congregation of the Inquisi-tion, but their primary concern was with the Prot-estant challenge and internal reform. A Spanish monk, Diego de Zuñiga (1536-1597), even pub-lished a commentary in 1584 on the Book of Job, in which he interpreted a reference to God who “shaketh the Earth out of her place” (Job 9:6) according to the Copernican theory. But criticisms of his view led him to revise his position before he died, rejecting the Earth’s daily rotation. However, sixteenth-century Catholic scientists worked under no formal prohibitions from the Inquisition or the Index of forbidden books. In spite of the fact that neither Luther nor Calvin supported the Copernican system, the Protestant Reformation was generally more posi-tive toward the development of the new science. The Reformers taught that the authority of the priests and the Catholic Church should be rejected and that individuals should study Scripture and seek to interpret it for themselves. In a similar way, early scientists began to turn from ancient authorities and interpret nature for themselves. A new confidence began to emerge in the power of mathematics and observations. Reformers recog-nized both the Holy Scripture and the “Book of Nature” as sources of evidence about God’s creation. Protestant Reformers also took exception to the medieval hierarchical view of the world expressed in the chain-of-being concept, as well as the hierarchies of the Catholic Church. Calvin minimized the role of angels and recognized a more direct and absolute control of the world by God. A similar transformation of values appears in the Copernican system, which rejected the celestial-terrestrial hierarchy and gave the Earth

the same status as the planets. In the Copernican view, the Sun had absolute rule over the solar sys-tem and events were subject to natural laws. Some Protestants also began to emphasize the utilization of science for “good works,” especially among the English Puritans. Although Luther taught that salvation is only by faith, and Calvin stressed the election of those predestined to salvation, their followers placed more emphasis on good works as a sign of salvation. The Puritans explicitly sanctioned scientific studies as a form of good works, both for the glory of God and for the welfare of human society. While Protestant anti-authoritarianism and individual interpretation were consistent with the new science, the Puritan promotion of good works was a more positive stimulus to scientific activity. 3. COPERNICAN MODIFICATIONS: REACTIONS TO INFINITY The Work of Tycho Brahe The Danish astronomer Tycho Brahe (1546-1601) provided the empirical basis for the simplification of the Copernican system, even though he couldn’t find the necessary evidence to support it. He was the last and greatest of the pre-telescopic observers, and the first to attempt a more systematic and comprehensive program of planetary observations. This was in contrast to the usual astrological practice of only recording special positions, such as conjunctions and stationary points during retrograde. He recognized the importance of comprehensive and accurate data to establish the true planetary orbits. From an aristocratic Protestant family, Tycho studied liberal arts and astrology at the Lutheran University of Copenhagen and then went to Leipzig to study law. He became interested in astronomy in 1560 when a predicted solar eclipse occurred on the scheduled day. In 1563 he observed that a close approach of Jupiter and Sat-urn was about a month off of the predicted time in the Alfonsine Tables (Toledo, 1252), and several days off from the Prussian Tables, so he began to obtain instruments for more precise observations. At the age of 20 he fought a duel over a mathe-matics argument and lost part of his nose, which


he repaired with a gold and silver replacement held in place with beeswax. When a “new star” suddenly appeared in the constellation Cassiopeia on November 11, 1572, Tycho was “astonished and stupefied.” He made careful measurements, finding that its posi-tion did not change from month to month as with the planets, nor did it have any detectable parallax (Figure 4.4a). He concluded that it was beyond the planets, leading Tycho to question the unchanging perfection of the heavens. His book De Nova Stella (1573, Copenhagen) established both the name “nova” for an exploding star and his own reputation as an observer. Tycho’s star became

brighter than Venus before fading away after 16 months. Such visible novae occur about once every 300 years, although a previous one, observed by the Chinese in 1054, went unrecorded in Europe, where observers must have either ignored it or thought it unimportant. Tycho’s reputation led King Frederick II of Denmark to subsidize the building of an obser-vatory, called Uraniborg (“Castle of the Heav-ens”), on the island of Hven between Denmark and Sweden. At Uraniborg from 1576 to 1597, Tycho built many large instruments for measuring angles, with brass scales subdivided to a fraction of a degree (Figure 4.4b). By increasing the size of

*

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pm

pc

p * *

010 20 30

40

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(a) Parallax Measurements (b) Angular Scales

Figure 4.4 Tycho Brahe’s Measurements of Celestial Distances and Angles (a) Tycho Brahe used the angles of celestial objects from two widely separated positions A and B to find the height of these objects from their parallax angles (p) and the distance between A and B. The parallax of a new star, or “nova,” which appeared in the constellation Cassiopeia, was similar to other stars in having no detectable parallax (p = 0). The parallax of a comet that appeared in 1577 had a smaller parallax pc than that of the Moon pm, and thus was beyond the Moon’s orbit. (b) Tycho increased the accuracy of angular measurements by increasing the size of his instru-ments. The size of an angular scale is increased in direct proportion to the length of the radii of that scale. For example, the length of scale 1 is tripled by increasing the size of the instrument by a factor of three, making the subdivisions of scale 2 three times longer.


these instruments, they could have more precisely graduated scales. One quadrant, among more than 20 astronomical instruments, had a radius of more than 5 meters, but proved to be unwieldy. Using various methods, he improved the accuracy of measurements to the limits of unaided vision at about 1 minute compared to the best accuracy of the Greeks at about 10 minutes of arc, and determined the length of the year to within about one second. He also attempted to measure planetary positions over most of their orbits and precisely catalogued a thousand stars. When a brilliant comet appeared over Europe in 1577, Tycho was ready to make detailed observations and measurements. By comparing his observations with those made elsewhere in Europe, he found that the comet had less parallax than the Moon and estimated that it was at least six times farther away than the Moon (Figure 4.4a). This was contrary to Greek and Medieval opinion that comets were atmospheric phenomena like meteors. He attempted to compute its orbit and suggested that it might be oval instead of circular, perhaps even moving through the planetary spheres. These results cast doubt on both the immutability of the heavens and the existence of crystalline spheres. The Tychonic System Tycho recognized the relative simplicity of the Copernican system compared to the Ptolemaic system, but could not accept the idea of a moving Earth. In addition to the usual physical problems, he felt strongly that it conflicted with certain passages of Scripture. In spite of the greatly improved accuracy of his measurements, he was still unable to find any trace of annual parallax in the fixed stars. This empirical failure was coupled with the fact that the brightest stars appear to have a diameter of about 2 minutes to the unaided eye. Unaware of diffraction effects due to the spreading of light waves as they pass through the pupil of the eye, he calculated that stars would be larger than the annual orbit of the Earth if stellar parallax was as great as one minute of arc. Tycho described his heliocentric objec-tions in a series of letters to Christopher Roth-mann, one of about a dozen Copernican astrono-mers in Europe at the time. He also explained his

rejection of the Ptolemaic system due to observa-tions showing that Mars at opposition was closer than the Sun, while Ptolemy had placed Mars beyond the orbit of the Sun. Thus he was led to devise a compromise theory, which he felt com-bined the best features of Ptolemy and Copernicus. In his 1588 book on the comet of 1577, he described his geoheliocentric system without working out its mathematical details. In the Tychonic system, the Earth remains stationary at the center of the universe, with the Sun, Moon and stars revolving about it. But the planets all revolve around the Sun, which carries them in its annual motion around the Earth, so that no epicycles are necessary to explain retrograde motion (Figure 4.5). The daily revolution of the celestial sphere carries the Sun, Moon and planets to account for their daily motion. The orbital radii of Mercury and Venus are smaller than the solar orbit, while the orbits of Mars, Jupiter and Saturn encircle the Earth. To account for Mars at oppo-sition being closer than the Sun, its orbit intersects the orbit of the Sun, so they cannot be on solid spheres. The Tychonic system is geometrically

StationaryEarth

Mars

Saturn

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Venus

MovingSun

Figure 4.5 The Tychonic System In the Tychonic system, the Sun moves around a stationary Earth carrying the planets with it.


equivalent to the Copernican system, except that the heliocentric motions of the planets are referred to a stationary Earth rather than the Sun. It had some of the advantages of the Copernican calcu-lations without requiring a moving Earth or stellar parallax, but lacked the more complete symmetry of the Copernican system. More conservative astronomers accepted the Tychonic system, though some preferred at least to allow the rotation of the Earth to avoid the daily revolution of the celestial spheres and keep open the possibility of an infinite universe. The few convinced Copernicans were persuaded more by aesthetic preferences than scientific evidence. The new king of Denmark, Christian IV, did not continue the support his father had given to Uraniborg, being alienated by Tycho’s extrava-gance and exploitation of the Hven islanders. In 1597 Tycho packed many of his instruments and left Denmark to become court astrologer to the German Emperor, Rudolph II, near Prague. Three years later he made his greatest discovery when he hired a young German Copernican named Johan-nes Kepler, to whom he gave the difficult problem of calculating the orbit of Mars around the Sun, albeit in the Tychonic system. When Tycho died in 1601 (from a strained bladder by Kepler’s account, or perhaps from mercury poisoning) Kepler gained control of his large collection of observations, but not his instruments. As a mathematical astronomer, Tycho’s data was all Kepler needed to begin applying it to the Copernican system. Early Work of Johannes Kepler The mass of data assembled by Tycho would have been useless without the commitment to analysis and creative interpretation provided by Johannes Kepler (1571-1630). His lifelong passion was to reveal the inner coherence and harmony of the heliocentric system, and Tycho’s accurate and comprehensive observations were just what he needed. Kepler’s preoccupations were a curious mixture of theology, mathematics and mysticism. He had a Pythagorean conviction of the unity and simplicity of the universe, revealing the mind of God. The fabric of the heavens was woven with patterns from the Great Designer.

Kepler was born in the south German town of Weil der Stadt in the principality of Wűrttenberg. His interest in astronomy began when his mother showed him the comet of 1577. As a passionate Lutheran, he began to prepare for the ministry at the University of Tübingen. There he was introduced to the heliocentric system of astronomy by Michael Maestlin (1550-1631), one of the few Copernican teachers of his day, who convinced him of its truth and of the consistency and order that it gave to the planetary periods in relation to their distances. His desire to pursue the ministry was interrupted by a request to begin teaching mathematics at the Protestant high school in the Austrian town of Graz. Kepler supplemented his meager income with astrological predictions, but was driven by a Pythagorean urge to find a law governing the order of the planets. While teaching at Graz in 1595, he was struck by a grand inspiration of cosmic unity between the planets and the five regular solids of geometry. The number of the visible planets was now six with a moving Earth included as a planet. Perhaps he could account for the number of planets as well as their distances by correlating the five gaps between their orbits with the five regular solids. In a Herculean effort of mathematical mysticism, he showed that the relative distances of the planets could be obtained by inscribing the regular solids successively within the orbits of the planets (Figure 4.6), starting with Saturn:

Day and night I was consumed by the com-puting, to see whether this idea would agree with the Copernican orbits, or if my joy would be carried away by the wind. Within a few days everything worked, and I watched as one body after another fit pre-cisely into its place among the planets.

By trial and error he found the solution to his cos-mographic mystery. Thus, by inscribing the cube within the sphere of Saturn’s orbit and just around that of Jupiter, the tetrahedron between Jupiter and Mars, the dodecahedron between Mars and the Earth, the icosahedron between the Earth and Venus, and the octahedron between Venus and Mercury, he finally reached success.


Kepler published his geometric fantasy in 1596 under the title Mysterium Cosmographicum, with the conviction that, “Through my effort God is being celebrated in astronomy.” By allowing space for the eccentricity of the planetary orbits, all the planets except Mercury fit within an aver-age margin of about 5 percent. After some effort to explain the astrological and other relations be-tween the solids and the planets, Kepler turns to “the proportions of the motions to the orbits.” Here he makes the important suggestion that the Sun is the cause of the planetary motions, sweep-ing them along by what he calls the anima motrix. Thus he insists that the motions must be referred to the Sun rather than the eccentric center of the Earth’s orbit, as Copernicus had done. But to carry out such calculations, he needed better obser-vations, so he began a correspondence with Tycho that led to the momentous invitation to join his staff in Prague.

Breaking of the Circle When Kepler joined Tycho in February, 1600, he began to work on the orbit of Mars, for which the most accurate data were available, but also the greatest eccentricity. He conscientiously tried to fit Tycho’s observations to each of the three systems of Ptolemy, Tycho and Copernicus, but finally established the latter system after some five years of effort. Unlike Copernicus, he tried to use the equant in place of any epicycles at all, feeling that a physical cause for the motion of a planet cannot act on the empty space at the center of an epicycle. His conception of the Sun’s anima motrix had the effect of a force acting directly on the planet’s motion. After more than 70 trials with various combinations of eccentric and equant, Kepler finally succeeded in fitting the radius of Mars’ orbit to Tycho’s data; but representing the orbit of Mars in the plane of its motion (longitude) with a

MarsJupiter

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octahedronicosahedronSaturn

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(a) Construction of Orbits (b) Order of Regular Solids Figure 4.6 Kepler’s Theory of Planetary Distances Using the Five Regular Solids (a) Kepler tried to show that the relative planetary distances as measured by Copernicus were determined by fitting the five regular solids between the six known planetary orbits in such a way that a given orbit is incribed within one solid and circumscribed about the next (shown here in a two- dimensional analog to Kepler’s three-dimensional model). (b) He found a “pretty good fit” to the measured planetary distances by arranging the solids in the order shown, starting with the octahedron between Mercury and Venus, followed by the icosa-hedron, dodecahedron, tetrahedron and cube in order of increasing distances.


circular orbit differed by 8 minutes of arc from Tycho’s observed positions. This was less than the 10-minute accuracy of the Greeks, but he could not ignore it in relation to Tycho’s maximum ob-servational error of about 2 minutes. In his As-tronomia Nova (1609) Kepler wrote:

Since divine kindness granted us Tycho Brahe, the most diligent observer, by whose observations an error of eight minutes in the case of Mars is brought to light in this Ptolemaic calculation, it is fitting that we recognize and honor this favor of God with gratitude of mind.... But as it is, because they could not be ignored, these eight min-utes alone have prepared the way for re-shaping the whole of astronomy, and they are the material which is made into a great part of this work.

In addition to this small error, the observed po-sitions of Mars perpendicular to the ecliptic (latitude) diverged even more widely from his theory, leading him finally to abandon the equant model and its assumption of circular motions. He would now have to start afresh with Mars to determine the shape of its orbit and the variations in its speed. Since Tycho made his observations of Mars from a moving Earth, Kepler set out to de-termine more accurately the shape and timetable of the Earth’s orbit. In the process he discovered that the orbits of the planets were in planes passing through the Sun at small inclinations relative to the orbit of the Earth, eliminating the need for a separate explanation for the motion of the planets above and below the ecliptic. From the known positions of the Earth about the Sun, he was able to show from Tycho’s somewhat limited data that the positions of Mars did not fit a circular orbit.. While studying the changing speed of Mars, Kepler made the unexpected discovery that a line drawn from the Sun to the moving planet sweeps out equal areas in equal times (Figure 4.7). Since Mars, like the Earth, moves faster when nearer the Sun, it moves further in a given time than when it is more distant from the Sun, but the resulting sectors swept by a line from the Sun to the moving planet have the same area.

Kepler continued with his analysis to find the shape of the orbit. After establishing some points on the orbit of Mars, he was able to see “...that the planet’s path is not a circle–it curves inward on both sides and outward again at opposite ends. Such a curve is called an oval.” For many months he tried to identify what type of oval the orbit formed, but finally showed that it had the shape of an ellipse as first described about 230 BCE by Apollonius. On such an orbit the sum of the distances from the planet to each of two focal points remains constant. Kepler also showed that the Sun lies at one focus of its elliptical orbit, with empty space at the other (Figure 4.7). The two foci lie on the longer or major axis of the ellipse, equidistant from the center and perpendicular to the shorter or minor axis. When the two foci converge to a single point, the ellipse becomes a circle with major and minor axes of equal length. Even in the case of Mars, with its greater than usual eccentricity, the axes differ by less than one percent. By rejecting epicycles and respecting Tycho’s empirical results, Kepler had finally bro-ken the spell of the circle. Instead of imposing forms upon nature, he sought to discover observ-able patterns that could be described by simple mathematical laws. The law of elliptical orbits is now called Kepler’s first law, even though he dis-covered it after the law of equal areas, now called the second law. “Elliptical orbits with the Sun at one focus” replaced Plato’s ideal of the circle, making the eccentric irrelevant. “Equal areas swept out in equal times” replaced Plato’s ideal of uniform planetary speed, making the equant un-necessary. Ten more years would pass before a third law would emerge from his study of musical harmony applied to planetary motion. Harmony of the Universe Kepler’s years in Prague came to an end in 1612 after his patron Rudolph II was declared insane and died. At the urging of his wife, he took a teaching position in Linz, Austria. His wife and son died in an epidemic before his departure. At Linz he remarried and his wife, 17 years his junior, bore him seven children, four of whom survived. He also returned to his earlier obsession with the


relationships among the various planetary orbits, guided by the Pythagorean idea of the “Harmony of the Spheres” based on musical ratios (1:2 for an octave, 2:3 for a fifth, etc.). The planetary distances derived from the five regular solids did not correlate with elliptical orbits and agreed more poorly with Tycho’s data, so Kepler came to see them as only approximations of the divine architecture. In his Harmonice Mundi (1619), Kepler discussed harmonic ratios in great detail. He then tried to find such ratios between the greatest and smallest distances of the planets from the Sun, and in their fastest and slowest speeds, often using musical notation to represent these variations. This led him to seek a relationship between the average radii (R = semi-major axis) of the planets and their average speeds or periods (T = time for one revolution) of their orbits. His search was amply

rewarded in 1618 with the discovery of a constant ratio T2/R3 = k, with each planet having the same value for Kepler’s constant k. The third law can be stated in words as, “The squares of the orbital periods for each planet are proportional to the cubes of their average distances from the Sun,” or in symbols as T2 = kR3, completing the celestial harmony. It is possible to summarize Kepler’s planetary laws as follows:

Law I. The planets move in elliptical orbits with the Sun at one focus.

Law II. A line from the Sun to a planet sweeps out equal areas in equal times.

Law III. The square of the period of each planet is proportional to the cube of its average orbital radius.

Although Kepler never achieved an actual music of the spheres, he certainly demonstrated the

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Figure 4.7 Kepler’s Three Laws of the Planets in the Copernican System Kepler discovered three important laws of planetary motion for the “heliocentric” system: I. Each planet travels in elliptical orbits with the Sun at one focus, the other being empty. II. The line from the Sun to each planet sweeps out equal areas A in equal times. III. The orbital period T is related to the average orbital radius R of each planet by T² = kR³. An ellipse is defined as the curve along which the sum of the distances R1 and R2 from two focal points to any point on the curve is constant. The law of equal areas shows that the planets have maximum velocity at perihelion (nearest point to the Sun), and minimum velocity at aphelion (furthest point from the Sun). In an elliptical orbit the average radius R = (R1+R2)/2 is equal to the semi-major axis a of the ellipse.


Pythagorean belief that the universe is based on numbers. His empirical laws accurately describe the shapes and speeds of the planets and their positions at any time. The third law relates all the planets by a single numerical constant. If T is in years and R is in astronomical units (T = 1 yr and R = 1 AU for the Earth) then Kepler’s constant has the value of k = 1 yr2/AU3 for all the planets. Thus for Jupiter with T = 11.87 years and R = 5.2AU, squaring T gives T2 = 141 and cubing R gives R3 = 141, and their ratio is k = 1. Though he despaired that his work might have to “wait a century for a reader, as God has waited six thousand years for a witness,” it was only some 50 years later that Newton would use them as the basis for a complete explanation of the heliocentric system. In 1621 Kepler published his Epitome Astronomiae Copernicanae, in which he suggested that the Sun rotates and carries the planets along by its anima motrix, adding that it would be better “if the word soul (anima) is replaced by force (vis).” He also suggested that the Sun exerts mag-netic forces of attraction and repulsion on the Earth’s magnetic poles, causing its non-circular orbit. This idea came from a careful reading of De Magnete, published in 1600 by William Gilbert (1544-1603), who had suggested that the Earth’s “magnetic soul” is the cause of its rotation, though not committing himself on its orbital motion. Both Gilbert’s magnetism and Kepler’s anima motrix tend toward the kind of occult forces typical of Renaissance naturalism. Gilbert rejected daily revolution of the stars since they were at “immeasurable” distances and “there can be no movement of infinity.” Although Kepler was the first to attempt a mechanical explanation of planetary motions, even suggesting that “the celestial machine is not so much a divine organism but rather a clockwork,” he did not reject his Neoplatonic and theological tendencies. He based his theories on a sacred foundation that compared the Sun with God the Father, source of light and power; the fixed stars stood for God the Son; and the all-pervading force of the Sun in the space between was the Holy Spirit. Because the world is a symbolic expression of the Triune God, embodying in its structure a mathematical order and harmony, Kepler rejected

infinite space. He believed that order and harmony cannot be found in an infinite and therefore formless universe. Thus he retains the celestial sphere, even though he allows for stellar changes based on his observation of the nova of 1604 in the constellation Ophiucus (Serpentarius). It is re-markable that Kepler’s star and Tycho’s star (both were supernovae) appeared so near in time. While Kepler was working out his har-mony of the heavens, he was experiencing any-thing but harmony on Earth. In the persecutions of the Counter-Reformation, he was attacked and his library was locked and sealed. His mother’s use of various herbal remedies led to an accusation of witchcraft by a neighbor, who became ill after drinking one of her potions. After trials and imprisonments, Kepler finally secured her acquit-tal and release. In 1627 he published the Rudol-phine Tables, in honor of Rudolph II, containing the positions of 1005 stars and rules for predicting planetary positions. These remained the most accurate astronomical tables available for over a century. In his calculations he made the first im-portant use of the newly invented logarithms of John Napier (1550-1617), appending a table of logarithms to his work. Kepler died three years later on a trip to recover one of the many debts owed to him by former employers. 4. COPERNICAN APPLICATIONS: VISIONS OF INFINITY Galileo and the Telescope Among the many scientists with whom Kepler corresponded, the best known is Galileo Galilei (1564-1642). He shared many of Kepler’s heliocentric views, but never endorsed elliptical orbits. Galileo is often portrayed as the first mod-ern scientist, yet he retained a strong commitment to the Platonic emphasis on circles. He preferred the mathematics of Euclid and Archimedes to the more qualitative approach of Aristotle, but sup-ported his mathematical theories with experiment and recognized the importance of observations. He used the telescope and his study of motion to support the Copernican system, but was unable to provide definitive evidence or an adequate expla-nation for the motion of the Earth. His work led to


a wider acceptance of the heliocentric system, providing a basis for the laws of Newton that fi-nally explained it. Galileo was born at Pisa, in northern It-aly, in the same year that Michelangelo died and Shakespeare was born. His father, Vincenzo Galilei, was a musician from Florence whose book, Dialogue of Ancient and Modern Music, was used by Kepler in his study of Pythagorean harmonies. In 1581 Galileo went to the University of Pisa to study medicine, but after four years he lost interest in medicine and dropped out. At home he studied Latin poetry and Greek mathematics with a tutor who introduced him to the works of Archimedes. In 1586 he published a booklet on the design of a hydrostatic balance. This led to a recommendation from a family friend for an appointment at the University of Pisa, and in 1589 he became professor of mathematics without a university degree. Friction with Scholastic colleagues led him to resign after three years. In 1592 Galileo obtained an appointment to the chair of mathematics at the University of Padua in the Republic of Venice, where he re-mained for 18 years. During these years he wrote De Motu (On Motion), which included the usual criticisms of Aristotle and unsuccessful efforts to apply the impetus concept of Buridan to falling bodies. His work differed from that of the impetus theorists in his emphasis on experiments, leading him to try to develop a mathematical description of accelerated motion. His interest in the Copernican theory was first expressed publically in a lecture on the new star of 1604, but did not appear in print until 1613 in his Letters on Sunspots. Galileo interrupted his work on motion in July of 1609, when word reached Venice about a magnifying tube made with a combination of lenses by a Dutch lens grinder. Hans Lippershey of Middleburg submitted a petition for patent of such an instrument, devised a few years earlier, to the States General of the Netherlands on October 2, 1608, but they rejected his petition due to con-flicting claims. As the device spread through Europe, it was put to use as a spyglass for com-merce and warfare. Upon hearing these reports, Galileo ground lenses and tried several arrangements before succeeding with a com-

bination of a concave and a convex lens to magnify objects. Galileo’s first telescope had a magnifica-tion of about three, but he soon improved his design to give a magnifying power of about thirty. When he presented one of his telescopes to the Venetian Senate in August of 1609, they renewed his professorship for life and doubled his salary. In the meantime, Kepler borrowed a telescope and worked out the geometry of image formation by two lenses in his Dioptrice of 1611, founding the modern science of optics. Kepler also used al-Haytham’s intromission theory of vision to show how the eye focuses inverted images onto the ret-ina. Ten years later (1621) the Dutch mathema-tician Willebrord Snell (1580-1626) discovered the law of refraction for the bending of light passing from one medium to another. The importance of Galileo’s telescope was not in its construction or terrestrial applica-tions, but in his use of it to look beyond the Earth to the heavens, opening up new vistas of space. Few of his contemporaries recognized how valu-able this would be for astronomy, and many doubted the validity of the device compared to direct vision. It could even be argued at the time that spying on God’s heavens was presumptuous, and perhaps even blasphemous. The celestial spheres were too majestic to submit them to such dubious scrutiny. Galileo himself spent many hours testing his telescopes for reliability. The English astronomer and navigator Thomas Harriot (ca. 1560-1621) made a similar effort, viewing the Moon during the summer of 1609. Galileo had no easy time trying to per-suade others of the value of the telescope for astronomy. The eminent Aristotelian Cesare Cremonini would not waste his time just to see what “no one but Galileo has seen...and besides, looking through those spectacles gives me a head-ache.” A colleague reported that Galileo went to Bologna to demonstrate his telescope, “with which he saw four feigned planets...but I tested this instrument of Galileo’s in a thousand ways, both on things here below and on those above. Below it works wonderfully; in the sky it deceives one, as some fixed stars are seen double.” The famous Jesuit astronomer Christopher Clavius (1537-


1612) said that he too could show the pretended four moons of Jupiter if he were allowed “first to build them into some glasses,” though he later was one of the first to confirm their existence. Galileo’s Telescopic Discoveries When Galileo turned his telescope heavenward, his amazement led him to quickly publish a description of his observations, inti-mating that he invented the telescope. The result was a 60-page booklet called the Sidereus Nuncius (Starry Messenger) published in March of 1610. The Moon appeared to be full of craters, valleys, and even dark areas that he thought were water (later named maria, or seas). Characteristically, he measured the heights of lunar mountains from the distances of their illuminated peaks into the dark half of the half-moon, finding them to be as high as mountains on the Earth. These Earth-like features of the Moon contradicted the Aristotelian view of celestial perfection, which assumed that the Moon was a per-fectly smooth sphere. Galileo also suggested that the visibility of the “old Moon” was due to reflected Sunlight from the Earth. This “Earth-shine” would make the Earth appear bright like a planet, contrary to arguments against Copernican theory that the dark Earth was unlike the planets. When Galileo looked at the Milky Way, he was able to show that Aristotle was wrong again in assuming that it consisted of “celestial exhalations.” His observations revealed that, “The Galaxy is nothing else but a mass of innumerable stars planted together in clusters.” In the vicinity of the Pleiades, he reported more than forty stars in addition to the six or seven that are visible. He also noted with the telescope that stars do not have round discs like the planets and “are never seen to increase their dimensions in the same proportions in which other objects, and the Moon itself, increase in size.” This implied that stars are at indeterminate distances without necessarily being much larger than our Sun, answering Tycho’s ob-jections as well as the lack of observable stellar parallax. Perhaps the universe was even infinite.

Galileo’s most dramatic discovery in-volved the four largest moons of Jupiter. On January 7, 1610, he noticed that,

beside the planet there were three starlets, small indeed, but very bright. Though I be-lieved them to be among the host of fixed stars, they aroused my curiosity somewhat by appearing to lie in an exact straight line, parallel to the ecliptic...

On subsequent evenings he observed that they were still aligned, but in different arrangements relative to Jupiter (Figure 4.8). On January 13 he saw all four and concluded that they were all revolving around Jupiter in the same plane, but at different distances and periods, which he also determined. The Earth was not the only center of motion in the universe! Surely, Galileo argued, if four moons can keep pace with Jupiter in its orbit, then our one Moon circling a moving Earth in a heliocentric system is not so unreasonable.

*

*

* *January 7

* * *January 8

* * *January 13

* *January 11

Figure 4.8 Galileo’s Discovery of Moons of Jupiter Observations made by Galileo in his discovery of the four largest moons of Jupiter are shown similar to some of those he recorded. Beginning on January 7, 1610, Galileo noticed three starlets near Jupiter through his telescope and was puzzled by their apparent alignment east and west of Jupiter. The next night all three were to the right of Jupiter. On the next clear night only two were seen, the third apparently hidden by the planet. Finally on the sixth night, Galileo saw all four moons and realized that they were revolving around Jupiter in nearly a flat plane parallel to his line of sight.


These discoveries of Galileo, and his first published support of the Copernican system, led to both positive and negative reactions. Kepler, in his excitement, suggested that there should be two “planets” around Mars, six or eight around Saturn, and one each around Mercury and Venus for the correct proportions. He also showed that the periods and orbits of Jupiter’s moons fit his har-monic law (T² = kR³). The Florentine astronomer Francesco Sizzi objected that seven was the correct number of planets, corresponding to the seven days of the week, the seven “windows” in the head, and the seven metals. He argued that the four satellites “are invisible to the naked eye and therefore can have no influence on the Earth, and therefore would be useless, and therefore do not exist.” These reactions did not deter Galileo, who named the moons of Jupiter the “Medicean plan-ets,” hoping for an appointment by the Grand Duke Cosimo II de’ Medici of Florence. His efforts were rewarded in June of 1610 when Galileo gained an appointment as “Chief Mathematician of the University of Pisa and Philosopher of the Grand Duke,” without obli-gation to teach or reside at Pisa. With this sinecure, he resigned his position at Padua and moved to Florence. Responding to an invitation, he visited Rome in April of 1611, where Pope Paul V received him. The pioneer scientific society, the Accademia dei Lincei (named for the keen eyesight of the lynx), held a banquet in his honor with several theologians and philosophers among the guests. On this occasion, the Jesuits confirmed his telescopic discoveries and suggested the name “telescope,” beginning the custom of giving Greek names to scientific instruments. At Florence Galileo wrote his Letters on Sunspots, published in 1613 under the sponsorship of the Accademia dei Lincei, to which he had been elected. He first observed sunspots in 1610 by using a telescope to project an image of the Sun on a screen, concluding that the Sun was imperfect like the Moon. From the motions of these spots, he concluded that the Sun rotated with a period of about 27 days. This led to a controversy with the Jesuit astronomer Christopher Scheiner, who had also observed them but thought they were objects orbiting the Sun rather than on its surface. They

were also observed independently with the tele-scope by Thomas Harriot, and by the Dutchman Johann Fabricius, who was the first to publish his observations in 1611. In his Letters on Sunspots, Galileo re-ported on two other important observations. He described bulges on either side of Saturn that he thought were moons, not having sufficient power to resolve the rings of Saturn. He also found that Venus exhibits a full range of phases like the Moon. He communicated this to Kepler in the form of an anagram to protect the priority of his discovery, later revealing its meaning to de’ Medici: “The mother of love (Venus) emulates the shapes of Cynthia (the Moon).” This could be explained in the Copernican system, in which Ve-nus would reach gibbous phases (more than half illuminated) on the opposite side of the Sun from the Earth; but Venus could only have crescent phases in the Ptolemaic system, since its epicycle always remains between the Earth and Sun. This did not constitute a proof of the Copernican sys-tem, however, because it could also be explained in the Tychonic system without motion of the Earth (Figure 4.9). Galileo and the Church Galileo’s successes with the telescope led him into a bolder polemic for the Copernican sys-tem, bordering on propaganda. Although none of his observations provided conclusive evidence for a moving Earth, taken together they began to turn the tide toward its wider acceptance. Here he met resistance, especially from the Dominicans who adhered to the Aristotelian ideas of Thomas Aquinas. As a devout Catholic, anxious to pre-serve his orthodoxy, he began an attempt to rec-oncile the Bible with Copernican theory. Galileo’s solution was to suggest that God’s revelation is not only in Scripture, where it is often in metaphorical language (as in the hand or mouth of God), but also in nature where its interpretation is often in mathematical language. God cannot contradict himself, so when nature appears to conflict with Scripture, it requires rein-terpretation and the recognition that it often uses observational language, as in the rising and setting of the Sun.


Galileo developed his clearest expression of the relation between science and Scripture in his Letter to the Grand Duchess Christina, dedicated to the mother of the grand duke Cosimo II and published in 1615:

Holy Scripture and nature proceed alike from the Divine Word, the former as the dictate of the Holy Spirit and the latter as the faithful executrix of God’s commands. Furthermore, Scripture, adapting itself to the understanding of the common man, is wont to say many things that appear to differ from absolute truth as far as the bare meaning of the words is concerned.... It would seem, therefore, that nothing physical that sense experience sets before our eyes, or that

necessary demonstrations prove to us, should be called in question, not to say condemned, because of Biblical passages that have an apparently different meaning. Scriptural statements are not bound by rules as strict as natural events, and God is not less excellently revealed in these events than in the sacred propositions of the Bible.

Galileo insisted that Scripture does not reveal what can be known about nature by our reason and senses, quoting Cardinal Baronius that, “The intention of the Holy Ghost is to teach us how one goes to heaven, not how heaven goes.” Meanwhile, resistance to Galileo’s ideas was building, including a sermon by the Florentine Dominican Tommaso Caccini in 1614 on the topic,

Mars

Earth

CrescentVenus

MovingEarth

StationaryEarth

GibbousVenus

Mars Mars

Sun

Sun

Epicycle Gibbous Venus

Sun

Ptolemic System Copernican System Tychonic SystemAll Phases of Venus All Phases of VenusCrescent Phases only

.

Figure 4.9 The Phases of Venus in Three Planetary Systems In the geocentric Ptolemaic System, the epicycle of Venus is on a line from the Earth to the Sun, so Venus is always illuminated on the side away from the Earth and only crescent phases are possible. In the heliocentric Copernican System, the orbit of Venus carries it from between the Earth and the Sun (conjunction) to the opposite side of the Sun from the Earth (opposition), so all phases are pos-sible, including both crescent and gibbous. In the geo-heliocentric Tychonic System, Venus also moves to both sides of the Sun, so all phases are possible in this system as well. Thus Galileo’s ob-servation of the gibbous phases of Venus does not prove the Copernican System since it is also supported by the Tychonic system, but it weighs against the Ptolemaic System.


“Ye men of Galilee, why stand ye gazing up into heaven?” Playing on the name Galilei, he sug-gested that mathematics was of the devil. Although Caccini was reprimanded, the matter was referred to Cardinal Robert Bellarmine, who reiterated Augustine’s argument that the literal meaning of Scripture should be taken as correct unless the contrary was “strictly demonstrated.” Galileo thought he had found just such a demonstration for the motion of the Earth in an argument from the tides, which he erroneously believed were caused by a combination of the Earth’s daily rotation and annual revolution. With his new “proof” in hand, Galileo journeyed to Rome at the end of 1615 to defend himself. During this visit, he was unable to per-suade the Church authorities to approve his belief that the Earth moved. The matter was referred to the Holy Office with a warning to Galileo in 1616, and the idea of the moving Earth was expressly condemned. The Revolutionibus of Copernicus was placed on the Index of Prohibited Books, but Galileo and his works were spared condemnation and he was even given a certificate by Cardinal Bellarmine stating that he was not required to recant any of his theories. Some positivists have argued that Bellarmine’s view of Copernican the-ory as a scientific hypothesis was more consistent with the available empirical evidence. After the election of the Florentine Car-dinal Barberini in 1623 as Pope Urban VIII, Galileo returned to Rome where he had several audiences with the new pope and received per-mission to write about the motion of the Earth as a scientific hypothesis. During the next six years, he worked on his masterpiece, the Dialogue on the Two Chief World Systems. Supposedly an evenhanded comparison of the Copernican and Ptolemaic systems, it ended up as a highly per-suasive book in favor of the heliocentric system. To make matters worse, Galileo wrote it in ver-nacular Italian, accessible to a wide audience, in-stead of the usual scholarly Latin. Using the dialectical form of Plato, Gali-leo developed his arguments through the voices of three persons: the Aristotelian Simplicio, the Co-pernican Salviati, and the open-minded Sagredo. On the first of four days, the dialogue compares

Simplicio’s arguments on celestial perfection with telescopic evidence. The phases of Venus appear as evidence for the Copernican system without mention of the rival Tychonic system, which could also account for them (Figure 4.9). The second and third days include arguments on the rotation and revolution of the Earth, indicating the failure to detect stellar parallax as evidence for a greatly ex-panded view of stellar distances. On the fourth day, Salviati presents Galileo’s erroneous theory of the tides as his conclusive evidence. Galileo submitted his manuscript to the chief censor at Rome in 1630. After several delays and minor revisions, permission was finally granted in both Rome and in Florence, where it was published in 1632. The closing paragraph of the Dialogue included a statement suggested by Pope Urban that the Copernican theory was “neither true nor conclusive” and that no one should “limit the divine power and wisdom to one particular fancy of his own.” Unfortunately, Galileo put these words in the mouth of Simplicio, leading to the accusation that all of his views rep-resented those of the pope. Sale of the book was stopped and Galileo was summoned to Rome. In the winter of 1633, the gravely ill Galileo was carried by litter to Rome. An investi-gation of the licensing of the Dialogue had led to the discovery of an unsigned and perhaps forged memorandum of 1616, prohibiting Galileo from defending or teaching the Earth’s motion “in any way.” After trial by the Inquisition, in which he vigorously denied that he had intended to teach the truth of the heliocentric system, he was judged guilty and the Dialogue was totally forbidden. On June 22 at the age of seventy, he was required to kneel before the tribunal and recant his belief in the reality of the Copernican system. He was then sentenced to life imprisonment at his country es-tate near Florence, with no visitors allowed except by special permission. In the last years of his life, Galileo re-turned to the study of matter and motion. His eyesight failing, he had to dictate part of his Dis-courses and Demonstrations Concerning Two New Sciences, which friends smuggled out of Italy for publication by the Elzevirs at Leyden in 1638. Writing again in Italian as a Platonic dialogue, it


includes a mathematical development of the laws of free fall and projectile motion with experiments added as verification. Although he avoids direct consideration of the motion of the Earth, his con-cepts of gravity and inertia provided the basis for the work of Descartes, Huygens and Newton that finally established a mechanical explanation for the heliocentric system. His attachment to circular motion prevented him from clearly accepting an infinite universe, but in his final years of blindness he wrote: “This universe that I have extended a thousand times...has now shrunk to the narrow confines of my own body.” Responses and Reactions to Galileo’s Work Although the condemnation of Galileo inhibited science in Catholic countries, his disci-ples and followers made some important contri-butions. One of Galileo’s contemporaries, Marin Mersenne (1588-1648), spread his experimental emphasis to France. He was a Franciscan priest in the ascetic order of the Minims, whose monastery in Paris became a center of scientific life that brought together many scientists of the day. He published a French version of some of Galileo’s unpublished works without endorsing the Coper-nican system. He reported on Parisian telescope experiments and repeated measurements of the rate of free fall. In his Harmonie Universelle (1636), he refined Galileo’s correlation between the pitch of sound and the vibrational frequency of its source. He also made the first measurement of the speed of sound by timing echoes from a wall over known distances. Another contemporary of Galileo suffered a similar condemnation for trying to develop the iatrochemistry of Paracelsus. The Flemish phy-sician Jan van Helmont (1579-1644) was one of the first to use the new quantitative experimental approach in biology, showing that the increasing weight of a growing tree gains little from the soil. He also was the first to distinguish different vapors from air, giving them the name “gas” from the phonetic sound of “chaos” in Flemish. He viewed gases as a kind of union between matter and spirit, suggesting that respiration exchanges gas in the lungs. He believed in spontaneous generation, even of mice from dirty wheat, and claimed to

have used the “philosophers’ stone.” Because of the Paracelsian association with alchemy, magic and Protestantism, Catholic authorities persecuted Helmont and finally the Louvain theological fac-ulty convicted him in 1630. As a result, very few Catholics pursued the field of chemistry. Galileo’s view of science was applied to physiology and medicine by a young Englishman, William Harvey (1578-1657), who went to study at the University of Padua from 1599 to 1602 during the time Galileo taught there. After he re-turned to England, Harvey developed his theory of the general circulation of the blood, suggesting that the venous valves prevent blood flowing from the heart, and that the heart valves permitted blood to flow only from the upper chambers (auricles) to the lower chambers (ventricles). After calculating that the heart pumped a quantity of blood three times the weight of a man in one hour, Harvey concluded that the blood circulated from the heart to the arteries, then to the veins and back to the heart, even though he could not find any connection from the arteries to the veins. Harvey described his theory in De Motu Cordis et Sanguinis (On the Motions of the Heart and Blood), published in 1628. He augmented his quantitative and experimental approaches by his belief that the heart is “the Sun of the microcosm, even as the Sun in his turn might well be designated the heart of the world.” He shared Galileo’s obsession with circular motion: “I began to think whether there might not be a motion as it were in a circle, in the same way Aristotle says that the air and the rain emulate the circular motion of the superior bodies.” Although he recognized the mechanical action of the heart, he also thought that it manufactured vital spirit constituting the soul. One of the last of Galileo’s disciples, Evangelista Torricelli (1608-1647), worked on the problem of the vacuum. Galileo agreed with Scholastic thought that water was lifted by raising a piston in a pipe because a vacuum could not form between the water and the piston, but he wondered why water could be lifted only about 10 meters by a piston pump. Torricelli suggested that the weight of the air on the water outside the pump pushed it up until it was balanced by the weight of the 10-meter column of water. He demonstrated


this “sea of air” hypothesis in 1643 by filling a glass tube about one meter long with mercury and inverting it in a dish of mercury, observing that the mercury fell to a height of about 76 cm, with a vacuum presumably in the gap at the top of this “barometer” tube. The idea that air has weight suggested that it was held near the Earth by gravity and moves with it by its inertia through the vacuum of space (Figure 4.10). The vacuum received further considera-tion from Blaise Pascal (1623-1662) in France. He repeated Torricelli’s experiment with red wine in a 14-meter tube. If the gap at the top was due to vapor instead of vacuum, then the volatile wine should fall lower than water; but if it was a vac-uum, the lower-density wine should fall less than water to balance the weight of the air, as was observed. He recognized that if air has weight, it should diminish with altitude. In 1646 he engaged

his brother-in-law to climb the Puy-de-Dôme with a mercury barometer, finding that the mercury level dropped about 7 cm at a height of about one mile. Together with the invention of this altimeter concept, he suggested using the barometer to pre-dict weather after noting that a falling air pressure usually preceded stormy conditions. Pascal believed that creation was in the image of God and thus the universe was infinite, but the complexity of nature filled him with a sense of dread:

The whole visible world is only an imper-ceptible atom in the ample bosom of nature. No idea approaches it. We may enlarge our conceptions beyond all imaginable space; we only produce atoms in comparison with the reality of things. It is an infinite sphere, the centre of which is everywhere, the cir-cumference nowhere. In short it is the

Mercury

Vapor

76 cm

Weightof air

Barometer

Vacuum in Space?

Earth

Gravity Air

Sea of Air

Inertia

Figure 4.10 Torricelli’s Air Pressure Barometer and “Sea of Air” Hypothesis Torricelli introduced the “sea of air” hypothesis to explain the height of the mercury column as being balanced by the weight of the air. He used Galileo’s inertia concept to account for the motion of the sea of air with the Earth through the assumed vacuum of space, and his gravity concept to account for the weight of the air holding it around the Earth’s surface. From the height of the mercury column, the weight of the air can be determined from the equivalent weight of the mercury column of about 15 pounds on each square inch, or an air pressure of : Pair = 15 lb/in² x 144 in²/ft² = 2160 lb/ft². This is more than a ton on every square foot at sea level!


greatest sensible mark of the almighty power of God, that imagination loses itself in that thought. (Pensées 72)

Galileo’s new telescopic vision of the world troubled many in Protestant countries as well. Shortly after his Starry Messenger appeared, the English poet John Donne, who admitted that the new astronomy “may very well be true,” gave classic expression in 1611 to concerns about Copernican ideas in The First Anniversarie:

And new Philosophy calls all in doubt, The Element of fire is quite put out; The Sun is lost, and th’Earth, and no man’s

wit Can well direct him where to looke for it. And freely men confesse that this world’s

spent... ‘Tis all in peeces, all cohaerence gone; All just supply, and all Relation... And in these Constellations then arise New starres, and old doe vanish from our

eyes...

The new cosmology was also troubling to John Milton, who as a young man of thirty had visited the blind Galileo and learned about the vastness of space. Twenty five years later when he wrote Paradise Lost, Milton described the two world systems of Ptolemy and Copernicus without choosing between them. But in his epic poem, his universe remained geocentric and he warned about presumption:

...Heav’n is for thee too high To know what passes there; be lowlie wise: Think onely what concernes thee and thy

being; Dream not of other Worlds.

His warning was too late, however, and the dream of the Earth moving through boundless space would soon be established in the awakening idea of a mechanical universe. REFERENCES

Butterfield, Herbert. The Origins of Modern Sci-ence, 1300-1800. New York: Free Press, 1957.

Cohen, I. Bernard. Revolution in Science. Cam-bridge, MA: Harvard University Press, 1985.

Copernicus, Nicolaus. De Revolutionibus Orbium Celestium, 1543. trans. E. Rosen. Baltimore: Johns Hopkins University Press, 1978.

Galileo, Galilei. Dialogue Concerning the Two Chief World Systems, 1632. trans. S. Drake. Berkeley: University of California Press, 1967.

Gade, J. A. The Life and Times of Tycho Brahe. Princeton: Princeton University Press, 1947.

Gingerich, Owen, ed. The Nature of Scientific Discovery: A Symposium Commemorating the 500th Anniversary of the Birth of Nicolaus Copernicus. Washington, D.C.: Smithsonian Institution Press, 1975.

Gingerich, Owen. The Book Nobody Read: Chas-ing the Revolutions of Nicolaus Copernicus. New York: Penguin Books, 2005.

Hall, A. R. The Scientific Revolution 1500-1800: The Formation of the Modern Scientific Attitude. 2nd ed. Boston: Beacon Press, 1962.

Kepler, Johannes. The Harmonies of the World, Book 5, 1619. In Great Books of the Western World, vol. 16. Chicago: Encyclopedia Britan-nica, 1952.

Koestler, Arthur. The Sleepwalkers: A History of Man’s Changing Vision of the Universe. New York: Macmillan, 1959.

Koyré, Alexandre. From the Closed World to the Infinite Universe. Baltimore: Johns Hopkins University Press, 1957.

Koyré, Alexandre. The Astronomical Revolution; Copernicus-Kepler-Borelli, trans. R. E. W. Maddison. Ithaca, N.Y.: Cornell University Press, 1973.

Kuhn, Thomas S. The Copernican Revolution. New York: Vintage, 1957.

Lindberg, David C. and Numbers, Ronald L. eds. God and Nature: Historical Essays on the Encounter between Christianity and Science. Berkeley: University of California Press, 1986.

Sobel, Dava. Galileo's Daughter: A Historical Memoir of Science, Faith, and Love. New York: Walker Publishing, 1999.

Westman, Robert S., ed. The Copernican Achieve-ment. Berkeley: University of California Press, 1975.

95

1. GALILEO AND MECHANICAL IDEAS The Scientific Revolution of the seven-teenth century emerged from the development of a mathematical physics confirmed by empirical methods that could explain motion in the Coper-nican system. From Kepler’s laws of the planets to Galileo’s analysis of projectile motion, to Huy-gen’s formula for centrifugal force and Newton’s law of universal gravitation, the tools of mathe-matics and measurement proved to be increasingly successful. The application of mathematical methods to the physical world was a reassertion of Platonic idealism over the qualitative realism of Aristotle that had dominated natural philosophy for 300 years. Although Plato’s eternal ideas were only imperfectly embodied in physical things, they could be represented by a mathematical descrip-tion that reduced physical reality to quantities and shapes. Aristotle rejected Plato’s mathematical emphasis because natural things changed as a result of inherent tendencies that do not easily reduce to mathematics. In replacing this Aristo-telian conception with a mathematical approach, the mystical ideas of Plato’s Timaeus faded in favor of a mechanistic conception of nature based on the assumption that matter is passive, possess-

ing no active internal forces. Matter had only the passive qualities of size, shape and impenetrabil-ity, and motion was explained by inertia and im-pact rather than by inherent tendencies. Nature now appeared as a collection of inert material par-ticles controlled by external laws. This new view of nature as a machine began to replace Aristotle’s conception of nature as an organic being. Free Fall and Gravity After his condemnation, Galileo returned to the study of motion that dominated his early career, now applying the mathematical methods of Archimedes. Even as a student at the University of Pisa, his interest in motion was evident in his observations of a swinging chandelier in the cathedral of Pisa. Using his pulse rate for timing, he noticed that the period of the swing did not change when the amplitude of the swing increased with the wind. Further experiments with a pendu-lum confirmed this result, at least for small oscil-lations, and also showed that the period of oscil-lation changed in proportion to the square root of the length of the pendulum. However, changing the weight of a pendulum with fixed length did not change its period, providing a clue that the rate of free fall was independent of the weight of a falling body.

CHAPTER 5

A Mechanical Universe

The Scientific Revolution and Newtonian Synthesis

Chapter 5 • A Mechanical Universe 96

Galileo’s study of free fall began early in his career, though not in the way suggested by the legend of dropping different weights from the Leaning Tower of Pisa. Such an experiment was reported in 1586 by the Dutch scientist Simon Stevin (1548-1620), in which he simultaneously dropped two lead balls of differing weights from a height of 30 feet onto a board, and heard no per-ceptible difference when they hit the board. Galileo began with a criticism of Aris-totle’s distinction between light and heavy bodies according to their natural tendencies to rise or fall. Following Archimedes, he recognized that heavy bodies that fall in air may rise in water, and he agreed with his predecessor at Pisa, Giovanni Benedetti (1530-1590), that bodies of the same material falling in a vacuum would have the same speed. Later he argued that the difference in speed of falling bodies of differing materials would be less with decreasing density of the medium in which they fall, and that in a vacuum all bodies would fall at the same rate inde-pendent of their weight or material. Under the influence of impetus theory, Galileo had as-sumed that the speed of free fall is proportional to the distance fallen. Later he abandoned im-petus theory at Padua and began to develop the idea that the speed of a falling object is pro-portional to the time of fall, giving a uniformly increasing speed. In Discourses and Dem-onstrations Concerning Two New Sciences (1638), Galileo used a graphical analysis like that introduced by Nicole Oresme (ca. 1320-82) to repre-sent uniformly increasing veloc-ity by the increasing height of a triangle to time t along its base.

This constant rate of change from rest to velocity v corresponds to a constant acceleration a = v/t as the dynamic principle of free fall (Figure 5.1). Thus, in modern notation, the uniformly increasing velocity of a body accelerating from rest is given by v = at. Like Oresme, Galileo used this idea to show that during any time t in which an object reaches velocity v = at, the average velocity would be v/2. The distance d of motion in a time t is then the area under the graph, or

d = v×t /2 = (at)×t/2 = at²/2.

Applied to free fall, this law is independent of

Graph of Velocity vs. Time on an Inclined Plane

d = 1t = 1

d = 4t = 2

d = 9t = 3

3

5

7

d = at²/2

1s 2s 3s 4s

v

t

v = at

1 d = 1+3 = 4 d = 4+5 = 9 d = 9+7 = 160

2

4

6

v = 2v = 4

v = 6

Figure 5.1 Galileo’s Analysis of Motion on an Inclined Plane Using a graphical representation, Galileo assumed that uniformly increasing velocity v = at with a constant acceleration a applies to the motion of a ball rolling down an inclined plane under the in-fluence of gravity. From the mean-speed rule, the average velocity is half the final velocity (v/2) so the distance at any time t is

d = vt /2 = (at)t /2 = at²/2 . Since vt /2 is the area under the graph to time t, the distance after successive units of time is the sum of odd numbers 1, 3 ,5 ,7,... up to that time, or d = 1, 4, 9, 16,... = 1², 2², 3², 4²,... as predicted and subsequently confirmed by experiment. Thus in this case, d in feet and t in seconds gives a constant acceleration:

a = 2d /t² = 2.1/1² = 2.4/2² = 2.9/3² = 2.16/4² = 2 ft/s².


weight as suggested by Galileo, at least in a vacuum. It describes gravity in terms of a constant acceleration, rather than as something acting on a body. Galileo differs from his scholastic predecessors in applying this law to a real physical motion. To test the law of constant acceleration, Galileo slowed the effect of gravity by rolling balls down inclined planes. He could predict that if a ball rolled one foot in the first second, then in the time intervals t = 1, 2, 3, 4, 5,...sec, the distances traversed would be d = 1, 4, 9, 16, 25,...ft, which are the squares of the corresponding time intervals. His experimental results agreed “roughly” with these values, confirming the law of constant acceleration on an inclined plane. Using the above distances and times, Galileo’s law gives a constant acceleration of

a = 2d/t² = 2 ft/s².

In free fall, distance d is vertical and can be desig-nated by a y-coordinate with a = g for the acceler-ation of gravity, giving Galileo’s law as:

y = gt²/2.

Measurements give a value for gravitational acceleration of g = 32 ft/s², or in metric units g = 9.8 m/s². Projectile Motion and Inertia Galileo applied his law of free fall to the motion of a projectile to show that it would move along a parabolic path (Figure 5.2). He assumed that the vertical motion of a cannon ball would have the acceleration g of free fall, independent of its horizontal motion. He considered a ball rolling on a horizontal surface as the limiting case of an “inclined plane” when it has zero slope, and thus the acceleration is zero, or con-stant velocity, in the idealized case of frictionless motion.

Calling this constant horizontal motion inertia, Galileo tried to explain it as equivalent to constant circular motion in the heavens, since horizontal motion is along the horizon or circle of the Earth’s circumference. A projectile whose horizontal distance increases uniformly (constant horizontal velocity vx) while its vertical distance changes with the square of the time (constant vertical acceleration g) has coordinates at any time given by:

x = vxt and y = gt²/2,

which combine with t = x/vx in the equation for y to give the equation of a parabola:

y = gx²/2vx² = cx²,

where the constants g/2vx² = c. Using geometric reasoning, Galileo showed that the angle of a cannon barrel that will give the projectile its maximum range is 45° above the horizontal. This agreed with the observations of Niccolo Tartaglia in 1537, but now could be explained by Galileo “without need of recourse to experiments” from the principles of inertia

20 40 60

4.9

19.6

44.1

x = 20 t

y = 4.9 t²

y(m)

x(m) 0

Horizontal and Vertical Positions of Projectile and Free Fall

t = 1s

t = 2s

t = 3s

0v = 20x

v = gty

parabolicpath y = cx²

Figure 5.2 Galileo’s Concepts of Projectile Motion and Free Fall A constant horizontal velocity (vx = 20 m/s shown here) due to inertia and a constant vertical acceleration (g = 9.8 m/s²) due to gravity combine to produce a parabolic path (y = 4.9 x²). The vertical positions of the projectile match those of an object in free fall as shown during the first 3 seconds.


(constant vx) and gravity (constant g):

The knowledge of a single fact acquired through a discovery of its causes, prepares the mind to understand and ascertain other facts, without need of recourse to experi-ments, precisely as in the present case, where by argumentation alone the author proves with certainty that the maximum range occurs when the elevation is 45 de-grees.

Galileo’s recognition that theoretical predictions of phenomena could provide an explanation of those phenomena, and experimental discovery of the predicted facts could verify that explanation, marked the maturing of the mathematical-experimental method of science. In his Dialogues Concerning the Two Chief World Systems (1632), Galileo used his “circular” inertia concept to illustrate the possibil-ity of a moving Earth without noticeable effects on its inhabitants. In the case of a ship moving with constant velocity at sea, observers on the ship would have no way to detect their motion. Ac-cording to Galileo, if an object falls from the top of the mast it would fall to the base of the mast, contrary to the Aristotelian answer provided by Simplicio that it would fall behind the mast. The falling body has an obvious vertical motion, but an undetected horizontal motion since it is shared by the ship and its observers. In the same way, observers on a moving Earth will see the vertical component in the motion of a falling body, but will not detect its inertial motion with the Earth since they share in it. Furthermore, Galileo explains the rotational motions of the Earth in a Copernican universe as the result of circular inertia, rejecting Kepler’s discovery of elliptical orbits. Gassendi’s Revival of Atomism In trying to develop a mathematical basis for mechanics in The Assayer (Saggiatore, 1623), Galileo drew upon the distinction made by the Greek atomists between qualities inherent in ob-jects and those produced by them. Inherent qualities, such as size, shape and speed, were quantifiable and thus could be used in a mathematical description of the reality behind

experience. Other qualities, such as taste, color, heat and sound, were produced in the observer by the activity of bits of matter impinging on the sense organs. This radical distinction between what Robert Boyle later called primary and secondary qualities became the cornerstone of mechanistic science. The rediscovery in 1417 of the great Latin poem De Rerum Natura of Lucretius, based on the atomism of Epicurus, led to increasing interest in atomism as an alternative to Aristotelian physics. For the ancient Greeks, atoms were not created, but eternal and subject to chance. Rationality and purpose appeared to be impossible in a world of randomness and materialism. The revival of atomism in Christian Europe required the idea of God as a cosmic lawgiver who imposed laws on the atoms to create an orderly and purposeful universe. This idea made it possible to establish a mechanical world view consistent with Christian thinking. In reacting against Scholastic philosophy, as well as alchemy, the French Catholic priest Pierre Gassendi (1592-1655) recognized in atomism the possibility of a thoroughly mechani-cal philosophy of nature. But he also was aware of the atheistic implications of atomism, so from about 1625 he began to develop a Christian ver-sion of atomism cleansed of atheism. For example, he assumed only a finite number of atoms in the universe, since he believed that the providence of God is inconsistent with a universe in which an infinite number of atoms would allow everything possible to happen. His Philosophiae Epicuri Syntagma (1649) recognized the existence of a vacuum, demonstrated five years earlier by Tor-ricelli, but rejected the Epicurean claim that mo-tion was inherent in matter. By introducing God as the source of motion, he helped to maintain the Christian view of the dependence of nature on God. Gassendi’s universe could be described by nothing more than the size, arrangement, shape, and motion of invisible and impenetrable atoms moving in an infinite void. God impressed motion on the atoms in the beginning and continues as a “moving urge,” rectilinear and indestructible except when acted upon by collisions with other


atoms. Gassendi made no greater attempt than Galileo had to explain how atoms cause sensible effects, but he believed that only such effects could be observed, leading to a strict empiricism. He especially opposed occult causes and effects, but believed that the order and harmony of the uni-verse demonstrated God’s goodness and purpose in nature. Borelli’s Development of Mechanics Another follower of Galileo was Giovanni Borelli (1608-1679), who began his ca-reer as a professor of mathematics at the Univer-sity of Pisa. He later befriended Galileo in Florence, where he participated in the Accademia del Cimento (Academy for Experiment) before leaving Tuscany. Borelli corrected Galileo’s con-servative emphasis on circles by publicizing Kepler’s elliptical orbits. He disguised his Copernican treatise, Theoricae Mediceorum Planetareum (1666) as a study of the satellites of Jupiter to avoid censure by the church. Borelli added to Kepler’s idea of a tan-gential force by the Sun on the planets, suggesting that the Sun also exerts an attractive force on the planets. He taught that Jupiter exerts a similar force on its satellites, as later developed by New-ton. He also suggested that the seemingly erratic behavior of comets might be the result of parabolic orbits, allowing them to pass around the Sun once and then recede into space forever. Borelli also applied the mechanical con-cepts of Galileo to biology, and became a founder of “iatrophysics” by applying physics to medicine. In a two-volume book published after his death entitled De Motu Animalium (On the Movement of Animals), Borelli explained muscular action by treating bones as levers acted upon by the pulling force of the muscles. He showed how the same laws of physics that governed the movement of the arms and legs also governed the wings of birds and the fins of fishes. In his second volume, Borelli applied mechanical laws to the movements of the muscles of the heart and to the process of respiration in the lungs. Carrying mechanical principles too far, he suggested that the stomach was a grinding device. His contemporary, the Flemish physician Francis-

cus Sylvius (1614-1672), followed the ideas of Paracelsus in showing that digestion was a chemi-cal process. 2. SCIENTIFIC PHILOSOPHIES AND SOCIETIES Bacon’s Empiricist Philosophy In England the new emphasis on experi-ment and observation began to mature with the appearance of William Gilbert’s (1544-1603) pio-neering book De Magnete (1600). Gilbert was president of the College of Physicians of London and became court physician to Queen Elizabeth I in 1601. He rejected much of scholasticism and favored a union between the craft tradition and scholarly knowledge. By his experiments he refuted many superstitions, but in his study of attractive forces he speculated that the movement of a lodestone was analogous to the soul in a body, and that the great magnet of the Earth “turns her-self about by magnetic and primary virtue,” which some viewed as an “occult” explanation. Among the first to recognize the histori-cal significance and importance of scientific experimentation and applications was Francis Bacon (1561-1626), who became Attorney Gen-eral and then Lord Chancellor of England under James I. More a philosopher than a scientist, he argued against mysticism and magic in his first book, The Advancement of Learning (1605), and recommended study of the “book of nature” by the methods of direct observation and experiment. His influential analysis of scientific method appeared in 1620 with the title Novum Organum (New Instrument), in contrast to Aristotle’s Organon with its emphasis on deductive reasoning in science. Bacon argued for the method of induction in science, which induces the laws of nature as generalizations from a large number of specific observations. Well-planned experiments can shed light on true causes if they proceed carefully from particulars to general laws. He contrasted the growth of the mechanical arts and crafts with the decline of rationalistic philosophy:

The best explanation of these opposite for-tunes is that, in the mechanical arts, the tal-


ents of many individuals combine to pro-duce a single result, but in philosophy one individual talent destroys many... For when philosophy is severed from its roots in ex-perience, whence it first sprouted and grew, it becomes a dead thing.

Bacon recognized that collecting data must not be haphazard. Observation and experimentation should be organized in a systematic way. His opposition to merely heaping up experimental data is evident in his famous parable of the ant, spider and bee:

The men of experiment are like the ant; they only collect and use; the reasoners resemble spiders, who make cobwebs out of their own substance. But the bee takes a middle course, it gathers its material from the flowers of the garden and of the field, but transforms and digests it by a power of its own.

Like the bee, the scientist must be both industrious and imaginative to be truly creative and effective. Bacon’s method depended on collecting a large body of facts. He thought that an encyclo-pedia about six times as large as Pliny’s monu-mental Natural History (37 books) might suffice to explain all natural phenomena. Study of a given phenomenon should begin by classifying together all facts relating to it, including a list of “positive instances” involving the phenomenon, a list of “negative instances” where it was absent, and “degrees of comparison” to indicate variations. Scientific knowledge could then be obtained from such lists by inducing hypotheses, excluding the weaker ones and testing further the stronger ones. Not surprisingly, he did not think there was sufficient evidence for either the Copernican or the Ptolemaic system, but favored the Tychonic system since it required neither a moving Earth nor epicycle complexities. Bacon illustrated his method with the example of heat, in which positive instances included the Sun’s rays, putrefaction, and flames. Negative instances included the Moon’s rays, air, and water, while degrees of comparison included the variation of animal heat with exercise, or fric-

tional heat with the speed of rubbing. In this way he reached the hypothesis that motion hidden beneath the surface of phenomena produced the sensations of heat. He believed that this invisible level was atomic in nature and that heat was a motion of particles. Ironically, one of his few actual experiments was an impulsive act of stuff-ing a chicken with snow to see if it would delay putrefaction, which led to a chill and fever that ended in his death. Bacon emphasized that knowledge should be “for the glory of the Creator and the relief of man’s estate.” One year after he died, Bacon’s ideas about organizing and applying science appeared in his posthumous book The New Atlantis (1627). In this utopian version of science, he described an organization of scholars called the “House of Salomon.” A team of these scholars was responsible to gather information and collect books, study these books and report on developments in the mechanical and liberal arts. Another team was to perform experiments, record and classify their results, and try to draw practical conclusions. A final team would devise new experiments from these results, and formulate the most general laws about nature. These ideas about organizing scientific research had considerable influence on the later development of scientific societies, especially the Royal Society. Descartes and Mechanistic Philosophy The French philosopher and mathemati-cian, René Descartes (1596-1650) developed a contrasting approach to science. Like Bacon, Descartes was not a professional scientist, but his ideas were equally influential, especially on the continent. Both tried to eliminate magical prin-ciples and occult tendencies from science. But while Bacon was a lawyer who believed in evi-dence, Descartes was a mathematician who believed in reasoning. He thought that science was like geometry, in which Euclid’s axioms seemed to stem from innate ideas that could be used to deduce the structure of geometry. Thus science could begin with a few “clear and simple ideas” that would lead by a process of deduction, with only a minimum of observations, to an un-derstanding of the structure of the universe.


Descartes was educated by the Jesuits in ancient languages, scholastic philosophy and mathematics. Only in the latter study did he find the clarity and certainty that he desired, so he left school in 1612 to travel and think, including a period of military service and three years in Paris with scientific friends. In 1629 he withdrew to Holland to prepare his works, and in 1637 he published his Discourse on Method in French. It consisted of two parts: his analysis of the mathematical-deductive method of science, and an outline of his mechanical view of the physical world, expanded in 1644 into his Principia Philosophiae. In an appendix to the Discourse, Des-cartes presented his ideas on the application of algebra to geometry, thereby founding the field of analytic geometry, along with Pierre Fermat (ca 1601-65). Descartes represented equations by pairing values of x on a horizontal axis with cor-responding values of y on a vertical axis to portray geometric curves. For example, if y = x² then x = 1, 2, 3... correspond to y = 1, 4, 9... after squaring the values of x. All such points graphed on these so-called “Cartesian coordinates” will give a smooth geometric curve, in this case a parabola. In spite of this brilliant contribution, paving the way for Newton’s calculus, Descartes failed to make much use of mathematics in his mechanistic theory. In his view, mathematics did not determine the structure of the universe, but instead served as a tool for describing the mechanical forms and motions in the universe. In trying to achieve the certainty of mathematics in his mechanistic philosophy, Des-cartes began with a method of radical doubt that led him to the one thing he could not doubt, his existence as a thinker who doubts, and thus his celebrated Latin phrase “Cogito, ergo sum” (“I think, therefore I am”). This indubitable proposi-tion, clearly and distinctly perceived, led to the general rule that clear and distinct ideas can be considered as true. One such innate idea is the idea of God as a perfect and infinite being. According to Descartes, the idea of God must come from an infinite being, and hence God must exist. This is the most important link in the Cartesian chain of deductions, since God’s perfection guarantees the

validity of reason and the reliability of clear and distinct ideas. Another innate idea, supported by the belief that God does not deceive us, is the exis-tence of the external world. Descartes defined substance as objects or beings independent of our thinking. God is the only absolute substance, but there are two independent relative substances: matter defined as extended and passive substance (res extensa: extended thing), and mind defined as unextended and active substance (res cogitans: thinking thing). Inert matter as mere extension cannot move itself, and thus God is the first cause of motion:

It is wholly rational to assume that God, since in the creation of matter He imparted different motions to its parts, and preserves all matter in the same way and conditions in which He created it, so He similarly pre-serves in it the same quantity of motion.

Descartes defined “quantity of motion” as the product of mass and speed (mv = momentum) and asserts the law of conservation of motion: if one object in a collision loses mass or speed, the other will gain an equal amount so that the total quantity of motion in the world remains constant (Σmv = constant). Thus for Descartes, God is more than just a first cause, since His immutability ensures the existence of nature and its laws. In contrast with Bacon, Descartes be-lieved he could deduce the laws of nature in a mechanical universe: “Give me motion and ex-tension and I will construct the world.” He goes beyond Galileo’s “circular” inertia in stating the principle of “rectilinear” inertia: a body in un-restrained motion preserves its state of motion in a straight line, thus implying an infinite universe. The identity of matter with extension leads to the concept of a “plenum” (full), in which matter is infinitely divisible, does not permit a vacuum, and fills all of space with a subtle invisible fluid. Matter interacts only by contact, which forms rotating vortices, or whirlpools, in the plenum around celestial objects. Thus Descartes explained the Copernican universe by his vortex theory: the vortex of the Sun carries the planets with their whirling vortices


around it, the outward pressures of each being balanced by its neighbors throughout the universe. The theory could even be viewed as geocentric, if that was preferred by the Church, since the Earth was at the center of its own vortex. Matter in motion also explained the mystery of gravity: the downward pressure of subtle matter in the Earth’s vortex on larger particles. Magnetism is not the occult action of a soul, but is caused by screw-shaped particles, right-handed and left-handed for attraction and repulsion. The vortex theory pro-vided the first mechanical explanation for helio-centric planetary motion, and was preferred in France for nearly fifty years after Newton had demonstrated its inadequacy. Such a mechanistic approach seemed to cleanse science of not only the occult, but of all mystery as well. Descartes even applied his mechanistic view to biology, treating animals as machines and only humans as having a soul: a kind of “ghost in a machine” to account for rationality and immor-tality. The soul or mind consists of unextended mental substance, the active agent of thought and will. This extreme dualism separates mind and body, leaving the mind free to operate independ-ently from nature, and the body governed by mechanical principles free of vitalism, except for animal spirits carried by the blood. Genuine knowledge must come from innate ideas in the mind rather than from the senses, and nature was stripped of wonder and made independent from God. By 1650 the English philosopher Thomas Hobbes (1588-1679) went the next step by elimi-nating mind as an independent reality and devel-oped a completely materialistic philosophy. Thus Cartesian dualism tended to separate science from religion and reinforce a growing individualism, in which unextended minds had no inherent connections with other minds. Descartes suggested a point of interaction between the mind and body in the pineal gland attached to the brain, thinking that it was unique to humans. He was shown to be wrong by the Danish naturalist Nico-laus Steno (1638-1686), a Catholic convert and eventual archbishop, who discovered the pineal gland in lower animals. Steno also proposed the organic origin of fossils and methods for dating rock strata, emphasizing that “Scripture and Na-

ture agree” and the compatibility of science and religion. Boyle and Corpuscular Philosophy The Christianized atomic theory of Gas-sendi was popularized in England by Walter Charleton (1620-1707), who later became physi-cian to Charles II. Gassendi attributed the motion of atoms to God, but Charleton suggested that the motion of such inert atomic particles was a proof of the existence of God. In The Darkness of Athe-ism Refuted by the Light of Nature (1652), he argued that an atheistic atomic theory could not account for activity and order in the universe. He also published an English paraphrase of Gas-sendi’s Syntagma, entitled Physiologia Epicuro-Gassendo-Charltoniana; or, A Fabrick of Science Natural upon the Hypothesis of Atoms (1654), which became the main source of Epicurean atomic ideas in England. Applications of the atomic theory were begun in England by Robert Boyle (1627-1691), who referred to it as the “corpuscular philosophy.” Boyle, the fourteenth child of the Earl of Cork, was a child prodigy who began the study of Gali-leo’s work while traveling in Italy with a tutor in his early teens. A fierce thunderstorm in Geneva led him to make a lifelong commitment to Chris-tian faith and its relation to science. Returning to London in 1646, he began meeting with a group of scientists calling themselves the “Invisible Col-lege,” who had similar interests in the empirical methods of Bacon and the iatrochemists. Boyle felt that the best explanation of empirical observations was by a revised version of the atomic theory. Descartes had rejected atomism in his mechanical philosophy because of his view that a vacuum was impossible. Boyle’s corpuscular theory gained support from news of Otto von Guericke’s ex-periments with the vacuum produced by an air pump in Germany. While at Oxford from 1654 to 1668, Boyle engaged Robert Hooke (1635-1702) in 1657 to build an improved version of the air pump, and together they began to experiment with reduced air pressures. They showed that a ringing bell produced no sound in a vacuum and that a feather and lead ball fall at the same rate in an


evacuated jar. In his first scientific work, New Experiments Physico-Mechanical Touching the Spring of the Air and its Effects (1660), Boyle described his experiments in both physics and the physiology of respiration. By gradually exhausting the air in a jar containing a mouse and a candle, he observed the resulting expiration of the mouse at about the same time as the candle. In 1662 Boyle found the pressure-volume law known by his name. He showed that the vol-ume of a gas is inversely proportional to the ap-plied pressure by pouring mercury in a U-tube closed at one end. By increasing the column of mercury, the pressure on the air in the closed end of the tube compressed it to a volume that was inversely proportional to the pressure (V = C/P) so that their product remains constant, giving Boyle’s law as PV = constant. He explained this “spring of the air” by two corpuscular hypotheses: the particles of air were either tiny stationary springs, or they were small spherical particles in rapid random motion whose collisions produced a pres-sure that resisted compression. Although Boyle believed in the possibil-ity of the transmutation of gold, he transformed alchemy into the rational science of chemistry with the publication of his Sceptical Chymist (1661). He ridiculed the four metaphysical elements of the Greeks and the three mystical elements of the alchemists. Instead, he defined an element as an irreducible material substance that could be iden-tified only by empirical methods. He made a clear distinction between elements and compounds, the former being any substance that cannot be broken down into simpler substances, and the latter consisting of two or more elements that can be separated and then recombined to form the original compound. Boyle separated phosphorus from urine in 1680, independently identifying the first new element not already known. He was unaware that it had been discovered about ten years earlier by German alchemist Hennig Brand (ca. 1630-1710). Boyle strongly supported the Reformation thought of Luther and Calvin on the radical sov-ereignty of God, resulting in the rejection of Aris-totle’s view of intrinsic powers in nature. They viewed nature as entirely passive, subject to the command of God as the only active principle in

the world. Boyle joined in this criticism of Aris-totle’s concept of nature as a living and active being. He felt that it detracted from the honor and glory of God as Creator, ascribing to nature what belonged to God. Thus, in his corpuscular phi-losophy, material bodies were completely passive and totally dependent on God. In The Excellency and Grounds of the Mechanical Hypothesis (1674), he describes the role of God in his me-chanical philosophy:

Thus the universe being once framed by God and the laws of motion settled and all upheld by his perpetual concourse and gen-eral providence; the same philosophy teaches, that the phenomena of the world are physically produced by the mechanical properties of the parts of matter, and that they operate upon one another according to mechanical laws. ‘Tis of this kind of cor-puscular philosophy, that I speak.

But the emphasis was shifting from the Reforma-tion view of God as sovereign Redeemer to God as a sovereign Ruler of the world machine. Scientific Societies and the Puritan Ethic The Baconian ideals of experimental and institutional science began to bear fruit in the 1640s in close conjunction with Puritanism and the English Revolution (1640-1660). Robert Boyle was a leading figure in this movement, having close relations with Puritans, though himself a moderate Royalist. His group of associates in London became known as the “Invisible College” because they had no fixed meeting-place. They were influenced by the Puritan ideal of edification through mutual cooperation in groups, and believed that science could further the glory of God and the welfare of humans. One of Boyle’s first essays was a call for the free communication of useful scientific information. He was also active in a number of projects for translation of the Scriptures, including the Turkish New Testament, the Indian Bible, and the Company for the Propa-gation of the Gospel in New England. About 1645 an informal group of me-chanical philosophers in London began meeting at Gresham College in Bishopsgate, which had been


a center of experimental philosophy and the study of medicine, astronomy, and navigation since 1598, before any university existed in London. The leading spirit of this so-called “Philosophical College” was the Puritan clergyman John Wilkins (1614-1672), whose Discourse Concerning a New Planet (1640) helped to popularize the Copernican system and to harmonize it with Calvinist theology. He became Oliver Cromwell’s brother-in-law in 1656. Of the ten known members of this group, six were Puritans siding with the Parliamentarians, and only one was definitely Anglican and Royalist. Several Puritans at Oxford University were removed from their posts when Charles I occupied Oxford and made it his capital in 1642. Oxford fell to Cromwell in 1646, and two years later a number of Royalist professors were replaced by Parliamentarians, including John Wilkins and several others from the London based “Philosophical College.” After Charles I was apprehended and beheaded in 1649, Puritanism shifted from a position of opposition to one of power, with Cromwell installed as Lord Protector in 1653. The Puritan ascendancy marked the beginning of a new emphasis on academic free-dom, in which old philosophies and new scientific ideas were both allowed free expression. However, the Puritan coherence that sustained the Revolution was insufficient to support the Com-monwealth after the death of Cromwell. With the restoration of Charles II in 1660, many scientists appointed by the Commonwealth left Oxford and returned to London, which became the main center of science in England. A meeting at Gresham College in 1660 proposed the founding of a “College for the promoting of Physico-Mathematical Experimental Learning,” and elected John Wilkins as chairman. In 1662, Charles II granted a Royal Charter incorporating the group as “The Royal Society for the Improvement of Natural Knowledge,” with Wilkins as first secre-tary and Henry Oldenburg (ca 1617-1677) as sec-ond secretary. Oldenburg was a German busi-nessman with extensive European connections, who handled the Society’s correspondence and conceived the idea of publishing a scientific jour-nal. In March of 1665, the first issue of The Philosophical Transactions appeared.

Membership of the Royal Society in-creased from about one hundred at its founding in 1660 to more than two hundred in the 1670s. The first Curator of Experiments was Robert Hooke, who proposed statutes in 1663 that were pervaded by the Baconian influence and recommended “not meddling with Divinity, Metaphysics, Moralls, Politicks, Grammar, Rhetorick, or Logick.” In the religious and political atmosphere of the Restora-tion, the Puritan affiliations of many of the mem-bers of the Royal Society became problematic. Out of the 68 Fellows in 1663 for whom information is available, some 42 (62%) had strong Puritan leanings while 26 were Royalist. About the same time in Paris, Marin Mersenne (1588-1648) initiated informal scientific meetings and correspondence. The wealthy Parisian Habert de Montmor organized later meetings and formalized the Montmor Academy by a constitution in 1657 that declared its purpose to be “the clearer knowledge of the works of God, and the improvement of the conveniences of life, in the Arts and Science which seek to establish them.” When the Montmor Academy requested aid from Louis XIV’s minister, Jean Colbert, he decided to establish a new scientific society. In 1666 the Paris Académie des Sciences was founded under the patronage of the crown with twenty one members, increasing to about fifty by the end of the century. In contrast with the self-supporting amateurs of the Royal Society, the Academicians were professional scientists, several recruited from other countries, who were paid a salary by the King to work as a group on problems set by the royal ministers. 3. MECHANICAL INSTRUMENTS & IDEAS The Clock and other Contributions of Huygens One of the most important foreign mem-bers of the Paris Academy, hired by Colbert in 1666, was the Dutch scientist Christiaan Huygens (1629-1695). In 1655 he had developed a better way to grind lenses, which he used to construct more powerful telescopes. A year later he identi-fied the rings of Saturn and announced the dis-covery of a satellite of Saturn. He named it Titan,


which is Saturn’s largest moon. Another foreign member of the Paris Academy, the Italian astronomer Giovanni Cassini (1625-1712), found four more moons and a gap in the rings of Saturn in 1675. Using Galileo’s laws of the pendulum in 1656, Huygens greatly improved the accuracy of measuring time by constructing the first pendulum clock, in which a weight-driven mechanism main-tained the oscillations. He made a micrometer in 1658 that gave a similar improvement in measur-ing angles with the telescope. In 1674 he invented the spring-driven clock regulated by a balance wheel, making possible the pocket watch. Huygens was elected to the Royal Society in 1663, even before he joined the Paris Academy. He moved back to Holland in 1681 when Louis XIV began moving against Protestants. In addition to his practical inventions, Huygens was an outstanding mathematical physi-cist. In his Horolgium Oscillatorium Sive de Motu Pendulorum (1673), he applied mathematics to the ideas of Galileo and Descartes, supporting the Cartesian vortex theory. He derived the formula for the period T (time) of small-amplitude oscillations of a simple pendulum, of length L:

T = 2π L/g ,

from which he obtained an accurate measurement of the acceleration of gravity at slightly more than g = 32 ft/s² (9.8 m/s²) by measuring the time for many oscillations. He invented the cycloidal pen-dulum, in which the swing is constrained to the form of a cycloid, and showed that its period was independent of the amplitude of its swing. His analysis of oscillating rigid objects (physical pen-dulums), established the basis for the mathematical study of rotation.

New Mechanical Ideas In discussing rotation, Huygens also de-scribed his theory of uniform circular motion, such as an object whirling on a string. He derived the concept he called “centrifugal force” in 1659, which he viewed as the outward inertial tendency of a rotating body to follow a straight line away from its curved path. He showed that this cen-trifugal force varied as the square of the speed v

and inversely as the radius R of the circle, later recognizing its dependence on the mass m of the rotating object (Figure 5.3), in the form:

F = mv²/R .

In 1669 Huygens set up a whirlpool experiment in a bowl of water, which showed that bits of wax were drawn to the middle, apparently confirming the Cartesian theory that gravity was caused by the outward tendency of the Earth’s vortex displacing heavier objects inward. In this view, weight resulted from a balancing of the centrifugal force

R

vt

at²/2

R

Figure 5.3 Huygen’s Centrifugal Force Idea Outward centrifugal force was later recognized to be the reaction to an inward centripetal force that produces a centripetal acceleration: the change in velocity toward the center of a circle that produces circular motion. A point with tan-gential velocity v for a time t moves a distance vt and would have to accelerate at rate a through the radial distance at²/2 (from Galileo’s law) to remain on the circle. The resulting right triangle with sides R and vt has hypotenuse R+at²/2, which are related by the Pythagorean theorem:

R²+(vt)² = (R+at²/2)² = R²+Rat²+(at²/2)² so v² = Ra + a²t²/4

Actual (smooth) circular motion corresponds to the limiting value of a as t approaches zero, or a centripetal acceleration given by

ac = (limit of a as t→0) = v²/R. Centripetal force is then F = mac = mv²/R, as shown independently by Newton.


of the vortex. Experiments with a revolving clay sphere revealed an equatorial bulge, explaining the shape of Jupiter and implying the same for the Earth. Huygens reported his solution to the problem of two colliding bodies to the Royal Soci-ety in 1668. The special case of an inelastic col-lision (Figure 5.4a) in which the two bodies stick together was also presented at this time by John Wallis (1616-1703) and Christopher Wren (1632-1723). For a mass m1 with speed v1 colliding with a mass m2 with speed v2, they obtained the final

speed V from conservation of the “quantity of mo-tion” (mv):

Σmv = m1v1 + m2v2 = (m1 + m2)V.

For a perfectly elastic collision, in which the speed of approach for two colliding bodies is equal to their speed of separation after impact (Figure 5.4b), Huygens showed that the Cartesian quantity of motion is not conserved unless the directions are taken into account. This leads to the concept of momentum as mass times velocity (a vector with both magnitude and direction) instead

of just speed, where the total momentum is conserved if the momenta of objects with opposite velocities are sub-tracted. But he also identified the quantity mv² as another conserved quantity in perfectly elastic collisions that can be added without concern for di-rection, later called “vis viva” (living force) and leading eventually to the energy con-cept. Ten years later Huy-gens published a wave like theory of light in his Traité de Lumière (1678). His waves were impulses in a finely di-vided aether, rather than peri-odic oscillations. He states the important idea, known as Huygens’ principle, that each aether particle receiving an impulse becomes a luminous source transmitting this im-pulse in every direction. He was able to use this idea to explain the laws of reflection and refraction, and even the phenomenon of double refrac-tion in calcite crystals discov-ered by Erasmus Bartholinus in 1669. Contrary to Descartes, his waves traveled at a finite speed.

m m m

m m m m

1 1 22

1 2 1 2

v V

v Vv V

v1 2

1 2 1 2

(a) Perfectly Inelastic Collision: Equal Final Velocity = V

m

Before Collision After

(b) Elastic Collision: Approach Velocity = Separation Velocity Figure 5.4 Conservation Laws in Inelastic and Elastic Collisions (a) In perfectly inelastic collisions, two objects with initial mo-menta m1v1 and m2v2 coallesce with a common velocity V as first predicted from conservation of momentum by Wallis and Wren:

m1v1 + m2v2 = (m1 + m2)V so V = m1v1 + m2v2

m1 + m2 .

(b) For an elastic collision, Huygens applied both conservation of momentum and vis viva to two masses m1 and m2 with velocities v1 and v2 in the form:

m1v1 + m2v2 = m1V1 + m2V2 or m1(v1 - V1) = m2(V2 - v2) , m1v1² + m2v2² = m1V1² + m2V2² or m1(v1² -V1²) = m2(V2² -v2²).

The second equation (conservation of vis viva) divided by the first equation (conservation of momentum), as shown on the right give:

v1 + V1 = V2 + v2 or v1 - v2 = V2 - V1, showing that the approach velocity is equal to the separation velocity in elastic collisions.


Another foreign member of the Paris Academy of Sciences, the Danish astronomer Ole Roemer (1644-1710), demonstrated the finite speed of light. He used the pendulum clock to detect that the moons of Jupiter had periods that were slightly longer (about 26 seconds) when the Earth is receding from Jupiter than when it is ap-proaching (Figure 5.5). He recognized that this was due to the increasing distance that light had to travel in reaching the Earth in each orbit of a moon (42.5 hours for the moon Io). In 1676 Roemer announced to the Paris Academy that an eclipse of one of the moons would be ten minutes later than the time predicted from the average period as measured by Giovanni Cassini in 1668. He then calculated that light would take 22 minutes to cross the Earth’s orbit (modern value: 16 minutes). Huygens combined this with the diameter of the Earth’s orbit, deter-mined by Cassini and Jean Richer in 1671, finding

the speed of light to be about 230 million m/s, or about three-fourths the modern value. The Air Pump and Other Machines As suggested by the work of Boyle and Hooke, the air pump was one of the most impor-tant devices in establishing the scientific revolu-tion. It was invented in 1650 by the German engineer Otto von Guericke (1602-1686) in the Protestant city of Magdeburg where he served as burgermeister. He used the principle of the water pump, but with better fitting parts to make it nearly airtight. He showed that a close-fitting piston in an evacuated cylinder could not be removed by the effort of twenty men. In 1654 von Guericke demonstrated the power of a vacuum to Emperor Ferdinand III by evacuating two large metal hemispheres fitted to-gether along a greased flange. Air pressure held these “Magdeburg hemispheres” together so tight-

Jupiter andits moon Io:T = 42.5 s

Sun

Orbital diameter d = 3 x 10 m11

Light crosses orbit in t = 1000 s

T + 13s

T - 13s

(Light takes 13s to go distanceearth goes in T = 42.5 h)

Figure 5.5 Roemer’s and Huygen’s Method of Measuring the Speed of Light Roemer determined that light from Jupiter’s moon Io takes 13 seconds longer between eclipses than its average period around Jupiter of T = 42.5 hours when the Earth is moving away from Jupiter, and 13 seconds shorter when the Earth is moving toward Jupiter. From this he estimated that light crosses the Earth’s orbital diameter d in a time t = 22 minutes (modern value is about 1000 seconds). Huygens used this to calculate the speed of light from its orbital diameter d. Using modern values, this gives: c = d/t = 3×1011m/1000s = 3 ×108 m/s.


ly that a team of sixteen horses could not pull them apart. He also did some of the vacuum ex-periments that Boyle performed independently a decade later. Even in an early study of electrical ef-fects, Guericke took a mechanical approach. In 1672 he described the first frictional electric machine to produce electricity by rubbing. He mounted a globe of sulfur on a shaft with a crank so that the globe could be charged by holding one hand on it while turning the crank. It is interesting to note that few electrical discoveries were made during the mechanically-oriented seventeenth cen-tury, but Guericke’s device did initiate a series of improved frictional machines. Work with the air pump led the French Huguenot physicist Denis Papin (1647-1712) to an early concept of a steam engine. After serving as an assistant to Huygens in the Paris Academy of Sciences, he left Paris due to the persecution of Protestants and became one of Boyle’s assistants. He developed a “steam digester” or pressure cooker, complete with safety valve, for cooking at higher temperatures. By boiling water in a cylinder with a piston, he showed the possibility of using the pressure of the expanding steam on the piston to do work. Robert Hooke suggested the possibility of creating a vacuum in a cylinder by condensing steam, and later contacted Thomas Newcomen (1663-1729), who developed the first effective steam engine using the resulting air pres-sure to pump water from coal mines. Hooke also studied the action of springs and found that spiral springs oscillate with a con-stant period. Huygens used this observation to make the first spring-driven clock, although Hooke contested the priority of his work. In 1678 Hooke discovered that the force tending to restore a stretched spring or other elastic material is pro-portional to the distance that the stretched end is displaced from its equilibrium position, now called Hooke’s law. He developed a spring-driven clock mechanism to keep a telescope pointed to a given celestial position when it is mounted on an axis parallel to the Earth’s rotation. He also introduced the cross-hair for precise positioning of a telescope, and the vernier for reading a fraction of the scale in measuring its orientation.

The Microscope Invented about the same time as the tele-scope, the microscope had a less dramatic devel-opment but was no less important in helping to establish mechanical and corpuscular ideas. Galileo tried to use an inverted telescope as a microscope, reporting in 1614 that, “I have seen flies which look as big as lambs, and have learned that they...walk on glass, although hanging feet upwards, by inserting the point of their nails in the pores of the glass.” Optical theory of the microscope was advanced by Kepler, Torricelli, and Huygens, the latter inventing an improved eyepiece. The Italian physician Marcello Malpighi (1628-1694) made the first major microscope dis-coveries, working at the University of Pisa under the influence of Borelli. In 1660, using a single lens that he called a “flea glass,” Malpighi saw that blood flowed through a network of tiny vessels over the lungs of a frog, indicating that respiration involved transfer of air to the blood. His observations revealed hair-like blood vessels, eventually called “capillaries.” They provided the missing link between the smallest visible arteries and veins, completing Harvey’s theory of blood circulation. Malpighi also made important studies of insect and plant anatomy. Like Galileo, his arguments against ancient authorities and in favor of “mechanist surgeons” led to his formal indict-ment at Rome in 1689 by church authorities, who claimed the microscope distorted reality. Robert Hooke and the Dutch naturalist Jan Swammerdam (1637-1680) also made studies of insects. Swammerdam founded modern ento-mology with his Historia Insectorum Generalis (1669), but his most famous discovery was the red blood corpuscle, announced in 1658, and now known to be the oxygen-carrying part of the blood. Robert Hooke published his observations with a compound microscope in his book Micrographia (1665), written in English. It contained fifty-seven remarkable illustrations of plant structures and insect anatomies, unrivaled by anyone but Swammerdam. Hooke’s method of making thin sections was of special importance. But his most important discovery was what he called “cells” in plant tissue


when he observed the honeycomb structure of a thin sliver of cork. The living cell came to have a role in biology during the nineteenth century similar to that of the atom in chemistry and physics, being the basic unit of an organism that is capable of independent functioning. The most unusual of the early microsco-pists was the Dutch draper Antoni van Leeuwen-hoek (1632-1723). He retained the use of single lenses, grinding more than four hundred of his own during his long lifetime. They were very small, but with a short focal length that could magnify up to more than two hundred times. He reported his discoveries in letters to the Royal Society that were translated and published in the Philosophical Transactions, including human capillaries, red blood cells, yeast cells, and para-sites on fleas, inspiring the English poet Jonathan Swift to write the following lines:

So naturalists observe, a flea Has smaller fleas that on him prey; And these have smaller still to bite ‘em And so proceed ad infinitum.

In 1677 Leeuwenhoek discovered the one-celled animals now called protozoa in a drop of water, and “animalcules” (spermatozoa) in human semen. In 1683 he described what were apparently bacteria at the optical limit of his lenses, not to be observed again for over a century. In 1680 he was elected to both the Royal Society and the Paris Academy. 4. TRIUMPH OF MECHANISTIC SCIENCE Early Newtonian Ideas During the latter half of the seventeenth century, Isaac Newton (1642-1727) and his con-temporaries corrected and correlated the mechani-cal concepts of Galileo, Kepler, and Huygens within a unified heliocentric system. For the first time, both terrestrial and celestial motions could be understood in terms of the same physical causes, and the world could truly be viewed as a universe. Since Newton was the central figure in the achievement of this consistent understanding of the mechanical universe, it is often called the Newtonian synthesis. But the emergence of this

new world view involved many other scientists, and it is difficult if not impossible to assign credit properly. Newton was born on Christmas Day 1642 at Woolsthorpe Manor, near Grantham in Lin-colnshire. The date is not as messianic as it might appear since England was still on the Julian cal-endar, having rejected the popish Gregorian cal-endar in which the corrected date was January 5, 1643. His father died before his birth and he grew up on the farm of his maternal grandparents. As a shy schoolboy, he made clocks and other me-chanical devices, but had no interest in farming. With financial help from an uncle, New-ton enrolled in Trinity College, Cambridge, in 1661, and studied mathematics under Isaac Barrow (1630-1677). Barrow also had strong interests in alchemy and the Hermetic philosophers, whose empiricism had left room for the vital spirit in nature that Descartes had tried to eliminate. When Newton finished his B.A. degree in 1665, he returned home for nearly two years to escape the Black Plague that was spreading in many English cities. During his isolation, he had time to start formulating his ideas. In a manuscript note some fifty years later, Newton described his recollection of those unusually creative years:

In the beginning of the year 1665 I found the Method of approximating series and the rule for reducing any dignity of any Binomial into such a series. The same year in May I found the Method of Tangents of Gregory and Slusius, and in November had the direct Method of Fluxions, and the next year in January had the Theory of Colours and in May following I had entrance into the inverse method of Fluxions. And the same year I began to think of gravity extending to the orb of the Moon and...from Kepler’s rule of the periodical times of the Planets..., I deduced that the forces which keep the Planets in their orbs must be reciprocally as the squares of their distances from the centres about which they revolve; and thereby compared the force requisite to keep the Moon in her Orb with the force of the gravity at the surface of the Earth, and found


them answer pretty nearly. All this was in the two Plague years of 1665-1666. For in those days I was in the prime of my age for invention and minded Mathematics and Philosophy more than at any time since.

If Newton’s memory was correct, these were indeed “miracle years,” comprising the three most important discoveries of one of the greatest centuries in the history of science. The direct and inverse methods of fluxions marked the beginning of differential and integral calculus, the basis of almost all later developments in mathematical sci-ence. The theory that white light consists of all the colors of the spectrum established the foundation of modern optics. The inverse-square law of gravity became the unifying concept of the new mechanical universe, ending the Greek division between celestial and terrestrial regions. Un-doubtedly, Newton’s early work was staggering, but documentary evidence seems to suggest some exaggeration. For more than two decades, much of Newton’s work remained unknown except for his theory of colors. After returning to Cambridge, he received his M.A. in 1668 and became Lucasian Professor in 1669 on the recommendation of Bar-row, who resigned to study theology. From his early experiments, he recognized that lenses act like prisms in dispersing light into a spectrum,

causing “chromatic aberration” in refracting tele-scopes. In 1668, he constructed a reflecting tele-scope by using a concave mirror instead of a lens. Although this first reflecting telescope was only six inches long, it had a magnification of forty times and was equivalent to a six-foot refracting telescope. He built a larger one in 1671, and demonstrated it to Charles II before presenting it to the Royal Society. As a result of this success, Newton was elected a Fellow of the Royal Society in 1672 and presented his first paper, describing his theory of colors. Descartes tried to explain color mechani-cally as the result of differing rates of spin of tiny spheres in the luminous aether, modifying white light passing through it. Newton challenged this view with his prism experiments, showing that white light was not simply modified, but was dis-persed into an elongated spectrum with red light refracted the least and violet bent the most. Using a second inverted prism, he showed that the col-ored rays could be refracted back together to form white light again (Figure 5.6). Thus he demon-strated that white light consisted of many rays, each having its own color and angle of refraction. Robert Hooke, who favored a wave theory of light, criticized Newton’s paper for avoiding a theory of the nature of light, leading the touchy Newton to distance himself from the Royal Society.

White light = ROYGBIV

Refraction

Dispersioninto

SpectrumROYGBIV = White

light

Prism

Inverted PrismRed

Violet

Figure 5.6 Newton’s Demonstration of the Composite Nature of White Light Newton showed that the colors of the spectrum are components of white light. Different colors are re-fracted through different angles, causing dispersion into the spectrum. By placing an inverted prism in the path of the dispersed light, Newton was able to demonstrate a reversed refraction of the component colors, combining them to obtain white light again. He designated seven colors in the spectrum: red, orange, yellow, green, blue, indigo, violet (abbreviated by the acronym ROYGBIV).


There are some reasons to question New-ton’s recollection of how much of his theory of gravity was completed in 1666. The evidence suggests that he had not yet developed clear ideas of mass, inertia or force. From 1666 to 1679 he worked on a theory of gravity based on the vortex ideas of Descartes. In 1679 he even suggested that the Sun and planets might be governed by “some principle of unsociableness in the aethers of their vortices.” Using his method of fluxions, he had derived Huygens’ centrifugal force law, apparently viewing circular motion as having an outward tendency. Thus the force on the Moon in its orbit would have involved the tendency of the Moon to recede. Only later did he introduce the term “centripetal” (center seeking) for the inward force on an object required for orbital motion instead of its natural straight-line inertial motion. Whatever Newton’s conceptual frame-work at the time, the inverse-square force on the planets is easily obtained for the special case of a circular orbit of radius R and circumference 2πR, in which the speed of a planet of period T (time for one orbit) is v = 2πR/T. Combining this result with Huygens’ formula F = mv²/R gives:

F = mv2/R = m(2πR/T)2/R = 4π2mR/T2.

Kepler’s third law T2 = kR3 in this equation gives:

F = 4π2mR/kR3 = 4π2m/kR2, which shows that the force F varies inversely as the square of the distance R. Newton claimed that the association of this inverse-square law (1/R2) with gravity on Earth occurred to him when he saw an apple fall-ing down and connected it with the “fall of the Moon” to remain in its orbit (Figure 5.7). From the orbit of the Moon with radius R (60 Earth radii) and period T (27.3 days), he calculated that the Moon falls 0.0044 feet per second in following its orbit instead of a straight-line inertial path. Since the apple is 60 times closer to the center of the Earth, the inverse-square law implies that it should fall faster by a factor of 60². This gives .0044 x 3600 = 15.8 feet in one second, “pretty nearly” the 16 feet obtained from Galileo’s law of free fall. Some historians believe that Newton may have waited to publish these results until he was able to

show that the gravity of spherical objects like the Earth and Moon act as if their matter were concentrated at their centers. In the meantime, Robert Hooke was try-ing to develop Gilbert’s view that gravity was similar to magnetic attraction. In discussing the comet of 1664 with Christopher Wren, he sug-gested that the gravitational attraction of the Sun caused the greater curvature of its orbit near the Sun. After Huygens’ formula for centrifugal force appeared in 1673, several scientists including Hooke, Wren and Edmund Halley (1656-1742) derived the inverse-square law for circular orbits.

a

g

R=60rr

T=27.3 days

v

Earth

Moonfalling

moonfallingapple

Lunar orbit Figure 5.7 Inverse-Square Law for the Moon Newton said that he recognized the cause of the Moon’s orbit as a gravitational attraction to-ward the Earth when he saw an apple fall. Combining the formula for centripetal acceler-ation a = v²/R with the orbital speed v = 2πr/T and the values for the orbital radius R = 60 Earth radii and period T = 27.3 days gives:

a = v²/R = 4π²R/T² = .0088 ft/s² = 32/60².

This is less than g at the surface of the Earth by a factor of 60² (a = g/60²), so Newton concluded that gravitational force diminishes as the inverse square of the distance from the center of the Earth since force is proportional to acceleration.


When Oldenburg died in 1677, Hooke became Secretary of the Royal Society and wrote to New-ton in 1679, inviting him to resume correspon-dence. Newton’s reply was stiffly courteous, but he did suggest an ingenious test of the Earth’s rotation by dropping an object from a tall tower. He argued that since the top of a tower is further from the center of the Earth than the bottom, the top must move faster, just as the outside of a wheel moves faster than the center. Thus a falling object should move slightly forward to the east. Newton also claimed that it would follow a spiral path in relation to the center of the Earth “if its gravity be supposed uniform.” Hooke immediately recognized Newton’s error of assuming uniform gravity. In his reply he suggested an inverse-square force of attraction toward the center of the Earth, which he believed would produce “a kind of Elleptueid.” Hooke’s last letter remained unanswered, but Newton ap-parently returned to the problem of planetary motion. With the new insight of attraction, he was able to show that an inverse-square force acted between the centers of spherical bodies and produced elliptical orbits. One day in 1684, Hooke, Halley and Wren met at a coffeehouse, where their discussion turned to the problem of demonstrating elliptical orbits from the inverse-square law. Hooke claimed to have solved the problem, but would not share his solution, even when offered a prize by Wren. A few months later Halley visited Newton at Cambridge and posed the problem to him. Newton immediately replied that he had computed an elliptical orbit from an inverse-square force of attraction on a planet toward the center of the Sun, but unfortunately was unable to find his calcula-tions. Three months later, he sent Halley a paper that successfully derived all three of Kepler’s laws. Recognizing the importance of Newton’s achievement, Halley returned to Cambridge and urged him to write a book on his new dynamics of the solar system. The Newtonian Synthesis For nearly two years, Newton concen-trated on writing his Philosophiae Naturalis Prin-

cipia Mathematica (Mathematical Principles of Natural Philosophy), usually referred to as the Principia. It is perhaps the single most important scientific treatise in the history of science, and it absorbed all of Newton’s energies. His secretary Humphrey Newton (no relation) noted that, “He ate very sparingly, nay, ofttimes he has forget [sic] to eat at all, so that...when I have reminded him, [he] would reply, Have I; and then making to the Table would eat a bit or two standing.” When Book I of three projected volumes reached the Royal Society in 1685, Hooke imme-diately claimed that Newton had plagiarized his ideas from earlier correspondence. Newton was furious and proceeded to delete all references to Hooke. Although the Society at first planned to publish the Principia, it was short of funds, so Halley agreed to pay the expenses himself. This act of generosity appeased Newton, who then lifted his threat to withhold Book III and agreed to full publication. Halley received the completed manuscript in April 1686, and it was published in the summer of 1687. In the second edition (1713), Newton even acknowledged the independent deduction of the inverse-square law by Hooke, Halley and Wren. In the Principia, Newton develops the full implications of the concept of gravitational attraction. In the first section, labeled “Definitions,” he defines the center-seeking cen-tripetal force required to keep the planets in their orbits, in contrast with Huygens’ outward cen-trifugal force to balance the vortex. The attraction of “universal gravitation” extends across space, acting on apples, moons and planets. Such an “active force” was viewed as “occult” in the Cartesian tradition because of the lack of a tangi-ble intervening mechanism. But Newton’s mathematical demonstrations reveal the value of such a force, even if he would “frame no hypothe-ses” about its source. Although the use of an active force in dynamics appears to be a new idea for Newton, it was not completely alien to his thinking. During his silent years, Newton followed Isaac Barrow in extensive alchemical researches and theological studies that supported this idea. His work in al-chemy had been from the corpuscular viewpoint,


leading him to the conclusion that active forces influence particles of matter. Hermetic writings reinforced this idea with their emphasis on vitality and activity in nature. His early notebooks refer to the Cambridge Platonist Henry More (1614-1687), who challenged Descartes’ idea of mind as unextended and suggested that infinite space is filled with spirit that acts on matter. Since only God is infinite, He fills space and gives it life. In Newton’s words, God is present “from infinity to infinity; He governs all things.” Newton would not allow Cartesian mechanisms to crowd out God’s active and creative role in His world, identifying space as the “sensorium of God.” However, the Principia suppresses these mystical and religious motivations in favor of the strict logical form of Euclidean geometry. After the definitions of mechanical terms such as mass, momentum, acceleration, and force, there is a short chapter entitled “Axioms or Laws of Motion.” The three laws of Newton appear here as the basis for his study of motion, although the first two had their origin in the work of Galileo and Descartes, and the Principia credits the last to Wren and Huygens. Newton indicates their fundamental nature by identifying them as axioms without proof, although their validity is consistent with empirical evidence. The first two laws define inertia and force, while the third law introduces the concept of a reaction force:

Law I. Every body continues in its state of rest or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it....

Law II. The change of motion is propor-tional to the motive force impressed; and it is made in the direction of the right line in which that force is impressed....

Law III. To every action there is always op-posed an equal reaction.

The “motion” of a body is its momentum (mv) and both it and force are known as “vector” quantities, having both magnitude and direction. In a corol-lary, Newton gives the rule for combining two forces as the diagonal of a parallelogram formed by the vectors.

The second law is the basic mechanical principle of cause and effect. The definition of force is that which changes the momentum. In the usual case where the mass of an object does not change, the force F (bold face for vectors) is equal to the mass m times the change in velocity (magnitude and direction), which is the accelera-tion a, giving:

F = ma.

For an object whirling on a string, the centripetal force on the object is the inward tension of the string, and the resulting effect is the inward cen-tripetal acceleration. The outward tension pulling at the center is the equal and opposite centrifugal reaction of the third law. After the introductory sections on defini-tions and axioms, the rest of the Principia divides into three books of propositions derived as theo-rems from the axioms. In Book I, entitled The Motion of Bodies, Newton proved 98 propositions on motion for various kinds of forces. He derives Kepler’s second law for any centripetal force to-ward a fixed point. If a planet receives impulses toward the Sun at equal intervals of time, its iner-tial motion will change direction each time, forming a series of equal triangles with the Sun at one vertex, so that “equal areas are swept out in equal times.” Passing to the limit of an infinite number of instantaneous impulses gives a con-tinuous orbit. Newton next obtains Kepler’s first law by showing that if the attracting force varies as the inverse square of the distance from a focal point, the orbit will be an ellipse, parabola or hyperbola, depending on the initial velocity that starts the motion. Kepler’s third law also follows from the laws of motion for elliptical orbits caused by an inverse-square centripetal forces (Figure 5.8). Al-though Newton derived these theorems for parti-cles, he next shows that homogeneous spheres attract each other as though their masses were concentrated at their centers. Book II, of the Principia, entitled The Motion of Bodies in Resisting Media, discusses mainly to the motion of bodies in fluids, including the Cartesian aether. Here he shows how to ac-count for the effect of air resistance on objects like


projectiles and pendulums. He also calculates the speed of sound waves by using Boyle’s law for the compression of air, erroneously assuming constant temperature. Finally he refutes Descartes by showing that the period of a planet in a vortex varies as the square of the distance from the center, rather than the three-halves power required by Kepler’s third law (T2 = kR3 → T = kR3/2). In a frictional fluid, the orbit would not even be stable. Book III, entitled The System of the World, applies the hypothetical laws of the first two books to the universe as observed. The central concept is the law of universal gravitation, which generalizes the inverse-square law to the mutual attraction of any two bodies of masses m and M separated by a distance R (Figure 5.8), or in modern notation:

F = G mM/R2,

where G is a universal constant. This law, perhaps the most important in the history of science, unifies terrestrial and celestial motions, assigning the same cause to the motion of projectiles and planets. It even leads Newton to the theoretical possibility of artificial satellites circling the Earth:

That by means of centripetal forces the planets may be retained in certain orbits, we may easily understand, if we consider the motions of projectiles; for a stone that is projected...the greater the velocity is with which it is projected, the farther it goes before it falls to the Earth. We may therefore suppose the velocity to be so increased, that it would describe an arc of 1, 2, 5, 10, 100,

R

Fm M

F = GmM/R²

M m

v

SunPlanet

Planetary orbit of radius R

F = ma

Figure 5.8 Newton’s Law of Universal Gravitation and Planetary Motion Newton generalized the inverse-square force of attraction between the Moon and Earth to include a similar force between any two masses in the universe. From his second and third laws of motion, he concluded that the force varies as the product of the masses m and M of each object. He showed that a spherical mass acts as though its mass were concentrated at its center, so that if the centers of m and M are separated by a distance R, the force of universal gravitation is given by

F = GmM/R². Applied to a planet of mass m with a circular orbit of radius R, period T and speed v = 2πR/T, moving around the Sun of mass M>>m, the planet experiences centripetal force F = ma = mv²/R from the Sun’s gravity, so that

F = GmM/R² = mv²/R = m(2πR/T)²/R = 4π²R/T². This expression leads directly to T² = (4π²/GM)R³, which is easily recognized as Kepler’s third law T² = kR³, where Kepler’s constant is k = 4π²/GM.


1000 miles before it arrived at the Earth, till at last, exceeding the limits of the Earth, it should pass into space without touching it.

Later editions of the Principia include a diagram showing projectile paths from the top of a moun-tain, beginning as parabolas that extend further and further until they become circular or elliptical orbits around the Earth. Terrestrial motions, including Galileo’s laws, now follow by considering gravity on a mass m near the surface of the Earth (at a distance R from its center where its mass M acts). From Newton’s second law (F = ma) the force of gravity causing acceleration g of a mass m is its weight W given by

W = mg = G mM/R2,

ignoring the centrifugal effect due to the Earth’s rotation. Newton assumes that “inertial mass” m associated with acceleration (g) is equal to “gravitational mass” m associated with attraction (GM/R2), so m cancels and g = GM/R2 is constant regardless of the value of the mass m as demon-strated by Galileo. Evaluation of G a century later made it possible to determine the mass M of the Earth, and thus its average density and internal composition. Newton calculated that the rotation of the Earth would tend to make it bulge at its equator if it was once hot enough to be elastic, causing an increase in R of 17 miles (Figure 5.9). This must have occurred before the Earth became rigid, since if the Earth was perfectly spherical the oceans would pile up l7 miles higher at the equator. Thus g is not truly constant, but will be largest at the

*Polaris

RpReq

F1

F2

Sun

Precession

N

S

at pole:

R > Req p by 25km

F > F2 1

26,000 yr.

equatorial bulge:at equator:

inverse-squareforces:

*Vega (A.D. 15,000)

g = 9.83m/s²

g = 9.78m/s²

Figure 5.9 Equatorial Bulge and its Effects on Gravity and Precession Newton showed that the centrifugal effect of the Earth’s rotation would cause an equatorial bulge. From this he used the law of universal gravitation to predict that g would be largest at the poles where R is smallest. The weight of a mass m at the pole separated from the center of the Earth by the radius Rp is

W = mg = GmM/Rp²

and thus g = GM/Rp² has its largest value since Rp is the smallest value of R. Newton also calculated the precession of the equinoxes from the fact that the force of attraction by the Sun on the Earth is slightly larger on the side of the Earth closer to the Sun than on the side further away (F2>F1), causing a small twisting effect. The inequality of these forces accounts for one complete precessional wobble of the Earth in 26,000 years, matching the observed precession rate of the equinoxes.


pole where R is smallest, and smallest at the equator where R (and the centrifugal effect of the Earth’s rotation) is largest, matching the pendulum meas-urements of g made in the tropics by Jean Richer in 1671 and by Halley in 1677. Newton was also able to give the first satisfactory explanation of the tides (Figure 5.10) by the gravita-tional action of the Moon on the oceans, causing two high tides in a lunar day (24 hours and 50 minutes). He explained variations between the highest “spring tides” and lowest “neap tides” by the additional force of the Sun, greater when it is aligned with the Earth and Moon (near the new or full Moon), and smaller when it is perpendicular to them (half Moon). Newton accounted for many new celestial phe-nomena, in addition to Ke-pler’s laws, by universal gravitation. The centripetal force on a planet of mass m and speed v in its orbit at a distance R from the Sun of mass M is given by:

F = mv2/R = GmM/R2.

This equation also applies to a satellite of mass m circling a planet of mass M, making it possible to compare the masses and densities of the Sun, Earth and other planets with moons. Newton explained the precession of the equinoxes by the slight dif-ference in the force of the Sun’s attraction on op-posite sides of the Earth’s equatorial bulge (Figure 5.9). This causes the Earth’s axis to wobble like a spinning top. Calculations from the forces on the Earth and its rate of spin give 50˝ of precession per year (one complete wobble every 26,000 years), as first observed by Hipparchus. He explained slight

deviations from Kepler’s laws in the motions of the planets, called “perturbations,” by the in-creased mutual attractions between the planets as they pass each other, but Newton could only ap-proximate a solution to this “three-body problem.” He thought these perturbations would destabilize the solar system, leading him to suggest that God intervenes to maintain stability. Newton devoted two of the longer sec-tions of Book III to calculations on the motions of the Moon and comets. These complex lunar cal-culations relate to precession and perturbations of the Moon’s elliptical orbit, setting the pattern for future work in celestial mechanics. He obtained data from the Greenwich Observatory Astronomer

24 hr. rotation

moonaligns with sun

50 min. later/day

sun atspring tide

sun at neap tidepartly cancels effect of moon

(90º from moon)

F1 F2 F3

earth

oceans at equatortwo tides every

24 h 50 m

27.3 dayrevolution

Figure 5.10 Newton’s Explanation of Tides from Gravitation Newton used the inverse-square law to show that the Moon has the largest gravitational effect on the oceans, resulting in the force F3>F2 pulling the ocean away from the Earth on the side toward the Moon, and the force F2>F1 pulling the Earth away from the ocean on the side away from the Moon. Thus there are two high tides in a lunar day (24 hours and 50 minutes), when any point on a coast lines up with the nearest or farthest point from the Moon. The highest (spring) tides occur when the Sun is aligned with the Earth and Moon (new or full Moon), and the lowest (neap) tides occur when the Sun is at right angles to the Earth and Moon.


Royal John Flamsteed (1646-1719), causing years of bitterness over what Flamsteed felt was prema-ture use of his work. Newton’s work on comets used observational data of Halley and others to show that comets follow gravitational orbits of either elongated ellipses or parabolas. After observing the comet of 1682, Hal-ley worked out the orbits of some two dozen com-ets. He was struck by the similarity of the orbits of comets that had appeared in 1456, 1531 and 1607 with that of 1682. In 1705 he suggested that these were orbits of a single comet in an elongated elliptical orbit with a period of about 75 years, visible only when it was near the Earth on its path around the Sun (Figure 5.11). His prediction of its reappearance in 1758 was confirmed after it was first observed on Christmas of that year by a farmer in Germany. Halley became the second Royal Astronomer in 1720.

Newton’s Fluxions and Optics Newton cast his impressive mathematical demonstrations of the Principia in the form of classical geometry, since that was the form under-stood by his contemporaries. But he obtained most of his results first by the method of fluxions, his version of the calculus invented some twenty years earlier. He claimed that he wrote his treatise on The Method of Fluxions and Infinite Series in 1671, but it was not published until 1736 when it was “translated from the Author’s Latin Original not yet made publick” by John Colson. In a modest introduction to one of the most important steps in mathematical progress, Newton says “I have endeavored to enlarge the Boundaries of Analyticks, and to make some Improvements in the Doctrine of Curved Lines.” The calculus was based on the method of Archimedes, which treated a curve as a large

SunUranusSaturn

Jupiter

Neptune

Ellipticalorbit of comet

in orbit of

(predicted fromperturbation

Uranus)

Figure 5.11 Comet Orbit, Planet Perturbations, and Discovery of Neptune Newton and Halley demonstrated the elliptical orbits of comets and showed that their periods would be affected by the gravitation of the planets, especially Jupiter. In the case of Halley’s comet, the position of Jupiter will cause it to speed up or slow down, producing an orbital period that varies between 74 and 79 years. Newton accounted for the perturbations of the planets by their mutual gravitational attraction, which causes small deviations in their speed and orbit. After the discovery of Uranus in 1781, an unexplained perturbation in its orbit led to the discovery of Neptune in 1846.


number of small straight tangents or chords. Newton showed how to calculate the rate of change of the curve at any point from the slope of the tangent to the curve at that point (differential calculus), and how to find the maximum and minimum values of the curve. By increasing the number of chords along a finite curve indefinitely while their length decreased proportionately, he was able to calculate the length of the curve or the area bounded by it (integral calculus). Others introduced the more precise concept of the limit as a magnitude that can be approached more nearly than any finite difference, however small, finally resolving Zeno’s paradoxes. Other mathematicians anticipated many ideas of the calculus, and the German philosopher and mathematician Gottfried Leibniz (1646-1716) independently invented a somewhat different ver-sion. The form introduced by Leibniz, including the differential dx as an infinitesimal difference in x and the elongated ‘s’ as the integral sign for a sum of infinitesimals, was developed in Europe and eventually adopted in England also. The infinitesimal ratio dx/dt, for expressing an instan-taneous rate of change in x, was represented by x: in Newton’s fluxions. It appears that Newton invented his fluxions first, but Leibniz published his version of the calculus first (1684), leading to a priority debate between their respective supporters. In 1700 Leibniz became the first president of the new Academy of Sciences in Berlin. Publication of the Principia brought fame to Newton. He defended the rights of Cam-bridge University in 1687 against King James II, and was elected to Parliament in 1689 after James was deposed. Perhaps as a result of his work on the Principia and the resulting controversies, Newton suffered a nervous collapse in 1693. By 1696, however, he was well enough to accept an appointment as Warden of the Mint and to initiate a reform in coinage. After Hooke died in 1703, Newton was elected President of the Royal Society and remained as its virtual dictator for nearly 25 years. With the passing of the man who had criticized his theories of light 30 years before, He finally agreed to publish his Opticks or a Treatise of the Reflections, Refractions, Inflections and Colours of Light, which appeared in 1704.

Newton wrote the Opticks in English and it was much easier to read than the mathematically forbidding Principia. It described Newton’s many experiments on light, providing the definitive example of Baconian empiricism and the basic metaphor for the eighteenth century “Enlightenment” (suggested by Immanuel Kant in 1785). His separation of white light with a prism associated quantitative angles of refraction with each of the colors, which he somewhat arbitrarily designated as seven: red, orange, yellow, green, blue, indigo and violet (easily remembered from the acronym ROYGBIV). He explained the color of a given object as the combination of colors it reflects after absorbing all others, and gave the first complete explanation of the rainbow. Newton seemed to favor a particle theory of light in the Opticks, but he retained elements of the wave theory. From Roemer’s speed of light, Newton calculated that light waves would require an aether with an elasticity of 490 billion times that of air if its density was 700,000 times rarer than air, a value that would not appreciably slow the planets in the 10,000 years he considered suf-ficient since the creation. Newton passed white light through a plano-convex lens with its curved surface pressed against a flat pane of glass to produce a series of colored circles, as first described by Hooke but called “Newton’s rings.” Newton calculated the thickness of the air gap between the two glass sur-faces at each ring, and suggested the idea of an internal vibration or “interval of the fits,” whose length determines which color of light will be reflected or transmitted. Since light of a single color produces bright and dark rings, the “fits of easy reflection and transmission” seem like inter-ference of waves, reinforcing or cancelling each other. Even though this analysis eventually led to an evaluation of the wavelength of light, New-ton still preferred a particle theory. Thus he sug-gested that different sizes of corpuscles might cause different colors, which refract differently in transparent materials of different densities. He de-duced the law of sines for refraction, discovered in 1620 by the Dutch physicist Willebrord Snell (1580-1626), by assuming that light particles


speed up by stronger attraction as they pass into denser materials like glass or water. He attempted to explain the 1665 account by Francesco Grimaldi (1618-1663) of colored fringes produced by white light passing through two successive slits (diffraction) in terms of attractive forces. His preference for the particle theory of light influ-enced others and delayed the wave theory for a century. In spite of his claim to the contrary, Newton developed many hypotheses. The me-chanical view demanded an explanation of un-known causes. To avoid controversy, Newton expressed many hypotheses in the form of Queries appended to the Opticks, growing to a total of 31 in later English editions. He even attempted to explain gravity by mechanical actions in the aether, but in the end he was driven back to his religious convictions. In Query 28 he tries to correlate the two:

The main business of natural philosophy is to argue from phenomena without feigning hypotheses, and to deduce causes from ef-fects, till we come to the very First Cause, which certainly is not mechanical; and not only to unfold the mechanism of the world, but chiefly to resolve these and such like question. What is there in places almost empty of matter, and whence is it that the Sun and planets gravitate towards one an-other, without dense matter between them? Whence is it that Nature doth nothing in vain; and whence arises all that order and beauty which we see in the world?... And these things being rightly dispatched, does it not appear from phenomena that there is a Being incorporeal, living, intelligent, omnipresent, who in infinite space, as it were in His sensory, sees the things them-selves intimately, and thoroughly perceives them, and comprehends them wholly by their presence to Himself.

Newton’s ideas of absolute space and absolute time as symbols of God’s omnipresence and eter-nity were criticized by Leibniz. He believed that only relative space and time have any meaning, as developed later in Einstein’s theory of relativity.

In a debate with Samuel Clarke (1675-1729) in 1715, Leibniz also protested against Newton’s suggestion that God intervenes to stabi-lize the solar system. Leibniz wondered why God, the most perfect Being, would create such an im-perfect machine that it would have to be corrected from time to time, thus violating a truly mechani-cal universe. Clarke responded on behalf of New-ton by accusing Leibniz of excluding God from the world. Actually both Leibniz and Newton held strong Christian convictions, although Newton harbored Unitarian tendencies. In spite of their differences, both men believed that a correct understanding of science would further the cause of Christianity. Perhaps both Newton and Leibniz would have agreed with Bishop George Berkeley in 1734 who said, “He who can digest a second or third fluxion, a second or third difference, need not, methinks, be squeamish about any point in Divin-ity.” In his old age, Newton compared himself with “a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.” Even his unified and mathematically ordered me-chanical universe could not explain everything in the vast and complex world. The Influence of Newtonian Ideas Descartes promoted the idea of a me-chanical universe in a vague way, but Newton presented the complete mechanism in a mathe-matically precise and compelling form. The col-lapse of the geocentric view had caused conster-nation and confusion, compounded by the idea of a moving Earth in infinite space. The Newtonian synthesis restored confidence (faith?) in reason based on experience, giving birth to a new sense of optimism and progress. It produced few immediate practical results, but provided a new picture of the world as a great machine consisting of inert particles subjected to universal laws in perfect order and harmony. Almost immediately it began to influence ideas about society and culture. The philosopher John Locke (1632-1704), a friend of Newton and fellow member of the Royal Society, began the task of translating


Newtonian science into political and philosophical theory in two important books appearing in 1690. His Treatise of Civil Government argued that individuals are the particle ingredients of the state, which should be structured by self-evident natural rights such as life, liberty and property, and the democratic ideals of equality and tolerance. Using mechanical analogies, he suggested that the state “should move that way whither the greater force carries it, which is the consent of the majority.” This reflected the new constitutional monarchy in England, which was limited by Parliament in the new “age of reason.” In his Essay Concerning Human Under-standing, Locke suggested that the human mind is a “blank tablet” at birth, in which simple “atomic ideas” gained by sensation are correlated by the laws of association and reason to form complex ideas. Locke presses the analogy of “the dominion of man in this little world of his own understand-ing, being much-what the same as it is in the great world of visible things.” Since reason must be based on experience, our knowledge is limited to the natural world and we can only know God through His laws in nature. He is the Clock-maker God, creator of the great machine and its First Cause. Locke’s book on the Reasonableness of Christianity (1695) initiated deism as a system of natural religion in which God is revealed only in nature. Newton’s discoveries found slower acceptance on the continent, where Cartesian ideas dominated until about 1740. After a period of exile in England from 1726-1729, the French philosopher François Marie Arouet de Voltaire (1694-1778) became an effective propagandist for the “enlightened” theories of Bacon, Newton, Locke and the English Deists, beginning with his Letters on the English (1734). Voltaire attacked superstition, organized religion, and Biblical revelation, but admitted that, “The world embar-rasses me, I cannot conceive of so beautiful a clock without a maker.” He wrote a popular ac-count of Newtonian theory with his mistress Mme. de Chatelet in 1738. The Newtonian idea that God created the world with a fixed order was extended to biology by the Swedish Lutheran botanist Carolus Linn-

aeus (1707-78). He believed in the “fixity of spe-cies,” each being a special creation of God at the beginning of the world. Building on the work of the English naturalist John Ray (1628-1705), who defined species as interbreeding organisms, Linn-aeus developed the system of “binomial nomencla-ture,” whereby he classified some 18,000 species by double Latin names that designate their genus and species. In his Systema Naturae (ten volumes: 1735-1758), he classified every known plant and animal by class, order, genus, and species, using an artificial system for plants based on the sexual organs in the flowers. The French naturalist George Leclerc, Comte de Buffon (1707-88), impressed with New-tonian mechanical philosophy, preferred a natural system of classification based on a mechanical uniformity that admitted no discontinuities in nature. His 36-volume Histoire Naturelle (1749-85) gave a vivid description of the diversity of nature. His biological mechanisms included “organic molecules” and “penetrating forces” modeled on Newtonian ideas. He preferred a physical origin of the solar system, suggesting the collision of a comet with the Sun and requiring as much as a million years for the Earth and planets to cool. In his Époques de la Nature (1778) he divided the Earth’s history into six epochs con-sisting of long periods of development, instead of the six Biblical days of immediate creation. He also proposed the degeneration and disappearance of some species. Another French philosophe influenced by English ideas was Charles Montesquieu (1685-1755), who extended the idea of natural law from laws governing human nature to the laws of nations in his Spirit of the Laws (1748). By mid-century the courts of Louis XV and Frederick the Great were full of philosophers who saw society as well as the universe ruled by reason. The Baconian emphases on experiment and progress also became evident in France with the publication of the great French Encyclopédie between 1751 and 1777. Its twenty-two volumes including illustrations were edited by Denis Diderot (1713-84) and the mathematician Jean le Rond d’Alembert (1717-83), with contributions from many French scientists.


The natural laws of society described by Locke and Montesquieu were put into practice in the American Revolution, as expressed by Thomas Jefferson in the Declaration of Independence:

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unal-ienable Rights, that among these are Life, Liberty and the pursuit of Happiness, that to secure these rights, Governments are insti-tuted among Men, deriving their just powers from the consent of the governed.

The Constitution formalized laws with a system of checks and balances between the three branches of government similar to the Newtonian equilibrium of forces. Benjamin Franklin developed some of these ideas in his essay, “On liberty and necessity; man in the Newtonian universe.” Even the capital city of Washington was designed about an ellipti-cal hub like the solar system, with the Capitol and White House at its foci. Democratic goals also replaced the Divine Right of Kings in the French “Declaration of the Rights of Man.” In the study of economics, mechanistic ideas influenced both the French Physiocrats, beginning with François Quesnay (1694-1774), and the Scottish political economist Adam Smith (1723-90). In his Wealth of Nations (1776), Smith set forth the natural laws that govern economics. Like Locke, he emphasized independent individuals subject to the forces of nature, which leads each of them “by an invisible hand to pro-mote an end which was no part of his intention.” Smith claimed that the impersonal market system required no interference (free enterprise) because it automatically adjusted itself to the forces of competition according to economic laws. The mechanical ideas of the Enlighten-ment also influenced the arts. English writers such as John Dryden, Alexander Pope, and Joseph Addison developed prose and poetic styles of simplicity and clarity as close to mechanical pre-cision as possible. The English novel received its modern form in Daniel Defoe’s Robinson Crusoe (1719) with its emphases on individualism and ‘factual’ detail. Baroque music formalized its modes of expression into set patterns and stan-

dardized mechanical instruments with develop-ments such as the equally tempered scale. The Mozartian synthesis of music and drama marked the culmination of the Enlightenment spirit with its logical clarity and constructive forces. French and Swiss mathematicians led the way in applying Leibniz’s form of the calculus to Newton’s celestial mechanics, beginning in Basel with the Bernoulli brothers Jakob (1654-1705) and Johann (1667-1748), and their nephew Daniel (1700-82). Alexis-Claude Clairaut (1713-65) and Jean d’Alembert (1717-83) developed the methods of differential equations applied to mechanics. Clairaut worked on the “three-body problem” of lunar motion, announcing that the law of universal gravitation was wrong until he corrected a mistake that confirmed the theory in 1749. He also worked out the effect of Jupiter and Saturn on Halley’s comet to improve on the prediction of its 1758-59 return. The most prolific mathematician of all times was the Swiss-born Leonhard Euler (1707-1783), who spent most of his life in scientific academies at the courts of Berlin and St. Peters-burg, publishing many papers after he lost his eyesight. Euler worked out a consistent analytical formulation of Newton’s mechanics in his Mechanica (1736), developed the equations for motion and rotation of rigid bodies in his Theoria Motus Corporum Solidorum (1760), and devised methods for solving problems with many variables in his work on partial differential equations and calculus of variations. The grand synthesis of mechanics in terms of pure analysis divorced from geometry was achieved by Joseph-Louis Lagrange (1736-1813) in his Mécanique Analytique (1788). The culmination of Newtonian mechanics came with d’Alembert’s protégé Pierre Simon Laplace (1749-1827), who had once taught Napo-leon Bonaparte at the Ecole Royale Militaire. In 1773 he presented his famous statement on de-terminism to the Paris Academy of Sciences:

The present state of the system of nature is evidently a result of what it was in the pre-ceding instant, and if we conceive of an In-telligence who, for a given moment, embraces all the relations of being in this Universe, It will also be able to determine


for any instant of the past or future their respective positions, motions, and generally their affections.

If Newton’s laws completely determine the future of all being, then free will is only an illusion, and Laplace’s “Intelligence” is more like a superhu-man calculator in the image of Newton than the God who created humans in His image. Laplace took another step in separating God from the universe in his Exposition du Système du Monde (1796, 1813), where he intro-duced his “nebular hypothesis” to explain the physical origins of the solar system. He calculated a very small probability that the motions and rotations of the planets and their satellites would all be in the same direction and nearly in the same plane by pure chance. While Newton saw this as evidence of Divine Providence, Laplace insisted that it was due to a single physical cause. He sug-gested that a nebulous rotating cloud of matter once surrounded the Sun; but centrifugal action formed a hot nebular disk that cooled and con-densed into the planets, which threw off their own satellites in the process. Laplace devoted himself especially to the problem of the stability of the solar system, which had led Newton to suggest divine intervention. In 1786 he presented his mathematical analysis showing that the slow acceleration of Jupiter bal-anced the deceleration of Saturn, reversing each other in about 900 years. When considered as a system, their long “secular perturbations” are found to slowly oscillate. With this self-correcting mechanism, applied also to the Moon, he was able to complete his Traité de Mécanique Céleste (five volumes from 1799 to 1825) without any mention of God, telling Napoleon Bonaparte, “I have no need of that hypothesis.” The gap in Newton’s analysis was filled, and his “God-of-the-gaps” was no longer needed. While the French were working out the theory of astronomy, the English were making important new observations. The third Astronomer Royal, James Bradley (1693-1762), tried to find direct empirical evidence for the Earth’s motion. He failed to detect stellar parallax, but did discover the “aberration of starlight” and explained it in terms of the motion of the Earth in 1728. This was

a tiny annual shift in the stars that required pointing the telescope slightly in the direction of the Earth’s motion, like holding an umbrella forward while moving in rain. It led to a good value for the speed of light and seemed to support the particle theory of light. In 1748 Bradley also discovered a slight “bobbing” of the Earth’s axis called nutation. Both effects improved the accuracy of astronomical measurements by introducing corrections to account for the fact that we live on a moving platform. Universal gravitation was tested experi-mentally on Earth in 1774 by the fifth Astronomer Royal, Nevil Maskelyne (1732-1811). He meas-ured the deviation of a plumb bob from the vertical on either side of a mountain. By estimating the mass of the mountain and comparing its pull with that of the Earth, he calculated the mass of the Earth and its mean density at 4.5 times that of water. In 1798 the amateur scientist Henry Cavendish (1731-1810) measured the Earth’s mass more accurately by using a torsion balance designed fifty years earlier by the Cambridge cler-gyman, John Michell (1724-93). This consisted of a horizontal “dumbbell” of two lead balls sus-pended from a fine wire (Figure 5.12). When Cavendish supported two large lead spheres, one near each ball on diagonally opposite sides, he measured a tiny attractive force by the twisting of the wire. This gave an accurate value for the universal gravitation constant (G = FR2/mM = 6.7 × 10-11 N.m2/kg2), and a mean density for the Earth of 5.5 times that of water. Observational astronomy reached its pin-nacle in England with the work of the German-born musicians William Herschel (1738-1822) and his sister Caroline Herschel (1750-1848). They ground their own lenses and mirrors and made some of the best telescopes of the time. In 1781 William observed a star-like object with an apparent disc, and he showed that its orbit was that of a new planet beyond Saturn, eventually named Uranus. With better telescopes, he later found two satellites of Uranus and two of Saturn. He cataloged more than 800 double stars and showed that some were circling each other in accord with Newton’s laws, extending gravity beyond the solar


system. In 1782, King George III awarded Herschel the post of King’s Astronomer. From a 1783 survey of the distribution of stars, Herschel concluded that the Milky Way was a disc-shaped revolving galaxy of stars including our Sun, an idea suggested in 1750 by the amateur English astronomer Thomas Wright (1711-86). A study of some 2000 nebulous sources led Herschel to propose that various nebulae represent different

stages in the evolution of other galaxies, following earlier suggestions in 1755 by the German phi-losopher Immanuel Kant (1724-1804). Kant also concluded that neither infinite space nor bounded space is rational, and thus space is not objectively real. He proposed in his Critique of Pure Reason (1781) that the human mind is endowed with Newtonian categories like space and time. These allow us to construct our own world independent of their reality, which along with God can be nei-ther proved nor disproved by reason. The most dramatic result of Newtonian theory came from an analysis of the anomalous perturbations in the orbit of Uranus by a young English student, John Couch Adams (1819-92), and the French astronomer Urbain Leverrier (1811-1877). During some sixty years of obser-vations since its discovery, the orbit of Uranus was found to deviate by 1.5 minutes of arc from Kepler’s law, corrected for known perturbations. By 1845 Adams had calculated the position of an unknown planet that would cause this deviation of Uranus. The prediction of Adams was largely ignored until a similar calculation by Leverrier in 1846 was used by Johann Galle (1812-1910), head of the Berlin Observatory, to discover the planet Neptune. On the same evening he received Leverrier’s letter, he found the new planet less than a degree from the predicted position. One year before this triumph of Newtonian theory, Leverrier discovered a similar anomaly in the orbit of Mercury; but this shift of 40 seconds of arc per century in the perihelion of Mercury’s orbit could not be explained until Newton’s theory was replaced by Einstein’s theory of general relativity. REFERENCES

Christianson, Gale E. In the Presence of the Creator: Isaac Newton and His Times. New York: Free Press, 1984.

Cohen, I. Bernard. The Newtonian Revolution. Cambridge: Cambridge University Press, 1980.

Fauvel, John, Raymond Flood, Michael Shortland and Robert Wilson, eds. Let Newton Be! New

York: Oxford University Press, 1988.

m

M

F R

mirror

lightbeam

Figure 5.12 Measurement of the Universal Gravitation Constant by Cavendish In 1798 Cavendish measured the constant of universal gravitation G with a torsion balance consisting of two lead balls each of mass m suspended on a rod with a fine wire. When two large lead spheres each of mass M were brought near on diagonally opposite sides from the suspended balls, a small attractive force F was measured by the twisting of the wire. A small twist of the mirror causes a large shift in the light beam. Using the law of universal gravitation F = GmM/R², the constant G could be determined from the values of F, m, M, and R, as:

G = FR²/mM = 6.7 x 10-11 N-m²/kg². From this value the mass of the Earth Me could be calculated by equating the weight W = mg of an object of mass m with the gravitational attraction between it and the Earth, whose centers are separated by the radius of the Earth Re so: W = mg = mMe/Re² or Me = gRe²/G = 6 x 1024 kg.


Galileo. Discourse Concerning Two New Sciences. H. Crew and A. deSalvio, trans. New York: Dover, 1954.

Gillispie, C. C. The Edge of Objectivity. Princeton: Princeton University Press, 1960.

Hall, A. R. Philosophers at War: The Quarrel Between Newton and Leibniz. New York: Cambridge University of Press, 1980.

Hankins, Thomas L. Science and the Enlighten-ment. Cambridge: Cambridge University Press, 1985.

Herival, John. The Background to Newton’s “Prin-cipia”: A Study of Newton’s Dynamical Re-searches in the Years 1664-1684. Oxford: Clarendon Press, 1965.

Manuel, Frank E. A Portrait of Isaac Newton. Washington: New Republic Press, 1979.

McMullin, Ernan. Galileo, Man of Science. New York: Basic Books, 1968.

Newton, Isaac. Mathematical Principles of Natu-ral Philosophy. A. Motte, trans. rev. F. Cajori. Berkeley: University of California Press, 1934.

Newton, Isaac. Opticks. (Fourth Edition, 1730). New York: Dover, 1952.

Nicholson, Marjorie. Newton Demands the Muse. Princeton: Princeton University Press, 1946.

Sabra, A. I. Theories of Light: From Descartes to Newton. London: Oldbourne, 1967.

Westfall, Richard S. The Construction of Modern Science. Cambridge: Cambridge University Press, 1977.

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1. ORIGINS OF THE ENERGY CONCEPT The successes of the Newtonian synthesis strengthened European confidence in mechanical thinking, but made few immediate contributions to practical developments in technology. The application of mechanical ideas to chemistry, initiated by Boyle, made little progress in understanding chemical reactions or phenomena such as combustion. Newton had struggled with the role of active principles in nature, but the me-chanical model of passive particles acted upon by external forces prevailed in the 18th century. It provided little guidance for the chemist beyond the new emphasis on quantitative measurements, but these would eventually lead to a revolution in chemistry. Even mechanical devices and early forms of steam power developed quite independently of Newtonian theory. But new inventions and me-chanical ways of thinking began to make dramatic changes in social and economic structures, espe-cially in England with the introduction of the fac-tory system of large-scale machine production. The development of steam power hastened the trend toward large urban factory centers, accom-panied by the mining of coal and iron and the building of roads and canals. By the end of the 18th century this Industrial Revolution was well

established, but its rationalizing tendencies and dehumanizing effects came increasingly under at-tack in the literary and artistic movement known as the Romantic Reaction. The Vis Viva Concept Even during Newton’s lifetime, debate arose concerning the inadequacies and dangers of the mechanical philosophy, and Newton’s old nemesis led the attack. In 1686 Gottfried Leibniz opened the debate by publishing a paper with the grand title “A short demonstration of a famous error of Descartes and other learned men, con-cerning the claimed law of nature according to which God always preserves the same quantity of motion; by which, however, the science of me-chanics is totally perverted.” Descartes defined “quantity of motion” as the product of mass and speed, leading to the law of conservation of mo-mentum (mv) and Newton’s definition of force in his second law as the rate of change (Δ) of mo-mentum (F = Δmv/Δt or F = ma if m is constant). Leibniz referred to the momentum mv as vis mortua (dead force), measuring the inertial tendency of inert objects to resist changes in their motion. By contrast, he defined vis viva (living force) as the quantity mv², which Huygens viewed as being conserved in elastic collisions. Leibniz insisted that, “Force must be evaluated by the

CHAPTER 6

An Energistic Universe

Chemical and Industrial Revolutions, Heat and Light

Chapter 6 ▪ An Energistic Universe 126

quantity of effect it can produce, for example by the height to which it can raise a heavy load.” Galileo’s law gives the distance (height) moved by an object starting from rest to a speed v with constant acceleration a = v/t (in time t = v/a) as:

d = at²/2 = a(v/a)²/2 = v²/2a.

Thus acceleration to a speed v over a distance d is a = v²/2d. For an object of mass m to be acceler-ated to a speed v in a distance d, the required force is given by:

F = ma = mv²/2d.

An object with weight mg (where g is the accel-eration of gravity) and upward velocity v has a “living force” proportional to mv² capable of raising it to a height d = v²/2g. Leibniz suggested that this vis viva is not lost in inelastic collisions, but merely “dissipated among the small parts” that make up the colliding objects. He also suggested that the “living force” given to an object thrown upward is stored in the object as mv² decreases during its rise, but is recovered when it falls. Thus he viewed vis viva as part of a more general conserved quantity, later called energy. The vis viva controversy was based on a metaphysical difference in opinion. The Cartesians and their Newtonian successors tried to explain phenomena by matter and motion as measured by momentum, without appealing to intrinsic forces in matter. Leibniz believed that force is the essence of matter, constituting a living and dynamic world of activity, rather than a dead world of passive inert particles. Only that which is active is real, and activity is the expression of force. Conservation of vis viva makes the universe self sufficient, dependent only on the “pre-established harmony” of its parts, rather than requiring continual intervention by God. According to Leibniz, the world may not be perfect, but it is the “best of all possible worlds.” By the middle of the 18th century, the “quantity of motion” debate was recognized as more verbal and metaphysical than material. As early as 1668, Huygens had recognized that both momentum and mv² are conserved in elastic col-lisions. In 1742 the French mathematician Jean d’Alembert (1717-1783) clarified the distinction

between momentum and vis viva. Using Galileo’s acceleration equation a = Δv²/2d in Newton’s sec-ond law F = ma = Δmv/Δt = Δmv²/2d, gives:

FΔt = Δmv and F.d = Δmv²/2. Thus he showed that the impulse “FΔt” of a force F acting on a mass m for a time Δt equals the resulting change in momentum Δmv, while the work “F.d” done by a force F acting on a mass m over a distance d changes the vis viva by Δmv²/2. The Croatian Jesuit priest Roger Boscovich (1711-1787) developed a further cri-tique of mechanism. He rejected the idea of material corpuscles and replaced it with the con-cept of matter composed of dimensionless points, which were centers of force extending out in every direction. These points exerted simultaneous forces of attraction and repulsion on each other to account for both the solidity and separability of matter. A similar idea was developed by German philosopher Immanuel Kant (1724-1804), who taught that we know substance only through forces, so that force was the essence of matter and the phenomenal basis of science. Following Kant, German nature philosophers and the Romantic movement came to view the world in terms of active principles and a unity of forces. In 1807 the English physician Thomas Young (1773-1829), who had completed his studies in Germany at the University of Göttingen, coined the word “energy” as the “capacity to do work” (F.d), and defined vis viva as “kinetic energy” (K.E. = mv²/2) to describe the energy of motion. Although Young’s suggestion was not widely adopted at first, the energy concept was eventually applied to phenomena in many other fields of science besides mechanics, including heat, light, electricity, magnetism, chemistry, biology, and atomic physics. It provided the kind of active principle and unifying concept that Leibniz had originally suggested and that was sought after in the nineteenth-century Romantic Reaction against mechanistic science.

The Phlogiston Theory A century before the emergence of the energy concept, German chemists tried to develop an active principle to account for chemical reac-


tions between matter and fire in their “phlogiston theory.” The Lutheran alchemist Joachim Becher (1635-82) of Speyer suggested that compound bodies consist of three kinds of earths, correspond-ing to the iatrochemical principles of salt, mercury and sulfur. He identified the sulfur principle with a “fatty earth” (terra pinguis) that gave bodies, especially organic substances, their qualities of odor, taste and combustibility. In 1703 Becher’s student, the physician Georg Ernst Stahl (1660-1734), gave the name phlogiston (Greek: inflammable) to this terra pinguis, and turned it into a unifying theory to explain combustion and calcination. The phlogiston theory explained com-bustion as the release of phlogiston. When a rib-bon of metal burned, it left an ash or calx (oxide), given by the reaction:

metal - phlogiston → calx.

With considerable insight, Stahl recognized that this process was analogous to the rusting of a metal. Phlogiston also accounted for properties like color and odor, and its escape from a burning object agitated atoms and produced heat. Organic materials like wood contained more phlogiston than metals and thus burned better. Since a metal can be recovered from its calx by burning it with charcoal, the metal seemed to absorb phlogiston from the charcoal:

calx + phlogiston → metal.

Since the charcoal mostly disappears, it appeared to be nearly pure phlogiston. By the middle of the eighteenth century, it became increasingly clear that the calx weighed more than the original metal! In the 1760s, scholars at the medical school of Montpellier in France suggested that phlogiston has “levity,” or negative gravity, as evidenced by its tendency to rise. Thus when phlogiston combined with a metal it made it lighter. This idea clearly contradicted the mechanical philosophy, but the phlogiston theory provided a better qualitative explanation of many chemical reactions. It gained wide acceptance by British chemists during the latter half of the eighteenth century, and inspired several of them to carry out experimental work that eventually

overthrew the theory and laid the foundations of modern chemistry. New Gases and Experimental Methods In the early eighteenth century, the An-glican clergyman Stephen Hales (1677-1761) developed quantitative methods of experimenta-tion with gases. He collected and measured the “airs” liberated by organic and inorganic materials by bubbling them through a “pneumatic trough” of water into an inverted flask, displacing its water. He recognized that a gas can exist free or fixed in a solid, but he thought all gases were forms of common air, since they all obeyed Boyle’s law. When he described his methods to the Royal Soci-ety in 1727 he explained the importance of meas-urements:

And since we are assured that the all-wise Creator has observed the most exact proportions, of number, weight, and measure, in the make of all things; the most likely way therefore to get any insight into the nature of these parts of the creation, must in all reason be to number, weigh and measure.

Hales was the first to quantify blood pressure in animals, measuring the height of the blood in a thin glass tube connected to a blood vessel. He also measured sap pressure in trees with a mercury-gauge manometer. In the eighteenth century, water and air were still regarded as elements, but the Scottish chemist Joseph Black (1728-99) showed that air is not a simple substance. During the preparation of his 1754 thesis for the medical degree at Glasgow, Black showed that magnesia (magnesium carbon-ate) and limestone (calcium carbonate) lost weight and released a similar gas when heated. Using the methods of Hales, he showed that if an acid dissolved the same amount of magnesia or lime-stone, it lost the same weight and type of gas, and that the gas could recombine with their residues to form the original substances. Black called the gas “fixed air” because it could be fixed into solid form again. The residue from limestone (calcium carbonate) was the caustic alkali quicklime (calcium oxide), then


assumed to be a compound of limestone and phlogiston, but Black established that limestone and magnesia were compounds of alkalis and “fixed air.” When bubbled through lime water made from quicklime, it formed a chalky precipitate that served as a test of its presence. He found that it did not support combustion or respiration, and that he could obtain it by passing common air over charcoal. This led him to conclude that this gas we now call carbon dioxide is a component of air as well as fixed in solids. The chemical nature of gases was studied further by the eccentric English scientist Henry Cavendish (1731-1810), who spent four years at Cambridge but was apparently too shy to be exam-ined for a degree. In London he collected a gas from the action of dilute acid on various metals and found that it burned with a blue flame. He was the first to measure the weight of a particular volume of gas, and showed that the density of his new gas was only 1/14 the density of air. In a 1766 memoir “On Factitious Airs,” he called it “inflammable air” (later named hydrogen by La-voisier) and identified it as rich in phlogiston be-cause of its lightness and inflammability. One of Black’s students at the University of Edinburgh, Daniel Rutherford (1749-1819), studied the portion of air that remains after com-bustion ceases. He removed its “fixed air” by passing it through a strong alkali, but it would still not support combustion. In his 1772 doctoral thesis, he concluded that it had absorbed all the phlogiston it could from the burning process, and thus he called it “phlogisticated air” (later named nitrogen). The Unitarian clergyman Joseph Priestley (1733-1804) became interested in the properties of gases when he served a church in Leeds next to a brewery. He collected the “fixed air” given off in the fermentation process and discovered soda-water when he dissolved it in water. Using a pneumatic trough with mercury, he was able to isolate several water-soluble gases. In the 1770s he isolated the gases now called ammonia, carbon monoxide, hydrogen chloride, oxygen, sulfur dioxide, and various oxides of nitrogen. When he treated metals with “spirit of nitre” (nitric acid) to form “nitrous air” (nitric oxide), he found that it

diminished a volume of common air by about one-fifth, causing it to lose its “goodness” for res-piration or combustion. In 1774 Priestley identified the missing one-fifth of air with a gas given off when he heated the red calx of mercury (mercuric oxide) under a bell-jar with a burning glass. He identified it with the source of “goodness” in common air by showing that it was especially effective in supporting the respiration of a mouse and the burning of a candle. He assumed that it lacked phlogiston, giving it a greater capacity for absorb-ing phlogiston during combustion, and thus he called it “dephlogisticated air” (later named oxy-gen by Lavoisier). The Swedish apothecary Carl Scheele (1742-86) had isolated the same gas two years earlier and named it “fire air.” He too iden-tified it with a lack of phlogiston, but his results were not published until 1777. In further experi-ments, Priestley showed that vitiated air could regain its “goodness” by the action of sunlight on green plants. Phlogiston theory made it possible to retain air and water as elements, explaining new gases in terms of the different ways they combine with phlogiston. Even the work of Cavendish in 1783 on the production of water from “inflammable air” could be explained by the the-ory. Using sparks of electricity from the newly discovered Leyden jar, he ignited inflammable air with common air in a closed flask, and produced a “dew” of water on the inside surface. Collecting the dew, he found “that almost all the inflammable air, and about one-fifth of the common air, are turned into pure water.” He again formed water when he exploded inflammable air with dephlo-gisticated air. His firm belief in phlogiston (φ) and the elementary nature of water led him to suppose that water was pre-formed in each of the gases as follows: dephlogisticated air + inflammable air → water, (water - φ) + (water + φ) → water.

He reported his results in his Experiments on Air (1784), noting that 2.02 volumes of inflammable air combined with one volume of dephlogisticated air to produce an equal weight of water (eventually leading to the formula H2O for water).


2. THE CHEMICAL REVOLUTION Lavoisier and the Elements The French chemist Antoine Lavoisier (1743-94), often called the “father of modern chemistry,” was well prepared to reinterpret the new discoveries of gases and their reactions. His father was a wealthy lawyer who sent him to the Collège Mazarin in Paris to study law, but he became interested in science and pursued studies in mathematics, physics, botany and chemistry. His sympathies were Newtonian and he combined the quantitative methods of physics with the prac-tical approach of the chemist. To support his chemical research and private laboratory, he invested in the tax-collecting “Ferme Général.” He also married the 14-year old daughter of an executive in the firm, who became his chief research associate. In the tradition of Newton, Lavoisier based his experimental work on the principle of conservation of mass in all chemical reactions. By experimenting with reactions in closed flasks, he was able to confirm this principle by careful weighing before and after a reaction, and to account accurately for any transformations that occurred. He expressed this idea in his Traité Élémentaire de Chimie (1789), the first modern chemical textbook:

We may lay it down as an incontestable axiom that in all the operations of art and nature, nothing is created; an equal quantity of matter exists both before and after the experiment,...and nothing takes place beyond changes and modifications in the combinations of these elements. Upon this principle, the whole art of performing chemical experiments depends.

In his first communication to the Académie Royale de Sciences (1765), to which he was elected in 1768, he reported that the water given off in heating gypsum to make plaster of Paris is exactly equal in weight to that required to set the same amount of plaster. In 1768 Lavoisier tested the claim of von Helmont that water could be transmuted to earth, based on the appearance of sediments after long

boiling of water. He boiled water for 101 days in a closed system, in which the condensed steam could be returned to the boiling water. He showed that the weight of the water did not change, while the flask lost an amount of weight equal to that of the sediments. This led him to suspect that the various “airs” identified by the English chemists were not “transmutations” of the element air, but were distinct gases in a mixture that constituted the atmosphere. In 1772 he began a systematic program of repeating past experimental work on calcination and combustion, “with new safeguards in order to link our knowledge of the air...with other acquired knowledge and so to form a theory.” Lavoisier began his revolution in chemi-cal theory by showing that the burning of phos-phorus and sulfur increased their weight. Rejection of the idea of levity (negative weight) led him to recognize that they must have united with something instead of losing phlogiston. He then heated tin and lead in closed containers with a limited supply of air, forming a layer of calx on each. The containers and their contents did not change weight. But after each was opened, air rushed in to replace the original air that had united with the metal, accounting for the increase in the weight of the calx. When he heated the red calx of lead with charcoal, it was converted back to lead along with a gas that he identified as “fixed air.” At first he thought that this must be the gas responsible for calcination and combustion, but further tests showed that it would not support any combustion. When Priestley visited Paris in October of 1774, Lavoisier dined with him and became acquainted with his discovery of “dephlogisticated air” from the red calx of mercury. Refining Priestley’s experiment, he heated four ounces of mercury in a flask with a long bent neck leading into an inverted bell-jar supported over a mercury bath. Starting with 50 cubic inches of air in the flask and bell-jar, Lavoisier heated the mercury in the flask to its boiling point for a period of 12 days, noting the formation of “red particles” on the surface of the mercury until the calcination was complete. He found the weight of the red calx to be 45 grains (about 2.9 grams) and the volume in


the bell-jar reduced by one-sixth, now filled with “azotic” (lifeless) air unable to support respiration or combustion. Reversing the process, he heated the 45 grains of red calx for a few minutes until it disappeared, and he collected 41.5 grains of mercury and about eight cubic inches of “respirable air” in the bell-jar. Basing his conclusions on the conserva-tion of mass, Lavoisier noted that the 45 grains of calx must have formed from the combination of 41.5 grains of mercury with 3.5 grains of respir-able air from the bell-jar, rather than the mercury losing its phlogiston. Furthermore, the conversion of calx to mercury released 8 cubic inches of respirable air, matching the loss of 1/6 of the 50 cubic inches of air in the original calcination of mercury. In 1775 he presented his results to the Académie in his most famous memoir, “On the Nature of the Principle that combines with Metals in Calcination and that increases their Weight,” without crediting Priestley’s contribution. Lavoisier revised his memoir in 1778 after repeating Priestley’s experiments that showed the complete disappearance of charcoal when heated with the red calx of mercury. He concluded that, “Fixed air is the result of the combination of the eminently respirable portion of the air with charcoal.” His report to the Académie in 1777 on “Experiments on Respiration of Animals...” had suggested that respiration is a process of slow combustion. In subsequent work with Pierre-Simon Laplace, they demonstrated this quantitatively by showing that the same amount of ice melts from animal heat in respiration as from charcoal combustion when these processes pro-duce the same amount of “fixed air,” anticipating the principle of conservation of energy. In 1780 Lavoisier reported that the atmosphere consisted of one-fourth respirable air and three-fourths azotic air. Priestley, who con-tinued to find evidence that seemed to support the phlogiston theory, gave the more accurate ratio of one-fifth dephlogisticated air and four-fifths phlogisticated air. Shortly after Cavendish had formed water in 1783 from the combustion of inflammable air with respirable air, Lavoisier repeated the experiment. He then reversed the process by passing steam over red-hot iron,

breaking down the steam and collecting inflam-mable air. Since inflammable air was the generic ingredient in water, he renamed it hydrogen (water-former). Thinking that respirable air was the generic ingredient of all acids (it was absorbed in reactions of acids with metals), he named it “the acidifying principle,” or oxygen (acid-former). Thus water was established as a compound of hydrogen and oxygen. In 1810 British chemist and physicist Humphry Davy (1778-1829) showed that muriatic (hydrochloric) acid contains hydrogen instead of oxygen. In 1783 Lavoisier began a revision of chemical terminology to match the clarifications of experimental work he had achieved over the previous decade. Madame Lavoisier celebrated the beginning of this “new chemistry” by burning the books of the phlogiston theorists. Following Boyle, Lavoisier defined an element as a “simple substance” that cannot be subdivided, and began to form a list of such elements. He could then assign names to chemical compounds based on the weighable elements of which they consisted. For example, he named carbon after charcoal (French: charbon) and renamed “fixed air” as “carbonic acid gas” for its carbon and oxygen components. Lavoisier’s first list of “simple sub-stances” included, among others, the seven tradi-tional metals and, ironically, such “imponderables” as caloric (heat) and light that lacked measurable mass. Since caloric changes liquids to gases, he classified the newly discovered gases as compounds containing caloric. Thus “oxygen gas” was the element oxygen plus caloric. In collaboration with other chemists, Lavoisier published a book in 1787 on Methods of Chemical Nomenclature, which was quickly adopted by most chemists and led to the modern system. In 1789 he presented his theories as a unified synthesis of chemical knowledge incorpo-rating the new terminology in his Traité Élémen-taire de Chemie, which listed some 23 authentic elements, none of which he had independently discovered. A new generation of chemists began to speak the new language, seeing calcination, combustion and respiration as oxidation processes, in which oxygen combined with substances rather than phlogiston being released.


In 1789 a political revolution began in France, inspired by ideas of freedom and equality that grew out of the scientific revolution. Lavoisier served the new regime in improving gunpowder and helping to establish the units of the new decimal metric system decreed by the National Assembly. But his tax-collecting investments led to further accusations by Jean Paul Marat, whose studies of fire Lavoisier had criticized. In the Terror of 1794, he and his father-in-law were executed with the guillotine. In the same year, Priestley left England for America after his home and chapel in Birmingham were burned by a mob who objected to his support of the French Revolution. Dalton’s Atomic Theory Lavoisier’s new chemistry led to several empirical discoveries that formed the basis for a quantitative atomic theory of the elements. In 1797 the French chemist Joseph Proust (1754-1826), working in Madrid, announced the law of “definite proportions.” He showed that copper carbonate always had a constant composition of 5 parts copper to 4 parts oxygen to 1 part carbon by weight, regardless of how he prepared it in the laboratory. He went on to demonstrate similar ratios in other compounds, and generalized these results to state that all compounds contain ele-ments in certain “definite proportions” by weight. This law of definite proportions was disputed for a few years by Claude Berthollet (1748-1822), one of Lavoisier’s collaborators in the new nomen-clature, who believed that the composition of a compound was variable, depending on the mass of the reacting elements. The Quaker school-teacher John Dalton (1766-1844) first applied the atomic theory to the new view of the elements in a paper read to the Manchester Literary and Philosophical Society in 1803, and in his New System of Chemical Phi-losophy (1808). Dalton’s interest in atoms began with meteorology and the nature of the atmos-phere. Following Boyle and Newton, he believed that gases consisted of particles that repel each other; but he thought that this repulsion was due to caloric, since in 1801 he found that gas pressure increased directly with increasing temperature. In

1802 the French chemist Joseph Gay-Lussac (1778-1850) found a similar relation for the volume of a gas, a result also demonstrated in 1787 by the French physicist Jacques Charles (1746-1823), but not published. Charles was the first to construct a hydrogen balloon, ascending in 1783 just 10 days after the first manned hot-air balloon flight. In 1804 Gay-Lussac used a hot-air bal-loon to ascend some four miles. In 1805 he collected air samples at high altitude and found little change in the composition of the atmosphere. This led Dalton to wonder why heavier gases do not settle closer to the ground. He also observed that water vapor added to dry air increased the pressure by the amount of the vapor pressure of the water at the same temperature. In 1801 he stated his law of “partial pressures,” suggesting that the total pressure of a mixture of gases is the sum of the pressures that each constituent gas would have by itself in the same volume. Each gas was like a vacuum to the others. To explain these results, he suggested that atoms of different substances differ in their weight, and only atoms of the same substance repel each other. Dalton applied these ideas to all matter and not just gases. The law of definite proportions seemed to show that elements combine to form compounds in small whole number ratios by weight. He saw that he could explain this by assuming that the atoms of different elements dif-fer in weight by similar ratios, and that when two elements combine to form a compound, each atom of one element unites with one or a small whole number of atoms of the other element. Dalton began to apply this atomic idea to the gases formed when carbon combines with hydrogen and with oxygen. He found that methane contained twice as much hydrogen as ethylene for a given quantity of carbon (methane 3:1, ethylene 6:1). Carbonic acid (carbon dioxide) contained twice as much oxygen as carbonic oxide (carbon monoxide): the carbon-oxygen ratio in carbonic acid was 3:8 and in carbonic oxide it was 3:4 by weight. These simple ratios for more than one compound of two elements led Dalton to his law of multiple proportions in 1804, and the suggestion that carbonic oxide is a compound with one atom


of carbon and one of oxygen, while carbonic acid consists of one atom of carbon and two of oxygen. By using the relative weights of the atoms of different elements, Dalton established the first quantitative atomic theory. Since hydrogen was the lightest element, he took the weight of the hydrogen atom to be one, and from his multiple proportions he could calculate integers greater than one for the atoms of the other elements. Thus ethylene with a ratio of 6:1 for carbon to hydrogen gave carbon an atomic weight of 6. Since he had no way of determining the numbers of combining atoms, he made the simplifying assumption that, “When only one combination of two bodies can be obtained, it must be presumed to be a binary one, unless some cause appears to the contrary.” This assumption that such compounds contain only one atom from each element later proved to be untenable. Using symbols for the elements, such as O. for hydrogen, O for oxygen, and O| for “azote” (nitrogen), Dalton drew up the first table of atomic weights. He showed possible combinations of these atoms to form various chemical substances (see Figure 6.1).

The Swedish chemist Jakob Berzelius (1779-1848) confirmed and extended Dalton’s results, finding many more definite proportions by about 1807. Berzelius also introduced the initial letter of the Latin name (plus a second letter in some cases) as symbols, such as H for hydrogen, Cl for chlorine, and Cu for copper (cuprum). This gave rise to the modern notation for compounds by writing the letters for each element together, with subscripts for more than one atom of a given element. Thus Berzelius designated carbon mon-oxide as CO and carbon dioxide as CO2. Dalton’s usual assumption of binary compounds led him to some mistaken relative atomic weights. For example, he assumed that the water “molecule” would consist of one hydrogen and one oxygen atom (HO instead of H2O) accord-ing to the reaction:

H + O → HO. Since he found that hydrogen and oxygen com-bined in a ratio of 1:7 (actually nearer 1:8), he assigned a relative atomic weight of 7 to oxygen. Avogadro’s Molecular Theory

A clue to the combining num-bers of atoms came from the discovery by Gay-Lussac in 1808 that the volumes of combining gases, as well as that of any gaseous products, are in simple numerical ratios. Cavendish had ob-served this for hydrogen and oxygen, combining in the ratio of 2:1 by volume to form water. Dalton’s theory did not directly explain this volume relation-ship. But from his view that the num-bers of atoms of two combining ele-ments are in simple numerical ratios, it seemed likely that the volume ratio of two combining gases was related to the ratio of their combining atoms. In 1811 the Italian physicist Amedeo Avogadro (1776-1856) sug-gested a simple explanation in his “molecular hypothesis”: equal volumes of different gases at the same pressure and temperature contain equal numbers of molecules. But this raised a problem:

Hydrogen Nitrogen Carbon Oxygen Phosphorus Sulfur

WaterEthylene Methane Nitric Acid(CH) (CH ) (HO) (NO )2 2

Acetic Acid Sulfuric Acid Nitrous Acid(SO ) (N O )2(C H O )2 2 3 2 3

Figure 6.1 Dalton’s Atomic Symbols and Combinations Dalton used symbols to represent atoms and showed possible combinations of these symbols to represent substances. However, he based, these combinations on over-simplified assumptions, leading to some later corrections based on Avogadro’s hypothesis.


one volume of hydrogen combines with one volume of chlorine to form two volumes of hydrogen chloride, implying that one hydrogen atom and one chlorine atom would form two hydrogen chlorine molecules. To “balance” this reaction, Avogadro suggested that some gases consisted of molecules with two atoms of the same element, so that:

H2 + Cl2 → 2 HCl,

where H2 and Cl2 are diatomic molecules. Also one volume of nitrogen combines with one volume of oxygen to form two volumes of nitric oxide gas, suggesting the reaction:

N2 + O2 → 2 NO.

From Gay-Lussac (and Cavendish before him) the ratio of combining volumes of hydrogen and oxygen to form water is 2:1, so for Avogadro the reaction would be:

2 H2 + O2 → 2 H2O.

Thus Dalton’s combining-weight ratio of 1:7 = 2:14 for two hydrogen to one oxygen mole-cule implies that the atomic weight of oxygen is 14 (actually 16) relative to one hydrogen. Avogadro confirmed this by calculating the gas-density ratio of oxygen to hydrogen, finding it to be slightly more than 15. This corresponds to their mass ratio in equal volumes, and thus their atomic-weight ratio by his hypothesis. Avogadro’s hypothesis was proposed independently in 1814 by the French physicist André Ampère, but was rejected by both Dalton and Berzelius. As a result, it was largely forgotten for nearly fifty years, and the atomic theory saw little development until after 1860. Dalton held that like atoms repel one another and cannot combine. Berzelius suggested in 1812 that this repulsion resulted from like charges in his “electrochemical theory” of chemical affinity, in which only unlike atoms with opposite charges could form molecules. Gay-Lussac proposed that identical volumes of gaseous elements contain the same number of atoms, but not their compounds. Berzelius accepted this idea and was able to use it to calculate many correct atomic weights for a

table drawn up in the 1830s. For example, he held that two atoms of hydrogen combine with one atom of oxygen to form water as follows:

2 H + O → H2O .

Although this reaction was not correct in assuming that hydrogen and oxygen as gases were monatomic, it gave the right formula for water and thus the right atomic weight for oxygen. The London physician William Prout (1785-1850) proposed another promising idea in 1815, but it was also rejected. Noting that atomic weights are approximately integers relative to hydrogen as unity, he suggested that atoms of the other elements were combinations of varying numbers of hydrogen atoms. However, Berzelius and others soon found non-integer atomic weights, such as 35.5 for chlorine. A new form of Prout’s hypothesis emerged in the 20th century with the idea that the nucleus of the atom contains an integer number of protons. In 1824 Prout identified hydrochloric acid in stomach secretions, and in 1827 he distinguished the organic groups we now call carbohydrates, fats, and proteins. Organic and Structural Chemistry Organic chemistry began to develop in the first half of the 19th century while atomic the-ory languished. Berzelius suggested the distinction between organic and inorganic substances, based on whether their origin is in living tissue or not. He believed that organic chemicals required a “vital force” essential to life for their production. In 1817 the French chemists Pierre Pelletier and Joseph Caventou isolated a green compound from plants that they called chlorophyll (green leaf), which converts sunlight into chemical energy in the photosynthesis process. In 1820 they isolated several alkaloids, such as quinine and strychnine. Two German chemists, Friedrich Wöhler (1800-82), a student of Berzelius, and Justus von Liebig (1803-73), a student of Gay-Lussac, inde-pendently identified silver compounds, which they found in 1824 to have identical composition but different properties. Berzelius suggested the name “isomers” (“equal parts”) for such compounds, which demonstrated the importance of the struc-


ture of molecules as well as their composition. In 1828 Wöhler challenged the organic distinction made by Berzelius, showing that a urea-like crystal formed by heating ammonium cyanate was identical to urea, a compound produced in the kidney and found in mammalian urine. Liebig helped to establish the view that oxidation of fats and carbohydrates produce body heat and vital activity, but for him “vitalism” was an effect rather than a cause. The problems of structural chemistry stimulated a revival of atomic and molecular the-ory. The French chemist Auguste Laurent (1807-53) showed that, contrary to Berzelius’ electro-chemical theory, some compounds did not seem to depend on electrical attraction. Laurent developed a theory of structural types, in which families of organic compounds were based on atomic groupings, called radicals, independent of electric charge. In 1850 the English chemist Edward Frankland (1825-99) prepared the first organic compounds with atoms of metals forming an inte-gral part of their molecules. His study of these organometallic compounds showed that each metal atom combined with a definite number of organic groups. His “theory of valence” in 1852 suggested that each type of atom has a fixed capacity (valence) for combining with other atoms. In 1858 at the University of Ghent in Belgium, the German chemist Friedrich Kekulé (1829-96) presented his theory that the atoms of organic molecules form structural patterns based on valence. Taking the valence of carbon as four, he showed how one carbon atom can combine with four other atoms, and several carbon atoms could form a chain linking other atoms in various geo-metric patterns to produce many different compounds. He assigned positions to the atoms based on a compound’s chemical behavior. Thus he could account for many hydrocarbons by simple structural formulas, such as the following: H H H H H H | | | | | | H—C—H H—C—C—H H—C—C—C—H | | | | | | H H H H H H Methane Ethane Propane

Since carbon atoms can combine in so many ways, isomerism is very common among organic com-pounds. Thus isomers of many hydrocarbons proved to have the same formula but different structures, such as butane (C4H10), which comes in the normal form and in the form of isobutane (with a boiling point about 10° lower), as shown in the formulas below. H H H H H

H H H H \ | | | / | | | | C—C—C

H—C—C—C—C—H / | \ | | | | H C H

H H H H / | \ H H H

Normal butane Isobutane

As early as 1837, Liebig and his French contemporary J. B. Dumas showed that certain radicals play the same part in organic reactions as atoms do in inorganic reactions. Kekulé was able to incorporate such radicals into his structure theory. For example, hydrocarbon derivatives contain radicals such as the hydroxyl group OH, which form alcohols, including the following:

H H H | | | H—C—OH H—C—C—OH | | | H H H

Methyl alcohol Ethyl alcohol

But the development of such structural models depended on a better molecular theory to guide the determination of valences, leading Kekulé to call the First International Chemical Congress at Karlsruhe in 1860. Here the Italian chemist Stanislao Cannizzaro (1826-1910) began a campaign to revive the molecular theory of Avogadro. In a pamphlet distributed at the con-ference, he showed how the molecular weights of many compounds could be determined from their vapor densities using Avogadro’s hypothesis. Most chemists soon recognized the validity of the methods of Avogadro and Cannizzaro, and began to determine the definitive atomic weights of the elements and their valences.


Struggling with the structure of benzene (C6H6) in 1865, Kekulé was in a dream state when he suddenly saw a carbon chain twisting like a snake trying to swallow its tail. This led him to propose a ring of carbon atoms, including three double bonds, for the basic structure of benzene (Figure 6.2). Combined with various radicals, the benzene ring quickly found a place in accounting for many other aromatic compounds.

Mendeléev’s Periodic Table With atomic weights and valences of the elements clarified in the 1860s, chemists began to try to classify them into related groups. In London the chemist John Newlands (1836-98) arranged the elements according to increasing atomic weights in 1864, and found that every eighth element, starting from any given one, had similar properties. This periodic repetition reminded him of musical octaves, so he called it the “law of octaves.” The first three of his octaves are as follows:

1 2 3 4 5 6 7 H Li Be B C N O F Na Mg Al Si P S Cl K Ca Cr Ti Mn Fe

However, in trying to form a complete classifica-tion, he tended to force some elements into anomalous relationships, leading some chemists to say that he could do better arranging them alphabetically. Except for hydrogen, pairs of ele-ments in the first two “octaves” do show strong mutual resemblances. But in the third octave beginning with chromium (Cr), these resemblances break down completely. The periodic law was developed inde-pendently and in its most complete form in 1869 by the Russian chemist Dmitri Mendeléev (1834-1907). He was the fourteenth child of a Siberian school teacher. Traveling thousands of miles to St. Petersburg for schooling at the age of 14, he eventually rose to great prominence as a professor in the university there between 1867 and 1890. In seeking to work out a periodic classification of the elements, he used the properties of the elements themselves to guide him, without any preconcep-tion about the sizes of the periodic intervals. Mendeléev stated the periodic law as follows: “The properties of the elements are in periodic dependence upon their atomic weights.” One of his principal guides was valence. For ex-ample, he dared to group tin with carbon and sili-con because each had a valence of four, even though only tin is a metal. In his earliest (1869) version of the periodic table, he arranged the 63 known elements according to increasing atomic weights and noticed a periodic variation of valence given by 1-2-3-4-3-2-1, from lithium to fluorine and from sodium to chlorine. This first effort identified six periods of elements, but he found that the periods could not contain equal numbers of elements if similar properties were to be matched without forcing their order. Mendeléev’s first period consisted solely of the two elements hydrogen and lithium. He set hydrogen apart since its properties did not match any known element. Since the noble gases were not yet known, helium was missing between hydrogen and lithium. The second period contained seven elements, each the first member of a family of five elements with similar properties extending over the last five periods, except for sodium (Na), which matches the properties of lithium. Elements in the third period match those of the second period down

H

C

C C

C C

C

H

H H

HH

Figure 6.2 Kekulé’s Structure for Benzene The benzene ring consists of six carbon atoms linked to each other in a ring that included double bonds and attached hydrogen atoms consistent with carbon’s valence of four.


to potassium (K), but Mendeléev extended the third period to 12 elements, since the properties of the next dozen elements did not match those of any lighter element. Thus he proposed that the elements from calcium (Ca) to copper (Cu) are the first members of new families, as shown in the table below based on Mendeléev’s first table.

Mendeléev’s Periodic Table (1869)

Period 1

Period 2

Period 3

Period 4

Period 5

Period 6

Ti - 50 Zr - 90 ? - 180 V - 51 Nb - 94 Ta- 182 Cr - 52 Mo -96 W- 186 Mn-55 Rh-104 Pt - 197 Fe - 56 Ru-104 Ir - 198 NiCo59 Pd -107 Os -199 H - 1 Cu - 63 Ag-108 Hg -200 Be - 9.4 Mg -24 Zn - 65 Cd-112 B - 11 Al - 27 ? - 68 U -116 Au -197 C - 12 Si - 28 ? - 70 Sn -118 N - 14 P - 31 As - 75 Sb -122 Bi - 210 O - 16 S - 30 Se - 79 Te -128 F - 19 Cl-35.5 Br - 80 I - 127 Li - 7 Na - 23 K - 39 Rb - 85 Cs -133 Tl - 204 Ca -40 Sr - 88 Ba -137 Pb -207 ? - 45 Ce - 92 ?Er -56 La - 94 ?Yt -60 Dy- 95 ?In -76 Th-118

Mendeléev expressed doubt about some measured atomic weights as underlined in the table, and he shifted the order of these elements to match the properties of other elements in a given row. Question marks next to symbols indicate elements that had been recently discovered and not suffi-ciently confirmed. Question marks in place of symbols represented elements as yet undiscovered at the time, but left unfilled to obtain a better match of the known elements. In 1870 the German chemist Lothar Meyer (1830-95) confirmed Mendeléev’s periodic law when he found that atomic volumes plotted against atomic weights showed a similar periodic

variation, with a series of peaks and valleys matching Mendeléev’s periods. Meyer obtained his atomic volumes from the ratio of atomic weight to density for each element, and he showed that they had clearly defined peak values corre-sponding to lithium (Li), sodium (Na), potassium (K), rubidium (Rb) and Cesium (Cs). These peaks were progressively higher with increasing atomic weight, indicating larger associated atoms. By 1871 Mendeléev was confident enough to predict the existence of elements corre-sponding to the gaps left in his periodic table, as indicated by question marks and estimated atomic weights. From the position of these three element gaps, he predicted their properties accurately enough to lead to their discoveries over the next few years. The element gallium was discovered in 1874, filling the position below zinc; scandium in 1879, fitting below calcium; and germanium in 1885, filling the second gap below zinc, each named for the country of its discovery. Most modern versions of the periodic table group the periods in seven horizontal rows, and each element has an atomic number indicating the order of its appearance in the periodic classification. Families of elements with similar properties then appear in vertical columns called groups. The first of the seven periods contains only hydrogen and helium. The second and third periods contain 8 elements each, ending with the noble gases neon and argon. The fourth and fifth periods contain 18 elements each, ending with the noble gases krypton and xenon. The sixth period contains 32 elements, including 14 lanthanide rare earths following lanthanum, usually set apart for reasons of space. The seventh and final period is incomplete, but includes another 14 actinide rare earths following actinium, with properties matching the lanthanides. 3. HEAT AND THERMODYNAMICS

Heat and the Steam Engine The study of heat and its relation to en-ergy paralleled the development of the new chemistry. In addition to his pioneering study of gases, Joseph Black (1728-99) also initiated the quantitative study of heat in 1761, treating it as an


imponderable material substance even before it received the name “caloric” in the new nomencla-ture of 1787. But his work on heat was not pub-lished until 1803, four years after his death, intro-ducing the quantitative techniques of calorimetry. Black was the first to clearly distinguish between heat and temperature, aided by the development of the thermometer. About 1600 Galileo used the expansion of air in a long-neck flask inverted over water to try to quantify temperature from the motion of water in the neck of this “thermoscope.” About 1650 his disciples in Florence used the expansion of alcohol with the flask upright. Newton suggested the need for two reference points for defining the size of the degree. The German-Dutch scientist Daniel Fahrenheit (1686-1736) reported on the first accurate mercury thermometer in 1724, using ice in salt brine and body temperature as reference points. Eventually the Fahrenheit scale was standardized with 32°F for the freezing point and 212°F for the boiling point of water. The Swedish astronomer Anders Celsius (1701-44) introduced the “centigrade” scale in 1742, with 100°C for freezing and 0°C for boiling, but this was reversed the next year. Black made the distinction between tem-perature as the intensity or degree of sensible heat versus the quantity of heat required to change the temperature or state (phase) of a substance. Based on careful measurements, he defined the quantity of heat added to a substance as proportional to the mass of the substance and its temperature change. He then found that the same mass of different sub-stances required different quantities of heat for the same change in temperature. Each substance had its own specific heat. Taking water as a standard (specific heat = 1), he defined one kilocalorie (Cal) of heat as the quantity required to change the temperature of 1 kilogram of water by 1°C. Black also observed that heat added in melting ice or boiling water does not change the temperature of either, and that the quantity of heat to change the phase of a substance is proportional to the mass changed. He measured this insensible or latent heat that is apparently stored in the water or steam without changing its temperature. Latent heat of about 80 Cal changes 1 kilogram of ice to

water at 0°C, and about 540 Cal changes 1 kilo-gram of water to steam at a constant 100°C. The same quantities of latent heat must escape to condense steam or freeze water. Black developed the methods of calorimetry to measure heat exchanges between substances by mixing them in an insulated “calorimeter” vessel and measuring their temperature changes. By assuming conservation of heat, he was able to equate the heat lost by the warmer substances to the heat gained by the colder substances. Black’s analysis helped to explain the improvements made in the steam engine by his associate at the University of Glasgow, the instrument-maker James Watt (1736-1819). In 1763 Watt was asked to repair a demonstration model of the Newcomen steam engine, which consisted of a boiler to introduce steam into a cylinder fitted with a piston that moved up and down in the cylinder as the steam expanded and condensed. Condensing steam produced a partial vacuum in the cylinder, permitting air pressure to act on the piston. While repairing the engine, he recognized that most of the heat was wasted in reheating the walls of the cylinder in each cycle after cold water was injected to condense the steam. In terms of Black’s measurements, 540 Cal per kg of condensed steam had to be removed in each stroke of the piston. In 1765 Watt devised a separate container to serve as an external condenser, which could be kept at low temperature and pressure while the cylinder could be kept hot all the time (see Figure 6.3). By not having to reheat the cylinder in each cycle, Watt’s engine operated more rapidly and could do more than twice as much work with the same amount of fuel. He also attached a pump to the condenser to remove the condensed steam and maintain a partial vacuum. Watt also allowed steam to enter alternately on either side of the piston, so that air pressure drove the piston both ways during condensation. In 1774 Watt joined with Matthew Boulton in Birmingham to manufacture steam engines, and by 1800 some 500 of their external-condenser engines were fueling the Industrial Revolution. In the English midlands, Watt and Boul-ton met on a monthly basis with a dozen other


businessmen and scientists in the so-called Lunar Society to further their interest in the practical utility of science. Several tended toward political radicalism and Nonconformist theology, including Priestley and Erasmus Darwin (grandfather of Charles). One study of English and Welsh indus-trial entrepreneurs in the 1770s concluded that 41% were Nonconformists compared to only 7% of the general population. They constituted a great diversity, including Quaker, Baptist, Methodist and Unitarian, but they usually shared a certain independence of mind and moral courage. As the principal heirs of Puritanism, they valued science for its material benefits. The use of steam power emphasized the connection between heat and motion in doing work. The Newtonian idea of heat as particle

motion rather than an impon-derable caloric fluid was re-vived by the American-born Benjamin Thompson (1753-1814), better known as Count Rumford. He sided with the British in the American Revo-lution, and left for Britain after the war. Knowing of Black’s measurement of the large quantity of heat given up by water when it freezes, he tried to detect any change in the weight of water in this change of phase. Finding none, he concluded that heat is not a caloric fluid, but is a form of motion. From 1785 to 1796, Rumford managed a munitions factory in Bavaria, where he received the title of count for his service. While boring can-non, he noticed the production of large amounts of heat, usually explained as the release of caloric as the metal was cut away. In a 1798 issue of the Philosophical Transactions he published “An Inquiry concerning the Source of Heat

which is excited by Friction,” in which he described his experiments:

Being engaged, lately, in superintending the boring of cannon in the workshops of the military arsenal at Munich, I was struck with the very considerable degree of heat which a brass gun acquires, in a short time, in being bored; and with the still more intense heat (much greater than that of boiling water, as I found by experiment), of the metallic chips separated from it by the borer.

He challenged the idea that caloric was released from the metal when it was chipped away by not-ing that even more heat escaped with a dull drill when no metal was cut, enough to melt the metal if it was trapped as caloric. He concluded that the

Condenser(partialvacuum)

water

Boiler

Cylindersteam

spentsteam

Exhaust

Intake

PistonConnecting

rod Flywheel

Valves

Heat added

Heat removed540 Cal/kg

airpressure

> Work done Figure 6.3 James Watt’s External Condenser Steam Engine In early steam engines, the cylinder was cooled in each cycle to condense spent steam. Watt introduced an external condenser, which could be kept cold while removing 540 Calories of heat per kilogram of condensed steam without cooling the cylinder. Steam from the boiler enters the cylinder through the intake valve and pushes the piston out. Steam condensation in the condenser produces a partial vacuum, so when the exhaust valve opens the spent steam rushes out of the cylinder into the condenser and air pressure pushes the piston back. Since the cylinder remains hot, the steam engine could operate at much higher speeds.


mechanical motion of the drill agitated particles in the metal to move, confirming that heat was a form of motion (Figure 6.4):

It is hardly necessary to add, that any thing which any insulated body, or system of bodies, can continue to furnish without limi-tation, cannot possibly be a material sub-stance: and it appeared to me to be extremely difficult, if not quite impossible, to form any distinct idea of any thing, capable of being excited, and communi-cated, in the manner the heat was excited and communicated in the experiments, except it be MOTION.

In spite of this evidence against the caloric theory of Lavoisier, only a few scientists accepted Rum-ford’s views during the next 50 years. In 1799 he established the Royal Institution in London, and in 1804 he went to Paris, where he married Lavoisier’s widow.

Dissipation of Heat The mathematical study of heat and the steam engine were pursued in France in the early 19th century by scientists and engineers trained in a more theoretical tradition than in Britain. The French mathematician Joseph Fourier (1768-1830) developed a new method of mathematical analysis

in 1807, in which he represented a certain class of functions by an infinite trigonometric series. He applied this theorem to the conduction of heat through solids in his Analytical Theory of Heat (1822). His interest was pri-marily in the “class of phenomena which are not produced by mechanical forces,” and viewed thermal phenomena as distinct from mechanics, as in the flow of heat from hot to cold until it reaches equilibrium. The relation between heat and mechanical effects was especially evi-dent in the steam engine, which was developed by the British but first ana-lyzed theoretically by the French army engineer Sadi Carnot (1796-1832). His father Lazare Carnot (1753-1823) was a

mathematician who had studied the operation of the water wheel. The younger Carnot saw in his father’s work an analogy for analyzing the operation of a steam engine and heat engines in general. His only publication, entitled Reflections on the Motive Power of Fire (1824), developed this analogy.

We may justly compare the motive power of heat with that of a fall of water. The motive force of a water fall depends on the height and quantity of fluid: the motive force of heat depends upon the quantity of caloric employed and what we may call the height of its fall, that is to say, the difference in temperature of the bodies between which the caloric is exchanged.

This analogy led Carnot to introduce the basic principle that the amount of work done by the pis-ton of a mechanically perfect steam engine depends only on the temperature difference between the boiler and the condenser and the amount of heat flow between them. But his adher-ence to the theory of caloric and its conservation led him to the wrong conclusion that no heat was converted into mechanical work. Carnot’s principle showed how to maxi-mize the thermal efficiency of heat engines by approaching as nearly as possible an ideal Carnot

Motion Heat

Drill bit Cannon barrel

Figure 6.4 Rumford’s Idea of Heat as Motion Rumford observed the heat produced in boring cannon barrels and theorized that the motion of the drill bit is transferred to the particles of the metal in the cannon barrel, and thus that heat is a form of motion. Opponents suggested that caloric fluid is trapped in the metal and released when the drill bit chips away metal filings. But Rumford noted heat production even by a dull drill bit without chipping any metal, confirming his theory.


cycle. In the Carnot engine, an idealized gas absorbs a quantity of heat Q at a constant upper temperature T1 (isothermal), cools without heat transfer (adiabatic), contracts and ejects heat Q at a constant lower temperature T2, and then returns to the original high temperature by adiabatic compression, allowing for maximum “heat fall” between T1 and T2. Such a cycle is “reversible” in that the work it produces can be used to run an identical engine backwards, transferring the same quantity of heat from the low to the high tem-perature. Carnot also established the idea that the maximum possible efficiency is the same for all heat engines of any type operating between the same two temperature levels. He demonstrated this by showing that two ideal heat engines with different efficiencies, operating between the same temperatures, would result in the absurd possibility of perpetual motion. If the more efficient engine drives the less efficient one in reverse, the second engine could pump heat from the lower to the higher temperature, maintaining or even increasing the temperature difference and thus doing endless work without adding fuel. In 1830 Carnot finally realized that some heat was converted into work and he abandoned the caloric theory, but he died in the cholera epidemic of 1832 before his notes could be published. Another French engineer B. P. E. Clap-eyron (1799-1864) analyzed Carnot’s ideas in 1834 with the aid of pressure-volume graphs of heat-engine cycles. He showed that the area of such a graph gives the work done in a cycle and suggested the quantitative definition of efficiency as the ratio of work done divided by the heat supplied. The relatively low efficiency of even ideal heat engines revealed the limitations of extracting work from heat. Furthermore, the natural tendency of heat to flow from high to low temperatures suggested that heat becomes increas-ingly less available to do work. This dissipation of heat was later formalized by Lord Kelvin in the second law of thermodynamics after caloric theory was replaced by the ideas of convertibility of heat into energy and conservation of energy in the first law of thermodynamics, leading to the absolute temperature scale.

Conservation of Energy While the English and French developed the mechanical view of nature, which separated matter from spirit, the Germans followed the iatrochemists and Leibniz in affirming that spiri-tual activity and vital forces permeated nature. In the eighteenth century, Immanuel Kant suggested that matter is constituted by the interaction and balancing of forces. The German school of nature-philosophy (Naturphilosophie), initiated by Friedrich Schelling (1775-1854) at the end of the century, supported the ideas of vitalism and the unity of the forces of nature. These ideas influenced Thomas Young, who suggested the word “energy” for the “living force” (vis viva) of Leibniz, but the Germans continued to use the word “force” (kraft) in developing the energy concept. Young and Humphry Davy developed Rumford’s idea that heat was a form of motion, but the caloric theory of heat still dominated the first half of the nineteenth century. The German physician Julius Robert Mayer (1814-1878) first suggested the general law of conservation of energy in all its forms. As a ship’s doctor in the tropics, Mayer noticed that the venous blood of European passengers, not yet acclimated to the tropics, was a brighter red than the working crew members. He reasoned that oxygen increases the redness of the blood, and that crew members were utilizing oxygen faster to combine with food in producing heat and work. Thus they converted chemical energy into me-chanical work by the muscles, and then into body heat. Mayer suggested that the ultimate source of all energy on Earth was the Sun. He tried to pub-lish his ideas in a German physics journal, but they were rejected due to lack of experimental data. In 1842 his work was published in a chemical journal edited by Liebig, who supported the idea of chemical combustion of food. Mayer’s paper was largely overlooked, but another German physician, Hermann von Helmholtz (1821-94), arrived at the same ideas independently from the study of muscle action, and worked them out in much greater detail. His work was also rejected at first, but in 1847 he published it in an influential booklet entitled Die Erhaltung der Kraft (On the Conservation of


Force). In arguing that heat and other kinds of energy (“force”) were equivalent and intercon-vertible, he was able to express the law of conser-vation of energy in a mathematical form, and to state the principle that the total amount of energy in the universe was constant. In opposition to vitalism, he showed that food can account for animal heat and motion, and that an additional vital force would make them into perpetual motion machines. In 1854 Helmholtz calculated that gravitational contraction of gas to form the Sun could provide enough energy to fuel the Sun for about 25 million years. Conservation of energy was established experimentally by the Scottish amateur scientist James Prescott Joule (1818-89), a student of Dal-ton, at his family brewery in Manchester from 1840 to 1847. By systematic measurements, he showed that several different forms of energy could be converted into the same quantity of heat.

In 1840 he measured the heat produced by a wire carrying an electric current by measuring the change in temperature of the water in which he submerged the wire. He showed that the quantity of heat generated in a given time was proportional to the electric energy, which he measured from the square of the electric current in a relation now known as Joule’s law. He suggested that the elec-tric energy converts into heat by the frictional effect of electric current flowing through the wire. Joule also recognized that work done against gravity produces a gravitational potential energy that can then do work. Thus an object of weight mg gains potential energy mgh when it is raised to a height h equal to the work done in raising it (P.E. = F.d = mgh). By attaching an object to a cord passing over pulleys and then wrapped around the axle of a paddle wheel submerged in water, he could release the object to convert its potential energy into rotational energy

h

Work = 2mgh Heat4,186 joules 1 Cal

watermm

Figure 6.5 Joule’s Measurement of the Mechanical Equivalence of Heat Between 1840 and 1848, Joule performed several experiments to show that the same amount of mechanical work always produces the same quantity of heat. In one experiment, Joule determined the work done in stirring water by measuring the distance (h) that hanging weights (mg) move under the influence of gravity to rotate the stirring blades. The heating of the water was measured from its change in temperature. In this way it can be shown that 4186 joules of work always produce one kilocalorie (Cal) of heat, confirming that heat is a form of mechanical energy.


of the paddle wheel to agitate the water (Figure 6.5). Again he found that the quantity of heat produced in the water was proportional to the mechanical work done. He also compared the work in compressing a gas to the heat generated. In all these cases, Joule found that the same amount of energy produced the same quantity of heat within his experimental limits. The modern unit of energy is named in Joule’s honor, where one joule (J) is the work done by one newton of force acting over one meter. Joule’s mechanical equivalent of heat is 4186 J/Cal. Initially the Royal Society rejected Joule’s work, but it appeared in a Manchester newspaper in 1847 after he presented it to the British Asso-ciation for the Advancement of Science (founded in 1831). There it caught the attention of the young Scottish mathematician William Thomson (Lord Kelvin), who recognized the importance of Joule’s work and was able to win its acceptance and secure Joule’s reputation. Together with the work of Helmholtz, who also gave public recognition to the contribution of Mayer, the law of conservation of energy was established on a firm theoretical and quantitative basis. Thermodynamics and Kinetic Theory William Thomson (1824-1907), who be-came Lord Kelvin in 1892, was the son of a mathematics professor at the University of Glas-gow, where he became a student at age eleven and professor in 1846 after graduate work in Paris. About 1850 he began an attempt to reconcile the ideas of Carnot and Clapeyron with those of Joule and Helmholtz in what he called “thermodynamics.” Carnot’s use of the caloric theory had led him to suggest that the heat Q ab-sorbed by a steam engine did not change into work in falling to a lower temperature. After showing that work does convert into heat, Joule argued that some of the heat absorbed by a heat engine transforms into work. Thus the work done by any heat engine is given by W = Q1 - Q2, where Q1 is the same as Carnot’s heat Q from the boiler, and Q2 is the heat returned to the condenser. Thomson recognized two principles of thermodynamics in the work of Carnot as modified by Joule: conservation of energy (but not heat) in

converting heat to work W = Q1 - Q2, and the dissipation of energy in the form of heat Q2 rejected at the lower temperature of the condenser. Energy is not destroyed, but it becomes less avail-able to do work as it dissipates in the form of heat at lower temperatures. Thomson recognized that useful energy is continually decreasing and that this dissipation of energy defines a direction for the flow of time. In 1846 he calculated that a steady rate of cooling would lower the Earth’s temperature to its present value in about 100 mil-lion years if it was originally at the temperature of the Sun. In 1848 Thomson saw in the Carnot cycle the possibility of an absolute temperature scale independent of the variable expansion rates of dif-ferent materials. In 1854 he proposed that equal increments of temperature in an ideal heat engine correspond to equal amounts of work, and he showed that this correlates closely with a gas thermometer in which the volume diminishes by 1/273 of its volume at 0°C for every drop of 1°C. Thus the so-called Kelvin scale begins with abso-lute zero temperature 0°K = -273°C (modern value: -273.15°C), and the freezing point of water is To = 273K. Thomson also expressed the effi-ciency of Carnot’s ideal heat-engine as 1-T2/T1 when operating between absolute temperatures T1 and T2 (T1>T2), and suggested that molecular energies fall to zero at absolute zero temperature. Working independently at the suggestion of Thomson, the German physicist Rudolf Clau-sius (1822-88) confirmed and extended the ideas of thermodynamics. He recognized that an ideal heat engine could convert all of its heat into work (100% efficiency) only if it operated with its lower (exhaust) temperature at absolute zero with no heat rejected. At higher temperatures the heat transfer Q increases in proportion to the absolute temperature T so that the ratio Q/T remains constant in an ideal heat engine, but increases in an ordinary engine due to larger heat rejection. In 1865 Clausius took this ratio as a measure of heat dissipation (heat unavailable to do work) and gave it the name entropy, suggesting that it increases in all isolated natural processes. For example, as an object loses heat to its surroundings, its temperature decreases so its entropy increases.


In his classic generalization of thermo-dynamics, Clausius could express the first and second laws in the twin statements:

Law I. The energy of the universe is constant.

Law II. The entropy of the universe always increases.

The second law appeared to put limits on the uni-verse. The deistic clock-world of the mechanists appeared to be running down. Although its energy is conserved by the first law, it becomes increasingly unavailable by the second. The steadily increasing entropy of the universe led some philosophers to speak of its eventual “heat death,” when the last temperature difference will disappear in cold conformity. The closed circle of mechanical laws was finally broken. In 1857 Clausius initiated a dynamical interpretation of thermodynamics in terms of molecular motions when he revived the kinetic theory of gases. The theory was introduced in 1738 by the Swiss mathematician Daniel Bernoulli (1700-82), who explained the pressure of a gas in terms of the collisions of atoms in random motion on the wall of its container. In 1848 Joule used similar assumptions with elastic collisions to derive the ideal gas law relating pressure, volume and temperature (PV/T = constant), and calculated the average speed of a water vapor molecule at 100°C to be more than 1 mile/sec. By treating heat as the total energy of the moving molecules, Clausius was able to connect kinetic theory, thermodynamics, and chemistry. Resorting to a statistical analysis, he could relate the measurable heat constants of a gas to the atomic structure of its molecules. The Scottish physicist James Clerk Maxwell (1831-79) devel-oped the statistical implications of kinetic theory in 1866. Using probability, he calculated the dis-tribution of molecular energies above and below the average. Kinetic theory showed that absolute temperature is proportional to the average kinetic energy of the molecules. Then, for example, cooling by evaporation (perspiration, etc.) could be explained as the more probable loss of faster molecules from a liquid, reducing the average energy of its molecules and thus its temperature.

Both Maxwell and the Austrian physicist Ludwig Boltzmann (1844-1906) demonstrated the statistical nature of entropy. Maxwell pointed out that heat could be made to flow from a cold gas to a hot gas by a unique being, later called Maxwell’s demon, who would only let the fastest molecules in the cold gas pass to the hot gas, and the slowest molecules in the hot gas pass to the cold. Such an idea for decreasing entropy was meant to show that the second law is not absolute. In fact, living organisms do reverse entropy in achieving greater molecular organization, but only by receiving an excess of energy from the Sun, and thus an increase in the entropy of the universe. In 1877 Boltzmann demonstrated statistically that entropy corresponds to the high probability that systems tend toward states of greater disorder. The mechanical universe of deism had removed God to a transcendent realm beyond any influence on the world. Now energy, with its uni-versal, indestructible and active character, pointed to an energistic universe anticipated by the ro-mantic poets and nature philosophers, with their pantheistic view of God immanent in nature. But entropy, by contrast, was like a satanic virus, pro-gressively destroying the creative works of energy in its march towards death. By the same token, the fact that the universe is winding down implies that it must have once been wound up. The fact that it has not yet completely unwound points to a creative beginning at a finite time in the past, and the possibility of a creative renewal in the future.

4. ENERGY PROPAGATION

Waves and Sound. The active nature of energy is especially evident in wave phenomena. A wave is the propagation of a disturbance, usually in the form of a periodic vibration, through an elastic medium. Waves differ from particle emission by the fact that only energy pro-pagates, but not matter. In longitudinal waves such as sound, the vibrations are parallel to the direction of propagation, while in transverse waves such as those on a string, the vibrations are perpendicular to the direction of pro-pagation. Sound has been long associated with


vibrations and waves, but the wave nature of light was not established until the nineteenth century. A water wave causes a floating cork to vibrate up and down as the wave moves along the surface of the water. The height of the crest or depth of the trough in a wave is called its ampli-tude. The frequency f of the wave is the number of vibrations per second at any point on the wave, and the wavelength λ (Greek letter lambda) is the distance from crest to crest (Figure 6.6). Since the crest of a wave travels one wavelength in each

vibration, it will travel f wavelengths per second, so the speed v of wave propagation is given by the equation:

v = λf.

Since the wave speed remains constant in any given medium, its wavelength will decrease as the frequency increases and vice versa. About 1600 Galileo recognized the me-chanical nature of sound vibrations. He established the relation between the pitch of sound and the

frequency of its vibrations by scraping along the notched edge of a coin at different rates. The French friar Marin Mersenne (1588-1648) reported the same relation in his Harmonie Uni-verselle (1636) by counting the vibrations of long strings. In 1640 he and his fellow Minorite friar Pierre Gassendi (1592-1655) estimated the speed of sound by timing echoes over known distances, showing that the speed was independent of the pitch. About 1660 Boyle and Hooke demonstrated that sound does not propagate in a vacuum, but required the “spring of the air.” In his Principia (1687), Newton obtained a theoretical value for the speed of a sound wave by assuming longitudinal vibrations of air are governed by Boyle’s law (isothermal pressure variations). In 1708 the English theologian William Derham (1657-1735) attempted to verify Newton’s result by measuring the difference in time between the flash of a cannon and its blast over a distance of 12 miles. He came close to the modern value of 344 m/sec (at 20oC), but his result exceeded Newton’s value by about 20 percent. Laplace corrected Newton’s analysis in

vibration

velocityλ λ λ

f = 1/ T

v = / T = f

λ

frequency (vib/sec)(a) Transverse Wave

compression - rarefaction

(b) Longitudinal Wave

v

Figure 6.6 Transverse and Longitudinal Waves (a) In a transverse wave, such as in light or on a string, vibrations of the wave medium are perpendicular to the direction of the wave propagation. The time for one vibration is called the period (T) and the number of vibrations per second is the frequency (f = 1/T). The wavelength is the distance from peak to peak. Since the wave travels one wavelength (λ) in one vibration (T), the speed of the wave is given by v = λ/T = λf. (b) In a longitudinal wave such as in sound, vibrations of the wave medium are parallel to the direction of the wave pro-pagation. When sound travels through air, molecules of air move closer together at some points (compression) and further apart at other points (rarefaction). These points are propagated at a characteristic speed (v) through the air. The time that air molecules take to vibrate back and forth from compression to rarefaction and back again is the period (T) and the number of such vibrations per second is the frequency (f). The distance from one point of compression to the next is the wavelength (λ).


1802 by accounting for tem-perature variations due to rapid vibrations without time for heat transfer (adiabatic heating and cooling during compression and rarefaction). In the same decade, the German physicist Ernst Chladni (1756-1827) meas-ured the speed of sound in various gases from the change in pitch they produced in a pipe, and demonstrated the various vibrational patterns of thin plates. At the beginning of the eighteenth century, the French physicist Joseph Sauveur (1653-1716) showed that strings can vibrate simul-taneously at a fundamental frequency and at higher in-teger multiples of the funda-mental that he called “harmonics” (Figure 6.7). The fundamental corresponds to a half wavelength along the length of the string, yielding the maximum amplitude by constructive interference, and causing the loudest tone called resonance. The second har-monic (first overtone) corre-sponds to one wavelength along the string, and thus twice the frequency of the fundamental (one octave higher). Sauveur also de-scribed the pulsations in loudness called “beats” that result from two closely spaced tones sounded together. He introduced the term “acoustics” for the scientific study of sound. The German physicist Georg Ohm (1789-1854) stated in 1843 that the ear perceives all sounds as a combination of their harmonics. Ohm’s “law of acoustics” was the basis of the “resonance theory of hearing” introduced by Her-mann von Helmholtz (1821-94) in 1863. This

theory proposed that differences in pitch are per-ceived by structures of the inner ear (now identi-fied with sensory hairs along a spiral membrane in the cochlea) that resonate at different frequencies. He showed how the particular combination of a fundamental and its overtones gives a sound source its unique quality. He also suggested that discordant sounds in music were the result of tone combinations that caused beats at unpleasantly low frequencies.

Destructive: cancellationConstructive: reinforcement

(a) Interference of waves traveling through the same medium

(b) Standing waves at resonant frequencies (natural vibrations)

DestructiveConstructive

1st harmonic 2nd harmonic 3rd harmonic(fundamental) (overtones: octave and fifth)

(resulting displacement: dotted lines)

Figure 6.7 Interference of Waves and Standing Wave Harmonics (a) Two waves in the same medium interfere with each other by the superposition of their displacements. When the waves are one-half wavelength out of phase, the crest of one wave overlaps the trough of the other so that they cancel each other in what is known as destructive interference. When the waves are in phase with each other, they reinforce each other in constructive interference with the resulting amplitude (maximum height of the wave) equal to the sum of the amplitudes of the individual waves. (b) When a wave is reflected at a boundary, it interferes with the transmitted wave. On a string fixed at both ends, these reflections interfere both constructively and destructively to produce standing waves with characteristic frequencies called harmonics. The lowest frequency (first harmonic) is called the “fundamental” and forms a half wavelength over the length of the string. At twice the fundamental frequency, a standing wave of one wavelength forms the first overtone of the fundamental (second harmonic) an “octave” higher than the fundamental. At three times the fundamental frequency, the third harmonic forms with three half wavelengths as an “octave” plus a “fifth” above the fundamental.


Revival of the Wave Theory of Light During the eighteenth century light was usually described by Newton’s particle emission theory, ignoring his idea that light particles also involved vibrations in the aether. Although some scientists supported Huygens’ “wave theory,” including Leonhard Euler (1707-83) and Benjamin Franklin (1706-90), they did not find a viable alternative to the particle theory. One difficulty was the fact that sound waves spread around corners (diffraction), but light seemed to cast sharp shadows. By the end of the century, however, the particle theory of light came under attack by the German nature philosophers, led by the poet-philosopher Johann von Goethe (1749-1832), who believed in the purity of white light and that colors were due to the conflict between light and darkness. Thomas Young (1773-1829) revived the wave theory of light on a more solid experimental basis about 1801, but it was not widely accepted for several years. Young was a child prodigy from a Quaker family, who knew a dozen languages by the age of twelve. He studied medicine under the aging Joseph Black at Edinburgh, where animal dissections led him to the discovery in 1793 of the principle of visual accommodation, whereby the eye focuses on objects at different distances by changes in the curvature of the eye lens. Later he explained astigmatism as an irregular curvature of the cornea, and introduced the three-color theory of vision. Young completed his physics degree in 1796 at the University of Göttingen in Germany, where he became interested in wave theories. In a thesis on sound, he suggested that both sound and light are wave vibrations, and that colors are analogous to tones of different frequencies. In 1799 he obtained a medical degree at Cambridge. About 1800 Young used the principle of interference of waves to demonstrate the wave nature of light and to measure its wavelength. He described how two waves can reinforce each other when their amplitudes overlap in constructive interference, or cancel when they oppose each other in destructive interference (Figure 6.7a):

When two undulations, from different ori-gins, coincide either perfectly or very nearly

in direction, their joint effect is a combina-tion of the motions belonging to each... It has been shown that two equal series of waves proceeding from centres near each other, may be seen to destroy each other’s effects at certain points, and at others to redouble them; and the beating of two sounds has been explained from a similar interference.

Thus when two identical waves are in phase (crest to crest), their combined amplitude doubles, but when they are out of phase (crest to trough) their combined amplitude cancels. Young explained Newton’s rings, formed when the curved surface of a lens is pressed against a flat glass surface, as the interference of light waves reflected from the two adjacent surfaces. From the length of the air gap separating the surfaces at a given ring, using Newton’s own data, he could calculate the wavelength that would be reinforced to give the ring its particular color. Young presented a paper to the Royal Society in 1801 on his double-slit experiment, which combined diffraction and interference. He found that light passing through two closely spaced parallel slits in a screen formed several alternating bright and dark bands of light on a second screen placed behind the first, instead of just the two bands of light expected from a particle view (Figure 6.8). Young explained this by suggesting that light waves spread out from each of the slits by diffraction, and then the spreading waves combine on the second screen through interference to form bright and dark bands by reinforcing and cancelling each other. From the separation of the slits, screens and bands, he calculated the wavelengths of various colors. He found red light to form more widely separated bands than violet light. The measured data give a wavelength for red light of about 0.7 micron (millionth of a meter) and a wavelength for violet light of about 0.4 micron. Colors appeared as continuous variations in wavelengths. In the double-slit experiment with white light, longer wavelengths reinforce at larger angles within a given band and shorter wavelengths reinforce at smaller angles, dispersing the light of


each bright band into a spectrum from violet to red at increasing angles from the center of the screen, much like the action of a prism. Young pointed out that the wavelengths of light were so small compared to visible objects that they would usually appear to travel in straight lines and cast sharp shadows. Such short wavelengths combine with the speed of light (c = λf = 3x108 m/sec) to give extremely high frequencies for light on the order of a million- billion (1015) vib/sec. Rather than the inert particles of the mechanists, light appeared to be an active vibration beyond the imagination of even Leibniz or Huygens.

Development of the Wave Theory of Light At first, Young assumed that light waves were longitudinal. But he was puzzled by the phenomenon of “polarization,” first named by Newton in connection with the formation of two images by double refraction in the calcite crystal (Iceland spar). If light passes through two such crystals rotated relative to each other, every 90° of rotation causes one image to disappear and the other to reappear. In 1808 the French engineer Étienne Malus (1775-1812) discovered that par-tially reflected light is polarized. Looking through a calcite crystal at the reflection of the Sun from

λ

d

Bright

Bright

Dark

Dark

Bright

Diffraction Interference

y{

redorangeyellowgreenblueviolet

white light:

*Lightsource

θ

θ

x

Figure 6.8 Young’s Double-Slit Experiment to Measure the Wavelength of Light By passing light through a pair of horizontal slits in a screen, Young was able to measure the wavelength of light from the pattern of bright and dark horizontal bands of light observed on a second screen. The formation of such bands could be interpreted by assuming that diffraction of light waves through the two slits allows it to spread out in wavelets, which then combine at the second screen to produce bright bands by constructive and dark bands by destructive interference. The first bright band above the center is formed at a point where the distance from the lower slit is one wavelength longer than the distance from the upper slit so that the light from the two slits is in phase. Then the large shaded triangle with sides x (screen separation) and y (bright band spacing) is nearly similar to the small shaded triangle of sides d (slit separation) and λ (wavelength), and the sides are approximately in the proportion λ/d = y/x, for a wavelength of λ = yd/x. For white light, the longer wavelengths have larger diffraction angles q, so the light is dispersed into a spectrum with violet at the smallest angles, and red at the largest angles.


nearby windows, he noticed that the two images were of unequal intensities, changing as he rotated the crystal. He then showed that candlelight reflected from a water surface at a 36° angle became completely polarized, producing a single image with a crystal; and if it passed through the crystal first, it produced only a reflected ray. His colleague at the Ecole Polytechnique in Paris, François Arago (1786-1853), found that in partial reflection of light the refracted ray is also polarized. In 1815 the Scottish physicist David Brewster (1781-1868) showed that complete po-larization occurs for reflection at that angle of incidence (Brewster’s angle) when the light splits into reflected and refracted rays at right angles to each other, both rays producing only one image with a calcite crystal. Two years later Young wrote Arago suggesting that a consistent explanation of these polarization phenomena is possible by assuming that light is a transverse wave. He suggested that transverse vibrations of light could separate into two perpendicular components at the reflecting surface, leaving the reflected ray with a single component of transverse vibration parallel to the reflecting surface, and the refracted ray polarized in a plane perpendicular to it. Young’s work was not readily accepted, and in 1818 he became interested in a completely unrelated field. A basalt slab with hieroglyphic, demotic and Greek inscriptions was found by troops of Napoleon in 1799 near the city of Ro-setta in northern Egypt. Young was the first to show how the hieroglyphics could be deciphered by showing that they were actually phonetic sym-bols. The French archaeologist Jean Champollion (1790-1832) then completed the deciphering of the Rosetta stone and the unraveling of Egyptian hieroglyphics. Frenchmen also completed and estab-lished Young’s work on the wave theory of light. About 1815 the French engineer Augustin Fresnel (1788-1827) began an effort to revive Huygens’ longitudinal wave theory of light. He independ-ently conducted some of the experiments that Young had done more than a decade earlier. In 1817 Arago told Fresnel about Young’s hypothesis of light as a transverse wave, and Fresnel used it as

the basis of a prize essay on optical diffraction submitted to the Institut National. He worked out a complete mathematical theory of transverse light waves and applied it to phenomena like interfer-ence and polarization in his “Mémoire sur la Dif-fraction de la Lumière” of 1819. He analyzed the diffraction of light through a single slit and ex-plained the resulting diffraction pattern. He also demonstrated the bright spot at the center of a circular shadow required by his theory. The transverse wave theory of light raised new problems regarding the presumed medium of propagation for light called the luminiferous (“light-carrying”) aether. In 1821 Fresnel pointed out that longitudinal waves could be propagated by a fluid medium, but transverse waves required a more rigid medium. It was hard to imagine an aether that was solid and rigid enough to allow the passage of both light and planets. In 1845 Irish physicist George Stokes (1819-1903) called attention to materials like wax that could support transverse vibrations and also yield to compressions. He suggested that the aether might have similar but more exaggerated properties, acting as an elastic solid with respect to light and a fluid with respect to matter. The French mathematician Augustin Cauchy (1789-1857) worked out several models of the aether at the Ecole Polytechnique that were physically awkward but seemed mathematically feasible. Difficulties with the aether concept led some like Arago to waver in supporting the wave theory, and a few like Brewster rejected the wave theory altogether in favor of Newton’s particle theory. But further confirmations of the wave theory were given during the 1850s by the French experimenters, Armand Fizeau (1819-1896) and Jean Léon Foucault (1819-68). Newton had deduced that light particles would travel faster in denser media due to attraction, while Huygens had shown that waves would slow down. In 1849, Fizeau and Foucault measured the speed of light by beaming it through the gap between the teeth of a rotating cogwheel to a mirror on a hilltop five miles away. By adjusting the speed of rotation, they were able to get the reflected light to pass back through the next gap, and they calculated the speed from the distance and time. A year later


Foucault improved the technique by using a rotating mirror. In 1853 he used this method to show that light was faster in air than water, in support of the wave theory. Radiation and Spectroscopy The study of the spectrum of light waves emitted and absorbed by various substances has revealed important connections between light, heat, chemistry and atomic structure. In 1752, the Scottish physicist Thomas Melvill made the first observations of the spectra of light emitted by various excited gases. He placed different sub-stances in a flame and, “Having placed a paste-board with a circular hole in it between my eye and the flame...I examined the constitution of these different lights with a prism.” He found a discontinuous spectrum of colored patches, differ-ent for each substance, each patch separated by dark gaps, and their colors corresponding to their location in the continuous spectrum. Later inves-tigators used a slit instead of a hole, and observed a series of characteristic bright lines of definite wavelengths for each substance.

Light has long been associated with radi-ant heat, which can be focused like light by a “burning glass” lens. The Swiss physicist Pierre Prévost (1751-1839) suggested in 1791 that all bodies radiate and absorb heat, with temperature changes dependent on their relative rates of radia-tion and absorption. In 1800, the astronomer William Herschel used a prism to test portions of the Sun’s spectrum with a thermometer. He found that the temperature increased toward the red end of the spectrum, but rose even higher beyond the red. This led him to conclude that there was an invisible component of light associated with radi-ant heat, now called “infrared” radiation (Figure 6.9). It was later shown to have all the properties of visible light, but at a longer wavelength invis-ible to the eye. A year after Herschel’s discovery of infrared radiation, the German physicist Johann Ritter (1776-1810) discovered radiation beyond the violet end of the spectrum, now called “ultraviolet” radiation (Figure 6.9). He was studying the chemical reaction that light produces in blackening silver chloride (later used for

RedOrangeYellowGreenBlueIndigoViolet

Ultraviolet(strongerchemical effects)

LightSource

White

slit

Refractionin prism

Infrared (highertemperature)

Dispersion intocontinuous spectrum

Line spectrum

6562Å

4861Å

4341Å4102Å

Differential refraction(red refracts less

than violet)

Visible

of hydrogen:

Red

Blue

Figure 6.9 Discovery of Infrared, Ultraviolet and Line Spectra In 1800, William Herschel discovered infrared radiation when he measured the temperature across the visible spectrum, finding that it increased toward the red end and was highest beyond the red. In 1801, Johann Ritter identified ultraviolet radiation from the chemical effect of light on silver chloride, which increased toward the violet end of the spectrum and was strongest beyond the violet. In the nineteenth century, the bright spectrum lines produced by incandescent gases were measured, and in 1885 Johann Balmer found that the wavelengths of the hydrogen lines fit a simple formula.


photography), and found that it was even more effective beyond the violet end of the spectrum. The English physician William Wollaston (1766-1828) had detected ultraviolet light even before Ritter, but the latter usually receives credit for his clearer identification. In 1802, Wollaston was the first to report the use of a narrow slit with a prism, and the first to describe dark lines in the solar spectrum, but he wrongly interpreted some of them as the natural boundaries of the four colors in the continuous spectrum:

The colours into which a beam of white light is separable by refraction, appear to me to be neither seven, as they are usually seen in the rainbow, nor reducible...to three, as some persons have conceived; but...four primary divisions of the prismatic spectrum may be seen....

Working with platinum ores in 1804, Wollaston isolated two platinum-like elements, which he named palladium and rhodium. While testing prisms for the characteris-tics of their glass in 1814, the German physicist and optician Joseph von Fraunhofer (1787-1826) observed some 600 dark lines of the several thou-sand that criss-cross the solar spectrum (Wollaston apparently saw only five). Fraunhofer measured the wavelengths of the more prominent lines, designating them alphabetically. He also found that these lines remained the same when he used different prisms, suggesting that they were characteristic of the sunlight rather than the glass. He also introduced the diffraction grating with many slits to form spectra. The British astronomer John Herschel (1792-1871), son of William Herschel, suggested in 1823 that gases could be identified from the unique spectrum of each. In 1849 Foucault found that certain bright lines in the spectrum from the light of an electric arc coincided with some dark lines in the solar spectrum. But it was the use of flame tests for chemical analysis by the German chemist Robert Bunsen (1811-99) that led to the development of a precise prism spectroscope with the German physicist Gustav Kirchhoff (1824-87). Using this instrument in 1859, Kirchhoff showed that when white light passed through a cool vapor, it

absorbed certain wavelengths and formed a dark-line spectrum. This suggested that cooler gases surrounding the Sun absorbed wavelengths from the white light produced by the Sun, causing its dark-line spectrum. Finally Kirchhoff showed that each dark line of the absorption spectrum of a given gas matched one of the more numerous bright lines in the emission spectrum of the same gas. Kirchhoff and Bunsen recognized two important applications of their spectroscope: the chemical analysis of compounds from the lines in their spectra, and the identification of the chemical constituents of celestial bodies. Their work benefited from the nearly colorless flame produced by the burner developed by Bunsen. In 1860, Kirchhoff and Bunsen observed a distinctive blue line, not associated with any of the known ele-ments, in the spectrum of a mineral. This led to their discovery of the element cesium (from the Latin for sky-blue). A year later, Bunsen discov-ered the element rubidium from a “ruby red” line in the spectrum of one of its compounds. The same year, the English physicist William Crookes (1832-1919) discovered thallium (Greek for “green twig”) in selenium ores from its green line, and in 1863 the German mineralogists Ferdinand Reich and Hieronymus Richter identified indium in a zinc ore from its indigo line. Kirchhoff continued his analysis of the Fraunhofer lines in the solar spectrum. He first showed that the prominent double lines of sodium in the yellow region of the spectrum matched the position of the D-lines in the Sun’s spectrum. He went on to identify half a dozen other elements in the atmosphere of the Sun. The Swedish physicist Anders Ångström (1814-74) had also realized that the dark lines of a gas should match its bright lines. In 1863, he announced the discovery of hydrogen in the Sun, and began a catalog of solar-spectrum wavelengths using a unit now called the angstrom (1Å=10-10m). In 1868, the French astronomer Pierre Janssen (1824-1907) observed an unknown solar-spectrum line during an eclipse of the Sun in India. He sent his data to the English astronomer Joseph Lockyer (1836-1920), who found no similar line for the known elements and concluded that it was an element not known on


Earth, which he named helium (from the Greek for “Sun”). It was identified in a mineral source in 1895 by the Scottish chemist William Ramsay (1852-1916). Spectroscopy reached the stars in 1863, just six years after the French philosopher Auguste Comte died, blasting his claim that the constitution of the stars could never be known. The English astronomer William Huggins (1824-1910) used a prism attached to the lens of a telescope to show that the stars have some of the same spectral lines as those on Earth. In 1868, he observed a small red shift toward longer wavelengths in the position of a hydrogen line in the spectrum of the star Sirius. A similar shift in the pitch of a moving sound source had been analyzed in 1842 by the Austrian physicist Christian Doppler (1803-53). Huggins applied this to the increase in the wavelength of light from Sirius to calculate the speed of its motion away from the Earth. By 1875 he developed photographic spectroscopy with the help of his wife Margaret Lindsay Huggins to form permanent records and time exposures of spectra from the dim light of stars and other objects. Half a century later, the study of red shifts of the spectra from distant galaxies would reveal the origin and structure of the universe. The Swiss mathematics teacher Johann Jakob Balmer (1825-98) discovered the spectral key that would eventually open the inner structure of the atom. While teaching at a girl’s school in 1885, he found an empirical formula that revealed the ordered pattern of the lines of the hydrogen spectrum, which are spaced more and more closely with decreasing wavelength. He showed that the measured wavelengths of the four visible lines of hydrogen (red, green, blue and violet), starting with the red line at 6562.1Å, were precisely related to the squares of the integers n = 3, 4, 5, and 6 by the formula:

λ = 3645.6 ( n²

n² - 2² )

in angstrom units. Balmer’s formula successfully predicted that there would be other lines for n = 6, 7, 8,... in the ultraviolet, ending at 3645.6Å for large values of n. Balmer also speculated that there might be other series of lines for hydrogen whose wave-

lengths could be found by replacing the 2² in the denominator by 1², 3², 4², and so on. Such series were found early in the 20th century in the ultra-violet and infrared regions of the spectrum, leading to a detailed theory of the hydrogen atom as a kind of miniature solar system of orbiting electrons. Thus spectroscopy became a guide to both the outer reaches of an energistic universe, and to the inner world of atomic activity. Light revealed the same physical laws governing matter and energy throughout the cosmos. But now the fixed stars of the Newtonian world were apparently moving. The myriad proliferation of spectrum lines would eventually lead to the replacement of the inert particles of the mechanists and the simple atoms of Dalton with complex structures and organized activities within the atom itself. But in the 19th century, these mysterious spectrum lines were merely a confusing reminder that not all phenomena were completely understood. REFERENCES

Brush, Stephen G. The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases in the Nineteenth Century, 2 vols. New York and Amsterdam: North Holland, 1976.

Carnot, Sadi. Reflections on the Motive Power of Fire. E. New York: Dover, 1960.

Guerlac, Henry. Lavoisier–the Crucial Year: The Background and Origin of His First Experi-ments on Combustion. Ithaca, N.Y.: Cornell University Press, 1961.

Ihde, Aaron J. The Development of Modern Chemistry. New York: Harper & Row, 1964.

Partington,, J. R. A History of Chemistry, vols. 2-3. London: Macmillan, 1961-62.

Thackray, Arnold. John Dalton: Critical Assess-ments of His Life and Science. Cambridge, Mass.: Harvard University Press, 1972.

Van Melson, A. G. From Atomos to Atom. Pittsburgh: Duquesne University Press, 1952.

Whittaker, Edmund T. A History of the Theories of Aether and Electricity, 2 vols. New York: Philosophical Library, 1951-53.

Yehuda, Elkana. The Discovery of the Conserva-tion of Energy. Cambridge, Mass.: Harvard University Press, 1974.

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1. EARLY EVOLUTIONARY IDEAS The energy concept emphasized activity in the universe and the unity of its physical laws. Instead of imponderable fluids, heat came to be viewed as the energy of molecules in motion, and light now appeared as the propagation of wave energy. The principle of conservation of energy now governed both chemical reactions and bio-logical processes. But the constant content of energy in the universe was also found to be dissi-pating into ever decreasing availability for useful work. The nineteenth century saw the arrow of time enter the physical sciences with the second law of thermodynamics. In other areas as well, the sciences finally began to grasp the significance of history. During this same period of time, the biological sciences began to question the fixity of species, and geologists took a new look at fossils and the processes shaping the crust of the Earth. From antiquity the great variety of plants and animals had been viewed as a continuous series of links in a “great chain of being” stretching from the highest creatures to the lowest forms of life and matter. Leibniz had suggested that the “best of all possible worlds” required that all creatures that

could exist must exist. To this principle of plenitude he added a principle of continuity, requiring that species merge into one another in an unbroken chain. But the chain was still static until evidence began to accumulate suggesting change and development in species. Temporalizing the Chain of Being In the eighteenth century, the French phi-losophes raised objections to the static chain-of-being concept in view of their optimistic ideas of progress. Some also opposed the idea of a graded scale of creatures because of their rejection of the medieval concept of hierarchy. Voltaire pointed out that the chain of being was already broken by the refutation of celestial hierarchies in the helio-centric theory of the planets. In suggesting alter-natives, some philosophes went back beyond Aris-totle to the pre-Socratic Greeks. Denis Diderot (1713-84) proposed a version of Empedocles’ the-ory in 1754, suggesting that various animal organs grew together at random, but only the more viable combinations survived. In Catholic France, the chain-of-being concept died hard, in spite of the efforts of the phi-losophes. Instead of rejecting it completely, it was combined with the idea of progress in some early

CHAPTER 7

An Evolving Universe

Developmental Concepts and Evolutionary Theories

Chapter 7 ▪ An Evolving Universe 153

evolutionary theories. The chain was reinterpreted as a plenitude of possibilities unfolding in history and giving rise to organisms of ever increasing complexity and perfection. It came to be seen as a scale of ascent up which organisms had evolved over time, rather than a static hierarchy of fixed species. Such a theory, incorporating a historical view of the chain of being, was published in five volumes (1761-68) by the former Jesuit Jean Bap-tiste Robinet (1735-1820). He proposed that organic species formed a graded scale of creatures that was complete, but progressively changing. All creatures receive “additions which they are able to give themselves by virtue of an internal energy, or to receive from the action of external objects upon them.” He saw this internal energy as “the most essential and the most universal attribute of being...a tendency to change for the better.” The additions which animals receive from external objects were similar to the environmental conditioning that the philosophes preached as an aid to progress. Unlike his contemporary French compa-triot Georges Buffon, Robinet did not see organic change as a process of degeneration, but as con-taining the seeds of progress culminating in the highest forms of life:

Envisaging the sequence of individuals as so many steps in the progress of being towards humanity, we shall compare each of these with man, first with respect to his higher faculties, that is, his reason.

Like other early evolutionary thinkers, Robinet thought of atoms as endowed with life and a soul, making it easier for inorganic matter to generate living beings. Differing combinations of these living atoms produced different species of plants and animals. His Catholic background and deistic tendencies led him toward a more continuous view of evolutionary progress within a dynamic chain of being. A more discontinuous idea of evolution was developed by the Swiss lawyer and naturalist Charles Bonnet (1720-93), whose Huguenot back-ground was in a Protestant tradition of greater emphasis on catastrophic change. In 1740, he

discovered that aphids (tree-lice) could reproduce without fertilization of the female egg (parthenogenesis), leading him to accept the widely held theory of preformation. In this theory all the future generations of each species are pre-formed and contained in miniature in the egg (or sperm), waiting to be activated in the process of reproduction. It involved a radical form of the fixity of species, with some preformationists holding that the entire human race existed inside Eve’s ovaries. Bonnet introduced the term “evolution” to describe the unfolding of preformed embryos. This apparent fixity of species conflicted with the increasing fossil evidence of creatures that no longer existed, leading Bonnet to postulate peri-odic catastrophes over the whole Earth, with the Mosaic flood viewed as only the last of many. In his Philosophical Palingenesis, or Ideas on the Past and Future States of Living Beings (1770), he proposed that all living creatures are destroyed in these catastrophes, but the seeds of their future generations survive and are resurrected on a higher level in the chain of being. He predicted a future catastrophe in which stones would become organisms, plants would move, animals would reason, apes would become men, and men would become angels. Evolutionary Speculations In the nineteenth century, Robinet’s con-tinuous dynamic chain was developed into one of the first evolutionary theories by Jean Baptiste Lamarck (1744-1829), another Jesuit-trained naturalist. Bonnet’s discontinuous catastrophism was adopted in opposition to evolution by Georges Cuvier (1769-1832), who like Bonnet also came from a Huguenot background. Lamarck became chair of invertebrate zoology in 1793 at the Paris Museum of Natural History (the King’s Gardens before the Revolution), and Cuvier was appointed chair of comparative anatomy in 1795 at the same institution. While their ideas were in marked contrast, their work finally ended the conception of organic species arranged in a linear sequence within the chain of being. Even before Lamarck, an organic theory of evolution was proposed by the English physi-


cian Erasmus Darwin (1731-1802), best known as the grandfather of Charles Darwin. In England the idea of progress developed as a secularized version of the Christian conception of a future paradise for the elect, leading to the popularity of Leibniz idea that this is the “best of all possible worlds.” These ideas were the topic of much discussion in the Birmingham Lunar Society, where both Erasmus Darwin and Josiah Wedgwood, Charles Darwin’s other grandfather, were both members. Erasmus Darwin wrote much of his early scientific thought in poetic form, dealing largely with botany and supporting the classification system introduced by Linnaeus. In 1794, Erasmus Darwin published his Zoonomia, which showed influences from Buf-fon’s work and anticipated some of Lamarck’s ideas, though not developed in the same detail. In this book he applied the secularized English idea of progress to the development of plant and animal species, recounting that,

...philosophers have been of the opinion that our immortal part acquires during this life certain habits of action or of sentiment, which become forever indissoluble, continu-ing after death in a future state of exis-tence.... I would apply this ingenious idea to the generation, or production of the em-bryon, or new animal which partakes so much of the form and propensities of the parent.

Thus Erasmus Darwin speculated that the habits acquired by an animal within its environment were passed on to its offspring, leading to an evolution of species as organisms progress through the accumulation of experience. Together with Lamarck, he believed in an inner force driving organisms to higher forms. Thus he asks the question:

Would it be too bold to imagine that all warmblooded animals have arisen from one living filament which the great First Cause endued with animality, with the power of acquiring new parts, attended with new propensities, directed by irritations, sensa-tions, volitions and associations; and thus

possessing the faculty of continuing to im-prove by its own inherent activity, and of delivering down those improvements by generation to its posterity, world without end.

Unlike Lamarck, Erasmus Darwin emphasized competition and the survival of more viable organ-isms, but he offered few facts and no mechanism for changes in species. His ideas were in tune with the new free enterprise concepts of economic capitalism, which became even more popular in Victorian England when they were developed by Charles Darwin. Unfortunately, Erasmus Darwin’s reputation in England suffered from a campaign of ridicule by the British government against sympathizers with the French Revolution. Equally speculative but more influential in the development of evolutionary theories were Laplace’s ideas on determinism and on the origin and evolution of the solar system. Determinism left little room for miraculous intervention or teleological causes, and spurred the search for natural explanations of all events. Laplace’s “nebular hypothesis” for the origin of the solar system was first suggested in a tentative form in 1796, but his Exposition du Système du Monde went through six editions by 1835. In explaining how the planets might have formed from a gas cloud surrounding the Sun, he set an example of natural explanations prior to the appearance of life and provided support for Buffon’s speculations about the great antiquity of the Earth required for the long processes of evolution. Lamarck’s Theory of Acquired Characteristics Jean Baptiste Lamarck (1744-1829) pro-posed the first comprehensive theory of organic evolution, although he did not use the word “evolution” nor its French equivalent. After a period in the army and medical studies, he began his career as a botanist in the King’s Gardens at Paris in 1782. He continued at the newly named Garden of Plants after the French Revolution, and was given the new chair of invertebrate zoology for the study of the lower animals without back-bones. In shifting his work up the chain of being from plants to lower animals, he saw evidence for


Robinet’s ideas of a continuous but changing scale of creatures. In his new position, Lamarck began to expand the classification of invertebrates from the two classes of insects and worms used by Linnaeus into ten invertebrate classes by 1800, which is the basis for the modern system. In that year he suggested that the simplest forms of life arose from spontaneous generation, which then produced all other forms of life by a process of successive transmutations. In 1802 he arranged his ten classes of invertebrates in a linear order, followed by the four vertebrate classes of fishes, reptiles, birds and mammals, and suggested that this was an evolutionary order through which the animals had passed over time. He also introduced the term “biology.” Lamarck published his ideas on what caused evolution in his Philosophie Zoologique of 1809. His principal explanation was similar to that of Robinet’s “inner force” acting continuously to improve the species. He thought that this would lead to a continuously ascending chain of being with no missing links. But fossil evidence of extinct animals seemed to suggest such gaps in the chain, so he suggested that they were ancestors of living animals that change over time, and species were not fixed. But since his zoological studies revealed some discontinuities in nature, he developed his theory of acquired characteristics through inheritance to explain deviations from a continuous linear sequence. In developing his theory of the inheri-tance of acquired characteristics, Lamarck recog-nized the historical nature of the environment and how its changing nature might affect living organ-isms. His theory proposed that animals respond to environmental changes by developing new habits, and plants respond by nutritional changes when new conditions arise. New needs produced by the changing environment lead to increased use of some organs and less use of others. As organs develop through continual use to satisfy new needs they grow stronger, while unused organs grow weaker, and these acquired changes pass on to descendants. Over long periods of time, useless organs disappear and others develop. After many

generations these changes become appreciable and eventually transform the species. Although Lamarck believed that minerals, plants, and animals, had all developed from a common source, he broke with the older idea of continuous connections between them.

All known living bodies are sharply divided into two special kingdoms, based upon the essential differences which distinguish ani-mals from plants, and in spite of what has been said, I am convinced that these two kingdoms do not really merge into one another at any point.

He held that plants and animals originally derived from two different kinds of particles, each brought together by the exciting forces of heat and electric-ity, which also acted on their waste products to form minerals. As these environmental factors pushed organisms to greater complexity, they eventually began to generate their own heat and electricity to sustain themselves, and provide their own evolutionary force. Lamarck also proposed a split in the linear series of animals from their original particles into two main branches, one leading from single-cell protozoa to animals with radial symmetry like the star fish, and the other leading to animals with bilateral symmetry that split into further branches. When Lamarck published his system in detail in the Histoire Naturelle des Animaux sans Vertèbres (1815-22), he largely abandoned the linear scale of the chain of being. The branched chain broke down even further, and he admitted that he was unable to find any evolutionary con-nection between the invertebrate and vertebrate animal series. He provided many examples of the kinds of animal habits that he thought would lead to acquired characteristics. Thus the snail feeling its way develops tentacles, and the snake slipping through narrow spaces becomes elongated and loses its legs through disuse. But his most famous example was the recently rediscovered giraffe, brought to Paris in the early 1800s, which he thought began as a primitive antelope stretching for the leaves of trees so that each generation developed slightly longer legs, neck and tongue.


Lamarck based his evolutionary mecha-nisms on natural explanations consistent with the dominant mechanical views of the 18th century. But he also believed in a general ascent in com-plexity that implied a purposeful direction, perhaps guided by a divine hand. His ideas were strongly opposed by Cuvier, the more dominant voice among French scientists, and he was resisted by the English as being too materialistic. Although he made enduring contributions to invertebrate classification and helped to break the chain of being with his concept of branching, his evolutionary theory based on the inheritance of acquired characteristics was not widely accepted. Early Evolution Debates One of Lamarck’s colleagues at the Paris Museum of Natural History, Étienne Geoffroy St. Hilaire (1772-1844), applied some of Lamarck’s ideas to vertebrate zoology, but rejected others. Hilaire agreed that changes in the environment led to variations in animal forms, forming a roughly linear evolutionary sequence. But he did not accept any active evolutionary force within animals, nor did new habits produce structural modifications. Instead he believed that the structures of animals determined their habits and functions, and that a vertebrate pattern was the basic structural plan for all animal species so that in essence there is only “one animal.” This idea that nature manifested a unified plan or “idea” was introduced near the end of the eighteenth century by German nature philosophers. In his Philosophie Anatomique (1818-22), Hilaire proposed principles of morphology, including the idea that all vertebrates have the same parts or “units of construction.” The same organs may have different forms and functions in different species, some even being atrophied or annihilated, but they are always in the same order and relationship, revealing a unity of plan behind the diversity of structure. With Lamarck he believed that changes in the environment led to variations in animal forms, but he thought that these were governed by the basic structural plan as changing conditions led to the development of some parts of an animal and the atrophy of others. This plan developed more fully as more suitable

environmental conditions arose, leading to an evolutionary sequence. Unlike Lamarck, he be-lieved that such changes were sudden mutations, citing the birth of monsters as evidence. He also believed that embryological development was evi-dence for evolution, recapitulating the evolution-ary history of a species. Georges Cuvier (1769-1832) vigorously debated the views of his colleagues at the Paris Museum of Natural History. Although he was an active Protestant in the Lutheran tradition of work and faith, his scientific eminence led to many honors in Catholic France. Starting at the museum in 1795, he became interested in anatomical studies of both living animals and fossils, practically establishing the fields of comparative anatomy and paleontology. With Hilaire he fol-lowed the German tradition of morphology, but like Lamarck, Cuvier held that the functions and habits of an animal shaped its structural form. Cuvier differed from both Lamarck and Hilaire in opposing the scale of nature, preferring a natural method of classification based primarily on the nervous and circulatory systems. In his best known work, Le Règne Animal (The Animal Kingdom, 1817), Cuvier extended the classification system of Linnaeus (1735), who used the categories of class, order, genera and species, the latter two providing his binomial nomenclature. Cuvier grouped related classes into still broader groups called phyla, dividing the animal kingdom into four phyla: vertebrates (now chordata), mollusks (soft-bodied), articulates (jointed), and radiates (radial). Thus animal species appeared as divergent modifications of these four basic plans or types, rather than a linear scale of beings. Cuvier stressed the internal structures of animals that most clearly indicate relationships, rather than superficial surface characteristics. His principles provided the basis for modern systems of classification (Figure 7.1), which have greatly increased in complexity with some two dozen animal phyla now recognized. Cuvier’s younger associate, the Swiss-French botanist Augustin Candolle (1778-1841), applied these same principles to the classification of plants. He invented the word “taxonomy” in 1813 to describe the science of classification.


Cuvier had no theory to account for the diversity of species, but instead held that they were fixed from the original creation. He developed the principle that the structures and functions of animals are so correlated that their whole structure can be inferred from a part. A famous story illustrates his method: Students dressed as devils with horns and hooves awakened him with shouts of “Cuvier, we’re going to eat you!” Cuvier woke to reply, “You can’t! Creatures with horns and hooves are herbivores.” He applied this principle to fossil parts of extinct animals, fitting them into his four phyla, and thus he was the first to extend classification to fossils. Beginning with his study of fossil ele-phants in 1796, Cuvier included reconstructions of some 150 extinct mammalian species in his four-volume Researches on Fossil Bones (1812). These included a flying reptile, which he named the “pterodactyl” (“wing-finger”) because its wing stretched along a huge “finger.” The evidence of fossils convinced him that extinctions had occur-red and that organic life had a very ancient history. Both living species and extinct forms stretched back over a long historical succession of animals in four branches of structural similarity. To explain the fossils and their occasional extinctions, Cuvier appealed to the catastrophism of Bonnet rather than the evolutionary hypotheses

of his colleagues. The fossil record revealed great jumps in nature, not the smooth transitions of a continuous chain of being. Cuvier found evidence for at least four such world-shaking catastrophes, involving powerful forces such as Earthquakes and floods. By assuming that the last one was the Noahic flood, he could square strange fossil creatures and the vast age of the Earth with the Biblical account, which revealed only recent history since the last catastrophe. In a debate with Hilaire in 1830, Cuvier emerged the victor with his evidence against a linear sequence of species. He finally broke the chain of being, but his insistence on the fixity of species slowed development of evolutionary ideas for several decades in France. In the meantime, his followers identified some 18,000 extinct animal species in France alone, and postulated 27 ca-tastrophes to account for them. 2. DESIGN & DEVELOPMENT IN BIOLOGY Natural Theology and Nature Philosophy Cuvier’s victory seemed all the more de-cisive because it tended to support the popular belief in the theory of design, especially in Eng-land. The English naturalist John Ray (1628-1705) had demonstrated the amazing adaptations that abound in nature, especially in plants and animals. In his book of 1691, The Wisdom of God in the Works of Creation, he described these adaptations in great detail and argued that they revealed the existence of purposeful design in the universe, and thus a Great Designer as creator of the universe. In the eighteenth century this argument was developed further to try to answer the growing skepticism of the enlightenment, especially by the bishop of Durham, Joseph Butler (1692-1752), in his work of 1736, The Analogy of Religion, Natural and Revealed, to the Course and Constitution of Nature. However, by claiming that natural theology was “the foundation and principal part of Christianity,” he overstated his case and contributed to the growing eclipse of revelation by reason. In the early nineteenth century, most English naturalists were clergymen who agreed that the exquisite complexity of nature and the

KINGDOMPHYLUMCLASSORDERFAMILYGENUSSPECIES

AnimalChordataMammal

PrimateHominid

HomoSapien

Example:

Figure 7.1 Modern Biological Classification The modern classification system as developed in the nineteenth century and an example as applied to the human species.


wonderful adaptations of organisms proved the existence of God. One of the most impressive books on this theme was by the archdeacon of Carlisle, William Paley (1743-1805), whose Natu-ral Theology; or Evidence of the Existence and Attributes of the Deity collected from the Appear-ances of Nature was first published in 1802. A bequest to the Royal Society continued this tradi-tion through a famous series of eight Bridgewater Treatises (1833-37) with a common theme, “On the Power, Wisdom, and Goodness of God as Manifested in the Creation.” These publications viewed any idea that the world resulted from chance occurrences as ignorance of nature. Even evolutionary progress could be regarded as a part of a larger design. In contrast with the deistic tendencies of natural theology, German interest in nature tended toward pantheism. The naturalist Lorenz Oken (1779-1851) applied German nature philosophy to biology in his Elements of Physio-Philosophy (1810). He believed that the universe was in a process of historical development generated by the World Spirit, and that humans were the final result of this process and thus a microcosm of the world. According to Oken, all creatures had a common origin in the World Spirit, but they had no historical connection with each other. But they did have resemblances, since higher organisms possessed qualities of the lower, and all came from a common source. This led Oken to suggest that the development of embryos should pass through stages similar to lower organisms in the scale of beings. His speculations also anticipated the cell theory as a material unit of life. Epigenesis and Embryology A more empirical approach to embryol-ogy grew out of the debate over preformation theories in the eighteenth century. Mechanistic thinkers tended to hold that organisms were fully formed in their seeds, and simply grew in size by a mechanical process. Among early microscopists, Leeuwenhoek and his Dutch followers believed that preformed men, or “homunculi,” were contained in the male sperm, while Swammerdam, Malpighi, and later Bonnet held that all offspring were fully formed in the female egg. By contrast,

German vitalists leaned toward the idea that a vital force within the seed caused material differentiation and physical development accord-ing to a predetermined pattern. William Harvey had suggested such a developmental view, which he called “epigenesis.” The German biologist Caspar Friedrich Wolff (1733-1794) suggested a theory of embryo-logical epigenesis in 1759, though his work was largely neglected for a half century. He believed that a vital force acted upon homogeneous organic matter to produce various tissues and then organs. In 1768, he described his observations of the for-mation of the chick intestine in the egg. He also discovered a primitive kidney in the embryos of higher animals. This so-called Wolffian body dis-appeared before the formation of the true kidney. Thus he demonstrated that the organs are not pre-formed, but must develop by differentiation of simple tissue into complex structures. Wolff also called attention to the greater resemblance of embryos than of the adult forms of different spe-cies of animals, and recognized the similarities in their development. German nature philosophers began to develop further the ideas of Wolff on embryologi-cal epigenesis in the early nineteenth century. The most important work was done by the Estonian biologist Karl Ernst von Baer (1792-1876), who was German by descent and training, and later served like Wolff at St. Petersburg. In 1827, von Baer described the minute mammalian egg of a dog, which could only be studied with a micro-scope after its removal from a follicle of the ovary. His two-volume textbook (1828, 1837) establish-ing the science of embryology showed that the embryos of many animals begin with the forma-tion of four tissue or “germ” layers (later reduced to three), each producing the same organs in dif-ferent animals. Baer also initiated the science of com-parative embryology by noting that the early stages of development of different groups of ani-mals are more alike than the developed individu-als, and earlier similarities produce greater differ-ences in adult forms. Nearly identical structures in the early stages of different embryos might develop into “homologous” structures with differ-


ent functions in the adult animals, such as an arm, a wing, and a flipper. He demonstrated this in vertebrates with his discovery of a primitive spinal column, called a notochord, which is eventually replaced by the true backbone. Later primitive fish-like creatures were found with the notochord in the adult forms, now classified with the verte-brates in the chordate phylum. Baer resisted the suggestion of some of his contemporaries that the development of em-bryos followed evolutionary stages of development or formed a linear scale of creatures. He identified four main types of animals based on embryology rather than anatomy, each having a different mode of development resulting in a different symmetry (vertebrates, annulates, mollusks, radiates). He followed the German nature philosophers in holding that species came from a common source, but their development stemmed from four divergent plans. The main purpose of bio-logical development was the production of inde-pendent and self-contained individuals, not unlike the emphasis of the romantic philosophers on the uniqueness of the individual. The Cell Theory Biology entered a new era with the an-nouncement of the cell theory in 1838. Robert Hooke described his microscope observations of cork “cells” in 1665. The French physician Xavier Bichat (1771-1802) developed a general theory based on minute structures without the use of a microscope. In his book on membranes (1800), Bichat distinguished twenty-one types of tissues in the body based on some 600 post-mortems conducted in his short life. In a book on anatomy (1802), he analyzed the organs of the body in terms of the tissues each contained, and he recognized that organs combined to form systems such as the digestive and nervous systems. Each organ had its own vital force related to its level of organization. The development in the 1820s of im-proved microscopes with achromatic objectives (combining two lenses to prevent spectrum for-mation) greatly advanced biology. In 1831 the Scottish physician and botanist Robert Brown (1773-1858) observed that the “nucleus of the

cell” is a general feature of plant tissues. Four years earlier, Brown had observed the irregular motions of pollen suspended in water, known as Brownian motion, which later provided support for the kinetic theory. The Czech physiologist Jan Purkinje (1787-1869) used the microscope in 1835 to observe the nucleus of the hen’s egg, and to reveal that animal tissues are also made up of cells. He introduced the term “protoplasm” (first-formed) for the embryonic material in the egg. In 1838, the German botanist Matthias Schleiden (1804-81) recognized the importance of the cell as the basic living unit of all plant struc-tures. Basing his theory on the ideas of nature philosophy, he emphasized the development of plants through a process of cell formation, whose arrangement expressed the unity of the plant as a whole. Each cell was an independent self-contained unit, but contributed to the organized plant structure by the action of “form-building forces.” Schleiden recognized the importance of Brown’s discovery of the cell nucleus, and sug-gested that new cells arise from the nucleus of old cells. After Schleiden described plant cells for him, the German physiologist Theodor Schwann (1810-82) extended the cell theory to animal tis-sues in his Microscopic Investigations of 1839. He followed Schleiden in emphasizing the develop-mental and unifying aspects of cellular structure, suggesting “that all the varied forms in the animal tissues are nothing but transformed cells, that uni-formity of structure is found throughout the animal kingdom, and that in consequence a cellular origin is common to all living things.” Schwann held that fertilized eggs of all animals were single cells, whether large like the hen’s egg or small like the mammalian egg, so that all organisms began as a single cell. He coined the term “metabolism” and taught that a “metabolic force” transformed intercellular material so that an “attractive force” could form it into new cells, giving them an autonomous life of their own. He applied cell theory to Bichat’s classification of tissues, differentiating these in terms of the types and arrangement of their cells. The cell theory provided a basis for the unification of the biological sciences, and was


rapidly corrected and developed. The Swiss botanist Karl Nägeli (1817-91) made a careful microscopic study of pollen formation in 1842 and described a process of cell division. The Polish-German physician and zoologist Robert Remak (1815-65) showed in 1855 that cell division involves the splitting of the nucleus first inside the cell, and then the latter splits into two daughter cells. The German pathologist Rudolf Virchow (1821-1902), who in 1842 was the first to describe leukemia, stated the principle that “all cells come from cells.” In his Cellularpatholigie (1858) he suggested that cells of diseased tissue are an altered condition of normal cells, and that these malignant cells multiply in the tissue. Improved microscopes and new techniques of staining tissue with synthetic dyes contributed to further understanding of cell division in the 1870s. The German anatomist Walther Flemming (1843-1905) discovered in 1879 that material inside the nucleus of animal cells strongly absorbed aniline dyes, calling this absorptive material “chromatin” (from the Greek word for color). During the process of cell divi-sion, he observed the chromatin forming several filaments, later called “chromosomes” (colored bodies). In his book, Cell Substance, Nucleus, and Cell Division (1882), he described his observations of how these filaments separated during cell division in a process he called “mitosis” from a Greek word for “thread” (Figure 7.2). Flemming’s work was expanded in 1887 by the Belgian cytologist Edouard van Beneden (1846-1910). He found that the chromosomes were generally paired, with the same number in the cells of a given organism (46 in human cells). During cell division their number doubled and separated equally into the two daughter cells. But in the formation of ova and spermatozoa, cell division was not preceded by a doubling of the chromosomes, so they contained only half the normal number (later called meiosis). During the union of the sex cells the chromosome number was restored, half from the mother and the half from the father. It now became clear that the chromosomes are the agents of reproduction, and that the cell is the key to all vital activities.

The Decline of Vitalism Most physiologists in the early nineteenth century held the vitalistic view that life cannot be explained without some properties that are neither physical nor chemical. But increasing experimental research began to reveal more and more aspects of living organisms that could be explained mechanistically by ordinary physical and chemical laws. The French physiologist François Magendie (1783-1855) established ex-perimental physiology in France and became an early exponent of mechanistic biology. His study of the nervous system in 1825 led to the discovery that the anterior spinal nerve roots transmitted motor impulses to the muscles, and that the pos-terior nerve roots sent sensory impulses to the brain. This sensory-motor division of the spinal nerve roots was discovered independently by the Scottish surgeon Charles Bell (1774-1842). The German anatomist and physiologist Johannes Müller (1801-58) established a famous school of experimental physiology in Berlin, but

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3 4 Figure 7.2 Stages in Cell Mitosis Simplified diagram of (1) chromosomes in the cell nucleus, (2) dividing into pairs joined at the center, (3) pulled apart, and (4) forming two new cells, each with the same number of chromosomes as the parent nucleus.


unlike Magendie, Müller strongly believed that a vital force was necessary to maintain organic compounds against the destructive effects of physiochemical forces in living organisms. How-ever, he rejected the more mystical ideas of nature philosophy, and viewed humans more like ma-chines than as a microcosm of the universe. He confirmed Magendie’s sensory-motor division, and by experiments on himself in 1826 he discov-ered that sensory nerves interpret impulses only in the way that is characteristic of a given nerve. Thus the optic nerve produces a flash no matter how it is stimulated. Müller’s Handbuch der Physiologie (1834) became the standard textbook of physiology for several decades. His students were among the most notable in the history of biology, demonstrating that many life processes did not involve vital forces. By 1840 in Müller’s laboratory, Theodor Schwann first isolated an extract from the stomach lining he called “pepsin” (from the Greek “to digest”), and showed that it increased the meat-dissolving power of acid. Jakob Berzelius called such speeding of reactions “catalysis,” and the name “enzyme” was later applied to organic cata-lysts. Another student of Müller, Emil Du Bois-Reymond (1818-96), showed that nerve impulses were electrical in nature, involving known physi-cal laws rather than some vital principle. Müller’s most distinguished student, Hermann von Helm-holtz (1821-94), showed in 1846 that animals produce heat by contracting muscles, and in 1850 he measured the speed of a nerve impulse. His treatment of the conservation of energy provided the strongest argument against vitalism, showing that vital forces would produce perpetual motion in living organisms. Magendie’s assistant and successor at the Collége de France was the French physician and physiologist Claude Bernard (1813-78), who de-veloped the experimental approach of his master. But Bernard agreed with the vitalists that organ-isms do exhibit processes unknown in the inor-ganic world, such as generation, development, and nutrition. In his 1843 thesis he showed that gastric juices change cane sugar to dextrose, leading to the discovery that pancreatic secretions in the small intestine reduce starches to dextrose, break

down fat molecules, and complete the digestion of proteins. In 1856 Bernard discovered a starch like substance in the liver he called “glycogen,” which formed from blood sugar and acted as a reserve to keep the sugar content of the blood in balance. He found that the liver secreted bile into the intestine in addition to secreting sugar into the blood, and that the nervous system regulated the blood supply. His experiments on living animals led him to insist that life can be explained only in terms of the physicochemical conditions of the internal environment (milieu intérieur). Thus Bernard held that organs must be closely integrated to regulate this internal environment as outer conditions change, in contrast with German reductionism on the one hand, and nature philosophers on the other, who viewed cells as having a nearly independent life of their own. Although the trend of the nineteenth cen-tury was toward mechanistic thought in biology, a limited form of vitalism proved to be especially fruitful in the work of the famous French chemist Louis Pasteur (1822-95). His strong Catholic convictions led him to maintain a separation between the organic and inorganic, in opposition to nature philosophers and evolutionists who believed in spontaneous generation as a link between matter and life. Chemists like Berzelius and Justus von Liebig held that inorganic catalysts caused fermentation. Pasteur thought that inorganic fermentation implied spontaneous gen-eration, and in 1856 he demonstrated that fermen-tation involved living organisms, leading to his idea of gentle heating of wine and beer to kill yeast that causes souring in a method now called “pasteurization.” The study of yeast cells led Pasteur to investigate more closely how microscopic organ-isms arose. In 1768 the Italian biologist Lazzaro Spallanzani (1729-99) had boiled solutions that seemed to breed microorganisms by spontaneous generation. After boiling he sealed the flask and showed that no microorganisms appeared, sug-gesting that spores in the air carried them. Some evolutionists claimed that heating killed any organisms on spores above the solution. So in 1860 Pasteur left boiled meat extract exposed to


unheated air by way of a swan-shaped neck that prevented dust particles from entering the flask, and showed that no organisms formed. In 1865 Pasteur found that diseased silk-worms were infested with microscopic parasites, leading him to propose the “germ theory of dis-ease” in which diseases could be communicated by microorganisms spread by infected individuals. This idea led to the development of chemical dis-infectants by the English surgeon Joseph Lister (1827-1912), and the classification of bacteria by the German botanist Ferdinand Cohn (1828-98). In 1881 Pasteur extended the work of Edward Jenner (1749-1823), who had developed cowpox inoculation to prevent smallpox, calling it “vaccination” (from the Latin vacca for cow). Pasteur heated a solution containing anthrax germs from an infected sheep, and showed that sheep inoculated with the “attenuated” germs gained immunity from the disease. In a dramatic climax to his career, he extended this method to the successful treatment of rabies in 1885. The German chemist Eduard Buchner (1860-1917) achieved an impressive demonstration of scientific materialism over vitalism by showing that fermentation did not require living organisms. Vitalists held that only living tissue could use the so-called “ferments” (enzymes) as catalysts within the cell for processes such as the conversion of sugar to alcohol. Buchner tried to demonstrate that alcohol fermentation was inseparable from life by grinding yeast cells with sand until none were alive to see if this would stop fermentation. In 1896 he placed his cell-free yeast in a thick sugar solution, and observed bubbles of carbon dioxide as evidence that the sugar was fermenting into alcohol in the same way that it would with yeast cells. Thus the cell was eliminated as the last refuge of nineteenth-century vitalism. For his work Buchner was awarded the 1907 Nobel Prize in chemistry. 3. EARTH HISTORY AND GEOLOGY Early Theories of the Earth The first clear principles for the study of the Earth’s surface came from the Danish natural-ist Niels Steensen, who Latinized his name to Nicolaus Steno (1631-86) when he converted to

Catholicism. While serving as physician to the Grand Duke of Tuscany, he began to study the rocks and minerals in the mountains near Florence. He published his geological observations and ideas in 1669, and was a correspondent of the Royal Society, but his interest shifted to theology after his appointment as Apostolic Vicar of Northern Germany and Scandinavia. Steno’s principles provided a basis for explaining many geological phenomena (Figure 7.3). First was the principle of superposition: as sediments settle in the sea, they form a sequence of strata in which the upper layers must be younger than the lower layers. Second was the principle of initial horizontality: sedimentary strata must have been deposited initially as flat layers parallel to the surface of the sea, so that any inclined layers are evidence of deformation of the Earth’s crust after the layers were consolidated. Third was the principle of lateral extension: strata were originally continuous, so that if two parts of the same stratum were separated by some event like a river, the intervening material was younger. Although Steno viewed rock structure as a tempo-ral sequence of events, he allowed insufficient time for their development, since he believed that fossil-bearing strata were deposited by the Flood.

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Figure 7.3 Steno’s Diagrams of Strata Changes Steno illustrated (1) horizontal strata from depo-sition of sedimentary particles, (2) eroded to form a cavity, (3) which collapses to form a valley. After invasion by the sea, (4) new strata form (dashed lines), with (5) further subterranean erosion and (6) collapse. [Adapted from N. Steno, Prodromus, Florence, 1669.]


Early theories of the Earth based on Noah’s Flood were developed in England by natu-ralists such as Thomas Burnet (1635-1715) and John Woodward (1665-1728). They used the idea of a universal Flood to explain phenomena such as the formation of mountains and valleys, irregu-larities in strata, and the existence and location of fossils. These ideas stimulated the collection of fossils as evidence of Biblical veracity. In Italy where volcanoes were active, the Venetian priest Anton Moro suggested in 1740 that the Flood was a more localized event, and that rock strata formed from a series of volcanic eruptions that entombed plants and animals, forming fossils in the rocks. These views were sometimes viewed as complementary, but by the late eighteenth century they led to a controversy between the Neptunists stressing the role of water, and the Vulcanists em-phasizing heat. In 1749 Georges Buffon (1707-1788), Keeper of the King’s Gardens in Paris, suggested an evolutionary theory of the Earth that was quite speculative, but important in proposing a vastly expanded time scale. Instead of a six-day creation some six-thousand years ago, he proposed seven epochs of development over a span of about seventy-five thousand years, adding a new dimension of history to nature. To understand the history of plants and animals, he began with a history of the Earth in the first volume of his 36-volume Histoire Naturelle (1749-85). Using a calculation of Newton for the rate of cooling of comets, Buffon experimented with the cooling of a red-hot globe of iron, and extrapolated to the size of the Earth to arrive at precisely 74,832 years for the Earth to cool to its present temperature. By the time he finished his Les Épochs de la Nature (1779), Buffon had divided his history of nature into seven “epochs” as metaphors of the seven “days” of creation in Genesis. In the first epoch, the Earth formed out of matter ejected from a collision of a comet with the Sun. As the Earth solidified in the second epoch, its crust wrinkled to form the mountain ranges. In the third epoch, vapors condensed as the Earth cooled, covering the Earth with a flood in which fishes flourished and sediments formed, enclosing fossils and organic deposits like coal. The fourth epoch began after

further cooling produced subterranean openings, causing a rush of waters, earthquakes, and volca-noes that produced dry lands. Land animals and plants appeared in the fifth epoch, and the conti-nents moved apart in the sixth after migrations of animals had separated various species. Finally humans appeared in the seventh epoch, in which Buffon concludes, “The power of man has sec-onded that of Nature.” Vulcanism and Neptunism Although Buffon’s theories were highly speculative, some of his contemporaries in France began making the kind of field observations that would turn geology into an empirical science. The French physician Jean Guettard (1715-86) produced in 1746 the first maps showing the sur-face distribution of minerals and rocks, extending them throughout France in the 1760s with the help of the chemist Lavoisier. He found that rocks and minerals run together in bands, in some cases even across the English Channel. In 1752, Guettard discovered that the highlands of Auvergne were a group of extinct volcanoes, supporting Vulcanist views. But his work on the Degradation of Mountains demon-strated the effects of water in shaping the topogra-phy of the land, thus tending toward the Neptunist view that rocks had an aqueous origin. In 1770 he suggested that the basalt rocks forming the columns of the Giant’s Causeway on the northern coast of Ireland had formed by crystallization from water. The observations of Guettard in Auvergne were followed up in 1763 by Nicolas Desmarest (1725-1815), a director of manufactures in France, who discovered basalt columns among the lavas of old volcanoes that were similar to those of the Giant’s Causeway. In 1777, he suggested that these prismatic structures were formed by solidify-ing molten rock, thus supporting the Vulcanist view. He described evidence of widespread but now extinct volcanic action by extrapolating from the location of basalt outcrops. But he also devel-oped a theory of the formation of valleys by the action of streams of water. Thus both Guettard and Desmarest combined Vulcanist and Neptunist views.


The British geologist Sir William Hamil-ton (1730-1803) developed in more detail the implications of Vulcanism with respect to the action of volcanoes. He also identified basalt and other rocks found near volcanoes as products of lava flows, suggesting that the prismatic nature of basalt resulted from slow cooling. He argued that volcanic action played a constructive role in uplifting new land from the sea, shaping the land-scape, and providing a safety valve for excess pressure below the crust. The German physician Georg Füchsel (1722-73) used a Neptunist view to work out a historical succession from vertical layers of rock strata, which he viewed as sedimentation from an earlier sea. Primary rocks without fossils formed the core of mountains, followed by secondary deposits containing simple sea fossils. Finally, the tertiary rocks formed last with fossils of land animals and plants. A purely Neptunist school was estab-lished by the German mineralogist and geologist Abraham Werner (1749-1817), who became direc-tor of the Freiberg School of Mines after his publication in 1774 of a book on mineral classifi-cation. He accepted the idea of geological suc-cession in sedimentary deposits, but did not develop its historical implications, since he clas-sified rocks by mineral content rather than fossils. Secularizing earlier Flood theories, Werner held that rock strata formed from a universal primeval ocean, which produced four types of rocks by sequential processes of crystallization, precipita-tion, sedimentation, and weathering. In Werner’s Neptunist theory, primitive rocks such as granite, crystallized out of the pri-meval ocean, and contained no fossils. Transi-tional rocks, such as micas and slates, followed by chemical precipitation, containing only a few fossils. Sedimentary rocks were next, rich in fossils such as coal and limestone. Finally deriva-tive rocks, such as sand and clay, formed from the other three by processes of weathering. He believed that volcanoes resulted from the burning of underground coal, and was not an important geological force. In the tradition of German nature phi-losophy, Werner viewed all rocks as originating

from a common source and belonging to four fun-damental types, similar to the view of German biologists at the time on the origin of species. His theory was very influential, even though it was based on limited observations and could not explain the disappearance of the primeval ocean after rock strata had formed. Uniformitarianism and Catastrophism Werner’s theory about the origin of sedi-mentary rocks was largely upheld, but most other rocks were eventually shown to have an igneous origin from a molten state. This later idea was developed by the Plutonist school of geology, which stressed the geological activity of the inter-nal heat of the Earth, in addition to the volcanic eruptions of the Vulcanists. This view was devel-oped by the Scottish amateur geologist James Hut-ton (1726-87), who trained as a physician, but ran a chemical factory rather than practicing medicine. He published The Theory of the Earth in 1795, ten years after presenting his ideas to the Royal Society of Edinburgh. Hutton believed that the geological forces seen in the present operated in the same way and at the same rate in the Earth’s past, and that this should be the basis of geological explanations. The present is the key to the past. This “uniformitarian principle” contrasted with Werner’s idea of a primeval ocean, which was a catastrophic event confined to the past and unobservable in principle. Hutton carefully observed the slow and steady erosion of the land as rivers carried silt into the sea. He examined the weathered beds of gravel, sand and mud brought down by the rivers, as well as the crystalline granites of the Scottish mountains. He concluded that sedimentary rocks formed from beds of mud and sand compressed by overlying seas and heat pressure from below, while crystalline rocks came from molten material inside the Earth and brought to the surface by volcanic action. Developing the idea that the interior of the Earth is molten, Hutton suggested that molten rock pushes into cracks beneath the Earth’s crust, tilting up sedimentary strata and solidifying to form granites. Thus mountains were built with a crystalline core and sedimentary surface. This


principle of injection was apparent in some granite intrusions into crevices in sedimentary rocks above, indicating that the granite was younger. Granites of differing ages were contrary to Werner’s assumptions. In some cases, Hutton found horizontal sedimentary strata covering tilted strata near the base of mountains, suggesting long periods of time since the strata tilted (Figure 7.4). The age of the Earth appeared to be indefinitely long, leading him to conclude that, “We find no vestige of a beginning, no prospect of an end.”

Two of Hutton’s friends developed his system. The Edinburgh professor John Playfair (1748-1819) published Illustrations of the Hutto-nian Theory (1802), clarifying the theory and adding his own view of the importance of glacial flows in moving masses of rocks. The amateur scientist Sir James Hall (1762-1831) conducted experiments in support of the idea that slow cool-ing would form crystalline rocks. He melted lava in a blast furnace and showed that fast cooling made it glassy like lava, but slow cooling made it crystalline like basalt. He also found that loose sand heated in a pot with sea water became hard like sandstone, as suggested by Hutton’s theory.

But this support was not enough to overcome religious objections to the theory, delaying its acceptance. In France, Georges Cuvier (1769-1832) opposed Hutton’s idea of slow geological processes in much the same way that he opposed Lamarckism. He applied his theory of “catastrophism” to geological development of the Earth in the introduction to his Researches on Fossil Bones (1812). Since there was no apparent continuity between successive strata and their

fossils, he believed that a series of catastrophic floods must have occurred, rather than continuous forces, each flood wiping out many species and eroding the Earth. These catastrophes also tilted strata left by earlier floods, ending with Noah’s Flood some six thousand years ago. Cuvier’s catastrophism applied Neptunism to the vast time scale of Hutton. His influence delayed both biological and geological evolution in France for several decades. In England, Cuvier’s catastrophism and Werner’s Neptunism were well received since they seemed to fit Biblical ideas of creation better than Hutton’s eternalistic views. An Eng-lish translation of Cuvier’s textbook The Theory of the Earth appeared in 1813 by the Scottish geologist Robert Jameson (1774-1854). In a pre-face he claimed a correlation between geology and the Genesis account of creation by repre-senting the “six days” as six long periods of time in the so-called “age-day theory” of creation. The first Oxford professor of geology, the Rev. William Buckland (1784-1856), also at-

tempted to combine geology and theology in his Reliquiae Diluvianae (Relics of the Flood), pub-lished in 1823. He suggested a “gap theory” in which several million years intervened between creation and the first day of Genesis, and it was during this pre-Adamite period that the geological catastrophes of Cuvier occurred. He based his argument for the historicity of the Biblical Flood in large part on his study of an assumed antedilu-vian hyena den, the famous Kirkdale Cave, con-taining the bones of extinct animals. He later abandoned the idea of a “universal deluge” in favor of glacial action to explain his findings.

Igneous intrusion

Erosion

Figure 7.4 Hutton’s Geological Processes Geological cross section showing two sedimentary episodes separated by igneous intrusion and erosion. Sedimentary strata covering tilted strata at the foot of a mountain indicated its great age.


Fossils and Stratification In England and France the systematic study of strata was made easier by many well-exposed horizontal layers rich in fossils. These were systematically studied by Cuvier in France between 1808 and 1811, and earlier in England by the English land surveyor and geologist William Smith (1769-1839). In 1793 Smith toured England in a survey of canals and discovered that each stratum had its own characteristic form of fossils, different from those in other strata no matter how the strata were inclined or interrupted. Furthermore, he found that the order of the strata as identified by their fossil content was the same in all localities, leading to the principle of faunal succession (Figure 7.5). In 1799, Smith published his method of rock classification with a geological map of the Bath region of England, the first to show succession of strata. In 1815 he published A Geological Map of England and Wales, showing the horizontal strata across the country, and in 1817 he published a chart of the vertical succes-sion of strata in England.

From the work of Smith and Cuvier, it became evident that strata nearer the surface were younger than those farther down, and a history of life forms could be worked out from their fossils. Smith had studied the later strata above the coal series (Carboniferous). The first Cambridge geol-ogy professor, the Rev. Adam Sedgwick (1785-1873), studied ancient Welsh rocks containing few or no fossils, and identified the Cambrian series (from an ancient name for Wales), which turned out to be the oldest fossil-bearing rocks. Both Sedgwick and his friend the Scottish amateur geologist Roderick Murchison (1792-1871) found that the rocks of Devonshire belonged to the age of fishes, and that this Devonian series was just below the coal series. Murchison also discovered the Silurian system (named from a Welsh Celtic tribe) with the earliest land plants between the Cambrian and Devonian. By 1829 after studying continental rocks to-gether, both men concluded that the oldest rocks were igneous, switching from Neptunism to Vulcanism.

The discoveries of the so-called “heroic age of geology” (1790-1830) were summarized and generalized by one of Buckland’s former students at Oxford, the Scottish lawyer turned geologist Charles Lyell. He revived Hutton’s uniformi-tarian ideas and applied them to a much greater range of obser-vations than Hutton had done. Lyell published his main work in three volumes from 1830 to 1833, entitled The Principles of Geology: being an Attempt to Explain the Former Changes of the Earth’s Surface by reference to Causes now in Operation. Assuming indefinitely long periods of time, Lyell in-sisted that geological forces had always been the same as they are now. Where the earlier mechan-ical philosophers had assumed that the material systems of

Quarry

Hill

Canal

Section

Figure 7.5 Smith’s Correlation of Fossil Beds with Rock Strata William Smith used fossil beds to match rock strata in widely separated and different localities, as shown here in a simplified sketch for a canal, a hill, and a quarry. This led to the type of section diagram shown at the right.


nature remain fixed, Lyell now took the forces to be constant, but changing the material systems of the Earth. Nearly one hundred years after Steno, Giovanni Arduino (1760) had classified rocks in northern Italy into three categories: primary crystalline rocks, secondary stratified rocks, and tertiary strata containing numerous fossil shells. Now Lyell (1833) defined the Eocene, Miocene, and Pliocene Series within the tertiary strata on the basis of the relative proportions of the living and extinct fossils each contained. Although the other categories of Arduino are no longer in general use, the “standard geologic column” and time scale (determined from modern studies using radioactivity) has been greatly expanded and revised since Lyell as shown in the table below:

Geologic Column and Time Scale (Based on modern data)

Era Period Typical life forms

Yrs. ago (millions)

Pleistocene Human 1 Cenozoic Pliocene Primates 5 (“recent Miocene Mammals 23 life”) Oligocene Carnivores 37 Eocene Modern birds 50 Paleocene Mod. plants 65 Mesozoic Cretaceous Placentals 140 (“middle Jurassic Dinosaurs 195 life”) Triassic Reptiles 230 Permian Insects 280 Paleozoic Carboniferous Ferns 345 (“ancient Devonian Fish 395 life”) Silurian Vertebrates 435 Ordovician Mollusks 500 Cambrian Invertebrates 700 Pre-cambrian

Proterozoic Archeozoic

Worms? Algae

3800

Lyell’s book influenced many scientists and shifted them away from Cuvier’s catastro-phism. The erosion of high mountains to sea-level and the deposition of many thousands of feet of successive strata by sedimentation implied the vast time spans needed for a viable theory of evolution. Lyell himself was so committed to the uniformity

of natural law that at first he rejected the changes necessary for organic evolution, since they smacked of creationism. But the succession of fossils in the strata that revealed geological changes seemed to imply either creative acts or the organic changes of biological evolution. Older geologists like Sedgwick recog-nized the evolutionary implications of Lyell’s work. He expressed opposition to it in 1831 because it seemed to require spontaneous genera-tion and transmutation of species. The young Charles Darwin also recognized the implications of Lyell’s ideas, and within a few years Lyell came to change his opinion, realizing that organic evo-lution paralleled the idea of a changing and evolving Earth. But few of Lyell’s contemporaries accepted his ideas before Darwin developed them, preferring the mechanistic concepts of Cuvier’s catastrophism and his idea of multiple creations. One of Cuvier’s later associates, the Swiss-American naturalist Louis Agassiz (1807-73), helped to modify the extreme uniformitarian-ism of Lyell. Between 1833 and 1844 he published a five-volume work on fossil fish. But his most important work was on glacial action in the Swiss Alps. From the distribution of boulders and the grooves scratched on solid rock, he showed in 1837 that Alpine glaciers had once stretched from the Alps across the plains to the west and up the sides of the Jura Mountains. He demonstrated their slow motion, leading him to his Ice Age theory that several thousand years ago glaciers covered much of Europe. In 1847 he accepted a position at Harvard University, and in North America he found evidence glaciers had also overrun its northern half. The Ice Age theory gradually won acceptance over more catastrophic flood theories, and evidence for several long ages of advancing and retreating ice over millions of years was eventually found.

4. THE THEORY OF EVOLUTION

The Darwinian Synthesis The ideas of slow geological change, the successions of species in the fossil record, embryo-logical development, and plant and animal breeding were first brought together by Charles


Darwin (1809-82) in his theory of organic evolu-tion by natural selection. Darwin began to study medicine at Edinburgh in 1825, but eventually left to prepare for the clergy at Cambridge. There Sedgwick introduced him to geology, and Darwin accompanied him on a field trip to Wales. His growing interest in natural history won out over theology, leading to an invitation to the post of ship’s naturalist aboard H.M.S. Beagle. Late in 1831 he joined a five year expedition to survey the coasts of South America and islands of the Pacific, taking with him the first volume of Lyell’s Principles of Geology, from which he learned the sequence of geological events and Lamarck’s the-ory of evolution. With a growing interest in Lyell’s views, stimulated by the second volume of the Principles reaching him by mail in South America, Darwin was deeply impressed “by the manner in which allied animals replace one another in proceeding southward on the continent.” Even more striking were his observations during five weeks in the Galápagos Islands, some 600 miles west of South America, although their significance did not regis-ter with him until later. Here he was struck by the South American character of the animals “and more especially by the manner in which they differ slightly on each island of the group; none of the islands appearing to be very ancient in a geological sense.” Unique adaptations were evident under similar conditions. Residents claimed they could tell which island in the chain was home to a certain giant tortoise by just looking at it. Darwin took special note of a variety of birds, now called “Darwin’s finches,” which he confused with wrens, gross-beaks and blackbirds. The English ornithologist John Gould (1804-81) later identified them as a dozen different species of closely related ground finches in spite of wide differences in their beaks. All were more closely related to each other than to a similar species on the mainland. Darwin identified three types of mockingbirds and noted that, “Each variety is constant in its own Island. This is a parallel fact to the one mentioned about the Tortoises.” On his return to England, Darwin pub-lished his observations, beginning with A Natural-ist’s Voyage on the Beagle (1839), which began to

establish his reputation. He also published Coral Reefs (1842), a theory of coral-reef formation by the accumulation of coral skeletons, which im-proved on a theory of Lyell and led to their close friendship. He started a systematic study of the diversification of species, beginning with artificial breeding. In his Autobiography he wrote:

My first notebook was opened in July 1837. I worked on true Baconian principles, and without any theory collected facts on a wholesale scale, more especially with respect to domesticated productions, by printed inquiries, by conversation with skil-ful breeders and gardeners, and by extensive reading.... I soon perceived that selection was the keystone of man’s success in mak-ing useful races of animals and plants. But how selection could be applied to organisms living in a state of nature remained for some time a mystery to me.

The key to understanding a possible mechanism of selection in nature came in 1838 from reading an Essay on the Principles of Popu-lation, published anonymously in 1798 by the Rev. Thomas Malthus (1766-1834) and expanded in 1803. In an attack on the idea of progress and its darker side in the industrial revolution, Malthus argued that populations increase exponentially, but the food supply at best increases only arithmetically. Thus unrestrained population increase must end in famine, disease, or war. Darwin thought that this must hold for other forms of life as well, and that those in an excess population that survived would be those best able to compete for food. He saw that this struggle for existence was the means of what he called “natural selection” and might lead to the possibility of the transmutation of species:

It at once struck me that under these cir-cumstances favourable variations would tend to be preserved, and unfavourable ones to be destroyed. The result of this would be the formation of a new species. Here then I had at last got a theory by which to work.

For the next twenty years, Darwin care-fully developed this theory. From breeding of


pigeons and other experience with domesticated animals, he knew that there are random variations among the offspring of any species in such fea-tures as size, strength and color; and some features are reinforced while others are suppressed by artificial selection. Now he realized that in nature environmental pressures would play the same role over long periods of time, and by such natural selection more efficient groups should replace less efficient ones in various environmental niches. Thus the giraffe’s long neck was not an “acquired characteristic” from stretching, as La-marck suggested, but resulted from random vari-ations and natural selection, in which giraffes with longer necks would thrive and leave more descendants with longer necks. This also explained its blotched coloring, which would hardly be acquired by some kind of effort, but could result from the natural selection of random variations that provided camouflage to help it survive. To explain how such random variations would carry over in succeeding generations, rather than being averaged out by random matings, Darwin later suggested that “sexual selection” would reinforce desirable characteristics. Thus the most vigorous males and females would breed together, producing more offspring, and animal ornamen-tation would provide greater attraction even if it has little survival value. The Origin of Species In 1844, Darwin began what he intended to be a multi-volume book describing his theory and the evidence that supported it. In the same year, a book appeared by an anonymous author entitled Vestiges of the Natural History of Crea-tion, describing a theory of evolution based on the idea of progression from lower forms to higher ones. The book was written by the self-educated Scottish publisher and naturalist Robert Chambers (1802-71), who mixed science with folklore and included human mental capacity as a product of evolution. It drew a storm of scientific and relig-ious protest and ridicule, and may have reinforced Darwin’s caution in any premature publication of his more rigorous approach. But it did serve to bring evolution to the attention of the English-speaking world.

For nearly ten years, Darwin studied bar-nacles to sharpen his theory. He observed how small changes had to be functional at every stage to be preserved in the process of evolution. Lyell urged him to publish his work before others developed the same ideas. Then in 1858 a letter came from Malay, where the English naturalist Alfred Russell Wallace (1823-1913) had arrived on a long expedition similar to Darwin’s two dec-ades earlier. In the Malay Peninsula, Wallace observed the same variations among species of neighboring islands, and came to the same conclusion of natural selection, even deriving his ideas from Malthus like Darwin before him. Wallace also noted that the animals of Australia seemed more primitive than those of Asia, and suggested that Australia had separated from the mainland before the more advanced species devel-oped. When the idea of natural selection oc-curred to Wallace, he immediately sketched a draft of the theory during a short period of illness, and sent it to Darwin for his opinion without spending additional time to collect evidence. The letter forced Darwin to take action or risk losing his priority. On the advice of friends, he arranged to have Wallace’s paper published together with one of his own in the Journal of the Linnaean Society in 1858, putting an inronic end to the Linnaean concept of fixity of species. He acknowledged Wallace’s independent discovery, and Wallace credited Darwin’s long years of labor. The brilliant insight of Wallace was just the opening introduction to Darwin’s theory, in which the fossil record and the geographic distribution of species now took on a new and meaningful order. A year later, in 1859, Darwin published his “Principia” of biology with the complete title On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life. It was a long book of 400 pages, but not the many volumes he had hoped to produce. The first printing of 1250 copies sold out in a day. His main arguments for evolution involved the fossil evidence for the distribution of extinct species in time, and the geographic evi-dence for the distribution of living species in space. To a lesser extent he discussed the em-


bryological and morphological evidence, including the vestigial organs, which were useless remnants that appeared to be left from some earlier useful function in a previous stage of evolutionary development. Darwinism marked a new and threatening stage in the history of science. The idea of natural selection from random variations clashed with the concept of predetermined design. Of the many variations in organisms, a few changes benefit survival and are preserved, but there is no higher and lower. Gills permit a fish to adapt and survive as well as the lungs of a mammal, and only a series of fortuitous modifications accompanied by many failures eventually changed the swim bladder of the fish into lungs. Natural selection was an argument against intelligent design. Purpose gave way to blind chance. A growing tree of genealogical descent replaced the linear progression of creatures in French thought and the ideal forms of the Germans. As Copernicus ended the fixity of the Earth, Darwin ended the fixity of species, both relating many observations that appeared to be mere coincidence. Where Newton had established purposeful design, Darwin introduced fortuitous development, but both described a dynamic force governed by natural laws. Like Newton, Darwin could not explain a mechanism for the production of variations any more than Newton could for uni-versal gravitation. He believed that such variations were small, leading to gradual and continuous evolution. He also borrowed from Lamarck the idea that selection was “aided in an important manner by the inherited effects of the use and dis-use of parts,” but he did not accept any inner driving force tending toward higher forms, as Erasmus Darwin and Lamarck had supposed. Al-though Charles Darwin never claimed proof for the transmutation of species, he argued that if evolution has occurred it explains many otherwise inexplicable facts. In The Origin of Species, Darwin did not develop the sensitive issue of human evolution. But this did not prevent conflict over the issue of human descent from apes. In 1863 Lyell published The Antiquity of Man, using Darwinian arguments for the evolution of humans, and evidence for

prehistoric humans from stone tools found in ancient strata. In the same year, the English biologist Thomas Huxley (1825-95) gave anatomical evidence relating humans to higher mammals in Man’s Place in Nature, showing that ape anatomy was closer to that of humans than to monkeys. Even Wallace was disturbed by this extension of the theory, feeling that natural selec-tion could not account for the human mind. In answer to the argument that mind required design and creation, Darwin published The Descent of Man in 1871. Here he presented evidence for human descent from lower forms of life, including such vestigial organs as the four bones at the bottom of the spine that appeared to be the remnant of a tail. He also showed mental similarities between humans and higher animals, claiming that natural selection of small variations could account for the human mind. It was in this book that he added the new factor of sexual selection to his general theory to account for secondary sexual characteristics such as horns and spurs used in fighting rivals. Reception and Reaction to Darwinism Even before Darwin published his theory, the English sociologist Herbert Spencer (1820-1903) had speculated that human society and cul-ture evolved from a simple to a complex level, similar to the development of an embryo. When The Origin of Species appeared in 1859, Spencer extended the idea of natural selection beyond Darwin’s theory to human society. He popularized the term evolution, seldom used by Darwin, and coined the phrase “survival of the fittest” to describe not only the mechanism of evolution, but also the mode of human progress. In his Synthetic Philosophy (1862-93) he used Social Darwinism to justify economic competition as the social form of natural selection consistent with the evolving cosmos. This helped to establish the popularity of evolution among the middle class in Victorian England. The chief defender of Darwinism was Thomas Huxley. His interest in natural history grew out of a voyage to Australia as a ship’s doc-tor. He opposed the Social Darwinists in a series of lectures and essays, asserting that human progress


is not the result of “imitating the cosmic process...but in combating it.” He also led the attack against the anti-evolutionists among the Anglican clergy, who especially opposed human evolution. In a famous debate in 1860 with the Bishop of Oxford, Samuel Wilberforce, he asked Huxley if he traced his own descent from the apes through his father or mother. Huxley prevailed with his reply that he would rather choose a mis-erable ape for an ancestor than an educated man who reduces serious scientific discussion to ridi-cule. His devotion to science took on the dimen-sions of religion, which he promoted and preached for the rest of his life. Darwinism was not only opposed on religious grounds. In France Cuvier’s followers opposed Darwinian evolution, as did Claude Ber-nard and Louis Pasteur, who associated it with spontaneous generation. When French theories of evolution did appear in the 1880s, they leaned toward Lamarckian views. The foremost biologist in both England and America opposed Darwin, London zoologist Richard Owen (1804-92) and Harvard professor Louis Agassiz (1807-73), who were both disciples of Cuvier. Kelvin’s calculation of the age of the Earth based on the time for it to cool had not yet been refuted, and his estimate of 100 million years was too short for the slow processes required by evolution. Darwin’s theory was rejected by most of the older scientists in Germany, who were steeped in the ideas of nature philosophy. But in its later stages, nature philosophy became more materialist and empirical, and a few younger biologists tried to combine evolution with the German traditions of embryology, comparative anatomy and cell the-ory. The cell-theorist Matthias Schleiden (1804-81) and the anatomist Ernst Haeckel (1834-1919) were among the first to accept Darwinism. Haeckel combined Darwinism with elements of nature philosophy and Lamarkism in his General Morphology (1866), suggesting that the inheri-tance of acquired characteristics was due to the “memory” of the atoms in the seed of the off-spring. In his History of Man (1874) he carried to an extreme the idea that the developing embryo of each organism follows the stages of its evolution, popularizing the descriptive phrase “ontogeny

recapitulates phylogeny.” His work was important in assimilating embryology and cell theory into the Darwinian system. In America, although Agassiz and some church leaders opposed evolution, it was strongly supported by the Harvard botany professor Asa Gray (1810-88), a colleague of Agassiz and corre-spondent with Darwin. Gray was an active Pres-byterian layman, who believed that evolution did not necessarily conflict with Christianity, and tried to develop a “Christian Darwinism.” He suggested that natural selection was not a random force but was guided by God, making the process of evolution itself the object of design by the Creator. Darwin’s response in his Variation of Plants and Animals Under Domestication (1868) was un-relenting: “However much we may wish it, we can hardly follow Professor Asa Gray in his belief ‘that variation has been along certain beneficial lines’ like a stream ‘along definite and useful lines of irrigation.’” Theologians in America were also di-vided in their response to Darwin. Princeton Uni-versity president James McCosh (1811-94) be-lieved that evolution was not incompatible with Christian doctrine, suggesting that, “Supernatural design produces natural selection.” Other theo-logically orthodox evolutionists included George Frederick Wright of Oberlin College and Benjamin B. Warfield at Princeton Seminary. But the more conservative Princeton theologian Charles Hodge (1797-1878) concluded, after a careful study of The Origin of Species, that the issue was whether one believed that history was an intellectual proc-ess guided by God, or a material process ruled by chance. He believed that chance cannot generate design and that, “Denial of design in nature is vir-tually the denial of God.” Warfield and the Scottish theologian James Orr were both contributors to the 12-volume Fundamentals (1910-15). They taught that evolution was God’s way of creating plants, animals, and even the human body, and did not believe that evolution was inconsistent with Bibli-cal inerrancy. The systematic theologian A. H. Strong (1836-1921) at Rochester Theological Seminary regarded evolution “as only the method of divine intelligence.” He also accepted the brute


ancestry of humans: “The wine in the miracle was not water because water had been used in the making of it, nor is man a brute because the brute has made some contributions to his creation.” An interesting extension of evolutionary ideas to astronomy was worked out by George Darwin (1845-1912), second son of Charles Dar-win, in his theory of the evolution of the Earth-Moon system beginning in 1879. He showed that the frictional effect on the ocean bottom caused by the tidal action of the Moon on the oceans was to slow the rotation of the Earth, compensated by an increasing distance of the Moon from the Earth. Eventually the Earth would slow to where its rotation would be equal to the Moon’s revolution at 55 times the length of the present day, with one side of the Earth per-petually facing the Moon. Working backward, Darwin calculated that when the Earth’s rotation was six times its present speed (4-hour day) it would have been in contact with the Moon. These calculations led George Darwin to propose the first evolutionary theory of the Earth-Moon system based on mathematical laws. He sug-gested that the Moon was formed out of the crust of the Earth and thrown into orbit by centrifugal action. This “fis-sion theory” explained why the Moon is less dense than the Earth and why the granite layer of the Earth’s crust was not continuous. He also tried to work out a theory of the evolution of stellar systems based on tidal friction. A generation later his ideas were further developed, and new approaches to stellar evolution were discovered. The German geologist Alfred Wegener (1880-1930) introduced a new approach to the evolution of the Earth’s surface in 1912. He pro-posed the theory of continental drift based on the similarity of the coast lines of South America and

Africa, suggesting that all the continents had formed from a single land mass called “Pangaea” about 200 million years ago (Figure 7.6). This made it possible to explain the unity of life on continents that have now widely separated as implied by the theory of organic evolution, as well as the divergence of the various forms of life. Continental drift was eventually confirmed, lead-ing to the modern theory of plate tectonics, in which sections of the Earth’s crust form moving plates that carry the embedded continents. Wegener also developed a theory of lunar cratering by meteor bombardment.

Genetics and Neo-Darwinism The missing link in Charles Darwin’s theory was the mechanism by which random vari-ations were produced and inherited, leading to revised versions of the theory. In his Mechanical-physiological Theory of Evolution (1884), the Swiss botanist Karl Nägeli (1817-91) rejected random forces and proposed that an inner pro-gressive force drove evolutionary changes in a definite direction, an idea called “orthogenesis.” He also believed that small continuous variations

Figure 7.6 Wegener’s Theory of Continental Drift The dashed line between the western and eastern hemispheres shows the similar shapes of the coastlines on the two sides of the Atlantic Ocean that led to Wegener’s idea of continental drift away from an original contiguous relation.


were not enough to explain the evolution of higher organisms, and suggested that the inner force fol-lowed a dialectical pattern of discontinuous jumps, later called “mutations.” Unfortunately, when Nägeli received the results of research on pea plants from the Moravian monk and plant breeder Gregor Mendel (1822-84) that would have supported his ideas, he considered them “empirical rather than rational” and ignored them. Mendel studied mathematics and science at the University of Vienna and became a science teacher at Brünn (now Brno in the Czech Repub-lic) in 1854. He began a decade of research in 1857 that combined botany and mathematics in growing sweet peas in the monastery garden. By self-pollinating various plants, he was able to en-sure that any inherited characteristics such as size, color or texture, were from a single parent. Seeds planted from dwarf pea plants “bred true” in that they produced only dwarf plants in succeeding generations. But only about one third of the tall plants bred true, while the other two thirds of the tall plants were not true, producing tall plants and dwarf plants in a ratio of three to one. When Mendel cross-bred dwarf plants with true-bred tall plants, every hybrid seed pro-duced a tall plant (Figure 7.7). When he self-pollinated these hybrid tall plants, they produced one quarter true-bred tall plants, one quarter true-bred dwarfs, and one half non-true-bred tall plants. He interpreted his results to mean that each plant had two height factors, one from each parent. The tallness factor (T) was dominant over the recessive shortness factor (d) in that all first-generation cross-bred plants were tall (Td). When these were self-pollinated, the height factors combined to give offspring with either two tallness factors (TT), or two shortness factors (dd), or a tall and a short (Td), or a short and a tall (dT). The first two combinations always bred true, while the second two combinations would give tall and short plants in the ratio of three to one. These results were consistent with the predictions of mathematical probability. Mendel obtained similar results for other characteristics than height, showing in every case that mixtures of characteristics did not average out, but retained their identity. Although he did not

realize it, this was an important result for Darwin’s theory. Natural selection of a given characteristic from random variations would fail if unrestricted mating blended varying characteristics in succeeding generations. Mendel’s discovery showed that varying characteristics did not blend, but remained distinct, suggesting that natural selection could work effectively on random variations. After failing to obtain Nägeli’s spon-sorship, Mendel published two papers in 1866 and 1869 in the Proceedings of the Brünn Natural History Society, where it remained dormant for thirty years.

Meanwhile, the German biologist August Weismann (1834-1914) began in 1882 to attack the Lamarckian idea of inheritance of acquired characteristics. Darwin had assumed that “elements” from an entire organism unite in the germ-cell (pan genesis), so that any change in the organism might alter its germ-cells and be inher-ited. In his “Essay on Inheritance and Related Biological Questions” (1892), Weismann argued that the body of higher animals is mortal, but

pure tall pure dwarf

Td Td dT dTxallhybridtalls

pollinated

parents

{

{

TT Td dT dd3 talls1 dwarf

self-

alltall

3 tall1 dwarf

3 tall1 dwarf

alldwarf

{

{

TT ddx

Figure 7.7 Diagram of Mendel’s Pea Plants Cross breeding (x) of a true tall plant (TT) with a dwarf plant (dd) results in hybrid talls (Td). The self-pollination of hybrid tall plants results in true tall plants, hybrid plants, and dwarf plants in proportions of 1:2:1, making a total of 3 talls and one dwarf.


“germplasm” is passed from one generation to an-other. The germplasm determines the form and characteristics of the body and is nourished by it, but the body has no effect on the germplasm, so that acquired characteristics would not be inher-ited. He cut the tails off of 1592 mice over 22 generations and observed that none produced offspring with shorter tails. Weismann went on to suggest that vari-ations resulted from the union of two germplasms, one from the mother and one from the father. In 1887 he recognized that the germplasm of each parent must split into two halves when eggs or sperms are formed, so that the union of egg and sperm will not double the germplasm of the off-spring. This prediction of what was later called “meiosis” was eventually confirmed empirically. He also proposed that the germplasm was con-tained in the chromosomes described by Walther Flemming five years earlier. Again Weismann’s idea was eventually shown to be correct. But in viewing the germplasm as the real essence of life, periodically growing an organism about itself as a kind of self-protection, Weismann seemed to allow no room for variation at all. If from generation to generation the germplasm was unchanged, evolution seemed impossible. At the end of the century, the solution to the evolutionary impasse finally appeared with the rediscovery of Mendel’s theories. For some twenty years, the Dutch botanist Hugo De Vries (1848-1935) conducted plant breeding experiments in Amsterdam and thought about the problem of variations. By 1900 he devised a theory for the combinations of hereditary traits that matched his work on plants. In preparing for publication, he discovered Mendel’s papers after working out his own theory in detail. In the same year, two other European botanists independently rediscovered the laws of inheritance and found Mendel’s papers, all three publishing their results as a confirmation of Mendel’s laws. Nearly fifteen years earlier, De Vries had noticed some unusual variations in a wild colony of evening primroses. He bred them separately and together with the usual results, but found that sometimes a very different variety would be pro-duced and perpetuate itself. By 1894, the English

biologist William Bateson (1861-1926) found ad-ditional and more reliable examples of such large variations. In 1901 De Vries published Die Muta-tionstheorie, proposing that evolution was not continuous but occurred in occasional jumps that he called “mutations.” In the next three years, De Vries and several other biologists noted that the combinations of Mendel’s inheritance factors cor-responded to that of chromosomes when the egg and sperm are produced and unite. Thus they suggested that the chromosomes carry the Men-delian factors (now called genes), in agreement with Weismann’s germplasm theory. In 1905, Bateson introduced the term “genetics” for the study of heredity and variations. In the same year, experiments on sweet peas showed that some characteristics are inherited together, indicating that Mendel’s genetic factors are sometimes linked together. This “gene-linkage” was clearly demonstrated by the work of the American geneticist Thomas Morgan (1866-1945). At Columbia University in 1907 he intro-duced the use of the genetic study of fruit flies, whose cells had only four pairs of chromosomes. He found many cases of mutations and showed that some characteristics were inherited together. This gene-linkage implied that the asso-ciated genes were on the same chromosome. Oc-casional separation of these inherited characteris-tics led Morgan in 1911 to the idea that the uniting of broken chromosomes could result in “cross-overs” that would separate the corresponding genes. When this was demonstrated in 1912, it became possible to map the gene locations on the chromosomes by assuming that the frequency of linkage between two genes was determined by their distance apart on the same chromosome. Morgan published The Theory of the Gene in 1926, but the determination of the molecular structure of the gene required the use of new techniques in chemistry and physics developed over the next two decades. The concept of an evolving world implies the unity of all living creatures in the growing tree of life, an idea as grand as the cyclical order of the mechanical universe or the pulsating activity of the energistic universe. Although molecular biology tries to reduce life to the mechanisms of chemistry


and physics, the laws of mechanics now appeared to operate within the larger framework of history, which has no predictable laws. Our universe is an evolving system with a past and a future, not just a machine with constantly recurring motions. But even chance variations fit within the regular patterns of nature. The mechanistic con-fidence in design gives way to the continuity and richness of history. In place of the comforting arguments of natural theology with its Cosmic Designer, an evolving universe suggests a Cosmic Planner and Sustainer who gives the world a po-tentiality and integrity of its own, balanced within the finely tuned laws of created order. In this view, God not only created the universe and its laws, but continues to create through the possibilities provided by “chance” within the framework of natural laws that He sustains. REFERENCES Allen, Garland E. Life Science in the Twentieth

Century. Cambridge, Eng.: Cambridge Uni-versity Press, 1978.

Asimov, Isaac. A Short History of Biology. Garden City, N.Y.: The Natural History Press, 1964.

Barthélemy-Madaule, Madeleine. Lamarck the Mythical Presursor: A Study of the Relations Between Science and Ideology, trans. M. H. Shank. Cambridge, Mass.: MIT Press, 1982.

Bowler, Peter J. The Eclipse of Darwinism: Anti-Darwinian Evolutionary Theories in the Dec-ades Around 1900. Baltimore: Johns Hopkins University Press, 1983.

Brent, Peter. Charles Darwin: “A Man of En-larged Curiosity.” New York: Norton, 1981.

Coleman, William. Biology in the Nineteenth Century: Problems of Form, Function and Transformation. Cambridge, Eng.: Cambridge University Press, 1977.

Collins, Francis. The Language of God: A Scientist Presents Evidence for God. New York: Simon and Schuster, 2006.

De Beer, Sir Gavin. Charles Darwin: Evolution by Natural Selection. New York: Thomas Nelson and Sons, 1963.

Dunn, L. C. A Short History of Genetics: The De-velopment of the Main Lines of Thought 1864-1939. New York: McGraw-Hill, 1965.

Eiseley, Loren. Darwin’s Century: Evolution and the Men Who Discovered It. Garden City, N.Y.: Doubleday, 1958.

Ghiselin, Michael T. The Triumph of the Darwin-ian Method. Berkeley: University of California Press, 1969.

Gillespie, Neal C. Charles Darwin and the Prob-lem of Creation. Chicago: University of Chi-cago Press, 1979.

Gillispie, Charles. Genesis and Geology: A Study in the Relations of Scientific Thought, Natural Theology and Social Opinion in Great Britain 1790-1850. Cambridge, Mass.: Harvard Uni-versity Press, 1951.

Glass, Bentley, Owsei Temkin and William L. Strauss, Jr., eds. Forerunners of Darwin 1745-1859. Baltimore: Johns Hopkins University Press: 1959.

Goodfield, Jane. The Growth of Scientific Physi-ology. London: Hutchinson, 1960.

Greene, John C. The Death of Adam: Evolution and Its Impact on Western Thought. Ames: Iowa State University Press, 1959.

Hull, David L. Darwin and His Critics: The Re-ception of Darwin’s Theory of Evolution by the Scientific Community. Cambridge, Mass.: Harvard University Press, 1973.

Irvine, William. Apes, Angels, and Vicgtorians: Darwin, Huxley, and Evolution. Cleveland: World Publishing, 1955.

Livingstone, David N. Darwin’s Forgotten De-fenders: The Encounter between Evangelical Theology and Evolutionary Thought. Grand Rapids, Mich.: William B. Eerdmans Publish-ing Company, 1987.

Mayr, Ernst. The Growth of Biological Thought: Diversity, Evolution, and Inheritance. Cam-bridge, Mass.: Harvard University Press, 1982.

Mayr, Ernst and William Provine. The Evolution-ary Synthesis: Perspectives on the Unification of Biology. Cambridge, Mass.: Harvard Uni-versity Press, 1980.

Watson, James D. The Double Helix: A Personal Account of the Discovery of the Structure of DNA. New York: Atheneum, 1968.

206

1. ELECTRIC CHARGE AND CURRENT

Although the concepts of an energistic and evolving universe challenged the mechanistic assumptions of the eighteenth century, the me-chanical view of the universe continued to domi-nate the physical sciences in the nineteenth cen-tury. But the study of active phenomena, such as those associated with electricity and magnetism, began to increasingly challenge the prevailing mechanical view of passive matter acted upon by external forces. As these topics were developed in the nineteenth century, every effort was made to explain them in terms of mechanical laws and to reduce them to mechanistic models. But new con-cepts like electric charge and field required radical revisions in ideas about matter and space, and could not be completely reduced to mechanical laws. The growing complexity of these phenomena eventually led to a new electromagnetic view of the universe that opened up new horizons never imagined by Newton and his followers. From antiquity many records describe active phenomena such as lightning, the jolting sting of the “torpedo fish” (electric eel), the glow of “St. Elmo’s fire” as sometimes seen on the points of Roman spears during stormy weather, and the attracting power of amber when rubbed.

But no connection between these various phenom-ena was recognized until the eighteenth century. Plato described the ability of amber to attract bits of straw and other light materials in his Timaeus, and some accounts say Thales observed it. The Greek word for this pale yellow fossil resin was elektron, from which the word electricity was later derived. Plato refers to both “the wonderful attracting power of amber and the Heraclean stone” or lodestone, linking electricity and mag-netism. The lodestone was a naturally magnetic iron ore found near two ancient towns in Asia Minor called Magnesia, leading to the name mag-netism for rocks that attract pieces of iron. In The City of God (De Civitate Dei, AD 428), Saint Augustine gives a good factual account of amber and magnetic phenomena as they were then known, characteristically distinguishing between verifiable and unverifiable knowledge:

For my own part, I do not wish all the mar-vels I have cited to be rashly accepted, for I do not myself believe them implicitly, save those that have either come under my ob-servation or that anyone can readily verify, such as...the magnet, which by its mysteri-ous or sensible suction attracts the iron, but has no effect on a straw.

CHAPTER 8

An Electromagnetic Universe

Electric Charge and Field Concepts

Chapter 8 • An Electromagnetic Universe 177

Augustine saw in these “mysterious” and unex-plained phenomena an answer to the question of the inexplicability of miracles by human reason. The early Christian view of a purposeful universe saw such moral and religious lessons as being more important than dubious rational theories. In the 12th century, interest in secular knowledge began to revive. By this time, Europe-ans knew that the lodestone or a magnetized iron needle placed on a short piece of wood floating in water would point toward the north. Application of this fact to the mariner’s compass led to renewed interest in the lodestone and the amber effect, and to the recognition that amber does not point in a particular direction. About this same time it was found that the hard compacted form of coal known as jet also exhibited the amber effect when rubbed. In 1269 Pierre de Maricourt (Peregrinus) published his Epistola...de Magnete, describing the similarity of a rounded lodestone to the celestial sphere in attracting a needle along lines which “meet in two points, just as all the meridian circles of the World meet in the two opposite poles of the World.” He called these two points the poles of the magnet. The Concept of Electric Charge The systematic study of electricity and magnetism began with the English physician William Gilbert (1544-1603), who studied medi-cine at Cambridge University and later became president of the Royal College of Physicians and one of Queen Elizabeth’s physicians. He published the results of more than fifteen years of research in his book On the Magnet (De Magnete, 1600), including a chapter on the amber effect. He carefully distinguished magnetism from the amber effect, showing that the lodestone required no rubbing, would only attract iron, and could act through screening materials like paper. He formed a spherical lodestone called a “terrella,” and showed that a magnetic needle near its surface would align with its poles, confirming his idea that the Earth is a large magnet. Gilbert began the modern study of elec-tricity with his discovery that many materials besides amber and jet can be electrified by fric-tional rubbing. These included many different

gems, several kinds of glass, sulfur, sealing wax, hard resin, and “a feeble power of attraction...by rock salt, mica, rock alum...when in midwinter the atmosphere is sharp and clear and rare–when the emanations from the Earth hinder electrics less, and the electric bodies are harder....” Thus Gilbert introduced the word electric into the language, coined from the Greek name for amber. He also showed that most materials could be attracted by “electrics.” He designed a kind of electroscope, which he called a versorium, consisting of a metal needle resting on a pointed support that would rotate when electrics were brought near. With this first electrical instrument, he showed that some materials could not be electrified by rubbing, especially metals, leading him to identify two classes of substances, electrics and nonelectrics. He tried to explain attraction by emission of material “effluvia,” released by rubbing, that “lay hold of the bodies with which they unite, enfold them, as it were, and bring them into union with electrics.” The Jesuit preacher Niccolò Cabeo (1586-1650), who taught mathematics in Genoa, may have been the first to observe electrical repulsion, even while denying that electrics transfer their power to other objects. In his book Philosophia Magnetica (1629), he pointed out that attracted bodies sometimes rebound from an electric, but he viewed this as merely a side effect of attraction. He suggested that the effluvia thin the air, causing a kind of breeze to drive light bodies toward the electric and sometimes bounce from it. By the 1660s in England, Robert Boyle (1627-91) used his newly perfected air pump to show that electrified amber could attract chaff in an evacuated glass vessel. He also demonstrated the mutuality of electrics by suspending amber on a thread and noting its attraction to other bodies. The German engineer Otto von Guericke (1602-86), burgermeister of Magdeburg, devel-oped a mechanical approach to the study of elec-trical effects. In his Experimenta Nova (1672) he described the first frictional electric machine, which he devised with a sulfur globe that could be rubbed with one hand while rotating it on a crank-turned shaft with the other hand. He showed that it would attract light objects, and more surprisingly,


that it could repel a feather and keep it suspended in air above the globe even when the globe was moved about. He also observed that the rubbed globe would glow in the dark, describing these various properties as “virtues” unique to such electrics. The Dutch scientist Christiaan Huygens (1629-95) repeated these experiments with an amber globe and clearly demonstrated repulsion between two electrified objects. He explained these phenomena with the vortex ideas of Descartes, but did not publish his results. An uneducated instrument maker and demonstrator at the Royal Society named Francis Hauksbee (1666-1713) revived interest in electric-ity in England in the eighteenth century. Encour-aged by Newton, who was serving as the new president of the Society, Hauksbee developed an evacuated glass globe that could be rubbed while rotating it with a hand crank. In 1705 he demon-strated the power of his globe to glow strongly enough to illuminate a book in a dark room. It appeared that frictional electricity might provide a link between the study of the two great divisions of Newtonian science, mechanical and optical phenomena. To further study these effects, Hauksbee enhanced his electrical experiments by using a long glass tube in place of amber and quickly rediscovered electrostatic repulsion. When he rubbed the glass tube, it not only attracted bits of matter, but they “would sometimes adhere to the tube...and sometimes would be thrown violently from it to good distances.” Suspending threads from a circular frame over the glass tube, he showed that their attraction was radially toward the center of the glass tube. In all these phenom-ena, he reverts to the old explanation of emitted effluvia. Electric Conduction and Fluids The Englishman Stephen Gray (1666-1736), a dyer by trade, discovered the conduction of electric charge, and the distinction between conductors and insulators. In 1708, Gray trans-mitted to the Royal Society the results of his experiments with a glass tube like that used by Hauksbee, some of which the latter claimed as his own while suppressing the rest. Gray became a

pensioner in 1719 at Charterhouse in London, an institution that provided schooling for “charity boys” and a living for “poor brethren.” His first paper appeared in the Philosophical Transactions in 1720. It described light and sparks from a glass tube when rubbed in the dark. A second paper in 1729 resulted from his suspicion that, “...since such a tube communicated light to bodies when it was rubbed in the dark, whether it might not at the same time communicate an electricity to them.” After placing corks in the ends of the tube to keep out dust, he found that the cork attracted and repelled a down feather, and concluded that, “There was certainly an attractive Vertue com-municated to the cork by the excited tube.” This hypothesis led to several more discoveries. In his 1729 paper, Gray described a series of experiments on conduction of “electric vertue.” He inserted a rod into one of the corks and observed attraction to an ivory ball on the other end of the rod. He then found that metal wire from the cork in the glass tube would conduct electricity to the ivory ball or to a lead ball, contradicting Gilbert’s classification of metals as “nonelectrics.” Working with gentlemen friends, he was able to observe attraction by the ivory ball suspended on 34 feet of “pack thread” from the glass tube. He then “made several attempts to pass the electric virtue along a horizontal line” suspended by pack thread from a roof beam, but his lack of success led him to conclude that the electricity escaped through the beam. He finally succeeded by using silk thread to support his “horizontal line,” assuming that its thinness would prevent the escape of electricity through the beam to the ground (now called grounding). Gray continued his experiments in a barn, succeeding with a pack thread line up to 293 feet; but when he used metal wire to support the heavier weight of the line, the experiment failed. With more silk supports, he then succeeded in transmitting electricity up to some 650 feet. Thus he finally recognized the basic distinction between insulators like silk (Gilbert’s electrics) and con-ductors like metals (Gilbert’s nonelectrics) as the important factor in his success, rather than thick-ness of the support. By suspending a small boy from silk threads, he was able to transmit electric-


ity from his feet to his face. In a 1732 paper, he reported on the electrification of materials without direct contact, now called “electrical induction.” In this paper he is finally designated as a “Fellow of the Royal Society” (F.R.S.). Electrical studies were soon begun in Paris at the French Académie des Sciences by Charles Dufay (1698-1739), a self-trained scientist who became superintendent of the Royal Gardens. In 1733 he repeated Gray’s experiments and obtained better results by using wet pack thread supported on glass tubes, reaching 1256 feet of conduction. He was the first to cite Otto von Guericke’s work, repeating his experiment on electrical repulsion of a feather and showing that, “The same effects were produced...by all electri-fied bodies whatsoever.” Dufay sent his work to the Royal Society, where it was translated into English and published in the Philosophical Transactions in 1734. Here he reports his discovery of two distinct electrici-ties, calling them “vitreous” and “resinous” elec-tricity. “The first is that of glass, rock crystal, precious stones, hair of animals, wool, and many other bodies. The second is that of amber, copal, gum lac, silk, thread, paper, and a vast number of other substances.” He then notes that, “A body of, say, the vitreous electricity repels all such as are of the same electricity; and on the contrary, attracts all those of the resinous electricity.” Al-though Dufay never referred to fluids, his discov-ery was called the “two-fluid theory of electricity,” with its basic principle that bodies with like “electric fluids” repel and those of unlike “fluids” attract. Correspondence between Dufay and Gray led the latter to a further study of electric sparks and the suggestion that, “In time there may be found a way to collect a greater quantity of...this electric fire, which by several of these experiments seems to be of the same nature with that of thunder and lightning.” In the 1740’s experimenters in Germany found that a bottle of liquid held in one hand could be electrified enough to give a large shock when touched by the other hand. This so called “electric condenser” was improved in Holland by setting the bottle on a metal support, so that it could then be discharged by touching the

metal with one hand and the top of the bottle with the other. In Paris this became known as the “Leyden jar,” and in England it was found that the liquid was unnecessary if the inside and outside of the jar were covered with metal foil and dis-charged by a wire from the outer coating brought near a metal rod extending from the inner coating. The Leyden jar led to dramatic experiments with electric shocks, culminating in a demonstration before the king by Dufay’s former collaborator, the Abbé Jean-Antoine Nollet (1700-70), in which a Leyden jar was discharged through 180 gen-darmes holding hands in a circle. Demonstrations of electric phenomena eventually reached Colonial America, where Benjamin Franklin (1706-90) was a spectator:

In 1746, being at Boston, I met there with a Mr. Spence, who was lately arrived from Scotland, and show’d me some electric experiments....Soon after my return to Philadelphia, our Library Company re-ceived from Mr. P. Collinson, Fellow of the Royal Society of London, a present of a glass tube, with some account of the use of it in making such experiments. I eagerly seized the opportunity of repeating what I had seen in Boston; and, by much practice, acquired great readiness in performing those, also, which we had an account of from England, adding a number of new ones.

Apprenticed to an older brother as a printer at the age of 12, Franklin later established himself in the printing business in Philadelphia. He spent two years (1724-26) in London as a printer, where he befriended Peter Collinson, F.R.S. In America he became a leading representative of the Enlight-enment, leaving his Quaker religion to become a deist with utilitarian morals, and eventually be-coming financially independent as a publisher in Pennsylvania. After purchasing Mr. Spence’s electrical equipment and acquiring or making additional apparatus, including a Leyden jar, Franklin wrote to Collinson in 1747: “For my own part, I never was before engaged in any study that so totally engrossed my attention and my time as this has


lately done...” Two months later he wrote a sec-ond letter describing “the wonderful effect of pointed bodies, both in drawing off and throwing off the electrical fire.” He then outlined his “one-fluid theory” of electricity based on experiments with two persons standing on wax, in which one rubs the tube and the other “draws the electrical fire,” so that both appear electrified to a third person on the floor until the first two touch each other:

These appearances we attempt to account for thus. We suppose, as aforesaid, that electrical fire [fluid] is a common element, of which every one of the three persons aforementioned has his equal share.... A, who stands on wax and rubs the tube, col-lects the electrical fire from himself into the glass; and his communication with the common stock being cut off by the wax, his body is not again immediately supply’d. B...receives the fire which was collected by the glass from A.... To C, standing on the floor, both appear to be electrized... If A and B approach to touch each other, the spark is stronger, because the difference between them is greater; after such touch there is no spark between either of them and C, because the electrical fire in all is reduced to the original equality.... We say B is electrized positively; A, negatively. Or rather, B is electrized plus; A, minus.

By using mathematical terms like plus and minus, Franklin suggests the possibility that electricity is quantitative and measurable. Later he identified positive and negative charge with Dufay’s “vitreous and resinous fluids,” respectively, which he viewed as a surplus or deficiency of one electric fluid. His assumption that electrification does not create or destroy charge, but only transfers it from one body to another, implies what was eventually called the “law of conservation of electric charge.” Adding positive charge to the inside of a Leyden jar repels an equal quantity of charge from the outside to the ground, leaving the outside negatively charged, which was a result not easily explained by Dufay’s two-fluid theory.

Franklin’s letters and papers on electricity were published in London by Collinson in a book entitled New Experiments and Observations on Electricity (1751-74). It went through many editions and translations, leading to his election as a foreign member of the Royal Society in 1756. He was also influential in the creation of the first scientific society in the colonies, the American Philosophical Society “for promoting useful knowledge.” In a 1749 paper he suggested an experiment for collecting electricity from clouds with a pointed metal rod from a high tower or steeple, and proposed the use of lightning rods to protect buildings:

I say, if these things are so, may not the knowledge of this power of points be of use to mankind in preserving houses, churches, ships, etc., from the stroke of lightning, by directing us to fix on the highest parts of these edifices, upright rods of iron made sharp as a needle, and gilt to prevent rusting, and from the foot of those rods a wire down the outside of the building into the ground, or down round one of the shrouds of a ship, and down her side till it reaches the water? Would not these pointed rods probably draw the electrical fire silently out of a cloud before it came nigh enough to strike, and thereby secure us from that most sudden and terrible mischief?

In France, the Comte de Buffon had Franklin’s work translated into French, and in May of 1752 his group set up an insulated pole outside of Paris, drawing sparks from the pole with an insulated brass wire during a thunderstorm. In October of 1752, Franklin performed his famous kite experi-ment with a pointed wire fastened to the top of the kite, and a metal key at the lower end of the string, which was held by a silk ribbon for insulation (Figure 8.1). Standing under a shed to keep the silk ribbon dry, he was able to draw sparks from the key and charge a Leyden jar from it, doing all the experiments “which are usually done with the help of a rubbed globe or tube.” In 1753 at the St. Petersburg Academy of Sciences in Russia, the German scientist G. W. Richmann (1711-53) re-


peated the experiment suggested by Franklin and was electrocuted. Electric Force and Quantity of Charge One difficulty with Franklin’s one-fluid theory was the repulsion of negatively charged bodies that have lost their electric fluid. In 1759 another German scientist at Saint Petersburg, Franz Aepinus (1724-1802), suggested that parti-cles of ordinary matter devoid of electricity repel each other, but attract electric fluid. In this view, uncharged matter contains its natural quantity of electric fluid, for which the forces due to the mat-ter and fluid balance each other, or perhaps remain slightly attractive to account for gravitation. From Franklin’s theory of the Leyden jar, Aepinus concluded that insulators are impermeable to the

flow of electric fluid. He demonstrated this even for air by showing that the metal surfaces of a Leyden jar remain charged when he replaced the glass with air. This led him to deny the existence of electric effluvia from charged bodies and to espouse a theory of electric force by “action at a distance.” The first statement of a quantitative law of electric forces was given by Joseph Priestley (1733-1804), who as a Nonconformist minister became interested in science through his belief that God could be known by studying His creation. After beginning a history of electricity, he made a trip to London where he spent several days with Franklin, who was seeking remission of the Stamp Act. In 1767 Priestley published The History and Present State of Electricity, with Original Ex-

-

--

KeyLeyden jar

insulation

- - - - - - - -

conductingstring

charged cloud+++ + + + + ++++

shed

Figure 8.1 Franklin’s Demonstration of the Equivalence of Lightning and Electricity Franklin used a kite to draw electric charge from clouds. He observed the effect of charge repulsion on the strands of the string, and was able to conduct electricity through a key to a Leyden jar by insulating himself from the string. Frictional charging of a cloud draws opposing charges from the ground to the highest point above the ground, such as the top of the steeple of a church. Concentration of charge in such pointed conductors produces large discharges in the form of lightning which often cause fires. Franklin proposed protecting buildings with conducting rods to carry the electricity into the ground.


periments, in which he included an experiment done by Franklin:

I shall close the account of my experiments with a small set in which, as well as in the last, I have little to boast besides the honor of following the instructions of Dr. Frank-lin. He informed me that he had found cork balls [suspended by silk threads] to be wholly unaffected by the electricity of [an insulated] metal cup, within which they were held; and he desired me to repeat and ascertain the fact, giving me leave to make it public.

In 1755 Franklin had written Dr. John Lining of Charleston, S. C., describing how he “electrified a silver pint cann [sic] on an electric stand, and then lowered into it a cork-ball.... The cork was not attracted to the inside of the cann as it would have been to the outside.” Priestley now recognized an analogy with the inverse-square law of gravitation, for which Newton had shown that the force of gravity on a mass point inside a spherical shell vanishes. Continuing the account of his experiment, Pries-tley infers that, “The attraction of electricity is subject to the same laws with that of gravitation, and is therefore according to the squares of the distances; since it is easily demonstrated that were the Earth in the form of a shell, a body in the inside of it would not be attracted to one side more than another.” The analogy was not completely accurate, since gravity does not quite vanish in a cylindrical shell (can). Henry Cavendish (1731-1810) performed an unpublished version of Pries-tley’s experiment in 1773. Using hollow concen-tric metal spheres, he found no transfer of charge from the outer to the inner sphere to an accuracy that implied an inverse-square force within less than ±1%. John Robison (1739-1805), of Edinburgh, inspired by a visit with Franz Aepinus in St. Petersburg, made the first direct measurement confirming the inverse-square law for electrical forces. Robison built a device to balance the weight of a cork ball on the end of a pivoted rod against the electrical attraction or repulsion of another cork ball above or below it. He published

this work in 1801 in an article on Aepinus in the Encyclopedia Britannica, but reports that it he did it in 1769. Robison’s four-volume Mechanical Philosophy, published posthumously in 1822, gives his conclusion based on many measurements that, “The mutual repulsion of two spheres, elec-trified positively or negatively, was very nearly in the inverse proportion of the squares of the dis-tance of their centres, or rather in a proportion somewhat greater, approaching to 1/r2.06.” The first published measurement of the inverse-square law of electric force was in 1785 by the French military engineer Charles Augustin Coulomb (1736-1806) and is now known as Cou-lomb’s law. He developed a torsion balance con-sisting of a horizontal rod suspended at its center by a thin wire in which he could measure the tor-sional force when the rod rotated in a horizontal plane. He then determined the force of repulsion between two charges by measuring the angle that the rod turned with a small charged sphere attached to one end when he brought a similar charged sphere near the first. He obtained a force that varied inversely as the square of the distance r between the centers of the spheres and directly proportional to the quantities of charge q and q’ on the two spheres, giving the equation

F = kqq΄/r2,

where k depends on the units chosen. In modern Standard International (SI) units, where F is in newtons (N) and r is in meters (m), the coulomb of charge (C) for q and q΄ corresponds to a value of k = 8.99×109 N×m2/C2. Although Coulomb only published three data points, which differed from the inverse-square law by as much as 6 percent, he evidently made many more measurements. He also used the torsion balance to measure an inverse-square force between the poles of bar magnets that were long enough to neglect the effects of their opposite poles. This confirmed a result obtained by the Reverend John Michell (1724-93) in 1750 with the aid of a torsion balance, which Coulomb and Michell invented independently. To measure the electrical force of attraction, Coulomb modified his apparatus to make a torsional pendulum in which he replaced the wire by a silk thread sup-


porting the rod with a charged object on one end. With an oppositely charged sphere brought near, the rod could be made to oscillate and the force calculated from the rate of oscillation, confirming the inverse-square law. Despite his thoroughness, Coulomb’s law was not widely accepted until after the publication in 1801 of Robison’s earlier work. Electric Current and the Battery Although Coulomb’s law established a quantitative basis for static electricity, few practi-cal applications were possible until current elec-tricity in the form of a sustained flow of electric charge through a conductor became possible from the work of the Italian scientists Galvani and Volta. After receiving a medical degree from the University of Bologna, Luigi Galvani (1737-1798) married Lucia Galeazzi, the only daughter of his anatomy professor, and eventually succeeded his father-in-law. In the late 1770s he began a series of experiments on electrophysiology, in which he stimulated muscles by electrical means. By 1780 he had acquired an electrical machine and a Ley-den jar for producing and storing electric fluid. With a conductor from his electrical machine attached to the exposed spinal cord of a frog, he could observe the contractions of the muscles in the legs when the he discharged the machine. In 1786, Galvani observed frog-leg con-tractions when he touched a scalpel to the crural nerve, even though the electrical machine was disconnected! According to some accounts, it was his wife Lucia who noticed that this happened at the same moment that someone discharged a spark from the machine. To see if this induction effect would result from natural electricity, he fastened some prepared frogs by brass hooks in their spinal cord to an iron railing surrounding a balcony of his house and observed contractions when lightning flashed. But the most surprising result was that contractions continued to occur even after the sky cleared, and these intensified when he pressed the brass hook in the spinal cord against the iron railing. Recognizing that electric fluid activated the muscles within the assembly of frog and met-als, Galvani confirmed this result in his laboratory by pressing the brass hook against the frog on an

iron plate. He showed that the strength of the contractions depends on the metals used, clearly demonstrating “galvanism” by producing an elec-tric current from the action of two dissimilar metals in the frog tissues. He believed that he had confirmed the existence of “animal electricity,” which he viewed as a vital force distinct from “natural electricity” such as lightning, and the “artificial electricity” produced by friction. In 1791, a year after the death of his wife at age 47, Galvani published De Viribus in Motu Musculari Commentarius. After Volta challenged his idea of “animal electricity” in 1793, Galvani demonstrated contractions by merely touching frog nerves to muscles without any metals. He also collected marine torpedoes and showed that their strong electrical discharge comes from structures similar to nerves and muscles. Although he failed to fully understand his discovery of galvanism, he confirmed the electrical nature of the “nervous fluid,” marking the beginning of electrophysiology. Alessandro Volta (1745-1827) received a classical education at the Jesuit school in his home town of Como in northern Italy. However, he never attended university, devoting himself instead to the study of electricity. Basing his work on Franklin’s one-fluid theory, he wrote two books on electrostatics followed by a letter to Priestley in 1775 describing his invention of the “electrophorus.” This device consisted of a flat insulating cake in a metal dish covered by a metal plate with an insulated handle. After rubbing the cake and replacing the plate, a brief touch trans-fers electric fluid from the plate. It can then be lifted and discharged into a Leyden jar as often as the process is repeated. This work led to his appointment as professor of experimental physics at the University of Pavia in 1778. He then per-fected a condensing electrometer by combining his electrophorus with the electroscope to accurately measure the “tension” on the plate, later called “voltage.” In 1792, Volta repeated Galvani’s ex-periments on the contraction of frog legs in contact with two different metals. At first he accepted Galvani’s view of “animal electricity,” but by the end of the year he concluded that the electricity


was from the metals rather than the muscles. This led to a long debate with Galvani’s nephew and defender, Giovanni Aldini. Volta strengthened his position by his measurements of what he called the “electromotive force” of different com-binations of metals with his condensing electrometer, ranking them in what now is called the “electrochemical series.” In 1794 he became the first foreigner to win the Copley Medal from the Royal Society of London, and finally took time to marry and begin a family. By 1796 he showed the identity of galvanic and common electricity by using only metals in contact to stimulate his electrometer. After trying various combinations of metals and moist conductors, Volta finally ob-tained a sustained galvanic current by placing a moist cardboard between two different metals. He increased this effect by stacking pairs of silver and zinc cells to form an electric pile, multiplying the flow of current (Figure 8.2). In 1800 he made these results public in a letter to Joseph Banks, president of the Royal Society, and they were published in its Philosophical Transactions in French under the English title “On the Electricity excited by the mere Contact of conducting Sub-stances of different kinds” (1800). The letter also described his “crown of cups,” consisting of a ring of cups filled with brine and connected by bimetallic arcs dipping into the liquid. He might have published his work earlier but for the French invasion of Italy in 1796 and the closing of the university in 1799 for a year. Both he and Galvani were deeply religious men who saw science and Christianity as allies, and Volta even wrote a confession of faith in 18l5, defending religion from scientism. Volta’s electric battery provided the first useful form of electricity and led to the electrical revolution of the nineteenth century. The battery produced a sustained electric current (I) defined as the flow of charge per unit time (I = q/t), with a unit now called the ampere (A) defined as one coulomb per second (C/s). Shortly after Volta’s announcement in 1800, the English chemist Wil-liam Nicholson (1753-1815) and surgeon Anthony Carlisle (1768-1840) built a “Voltaic pile” and used it to decompose water into hydrogen and

oxygen by passing a current through it, publishing their results even before the publication of Volta’s letter.

Sir Humphry Davy (1728-1829) then constructed a powerful electric battery of 500 plates at London’s Royal Institution and began work on the electrolytic decomposition of sub-stances such as lime, magnesia, potash and soda. By 1808 he had discovered the elements potassium (K), sodium (Na), calcium (Ca), magnesium (Mg), barium (Ba), strontium (Sr), and chlorine (Cl). In 1810 Davy demonstrated the first electric light with an arc discharge using charcoal electrodes with a battery of 2000 cells.

Cu Znweakacid

+ -

Cu

Zn

+

-

damp -+V

Voltaic Pile

cardboard

Equivalent circuit

R

I

Figure 8.2 Volta’s Electric Battery Volta established an electric voltage across two dissimilar metals such as copper (Cu) and zinc (Zn) by inserting them into a weak acid solution. This voltage multiplies by connecting the zinc plate (-) in one container to the copper plate (+) in the next container. He also formed a series of electric cells by stacking zinc-copper pairs separated by damp cardboard fillers to form a “voltaic pile.” In an equivalent circuit diagram, the dissimilar metals of an electric battery are represented by parallel lines of unequal length. The battery voltage (V) produces a current (I) from positive to negative through a conductor with resistance (R) shown by a zig-zag line.


Davy theorized that the source of such electric energy was from chemical reactions in the electrolyte of the pile. In 1813 the French mathematician Siméon-Denis Poisson (1781-1840) established the basic (differential) equation of electrostatics in terms of the electric energy (W) per unit charge (q), later called “electric potential” or voltage (V = W/q). Among the many honors paid to Volta was the international agreement in 1881 to name the unit of electric potential the volt (V), defining it as a joule of electric energy per coulomb of charge (J/C) available for doing work. 2. ELECTROMAGNETISM Magnetic Effects of Electric Current The connection between electricity and magnetism was finally established in 1820 by the Danish physics professor Hans Christian Oersted (1777-1851) during experiments with electric cur-rent at the University of Copenhagen. Earlier in his career he had met the German romantic phi-losophers Frederick Schelling (1775-1854) and Johann Fichte (1762-1814). Influenced by nature philosophy and the romantic ideas of the unity of the forces of nature, Oersted began a course of lectures in the winter of 1819-20 on “Electricity, Galvanism and Magnetism.” Having observed variations of a magnetic needle during a thunderstorm, Galvani tried to obtain a similar effect by placing a compass needle at right angles to a wire carrying an electric current during a lecture, but observed no effect. After the lecture, he tried placing the wire parallel to the needle, and immediately obtained a definite deflection of the needle transverse to the wire. He confirmed this result with a more powerful battery, and published it in July 1820 in a pamphlet entitled Experimenta circa effectum conflictus electrici in acum magneticam. He concluded that this transverse magnetic effect of an electric cur-rent “takes place in the conductor and in the sur-rounding space,” and he called it the “conflict of electricity,” describing it as follows:

From the preceding facts we may likewise collect that this [electric] conflict performs circles; for without this condition, it seems

impossible that the one part of the uniting conductor, when placed below the magnetic pole, should drive it towards the east, and when placed above it towards the west.

This transverse electromagnetic effect (Figure 8.3) differed from Newtonian and Coulomb forces, which always acted along a line between the cen-ters of two interacting objects.

Oersted’s discovery was presented to the Académie des Sciences in Paris on September 11, 1820, by François Arago (1786-1853) after he returned from a trip abroad, leading to further investigations in France. The first quantitative analysis of the electromagnetic force from the cur-rent in a straight wire on a magnetic pole was an-nounced by Jean-Baptiste Biot (1774-1862) and Félix Savart (1791-1841) at a meeting of the Académie on October 30, 1820. They stated the Biot-Savart law as follows:

Draw from the pole a perpendicular to the wire; the force on the pole is at right angles to this line and to the wire, and its intensity is proportional to the reciprocal of the dis-tance.

magneticcompass

abovewire

belowwire

+V

current I

N S

S N

N

S

Figure 8.3 Oersted’s Electromagnetic Effect Oersted observed the deflection of a magnetic compass needle at right angles to an electric current in a wire, in opposite directions above and below the wire. (North is up.)


Biot also showed that each element of the wire contributes to the magnetic force in proportion to the current and inversely proportional to the square of the distance from the element. Shortly after this, Arago showed that electromagnetism could induce magnetism in iron, and Oersted himself showed that a current-carrying wire is moved by a magnet. The French mathematician and chemist André-Marie Ampère (1775-1836) reported the direct action of electromagnetism between two electric currents to the Académie on September 18, 1820, just one week after Arago’s announcement of Oersted’s discovery. Ampère showed that two parallel wires attract each other if they carry currents in the same direction, and repel each other if the currents are in opposite directions (Figure 8.4). Later he measured the strength of such forces for various arrangements of the wires.

Ampère also distinguished clearly be-tween electric potential (voltage) and electric cur-rent, defining the direction of the current as that of a positive fluid. He noted that the electric potential of a voltaic pile was observable with an elec-trometer before he closed the circuit, but that he could detect current only after connecting the terminals. He found that he could measure current best by its magnetic effect in what he called a “galvanometer,” consisting of a pivoted coil of wire free to rotate between the poles of a U-shaped magnet when it carried current. It was later used as in the ammeter and voltmeter. For three years Ampère continued a series of careful experiments on the interactions between current carrying wires, and in 1825 he published his famous Memoir on the Mathematical Theory of Electrodynamical Phenomena Uniquely Deduced from Experiment. Here he developed the law of force between two current elements from many experiments on a variety of wire arrangements. The force between two parallel wires of length L with currents I and I΄ separated by a distance d is given by:

F = 2k΄I I΄L/d.

In modern SI units, the unit of current is defined as the ampere (A) for F in newtons (N), L and d in meters, and the constant k΄ = 10-7 N/A². Ampère also showed that the magnetic actions outside of a permanent bar magnet are exactly equivalent to those of a cylindrical coil of wire carrying a current, except that the electromagnetism of such a “solenoid,” as he called it, can be turned off by interrupting the current (Figure 8.5a). In Ampère’s electrical theory of permanent magnetism, a substance such as iron has molecules that contain perpetually flowing closed currents, all oriented alike; but this theory was too advanced for his contemporaries to accept (Figure 8.5b). The German school teacher Georg Simon Ohm (1787-1854) worked out the relationship between electric voltage and the resulting current in a conductor, and published his results in a series of papers beginning in 1826. Using Fourier’s theory of heat, published in 1822, Ohm proposed that the flow of electric current is proportional to

F

I I

d

Figure 8.4 Ampère’s Current Measurement Ampère measured the forces between two current-carrying wires, finding attraction for currents in the same direction (as shown) and repulsion for opposing currents. He established that the strength of the force F for currents of equal magnitude I separated by a distance d is proportional to the square of the current and inversely proportional to their separation:

F = 2k΄ I²L/d.


the potential difference, just as the flow of caloric is proportional to the difference in temperature. Constructing his own galvanometer, he showed that the current is proportional to the number of electric cells placed in series in a circuit, so that the resistance of a circuit is the ratio of voltage divided by current (R = V/I or V = IR). From Ohm’s law, a conductor in which one ampere flows when one volt is applied has one unit of resistance, now called the ohm. Ohm also drew wires from various metals with differing lengths and thicknesses, and showed that the cur-rent varies with the metal and is proportional to the cross-sectional area of the wire and inversely proportional to the length of the wire. His work was ignored in Germany, or else criticized by idealistic philosophers for being too empirical, until he was awarded the Copley Medal by the Royal Society in 1841. Finally in 1849, he re-

ceived an appointment as a professor at the Uni-versity of Munich. Electromagnetic Force and the Electric Motor Ampère is sometimes called the “Newton of electricity” for developing the mathematical law describing how electric currents produce magnetic forces. Although he expressed his laws of electromagnetism in terms of action-at-a-distance forces, he did allow for the possibility that such forces may be due to “the reaction of the elastic fluid which extends throughout all space, whose vibrations produce the phenomena of light.” This was a prophetic insight, which was eventually realized through the development of the field concept. In the meantime, electromagnetic force was dramatically demonstrated about 1823 by the English physicist William Sturgeon (1783-1850), who developed Ampère’s solenoid into a practical

north

south

north

south

of permanent magnetism

switch

(a) Coil-woundelectromagnet

(b) Amperian-current theory

Figure 8.5 Electromagnet and Ampère’s Electrical Theory of Permanent Magnetism (a) A current-carrying coil wound on a cylindrical core to form a solenoid produces magnetism equivalent to a bar magnet with the advantage that it can be turned on and off with a switch. (b) Ampère proposed that permanent magnetism could be explained by the alignment of internal electric current loops, all circulating in the same direction. Adjacent currents in these loops will be in opposing directions and thus cancel each other, leaving only a single loop around the outside equivalent to the coil of an electromagnet.


electromagnet. Sturgeon found that he could greatly increase the electromagnetic force by wrapping a coil of wire on an iron core, which he varnished to insulate it from short-circuiting the wires. By bending his electromagnet into the form of a horseshoe, he was able to lift nine pounds while the current was running. Most of the electricians of the nineteenth century followed Ampère in trying to develop a mathematical law of force between currents or moving charges. This attempt to reduce electro-magnetism to Newtonian physics was followed by several German physicists, including Wilhelm Weber (1804-91) and Franz Neumann (1798-1895). In 1846 at the University of Göttingen in Germany, Weber worked out a logical system of units for electricity in terms of the fundamental mechanical units of mass, length and time. In many cases they were able to find formulas that described the experimental facts of electromagnet-ism in terms of action at a distance, but these for-mulas were limited in their application. The breakthrough leading to the successful synthesis of electricity and magnetism was achieved largely through the work of Faraday and Maxwell by introducing the field concept as a medium through which electromagnetic forces propagate. Michael Faraday (1791-1867) was one of the finest experimentalists in the history of sci-ence. He was born in the village of Newington, now a part of London, one of ten children of a blacksmith. His formal education ended at the age of 13 when he was apprenticed to a bookbinder, giving him opportunity to read many books and an interest in performing simple chemical experiments. In 1812 he attended a series of scientific lectures by Sir Humphry Davy at the Royal Institution. He took careful notes and bound them into a book, presenting them to Davy with his application for a job as an assistant. Davy hired young Faraday in 1813, at a salary less than the one he earned as a bookbinder, and shortly thereafter he took him on a grand tour of Europe as his secretary and valet. For a period of 18 months Faraday had opportunity to meet scientists such as Ampère, Arago and Volta, and began to learn about different approaches to sci-ence in the French mechanistic and German nature

philosophy traditions. With Davy’s encourage-ment, Faraday published his first paper in 1816 on the nature of caustic lime in Tuscany. Faraday spent the rest of his life at the Royal Institution, becoming the director of the laboratory in 1825 and professor of chemistry in 1833. Over the course of his career, his laboratory notes included more than sixteen thousand entries, the most famous of which were published in his Experimental Researches on Electricity (1839-55). His research included work on alloys of steel (1818-24), a study of compounds of chlorine and carbon (1820), electromagnetic rotations (1821), the liquefaction of gases (1823, 1845), the discov-ery of new carbon compounds including benzene (1825), electromagnetic induction (1831), the laws of electrolysis (1832), the study of dielectrics and discharges in gases (from 1835), and the study of diamagnetism and electromagnetic effects on light (from 1845). In 1821, shortly after Oersted’s discovery of the electromagnetic force, Faraday invented the first electric motor. His interest ignited when the English physician turned researcher, William Wol-laston (1766-1828), attempted to make a current-carrying wire rotate around its own axis in the presence of a magnet. After repeating many of the experiments of Ampère, Wollaston and others, Faraday suspended a current-carrying wire with its lower end in a mercury bath free to rotate about a magnet as described in his abbreviated laboratory notes:

Magnets of different power brought per-pendicularly to this wire did not make it re-volve as Dr. Wollaston expected, but thrust it from side to side.... The effort of the wire is always to pass off at a right angle from the pole, indeed to go in a circle round it; should make the wire continually turn round. Arranged a magnet needle in a glass tube with mercury about it and by a cork, water, etc., supported a connecting wire so that the upper end should go into the silver cup and its mercury and the lower move in the channel of mercury round the pole of the magnet.... Very Satisfactory, but make more sensible apparatus.


Faraday soon improved his rotating wire apparatus and even demonstrated rotation in the Earth’s magnetic field. He also arranged one end of a sus-pended bar magnet to rotate around a vertical current-carrying wire. Having demonstrated the possibility of such a device but he left the devel-opment of practical electric motors to others. Faraday was a deeply religious man with strong Christian principles. He belonged to a small dissenting church started by Robert Sandeman, a Presbyterian minister, and known as the Sande-manians. In 1821 he married Sarah Barnard who was also a member of the Sandemanian fellowship, in which they remained active throughout their lives. Three years later he was elected a fellow of the Royal Society over the opposition of Davy, who was then president of the Society and had apparently become embittered with Faraday’s success. As a matter of religious conviction, Fara-day declined most honors offered to him, including an offer in 1857 of the presidency of the Royal Society. He participated in few public activities, devoting himself mostly to experimental research. He had a long history of headaches, dizziness and loss of memory, and was forced to take a long va-cation in the early 1840s to recover from a serious illness. His symptoms appear to be the result of mercury poisoning similar to those suffered earlier by Newton and other scientists. Electromagnetic Induction and the Generator Shortly after his invention of the electric motor, illustrating how an electric current could produce magnetic effects, Faraday began to think about the possibility of using magnetism to induce electricity. A notation in his laboratory notebook in 1822 indicated, “Convert magnetism into elec-tricity.” An entry dated December 28, 1824, described an experiment in which he placed a magnet inside a solenoid, “But in no case did the magnet seem to affect the current so as to alter its intensity as shewn upon a magnetic needle placed under a distant part of it.” Again, on November 28, 1825, his notes describe a current-carrying wire “parallel to which was another similar wire separated from it only by two thicknesses of paper. The ends of the latter wire attached to a galva-

nometer exhibited no action.” Even when he replaced either of the straight wires with a helical coil, he detected no induced current. Several other scientists at the time were also trying to induce electricity from magnetism, including Ampère and Arago in France, but no one seemed to have any appreciable success. The problem was that they were all looking for the induction of a constant current. In 1824 Arago suspended a magnetic needle over a rotating cop-per plate and observed that the end of the needle began to revolve. He even noted that this dragging effect depended on the conductivity of the rotating plate. Faraday repeated this experiment in 1825, but neither he nor Arago suggested the possibility of induced currents in the plate. On April 22, 1828, Faraday suspended a copper ring by a thread and placed a bar magnet inside the ring, but still could detect no induced current. Finally, on August 29, 1831, Faraday made the long-sought discovery of electromag-netic induction that had eluded so many attempts. On that day he made the following notation:

Have had an iron ring made (soft iron).... Wound many coils of copper wire round one half, the coils being separated by twine and calico.... Will call this side of the ring A. On the other side but separated by an interval was wound wire in two pieces together amounting to about 60 feet in length, the direction being as with the former coils; this side call B. Charged a battery of 10 pr. plates 4 inches square. Made the coil on B side one coil and connected its extremities by a copper wire passing to a distance and just over a magnetic needle (3 feet from iron ring). Then connected the ends of... A side with battery; immediately a sensible effect on needle. It oscillated and settled at last in original position. On breaking connection of A side with Battery again a disturbance of the needle.

Faraday’s discovery of this inductive action led him to an appreciation of the importance of changing current and its associated changing magnetism. On October 1 he repeated this induc-tion experiment with a wooden core. Again he


obtained the same effect, but enough weaker that he had to use a galvanometer instead of a magnetic needle near an indicating helix. Thus he concluded that, “There is an inducing effect without the presence of iron.” On October 17, 1831, Faraday described his most important experiment on electromagnetic induction, using a hollow helical coil in the form of a cylinder:

A cylindrical bar magnet ¾ inch in diame-ter and 8½ inches in length had one end just inserted into the end of the helix cylin-der–then it was quickly thrust in the whole length and the galvanometer moved–then pulled out and again the needle moved but in the opposite direction. This effect was repeated every time the magnet was put in or out and therefore a wave of Electricity was so produced from mere approximation of a magnet and not from its formation in situ.

This result was the basis for Faraday’s invention of the electric generator, or dynamo, in which the mechanical energy required to move the magnet is converted into electrical energy in the form of changing voltages and currents. On October 28, 1831, he described the first direct-current genera-tor, consisting of a copper disk rotating between magnetic poles at its edge. As the circumference of the disk moved through the magnetic field lines, a radial current was generated. He now saw that similar currents generated in Arago’s experiment would produce magnetic lines to drag the magnetic needle. As the electric generator was developed by others over the next few decades, it became the prime source of electric energy from mechanical sources, and a contemporary poet (Herbert Mays) even celebrated Faraday’s fame in verse:

Around the magnet Faraday Is sure that Volta’s lightnings play; But how to draw them from the wire: He took a lesson from the heart; ‘Tis when we meet--’tis when we part, Breaks forth the electric fire.

Mutual and Self-Induction The American physicist Joseph Henry (1797-1878) independently discovered electro-magnetic induction, perhaps even before Faraday. Henry missed receiving credit because he delayed publication until 1832 and this, along with his geographical isolation, made his work much less influential. Like Faraday, Henry came from a poor family, was apprenticed at age fifteen to a watchmaker, and was an active Presbyterian lay-man throughout his life. In 1819 he entered the Albany Academy, and seven years later he began teaching mathematics and science there. In 1827 Henry read about electromagnetism and began to develop more powerful electromagnets. In 1831 he designed a telegraph with one mile of wire, through which he could send current to activate an electromagnet, but he never sought a patent. After reading about Faraday’s discovery of electromagnetic induction, Henry reported his own independent work “On the Production of Currents and Sparks of Electricity from Magnet-ism” in the American Journal of Science (July 1832):

I commenced, last August, the construction of a much larger galvanic magnet than, to my knowledge, had before been attempted, and also made preparations for a series of experiments with it on a large scale, in ref-erence to the production of electricity from magnetism.

He first described the mutual induction in a coil, wound around a large electromagnet but insulated from it, when he switched the current in the elec-tromagnet on or off. He then described how a changing current in a coil can induce another cur-rent in the same coil, an effect called “self-induction.” This was observed when a moderate current in a coil was interrupted, causing a surge of current and a spark at the break in the circuit, induced by the diminution of the original current. Faraday independently discovered self-induction two years later, but the unit for the inductance of a coil, in which one volt is self-induced by a current change of one ampere per second, is now called the henry. The Russian physicist Heinrich Lenz (1804-65) was the first to


state the general principle known as Lenz’s law: An induced current always opposes the change that produced it. Thus in Henry’s observation of a spark when a circuit was disconnected, the diminishing current was opposed by the induced current, which caused a spark by reinforcing the original current. After demonstrating an electro-magnet that could lift more than a ton of iron, Henry was appointed as a professor at the College

of New Jersey (later Princeton) in 1832. During the next five years, he invented the electromag-netic relay and the electric transformer, showing how voltage could be stepped up or down by the proper ratio of turns in the primary and secondary coils of a transformer. Neither Faraday nor Henry developed their discoveries into practical applications, but they did not hesitate to share their knowledge with others. Samuel Morse (1791-1872) constructed his

first model of the telegraph in 1835 after con-ferring with Henry, and applied for a patent in 1837. The corresponding work in England by Charles Wheatstone (1802-75) in 1837 occurred after he had a long visit with Henry on his visit to England. As early as 1832 in France, Ampère’s instrument maker, Hippolyte Pixii, constructed a practical generator with a rotating horseshoe magnet near two coils of wire. Such a device using a permanent magnet is called a “magneto,” and produces an alternating current since opposite poles of the magnet pass the coils in each rotation, inducing currents in opposite directions. In the same year, Pixii invented a split metal cylinder called a “commutator” to switch the current in each rotation so that it would flow in only one direction as a direct current. In 1834 a young American blacksmith named Thomas Davenport (1802-51) learned about Henry’s electromagnets and constructed one of the first practical electric motors incorporating rotating coils, called an “armature,” fixed coils called “field magnets,” and a commutator (Figure 8.6). The Russian physicist Moritz von Jacobi (1801-74) independently invented a similar device in 1834. 3. ELECTROMAGNETIC FIELDS & WAVES The Field Concept and Electrolysis From about 1821, Faraday began to de-velop his idea of “lines of force,” which led to the field concept as a new way of viewing the universe that was more flexible and useful than the me-chanical picture of Galileo and Newton. Such fields of force provided a unified and interrelated way of viewing electric and magnetic phenomena, consistent with his Christian faith in the unity of the created order. A field was an influence filling the space surrounding electric charges or magnets and forming patterns like those made by iron fil-ings sprinkled around a magnet. Due to his lack of mathematical training, Faraday tended to form pictorial representations of electromagnetic phenomena like his rotating wire motor. This led him to think in terms of curved lines of force propagated through a medium, rather than Newtonian straight-line forces acting at a

Field Magnet

North

South

Brush

CommutatorArmatureCoil

Split-ring

Axis ofRotation

Figure 8.6 Direct-Current Electric Motor In the position shown, the armature coil has a north pole at the top and south pole at the bottom, so it is repelled from the field magnet poles and begins to rotate as shown. After a half turn, the direction of the current will change due to rotation of the commutator so that the north pole of the armature is again at the top and the south pole at the bottom, and thus is again repelled from the field magnets and continues to rotate.


distance. For Faraday each line of force corres-ponded to a unit of magnetic or electric force, and a number of lines made up a tube of force connecting opposite magnetic poles or electric charges (Figure 8.7). The cross-sectional area of these tubes increased and then decreased along their length as the lines of force diverged from their points of origin and converged again on op-posite poles or charges, the cross-sectional area of a tube of force providing a measure of the strength of the electric or magnetic field at that section. Faraday explained electromagnetic in-duction in terms of an interaction of conductors with magnetic field lines in his laboratory notes of August 1, 1851, later refined for presentation to the Royal Society:

Hence it follows that whether the curves are intersected directly or obliquely makes no difference provided they are intersected.

The effect depends upon the number of curves intersected. A wire moving obliquely may intersect fewer curves and therefore have a feebler current evolved in it; but if it intersected only the same curves directly across, it would have no larger a current. So with a given moving wire or with a given wire under which a magnet is moving, the quantity of electricity generated is directly as the amount of curves passed over or through. With the same curves therefore it varies directly with the velocity of the motion.

Thus in Faraday’s law of electromagnetic induc-tion, the induced voltage or “electromotive force” (emf) in a wire varies directly with the rate at which the magnetic field changes. In an electric generator, the induced voltage in the armature will alternate at the same frequency as its rotation,

B B

I I E

+Q

(a) Magnetic Field (B) (b) Magnetic Field (B) (c) Electric Field (E)

in an electromagnet in a straight wire charge (Q)

Force on

in E field+ charge

N

S

⊕

fieldlines

tube

due to current from current from positive( I ) ( I )

tube

fieldlines

Figure 8.7 Faraday’s Concept of Magnetic and Electric Fields Faraday invented the field concept to account for the effects of electric currents and charges. Magnetic fields arise from electric currents and circulate around them (a and b). They exert forces on other currents and moving charges. Electric fields are produced by electric charges (c) and exert forces on other charges.


producing an alternating current with the use of slip rings to complete the circuit (Figure 8.8). In 1832 Faraday announced the quanti-tative laws of electrolysis. After devising methods for measuring the quantity of electricity, he dis-covered that in the electrolytic separation of ele-ments by passing current through a solution, “The chemical power, like the magnetic force, is in direct proportion to the absolute quantity of elec-tricity which passes.” His laws of electrolysis established that the mass of an element separated by a given quantity of electricity is proportional to its atomic weight and inversely proportional to its valence (combining power). This fact could be explained by the atomic theory, but Faraday did not take this step:

If we adopt the atomic theory or phraseol-ogy, then the atoms of bodies which are

equivalents to each other in their ordinary chemical action, have equal quantities of electricity naturally associated with them. But I must confess I am jealous of the term atom; for though it is very easy to talk of atoms, it is very difficult to form a clear idea of their nature, especially when compound bodies are under consideration.

Apparently it was easier for him to conceive of the continuous lines of force in his field concept than the discontinuities implied by the atomic theory. In his electro-chemical studies, Faraday introduced many new scientific terms, including electrolysis, ion, electrode, anode and cathode (positive and negative electrodes). Faraday extended his ideas about mag-netic lines of force associated with electric currents to electric lines of force (fields) associated with

Field Magnet

North

South

ArmatureCoil

GeneratorCrank

fieldlines

Brush

motor

generatorMechanical energy Electrical energy

(at crank) (at V)

alternatingvoltage V

(rotate witharmature)

Slip rings

axis ofrotation

Figure 8.8 Alternating Current Generator/Motor with Slip Rings An electric generator requires mechanical rotation of the crank, changing the number of magnetic field lines through the armature coil (shown with a single turn) to produce electrical energy at V. The induced voltage at V alternates in polarity as the armature rotates, producing an alternating current if the armature circuit is completed with brushes and slip rings as shown. An alternating-current electric motor requires an alternating voltage at V to produce current in the armature coil, which causes it to rotate due to a force from the magnetic field of the field magnets, producing mechanical energy at the crank. In each half rotation of the armature, the direction of the current from the brushes switches, ensuring rotation in the same direction.


electric charges. In 1835 he demonstrated that electric charge resides on the outside surface of any conductor, with no electric force lines inside, by entering a charged metal cage and showing that there was no electric influence inside. He experimented with insulators between charged conducting bodies, and showed in 1837 that insulators increase the capacity of such “condensers” (capacitors) to store charge for a given voltage, measuring the dielectric constant for a variety of solid and fluid insulating materials. He proposed a model to explain this effect:

The particles of an insulating dielectric whilst under induction may be compared to

a series of small magnetic needles, or more correctly still to a series of small insulated conductors.... If [the condenser] were charged, these little conductors would all be polar; if...discharged, they would all return to their normal state...

This model led him to deduce that the polarization of the dielectric would be opposite to the charge on the condenser, explaining the increase of its capacity to store charge at a given voltage. In honor of Faraday, the SI unit of capacitance for a capacitor that can store one coulomb of charge at one volt is called the farad. Electric Circuits and Oscillations In 1837 Joseph Henry visited Faraday in England and conferred with him about their work. In the few years since their independent discover-ies of induced electricity from changing magnet-ism, development of the alternating-current gen-erator (Figure 8.8) and the transformer (Figure 8.9) made it possible to exercise increasing con-trol over electric circuits. Further applications of circuits came from Henry’s study of the discharge of a Leyden jar condenser through a coil and its effect on a magnetic needle, leading him to rec-ognize in 1842 the oscillatory nature of the result-ing spark:

The discharge, whatever may be its nature, is not correctly represented by the single transfer of an imponderable fluid from one side of the jar to the other. The phenomena require us to admit the existence of a prin-cipal discharge in one direction, and then several reflex actions backward and forward, each more feeble than the preceding, until the equilibrium is obtained.

He explained this oscillatory discharge as the result of self-induction in the coil reinforcing the current from the condenser enough to reverse its charge, followed by an alternating series of con-denser rechargings and dischargings. He also noted that the effect of the spark in causing vari-ations in a compass needle propagated over several feet, and that of a lightning flash over 7 or 8 miles, speculating that waves are excited in an electric

~V1

V2

ChangingMagnetic

Field B

N1

N2

Figure 8.9 Mutual Induction & Transformer In 1831 Faraday and Henry each observed that a changing voltage V1 across the turns of a coil induced a changing voltage V2 across a second coil wrapped on the same core. From Faraday’s field perspective, this is explained by the changing magnetic field (ΔB) produced by the current in the primary coil inducing a voltage in the secondary coil. This mutual induction effect is applied in a transformer, in which an alternating voltage V1 produces a voltage V2 increased by a factor equal to the ratio of the turns N2 /N1 of the coils.


plenum by the oscillating currents. The oscillator made it possible to control the frequency of a circuit by adjusting either its capacitance or inductance (Figure 8.10). A few years after this discovery, Henry moved to Washington, DC, where he became the first director of the newly founded Smithsonian Institution in 1846.

Faraday also anticipated the connection between electromagnetism and waves, even sug-gesting its relation to light. In 1845 he began to investigate this relationship, guided by his belief in the unity of the forces of nature: “This strong persuasion extended to the powers of light, and led, on a former occasion to many exertions, hav-ing for their object the discovery of the direct relation of light and electricity...” After several

attempts, Faraday finally succeeded in demon-strating that light could be affected by a magnetic field. Passing polarized light through a heavy glass plate, he showed that the plane of polarization of the light could be rotated by a magnetic field with its lines of force parallel to the direction of propagation. The complete connection between light and electromagnetism, however, was not es-tablished until after Faraday’s field concept was developed by others into a mathematical theory. The German physicist Gustav Kirchhoff (1824-87) extended Ohm’s theory of electric cir-cuits to clarify the concept of electric voltage, showing in 1849 that Ohm’s “electroscopic force” in a circuit is equivalent to electrostatic potential. Kirchhoff’s circuit laws made it possible to calcu-late the distribution of voltages and currents in complex circuits with several loops and junctions. His “loop law” established that around a closed loop in a circuit the voltage increases from any sources of electric energy (battery or generator) must equal the voltage decreases from losses of electric energy (resistance or motor) to conserve energy. His “junction law” stated that the currents in and out of any junction in a circuit must be equal to conserve charge. In 1853 the Scottish physicist William Thomson (1824-1907), later Lord Kelvin (1892), used Kirchhoff’s loop law to analyze electric oscil-lations in a circuit containing a Leyden jar or condenser of capacitance C (charge stored per unit voltage), and a coil of self-inductance L (voltage induced per unit change in current). He obtained an oscillation frequency (vib/sec) given by

f = 1/2π LC ,

and this result was verified five years later by Wilhelm Feddersen (1832-1918), who improved Wheatstone’s rotating-mirror technique to obtain photographs of spark discharges showing a se-quence of damped oscillations. Using Faraday’s field concept, Thomson obtained expressions for the amount of energy stored in the magnetic field of a coil, and showed that electric oscillations in a circuit involve the alternating transfer of energy between the magnetic field of the coil and the electric field of the condenser. In 1854 he derived

ΔΔ E

Δ I

+

-+

-

Switch

OscillatingCurrent

B

Figure 8.10 Henry’s Electric Oscillator In 1842 Henry observed that the discharge of a Leyden jar (capacitor) through a coil pro-duced a sustained spark at the switch as it was being closed, which he recognized as resulting from an oscillation of current in the circuit. Discharge of a capacitor produces a changing magnetic field (ΔB) in the coil that induces a voltage to recharge the capacitor with oppo-site polarity, leading to a series of oscillations due to continuing discharging and charging. Thus the energy of the electric field E in the capacitor transfers to the magnetic field B in the coil and back again in each oscillation.


the equation of telegraphy for underwater cables that led to the successful design of the Atlantic cable. He also introduced Alexander Graham Bell’s (1847-1922) telephone into Great Britain. In 1857 Kirchhoff showed that the speed v with which an electric disturbance propagates along a wire is equal to the ratio of the electro-magnetic units (emu) based on the force between two electric currents and the electrostatic units (esu) based on the force between two electric charges. This ratio has the dimensions of velocity (length/time) since electrostatic force between charges has the same form as electromagnetic force between two lengths of wire carrying cur-rents given by the charge traveling past any point in unit time. A year earlier Wilhelm Weber (1804-90) and Rudolph Kohlrausch (1809-58) measured this ratio by comparing the electrostatic repulsion of the charge of a Leyden jar with the electromagnetic effects of the current produced by discharging the jar. They obtained a value of about 3.1 x 108 m/sec, equal to the speed of light in space within the limits of error. Kirchhoff rec-ognized this coincidence and thus was the first to discover that an electric signal propagates along a wire at the speed of light. Maxwell’s Electromagnetic Field Theory James Clerk Maxwell (1831-79) achieved the unification of electricity, magnetism and optics in his electromagnetic field synthesis, the intellectual equivalent of the Newtonian synthesis of the laws of mechanics some 200 years earlier. Maxwell was born in Edinburgh in the year that Faraday discovered electromagnetic induction; but he grew up in an isolated country home at Glenlair, south of Glasgow, where his mother died of cancer when he was eight years old. At the age of sixteen he entered Edinburgh University. There he began a study of color vision that later led to the first color photograph (1861) by using three color filters. In 1850 he moved to Peterhouse college at Cambridge, where William Thomson was already a fellow. Here he completed an analysis of Saturn’s rings, showing that they would be unstable unless they consist of loose orbiting particles with a variety of speeds governed by Kepler’s laws.

Maxwell was inspired to study electricity by Thomson’s mathematical development of the field concept and analogies with the theory of heat flow. After reading Faraday’s Experimental Re-searches, Maxwell wrote his first electrical paper “On Faraday’s Lines of Force” (1856). He stated that his goal was “to show how, by a strict appli-cation of the ideas and methods of Faraday, the connection of the very different orders of phenom-ena which he has discovered may be clearly placed before the mathematical mind.” After defining a line of the electric or magnetic field as a curve in space whose direction at each point is that of the force on a positive charge or elementary north magnetic pole, respectively, he defined the intensity of the force at any point with a fluid-flow analogy:

If we consider these curves not as mere lines, but as fine tubes of variable section carrying an incompressible fluid, then, since the velocity of the fluid is inversely as the section of the tube, we may make the velocity vary according to any given law, by regulating the section of the tube, and in this way we might represent the intensity of the force as well as its direction by the motion of the fluid in these tubes.

Maxwell was then able to show that these tubes of force could give the same results for static charges and permanent magnets as those given by the usual action-at-a-distance formulas. He also showed that current elements are equivalent to magnetic dipoles. Faraday had explained the induction of electricity from a changing magnetic field as the result of an “electrotonic state” produced by magnetism. Although Maxwell’s fluid analogy could not account for this state, he was able to define it by a mathematical rotation operator that he called a “curl,” a concept borrowed from Thomson, and thus gave mathematical expression to all known electric and magnetic phenomena in terms of Faraday’s field concept. In 1856 Maxwell left Cambridge to teach physics at Marischal College in Aberdeen, Scot-land, where he married the daughter of the princi-pal of his college, Katherine Mary Dewar. She helped him with experiments on gases and color,


and his letters to her reflect deep Christian piety, including many Biblical quotations. When Marischal College closed in 1860, he moved to King’s College in London. His second great memoir, “On Physical Lines of Force,” was a se-ries of three papers published in the Philosophical Magazine (vol. 21) in 1861-62. Here he developed an elaborate mechanical analogy to account not only for electric and magnetic forces, but also to explain Faraday’s law of electromagnetic in-duction. In Maxwell’s new model, a magnetic field results from what he called “molecular vor-tices” rotating around the lines of magnetic force. Along these tubes of ether, the velocity of rotation determines the intensity of the magnetic force, exerting both longitudinal tension along the lines of force and lateral pressure from the centrifugal effect of the rotation. In this description of the field,

all the vortices in any one part of the field are revolving in the same direction about axes nearly parallel, but...in passing from one part of the field to another, the direction of the axes, the velocity of rotation and the density of the substance of the vortices are subject to change.

For adjacent vortices to rotate in the same direc-tion, Maxwell supposed that the tubes are sepa-rated by rows of spherical particles that roll like ball bearings, or what he called “idle wheels.” By assuming that these particles constitute electricity, it follows that a change in the magnetic field, equivalent to one of the vortices beginning to rotate faster than an adjacent one, will cause the particles between them to change position, result-ing in an electric current. In this way, Maxwell’s model demonstrated the induction of electric cur-rent from changing magnetism, and provided the basis for a mathematical statement of Faraday’s law of induced emf (voltage). But the great value of this model was in suggesting to Maxwell the converse of Faraday’s law as a generalization of Ampère’s law describing how electricity produces magnetism. If a change in vortex motion causes a displacement of the idler particles, then a displacement of the idler particles

should produce a change in vortex motion. Ex-pressing this in terms of fields: a changing magnetic field creates an electric field (Faraday’s law), so a changing electric field should create a magnetic field (Ampère’s law). In describing his system, Maxwell says:

I do not bring it forward as a mode of con-nection existing in Nature.... It is, however, a mode of connection which is mechanically conceivable and easily investigated, and it serves to bring out the actual mechanical connection between the known electromag-netic phenomena.

After identifying electromotive force (voltage due to magnetic effects) with electric tension (voltage due to charge separation), Max-well introduced his crucial distinction between conduction current and displacement current:

Electromotive force acting on a dielectric produces a state of polarization of its parts.... The effect of this action on the whole dielectric mass is to produce a general displacement of the electricity in a certain direction. This displacement does not amount to a [conduction] current because when it has attained a certain value it re-mains constant, but it is the commencement of a current, and its variations constitute currents in the positive or negative direction, according as the displacement is increasing or diminishing. The amount of the displacement depends on the nature of the body, and on the electromotive force.

In his model, the motion of the idler particles could represent either the conduction current of free charges, or displacements of bound charge. Thus an electrical disturbance could propagate either through a conductor, or in the form of the displacement current transmitting field changes through dielectric media, including air or even the ether that Maxwell regarded as filling space. Maxwell’s Prediction of Electromagnetic Waves Initially Maxwell described the propaga-tion of an electrical disturbance through an ether medium by suggesting that a displacement of one


layer of idler particles would initiate a change in the angular velocity of the vortices around the adjacent tubes of ether. These would then displace the next layer of idler particles so that the disturbance would transmit through a sequence of layers. By computing the energy transferred in this process, he obtained a velocity of propagation. This involved associating the kinetic energy with the magnetic field and the potential energy with the electric field, leading to a velocity for the elec-tromagnetic disturbance governed by the electric and magnetic force constants of the transmitting medium. Using the values measured in air by Kohlrausch and Weber, Maxwell obtained a veloc-ity of 193,088 mi/sec (3.11 x 108 m/s), and immediately recognized its significance:

The velocity of light in air, as determined by M. Fizeau is 195,647 miles per second [3.15 x 108 m/s]. The velocity of transverse undulations in our hypothetical medium, calculated from the electromagnetic ex-periments of MM. Kohlrausch and Weber, agrees so exactly with the velocity of light calculated from the optical experiments of M. Fizeau, that we can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.

Thus Maxwell’s awkward mechanical model led to the brilliant insight that he emphasized with italics, linking light with electromagnetic waves even though no one had yet detected the latter. He wrote his friend Thomson at the University of Glasgow in late 1861, reporting this unexpected agreement between his electromagnetic calculations and the speed of light:

I made out the equations before I had any suspicion of the nearness between the two values of the velocity of propagation of magnetic effects and that of light, so that I think I have reason to believe that the mag-netic and luminiferous media are identical.

In his next paper, entitled “A Dynamical Theory of the Electromagnetic Field” (1865), Maxwell discarded his mechanical ether model,

which had served him so well as a scaffolding to develop his theory, and concentrated on the mathematical equations relating the electric and magnetic fields. He described the properties of these fields in terms of 20 equations. In modern notation, they reduce to just four equations that describe the magnitudes and directions of the fields at any point in space and are known con-ventionally as Maxwell’s equations. The first of Maxwell’s field equations generalizes Coulomb’s law by defining the electric field E in relation to static electric charges. The second expresses the continuity of the magnetic field B at any point in space that results from the fact that magnetic poles cannot be separated. The third and fourth equations describe Maxwell’s generalization of Ampère’s and Faraday’s laws in terms of the electric constant ε (permittivity) and magnetic constant μ (permeability) of the support-ing medium, which are related to Coulomb’s force constants (k = 1/4πε, k΄ = μ/4π). In standard in-ternational units (SI), these equations take the following symbolic form:

Ampère’s law: curl B/μ = i + ε ∂E/∂t

Faraday’s law: curl E = – ∂B/∂t .

The equation for Ampère’s law expresses the idea that the circulation (mathematical curl) of the magnetic field B around any point is proportional to the sum of the conduction current i and dis-placement current ∂E/∂t (rate of change of E) through that point and perpendicular to B. The equation for Faraday’s law states that the circula-tion (curl) of the electric field E around any point is proportional to ∂B/∂t through that point. Maxwell’s equations relating E and B take on an elegant symmetric form in free space where the conduction current i is zero:

curl B = (με) ∂E/∂t , curl E = – ∂B/∂t .

These equations indicate that changing electric fields generate magnetic fields, and that changes in these magnetic fields will in turn generate electric fields, so that the two will reinforce each other in space. When Maxwell combined these equations mathematically, they yield the classical (differential) equations for the propagation of E


and B through space as a transverse wave, in which these fields are perpendicular to each other and to the direction of the wave propagation (Figure 8.11). The speed of the wave appearing in these equations is given by:

c = 1/με = k/k' = 9×109/10-7 = 3.0×108 m/s, which is the measured speed of light. This result led Maxwell to his famous identification of light as an electromagnetic wave, and his prediction that oscillating charges produce the changing electric and magnetic fields that propagate as electromagnetic waves at the speed of light. In 1865 Maxwell returned to Glenlair to write his monumental Treatise on Electricity and Magnetism, first published in 1873, in which the Maxwell equations appear only in Chapter IX of Part 4, well into the second of two volumes. The book seemed inaccessible to all but a few contem-porary physicists, much of it abstract and separated from the earlier mechanical models. When Cambridge University received a grant to establish the Cavendish Laboratory, Maxwell was offered

the first Chair of Experimental Physics in 1871 and he began the development of the famous labo-ratory. His contributions were in many fields besides electromagnetism, including statistical mechanics, thermodynamics, geometrical and physiological optics, elasticity, statics, and cyber-netics. In the fall of 1879, at the age of 48, Max-well died of the same abdominal cancer that had killed his mother, in the year of Einstein’s birth. From early in his career, Maxwell leaned toward the Kantian idea that only the relations between things can be known. In his electromag-netic theory, he made one of the greatest connec-tions in the history of science: the mutual relations between electricity, magnetism and light. Optics and electromagnetism were now united, and the possibility of relating these to other forms of radiation at different frequencies was apparent in the connection between the speed, wavelength and frequency of a wave (c = λf). These ideas led not only to a host of practical developments in modern communications, but also to a whole new way of viewing the universe. As the mechanical pictures

B

~

±

±

Oscillator

Antenna

E

BΔ

Δ

v = k/k' = c√

Figure 8.11 Maxwell’s Electromagnetic Wave Concept Maxwell predicted that oscillating charges would produce changing electric and magnetic fields that would propagate as an electromagnetic wave in space at the speed of light v = c. Oscillating charges in a vertical antenna will produce a vertical electric field and a horizontal magnetic field. By Ampére’s law, the changing electric field will induce a changing magnetic field (ΔE→ΔB) and by Faraday’s law the changing magnetic field will induce a changing electric field (ΔB→ΔE), etc. Thus the fields will mutually reinforce each other as an electromagnetic wave with vertical electric field variations and horizontal magnetic field variations.


faded into the background, the world began to look increasingly like a system of interpenetrating fields and energies that no machine could duplicate. This picture would be reinforced by the special theory of relativity, which followed almost directly from Maxwell’s field theory. 4. ELECTROMAGNETIC APPLICATIONS Reception of Maxwell’s Theory Many of Maxwell’s contemporaries were slow to accept his mathematical formulation of the electromagnetic field theory due to their reliance on mechanical models of the ether. Even William Thomson (Kelvin) exemplified this attitude, as in the following comment in 1884, some 20 years after the introduction of Maxwell’s equations:

I am never content until I have constructed a mechanical model of the object that I am studying. If I succeed in making one, I understand; otherwise I do not. Hence I cannot grasp the electromagnetic theory of light. I wish to understand light as fully as possible, without introducing things that I understand still less. Therefore I hold fast to simple dynamics for there, but not in the electromagnetic theory, can I find a model.

As late as 1890, Thomson attempted to explain the phenomena of electricity, magnetism and optics in terms of a mechanical ether that resisted rotational stresses but not linear displacements. He suggested that electrical effects were due to a linear motion in the ether, while rotations caused magnetism and vibrations caused light waves. Many other mechanical models of the ether were proposed in the latter half of the nineteenth century, but none proved to be successful. A connection between electric oscilla-tions in a circuit, first analyzed by Thomson in 1853, and the radiation of electromagnetic waves predicted by Maxwell in 1861, was first suggested by the Irish physicist George Fitzgerald (1851-1901) in 1883. He proposed that the oscillations produced by the discharge of a condenser through a coil might be a good source of electromagnetic waves, and he showed that increasing the fre-quency of oscillations should increase the energy

radiated, making it easier to detect. In the Fitzgerald oscillator, the condenser plates were placed close together and served only to store energy in the electric field between the plates during each cycle of oscillation. The source of radiation was the alternating magnetic field due to the coil. But he found that if waves were produced by such a magnetic oscillator, they were too weak to be detected. He had the misfortune of publishing a paper “On the Impossibility of Origi-nating Wave Disturbances in the Ether by Means of Electric Forces.” Maxwell’s theory became known on the continent largely through the work of Hermann von Helmholtz (1821-94). After his early work on the conservation of energy, and his important research on the physiology of optics and sound at Heidelberg, Helmholtz accepted the chair of physics at the new Physical Institute in Berlin in 1871, where he began a series of papers on elec-trodynamics. In Europe, the interaction of electric charges was usually explained by Wilhelm We-ber’s law of instantaneous action at a distance rather than action mediated by a field in an inter-vening ether. Helmholtz showed that Weber’s law violated conservation of energy, and then he developed a more general action-at-a-distance theory that included Maxwell’s theory as a limit-ing case, allowing for wave propagation at the speed of light. Helmholtz was a leader in the transition of German universities from teaching academies to research institutions. The great laboratories he established placed Germany in the forefront of scientific research. His students included such famous scientists as Heinrich Hertz who finally discovered radio waves, Max Planck who intro-duced quantum theory, and the Americans Henry Rowland and Albert Michelson. As a graduate student under Helmholtz, Rowland (1848-1901) conducted an experiment in 1876 that showed the equivalence of moving charge and electric current. By rapidly rotating a glass disk with charged metal foil attached, he observed the deflection of a magnetic needle. Thus the changing electric field associated with the rotating charge produced a magnetic field, confirming the prediction of Maxwell.


Hertz and the Discovery of Radio Waves Heinrich Rudolf Hertz (1857-94) was a Lutheran of Jewish descent from Hamburg, who studied engineering at the University of Munich and then enrolled at the University of Berlin in 1878, where he studied under Kirchhoff and Helmholtz. After earning his doctorate, he served for three years as assistant to Helmholtz, pub-lishing 15 papers on both electrical and mechan-ical topics. Using Helmholtz’s approach in 1884, he wrote his first paper on Maxwell’s theory, sim-plifying his equations and showing their equi-valence with those of Helmholtz. Thus he stated what has become the accepted modern view:

Maxwell’s theory is Maxwell’s system of equations. Every theory which leads to the same system of equations, and therefore comprises the same possible phenomena, I would consider as being a form or special case of Maxwell’s theory; every theory

which leads to different equations...is a dif-ferent theory.

In 1885 Hertz accepted a position at the Technical School at Karlsruhe, where he married a profes-sor’s daughter. The Technical School had a well-equipped laboratory where Hertz could begin the electrical investigations that confirmed the con-nection between light and electricity and estab-lished his place in history. Shortly after arriving at Karlsruhe, Hertz found some Ruhmkorff induction coils for pulsed high voltages and a pair of Riess spark microme-ters that provided variable spark gaps. He con-nected one of the spark micrometers to an induc-tion coil to produce an oscillating circuit, and added conducting plates on either side of the spark gap to increase the capacitance, much like a Ley-den jar with opened foils (Figure 8.12). The sepa-ration of these conductors (up to 3 m) determined the frequency of the oscillations and allowed them

oo

oo

InductionCoil

CapacitorPlate

Spark Gaps

Variable frequency coil

Transmitter

Receiver

λ

adjustable lengthf = 50 MHz

= 6m

Figure 8.12 Hertz’s Discovery of Radio Waves and Determination of their Speed Hertz obtained oscillations at about 50 MHz with an induction coil and capacitor plates spread out with variable separation to adjust the frequency and act as a radiating antenna. When a spark appeared in the transmitting spark gap, Hertz observed a simultaneous spark in the spark gap of the single-loop receiving coil with dimensions that could be varied to maximize the spark at the resonant frequency. The spark in the receiving coil alternated in intensity as it was moved toward the receiver, giving a measurement of wavelength at about 6 meters between positions of maximum intensity. The speed of the electromagnetic wave was then v = λf = 6m×(50×106Hz) = 3×108m/s, which is equal to the speed of light c as predicted by Maxwell.


to act as a radiating dipole antenna fed by the spark, thus providing a kind of primitive “tran-smitter.” With the other spark micrometer conected to an adjacent loop of wire with a variable perimeter, he observed an induced spark in this simple “receiver” whenever there was a discharge across the larger spark gap of the induction coil. By adjusting the length of the receiving loop, he was able to increase the length of its spark to a maximum value corresponding to the resonant frequency for oscillations in the loop. This discovery of radio waves occurred in the fall of 1887 by a combination of trial and error. Hertz began to notice the induction of sparks at increasing distances of up to 12 m from the primary sparks. He then realized that he could confirm Maxwell’s prediction of electromagnetic waves “if one could succeed in demonstrating in air a finite rate of propagation of waves” from a direct measurement of their frequency and wave-length in air. In a lecture hall about 15 m long, he set up a transmitting induction coil near one end and covered the opposite wall with zinc so that wave reflection would form standing waves. By moving his receiving loop between the walls of the lecture hall, Hertz was able to ob-serve changes in the spark, including points where he could detect no spark corresponding to the nodes of the standing wave about 4.8 m apart. Since the nodes are separated by half waves, this gave a wavelength of 9.6 m at a calculated fre-quency of 35.7 million vibrations/second (or 35.7 MHz, since a vib/sec is now called the hertz) giv-ing a speed of:

c = λf = 9.6 m×(35.7×106 vib/sec) = 3.4×108 m/s,

close to the measured speed of light. Later cor-rections revealed that the actual frequency was about 50 MHz, and the wavelength about 6 m, giving c = 3.0×108 m/s. This work was published in 1888 in his paper “On Electromagnetic Waves in Air and their Reflection.” Hertz now began to improve his equip-ment by using a higher frequency and concave parabolic reflectors behind his spark-fed dipole antenna. He now observed at least four nodes with an average separation of 33 cm, or a wavelength of 66 cm at a frequency of 455 MHz. With this

equipment he could observe sparks even in an adjacent room 16 m from the transmitting spark, leading him to comment that:

Insulators do not stop the ray--it passes right through a wooden partition or door; and it is not without astonishment that one sees the sparks appear inside a closed room.

He also demonstrated the transverse nature and polarization of the waves by rotating the receiving spark gap to eliminate the sparking when it was at right angles to the transmitting spark gap. Further experiments showed that reflection and refraction of the rays followed the same laws as light, leading to his conclusion that, “The experiments described appear to me...to remove any doubt as to the identity of light, radiant heat, and electromagnetic wave-motion.” Early in his work, Hertz made the unex-pected discovery of what later was called the “photoelectric effect” as described in his 1887 paper “On an Effect of Ultra-Violet Light upon the Electric Discharge.” In a series of careful experiments, he showed that a spark discharge was strengthened when it was illuminated by light and that this effect was even more pronounced with ultraviolet radiation. These results would later provide the basis for development of the quantum theory. Finally, in 1889, Hertz returned to Max-well’s theory to show that electromagnetic waves could be accounted for without any reference to direct action at a distance in a paper on “The Forces of Electric Oscillations, Treated According to Maxwell’s Theory.” Here he obtained solutions for dipole radiation and mapped the shape of the resulting waves. His work greatly clarified Max-well’s theory, leading to its wider acceptance and further development. This finally broke the hold of the mechanical model and helped to give birth to relativity theory. Applications of Radio Waves Hertz never mentioned the possibility of applications of radio waves in any of his papers. He died at the age of 36 from blood poisoning after operations on his head for malignant bones, too early to see the results of his discovery. Radio


waves were soon confirmed by Oliver Lodge (1851-1940) in England, who improved the receiver in 1889 by placing the spark gap in a glass tube connected to a battery and galvanometer. This device, called a “coherer,” would produce a current even when radio waves were too weak to produce a spark. In 1892, Sir William Crookes (1832-1919) suggested the possibility of communication with Hertzian waves. Earlier Crookes had discov-ered the element thallium in 1861 from its charac-teristic green spectrum line. He also developed the “Crookes tube” in 1875, showing that the rays produced by a high voltage across two electrodes in an evacuated glass tube emanated from the negative cathode and could be deflected by a magnetic field. This “cathode-ray tube” led later to the discovery of the electron and development of the oscilloscope for television and other appli-cations. One of the earliest applications of radio waves was in 1894 by the Russian physicist Alex-ander Popov (1859-1905). He used a receiver to detect signals from lightning strokes and then developed an antenna in 1897 that could send a signal some three miles from ship to shore. The Italian engineer Guglielmo Marconi (1874-1937) was the first to recognize the commercial possi-bilities of “wireless” communications. After reading papers by Hertz in 1894, Marconi devel-oped an improved coherer, consisting of a tube of loosely packed metal filings in which radio waves produced a substantial increase in current. By 1896 he succeeded in sending coded messages far enough to warrant a patent, and by 1898 he transmitted signals from Ireland to Scotland. His greatest success came on December 12, 1901, when he sent radio waves across the Atlantic from Cornwall in England to Newfoundland in Canada, using balloons to lift his antennas as high as pos-sible. One year later, an explanation for why these waves followed the curvature of the Earth was suggested by Arthur Kennelly (1861-1939) at Harvard and Oliver Heaviside (1850-1925) in England. Independently in 1902, they proposed the existence of a layer of charged particles sur-rounding the Earth that reflected radio waves back

and forth between the Earth and what is now called the “ionosphere.” The Canadian-American physicist Regi-nald Fessenden (1866-1932) pioneered the modu-lation of radio waves to carry sound. He devised a method to vary the amplitude of radio waves to match the lower frequency and shape of sound waves, and he used these “amplitude modulated” (AM) carrier waves to reproduce the original sound waves at the receiver. In 1906 he transmit-ted and received the first music signals along the Massachusetts coast. The English engineer John Fleming (1849-1945) aided in the demodulation of radio waves by his 1904 invention of the diode rectifier tube. Current flowed across the two electrodes of this vacuum tube only when the heated cathode was negative, thus changing alternating currents into pulsating direct currents. The American inventor Lee Deforest (1873-1961) demonstrated the amplification of radio waves by the invention of the triode tube in 1906. He added a “grid” be-tween the two electrodes in the diode, which could control the flow of current across the tube. Using these devices, Deforest established the first radio station in 1916 to broadcast news and music.

Extensions of the Electromagnetic Spectrum Maxwell’s electromagnetic theory, as confirmed by Hertz, opened up a new understand-ing of the whole spectrum of electromagnetic waves, all of which traveled at the speed of light but differed in their frequencies and wavelengths (c = λf). By measuring temperature variations across the colors of the visible spectrum produced by Sunlight, William Herschel (1738-1822) in 1800 had discovered infrared radiation (IR) at wavelengths longer than visible light beyond the red end of the visible spectrum. A year later Johann Ritter (1776-1810) found that chemical reactions produced by light were even stronger beyond the violet end of the spectrum, revealing ultraviolet radiation (UV) at wavelengths shorter than visible light. These wavelengths were later measured by passing IR and UV radiation through closely spaced slits ruled on thin glass (diffraction grating) and observing the resulting interference pattern. Infrared was found to have wavelengths


up to about 100 times longer than light waves, and ultraviolet waves were up to 100 times shorter than visible light. Electromagnetic waves even shorter than ultraviolet were first discovered by the German physicist Wilhelm Roentgen (1846-1923) in 1895. They were generated by a high-voltage cathode-ray tube in which high-energy electron collisions produced radiation that caused a glow at some distance away on a paper covered with a fluores-cent substance. Roentgen studied the penetrating effect of these “x-rays” using photographic meth-ods, and proposed their use in medicine. He reported his work in a paper “On a New Kind of Rays” in January, 1896:

The most striking feature of this phenome-non is the fact that the active agent passes through a black card-board envelope which is opaque to the visible and the ultra-violet rays... A further difference, and a most im-portant one, between the behavior of cath-ode rays and of X-rays lies in the fact that I have not succeeded, in spite of many at-tempts, in observing a deflection of the X-rays by a magnet... I have observed, and in part photographed many shadow pictures... I possess, for instance, photographs of...the shadow of bones of the hand.

In 1913 the English physicists William Henry Bragg (1862-1942) and his son William Lawrence Bragg (1890-1971) worked out a diffraction method for measuring the wavelength of x-rays by reflection from a crystal. Using the known atomic spacing of the crystal lattice and the diffraction angles of the reflected x-rays, they found wave-lengths about 100 times shorter than ultraviolet wavelengths. Both father and son shared the 1915 Nobel prize for their work. After the discovery of radioactivity in 1896 by Henri Becquerel (1852-1908), further studies showed that it consisted of positively and negatively charged particles designated as “alpha and beta rays,” respectively, which were deflected in opposite directions by a magnetic field. A third component of radioactivity called “gamma rays” (Greek letter γ) were discovered by the French physicist Paul Villard (1860-1934) in 1900. These

rays penetrated metal sheets, produced photo-graphic images, and were undeflected by mag-netism. They were identified as electromagnetic waves even shorter than x-ray wavelengths when their diffraction pattern from crystal reflections was obtained in 1914. In general, electromagnetic waves are generated by oscillating charges and detected from the effects of their electric and magnetic fields. Controlled radio waves are generated by electronic oscillators feeding various types of antennas, and are detected by electronic circuits whose elements can be adjusted for maximum response (resonance) at the frequency of transmission. With the development of radar (radio detection and ranging) during World War II, methods were developed for generating centimeter radio waves called “microwaves,” about 100 times shorter than infrared waves. High frequency oscillators such as klystrons and magnetrons were developed, and the resulting microwaves were focused by reflectors or horns to produce directional beams. Radio waves up to about three meters long are used to transmit television signals and FM radio, in which the frequency is modulated by sound waves in a frequency band between 88 and 108 MHz. AM radio waves average about 300 meters in the 550-1600 kHz band. Thus the electromagnetic spec-trum spans the approximate ranges shown in the following table:

The Electromagnetic Spectrum Waves Frequency Wavelength VibrationsAM radio 106 Hz 300 m oscillator FM/TV 108 Hz 3 m & antenna Microwave 1010 Hz 3 cm resonator Infrared 1012 Hz 3×10-4 m molecular Visible Light 1015 Hz 7 - 3×10-7 m

ROYGBIV atomic & molecular

Ultraviolet 1016 Hz 3×10-8 m atomic X-ray 1018 Hz 3×10-10 m subatomic γ-ray 1020 Hz 3×10-12 m nuclear

Since all of these waves travel at the speed of light c, the wavelengths are given by λ = c/f = 3 x 108/f. The electromagnetic theory contributed greatly to the transition from the mechanical view


of the universe to a more abstract view in which the isolated particles of the Newtonian world now become interrelated by electromagnetic waves and fields pervading all space and influencing all mat-ter. Applications across the electromagnetic spec-trum have provided a variety of new communica-tion technologies to bridge the distance between individuals and continents. The electromagnetic view of the universe led directly to relativity and quantum theory and a new understanding of both atoms and galaxies. Field and wave concepts provided a new basis for a richer understanding of the universe in the twentieth century. Although the end of the nineteenth cen-tury marked the launching point of a new view of the universe, few were aware of what was to come. The first American physicist to win a Nobel prize, Albert Michelson (1852-1931), wrote the follow-ing words in 1899:

The more important fundamental laws and facts of physical science have all been dis-covered, and these are now so firmly estab-lished that the possibility of their ever being supplanted in consequence of new discover-ies is exceedingly remote.... Our future dis-coveries must be looked for in the sixth place of decimals.

In 1900 the director of the U. S. Patent Office asked President McKinley to close the Patent Of-fice because “everything that can be invented has been invented.” REFERENCES Aitken, H. G. Syntony and Spark: The Origins of

Radio. New York: John Wiley, 1975. Cantor, G. N., and M. J. S. Hodge. Conceptions of

the Ether: Studies in the History of Ether Theories. Cambridge, Eng: Cambridge Uni-versity Press, 1981.

Cohen, I. B. Benjamin Franklin, Scientist and Statesman. New York: Scribners, 1975.

Everitt, C. W. F. James Clark Maxwell, Physicist and Natural Philosopher. New York, Scrib-ners: 1975.

Faraday, Michael. Experimental Researches in Electricity, 3 vols. London: Taylor, 1839-55.

Goldman, M. The Demon in the Aether: The Story of James Clerk Maxwell, the Father of Modern Science. Edinburgh: Adam Hilger, 1983.

Heilbron, J. L. Electricity in the Seventeenth and Eighteenth Centuries. Berkeley: University of California Press, 1979.

Hesse, Mary B. Forces and Fields: The Concept of Action at a Distance in the History of Physics. London: Thomas Nelson and Sons, 1961.

Hertz, H. Electric Waves. transl. D. E. Jones. London: Macmillan.

Hertz, H. Miscellaneous Papers. London: Mac-millan, 1896.

Hertz, J. H. Hertz. Leipzig: Akademische Verlags-gesellschaft, 1927.

MacDonald, D. K. C. Faraday, Maxwell and Kel-vin. Garden City, N.Y.: Doubleday, 1964.

Maxwell, James Clerk. A Treatise on Electricity and Magnetism, 2 vols. Oxford: Clarendon Press, 1891.

Niven, W. D., ed. The Scientific Papers of James Clerk Maxwell, 2 vols. repr. New York: Dover, 1952.

Polvani, G. Alessandro Volta. Pisa: Domus Gali-laeana, 1942.

Segrè, Emilio. From Falling Bodies to Radio Waves: Classical Physicists and Their Discov-eries. New York: W. H. Freeman, 1984.

Whittaker, Edmund T. A History of the Theories of Aether and Electricity, 2 vols. New York: Philosophical Library, 1951-53.

Williams, L. Pearce. Michael Faraday: A Biogra-phy. New York: Basic Books, 1965.

Williams, L. Pearce. The Origins of Field Theory. New York: Random House, 1966.

206

1. ETHER AND RELATIVITY THEORIES At the end of the nineteenth century, only a few doubted the power of science with its posi-tivistic confidence in accumulated “facts” and “truths.” The fruits of science were evident in the new technologies of communication and power. But the foundation for truth in Western culture, the Christian conviction that “God is Truth,” was being questioned by the very science it had fos-tered. The search for truth in the questioning ideas of Darwin and other critics seemed to place the basis for truth itself in doubt. Before he sank into insanity in 1889, Friedrich Nietzsche had announced the death of God and its corollary, the subjectivity of truth, concluding that, “It is still a metaphysical faith that underlies our faith in sci-ence.” At the turn of the century, Sigmund Freud published The Interpretation of Dreams, revealing the illusions of individual consciousness and the repressed desires of the unconscious that motivate so much of human action and thought. But few could have guessed that science itself was entering a crisis of confidence and a new revolution. The source of the problem in science was rooted in its most successful field. Classical physics faced the intolerable dilemma of two divergent ways of viewing the universe. The

mechanical view of the universe focused on dis-crete particles subject to instantaneous forces governed by Newton’s laws, which could account for motion, heat and sound. The electromagnetic view of the universe envisioned forces transmitted over time by continuous fields according to Max-well’s equations, which could explain electricity, magnetism and light. The question that begged an answer was the connection between these two views, and especially how to understand electro-magnetism in terms of Newtonian mechanisms. At first the ether seemed to provide an answer by reducing electromagnetic waves to mechanical vibrations of an ethereal medium to transmit light through space, but this approach led to failure. The new physics that emerged from this failure of mechanistic science recognized the pri-ority of electromagnetic fields and waves, leading to radical revisions in the fundamental mechanical concepts of matter, space and time. In Einstein’s theory of relativity, these were all linked to electromagnetism through the constant speed of light c in empty space, revealing the integral connections between space, time, matter and energy. This new relational view was reinforced by the interconnected development of quantum theory with relativity, showing a direct relation between particles and waves. Simple mechanical

CHAPTER 9

A Relational Universe

Relativity and Quantum Theories

Chapter 9 • A Relational Universe 207

causation gave way to a statistical description based on probability relationships. The resulting principle of uncertainty established a new connection between the observing subject and the objects observed, shattering confidence in scientific knowledge and objectivity. The Michelson-Morley Experiment With the overthrow of geocentric cos-mologies, location and motion in space became problematic in view of the motion of the Earth. Newton held to a concept of absolute space, time and velocity by viewing God as the one privileged observer and governor of the universe. In New-ton’s view, the Deity “endures for ever, and is everywhere present, and by existing always and everywhere, He constitutes duration and space.” Thus classical physics viewed space, time and velocity as absolute quantities that could be measured in relation to an ethereal medium filling all of space and constituted by the presence of God. Newton defined these quantities in his Principia:

Absolute, true, and mathematical time, of itself, and from its own nature, flows equably and without relation to anything external, and by another name is called duration.... Absolute space, in its own nature, without relation to anything external, re-mains always similar and immovable.

In the nineteenth century, ether theories were based on a similar idea that in principle there is a frame of reference at rest in the cosmic ether from which it is possible to measure the absolute velocities of moving objects. In the 1880s, the German-American physicist Albert A. Mi-chelson (1852-1931) made several

attempts to establish the mechanical idea of electromagnetic waves by measuring the speed of light in different directions in an all-pervading ether. At Helmholtz’s Berlin laboratory in 1881, Michelson constructed an interferometer designed to split a beam of light in two with a semi-transparent mirror, sending one ray at right angles to the other to mirrors where they could be reflected back together (Figure 9.1). When the two rays converge, they form an interference pattern consisting of dark and bright rings determined by their relative phases. If the Earth travels with

LightSource

Ether wind

c

v

v

c - v

c + v

M1

M2

M

90°Rotation√c²-v²

movingwith Earth Interference ring pattern

perpendicular to light rays

Equivalent

Figure 9.1 Michelson-Morley Experiment to Detect the Ether In Michelson’s interferometer, a beam of light (speed c) is split into a reflected ray (vertical) and a transmitted ray (horizontal) by a half-silvered mirror (M). These rays are brought back together and form an interference pattern after the first ray is reflected by mirror M1 back through M and the second ray is reflected by mirrors M2 and then M. A one-quarter wavelength change in the distance from M to M2 would change the pathlength of the second ray by a half wavelength, changing each bright ring to dark, and vice versa. Michelson and Morley tried to detect motion of the Earth through an assumed ether (equivalent to an ether wind in the opposite direction) by noting that the time T1 for the first ray is shorter than T2 for the second ray until the apparatus is rotated by 90°, when T1 becomes longer than T2. They calculated that this should cause a shift equivalent to about 0.4 of a wavelength, but no shift was observed.


velocity v through a motionless ether that transmits light at a velocity c, then light sent in the direction of the Earth’s motion should travel at a velocity c-v relative to the Earth. A 90-degree rotation of the entire interferometer apparatus would interchange the two rays of light relative to the Earth’s motion, and thus should produce a noticeable shift in the rings of the interference pattern. Michelson first attempted his ether ex-periment in 1881 without success. When he returned to the U.S., he accepted a position at the Case School of Applied Science in Cleveland, where in 1882 he made the most accurate meas-urement yet of the speed of light (299,853 km/s). In 1887 he repeated his ether experiment with Edward Morley (1838-1923), using improved ap-paratus sensitive enough to detect motion relative to the ether about 40 times smaller than the orbital velocity of the Earth. To his dismay, there was still no sign of a shift in the interference pattern due to the Earth’s motion through the ether. The Michelson-Morley experiment seem-ed to imply that the Earth was motionless relative to space! Michelson considered the possibility that the Earth dragged ether with it. But then the planets must also drag the ether, which would cause light to travel faster from a planet moving toward the Earth than away from it. Variations in the speed of light from the planets would produce apparent deviations from Kepler’s laws, but no such anomalies appeared. Despite his failure to detect the ether, Michelson was recognized for his optical studies in 1907 when he became the first American to win a Nobel Prize in science. The Lorentz-Fitzgerald Contraction In 1892, the Irish physicist George Fitzgerald (1851-1901) suggested a possible way to account for the negative result of the Michelson-Morley experiment. He proposed the ad hoc hypothesis that the length of a material body parallel to its velocity v is reduced slightly by its motion through the ether. He showed that a con-traction of the interferometer by a factor of

1-v²/c² in the direction of the Earth’s motion would just compensate for the longer time that

light would otherwise take to travel along that direction between the mirrors of the interferometer. A few months later, the Dutch physicist Hendrik Lorentz (1853-1928) adopted this hypothesis and showed that it was consistent with his application of Maxwell’s equations to the motion of electrons in an ether. In his Theory of Electrons (1895), charges moving in the ether produce magnetic effects, which contract them in the direction of their motion. The Lorentz-Fitzgerald contraction hy-pothesis led to a discouraging result. If all in-struments contract in just the right proportion to conceal the existence of the ether, absolute motion would be impossible to detect. Lorentz stated this idea as a general principle, and Fitzgerald’s Dublin colleague, Sir J. Larmor (1857-1942), observed in 1900 that clocks would have to slow down by the same factor of 1-v²/c² if absolute motion relative to the ether is undetectable. In 1903 Lorentz showed that for an electrical system moving with a velocity v, Maxwell’s equations remain unchanged if space and time coordinates are transformed by an amount involving the same factor. In a coordinate system moving parallel to the x-axis the coordinates for the Lorentz transformations are given by:

x΄ = (x - vt)/ 1-v²/c², y΄ = y, z΄ = z,

t΄ = (t - vx/c²)/ 1-v²/c² ,

which lead to the Fitzgerald contraction except at low velocities (v << c, v²/c² → 0) when they re-duce to the Galilean-Newtonian transformations:

x΄ = x - vt and t΄ = t.

In 1904 the French mathematician Henri Poincaré (1854-1912) spoke of the “principle of relativity” according to which,

the laws of physical phenomena must be the same for a “fixed” observer as for an ob-server who has a uniform motion of trans-lation relative to him: so that we have not, and cannot possibly have, any means of dis-cerning whether we are, or are not, carried along in such a motion.... From all these results there must arise an entirely new kind


of dynamics, which will be characterized above all by the rule, that no velocity can exceed the velocity of light.

The concluding phrase is evident from the fact that 1-v²/c² → 0 as v → c. In his 1905 book Science

and Hypothesis, Poincaré argued that scientific concepts and even geometric axioms are conventions rather than metaphysical truths. Thus absolute space and time are merely conventions to represent the relation between bodies. Natural law itself should not be seen as absolute and unchanging, but as a more subtle kind of “constant relation” between phenomena that may change in the light of new evidence.

Einstein and the Special Theory of Relativity Albert Einstein (1879-1955) was born in Ulm, Germany, in a liberal Jewish family whose engineer father rejected the authority of the ancient Jewish laws. He showed little promise as a child and received his earliest education in a Catholic grammar school in Munich. When his family emigrated to Milan in 1894, he applied to the Polytechnical School in Zurich; but he was not accepted until he completed further studies in Switzerland, where he later took citizenship. At Zurich he studied mathematics and physics, but after graduation the only work he could find was that of a private tutor. In 1902 he accepted a job as a junior official at the Swiss patent office at Bern, where he married Mileva Maric, a former student companion, and had two sons. It is hard to know how much Einstein’s Jewish background affected him, but an early interest in the Bible gave way to a skeptical atti-tude and a “cosmic religious feeling” that fostered creative freedom and simplicity. He remembered his sense of wonder when he was only 4 or 5 at the way a compass needle lines up without any apparent outside influence. After receiving a geometry book at the age of 12 from an uncle, he fell in love with “holy geometry.” But at Zurich he turned away from the diversions of mathemat-ics to concentrate on the laws of physics. In the ancient Hebrew tradition, God was known through His Laws and could not be defined by human standards. In later Jewish mysticism, knowledge of

the divine could be gained only through con-templation of the relationship between God and creation. In a similar manner, Einstein tried to avoid things that “clutter the mind” and “divert it from the essentials.” His interest was not in the details of experiments like that of Michelson and Morley. He desired to know the thoughts of God beyond and within nature: “I want to how God created this world.” Einstein was especially influenced by the Austrian physicist Ernst Mach (1838-1916), whose 1883 book The Science of Mechanics suggested that space is not absolute, but is dependent on the relation between masses. So too, inertia is not intrinsic to mass, but is a relationship between all material bodies in the universe. Einstein mentions that at age 16 he was puzzled after reading an account of the electromagnetic nature of light and the recent discovery of radio waves by Hertz. He wondered what an electromagnetic wave would look like to an observer who caught up with it and was traveling at the speed of light (v = c). Relative to such an observer moving with the crest of the wave (maximum electric and magnetic fields), it would appear that the fields were constant. But according to Maxwell’s equations, light consists of changing electric and magnetic fields. In the light of these new field “truths,” Einstein saw that the accepted “truths” of mechanics must be replaced by a new principle: Only light can reach the speed of light. While working at the patent office, Ein-stein had time to think about recent developments in physics without distraction. From 1901 to 1904 he submitted five papers to Annalen der Physik on statistical mechanics, but most of the work had been anticipated by the American physicist Josiah Willard Gibbs (1839-1903). Then between March and June of 1905 at the age of 26, Einstein pub-lished three major articles in volume 17 of the Annalen der Physik, an achievement comparable only to Newton’s at the age of 23. The first paper extended the quantum theory to the photon con-cept of light. The second established an empirical basis for the size and existence of the atom, which some positivists such as Mach had begun to doubt, along with the idea of absolute space. The third paper was a 30-page article entitled “On the


Electrodynamics of Moving Bodies,” which founded the theory of relativity and led to the famous formula E = mc². Einstein begins his paper on relativity with the idea that Maxwell’s equations should have the same form in all inertial systems (moving at constant velocities relative to each other) and that the absolute velocity of a body cannot be known. Thus absolute space and time are meaningless and the ether is “superfluous.” Instead of reducing electromagnetic waves to mechanical vibrations of an ether, he suggests that the ideas of mechanics should be revised consis-tent with the electro-magnetic field concept of the constant speed of light. Later he would say that he should have called the theory “invariance the-ory” because of the central role of the invariant speed of light; but it is now called the “special theory of relativity” because of its restriction to inertial systems. Ten years later this restriction was lifted in the “general theory,” allowing for accelerated systems. Using these ideas, Einstein was able to clear the growing confusion in classical physics and introduce a new economy and simplicity. Thus the special theory of relativity is based on the two postulates of relativity and invariance:

(1) Relativity: The laws of nature are the same in all inertial systems.

(2) Invariance: The speed of light is the same for all observers.

The second postulate assumes that the speed of light in vacuum is independent of the motion of either its source or observer. It leads directly to the Lorentz transformations as a general result, applying to all of physics rather than to Maxwell’s equations only. For example, if a spaceship moves at a speed v past the Earth, a ray of light should have the same speed c relative to both, even though the spaceship is moving faster than the Earth. But Einstein saw that this is only possible if time differs in the two systems, so that an interval on Earth of time T (t - ti) would have a different duration To (t΄ - t΄i) in the spaceship. Einstein often developed his ideas in terms of thought experiments, known from the German as gedanken experiments. For example, if

a ray of light travels a distance cTo inside the spaceship perpendicular to its velocity v, then relative to the Earth it would travel a diagonal dis-tance cT (constant c requires a different T) com-pounded of both cTo in the spaceship and the distance vT that the spaceship itself moves (Figure 9.2). Thus the two time intervals are related by the Pythagorean theorem:

(cT)² = (cTo)² + (vT)²,

which can be solved for T to show that time intervals in the two systems are consistent with the Lorentz transformations in what is known as the time dilation equation:

T = To / 1-v²/c².

Since 1-v²/c² < 1, T > To, meaning that clocks in uniform motion relative to an observer run slower than clocks at rest relative to the observer. Time dilation implies a coupling between space and time. The time duration between two events, such as two ticks of a clock, will be short-est in the system where the two events are at the same spatial location. Thus the observer at rest relative to the clock will measure the shortest time duration between the ticks. An observer moving relative to the clock will measure a longer duration between ticks, concluding that the moving clock runs slow. Since this is true for all inertial systems, the laws of nature appear the same to any observers in relative motion, and measurements made by any pair of observers would be com-pletely symmetric. If in time T the spaceship is seen from Earth to travel between two mountain tops a dis-tance Lo = vT, then as observed from the spaceship it will travel a distance L = vTo, so that their relative velocity v = L / To = Lo / T and

L = Lo(To / T) = Lo 1-v²/c² ,

using the time dilation equation. This length con-traction is the same as that suggested by Fitzger-ald to account for the failure of the Michelson-Morley experiment, but in relativity theory it is a general spatial relationship between moving sys-tems rather than just a shortening of objects. In ordinary motion, v << c and v²/c² → 0 so that T→To and L → Lo as in ordinary experience.


Time dilation has a number of unexpected results. Simultaneous events at different locations in one system are not simultaneous for an observer in a system moving with respect to the first. For example, if light rays propagate fore and aft from the middle of a spaceship, no matter how fast it is going an observer in the spaceship will see them strike the front and back walls at the same time. But an observer on Earth would see the front wall moving away from the light and the back wall moving toward it, so that the light waves reach the back wall before the front wall. Another unexpected result is the paradox of the twins: If time in a moving system slows down, then a twin sent away in a spaceship for a period of time will be younger upon returning than the other twin who remained behind. Al-

though the twin paradox is not strictly based on special relativity due to the accelerations required in such an episode, its results are consistent with the time dilation equation. For example, if the twin travels for a time To = 6 years at speed v = 0.8c, then the quantity 1-v²/c² = 1-0.64 = 0.36 and the twin on Earth will have aged a time:

T = To / 1-v²/c² = 6 yrs / 0.6 = 10 years.

Time dilation was first measured experimentally in 1941 with particles called muons, which can be produced in the laboratory with a characteristic half-life To of 2 microseconds before they decay into electrons and neutrinos. In 1963, high-speed muons from cosmic-ray collisions in the upper atmosphere were observed in detectors at two dif-ferent elevations. The muon rate at the lower de-

cToTo

cT

vT

v = 0.8c

T

Earth observer sees moving systemat speed v moving for time T

Moving observer sees light travel for time To

Clock fixed on earth

Movingclock

Figure 9.2 Invariance of the Speed of Light and Relativity of Time According to Einstein, light traveling at speed c relative to observers (O) in a spaceship moving at speed v relative to the Earth, will also travel at speed c relative to observers on Earth. This is only possible if time To in the spaceship runs more slowly than time T on Earth, so that the distance between the passengers as seen inside the spaceship (cTo) is less than that seen from the Earth (cT), as a result of the distance (vT) moved by the spaceship. Thus the time intervals T and To must be related by the Pythagorean theorem (cT)² = (cTo)²+(vT)², which can be solved for T to give the time

dilation relationship T = To / 1 - v²/c² .

For a spaceship at speed v = 0.8c, v²/c² =.64 and 1 - v²/c² = 1 - .64 = .6, so T = To /0.6; and thus a time interval of To = 6 days in the spaceship at speed 0.8c corresponds to a time interval of T = To/0.6 = 6/0.6 = 10 days on Earth.


tector was less by one half from that of the upper detector when they were separated by h = 1800 meters. In a time of To = 2 microseconds even near the speed of light, muons travel less than a dis-tance of cTo = (3×108m/s)×(2×10-6s) = 600m as seen from the moving muons. A decay time of T = h/c = 1800m /(3×108m/s) = 6 microseconds, as seen from the Earth, corresponds to a time dilation resulting from v = 0.94c for the muons. Einstein also obtained a relativistic change in mass by assuming invariance of mo-mentum in inertial systems. For example, if an object of mass mo moves a distance d in a time To in a spaceship transverse to its velocity v, it will have no spatial contraction along d so its momen-tum is mod/To relative to the spaceship. and md/T relative to the Earth. Invariance of momentum requires a different mass m relative to the Earth, due to the different time T, so that for equal momenta md / T = mod / To, and thus

m = moT / To = mo / 1-v²/c²

is the relativistic mass as seen from the Earth. As v approaches c, 1-v²/c² → 0 and m approaches infinity. But as the relativistic mass m approaches infinity, an infinite force would be required to accelerate it to speed c, so no material object can ever reach the speed of light. Relativity theory imposes an electromagnetic speed limit of v < c in the universe. In subsequent papers on special relativity, Einstein explained the relativistic increase in mass of a body when its velocity increases relative to an observer as the result of the additional energy it gains. Expanding the equation for relativistic mass by the binomial theorem gives the following diminishing series:

m = mo(1-v²/c²)-½ = mo(1+ v2/2c2 +3v4/8c4 + ...),

where the second term of the series contains the classical kinetic energy mov²/2. Ignoring higher order terms, which are increasingly smaller than 1, and multiplying the equation by c² lead to Ein-stein’s most famous result:

moc² + K.E. = mc² = E,

where moc² is energy associated with the rest mass mo and E = mc² is the total energy.

Einstein concluded that “the mass of a body is a measure of the energy it contains” and that mass and energy are equivalent. A decrease in mass from m to mo implies a release of kinetic energy given by

K.E. = (m - mo)c²,

which is very large, even for a small mass change, since c² is so large (9×1016 m²/s²). In his 1905 paper entitled “Is the Inertia of a Body Independ-ent of its Energy?” he stated that, “It is not impossible that the theory will be successfully tested in the case of bodies whose inherent energy can be altered to a great extent (e.g. the salts of radium).” In fact, the theory solved the mystery of the source of radioactive energy, which could now be accounted for by a small change in mass. The General Theory of Relativity In 1908 Einstein’s former mathematics professor, Hermann Minkowski (1864-1909), pre-sented a new mathematical formulation of space and time based on special relativity. He recognized that space and time can no longer be viewed independently, but are interrelated much like mass and energy: “Henceforth space by itself, and time by itself, are doomed to fade away into mere shad-ows, and only a kind of union of the two will pre-serve an independent reality.” He showed that distances cannot be given by the usual Pythago-rean formula for three dimensions:

s² = x² + y² + z²,

but events must be expressed in terms of a four-dimensional space-time given by:

s² = x² + y² + z² - c² t²,

in which spatial and temporal coordinates change with motion, but the total remains constant. Since the space and time terms in s² have opposite signs, an observer who sees a larger spatial distance between two events will also measure a longer time duration between these events. The space-time interval between two events is the same for all observers, and thus is an absolute quantity compared to space and time taken separately. After his papers of 1905, Einstein’s repu-tation began to grow, although leading physicists


such as Michelson, Poincaré and Lorentz still resisted his ideas. In 1909 he finally received an academic appointment at the University of Zurich, moving on in 1913 to the Kaiser Wilhelm Physical Institute in Berlin. Strongly influenced by Minkowski’s geometric formulation of space-time, Einstein began to extend his theory beyond the restricted limits of uniform motion to include accelerated systems. No real system could be independent of the accelerating action of external forces such as universal gravitation, which itself could no longer be viewed as acting instantane-ously across space in a universe where events could not be influenced faster than the speed of light. For ten years Einstein devoted himself to a general theory of relativity, in which the laws of nature would be the same for all systems, whether accelerated or in uniform motion. He began with the conception of a gravitational field acting between masses rather than instantaneous action at a distance. The key to his new theory was bor-rowed from Newton’s identification of the inertial mass of a body based on its acceleration (m = F/a), and its gravitational mass based on its weight (m’ = W/g). This ensures that the gravitational force acting on a body always produces the same accel-eration (W = m’g = ma so a = g if m’ = m) inde-pendent of its mass or material state, but it does not account for their apparent equality. Einstein took as his basic principle the equivalence of inertial and gravitational mass, assuming the identity of gravitational fields with accelerations. Thus an observer in a spaceship accelerating “upward” at a rate g would experience the same effects as those of a gravitational field on an observer at rest on the Earth. In free fall near the Earth, conditions in the spaceship would be like those in empty space with no perception of gravitational forces, while an observer outside would see the spaceship accelerating. Thus the results of acceleration and gravitation are relative to the observer, and a gravitational field is equivalent to relative acceleration. Einstein referred to this insight as “the happiest thought of my life.” It led him to recognize that gravity might also have an effect on light and on time.

Einstein realized that a ray of light sent across the inside of an accelerating spaceship would reach the other side to the rear of its point of origin and thus appear to bend (Figure 9.3). By the principle of equivalence, a gravitational field should cause the path of light to bend and its fre-quency to slow down from time dilation, causing a shift in the lines of its spectrum toward the red (gravitational red shift). Both of these results appeared to be testable. In 1911 Einstein made a preliminary calculation of the bending of light from a star as it passes near the Sun, and predicted a deflection of 0.83 seconds of an arc that might be observable during a solar eclipse. Such an eclipse occurred in Russia in 1914, but war in Europe

g

g

light

Figure 9.3 Principle of Equivalence In a spaceship accelerating at one g far away from the Earth’s gravity, an occupant feels his normal weight, objects fall at a rate g, and a bullet fired in a straight line passes through the spaceship on what appears to be a curved trajectory (dashed line). All inertial forces due to the acceleration are locally equivalent to the force of gravity. The dashed line could equally well represent the path of a light beam, suggesting that light is bent by gravity also.


prevented astronomer’s from testing this premature prediction of the gravitational bending of light. In the meantime, Einstein began to de-velop the idea that gravitational fields might be explained geometrically by assuming that Min-kowski’s space-time was curved in such a way that straight lines could be defined by the paths of light rays. This led him to consider the use of non-Euclidean geometry for curved spacetime. That the geometry of space-time is not that of Euclid is evident from consideration of a rotating circle like that of the Earth’s equator. An observer at rest relative to a circle of diameter d measures its cir-cumference as C = πd. An observer in a spaceship that is not rotating with the Earth sees a con-traction of the Earth’s equator (less than a mil-limeter!) in the direction of its rotation, but not in its diameter. Thus C is less than πd, contrary to Euclidean geometry. This non-Euclidean result also applies to a stationary circle on a sphere where d is measured along its curved surface. With the help of his friend Marcell Grossmann, Einstein found that the tensor calculus invented by Bernard Riemann (1826-66) in 1854 could be applied to the development of the gravitational field equations for curved space. Riemann had used the idea of a generalized vector to describe a non-Euclidean space in which he replaced the parallel postulate of Euclid with the assumption that through a point no line could be drawn on a surface without intersecting a given line. An example of this is the geometry of a spherical surface where the lines of longitude all intersect at the poles. Where a vector in three-dimensional space has three components, Ein-stein’s gravitational field tensor describing a curved four-dimensional space-time required ten components. Thus he was able to describe gravity by ten tensor field equations, which revealed that the intrinsic curvature of a given region of space-time was dependent on the amount of matter in that region. Einstein published his General Theory of Relativity in 1915, describing gravitational mo-tions as the shortest paths in space-time, called geodesics. Thus he showed that gravity is a geo-metric property, the very structure of space-time

itself rather than a separate force. Relativistic effects are not on objects themselves, but on their space-time coordinate system. The field equations express the laws of physics in a form that is the same for all such systems, a result that Einstein called the principle of general covariance. Thus matter, space, time, energy and gravity were all unified by gravitational fields in dynamic relation-ships that were free from fixed coordinate systems. Einstein had achieved the scientific equivalent of the Jewish conception of a God who transcends local nature gods confined to some sacred place. Even when the Hebrews were dispersed into exile, their special relationship with God remained as a “covariant” covenant in history. Einstein now recalculated the deflection of light passing the Sun, taking into account the curvature of space-time with his field equations, and found a corrected value of 1.7 seconds. This was twice that of his 1911 value based only on direct attraction of the relativistic mass equivalent of light energy. Observations made during an eclipse expedition in 1919 by the English as-tronomer Arthur Eddington (1882-1944) con-firmed this new prediction, thus providing support for both the theories of relativistic mass and space-time curvature (Figure 9.4). The result established Einstein’s reputation and made him world famous. His prediction of the gravitational red shift of lines in the solar spectrum was confirmed in 1923. When Einstein applied his field equations to the motions of the planets in the gravitational field of the Sun, he found that the results agreed with Kepler’s laws except for the planet Mercury with its orbit closest to the Sun where space-time curvature was the greatest. As Mercury draws closer to the Sun in its elliptical orbit, its speed increases and thus it experiences a small relativistic increase in mass with a corresponding increase in force from the Sun. This causes the major axis of Mercury’s elliptical orbit to slowly revolve about the Sun, rather than the stationary orbit indicated by Newtonian theory. Einstein’s theory showed that the perihelion of Mercury (the point in its orbit nearest the Sun) would advance 43 seconds of an arc per century, as observed by


the French astronomer Urbain Leverrier in 1845. Many other effects of general relativity have emerged in recent astronomical studies.

2. RADIOACTIVITY AND ATOMIC MODELS Discovery of Radioactivity and the Electron Some of the first successes of special relativity involved discoveries at the end of the nineteenth century that could not be explained by classical physics. This was especially true of the mysterious phenomenon of radioactivity. Follow-ing the discovery of x-rays by Roentgen, several

scientists began to study this kind of penetrating radiation. A glow on the glass of Roentgen’s x-ray tube led the French physicist Henri Becquerel (1852-1908) in 1896 to see if fluorescent materials might emit x-rays after exposure to the Sun. Both his father Edmond and grandfather Antoine were physicists who had studied such materials at the Natural History Museum in Paris. By exposing a uranium salt to the Sun, Becquerel found that it would darken a photo-graphic plate wrapped in black paper. After leaving his uranium salt on another wrapped pho-tographic plate for several cloudy days, he then developed it to see if there was any residual fluorescent effect and was surprised to find the plate more strongly darkened than before. Further studies showed that all uranium compounds emit-ted a highly penetrating radiation spontaneously and continuously without exposure to Sunlight. Becquerel then showed that the radiation ionized gases. He measured the resulting electric charge with a gold-leaf electroscope, showing that the activity was proportional to the uranium content. Ionization involved the separation of electrons from gaseous atoms. Electrons were finally identified as negatively charged particles in 1897 by the English physicist Joseph John Thom-son (1856-1940), third director of the Cavendish Laboratory at Cambridge. J. J. Thomson suc-ceeded in showing that the cathode rays from the negatively charged electrode in a highly evacuated glass tube could be deflected by an electric field, and that the direction of the deflection was that of negative charges. Others had shown that cathode rays were deflected by a magnetic field. Now Thomson carefully measured the amount of de-flection for a given field and accelerating voltage, using a fluorescent material on the end of the tube opposite the cathode to register the deflection. The fact that a well-defined beam of cathode rays was always deflected by a fixed amount suggested that it consisted of identical particles, each with the same mass and charge. Using the deflection data, Thomson calculated the ratio of the charge e to mass m for such particles, which gives a modern value of

e/m = – 1.76×1011 coulomb/kg.

* *

Observer in eclipse shadow

Moon

Sun

S S'

Figure 9.4 Gravitational Bending of Light In 1919 A. S. Eddington observed the gra-vitational bending of light from a star at a known position S as it passed by the Sun during a solar eclipse, making it possible to see the star at midday in the apparent po-sition S’. The measured deflection matched the value predicted by Einstein due to the curvature of space near a massive object like the Sun.


Thomson’s measurement gave him credit for the discovery of the electron (Figure 9.5). The largest prior value for such a charge-to-mass ratio was about 9.6×107 C/kg for the hydrogen ion from electrolysis measurements. Assuming the ionic charge to be equal and opposite to that of the electron, the mass of the hydrogen atom would be some 1840 times that of the electron, indicating that the electron is a tiny fraction of the atom. Thomson’s work suggested that the atom is not indivisible, but has component parts. In 1904 he suggested that the atom consisted of a sphere of positive charge with electrons embedded in it like plums in a pudding. He tried to develop a theory of this “plum-pudding” model to account for spectra, but was unsuccessful. After several estimates of the value of the electronic charge, the American physicist Robert A. Millikan (1868-1953) determined a fairly accurate value at the University of Chicago in 1911. By balancing charged oil droplets in an electric field, he was able to calculate the charge on a droplet and show that it was always an integer multiple of the same charge (q = ne), giving e = –1.6 × 10-19 coulomb.

Combining this with measurements of e/m gives m = 9.1×10-31 kg for the electron mass. Millikan’s oil-drop experiment to measure electron charge (Figure 9.6) earned him a Nobel Prize in 1923. Meanwhile, Becquerel’s discovery of ra-dioactivity became the subject of further research in 1897 by the Polish doctoral student Marie Sklodowska Curie (1867-1934) and her physicist husband Pierre Curie (1859-1906). After working for five years as a governess to save enough money for school in Paris, Marie began to study science and mathematics in 1891 at the Sorbonne. She was the first woman to study physics there and graduated at the top of her class. In 1895 she married Pierre Curie, who was known for the dis-covery of piezoelectricity with his brother Jacques by observing an electric voltage that appeared across certain crystals under pressure. He had just completed his doctorate on the effect of heat on magnetism, including the discovery that materials lost their magnetism above a characteristic tem-perature, now known as the Curie point. Marie Curie applied her husband’s dis-covery of piezoelectricity to calibrate an elec-

V

Negativecathode Slotted

anode

⊗ ⊗ ⊗ ⊗

⊗ ⊗ ⊗ ⊗

B

Evacuatedglass tube

e?

Deflectedcathode ray

Phosporescentsurface

Figure 9.5 Thomson’s Identification of Electrons from Deflection of Cathode Rays J. J. Thomson used a magnetic field B perpendicular to a beam of cathode rays in a vacuum tube to deflect the rays. A given accelerating voltage V and magnetic field B produced the same deflection for the entire beam, indicating that it consisted of identical negatively charged particles called electrons. From the values of V and B and the associated deflection of the cathode rays, the charge-to-mass ratio of the electron could be calculated as e/m = -1.76×1011 coulomb/kg.


trometer for measuring the intensity of radioactiv-ity (a term she coined) from the current it produced by ionizing air between two conducting plates. In 1898 she showed that the element thorium was also radioactive. She also showed that the intensity of the radioactivity from certain uranium minerals was about four times greater than that from uranium by itself, suggesting the existence of small traces of other radioactive elements. Pierre Curie now joined his wife in her heroic effort to separate these trace elements by methods of chemical analysis from a uranium oxide ore called pitchblende. By July of 1898 the Curies succeeded in isolating a residue of bismuth compounds some 400 times more radioactive than uranium. Since none of the elements in these compounds are radioactive, they concluded that it contained a new element that they called polonium after Marie’s native land. By the end of the year they separated a residue of barium compounds with a trace

impurity about 900 times more radioactive than uranium. The French chemist Eugéne Demarçay (1852-1904), who later isolated the element europium, showed that the barium residue had the distinctive spectrum lines of another new element that they named radium. An associate of the Curies, André Debierne (1874-1949), used their methods to discover the radioactive element actinium in 1899 from pitchblende. The Curies now obtained from mines in Bohemia a ton of pitchblende residues, from which most of the uranium had been extracted. Working under primitive conditions in an old shed, they were able to separate one tenth of a gram of radium chloride by 1902, and used it to determine the atomic weight of radium. Marie Curie completed her unprecedented dissertation in 1903, and in the same year she and Pierre shared the Nobel prize in physics with Becquerel. Marie worked for eight more years before she finally isolated radium as pure metal. In the meantime,

+V

E

qE

Oil vaporizer

Short focustelescope

oil drop

Radioactivesource

EW

Figure 9.6 Millikan’s Oil-drop Experiment to Measure the Electron Charge Millikan used a variable voltage V to establish an electric field E between parallel metal plates to act on an oil drop carrying negative charge q with an upward electric force qE. Oil drops produced from an atomizer were charged by exposing them to a radioactive source to ionize the air and produce free electrons. When a charged oil drop of weight W fell through a small hole in the upper plate, the voltage was adjusted until the electric force qE stopped the oil drop in the cross hairs of a viewing telescope. Then qE = W, so the charge on the oil drop could be calculated as q = W/E, which was always found to be a multiple q = ne of a smallest charge e = -1.6 × 10-19 coulomb.


Pierre was killed in 1906 by a horse-driven vehi-cle and Marie took over his position to become the first woman professor at the Sorbonne. In 1911 she won the Nobel prize in chemistry for separating radium. The Analysis of Radioactivity In her dissertation, Marie Curie noted the vast energy given off by radium, which Pierre had measured as 140 calories/gram each hour. This remained a mystery until 1905 when Einstein showed how mass might be converted to energy. In 1900, the German physicist Friedrich Dorn (1848-1916) showed that radium not only gave off radiations, but also produced a gas that itself was radioactive. It was later called radon, and was the first clue that radioactivity involved the transmutation of one element into another. It also indicated a possible source of the frequent respiratory difficulties the Curies experienced, and of Marie’s aplastic anemia leading to her death in 1934. In the same year, her daughter Irène and son-in-law Frédéric Joliot discovered artificial radioactivity induced by neutrons, for which they won the Nobel Prize in chemistry. The first observation of more than one type of radiation from radioactivity was made in 1898 by Ernest Rutherford (1871-1937), who came from New Zealand to study under J. J. Thomson at Cambridge. He showed that most of the radioactivity from uranium could be stopped by a sheet of paper, but the remainder could pene-trate through about 100 sheets of paper. This suggested two components of radioactivity, so he called the first alpha (α) rays and the second more penetrating beta (β) rays. A year later, Becquerel observed that the beta rays could be deflected by a magnetic field, and in 1900 he showed that they were high-speed electrons like cathode rays. In 1908 at Bern, the German physicist Alfred Bucherer (1863-1927) showed that the value of e/m obtained from their deflection was less than e/mo for the slower cath-ode rays as measured by Thomson. His results showed that:

e/m = (e/mo) 1-v²/c²,

which agreed with Einstein’s equation for a rela-tivistic increase in mass. A third component of radioactivity was identified in 1900 by the French physicist Paul Villard (1860-1934) from its effect on a photo-graphic plate at a considerable distance from the source. It was more penetrating than either alpha or beta rays, and could not be deflected in a mag-netic field (Figure 9.7). These rays were called gamma (γ) rays and were later shown by Rutherford to be electromagnetic waves with wavelengths shorter than x-rays. Thus radio-activity could be classified into three components. The least penetrating alpha-rays are absorbed by 7 cm of air and produce the most ionization. Beta-ray electrons penetrate about ten times further in air but produce less ionization. Gamma-rays can penetrate through all materials, but cause only weak ionization.

⊗ ⊗

⊗ ⊗

α γ βFluorescentscreen

Radioactivesource

Leadcontainer

Magnetic fieldinto paper

Figure 9.7 Separation of Radioactivity by a Magnetic Field In her 1903 doctorate thesis, Marie Curie represented the behavior of radioactivity in a magnetic field by showing the separation of alpha (α), beta (β) and gamma (γ) rays. The deflection of the alpha rays corresponds to that of doubly-charged helium ions (He++). Beta rays are deflected much more, but in the opposite direction, corresponding to the much smaller mass and negative charge of electrons (e-). Gamma rays are undeflected and were shown to be high frequency electromagnetic radiation.


Meanwhile Rutherford took a position at McGill University in Montreal. Here in 1903, he succeeded in deflecting alpha rays with a strong magnetic field, showing that they were positively charged. By 1906 using both electric and magnetic deflections, he found that the charge-to-mass ratio of alpha particles was about one half of e/m for the hydrogen ion H+, later called the proton. This suggested either a singly charged hydrogen molecule H2

+ (e/2m) or a doubly charged helium ion He++ (helium atom with atomic mass 4 times that of hydrogen that has lost two electrons: 2e/4m), both of which would have a value of half the e/m value for a proton. In 1909 Rutherford trapped alpha particles in a thick-walled glass tube and showed that they gave a helium spectrum, confirming that they consisted of helium ions. Radioactive Decay and Isotopes By 1900, five elements were known to be radioactive: uranium, thorium, polonium, radium and radon. In the same year, William Crookes (1832-1919), inventor of the cathode-ray tube, found that a residue from a uranium solution was more active than the uranium that remained in the solution. He called the active substance uranium-X (UX). Becquerel confirmed this result, but he then set aside the materials and tested them 18 months later. At this later time, he found that the residue had lost its activity while the uranium solution had regained its activity. Rutherford and his coworker, the English chemist Frederick Soddy (1877-1956), made similar observations in 1902 at McGill University. They used a thorium solution to obtain an active residue they called thorium-X (ThX), and found that it lost its activity over a few days while the thorium solution recovered its activity. Measurements showed that both changed at exponential rates. Rutherford and Soddy now began to un-ravel these complexities with their theory of radioactive disintegration, suggesting that,

The disintegration of the atom and the ex-pulsion of a...charged particle leaves behind a new system lighter than before and pos-sessing physical and chemical properties

quite different from those of the original parent element.

Thus they proposed that uranium slowly disinte-grates to form highly active uranium-X. The UX residue decays rapidly and loses its activity, while the solution recovers its activity by producing more UX. They found that each radioactive sub-stance has a characteristic decay rate that could help to identify it. In 1904 Rutherford introduced the concept of half-life T as the time in which half of the substance decays, and thus after 2T only one fourth remains, and so on. If the parent element has a long half-life and the daughter element is not separated, they reach an equilibrium in which the daughter disintegrates as fast as it is formed. For example, they suggested that uranium decayed into radium and that the uranium-radium ratio in uranium minerals should be constant. The American chemist Bertram Boltwood (1870-1927) confirmed this constant uranium-radium ratio at Yale University. Boltwood also found evidence for what he thought was a new element between uranium and radium, calling it ionium. In 1905 he suggested the idea of a radioactive series of elements decaying one into another, finally ending in the stable element lead. In 1907 he proposed that the half-life of uranium and the uranium-lead ratio in rocks could be used to measure their age. Uranium minerals were found to contain about 1 atom of radium to every 2.8 million atoms of uranium. This ratio should correspond to the ratio of their respective half-lives to maintain their equilibrium. The half-life of radium was measured di-rectly at about 1620 years, but uranium decay was too slow to measure. However, from their constant ratio the half-life of uranium is found to be:

T = (2.8×106) × 1620 yr. = 4.5 billion years.

Many elements with short half-lives still exist in the crust of the Earth because they are continually being produced by uranium with its very long half-life. In 1904 Rutherford pointed out that the heat produced by radioactivity would slow the cooling of the Earth, requiring a much longer time than estimates made by Kelvin of less than 100 million


years to reach its present temperature. Uranium-lead ratios have led to estimates of about 4.5 billion years for the age of the Earth, so about half of the uranium originally in the Earth should still survive. In 1911 at University College in London, Soddy suggested that, “The expulsion of the alpha particle causes a radio element to change its posi-tion in the periodic table” by two places, its atomic number being reduced by two from the loss of the two protons of the helium ion. He also proposed that beta emission increases the atomic number by one due to the loss of the negatively charged beta electron. These displacement rules helped to clarify the identity of the nearly 40 radioactive substances known by 1912. Several investigators showed that their chemical properties corre-sponded to only 12 positions in the periodic table of the elements, with atomic numbers of 81 to 92. These results led Soddy to suggest in 1913 that elements occupying the same place in the periodic table be called isotopes (Greek: same place), even though they differ in mass. Thus an element X with atomic number Z might have more than one isotope, each with different atomic mass A designated by Z

AX. For example, uranium-X was

found to be the thorium isotope 90234Th with a half-

life of 24 days, and ionium was identified as 90230Th

with the same chemical properties but a half-life of 80,000 years. Since the alpha particle is an ion of 2

4

He, alpha-decay reduces the atomic mass by 4 while beta-decay doesn’t change the atomic mass, so the displacement rules relate parent P and daughter D isotopes as follows:

alpha decay: ZAP → 2

4He + Z-2A-4D;

beta decay: ZAP → e + Z+1

A D.

This leads to four radioactive series, each corre-sponding to a different set of values of A differing by multiples of 4. The uranium series begins with

92238U and after about twenty alpha and beta decays

ends in the stable lead isotope 80206Pb. The thorium

series begins with 90232Th and ends in another stable

lead isotope 80208Pb. The actinium series begins with

92235U and ends with 80

207Pb. A fourth series is not

found in nature since its longest lived isotope neptunium ( 93

237Np) has a half-life of only about 2.2 million years, which is so much shorter than the age of the Earth that it is no longer detectable. The Nuclear Model of the Atom After returning to England from Canada, Rutherford accepted a position at the University of Manchester, where in 1908 he began to study the scattering of alpha particles in passing through matter. Working with the German physicist Hans Geiger (1882-1945), who later invented the Geiger tube for detecting particles, they found that most alpha particles passed through a thin sheet of metal foil with only a slight deflection, but about one in 8000 was scattered more than 90° from the direction of incidence (Figure 9.8). Later Rutherford described this unexpected result as “about as credible as if you had fired a 15-inch shell at a piece of tissue paper and it came back and hit you.” In 1911 Rutherford published his classic analysis of alpha-scattering, in which he concluded that, “Considering the evidence as a whole, it seems simplest to suppose that the atom contains a central charge distributed through a very small volume.” From the energy and size of the scattered alpha particles, he concluded that this small positive nucleus in the atom would have a radius of about 10-15 m. This is about 100 thousand times smaller than the atom itself, but would contain most of the mass of the atom. Atomic sizes of about 10-10 m were first measured in 1908 by the French physicist Jean Perrin (1870-1942) using Einstein’s 1905 analysis of Brownian motion. To account for the size and stability of the neutral atom, the electrons would be held in orbits about the nucleus by electrical attraction at a radius of about 10-10 m. Thus most of the volume of the atom in this nuclear model would be empty space between the nucleus and the orbiting electrons. The nuclear charge was determined at Rutherford’s Manchester laboratory in 1913 by the young English physicist Henry Moseley (1887-1915), who was killed at the battle of Gallipoli during World War I. Moseley used diffraction from crystals to measure the wavelengths of the characteristic x-ray spectrum lines produced by


scattering high-voltage cathode rays from 38 dif-ferent elements. He found that these wavelengths change in a regular manner with increasing atomic number in the periodic table of the elements. From these results, he concluded that the atomic number Z is the number of positive electronic units of charge in the nucleus, later identified with the number of protons. Thus he was able to establish that the number of elements from hydrogen up to uranium is 92, and that 7 elements lighter than uranium were as yet undiscovered. Rutherford was unable to specify any condition that would determine the radius of elec-tron orbits in the nuclear model of the atom. Fur-thermore, from Maxwell’s theory, orbiting elec-trons should continuously radiate electromagnetic waves. In the process they would lose energy and

quickly plunge into the nucleus. Thus the atom would not only collapse, but it would radiate a continuous range of frequencies as it loses energy, rather than the discrete frequencies observed in the characteristic line spectra of the elements. This problem was first solved in 1913 by applying the newly emerging ideas of the quantum theory, which was first introduced in 1900. 3. QUANTUM THEORY AND THE ATOM Planck’s Analysis of Thermal Radiation Relativity theory modified the causal de-terminism of Newtonian mechanics, but did not abandon it. The new theory was still causal, deter-ministic and objective, even though quite abstract. Radioactivity began to challenge this determinism

Rotating telescopeZnS

detector

Metalfoil

ReflectedalphaRadioactive

alpha source

Outer electronorbit

Positivenucleus

atomsin foil

1 reflectedin 8000 alphas

⊕ ⊕ ⊕

⊕ ⊕ ⊕

Figure 9.8 Rutherford’s Scattering Experiment and Nuclear Model Rutherford and Geiger observed one alpha reflected backward out of some 8000 alphas that went through a thin metal foil with only small deflections. They showed that the few positive alpha particles which were reflected must have been close to a direct hit on a small positive and massive nucleus, while the others were only slightly deviated by the electrons. From this Coulomb repulsion they were able to calculate a nuclear radius of about 10-15 m compared to an atomic radius of the outer electron orbit of about 10-10 m, with each of the positive protons in the nucleus having a mass about 2000 times the electron mass. Thus the nucleus is about 100,000 times smaller than the atom.


by the unpredictability of when a radioactive particle will be emitted, even though its energy could be accounted for by relativity theory. Average decay rates were steady for a given radioactive element, as evidenced by its characteristic half-life, but individual emissions appeared to be random events. The quantum theory poses the ultimate challenge to deterministic certainty in physics, even though it is able to account for the average decay rates in radioactivity. Quantum theory led to a new emphasis on probabilities and statistical relationships, rather than direct causal relations. Quantum theory began with the study of thermal radiation from hot objects. A black surface is the most efficient radiator and absorber of radiation. As early as 1859 Gustav Kirchhoff introduced the concept of an ideal “black body,” which absorbs all radiation incident upon it. The

radiation emitted from such a body depends only on its temperature and forms a continuous spec-trum with intensities that vary smoothly over dif-ferent wavelengths, rather than the discrete line spectra of the elements. Measurements of these continuous spectra gave an asymmetric bell-shaped curve, in which the maximum intensity shifted to shorter wavelengths as the temperature increased, shifting from infrared emissions to become “red hot” and finally “white hot” at higher temperatures (Figure 9.9). The study of thermal radiation was con-tinued by the German physicist Wilhelm Wien (1864-1928), who in 1896 devised a formula from thermodynamic reasoning that could account for the shape of the black-body radiation spectrum at short wavelengths. He also suggested that a hole in a cavity would absorb all incident radiation and

UV-catastrophe

RadiationIntensity

5000K

3000K

Thermal Radiation

UV (V B G Y O R) IR MWWavelength (colors)

Heatedsolid

Figure 9.9 Thermal Blackbody Radiation and the Quantum Theory Thermal radiation from a blackbody (ideal) radiator has a spectrum of intensities with a peak that shifts toward longer wavelengths as the temperature is lowered. Rayleigh and Jeans attempted to derive these spectrum curves from Maxwell’s electromagnetic theory by calculating the standing waves inside a heated solid. They found that the shorter waves will predominate, leading to agree-ment with the measured intensities at longer wavelengths, but giving intensities that approach infinity at the shorter wavelengths (dashed line). This ultraviolet catastrophe was resolved by Max Planck’s quantum theory, in which radiation occurs in discrete units of energy proportional to the frequency (E = hf ). Thus the higher frequency ultraviolet quanta require higher energy than infrared, accounting for the fall off of the intensity at shorter wavelengths.


behave like a black body. In 1900 the Cambridge physicist Lord Rayleigh (J. W. Strutt, 1842-1919) applied electromagnetic theory to thermal radiation in a cavity, and was able to account for the shape of the spectrum at long wavelengths but not at the short ones. He assumed that the walls of the cavity contained oscillating charges to produce electromagnetic waves resonant with the dimen-sions of the cavity. The modes of vibration corre-spond to whole number multiples of half wave-lengths fitting across the cavity, so there is an infinite number of modes with the same energy at ever shorter wavelengths. Thus the radiation would approach infinite intensity at high fre-quencies. This failure of electromagnetic theory was called the “ultraviolet catastrophe,” and was confirmed in further work by Sir James Jeans (1877-1946) in 1905. At Berlin in 1900, the German physicist Max Planck (1858-1947) proposed a solution to this dilemma. He was able to interpolate between Wien’s formula and Rayleigh’s formula by com-bining thermodynamic and electromagnetic ideas to obtain an equation that fit the experimental results for black-body radiation at all wavelengths. But Planck’s success depended on dividing the energy of the oscillators into small but discontinu-ous “energy elements,” which could only be radi-ated or absorbed in bundles of a discrete quantity, or quantum. For the results to agree with Wien’s formula, the energy E of the quantum had to be proportional to the frequency f of the oscillator, giving the fundamental quantum equation:

E = hf,

where h is a new universal constant called Planck’s constant. Planck’s quantum of energy is similar to the discrete unit of electric charge in the electron, except that energy quanta vary with frequency, so that infrared quanta carry less energy than the higher frequency ultraviolet quanta. At any given temperature more high-frequency resonances are possible, causing the intensity of thermal radiation to increase at higher frequencies; but eventually the frequency reaches a point at which the energy required for a quantum is too high and the radia-tion intensity begins to fall off. From the observed

shape of this spectrum, Planck obtained a value of h = 6.52×10-34 joule.sec, close to the modern value of 6.63×10-34 J.s. Thus a quantum associated with an infrared frequency of f = 1014 Hz has an energy of only E = 6.63×10-20 J. Such a tiny value means that quantum jumps in energy are so small as to appear to be continuous, but the idea of even a small discontinuity seemed like “an act of des-peration” to Planck and he spent many years trying to reconcile it with classical theory. In the meantime, Einstein recognized the full signifi-cance of the quantum of energy. Einstein and the Photoelectric Effect The most direct evidence for the quantum theory and its wider interpretation came from study of the photoelectric effect, discovered by Hertz in 1887. He observed the enhancement of electric sparks used to generate radio waves when he illuminated the spark gap with ultraviolet light. In 1902 the German physicist Phillipp Lenard (1862-1947), who had assisted Hertz, discovered that electrons emitted in a vacuum tube with light shining on the cathode gained higher speeds by increasing the frequency of the light. Below a certain frequency, none of these photoelectrons were emitted regardless of the intensity of the incident light. Classical physics could not explain this increase in electron energy with frequency rather than with the intensity of the light, since greater intensity carries more total energy. In his first paper of 1905, Einstein sug-gested a simple but revolutionary explanation of the photoelectric effect using Planck’s quantum of energy. However, while Planck assumed that radiation was emitted and absorbed in discrete amounts, Einstein proposed that it is also propa-gated through space in quantum units of energy E = hf at the speed of light. These quanta, later called photons, combined aspects of both the particle and wave theories of light. Although they seemed to reduce the need for the ether, they introduced a paradoxical particle-wave relation between mechanical and electromagnetic views. In the photoelectric effect, a photon gives up all its energy to just one electron, so the resulting photoelectron gains kinetic energy proportional to the frequency of the photon it absorbs.


The minimum frequency fo required for photoelectron ejection corresponds to the mini-mum energy W = hfo, called the work function, required to remove an electron from the metal. Thus the photon energy hf must be greater than W and any excess energy (hf - W) is available to eject electrons (Figure 9.10), giving Einstein’s photoelectric equation for the maximum kinetic energy of the photoelectrons:

mv²/2 = hf - W.

This equation accounts for the fact that the maxi-mum speed of the photoelectrons increases with

the frequency, and provides a much more direct way to measure h. In 1916, Robert Millikan made detailed measurements to show that Einstein’s equation was correct in every detail and obtained a value of h = 6.55×10-34 J.s, in excellent agreement with Planck’s value. For his work on the photoelectric effect, Einstein was fi-nally awarded the Nobel Prize for Physics in 1921. Bohr Theory of the Hydrogen Atom In 1913, the Danish physicist Niels Bohr (1885-1962) resolved some of the difficulties with Rutherford’s nuclear model of the atom by using the quantum concept. After completing his doctoral dissertation on the electronic theory of metals in 1911, Bohr went to the Cavendish Laboratory at Cambridge to work with J. J. Thomson. Later in the year he went to Manchester to study with Rutherford and became interested in the alpha-scattering experiments and the nuclear model. Here he began to think about how quantum ideas might be used to permit stable electron orbits and account for the size of the nuclear atom. When his attention was drawn to Balmer’s formula for the line spectra of hydrogen, Bohr said that, “The whole thing was immediately clear to me,” and he began to work out a quan-

tum theory of the hydrogen atom. Bohr began his theory with two postulates that contradicted classical physics. The first allowed him to define stable orbits, in which an electron circling a positive nucleus does not radi-ate. The second described quantum transitions between orbits to account for discrete radiation consistent with the line spectra. His theory was guided by what he called the correspondence principle, which required that,

The conditions which will be used to de-termine the values of the energy in the sta-

A

photons

Lightf > fo

Vs

photo-cathode e

Figure 9.10 Photoelectric Effect and Photon Concept Light shining on a cathode ejects electrons (e) when its frequency (f) is above the threshhold frequency (fo), producing a current in the circuit connecting the anode and cathode. Philipp Lenard measured the kinetic energy (K.E.) of these photoelectrons by determining the stopping voltage (K.E. = eVs) that reduces the current in the ammeter (A) to zero, finding that it was proportional to the frequency (K.E. ~ f). Einstein proposed that the light is transmitted and absorbed by the cathode in quantum units (later called photons) of energy E = hf. The minimum energy to overcome the binding energy of the electrons in the cathode is called the work function (W = hfo). Thus the difference between the photon energy hf and the work function W, is the photoelectron kinetic energy K.E. = hf - W, which is the equation Einstein used to explain Lenard’s result.


tionary states are of such a type that the fre-quencies calculated in the limit where the motions in successive stationary states com-paratively differ little from each other, will tend to coincide with the frequencies to be expected on the ordinary theory of radiation from the motion of the system in the sta-tionary states.

This principle led him to the conclusion that the radii rn of stable orbits (stationary states: n = 1, 2, 3,...) are determined by a new quantum condition in which the angular momentum mv×rn of an electron in a stable orbit is a multiple of h/2π. Transitions between orbits were based on Planck’s energy equation. Thus his two non-classical or quantum postulates can be stated as follows:

(1) Electrons can exist in atoms only in dis-crete non-radiating orbits given by:

mvrn = nh/2π.

(2) When an electron “jumps” between two stable orbits of energy En and Ei, it emits or absorbs a single quantum of radiation whose frequency is given by:

En - Ei = hf.

Here n is the number of the outer orbit, i is the number of the inner orbit, and f is assumed to be the frequency of a particular line in the spectrum of an element. By applying these quantum postulates to the hydrogen atom, Bohr was able to combine them with classical equations to account for much of the empirical data available for hydrogen at the time. The centripetal force F = mv²/r to hold the electron in a circular orbit around a proton is provided by the electrostatic attraction between them, each of charge e, so Coulomb’s law gives:

F = ke²/r² = mv²/r

in exactly the same way that Newton applied the inverse-square law of universal gravitation to planetary orbits. Combining this with the first postulate to eliminate v gives the orbital radii rn for any value of n in terms of known quantities as:

rn = n²h²/4π²kme² = 0.53×10-10 × n² meter.

For the lowest energy, n = 1, corresponding to the most stable state called the ground state, the radius r1 matches the size of the atom estimated from the kinetic theory as about one angstrom unit (1 Å.= 10-10 m). The second stable orbit is then r2 = 0.53 Å × 2² = 2.12 Å and the third orbit has radius r3 = 0.53Å × 3² = 4.77 Å. Thus the size of the atom was related to such diverse quantities as Planck’s constant h, Coulomb’s constant k, and the charge e and mass m of the electron. In addition to the size of the atom, it was known that hydrogen gas in a vacuum tube could be ionized when a voltage of 13.6 V was applied across the tube. This means that 13.6 electron-volts of energy is required to separate an electron from the proton in hydrogen, where 1eV = 1.6×10-19 joule is the energy an electron gains in moving through 1V. Bohr used his equation for stable orbits to calculate the energy of an electron from its kinetic energy and electrostatic potential energy in radius rn of the hydrogen atom as:

En = -2π²k²me4/n²h² = -(13.60/n²) eV.

This energy is negative because the electron is bound in the atom by the Coulomb force of attrac-tion. To remove an electron from the ground state (n = 1) it must gain 13.60 eV of energy, matching the measured ionization energy. The most important success of Bohr’s theory was in accounting for the spectrum lines of hydrogen. In 1890 the Swedish spectroscopist Johannes Rydberg (1854-1919) put Balmer’s for-mula for the wavelengths of the visible hydrogen lines into the form:

1λ = RH(

12²

- 1n²),

where the Rydberg constant has a measured value RH = 1.0968×107 m-1 and n >2. Using his second postulate hf = En-Ei, Bohr was able to calculate the wavelengths of emitted photons from the hydrogen atom when the electron jumps from an outer orbit of energy En = -13.6e/n² J to an inner orbit of energy Ei = -13.6e/i² J from the fact that a ra-diated photon travels at the speed of light c = λf, giving

1λ =

fc =

En-Eihc =

13.60ehc (

1i²

- 1n²).


This has exactly the same form as the Balmer-Rydberg formula when i = 2, and the constant 13.60e/hc = 1.0974×107 m-1 differs from RH by less than one percent. Thus the visible Balmer lines correspond to an electron transition from outer orbits to the second orbit i = 2 (Figure 9.11). When i = 3 and n >3 the formula gives infrared wavelengths, which had been discovered in 1908 by the German physicist L. C. Paschen (1865-1947) and were now interpreted as electron tran-sitions to the third orbit. Bohr predicted the existence of additional hydrogen spectra for other values of i, and in 1914 the Harvard physicist Theodore Lyman (1874-

1954) announced the discovery of ultraviolet lines with wavelengths corresponding to i = 1 and n >1. Similar series were later discovered for larger val-ues of i. Despite these successes, Bohr realized the limitations of his theory. He could not explain what causes an electron to “jump” from one orbit to another, thus eliminating causality at the heart of matter. Electrons seemed to have their own tendencies, seeking their own natural place. Fur-thermore, Bohr could not extend the theory to atoms with more than one electron, since the force holding electrons in their orbits is then greatly complicated by forces of mutual repulsion between electrons.

E - E = hfn i

i

n•

>

>

> Red (n=3)

Blue (n=4)

Violet (n=5)

5

4

3

21

Lymanseries

UV (i=1)

ionization

absorptionlines

emissionlines

Balmer series (i=2)

electronorbits

i=3 Balmer (i=2) i=1

IR R B V UVn = 3, 4,5,6

Hydrogen spectrum lines

⊕

e

Figure 9.11 Bohr’s Model of the Hydrogen Atom Niels Bohr explained the radiation from hydrogen by assuming that when the electron makes transitions from an outer orbit of energy En to an inner orbit of energy Ei, it produces a photon of frequency f given by En - Ei = hf. In this way he was able to derive the Balmer-Rydberg formula for

the hydrogen spectrum wavelengths: 1λ = R(

1i² -

1n² ), identifying n with an outer orbit and i with an

inner orbit and thus accounting for the bright emission lines from hydrogen. He also calculated a theoretical value for the Rydberg constant R = 1.09678 × 107 m-1 compared to a measured value of 1.09740 × 107 m-1. When cool hydrogen (i = 1) absorbs energy, it produces transitions from inner to outer orbits, explaining the dark lines of the absorption spectra as mostly ultraviolet Lyman lines.


Extensions of the Bohr Theory For about ten years, efforts were made to extend the Bohr theory, though these were ham-pered by the intervening tragedy of World War I. In 1916 Einstein used Bohr’s idea of energy levels in an atom to derive Planck’s law for blackbody radiation by introducing the idea that probabilities governed transitions of electrons between energy levels. In addition to the absorption of a photon to raise an electron to an excited energy level En, and the spontaneous emission of a photon when it falls back to a lower energy level Ei, he suggested the concept of stimulated emission of a photon of energy hf = En-Ei when acted upon by another photon with the same frequency f. In deriving Planck’s law from these ideas, Einstein was able to calculate the probabilities of these transitions from blackbody radiation data. Nearly 50 years later in 1960, the Hughes Research Laboratories in Cali-fornia used the stimulated emission concept to de-velop the laser (acronym: “light amplification by stimulated emission radiation”), in which a cas-cade of stimulated photons is used to produce nearly pure single frequency light (Figure 9.12).

Spectroscopes with greater resolving power began to reveal that the lines in atomic spectra had a “fine structure” of closely spaced neighboring lines. At Munich in 1916, the German physicist Arnold Sommerfeld (1868-1951) suggested that an electron with principal quantum number n might have several elliptical orbits with angular momenta mv×r = kh/2π determined by a second quantum number with values of k = 1, 2, 3,...n, giving slightly different energies. This gave rise to additional electron transition possibilities and their associated spectrum lines. A third quantum number m with values from -(k-1) to +(k-1) was also introduced to account for the splitting of spectrum lines due to the effect of a magnetic field as first observed at Leiden in 1896 by Pieter Zeeman (1865-1943). Even closer investigation of the spectrum lines accounted for by Sommerfeld revealed that many of them were closely spaced pairs, called doublets, representing slightly different energy levels. In 1925 at Leiden, the Dutch graduate stu-dents George Uhlenbeck and Sam Goudsmit sug-gested that the electron could spin on its axis in one of two opposite directions with an intrinsic angular momentum sh/2π, where the spin quantum number s has the two half-integer values s = ±½. Thus the energy of an electron can differ by one quantum unit hf in its two spin orientations, splitting the Sommerfeld energy levels to produce the observed doublets. In the same year at Hamburg, the Aus-trian physicist Wolfgang Pauli (1900-1958), who had studied under Sommerfeld and Bohr, formu-lated his exclusion principle that no two electrons in a multi-electron atom could have the same set of quantum numbers (n, k, m, s). Thus the first orbit or shell could contain up to two electrons (1,1,0,±½), giving helium a filled shell. The sec-ond shell could contain up to eight electrons: (2,1,0,±½), (2,2,-1,±½), (2,2,0,±½), (2,2,+1,±½). With n = 3, 18 electrons are possible, but the order in which they fill the higher shells depends on their energy. This proposed electronic structure of atoms provided a classification of the elements that correlated closely with the arrangement of the

E

E

E1

2

3

absorptionspontaneous emission

stimulated emissions

mirrors / partially silvered

Figure 9.12 Stimulated Emission and Laser In a laser, light of energy hf = E3-E1 is ab-sorbed, lifting electrons from energy E1 to E3. This is followed by spontaneous emission to energy level E2, where electrons remain until either spontaneous or stimulated emission causes them to fall to energy level E1. Photons (hf = E2-E1) from stimulated emissions multiply as they reflect between mirrors, and are emitted from the partially silvered mirror.


elements in the periodic table. The noble gases, which did not tend to form compounds, were cor-related with filled shells, such as helium with two electrons and neon with ten electrons. This insight was applied earlier to the formation of stable chemical compounds by the American chemists Gilbert N. Lewis (1875-1946) in 1916 and Irving Langmuir (1881-1957) in 1919. They indepen-dently developed the idea that atoms combine to form stable molecules by either transferring elec-trons or by sharing electrons in ways that complete an electronic shell or sub-shell. Later it was recognized that most chemical bonding is a com-bination of these electrovalent and covalent bonds. A more complete understanding of electronic structures and chemical bonding required the de-velopment of a more consistent quantum theory. 4. QUANTUM WAVE THEORY Wave-Particle Dualities Although the Bohr theory was a useful model for understanding the structure of atoms and molecules, it was unable to explain the spectra of multi-electron atoms and could not account for the relative intensities of spectrum lines. In spite of its concessions to the ambiguities of the quantum theory, it retained too much of the mechanical scaffolding of the nineteenth century. In the meantime, World War I intervened to challenge the confident certainties of the nineteenth century, demolishing the great empires of Europe. In Germany the new Weimar Republic began its experiment with democracy in a world no longer determined by authoritarian monarchies. In Vienna logical positivism had emerged with its insistence on empirical verification, suspicion of mechanical models, and scorn of metaphysical speculation. The transition from mechanistic assumptions to mathematical abstractions was even mirrored in the rise of modern art with its multiple perspectives and forms. A more successful approach in physics grew out of the wave-particle duality, which was first utilized by Einstein in his photon concept of radiation and later extended to matter itself. The particle concept of electromagnetic waves gained ground from work on x-ray scattering by the

American physicist Arthur H. Compton (1892-1962) in 1923. He found that x-rays scattered from carbon included some radiation with longer wavelengths than the incident x-rays, increasing with the angle of scattering (Figure 9.13). He was able to explain this so-called Compton effect by assuming that the x-ray photon had both relativis-tic energy and quantum energy:

E = mc² = hf.

By assuming that some x-ray photons collide with electrons, he suggested that they would behave like particles in transferring momentum to eject the electron. Since a photon travels at the speed of light c = λf, its momentum can be obtained from the energy equation and is given by:

mc = hf/c = h/λ.

This inverse proportion between momentum and

o

e

wavelengthλ

λ > λ'

scattered photonincreasedwavelength

x-ray photon

atom

scatteredelectron

⊕

Figure 9.13 Compton’s X-ray Experiment Compton observed that x-rays scattered in the process of dislodging loosely bound electrons from atoms experience an increase in wave-length dependent on the angle of scattering. He explained this by treating x-ray photons with speed c = λf as particles of relativistic mass m and equating their relativistic and quantum energies E = mc² = hf = hc/λ, so that their momentum would be given by mc = h/λ. Thus when the photon loses momentum in dislodging an electron (e) its wavelength λ=h/mc increases in proportion to the decrease in the momentum mc.


wavelength allowed Compton to account precisely for the increased wavelength of x-ray photons at various angles of scattering after losing momen-tum in electron collisions. The particle behavior of electromagnetic waves led the French physicist Louis de Broglie (1892-1987) to suggest in his 1924 doctoral dis-sertation that particles of matter behave like waves. By reasoning similar to Compton, equating relativistic and quantum energies, de Broglie proposed that a material particle such as an elec-tron has a wavelength inversely proportional to its momentum mv, where v must be less than c for material objects. Thus in place of the Compton wavelength h/mc for a photon, de Broglie’s matter wavelength is given by:

λ = h/mv.

In support of this extension of wave-particle duality, he suggested that a stable orbit in the Bohr theory could be accounted for by treating the electron as a rein-forcing wave in which a whole number of wavelengths would fit around the circumference of an allowed orbit, but would cancel itself in any other orbit (Figure 9.14). Thus in a stable orbit with quantum number n, the circumference would be given by:

2πrn = nλ = nh/mv,

which reduces to Bohr’s first postulate (mv×rn = nh/2π), thus explaining Bohr’s stable orbits. The wave nature of the electron was used in 1925 to explain an accidental observation at the Bell Telephone Laboratories in New York by Clinton Davisson (1881-1958), who confirmed the de Broglie wavelength two years later. He ob-served that a beam of electrons in a vacuum tube reflected from a nickel crystal formed a diffraction pattern corresponding to a wavelength of 1.65 Å. The speed of the electrons determined from their

accelerating voltage of 54 volts made it possible to calculate their de Broglie wavelength as 1.67 Å, in good agreement with the measured value. Such a short wavelength was later applied to the development of the electron microscope. Also in 1927 at the University of Aberdeen, George P. Thomson (1892-1975) independently confirmed the matter wavelength of electrons by obtaining a diffraction pattern from a beam of cathode rays passing through a thin metal foil in a vacuum tube. Even though the particles appear to pass through the tube as particles, as shown thirty years earlier by G. P. Thomson’s father J. J. Thomson, they are scattered by the foil as though they were waves.

The New Quantum Mechanics The first major break with the Bohr-Sommerfeld types of mechanical orbits was made in 1925 by the German physicist Werner Heisen-berg (1901-1976), a student of both Sommerfeld

⊕ ⊕

π λ2 r = 4

r

2 r = 3½π λ

r

constructive interference destructive interferencestable orbit - reinforces forbidden orbit - cancels

Figure 9.14 DeBroglie Wavelength for an Orbiting Electron DeBroglie used his concept of a particle wavelength λ = h/mv to explain stable and forbidden orbits in the Bohr model of the hydrogen atom. A whole number of wavelengths around the circumference of an orbit would be reinforced by constructive interference to produce a stable orbit with a resonant standing wave of constant energy, while a non-integer number of wavelengths would cancel itself by destructive interference. The condition for a stable orbit of radius rn is that the circumference 2π rn = nλ = n(h/mv), which is equivalent to the Bohr equation for angular momentum mvrn = nh/2π.


and Bohr. He abandoned all attempts to picture the atom and developed an abstract mathematical method in which he placed directly measurable quantities, such as the frequencies and intensities of the spectrum lines, in square arrays called ma-trices. He related these matrices to each other by Planck’s constant. This new matrix mechanics presented many difficulties, but led to several suc-cesses. After considerable effort, Pauli was able to use it to obtain Bohr’s results for the hydrogen atom without his inconsistent semi-classical as-sumptions. But it seemed to be based on nebulous concepts and appealed to only a small group of theoreticians. At the University of Zurich, the Austrian physicist Erwin Schrödinger (1887-1961) inde-pendently developed another form of quantum mechanics based on de Broglie’s wave-particle duality and published it in January of 1926. En-couraged by Einstein’s favorable reaction to de Broglie’s work, Schrödinger used the matter wavelength to formulate a quantum wave equation based on the well known classical wave equation, which can be written for standing waves as

∇²ϕ(x,y,z) = (2π/λ)²ϕ(x,y,z),

where ∇² is a differential operator and ϕ(x,y,z) is the amplitude of the wave at any position (x,y,z) in space. This equation was solved in the nine-teenth century for many kinds of standing waves in many different geometrical configurations. Schrödinger modified this wave equation by inserting the de Broglie wavelength for a particle of mass m expressed in terms of its total energy E and potential energy V(x,y,z), obtaining his famous equation known as the Schrödinger equa-tion:

∇²ψ(x,y,z) = (8π²m/h²)[E-V(x,y,z)]ψ(x,y,z),

where the wave function ψ(x,y,z), or psi-function, is analogous to the classical wave amplitude but had to be given a new interpretation for matter waves. When Schrödinger applied his equation to the hydrogen atom, he found that it had allowable (finite) solutions for only certain values of E, which corresponded exactly to Bohr’s energy

levels and thus gave the same spectrum lines. But it had a number of advantages over the Bohr theory. Bohr’s postulates and three of the quantum numbers could now be derived from Schrödinger’s equation. The energy quantum number n re-mained the same, but the angular momentum k×h/2π now became l(l+1)×h/2π, where the or-bital quantum number l = 0, 1, 2,..., (n - 1), and the magnetic quantum number m was limited to the range of integers -l ≤ m ≤ l, which agreed much better with observations such as the splitting of spectrum lines. The Pauli principle allows the first orbital (l = 0) to contain only two electrons (m = 0, s = ±½), corresponding to their two spin states. The second orbital (l = 1) can contain 6 electrons, two for each value of m (m = 0, ±1). The third orbital (l = 2) can contain 10 electrons (m = 0,±1,±2), the fourth (l = 3) can have 14, etc. Up to argon (atomic number 18), electrons fill orbitals in the order of their quantum numbers before beginning a new one. But starting with potassium (19), some electrons begin new orbitals before lower quantum numbers have been used. The Schrödinger theory explains this result by showing that these new orbitals have lower energies than those with lower quantum numbers. Thus, for example, the noble gas xenon (54) has its energy levels for n = 1, 2 and 3 filled; but the fourth level has only 18 electrons instead of the 32 possible by the Pauli principle before beginning to fill the fifth level, giving it an electron configuration of 2-8-18-18-8. The dif-ference between 18 and 32 electrons in the fourth (n = 4) quantum level accounts for the known number of 14 elements in the rare Earth transition series (58-71). The new theory also made it possible to account for the relative intensities of spectrum lines as well as their splitting. More importantly, the theory could be applied to many different kinds of atomic and even nuclear systems, although most calculations for multi-electron atoms and molecules were quite difficult and could only be given as approximations. Finally, Schrödinger and others were able to show that quantum wave theory and Heisenberg’s matrix mechanics were


mathematically equivalent, but Schrödinger’s equation was easier to understand and apply. In 1928 Schrödinger succeeded Planck at the University of Berlin, but in 1933 he left Hitler’s Germany in the same year that he won the Nobel Prize in physics, and eventually settled at the School for Advanced Studies in Dublin. Interpretations of Quantum Wave Mechanics Although wave mechanics gave the same energy levels for the hydrogen atom as the Bohr theory, it did not define definite orbits in which electrons move. The square of the wave function ψ(x,y,z) for an electron in the hydrogen atom did have maximum values corresponding to the Bohr orbits, but it was otherwise spread out around the nucleus in a variety of shapes and densities that chemists call orbitals. At first Schrödinger thought that these wave forms were related to the electron charge distribution, forming a kind of electron cloud. But this was contrary to evidence that electrons usually behave like point charges occupying only a small region of space. At Co-penhagen, Niels Bohr expressed this wave-particle dilemma in terms of his principle of complemen-tarity, suggesting an indeterminate approach called the “Copenhagen Interpretation,” in which waves and particles are complementary descriptions of how matter and radiation behave under different conditions. The most widely accepted interpretation of the wave function ψ was suggested in 1926 by the German physicist Max Born (1882-1970), who like Schrödinger left Germany in 1933 and later became a British citizen. Instead of electric charge density, Born suggested that ψ(x,y,z) was related to a probability distribution over space. In this view, ψ²(x,y,z) is a measure of the probability of finding an electron at a position with coordinates x, y, z. Thus a particle could not be located with complete precision, but its position could only be determined within a given range of probabilities represented by the spread and variation of the wave function ψ. In the hydrogen atom, the maximum probabilities corresponded to the Bohr orbits, but there were also lower probabilities that made it possible for an electron in a quantum

energy level to be found between orbits or even in a neighboring orbital. At the atomic level, these probability dis-tributions seem to allow for alternate possibilities for the future state of a system, rather than the determinate futures of Newtonian mechanics (Figure 9.15). Bohr even suggested that nerve impulses in the brain might be near enough to individual atomic events to leave room for the alternate choices associated with free will. But it was also shown that on a larger scale these wave probabilities tended increasingly toward the clas-sical limit, consistent with Bohr’s correspondence principle.

Heisenberg extended Born’s indetermin-acy in the position of a particle to its momentum and energy in 1927 by his principle of uncertainty. Since the location of a particle is indeterminate over a range of positions governed by its wave function ψ, Heisenberg was able to define a measure for the spread of ψ as the uncertainty Δx

Newtonian particle

Wave function

xp = mv

ΔΔ

xp

ψ

Figure 9.15 Free Particle Wave Function If the position x and momentum p of a particle is known in classical physics, its future states are determined by Newton’s laws. In quantum physics, the wave function of a free particle defines the probabilities of its location. The maximum probability corresponds to the classical position x, but there are other possible positions over a range that defines the uncertainty in its position Δx. An associated uncertainty in its momentum Δp is given by the Heisenberg principle as Δx . Δp ≈ h.


in its position. This spread increases with the de Broglie wavelength λ = h/p (p = mv), leading Heisenberg to show that Δx is related to h and a corresponding uncertainty in the momentum Δp by the uncertainty relation:

Δx . Δp ≥ h/2π.

This relation means that even if there are no errors of measurement, it is still impossible to have a precise knowledge of position and momentum at the same time. This inherent uncertainty at the heart of matter is a result of Planck’s constant and would not exist if h were zero. For most events above the atomic level, h is so small as to make these uncertainties negligible, but their effects sometimes become evident on a larger scale in phenomena such as radioactivity. In the nucleus Δx is so small that Δp can be large enough for nuclear particles to have a range of energies that allow some to escape the nucleus. If the position of a particle could be determined precisely so that Δx is zero, then nothing could be known about its momentum since Δp would have to approach infinity for their product to be finite. The Heisenberg uncertainty principle has profound implications. The classical idea sug-gested by Laplace of an omniscient Intelligence who could use Newton’s laws to calculate all fu-ture events from the present knowledge of all par-ticle positions and motions is impossible if such knowledge is uncertain, leading to an inherent indeterminacy. On the other hand, an omnipotent Being could control atomic events within the range of their uncertainties to achieve alternate possibilities consistent with the laws of nature and their associated probabilities. At the atomic level, only probabilities can be determined and causality can only be described in terms of statistical rela-tionships. This idea of chance inherent in the structure of matter deeply disturbed Einstein, who insisted that, “God does not play dice!” even though he recognized and contributed to the great success of quantum theory. He hoped to find a deeper level of quantum theory that would restore causal determinism. Another implication of the quantum the-ory is the apparent loss of complete objectivity in

the process of observing nature, which is unavoid-ably altered in the act of observation. To increase the accuracy of measuring the position of an atomic particle, it is necessary to decrease the wavelength of the radiation used to observe it, and thus increase the energy of the quanta reflected from it. But the higher the quantum energy, the more it would alter the particle momentum. To measure its momentum requires low energy quanta with long wavelengths, making its position more indeterminate. Thus an observer cannot escape a degree of subjective relationship to any system that is observed. In his “Copenhagen Interpretation” of quantum theory, Bohr accepted these paradoxical implications of wave-particle duality as the nature of reality without need of further levels of expla-nation. In this view, he mirrored his Danish predecessor, the philosopher Kierkegaard, who taught that explanation always involves participa-tion and that “truth is subjective.” His great con-cern was with the paradox of Christianity, and the fact that the ultimate concerns of religion always involve the risk of faith in objective uncertainties Extensions of Quantum Mechanics In 1926 the English physicist Paul Dirac (b. 1902) worked out an elegant generalization of quantum mechanics that incorporated both matrix and wave mechanics. A year later he combined this with Maxwell’s equations to show that the electromagnetic field could be quantized to ac-count for electromagnetic forces by the exchange of a photon. In this form of quantum field theory, called quantum electrodynamics (QED), the pho-ton is created by one particle and absorbed by another as it transmits the force in quantum units at the speed of light, rather than an instantaneous action at a distance. Such exchange photons are called “virtual particles” because the energy for their creation and annihilation seems to violate conservation of energy, but in fact it is accounted for by Heisenberg’s uncertainty principle ex-pressed in terms of energy and time as:

ΔE . Δt ≥ h/2π . Creation of a virtual photon occurs in such a brief period of time Δt that its required energy falls


within the range of uncertainty ΔE and is balanced again when it is absorbed. Dirac’s QED theory was modified in 1948 to account for mathematical problems. The corrected theory has been extremely successful in accounting for electron behavior. In 1928 Dirac formulated a relativistic wave equation for particles that gave surprising results. His work required a new form of mathe-matics to describe the electron, which included a new internal degree of freedom with all the prop-erties of an axial spin. He was now able to derive the electron spin quantum number s = ±½ mathe-matically, so that all four quantum numbers needed to account for the periodic properties of the elements had a theoretical basis. A more puzzling implication of relativistic quantum theory led to the concept of antimatter and the discovery of the positron. Dirac’s relativistic wave equation permit-ted an electron to have both positive and negative energy states, even when not bound within the atom. Since electrons are not observed to fall into such negative states, he assumed that if they exist they were completely filled according to the limits set by the Pauli exclusion principle. But if an electron in such a state was given sufficient energy, it could become an ordinary electron with positive energy, leaving a “hole” in the negative energy states that would behave like a positively charged particle. At first Dirac thought such positively charged particles might account for the existence of protons, even though they were some 1836 times more massive than the electron. It was soon shown that the theory required such anti-particles to have the same mass as the electron, but opposite charge and spin. Other forms of antimatter were also possible if enough energy could be supplied to raise heavier particles to positive energy states, indicating the possibility of anti-protons with negative charge. The few theorists who could understand Dirac’s theory felt that it could not be correct because of its unobserved consequences. But in 1932 the American physicist Carl D. Anderson (b. 1905) reported his discovery of the positive elec-tron, or positron. Anderson was an associate of Robert Millikan at the California Institute of

Technology, where Millikan had established a research program for studying the high-energy particles from space called “cosmic radiation.” Millikan viewed these mysterious cosmic rays as the “birth cries of atoms” and saw them as evi-dence of God’s continuing creative activity. Anderson constructed a large cloud chamber so that he could detect charged particles from the condensation trails left in their paths. He also built a powerful electromagnet to identify the particles from their magnetic deflection. He soon obtained several photographs showing two tracks starting at a common point in the chamber and curving in opposite directions with what appeared to be equal and opposite electron charges. To confirm his results, Anderson placed a 6-mm sheet of lead across the diameter of the cloud chamber to slow particles with enough en-ergy to penetrate the barrier, and thus show their direction from the increase in their magnetic deflection. Single track particles could then be analyzed, and their change in curvature showed that they did have the charge-to-mass ratio of positive electrons. He then recognized the paired tracks as electron-positron pair creation from gamma rays with sufficient energy to produce them. This process is the most striking example of the equivalence of mass and energy, and may be represented by the reaction:

γ → e- + e+,

where γ represents a photon with energy hf. En-ergy and frequency requirements are given by equating the photon energy to electron-positron relativistic energies:

E = hf = 2 mc²,

where m is the electron mass. This gives a required energy of 1.02 MeV (1.02×106 electron-volts) and a minimum frequency for pair creation of 1.24×1020 Hz. Earlier measurements of radiation ab-sorption at even higher frequencies had revealed anomalous secondary radiation with energy of about 0.55 MeV. This was now explained as the result of the combining of an electron and a posi-tron to produce radiation energy. Such a process of


mutual annihilation might begin with an electron and positron coming together with equal and opposite momenta, so conservation of momentum requires that two photons be produced to carry momentum off in opposite directions. The reaction and energy are then given by:

e+ + e- → 2γ ,

E = 2 mc² = 2 hf ,

with an energy for each photon of hf = 0.511 MeV at a frequency of 0.62×1020 Hz. These confirma-tions of Dirac’s theory suggest that when antimat-ter is formed by pair creation, it is quickly destroyed by mutual annihilation from ordinary matter. Also by 1932 at the University of Cali-fornia at Berkeley, the American physicist Ernest O. Lawrence (1901-58) had developed the first cyclotron. He accelerated charged particles to high energies by using a magnetic field to move them in circles so they could pass through an accelerating voltage in each orbit. With the development of more powerful cyclotrons at Berkeley, enough energy was finally reached in 1955 to observe the pair creation of the proton and anti-proton, along with the creation of many other new forms of matter. Thus from Dirac’s theories there emerged a new vision of energy transmuted into elementary particles and vice versa. The vacuum of space was no longer empty, but seemed to be the source of interrelated matter and energy in the process of continuing creation and destruction. Investigations of the nucleus near the beginning of World War II would reveal new sources of energy and an expanding universe of strange new particles, along with the grim possibility that the world itself might explode.

REFERENCES

Born, Max. Einstein’s Theory of Relativity, rev. ed. New York: Dover, 1955.

Capek, Milic. The Philosophical Impact of Con-temporary Physics. Princeton: D Van Nostrand, 1961.

Einstein, Albert and Leopold Infeld. The Evolution of Physics: From Early Concepts to Relativity and Quanta. New York: Simon & Schuster, 1938.

Gamow, George. Thirty Years that Shook Physics: The Story of the Quantum Theory. New York: Dover, 1985.

Glasstone, Samuel. Sourcebook on Atomic Energy. Princeton: D. Van Nostrand, 1967.

Graves, John C. The Conceptual Foundations of Contemporary Relativity Theory. Cambridge, Mass.: MIT Press, 1971.

Guillemin, Victor. The Story of Quantum Me-chanics. New York: Scribner’s, 1968.

Heisenberg, Werner. The Physical Principles of the Quantum Theory, trans. Carl Eckart and Frank C. Hoyt. New York: Dover, 1949.

Hoffmann, Banesh. Relativity and Its Roots. New York: Scientific American Books, 1983.

. The Strange Story of the Quantum, 2nd ed. New York: Dover, 1959.

Holton, Gerald. Thematic Origins of Scientific Thought: Kepler to Einstein. Cambridge, Mass.: Harvard University Press, 1973.

Jammer, Max. The Conceptual Development of Quantum Mechanics. New York: McGraw-Hill, 1966.

Mehra, Jagdish and Helmut Rechenberg. The Historical Development of Quantum Theory, 4 vols. New York: Springer, 1982.

Moore, Ruth, Niels Bohr: The Man, His Science, and the World They Changed. Cambridge, Mass.: MIT Press, 1985.

Pagels, Heinz R. The Cosmic Code: Quantum Physics as the Language of Nature. New York: Simon & Schuster, 1982.

Pais, Abraham. ‘Subtle is the Lord...’: The Science and the Life of Albert Einstein. New York: Oxford University Press, 1982.

Romer, A. ed. The Discovery of Radioactivity and Transformation. New York: Dover, 1960.

Segrè, Emilio. From X-rays to Quarks: Modern Physicists and Their Discoveries. New York: W. H. Freeman, 1980.

Swenson, Loyd S., Jr. Genesis of Relativity: Ein-stein in Context. New York: Burt Franklin, 1979.

235

1. EVIDENCES OF AN EXPANDING UNIVERSE The twentieth century began with the confidence of classical physics and the naive belief that war was a thing of the past. Relativity and quantum theory shattered that confidence in sci-ence, and World War I followed by worldwide depression added to the uncertainty and doubt of the new age of anxiety. Although both relativity and quantum theory began to reveal new relation-ships between diverse phenomena, there seemed to be little connection between the large scale di-mensions of general relativity and the microscopic world of quantum theory. In the 1920s the theory of general relativity opened up a new vision of an expanding universe, and in the 1930s quantum theory led to the discovery of a confusing array of new elementary particles. Then in the wake of World War II, these theories and discoveries be-gan to merge in the development of the big bang theory, revealing the relationship between the very large and the very small. At the end of the nineteenth century, most astronomers viewed the universe as consisting of the solar system surrounded by a vast number of stars in roughly the shape of a disk forming the Milky Way galaxy. The German-English astronomer William Herschel (1738-1822) had

arrived at this picture of the universe by counting stars in all directions and noting their greater con-centration in the Milky Way, which defined the plane of the galactic disk. The distances of the nearest stars could be measured by the slight annual shift in their directions due to the Earth’s motion around the Sun. This angle of stellar parallax was first detected in 1838 by the German astronomer Friedrich Bessel (1784-1846), who found that a dim star in the constellation Cygnus shifted in half a year by less than a half second of arc. Calculations from this angle and the size of the Earth’s orbit showed that light from the star required eleven years to reach the Earth, or a dis-tance of 11 light years. At about the same time, the parallax of the bright star Alpha Centauri (actually a triple star) was measured from the southern hemisphere, showing it to be our nearest neighbor at a distance of 4.3 light years. The distance of the Sun is only 8 light minutes compared to the brightest star, Sirius, at 8 light years. Galaxies and the Red Shift During the nineteenth century, most as-tronomers considered the Sun to be at the middle of the Milky Way galaxy, which they assumed to contain all the stars of the universe in a more or less static system. The French astronomer Charles

CHAPTER 10

An Expanding Universe

The Big Bang Theory and Elementary Particles

Chapter 10 • An Expanding Universe 236

Messier (1730-1817) had cataloged about 100 fuzzy-appearing nebulae among the stars to avoid confusing them with comets. Herschel later iden-tified some of these blurry objects as huge clusters of stars, and his sister Caroline (1750-1848) compiled a catalog of some 2500 nebulae and clusters. At the Mount Wilson Observatory, the American astronomer Harlow Shapley (1885-1972) studied the spherically shaped globular clusters from 1914 to 1921, using the new 100-inch reflecting telescope. He found that they were distributed in a spherical arrangement outside the main disk of the Milky Way, but apparently with the same center as our galaxy, which he estimated to be about 50,000 light years from the Sun. Later work reduced this figure, showing that our Sun is about 30,000 l.y. from the center of the galaxy. The Milky Way galaxy contains more than 100 billion stars in a disk of about 120,000 l.y. in diameter and 1000 l.y. thick. A halo above and below the disk contains about 120 globular clus-ters, some with as many as a million stars crowded into a spherical volume of diameter about 100 l.y. In 1833 John Herschel (1792-1891), the son of William Herschel, began his survey of the southern skies from South Africa and soon dis-covered that the two patches of light known as the clouds of Magellan were thick clusters of stars. In 1912 the Harvard astronomer Henrietta Swan Leavitt (1868-1921) completed a study of 1,777 variable stars in the Magellanic clouds. One type of variable, first observed in the constellation Cepheus, varied in brightness over a highly regular period that ranged from about 1-50 days. Leavitt discovered that the longer the period of these cepheid variables the brighter they were. Assuming that all stars in a given Magellanic cloud are at about the same distance from the Earth, she concluded that a brighter cepheid must have a greater intrinsic luminosity and thus its period was a measure of its luminosity. Harlow Shapley used Leavitt’s period-luminosity law to measure the distances of cepheids by comparing their apparent magnitude (brightness) with their absolute magnitude (luminosity), since the dimmer a cepheid of a given period the further away it must be. Thus the

Large Magellanic Cloud is found to be at a distance of about 160,000 light years, and the Small Magellanic Cloud at 180,000 light years. Both are outside our galaxy and are apparently satellite galaxies of the Milky Way. The American astronomer Vesto Slipher (1875-1969) studied the spectra of light from nebulae at the Lowell Observatory in Arizona. In 1912 he began to measure the observed shift in spectrum lines in the light from various nebulae and found that nearly all of them were displaced toward the longer wavelengths of the red end of the spectrum. By applying the Doppler effect to this “red shift,” he inferred that they were moving away from the Earth at rates far exceeding the radial velocities of ordinary stars. For some time these results were not fully appreciated, especially since the nebulae were thought to be inside our galaxy while the speeds measured by Slipher were large enough to remove them from the Milky Way altogether. In 1920 Heber Curtis (1872-1942) of the Lick Observatory used an under estimate of the size of the Milky Way to argue that some of the nebulae were at great distances and were systems of stars comparable to the Milky Way itself. In a famous debate at the National Academy of Sci-ences in Washington, Curtis was opposed by Harlow Shapley who used an over estimate of the size of the Milky Way to argue that the nebulae were not very distant nor as large as our galaxy, and were “truly nebulous objects.” The American astronomer Edwin Hubble (1889-1953) finally resolved the debate over the nature of the nebulae by the using the 100-inch telescope at Mount Wilson. Hubble was a Rhodes scholar at Oxford and obtained a law degree before turning to astronomy. After World War I he began work at the Mount Wilson Observatory and eventually turned his attention toward the only nebula besides the Magellanic clouds that can be clearly seen with the unaided eye, near the constellation Andromeda. In 1924 Hubble finally succeeded in resolving individual stars in the Andromeda nebula and discovered that some were cepheid variables. Using the period-luminosity law, he estimated its distance at 800,000 light years, nearly ten times further than the most dis-


tant star in the Milky Way, and thus established that it was a galaxy similar to our own, even with its own satellite galaxies. Later corrections showed that the Andromeda galaxy is some two million light years away, one of the nearest galaxies to our own. Hubble was able to identify many other galaxies, classifying them by shape in the three categories of elliptical, spiral and irregular galaxies. Relativistic Cosmologies After completing the general theory of relativity in 1915, Einstein began to apply it to the universe at large. In the new theory, space and time had become actively related to the matter of the universe, but Einstein resisted the dynamic nature of the solutions he obtained, which seemed to imply a steady expansion of space-time and thus a finite beginning of the universe. In his 1917 paper “Cosmological Considerations on the General Theory of Relativity,” he concluded that, “The field equations of gravitation which I have championed hitherto still need a slight modifica-tion.” This modification involved the intro-duction of a cosmological constant representing a force of repulsion to balance the effect of gravitational attraction, thus ensuring a static universe rather than an expanding one. To maintain this condition, Einstein’s static universe required a spherical curvature of space that was closed and finite with no center and all positions equivalent. Such a universe is spatially finite but without boundaries, similar to the surface of a sphere, which is finite but unbounded. Light rays would thus return to their starting point after circling the universe. One problem with a static universe of eternally bright stars is that radiation from stars would accumulate in space and the night sky could not be dark, as pointed out in 1826 by the German astronomer Heinrich Olbers (1758-1840). In 1918 the American astronomer William MacMillan (1861-1948) at the University of Chicago tried to resolve Olbers paradox of the night sky by suggesting that atoms are “generated in the depth of space through the agency of radiant energy.” These atoms would then collect to form stars, which would eventually radiate away their entire mass. This radiation would then be mysteriously

reconstituted back into atoms without accumulating in space to brighten the night sky. The physicist Robert Millikan (1868-1953) adopted this perpetual universe and suggested that the cosmic rays from outer space discovered in 1911 were the “birth cry” of newly created matter in the depths of space and were evidence that, “The Creator is still on the job.” We now know that radiation of sufficient energy can produce particles and antiparticles, but starlight in space is far too weak to produce matter. The Dutch astronomer Willem de Sitter (1872-1934) worked out another solution to Ein-stein’s equations of general relativity in 1917. He applied them to a simplified model of the universe containing no matter. The de Sitter universe consists of flat Euclidean space, which he inter-preted as static. But when Einstein’s repulsive cosmological force is included in this model, it causes space to expand in a way that Einstein had attempted to avoid. Instead of expanding space, however, de Sitter interpreted his results as an intrinsic property of space-time that causes the red shift observed by Slipher instead of a Doppler effect, and he predicted that the greater the dis-tance of a galaxy the greater would be its red shift. Thus, for about a decade, the two leading cosmo-logical models were the closed Einstein universe with matter but no motion, and the flat de Sitter universe with motion but no matter. In the meantime, the young Russian mathematician Alexander Friedmann (1888-1925) at the University of Leningrad discovered the first non static solutions to Einstein’s relativistic field equations for a universe containing matter. After finding an error in Einstein’s 1917 paper on cos-mology, Friedmann wrote Einstein about his own more general conclusions, which Einstein reluc-tantly accepted. Friedmann then published his 1922 paper “On the Curvature of Space” in the German journal Zeitschrift für Physik, which showed the possibility of an expanding universe with positive spatial curvature (sphere-like), even without the cosmological constant, and that such a closed universe would eventually begin to col-lapse. Einstein wrote a short critique in the same journal, only to retract his objection in 1923. Friedmann published a second paper in 1924 “On


the Possibility of a World with Constant Negative Curvature,” leading to an open universe that would expand without limit if the average density of matter in the universe were less than a certain critical value (about 10 hydrogen atoms per cubic meter). A solution for zero curvature also gave an open universe if the density of matter was equal to the critical value (Figure 10.1). Unfortunately, Friedmann’s work went largely unnoticed for sev-eral years.

Hubble’s Law of Expansion The idea of an expanding universe became widely accepted through the continuing work of Edwin Hubble with the 100-inch telescope in California. In 1929 he correlated his distance measurements of the galaxies with their red shifts as first measured by Slipher. These red-shift measurements were refined and extended by Hubble’s associate, Milton Humason (1891-1972), who began his career as a janitor at the Mount Wilson Observatory. Hubble found that the more distant a galaxy the larger was its red shift, except for a few of the nearest galaxies in the same local

group as the Milky Way. Interpreting these red shifts as resulting from the Doppler effect, he showed that the radial velocities of the galaxies were directly proportional to their distances. Thus the recession velocity V of a given galaxy is related to its measured distance R by the simple equation V = HR, where H is the Hubble constant. Hubble’s law implies the steady expan-sion of the universe from a common beginning point in time. Galaxies with a greater initial speed will have reached a greater distance, and a galaxy at twice the distance of another will have twice its recession velocity. This would cause the distance between all galaxies to steadily increase, and all would appear to recede from each other no matter which galaxy served as the point of observation. Thus there is not a single galaxy, ours included, that may be considered the center of the universe. A two-dimensional analogy of this kind of expansion can be illustrated by considering dots representing galaxies on the surface of a balloon as it is being inflated. All the dots move away from each other, but none is at a center. Actually, the most distant galaxies are being seen nearest the point of beginning since their light has been traveling for the longest time. The distance R at which velocity V reaches the speed of light defines the effective “Hubble radius” of the observable universe, since no information can reach us from greater distances. Hubble’s law makes it possible to estimate the distances of galaxies beyond the limit of resolving individual stars by measuring their red shift. From its distance, the true size of a galaxy can be determined. At first, Hubble’s method seemed to show that all of the galaxies were considerably smaller than the Milky Way and that the universal expansion of the galaxies began only about two billion years ago, less than the estimated age of the Earth. However, the discovery of two different populations of stars by the German-American astronomer Walter Baade (1893-1960) led to a correction of the period-luminosity law in 1952, increasing the Hubble constant by a factor of more than two. A second revision came in 1958 when Allan Sandage and Humason, using the 200-inch telescope at Mount Palomar, discovered that some apparent stars in distant galaxies were really lu-

Size

Timepresent time

expansioncontraction

openflat

closed

Creation Collapse(Big Bang) (Big Crunch)

R

T

Figure 10.1 Friedmann Universes Friedmann found solutions to Einstein’s field equations for open universes (less than critical density) that expand forever, and closed uni-verses (greater than critical density) that even-tually begin to contract. At the present time, it is hard to determine if the universe is open, closed, or flat (average density of the universe equal to the critical density).


minous regions of hot gases, greatly increasing their distance. This showed that other galaxies were comparable in size to the Milky Way and also increased earlier estimates of the age of the universe. If the age of the universe is a length of time T and the recession velocity V was constant, then Hubble’s law can be written as V = R/T = HR and T = 1/H (Figure 10.2). This leads to estimates for the age of the universe of between 10 and 20 billion years.

The Exploding Universe Even before Hubble discovered his law of expansion, it had been predicted and extended in theoretical work done by the Belgian priest and astronomer Georges Lemaître (1894-1966). Un-aware of Friedmann’s earlier work, he obtained solutions of Einstein’s field equations for an expanding universe in 1927, and recognized a cosmic connection to the radial velocities of the galaxies. Abbé Lemaître was ordained as a priest in 1922, and then studied astrophysics at

Cambridge University under Arthur Eddington and at Harvard under Harlow Shapley. In post-graduate studies at Harvard and M.I.T. in 1924-25, Lemaître gave particular attention to a closed solution of Einstein’s field equations that included the cosmological constant with a value slightly larger than Einstein’s value to allow for an expanding universe. Lemaître’s work led him to suggest that the red shift of light from the galaxies was the result of their recessional velocities associated with the expansion of the universe, and should be proportional to their distances from our galaxy. Although Lemaître published this work in 1927 after returning to Belgium, it received little atten-tion until 1930 when Eddington sponsored an English translation in the Monthly Notices of the Royal Astronomical Society under the title “A Homogeneous Universe of Constant Mass and Increasing Radius Accounting for the Radial Velocity of Extra-Galactic Nebulae.” In 1931 Lemaître published the first sci-entific creation cosmology (cosmogony) based on his belief that God hides nothing about the uni-verse from human scrutiny. This article appeared in the British journal Nature under the title, “The Beginning of the World from the Point of View of Quantum theory.” Here he suggested that the motion of the galaxies could be extrapolated backward in time to a unique beginning point where they would have been crushed together in an initial high-density state containing all the matter and space of the universe in what he called the “primeval atom.” He estimated that if all the atomic nuclei in the universe were contiguous, they would fit into a sphere of radius the same as that of the Earth’s orbit. The origin of the universe could then be associated with the explosion of this primeval atom, initiating the expansion of curved space and its fragmented matter, which would then form the receding galaxies. However, he did not work out the details of such a super-radioactive disintegration. Using data from Hubble, it appeared that the explosion of the primeval atom was two billion years in the past, much shorter than the age of the Earth as determined by studies of radioactivity. Lemaître tried to solve this problem by adjusting

••

••

••

••

• Virgo

Ursa Major

Boötes

Hydra60

40

20

0

V

R1 2 3

RV

2R

2V

Figure 10.2 Hubble’s Law of Expansion Hubble represented the expanding universe by a velocity-distance line. Recession velocities (V) are shown in thousands of km/sec, and gal-actic distances (R) in billions of light years. The shaded area in the lower left is the region surveyed by Hubble up to 1929. As shown at the right, doubling distance doubles speed.


the cosmological constant in such a way that the universe would expand in two stages. In the first stage the expansion decelerates under the influence of gravity until it begins to approach a static condition, then expansion begins again at an accelerating rate as the cosmological repulsion becomes greater than gravity. The age of such a “hesitation universe” could be adjusted to allow for the age of the Earth (Figure 10.3). This dilemma was resolved by the later studies that led to a correction of Hubble’s data, giving the age of the universe at about 15 billion years. The possibility that an expanding uni-verse would eventually begin to collapse under the influence of gravity led to the suggestion that such a collapse might result in a rebound that would produce another stage of expansion and collapse, producing an infinite series of oscillations. Al-though no mechanism is known for this kind of rebound, the thermodynamics of such an “oscillating universe” was analyzed in 1932 by Richard Tolman (1881-1948) at the California In-stitute of Technology in an article on “Models of the Physical Universe” in the journal Science. His work showed that even an oscillating universe would have to have a finite beginning in time: In

each period of oscillation, stars and other sources would produce radiation that increases the number of photons during any period, and thus the entropy increases from cycle to cycle, making each cycle hotter than the previous one. Tolman showed that this increase in background radiation and temperature causes each succeeding cycle to increase in size and period. If the universe did not have a finite beginning in time, it would now be too hot for stars to form, to say nothing of matter reforming after a collapse.

2. NUCLEAR PARTICLES AND ENERGY

Discovery of the Neutron and Neutrino Until about 1930, physicists thought that they could describe all of matter in its different states in terms of just three elementary particles: the electron, the proton, and the photon. However, some questions began to arise when atoms were found to have atomic masses about double their nuclear charge, since each proton had one unit of charge and mass. This seemed to require either electrons inside the nucleus to reduce its positive charge, or neutral particles with mass similar to the proton. For example, the helium nucleus (alpha particle) has a mass 4 times larger than the proton (4 amu) but a charge only two times larger (+2e), suggesting that its nucleus might contain 4 protons and 2 electrons. In his Bakerian Lecture to the Royal So-ciety in 1920, Ernest Rutherford suggested that, “Under some conditions...it may be possible for an electron to combine much more closely with the hydrogen nucleus [proton], forming a kind of neu-tral doublet.” Such a “possible” neutral particle was referred to as a “neutron” as early as 1921. By 1926, the development of quantum wave mechan-ics showed that electrons could not be bound inside the nucleus since their de Broglie wave-lengths would be at least h/mec, which is about a thousand times longer than the diameter of the nucleus. A stable energy configuration in the nucleus requires standing waves of length compa-rable to the size of the nucleus. The discovery of the neutron resulted from an observation in 1930 that alpha-ray bom-bardment of beryllium produced a highly penetrat-

Hubble age

Einstein

universe

SizeR

Time

expansion

Lemaîtreuniverse

static

Creation

Figure 10.3 Lemaître’s Hesitation Universe Lemaître’s hesitation universe began with expansion from a “primeval atom,” but included a static stage that could be adjusted to allow for the age of the Earth before expansion began again. This “hesitation” was not needed when it was found that the Hubble age was greater than the age of the Earth.


ing radiation. While checking this result, Irène and Frédéric Joliot-Curie found that this radiation ejected high-energy protons from a sheet of paraf-fin placed in its path. They proposed that the radiation might be gamma rays, but were unable to show how so much energy could be transferred to the protons. The problem was resolved at Cambridge in 1932 by Rutherford’s associate, James Chadwick (1891-1974), who showed that, “The experimental results...followed immediately if it were supposed that the radiation consisted of particles of mass nearly equal to that of the proton and with no net charge.” From the mechanics of a neutron-proton collision, Chadwick was able to estimate the neu-tron mass at about one percent greater than the proton mass. Also in 1932, Harold Urey at Columbia University discovered an isotope of hy-drogen called deuterium, consisting of a proton bound to a neutron. Separating them with gamma radiation of a precise frequency led to accurate measurements of the mass of the neutron at 1.00867amu compared to the proton at 1.00728 amu. Because of their lack of charge, neutrons are not repelled by electric charges and thus penetrate matter easily. Isotopes of an element were now recognized as having the same number of protons in the nucleus, but differing numbers of neutrons. Outside the nucleus, neutrons were found to decay into a proton and an electron with a half-life of about 12 minutes, corresponding to the most basic form of beta decay (n → p + e). However, as early as 1914 Chadwick found that the electrons in beta decay possessed a continuous distribution of energies up to a maximum value that corresponded to the expected energy based on the decrease in mass in the associated nuclear transmutation (Eβ < Δmc², Δm = mn-mp-me). This problem of missing energy led Niels Bohr to suggest in his Faraday lecture of 1931 that energy conservation might not apply to beta decay. Fur-thermore, since the neutron, electron and proton all have a half-unit of quantum spin, it appeared that angular momentum might not be conserved in beta decay (½ ≠ ½ ± ½).

These anomalies led Wolfgang Pauli to suggest in June of 1931 that the beta-decay elec-trons might be accompanied by light neutral par-ticles too penetrating to be observed, but with en-ergy and spin that would account for the missing beta energy and momentum. Such a particle would have near zero rest mass since some beta electrons were at or near the maximum possible energy (Δmc²). It would be neutral to conserve charge and have spin equal and opposite the electron spin to conserve angular momentum. In Rome at the end of 1933, the Italian physicist Enrico Fermi (1901-1954) began to de-velop a quantum theory of beta decay, including the role of Pauli’s light neutral particle, which he called the “neutrino” (Italian diminutive for a neu-tral particle). Following the approach that Paul Dirac used in his 1928 photon-exchange theory of electromagnetic force (Figure 10.4a,b) and pair creation (particle and antiparticle), he postulated the simultaneous creation of an electron and an antineutrino (ν, same as neutrino ν except for opposite spin in direction of motion) when a neutron converts into a proton during beta decay:

n → p + e + ν.

In doing this, Fermi introduced a new weak force of much shorter range than the familiar gravita-tional and electromagnetic forces. His equation for the probability of beta emission contained a coupling constant for the weak interaction that was 100 billion times smaller than the corresponding coupling constant in Dirac’s theory of electromagnetic interactions, leading to a long half-life for beta decay. Fermi’s neutrino theory successfully explained the exact form of the beta-decay energy spectrum, the decay half-life, and other character-istics of beta decay. After the 1934 discovery of artificial radioactivity with positron emission (positive electrons) by Irène and Frédéric Joliot-Curie, Fermi’s theory was found also to fit this positive beta decay in which nuclear protons con-vert to neutrons by the emission of a positron and neutrino:

p → n + e+ + ν.


The neutrino was very difficult to detect since it passes readily through matter. In 1956, Clyde Cowan and Frederick Reines of Los Alamos con-firmed the effects of neutrinos near a nuclear reac-tor at Savannah River, South Carolina. The reactor produced enough antineutrinos for a few to inter-act with protons, easily detected by the simultane-ous appearance of a neutron and positron in this reverse beta decay:

ν + p → n + e+.

Theories predicting a large production of neutrinos when stars explode were confirmed by the supernova of February 24, 1987, in the Large Magellanic Cloud. Nuclear Forces and the Meson In 1932, Werner Heisenberg proposed a neutron-proton model of the nucleus held together by electron-exchange interactions, in a way similar to the electron bonding of the two hydrogen atoms in a hydrogen molecule. When his papers reached Japan, they were read by a young lecturer at Kyoto University named Hideki Yukawa (1907-1981), who published a Japanese translation with an

introduction noting inadequacies in Heisenberg’s theory of nuclear forces. Yukawa then attempted to modify Heisenberg’s theory to explain nuclear forces by an electron-exchange field similar to Dirac’s photon-exchange field for electro-magnetic forces. But he was dissatisfied with the theory because it implied a force range much larger than the nucleus of the atom and a spin ex-change that would violate conservation of angular momentum. After reading Fermi’s 1934 neutrino the-ory for the weak force of radioactive beta decay, Yukawa thought of a way to use a zero-spin ex-change particle as the field quantum for both nu-clear forces and beta decay (Figure 10.4b,c). He recognized that the range of interaction for the ex-change of such a field particle between protons and neutrons in the nucleus should be about the size of the nucleus (R ≈ 10-14m). Using a form of Schroedinger’s equation for a particle without spin, he found that he could approximate its mass for a virtual exchange at the speed of light c by equating the range of the interaction to the de Broglie wavelength:

λ = h/mc = R.

γ

p

p

e

e

n

p W

en

p

p

n-ν_

π −

(a) Electromagnetic (b) Weak Force

(c) Nuclear ForceForce (radioactivity)

nucleus

Figure 10.4 Quantum Fields and Exchange Forces of Dirac, Fermi and Yukawa (a) Dirac explained the electromagnetic interaction between a proton (p) and an electron (e) by the

exchange of a photon (γ) as the quantum of the field. (b) Fermi used a similar model to explain the weak force in the beta decay of a neutron (n) into a

proton (p) with the emission of an electron (e) and an antineutrino (ν). Yukawa added an exchange particle to the interaction, later identified as the W-particle.

(c) Yukawa explained the strong nuclear force between nucleons (p and n) inside the nucleus by the exchange of a meson, later called the pion (π).


This gave a predicted value for the mass:

m = h/Rc > 200 electron masses.

Yukawa called his predicted particle a “heavy quantum,” but the name “meson” was accepted later after its introduction by the Indian physicist Homi Bhabha in 1939 to describe its intermediate mass (200me) between that of the electron and the proton: me< m < mp, where mp = 1846me. Yukawa published his theory “On the Interaction of Elementary Particles” in a Japanese journal in 1935. It allowed for mesons to exist with either positive or negative electrical charge. He also showed how to obtain Fermi’s results for beta decay in terms of a similar particle exchange with the electron and antineutrino when a neutron decays into a proton, leading eventually to the discovery of the W-particle in 1983:

N → p+W-, W- → e+ν.

This interaction required a much smaller coupling constant to distinguish the weak force of radio-activity from the strong nuclear force. Thus by 1935, four basic forces had been identified. The nuclear force mediated by the meson is about 100 times stronger than the electromagnetic force mediated by the photon, and about 1012 times stronger than the weak force. All of these are much stronger than the force of gravity. Yukawa noted that any observation of free mesons having such a large mass would require the high energy of cosmic rays. But the theory was largely ignored until 1937 when S. Neddermeyer and Carl Anderson (who discovered the positron in 1932) published their discovery of a charged particle with a mass of about 200 electron masses in cosmic ray studies with a cloud chamber. By 1939 Yukawa had calculated the decay time of the meson to be about .01 μsec (10-8 sec), but several measurements of the cosmic-ray meson, later called a mu-meson or muon, indicated a mean lifetime of 1 μsec, 100 times longer than required by theory and thus much more pene-trating in matter than would be expected of Yuk-awa’s meson. This problem was resolved in 1947 when Cecil F. Powell (1903-1969) and his associ-ates at Bristol University discovered a cosmic-ray particle in a photo emulsion that quickly decayed

into the muon. This new particle, which Fermi designated as the pion, had all the characteristics predicted by Yukawa. The pion (π) has a mass of 273me compared to the muon mass of 207me, and decays into a muon (μ)and a neutrino:

π → μ+ν, μ → e+ν+ν.

For his contributions to the expanding world of elementary particles, Yukawa received the physics Nobel Prize in 1949. Discovery of Nuclear Fission Beginning in 1934, Fermi and his associ-ates in Rome began a systematic study of some 60 elements bombarded with neutrons, whose lack of electric charge allowed them to penetrate the positive nucleus and transmute them to heavier atoms. About 40 were converted into radioactive isotopes, which were assumed to be of elements of atomic number one higher than the target material. In the course of their work, they found that “slow neutrons” obtained by passing them through water or paraffin were more effective in producing these radiative capture reactions. In 1935, Fermi thought he had produced a “transuranic element” of atomic number 93 by bombarding uranium (atomic number 92). Al-though he did not realize it at the time, he had probably observed the splitting of uranium nuclei. In the same year at the University of Chicago, Arthur Dempster (1886-1950) discovered the rare uranium-235 isotope (92 protons and 143 neu-trons) by magnetic deflection of uranium ions in a mass spectrograph. In 1938, Fermi received the Nobel prize for his work and used the opportunity to escape from Fascist Italy to the United States. Fermi’s claim to the possible discovery of a transuranic element was challenged by German chemist Ida Tacke, who first suggested the idea of nuclear fission. Working with her future husband Walter Noddack (1893-1960) in Berlin, she was only 29 when they discovered element number 75 in 1925 after a three year search. The last stable element to be discovered, they named it rhenium after the Rhine River. In 1934 Ida Tacke Noddack expressed criticism of Fermi’s lack of convincing evidence for his transuranic element claim in a paper entitled “On Element 93,” advancing the


possibility that he might have produced light elements by splitting uranium:

It would be conceivable that when heavy nuclei are bombarded with neutrons the nuclei in question might break into a number of larger pieces, which would no doubt be isotopes of known elements but not neighbours of the elements subjected to radiation.

At the time, her suggestion was not taken seriously and she made no attempt to test her hypothesis. In 1937 Irène Joliot-Curie did check the neutron bombardment of uranium and found a radioactive isotope with a 3.5-hour half-life that seemed to resemble lanthanum (atomic number 57). Had she recognized that it actually was a lanthanum isotope, she would have probably discovered nuclear fission. Nuclear fission was finally discovered late in 1938 by the Austrian physicist Lise Meitner (1878-1968) after a four-year search for trans-uranic elements at the University of Berlin with the radio chemist Otto Hahn (1879-1968), with whom she had collaborated for nearly 30 years. In 1917 they had discovered element number 91, the radioactive precursor of actinium (89) called protactinium. In July of 1938, Lise Meitner had to flee Germany after the annexation of her native Austria by the Nazi regime because of her Jewish background, even though she was baptized and raised as a Protestant in Vienna. After Meitner’s departure, the transuranic experiments led to the unexpected presence of radium and barium among the products resulting from neutron bombardment of uranium. Since barium (56) is far removed from uranium in atomic number, Hahn was confused and wrote Meitner about the problem at Christmas of 1938 in Sweden. She immediately recognized that the only way barium could result was the splitting of the uranium nucleus into two nearly equal fragments. Meitner shared the possibility of nuclear fission with her visiting nephew Otto Frisch (1904-1979), who was also a refugee from Nazism and working at Niels Bohr’s Institute in Copenhagen. He calculated the kinetic energy of electric repulsion between the fragments of such a fission event from

Coulomb’s law. She calculated the mass dif-ference between the uranium nucleus and the slightly reduced mass of the fragments, which would include krypton (36) along with barium (56) to account for the 92 uranium protons, obtaining the equivalent energy (K.E.=Δmc²). Meitner and Frisch published their results in the February 1939 issue of Nature under the title “Disintegration of Uranium by Neutrons: A New Type of Nuclear Reaction,” showing that the mass-energy agreed with the repulsion energy:

These two nuclei will repel each other and should gain a total kinetic energy of about 200 MeV, as calculated from the nuclear radius and charge. This amount of energy may actually be expected to be available from the difference in packing fraction be-tween uranium and the elements in the middle of the periodic system. The whole “fission” process can thus be described in an essentially classical way.

This work introduced the term “fission” for such processes and suggested evidence for the forma-tion of uranium-239 and its decay into transuranic element 93 (later called neptunium when it was identified in 1940). Within weeks several re-searchers reported on successful fission experi-ments in which the large pulses produced by the fission fragments from neutron bombardment of uranium were observed in an ionization chamber, including Otto Frisch and Irène Curie-Joliot. As estimated by Meitner and Frisch, each nuclear fission releases about 200 million electron-volts (MeV) of energy. Chemical reactions release only a few electron-volts per atom (1 eV is the energy gained by an electron accelerated by one volt). Most of the energy of fission appears in the motion of the fragments, which dissipates by collisions with surrounding atoms to produce heat. Thus a series of nuclear disintegrations should produce about 100 million times as much energy as a chemical reaction. In 1939 Frédéric Joliot-Curie and his associates in Paris made the crucial discovery that each fission releases two or three high speed neutrons. This made it evident that a self-sustaining or chain reaction was possible, since each fission neutron could produce two or


three more disintegrations, each resulting in more neutrons to set up an exponential series of fissions and the release of large quantities of energy (fissioning of 1 gm of uranium releases energy equivalent to burning 3 million tons of coal). The Hungarian-American physicist Leo Szilard (1898-1964) had obtained a British patent in 1934 for a similar chain reaction with neutron bombardment of beryllium, but such a process proved to be un-workable with light elements.

Even before the discovery of fission, Niels Bohr had developed a theory of the nucleus in 1936 showing that neutron capture by a heavy nucleus would cause it to oscillate like a liquid drop or bubble. While visiting the United States early in 1939, Bohr and John Wheeler of Princeton University derived a theory of fission from the liquid-drop model of the nucleus, in which oscil-lations in some nuclei would allow electric repul-sion to exceed the short-range nuclear force of attraction (Figure 10.5). This theory led Bohr to predict that the common uranium-238 isotope (99.3% in nature) would require fast neutrons for

fission, but the rarer uranium-235 isotope would fission with neutrons of any energy. Two typical reactions for the fission of U-235 with slow neutrons are as follows:

10n + 235

92U → 141 56Ba + 92

36Kr + 3 × 10n, 10n + 235

92U → 140 54Xe + 94

38Sr + 2 × 10n .

This suggested the idea of studying fission in a systematic way with a controlled chain reaction using slow neutrons and uranium enriched with U-235 above the usual 0.7% in natural uranium, although separation of this isotope from U-238 posed many problems. The Development of Nuclear Energy By July of 1939, the need for government support and secrecy led Szilard and another Hungarian immi-grant, Eugene Wigner (b. 1902), to ap-proach Einstein about writing a letter to President Franklin Roosevelt. The President responded by forming an Advisory Committee on Uranium, which provided six thousand dollars to Columbia University for the purchase of 50 tons of uranium oxide and 4 tons of graphite to study its ability to slow neutrons. Meanwhile in England, Frisch and Rudolf Peierls worked out the requirements for an atomic bomb in a paper sent to the English government in the spring of 1940. They estimated

that less than one kilogram is required for a criti-cal mass to sustain a chain reaction in pure uranium-235, in which more neutrons would cause fission than those that escaped. If two or more sub critical masses could be brought together rapidly enough, they would produce an explosion equivalent to several thousand tons of dynamite. They also outlined the extensive effort that would be needed to separate U-235 from U-238. By December 1941, when the United States entered World War II, contracts had been arranged with about 12 American Universities for nuclear research. War-time research was super-

Kr

Ba

36p

56p

92p143n

U92235

n

n

n

n

n

n

n

n

n

n

n

n

+

+

Coulombrepulsion

nuclearoscillation

chain reaction

U-235

U-235

U-235

Figure 10.5 Liquid-drop Model of Nuclear Fission Bohr’s liquid-drop model explained fission as the result of nuclear oscillations due to the absorption of a neutron, which narrows the neck over which the short-range nuclear force acts and allows the electromagnetic repulsion to dominate. The fragments of light-element isotopes thus gain Coulomb energy, and a chain reaction is initiated by the surplus neutrons.


vised by Vannevar Bush, with James Bryant Conant as his deputy for uranium research. Three major projects included the study of uranium enrichment methods under Harold Urey at Co-lumbia, chain-reaction studies under Arthur Holly Compton at the University of Chicago, and cyclo-tron studies by Ernest O. Lawrence (1901-1958) at the University of California. Lawrence and his student M. S. Livingstone operated the first cyclo-tron in 1932, using a strong magnet to accelerate protons in a spiraling orbit up to 1.2 MeV with only 4000 V across the gap between two 6-inch semi-circular cavities. In 1940 bombardment of uranium in the 60-inch Berkeley cyclotron led to the discovery of plutonium (94) and the fact that plutonium-239 was fissionable. Since U-238 was found to absorb neutrons without fission at some high energies, it could not be used for a bomb but offered the possibility of breeding plutonium in the following reactions:

10n + 238

92U → γ + 239 92U → 0-1e + 239

93Np,

239 93Np → 0-1e + 239

94Pu .

U-239 has a half-life of 23.5 min. and neptunium-239 has a half-life of 2.35 days, so plutonium with a half-life of 24,360 years can then be separated from the remaining uranium by chemical methods since it differs chemically from uranium isotopes. At Columbia University in 1941, Fermi began research on fission rates in a sub critical lattice of uranium oxide and graphite, and showed that a chain reaction would be sustained if impu-rities are reduced to less than one percent. His group moved to the University of Chicago in 1942, where they constructed a nuclear reactor with 40 tons of natural uranium fuel and 385 tons of graphite as a moderator to slow the neutrons. When neutron absorbing cadmium control rods were partially removed on December 2, 1942, a sharp increase in neutrons indicated a sustained chain reaction, which was stopped by reinserting the control rods (Figure 10.6). However, much larger reactors were

Control rodsReactor core

Coolant

Fuelrod

ModeratorNeutron

Containment

Turbine Generator

Condenser

Steam

WaterCoolant

Boiler

Figure 10.6 Nuclear Reactor for Generating Electric Power In the core of a nuclear reactor, the fuel rods contain enriched unranium that produce neutrons when they fission. The neutrons are slowed by the moderator to increase the absorption rate by neighboring fuel rods to sustain a chain reaction, which can be slowed or stopped by inserting the neutron-absorbing control rods. A liquid moderator can double as a coolant to transfer the heat generated by the fission products to a heat exchanger (boiler), producing steam to drive a turbine and generate electricity.


needed to breed plutonium for a bomb. During 1942 the $2-billion “Manhattan Project” was es-tablished under General Leslie Groves to construct three “atomic cities.” At Oak Ridge, Tennessee, 25,000 workers built a $500-million electromag-netic separation plant and a 5000-stage gaseous diffusion plant to enrich uranium. At Hanford, Washington, 60,000 workers built three large reactors and a chemical-separation plant to pro-duce plutonium. A third atomic city was built at Los Alamos, New Mexico, in 1943 for the design and construction of a nuclear bomb. Here some two hundred of the best scientists of the Manhattan Project came to work under the leadership of J. Robert Oppenheimer (1904-1967) on such prob-lems as neutron absorption, uranium and pluto-nium purification and fabrication, and explosive methods for forming a critical mass. Two bomb designs were developed. A gun-type bomb called “Little Boy” used 15 kg of U-235 in a 4,500-kg

cylinder about 2 m long and 0.5 m in diameter, in which a uranium bullet could be fired into three uranium target rings to form a critical mass (Figure 10.7). An implosion-type bomb called “Fat Man” had a 5-kg spherical core of plutonium about the size of an orange, which could be squeezed inside a 2,300-kg sphere about 1.5 m in diameter by properly shaped explosives to make the mass critical in the shorter time required for the faster plutonium fission. By May of 1945, enough plutonium and uranium had arrived from Hanford and Oak Ridge to begin critical-mass studies by a group led by Otto Frisch. By July one uranium (about 90% U-235) and two plutonium bombs were finished and a test site named Trinity was chosen in the Alamogordo desert. On July 16 one of the pluto-nium bombs was detonated at 5:30 a.m. The re-sulting implosion initiated a chain reaction of nearly 60 fission generations (260 nuclei) in about a micro-second. It produced an intense flash of light, followed by a fireball expanding to a diame-ter of about 600 meters in two seconds, and then it rose to a height of more than 12 km, forming its ominous mushroom shape. Forty seconds later an air blast hit the observer bunkers 10 km away, followed by a sustained and awesome roar. Meas-urements confirmed an explosive power equivalent to 18.6 kilotons of TNT, nearly four times the predicted value. Early in the Manhattan Project, the Hun-garian-American physicist Edward Teller (b. 1908) proposed the development of a thermonuclear fusion bomb, in which hydrogen isotopes would be fused together by the force of a fission explosion to produce helium nuclei and almost unlimited energy. A simple fusion reaction with deuterium nuclei combining to form helium,

21H + 21H → 42He,

requires an ignition temperature of about 100 million degrees to overcome electrical repulsion. However, it would release about 25 MeV of energy from a decrease in mass of only about 0.7%. After the surprise explosion of a Soviet atomic bomb in 1949, Teller led the development of the first H-bomb, which used a fission bomb to obtain the required ignition temperature for fusion.

••

•

n

nn

U

Super-critical: fission>escape

Sub-critical: fission<escape

U

U

Figure 10.7 Critical Mass Concept In a super-critical mass of fissionable material (enriched uranium or plutonium), there is enough mass that more neutrons are absorbed and cause fission on average than those that escape from the mass (shown here, 2 are absorbed and one escapes), thus sustaining a chain reaction. In a sub-critical mass, more neutrons escape than are absorbed (here 2 escape and 1 is absorbed), so that a chain reaction does not occur.


It was exploded in 1952 with a yield of more than 10 megatons of TNT. The development of nuclear reactors has made a major contribution to world energy resources. Nearly 20% of electrical energy in the United States is generated by more than 100 reac-tors, and there are more than 400 reactors worldwide. Most of the problems associated with fission power, such as waste disposal and the threat of fallout from a reactor accident, could be eliminated with nuclear fusion reactors. The fusion of hydrogen isotopes to produce helium releases energy comparable to fission, but requires no critical mass of fuel that might cause meltdown, has fewer radioactive waste products, and uses a fuel of almost unlimited supply (natural water contains .015% deuterium). Because of the extremely high temperatures required, ignition and isolation of such reactions require some kind of magnetic confinement of ionized gases or inertial confinement (free fall) of deuterium pellets. Practical sources of such power are being devel-oped, but are several years from completion. 3. BIRTH OF STARS AND THE UNIVERSE Energy Processes in the Stars In 1854 Hermann von Helmholtz pro-posed that stars like the Sun gain their energy from the compression of gases in the gravitational collapse of gaseous clouds until they are balanced by the hydrostatic pressure of the gases. However, his calculations showed that such a source of energy for the Sun would only last for about 25 million years at its present rate of radiation. Between 1916 and 1920, Sir Arthur Eddington worked out a model for the interior of a star that included the effect of radiation pressure, showing that the internal temperatures would reach into the millions of degrees and that gravitational energy would suffice for only about 100 thousand years. He showed that this radiation pressure increased rapidly with increasing mass and would blow a star apart if its mass exceeded more than about 50 solar masses. Eddington also worked out a theory for the pulsations of large stars, which could explain the behavior of variable stars such as the cepheids with their period-luminosity law. His

most prescient suggestion was that the energy of the stars might come from the transformation of hydrogen into helium. Even before World War II, it was estab-lished that the stars were powered by nuclear fusion processes. These processes were worked out in 1938 at Cornell University by the German-American physicist Hans Bethe (b. 1906), who came to the United States in 1935 and later headed the theoretical physics division at Los Alamos during the war. After spectroscopic analyses by Cecelia Payne (1900-1979) and others had shown that the stars are made up mostly of hydrogen and helium, Bethe worked out two mechanisms to account for the fusion of hydrogen into helium in the stars. The simpler of the two is the proton-proton reaction:

11H + 11H →

21H + 0 +1e + ν + energy,

21H + 11H → 32He + γ + energy,

32He + 32He → 42He + 11H + 11H + energy.

In the first reaction, two protons ( 1 1 H) combine to

form a deuteron ( 2 1 H), a positron ( 0 +1e) and a neu-

trino (ν). In the second, a deuteron combines with a proton to form helium-3 and a photon (γ). These two reactions must occur twice in order to produce two He-3 nuclei for the third reaction, which produces He-4 and two more protons. The net result of these reactions is the fusion of two protons into helium plus positrons, neutrinos, and enough energy to permit a star like the Sun to “burn” with internal temperatures of about 15 million degrees for about 10 billion years. Bethe also showed that stars of more than about 1.5 solar masses with internal temperatures above about 20 million degrees, would require a second mechanism involving six different reac-tions for fusion of hydrogen into helium, called the CNO or carbon cycle:

12 6C + 11H → 13

7N + energy,

13 7N → 13

6C + 0 +1e + ν,


13 6C + 11H → 14

7N + energy,

14 7N + 11H → 15

8O + energy,

15 8O → 15

7N + 0+1e + ν,

15 7N + 11H → 12

6C + 42He.

Here four protons fuse into helium by transmuting carbon into isotopes of nitrogen and oxygen (plus positrons and neutrinos) before regenerating into carbon again, which functions like a catalyst in the cycle. One way to confirm these hypothetical processes is to detect the neutrinos generated in the Sun by measuring the argon produced whenever chlorine absorbs a neutrino. In the 1950s, 100,000 gallons of a chlorine-containing liquid were placed a mile below the surface of the Earth in the Homestake Mine in South Dakota. The rock above the detector absorbs cosmic-ray particles, leaving only neutrinos to interact with the chlorine; but only about one-third of the predicted flux of solar neutrinos incident on the Earth was detected. Several possible solutions to this solar-neutrino problem have been proposed, including one of the most promising in 1985 by Bethe himself involving the oscillation of neutrinos from one type into another. Steady-State Theory and Continuous Creation Hubble’s discovery of an expanding uni-verse strongly implied a beginning of the universe within a finite period of time. However, his data at the time seemed to imply that the galaxies had been receding from each other for only about two billion years, while evidence from astronomy seemed to suggest that star clusters might be older than 10 billion years. An attempt to resolve this dilemma was suggested in 1948 by the Austrian-American astronomers Hermann Bondi (b. 1919) and Thomas Gold (b. 1920) in a paper entitled “The Steady-State Theory of the Expanding Uni-verse.” This theory did not require an origin of the universe in time, but assumed the continuous creation of matter throughout space at a rate that

keeps the mean density of the universe constant at all times as the universe expands. Calculations by Bondi and Gold showed that the density of the universe would be sustained if one atom of hydrogen is created ex nihilo (from nothing) in each cubic meter of empty space be-tween the galaxies every 300,000 years, too slowly to be directly observed. When the distance be-tween neighboring galaxies had doubled, enough matter would have then emerged between them to form a new galaxy without changing the density of the galaxies filling space. As galaxies recede from a given point of observation their speed increases until they reach the speed of light and thus can no longer be seen, keeping the total number of observable galaxies the same. Ironically, although such a steady-state universe would be eternal, it required the Christian concept of creation ex nihilo to avoid the Biblical idea of a unique creation in the finite past. One of the strongest supporters of the steady-state theory was the English astronomer Fred Hoyle (b. 1915) at Cambridge University. In 1948, following a “discussion with Mr. T. Gold,” Hoyle showed how to modify the general theory of relativity to allow for continuous creation of matter by introducing a creation field (C-field) into the field equations in the same way that Einstein introduced the cosmological constant. Although the theory violates the law of conservation of mass-energy, Hoyle claimed that the combined matter and creation field are conserved. The re-sulting model balanced the expansion of the uni-verse and the origin of new matter, but required a constant matter density at least an order of magni-tude higher than the measured mean density of visible matter. The steady-state theory began to decline by the end of the 1950s when the corrections in the Hubble period showed that the expansion of the universe was longer than the age of the galaxies. Several discoveries in the 1960s made the continuous-creation theory untenable, and strongly supported its chief rival called the big-bang theory, a new form of Lemaître’s idea of an explosive beginning of the universe in which elements formed by processes of fusion rather than the disintegration of a primeval atom.


The Big-Bang Theory and Nucleosynthesis Starting in 1935, the Russian-American physicist George Gamow (1904-1968), a student of Alexander Friedmann at Novorossia University, proposed the idea that the early dense stages of the universe were hot enough to produce thermonu-clear reactions that could synthesize the elements. By 1946 at Washington University, Gamow sug-gested that the primordial substance, which he called ylem, consisted of neutrons bathed in high energy radiation at a temperature of more than 10 billion degrees, which decayed during the early stages of expansion to form protons and electrons. Successive captures of neutrons by the newly formed protons would then lead to the formation of the elements, and perhaps account for their relative abundances in the universe. The initial high temperature that Gamow calculated implied that the universe began with a radiation era of more than 100,000 years during which the density of radiation greatly exceeded the density of matter. As the temperature continued to fall, the radiation density dropped below the matter density, initiating a matter era in which the galaxies formed and the radiation cooled by expansion to a very low temperature. Gamow published these ideas in a 1948 issue of Nature under the title “The Evolution of the Universe,” in which he indicated a possible cosmic background of remaining radiation at an absolute temperature below 50K. Gamow began to work out the details of the primeval nucleosynthesis of the elements by neutron capture with his student Ralph Alpher (b. 1921) in 1948. They persuaded Hans Bethe to add his name to their article on “The Origins of the Chemical Elements” to make the list of authors “Alpher, Bethe, Gamow” as a pun on the first three letters of the Greek alphabet. This “alpha-beta-gamma theory” for the origin of the universe was first called the “big-bang theory” by Fred Hoyle to distinguish it from his continuous-creation theory. Later in 1948 at the Johns Hop-kins Applied Physics Laboratory, Alpher and Robert Herman (b. 1914) published a further analysis of the early universe with several correc-tions of Gamow’s earlier calculations. By assum-ing that element synthesis began when the uni-

verse had cooled to about 1 billion degrees. This was low enough to avoid the dissociation of deu-terium nuclei into neutrons and protons. They calculated that about 50 percent of matter would be converted into helium and predicted a cosmic background radiation of only about 5K above absolute zero at the present time. Gamow and his colleagues were able to explain the origin of helium, but their hope of explaining all of the elements by neutron capture was not successful. The problem, as pointed out by Enrico Fermi and A. Turkevich in 1950, was that elements heavier than He-4 cannot be produced in sufficient abundance because of the absence of stable isotopes containing 5 or 8 nucleons (protons and neutrons). As stated by Gamow in his 1952 book The Creation of the Universe:

The trouble lies in the fact that the nucleus of mass 5, which would be the next stepping stone, is not available. Due to some peculiar interplay of nuclear forces, neither a single proton nor a single neutron can be rigidly attached to the helium nucleus, so that the next stable nucleus is that of mass 6 (the lighter isotope of lithium), which contains two extra particles. On the other hand, under the assumed physical conditions, the probability that two particles will be captured simultaneously by a helium nu-cleus is negligibly small, and the building-up process seems to be stopped short at that point.

The only reasonable mechanism for bridging this gap is the nearly simultaneous collision of several nuclei, which was highly unlikely under the con-ditions of the big bang at temperatures below one billion degrees. Ironically, the problem of nucleosynthesis beyond helium was resolved by Fred Hoyle in 1954 when he showed that three alpha particles could combine at the higher densities in the core of a red giant star at a temperature of about 100 million degrees. This triple-alpha process would produce carbon-12, which could then capture alpha particles to form heavier elements. Hoyle and his colleagues identified a number of processes that could synthesize elements in massive stars up to


iron-56. In such a star, compression of iron causes it to disintegrate and absorb energy, leading to a collapse of the star that blasts it into space as a supernova explosion. Elements beyond iron are formed in this explosion by neutron capture, which are dispersed into space and even-tually coalesce to form second-generation stars like our Sun with the heavier elements needed to support life. Successes of the Big Bang Theory The big-bang theory for the beginning of the universe became widely accepted after the accidental discovery in 1965 of the cosmic back-ground radiation at the Bell Telephone Laborato-ries in New Jersey by Arno A. Penzias and Robert W. Wilson. Radio astronomy began in 1932 when Karl Jansky (1905-1950), also at Bell Labs, detected radio signals from the Milky Way. The first radio telescope (a 30-ft dish reflector) was built in 1937 at Wheaton, Illinois, by Grote Reber (b. 1911), who discovered several extra galactic radio sources. Wilson and Penzias were testing a 20-ft microwave “horn antenna” to measure galactic noise when they found uniform radiation corresponding to a few degrees of unexpected noise temperature with no directional variations. After checking the antenna and cleaning pigeon droppings from it, they could only slightly reduce the persistent radiation to an antenna temperature of 3.5 ± 1.0 K at a wavelength of 7.3 cm in the microwave spectrum. The discovery of Penzias and Wilson came to the attention of Robert Dicke and his colleagues at Princeton University. In a companion letter in the same issue of the Astrophysical Journal, they explained this excess noise as the cosmic background radiation from the primeval fireball, which had expanded and cooled as pre-dicted by the big-bang theory. One member of the Princeton group, P. James Peebles, was repeating the calculations of the Gamow group and found that the background radiation should be near 3K. Big-bang theory requires that cosmic radiation have the very well defined blackbody spectrum that is characteristic of the thermodynamic equi-librium caused by the interactions of matter and radiation in the primeval fireball. This thermal

spectrum, like a fossil relic of the big bang, should be preserved for all time as the universe expands and cools. Subsequent measurements have revealed a 2.726 ± 0.01K background temperature with a blackbody microwave spectrum that fits precisely the shape predicted by the big-bang the-ory, as confirmed in 1990 by the Cosmic Back-ground Explorer (COBE) satellite. In 1992 the Differential Microwave Radiometer on board COBE detected minute structure in the background radiation that gives predicted evidence of the conditions required for galaxy formation. After World War II, astronomers identi-fied many discrete radio sources with galaxies. Then in 1960, Allan Sandage and his associates at the Mount Palomar Observatory detected optically a faint star-like object at the same location as a radio galaxy with an emission spectrum that they could not identify. In 1963 the spectra of two of these “quasi-stellar objects,” or quasars, were deciphered by Maarten Schmidt of Mount Wilson Observatory, who found that the emission lines were those of hydrogen with large red shifts of 16 and 37 percent. This implied that they were at distances of more than 2 billion light years and radiating at least 100 times the rate of all the stars of a galaxy such as our own. Hundreds of quasars have now been found, some smaller than a light year in diameter, emitting more radiation than 10,000 galaxies. Most are at great distances, out as far as 13 billion light years, and thus appear to be the highly energetic nuclei of galaxies in the early stages of development. This is exactly what would be expected from the big-bang theory at 13 billion years in the past when galaxies were beginning to form. By contrast, the steady-state theory predicted that such infant galaxies would be found uniformly through space, rather than only at the greatest distances. One of the greatest successes of the big-bang theory is its ability to account for the cosmic abundances of the light elements, including about 25% helium (±3%), 75% hydrogen, .001% deu-terium (using data from the first Moon landing), .001% helium-3, and 10-6 percent lithium. Theo-retical values are within the limits of current observational uncertainties after accounting for the


helium produced in the stars since the big bang, which increases the total abundance of helium-4 to about 30 percent. Extrapolating back in time from the cur-rent mass density of the universe to within 100 seconds after the big bang, high-energy conversion processes gave about 2 neutrons and 14 protons out of every 16 nucleons, due to the larger mass and decay rate of the neutron. At this time the temperature had dropped to 1 billion degrees, low enough for the 2 neutrons to combine with 2 protons, leaving 2 deuterons ( 2

1 H+) and 12 pro-tons. The 2 deuterons combine to form 1 helium nucleus, giving 1 helium nucleus for every 12 pro-tons within another 100 seconds. Thus 4 of every 16 nucleons form a helium nucleus, so 25 percent of all matter was converted into helium shortly after the universe was 3 minutes old. Most of the remainder is hydrogen, but not all deuterons are able to form helium nuclei, and slight amounts of deuterium, helium-3, and lithium are produced in amounts that depend more critically on the density of matter. 4. ELEMENTARY PARTICLES & FORCES Strange Particles and Particle Families After World War II, larger and larger particle accelerators were built, permitting colli-sions at energies that could create new particles and conditions simulating the first few seconds of the big bang. The first such machine was the 184-inch Berkeley cyclotron, which confirmed the existence of charged pions in 1948. It led by 1950 to evidence for a neutral pion (πo) with a very rapid gamma decay (~10-16 sec) due to an elec-tromagnetic rather than weak interaction. In 1952 the “cosmotron” at Brookhaven National Labora-tory in New York surpassed 1000 MeV (1 GeV), and a year later confirmed the earlier cosmic-ray discovery of the Ko meson at 498 MeV (975 me). Several cosmic-ray particles now called baryons had nucleons among their decay products, such as the lambda particle (Λ → p + π−) and the sigma particle (Σ+ → p + πo). The lambda particle (~1.2 mp) was es-pecially puzzling when it was found to decay

much more slowly than its production process. Lambda production was found to occur only in association with a kaon, but its decay does not:

π− + p → Λ + Ko, Λ → p + π−. The associated production is by the strong Yukawa interaction, while the decay is by the weak Fermi interaction. Previous reactions had always been reversible with respect to production and decay interactions. In 1953 at the University of Chicago, Murray Gell-Mann (b. 1929) accounted for the behavior of such “strange particles” by the introduction of a new quantum number that he called strangeness. The same idea was suggested independently by the Japanese physicists T. Nakano and K. Nishijima, in which such particles were given a strangeness of ±1, ±2, and so on, such that the sum of the strangeness of all parti-cles in any strong interaction does not change. This led to selection rules that allow or forbid certain reactions consistent with experimental evidence. Particles that decay by a weak interaction have lifetimes of about 10-8 sec and leave a track of several centimeters in a detector. Particles de-caying by electromagnetic interactions live about 10-16 sec and must be detected by their gamma-ray products. In 1952, two years before he died of cancer, Fermi and his associates at the University of Chicago found evidence in their new “synchrocyclotron” for very short-lived particles called resonances that decay by the strong nuclear interaction. They used a positive-pion beam to strike a hydrogen target, observing the partial ab-sorption of pions and their associated probability of interaction with protons. The probability varied with the energy of the pions and had a large maximum at a particular energy. This resonance peak was viewed as a brief pion-proton fusion, and thus a new particle whose energy resonance determined its mass of about 1236 MeV and life-time of about 10-24 sec. Four similar delta particles in different charge states (Δ++, Δ+, Δo, Δ−) were identified. Many more resonance particles were later found at other energies. By 1960 some 40 particles had been dis-covered and theorists began to try to organize and classify them. They identified three families by


their interactions and decay products: (1) Particles that only interact weakly, such as the electron, muon and neutrino, were called leptons (Greek for light ones); (2) Strongly interacting particles with only leptons and photons as their decay products were called mesons (intermediate ones); and (3) strongly interacting particles, including nucleons and those with nucleons as their decay products, were called baryons (heavy ones). In addition to conservation of charge in particle interactions, angular momentum is also conserved in terms of the total spin of the particles, where mesons have integer units of the intrinsic spin h/2π, while leptons and baryons have half-integer spins. Baryon numbers (+1 for baryons, -1 for anti baryons, 0 for leptons and mesons) and similar lepton numbers are also conserved Strangeness number is conserved in strong inter-actions if nucleons and resonance particles are designated with zero strangeness and weakly decaying particles with non-zero strangeness. The first step toward relating the growing numbers of mesons and baryons was suggested in 1961 by Gell-Mann, who had moved to the California Institute of Technology, and inde-pendently by the Israeli physicist Yuval Ne’eman (b. 1925). They recognized that particles with the same spin and nearly equal masses could be ar-ranged by their quantum numbers (charge, baryon and strangeness) into symmetrical groups related to a special unitary “SU(3)” mathematical group. Some of these groups formed octets, leading Gell-Mann to call this approach the “eight fold way.” Several baryons of spin 3/2 fit a 10-fold triangular symmetry consisting of the 4 delta par-ticles (strangeness 0) of mass equivalent to 1236 MeV, a group of 3 sigma particles (strangeness -1) of mass 147 MeV above the deltas, and a third group of 2 particles (strangeness -2) 149 MeV higher. The symmetry was incomplete without a tenth particle at the apex with strangeness -3 about 150 MeV higher. Such a particle called the omega-minus (Ω−) was predicted from this symmetry to have a mass equivalent to 1236+147+149+150 = 1682 MeV. After an extensive search, the Ω− was discovered in February 1964 with mass 1672 MeV from tracks in a bubble chamber (liquid-hydrogen

equivalent of a cloud chamber) produced by a Brookhaven accelerator reaction:

K− + p → Ω− + K+ + K−.

Tracks corresponding to a chain of three slow decays of Ω− matched its strangeness of -3.

Quarks and Leptons Later in 1964, Murray Gell-Mann and the Russian-American physicist George Zweig (b. 1937), also at Caltech, independently proposed subunits with fractional charges (multiples of e/3) that could explain the mathematical results of the SU(3) symmetries for mesons and baryons (collectively called hadrons for “strong ones”). Gell-Mann facetiously called these subunits quarks after the line “Three quarks for Muster Mark” in James Joyce’s Finnegan’s Wake, since all baryons in his theory were made up of three quarks, while all mesons consisted of a quark-antiquark pair. The original three quarks were called u, d, and s, for up, down, and strange, and antiquarks were denoted by u, d, and s. In units of the electron charge e, the u quark charge number is +2/3, while the d and s quark charge numbers are -1/3 each. The s quark has strangeness -1, while the others have strangeness 0. All three quarks have spin 1/2 and baryon number 1/3, and all antiquarks are the negatives of their corresponding quarks. In this way, electric charge, strangeness and baryon number were conserved in all reactions except weak interactions, in which strangeness can change. Quarks (q) combine mathematically to give the correct spin, charge and strangeness for a given baryon (qqq) or meson (qq ). Thus the pro-ton is given by uud (2e/3+2e/3-e/3 = +e), and the neutron is given by udd (2e/3-e/3-e/3 = 0), each with two spins parallel and one anti parallel to give a spin of 1/2 (Figure 10.8). The Δ+ is also uud, but all three spins are parallel to give spin 3/2, revealing an essential connection between the Δ+ and the proton. The Δ++ is then uuu with parallel spins, and the Ω- is sss, giving it strangeness -3. Similarly for the mesons, π+ is ud (2e/3+e/3 = +e),


π− is ud (-2e/3-e/3 = -e), πo is dd (-e/3+e/3 = 0), and K+ is us, each with anti parallel spins for total spin 0. In a fast decay like Δ+ → p + πo, the spin of the d quark flips to change Δ+ into p, and a dd pair (πo) is created from excess mass-energy. In a slow decay like Σ+ → p + πo the s quark in the Σ+ (uus) must change its identity to a d quark, requiring more time than flipping a spin. The quark theory was highly successful in accounting for not only the SU(3) symmetries, but also such properties as masses, charges, spins, magnetic moments, and interaction probabilities of the baryons and mesons. In fact, all such particles known at the time could be accounted for by the quark theory, including several predicted by it. However, no free quarks have ever been con-firmed, even though some might have been left over from the formation of matter in the big bang and should be distinguishable by their unique fractional charge. Theory suggests that free quarks are pre-vented in much the same way that free magnetic poles are prevented when cutting a magnet pro-duces two complete magnets. For example, the energy supplied to separate a quark and antiquark in a pion generates a new quark-antiquark pair, which attach to the original antiquark and quark

respectively, producing two pions but no free quark. Direct evidence for the existence of quarks was obtained in 1969 by scattering high-energy electrons from protons at the Stanford Linear Ac-celerator Center (SLAC). The energy of scattered electrons was more than expected from simple collisions with protons, and was consistent with scattering from point-like particles within the pro-tons (Figure 10.8). New particle discoveries in the 1970s could not be fit into the original three-quark scheme, and confirmed an extension of the quark theory that was already under consideration. At Brookhaven in 1974, a proton-beryllium collision experiment directed by the MIT physicist Samuel Ting obtained a narrow resonance at 3.1 GeV, which they called the J particle. In the same year, a group at SLAC directed by Burton Richter (brother of the Earthquake-scale Richter) began to use colliding beams of electrons and positrons from oppositely circulating storage rings and found the same resonance in e+e-collisions, calling it the Ψ particle. The sharpness of the J/Ψ resonance gave its lifetime as 10-20 sec, about 1000 times longer than expected for such a massive particle. Such a “slow” decay suggested the need for a new quantum number and associated quark, in the same way that the slow decay of strange particles required the strangeness quantum number and the s quark, which took extra time in changing identity to a u during decay. At Harvard University in 1970, Sheldon Glashow and his associates had predicted a fourth quark to explain certain unobserved transitions, such as an s into a d quark. The new quark was called c for charmed, and it carried a new quantum number called charm, which is conserved in strong interactions. The c quark has spin 1/2, baryon number 1/3, charge 2/3, strangeness 0, and charm 1, while u, d, and s have charm 0. Since the J/Ψ particle was produced from an electron-positron interaction, it has baryon number 0 and could be explained as a charmed meson consisting of cc. Its decay is long compared to most strong interactions if a c converts to a u or d quark. The theory predicted several related charmed particles, which were soon discovered including the Do meson consisting of cd.

u u

d

e

proton

Figure 10.8 Quark Model of the Proton In the quark model of the proton, its properties are accounted for by two u-quarks (each of charge +2e/3) and one d-quark (charge -e/3), giving it a net charge of 2e/3+2e/3-e/3 = +e. Electron scattering from the proton is con-sistent with this model. The quarks are held together by the exchange of gluons.


Additional support for the theory that predicted the charmed quark came from symme-tries between quarks and leptons that required each to come in the same number of pairs. In 1962 at the Brookhaven National Laboratory, Leon Lederman and his associates from Columbia University did an experiment that distinguished the muon neutrino (νμ) from the electron neutrino (νe), giving two lepton pairs (e-νe and μ-νμ). They found that when the neutrinos associated with pion decay (π+→μ++νμ) interacted with neutrons they produced muons, but never electrons:

νμ+ n → p + μ-, νμ+ n →/ p + e.

An electron lepton number (+1 for leptons, -1 for anti leptons) is conserved separately from a muon lepton number, so in neutron beta decay we have:

n → p + e + νe ,

so that the electron antineutrino conserves electron lepton number, while in muon decay:

μ−→ e + νe+ νμ ,

both types must be produced to conserve both electron and muon lepton number. The existence of the e-νe lepton pair matched the u-d quark pair, and the μ−νμ lepton pair now matched the s-c quark pair, as suggested by Glashow’s theory. Evidence for a third lepton-neutrino pair was presented in 1975 by Martin Perl and a group of 35 collaborators at SLAC. In electron-positron collisions, they found 64 events of the type:

e++ e-→ μ + e + neutrinos,

which were forbidden by the electron and muon lepton conservation laws. They proposed a third lepton called the tau lepton (τ) with a mass-energy of 1.8 GeV (1,800MeV~3500me) so that:

e++ e-→ τ++ τ−,

which would then decay into muons and electrons:

τ± → e± + νe+ νe, τ± → μ± + νμ+ νμ.

A third neutrino (ντ) is to be expected, giving the τ−ντ pair and implying the existence of a third quark pair.

In 1977 at the Fermi National Accelerator in Illinois, largest in the U.S. at 500 GeV with a 4-mile main ring, a group led by Leon Lederman discovered a fifth quark called the bottom or b quark (quantum number called beauty). They used high-energy protons on a nuclear target to produce muon pairs at different energies and found resonances at 9.4, 10.0 and 10.4 GeV. These upsilon (Υ) particles were identified as different spin states of a bb meson, where the b quark has charge -e/3 and mass of about 5mp. Since theory predicts a pair of quarks, a sixth quark called the top or t quark (quantum number called truth) is expected with charge +2e/3. Fermilab announced its discovery in 1995 with a measured mass of 165mp (176GeV). In 1983 David Schramm and his associ-ates at the University of Chicago used the meas-ured ranges in the cosmic abundance of helium-4 and the density of nucleons in the universe to show that no more than three types of neutrinos can exist if they have less than 10 MeV of mass, so this may end the quark-lepton proliferation. All the quark flavors and their associated lepton generations are included in the following table:

Quarks and Leptons

Quark flavors

Chargeunit of e

Mass MeV

Lepton generations

MassMeV

u up +2/3 5 e- electron 0.511d down −1/3 8 νe neutrino ∼ 0 c charm +2/3 1,500 μ- muon 105.7s strange −1/3 160 νμ neutrino ∼ 0 t top +2/3 176K τ- tau 1777 b bottom −1/3 4,250 ντ neutrino? < 35

Unified Force Theories Along with the development of the quark theory was a parallel effort to unify the forces that act upon them, in much the same way that Max-well unified the forces of electricity and magne-tism. These forces (and their relative strength) include the strong nuclear force (S), the electro-magnetic force (S/137), the weak force (10-13×S), and the gravitational force (10-38×S). The first successful unification was the electroweak theory


of electromagnetic and weak forces, begun by Sheldon Glashow in 1961 and completed in 1967 by his high school friend Steven Weinberg (b. 1933), and independently in 1968 by the Pakistani physicist Abdus Salam (b. 1926). The electroweak theory is a quantum field theory in which particles interact by means of a field in which forces are transmitted by the exchange of particles with integer multiples of spin called bosons, named after the Indian physi-cist S. N. Bose (1894-1974) who studied their quantum statistics. It represents the merger of Paul Dirac’s quantum electrodynamics (QED) and Fermi’s theory of weak forces. Like Maxwell’s electromagnetic theory, the electroweak theory is a gauge theory, in which the equations describing physical processes remain unchanged in form by certain symmetry transformations. The equation for interacting particles can be made gauge-invariant by adding new terms, which correspond to new particles (bosons) that mediate interactions between the original particles. QED combined electromagnetic theory with special relativity and quantum theory to explain interactions between charged particles by the emission and absorption of photons (the quantum unit of the field). QED was revised in the 1940s by the independent work of Shin’ichiro Tomonaga (1906-1979) in Japan, Richard Feynman (1918-1988) at Caltech, and Julian Schwinger (b. 1918) at Harvard, using its gauge symmetry to correct for infinite charge densities that resulted from treating the electron as a point charge. Fermi’s theory was revised by Yukawa in 1935 to account for the non-zero range of the weak force by introducing the charged bosons W+ and W- to mediate the weak force. His theory showed that the boson mass is inversely proportional to its range, so the infinite range of the electromagnetic force gives photons zero mass, and the short range of the weak force requires massive W bosons. In 1956, results from kaon-decay obser-vations led the Chinese-American physicists T. D. Lee (b. 1926) and C. N. Yang (b. 1922) to predict that weak forces violate the conservation of parity, which is a reflection symmetry in which a beta decay and its mirror-image were thought to behave the same. The violation of parity was confirmed in

1957 by a group at Columbia University led by Mrs. C. S. Wu (b. 1912), when they showed that beta particles from cobalt-60 were emitted in a preferential direction relative to the spin of the cobalt nucleus. This led to a generalization of weak-interaction theory by Feynman, Gell-Mann, and Schwinger in 1958, but the revised theory failed to maintain gauge invariance. In 1961 Sheldon Glashow set up an elec-troweak gauge theory by combining QED gauge symmetry (the unitary “U(1)” group) with a rota-tion symmetry (special unitary “SU(2)” group) for the weak force to obtain a unified symmetry (the “SU(2)×U(1)” group) that required four bosons: the photon, the charged vector (non-zero spin) bosons W+ and W-, and an unanticipated neutral vector boson Z°. But this form of the electroweak theory required massless bosons for gauge symme-try. The problem of vector boson masses was solved in 1967 by Steven Weinberg at MIT, who was then able to complete the formulation of a successful electroweak theory. He used an idea suggested by Peter Higgs at the University of Edinburgh in 1964 to restore the gauge symmetry of the weak interactions at sufficiently high ener-gies by introducing a new field, and found that the W and Z bosons can acquire mass by coupling to this field. At lower energies this Higgs mechanism breaks the symmetry that unites the electro-magnetic and weak force, suggesting the possibil-ity of a fifth force in nature and its exchange par-ticle called the Higgs boson. The predicted Z° particle suggested the possibility of previously unknown neutral-current processes, such as the scattering of neutrinos by protons with no charge exchange, in which the Z° would mediate their weak interaction. Neutral-current interactions were observed in 1973 with accelerators at the Centre Européen de Recherche Nucléaire (CERN) in Geneva and at Fermilab. The electroweak theory made it possible to use neutral-current measurements to predict the masses of the W and Z particles at between 85 and 100 times the mass of the proton. In 1983 Carlo Rubbia and 135 CERN colleagues reported the discovery of all three heavy bosons from proton-antiproton collisions.


The W particles at 81 GeV (85 mp) and the Z° at 93 GeV (97 mp) rapidly decay into various quark-antiquark and lepton-antilepton pairs. These par-ticles were confirmed at Fermilab in 1985 after the completion of their proton-antiproton collider. The electroweak theory established the link between quark and lepton pairs (u, d with e, νe, etc.) and set the upper limit for the mass of the top quark at about 200 GeV, while experiments set a lower limit of about 90 GeV. The success of the electroweak theory is the first step toward a theoretical unification of the fundamental forces of nature and their associated elementary particles. The next major step would be a grand unification of the electroweak and strong forces in a unified gauge-symmetric field theory. A quantum theory for the strong force between quarks is called quantum chromodynamics (QCD) because of an additional property required of the quarks, whimsically called color. It was introduced in 1964 by Oscar Greenberg of the University of Maryland to satisfy the Pauli exclusion for particles with half-spin, which requires that no two particles with the same quantum numbers can occupy the same state. Thus three otherwise identical quarks in a baryon must be distinguishable. By assigning a different “color charge” to each, they can exist together without occupying the same quantum state. Three colors are required, say red, green, and blue, so that the six flavors of quarks come in 18 different color varieties. Since baryons do not exhibit such an additional property, it is assumed that the three quarks in any baryon must come in all three colors to render it “white” or color-neutral. The quark and antiquark in a meson must rapidly fluctuate between the three colors, which can be used to account for the observed decay rate of the neutral pion into two photons. As developed by Sheldon Glashow and others, the QCD color gauge theory requires eight massless exchange particles called gluons, which are the carriers of the strong force that “glues” quarks together. They are electrically neutral but color-charged, and are vector bosons with a spin of 1. Emission or absorption of a gluon changes the color of a quark, but not its flavor; while in a weak

interaction a quark can change its flavor, but not its color. In QCD the force between quarks increases with distance rather than decreasing, leading to the concept of quark confinement, which does not permit free quarks nor their further division into parts. The theory also predicts that in particle collisions of high enough energy, quarks and antiquarks produced in the collision will each form a jet of hadrons (mesons and baryons) accompanied by a third hadron jet produced by the emission of a gluon, a feature commonly seen in high-energy collisions. Development of grand unification theo-ries (GUTs) of the strong and electroweak forces was begun by Glashow and his colleague Howard Georgi in 1973, but was hindered by the lack of mathematical methods to cope with the greater strength of the strong interactions. However, in some gauge theories the effective strength of the strong force decreases enough at the short ranges reached in high-energy collisions to produce an “asymptotic freedom” that yields to approximation methods. At very high energies, these theories predict that the electroweak and strong forces converge to a single unified force. Such a grand unified theory predicts the pair creation of a very massive X-particle and its antiparticle to mediate transmutations between quarks and leptons at sufficiently high energies. If the X-particle exists, it would make the proton slightly unstable, with a mean lifetime of 1030 years or more. An experiment in a salt mine near Cleveland has monitored some 1033 protons in purified water for several years without any ob-served decay, implying that the proton’s lifetime is even longer than this simplified theory predicts. The ultimate goal of unification would be to in-clude the force of gravity, but this would require a quantum theory of general relativity that is yet to be achieved. Creation of the Universe Unified force theories cast new light on the earliest fractions of a second after the creation of the universe. Conditions in the earliest stages of the big bang now provide evidence to unite cosmology and elementary particle physics, relat-


ing the largest and smallest structures of the uni-verse. Extrapolation of equations describing the expansion of the universe back to the beginning of time, some 15 billion years ago, reveals a mathe-matical singularity of infinite density and tem-perature from which all of space and time appar-ently began. As the temperature fell due to the expansion of the universe, the first particles and antiparticles would begin to materialize by pair creation. At very high temperatures, particles move so fast that they escape any binding by the emerging fundamental forces, but as they cooled they would interact to produce new forms of mat-ter consistent with prevailing temperatures at each stage of expansion (Figure 10.9).

A complete unity of forces would exist during the earliest intelligible instant allowed by quantum theory (10-43 sec) when the temperature (1032K) would be high enough to equalize the strengths of their interactions. In this supergravity era, the first force to become distinct would be gravity. Grand unified theories give some insight until the time (10-34 sec) when the temperature (1027K) is low enough for the strong nuclear force to become distinct. During this grand unification era, quark-antiquark and lepton-antilepton creation and mutual annihilation would be accompanied by pair-creation of the assumed massive X-particles to mediate rapid transmutations between free quarks, leptons and their antiparticles.

electroweak

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Figure 10.9 Creation and Expansion of the Universe The earliest intelligible moment allowed by quantum theory after the big bang is about 10-43 second when all forces were probably unified. With expansion and cooling, the gravitational and strong nuclear force separate, leading to a possible inflationary expansion of the universe by a factor of at least 1050. Further cooling and expansion leads to the creation of particles out of energy and the separation of the weak and electromagnetic forces until the temperature is cool enough to permit nucleosynthesis of light elements about 3 minutes after the big bang. Nearly a million years is then required before the temperature is cool enough (about 3000K) for the plasma of charged particles and radiation to form atoms, which then condense to form the galaxies.


At the end of the grand unification era, X-particles would begin to decay slightly faster than X-antiparticles, producing slightly more quarks and leptons than their antimatter counterparts. Such an asymmetric decay violates the combined CP symmetry (charge conjugation and parity), but was first observed in 1963 by James Cronin and Val Fitch of Princeton in a small fraction of neutral kaon decays. In 1967, the Russian physicist Andrei Sakharov suggested a similar type of pro-cess in the big bang to explain why the universe now contains virtually no antimatter and only about one proton for every billion photons. A possible result of the decoupling of the strong nuclear force is a release of energy that might account for a brief exponential expansion of the universe during an inflation era, as suggested by Alan Guth at Stanford in 1979. Such a rapid inflation would prevent the formation of magnetic monopoles, predicted by grand unification theories but not presently observed. It would also smooth out initial irregularities in the universe, much like blowing up a wrinkled balloon, to account for the unusual uniformity of the cosmic background radiation. Only initial quantum fluctuations required by the uncertainty principle would remain to produce the variations in density needed to explain galaxy formation. After the separation of the strong force, W and Z particles would maintain the symmetry of electromagnetic and weak interactions. Decay of the X-particles leads to a period dominated by free quarks and leptons. About a trillionth of a second (10-12 sec) after creation, the known laws of physics begin to account for the particles that would exist in this quark era at the expansion temperature of about 10 million billion degrees (1016K), corresponding to the limit of accelerator energies at Fermilab and CERN where these laws can be tested. By this time, all observ-able space would occupy a few cubic meters at energies too high for quarks to combine into more familiar particles. At about a tenth of a nanosecond (10-10 sec) and a temperature of about a million billion degrees (1015K, 100 GeV), the electroweak transition occurs when the W and Z particles are too massive to be produced, so weak and electromagnetic forces would become distinct.

The quark era ends after about a micro-second (10-6 sec) of cosmic expansion to about 300 meters of observable space and temperatures of about 10,000 billion degrees (1013K, 1 MeV). This was cool enough for quarks to combine and form mesons and baryons. As this particle era began, there was a slight excess of particles over antiparticles of about one part in a billion due to the earlier asymmetry of X-particle decay. Near the end of this era, mutual annihilation of baryons and antibaryons into photons produced a brilliant fireball of radiation, eliminating most antibaryons and leaving a surplus of about 1 billion photons to each baryon in a sea of leptons and mesons. The lepton era began at about a tenth of a millisecond (10-4 sec), when the temperature had dropped to about a trillion degrees (1012K, 100 MeV per particle). Now photon energies were only enough to make leptons and antileptons, and electrons began to combine with protons to make neutrons. Below 1011K, there was not enough energy to produce the slightly heavier neutron, so protons began to exceed neutrons in a sequence that determined their relative availability in the early universe. At about 1 second after the creation, neutrinos had insufficient energy to inter-act with other particles and began to decouple from matter, to exist free from other particles. At about 10 billion degrees (1010 K) and 10 seconds of expansion, the temperature dropped below the threshold for producing electrons and positrons, so they began to annihilate faster than they could be recreated out of radiation, and the universe became dominated by photons. Soon, all positrons and all but one electron out of a billion disappeared, reinforcing a radiation era during which the density of radiation exceeded that of matter. At about 100 seconds after the creation the temperature was low enough for protons and neutrons to combine and nucleosynthesis began, producing about 25% helium nuclei and leaving most of the rest as protons plus traces of deuterium, lithium and beryllium nuclei. After the primeval nucleosynthesis of the light elements, lasting for about 200 seconds, one electron remained for each free or bound proton. But the universe was much


too hot for electrons to bind with nuclei to form atoms. During the radiation era, the universe expanded for about 700,000 years before it was cool enough for electrons to combine with nuclei to form stable atoms. When this happened, the lack of free electrons made the universe transparent to radiation for the first time, marking the earliest possible stage that could be observed today. The decoupling of matter and radiation occurred at about 3000 K and allowed the now neutral atoms to begin to form into clumps of matter. In this matter era, the universe continued to expand and cooled the primeval radiation until it reached the 2.726 K temperature of the present cosmic background radiation discovered in 1965. Because of small density variations in the generally smooth distribution of expanding matter, clouds of matter began to condense under the influence of gravity to form quasars and galaxies of stars. Although the big bang theory has been extremely successful in accounting for the origin of elementary particles, the cosmic abundances of the light elements, the evolution of galaxies, and the cosmic background radiation, it has raised new questions about the nature of matter itself. The very success of the big bang model in predicting the chemical composition of the early universe requires that the density of ordinary matter (protons, neutrons and electrons) be less than 10% of the critical density required to close the uni-verse at the limit of flat space. Measurements of deuterium and other light elements with the Hub-ble telescope even before it was repaired con-firmed this requirement. Luminous matter con-tributes less that 1% of the critical density. For some time, astronomers have known that galaxies rotate too fast to stay in one piece without some kind of invisible matter to hold them together (10 to 20% of critical density). The inflationary model of the big bang predicts a den-sity of the universe nearly equal to the critical density, which implies that most of the matter in the universe is not ordinary! Furthermore, recent measurements and discoveries have confirmed that the universe is close to the critical density, indicating that nearly 90% of the mass of the

universe is made up of “dark matter” that interacts with gravitation but does not radiate. The 1992, COBE satellite measurements of the background radiation revealed that it has a temperature 3.4 mK higher in the general direction of the constellations Hydra and Centaurus, and lower by the same amount in the opposite direction. The accepted interpretation of this tiny difference in temperature (shift in wavelength) is that our galaxy is moving at a speed of about 620 km/s due to larger gravitational forces in the direction of Hydra-Centaurus (COBE also detected a much smaller annual variation in temperature that correlates with the Earth’s motion around the Sun at 30 km/sec). This motion of our galaxy permits a measurement of the average density of matter over the largest spatial sample of any method yet, and indicates a value very close to the critical density. In 1993 astronomers using the ROSAT (Roentgen) satellite discovered a huge cloud of gas that was hot enough to emit x-rays and was spanning a small cluster of galaxies. They calculated that dark matter in the cluster would have to outweigh visible matter by 10 to 30 times to keep the cloud from boiling away. Astronomers are considering two possi-bilities for this apparent preponderance of invisible dark matter in the universe. One candidate for some of this matter, but probably not all of it, is in Jupiter-like objects of ordinary matter that is too cold to radiate. Such objects are called “MACHOS” (Massive Compact Halo Objects), and some evidence began to accumulate in 1993 for their existence in the halo surrounding our Milky Way galaxy as the cause for an occasional flickering of light from the Large Magellanic Cloud. The other possibility for dark matter is in the form of exotic particles called “WIMPS” (Weakly Interacting Massive Particles) that do not absorb or emit radiation. Several candidates for exotic dark matter are under consideration by theorists, mostly in the form of elementary particles left over from the early stages of the big bang. They include axions, photinos, and massive neutrinos with no associated leptons. Nearly massless axions arise from a new symmetry needed to explain the quark structure of


the neutron. The photino is the half-integer spin partner of the photon in some supersymmetry theories that require each elementary particle to have a super symmetric counterpart that differs in spin by a half-integer (sleptons, squarks, gluinos, etc.). The photino is predicted to have a mass several times as large as the proton. Although such exotic particles have not yet been observed, they resolve one other problem in cosmology. The tiny density fluctuations in the early universe that account for galaxy formation (detected by the Differential Microwave Radiome-ter on the COBE satellite) could not arise from ordinary matter before the decoupling of radiation with which it was in equilibrium. Since dark mat-ter does not interact with radiation, it could account for the primeval fluctuations that gave birth to the galaxies. Perhaps the most important discovery in recent years, announced in 1998, was new evidence from supernovae studies that the expan-sion of the universe is speeding up in spite of gravitational attraction on all the matter and dark matter of the universe. This evidence of an accel-erating universe suggests a new form of “dark energy” repelling and dominating the mass-energy content of the universe. Current measurements indicate that only 4% of the universe is ordinary matter while 22% is dark matter and 76% is dark energy. The word “dark” in these new entities is a reminder of how little is known about our universe.

REFERENCES Barrow, John D. and Joseph Silk. The Left Hand of

Creation: The Origin of the Expanding Uni-verse. New York: Basic Books, 1983.

Davies. P. C. W. The Accidental Universe, Cam-bridge: Cambridge University Press, 1982.

Harrison, Edward R. Cosmology: The Science of the Universe. Cambridge: Cambridge Univer-sity Press, 1981.

Hawking, Stephen W. A Brief History of Time. New York: Bantam Books, 1988.

Kolb, E. W. and Michael S. Turner. The Early Universe. Redwood City, CA: Addison-Wesley, 1990.

Munitz, Milton K. Space, Time and Creation: Phuilosophical Aspects of Scientific Cosmol-ogy, 2nd. ed. New York: Dover, 1981.

North, J. D. The Measure of the Universe: A His-tory of Modern Cosmology. Oxford: Clarendon Press, 1965.

Peebles, P. J. E. Principles of Physical Cosmology. Princeton, NJ: Princeton University Press, 1993.

Rees, Martin. Our Cosmic Habitat. New Jersey: Princeton University Press, 2001.

Riordan, Michael and David N. Schramm. The Shadows of Creation: Dark Matter and the Structure of the Universe. New York: W. H. Freeman, 1991.

Ross, Hugh. The Creator and the Cosmos: How the Greatest Scientific Discoveries of the Cen-tury Reveal God. Colorado Springs: NavPress, 1993.

Smith, Robert W. The Expanding Universe: Astronomy’s “Great Debate” 1900-1931. Cambridge: Cambridge University Press, 1982.

Trefil, James S. The Moment of Creation: Big Bang Physics from before the First Millisecond to the Present Universe. New York: Scribner’s 1983.

Weinberg, Steven. The First Three Minutes: A Modern View of the Origin of the Universe. New York: Bantam Books, 1977.

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Science was born in the religious sensi-bilities of the earliest civilizations. The desire to understand and appease the behavior of the gods led to the first records of regularities in the uni-verse. Even the rational achievements of the Greeks in seeking to account for these regularities did not lead them to lose sight of mind (nous) animating the universe. The Western tradition of monotheism, both Islamic and Christian, kept this vision alive, adding a new sense of the unity of God’s creation, the intelligibility of natural law, and the centrality of human purpose in the uni-verse. However, the revival of learning in the West opened up the frightening prospect of an infinite universe subjugated by mechanical laws, in which humans were insignificant if not irrele-vant. In the seventeenth century, Blaise Pascal recognized the dilemma: “For in fact what is man in nature? A Nothing in comparison with the Infinite, an All in comparison with the Nothing.” Pascal could respond in faith that, “The infinite abyss can only be filled by an infinite and immutable object, that is to say, only by God Himself.” But a century later, in the so called Enlightenment, Bernard de Fontenelle (1657-1757) caught the mood of his generation as new discoveries seemed to diminish and alienate

humanity: “Behold a universe so immense that I am lost in it. I no longer know where I am. I am just nothing at all. Our world is terrifying in its insignificance.” A few voices like that of Leibniz tried to keep alive the idea of an active universe that was more than just inert matter weighed down by causal determinism and mechanical reductionism. Their vision was revived by the discovery of new sources of energy, offering the possibility of pro-gress toward freedom from human bondage to manual labor and a new conception of develop-mental processes in nature and history. Evolu-tionary theories captured a vision of these histori-cal processes and the unity of all life, but tended to reduce humans to the whim of mechanical laws. Electrical discoveries and the field concept opened up new ways to energize and interconnect the shattered pieces of a fragmented mechanistic world. But determinism and materialism domi-nated until the 20th century. The revolutions in physics at the begin-ning of the century revealed the relation between space and time, the interconvertability of matter and energy, and the limitations of causal deter-minism at the quantum level of matter. Relativity theory broke the mechanical assumptions of abso-lute space, time and matter, and related them to the

CONCLUSION

A Living Universe

Evidence for Design and Human Significance

Conclusion • A Living Universe 263

macro world of electromagnetic and gravitational fields. In the micro world of the atom, quantum theory challenged causal determinism at the heart of matter. The new theories returned the observer to an essential role in the description of nature, ending the positivistic myth of objective detachment. Time, space and mass all depend on the motion of the observer, and the most basic ideas of location and motion must be related to human perceptions. Even in the most “objective” sciences, human consciousness has become an irreducible element. 1. THE SECRET OF LIFE Ironically, the life sciences have moved closer to the mechanistic view that seeks to reduce life to the categories of chemistry and physics. However, the new synthesis of molecular bio-chemistry has raised new questions about the relation between the parts of a living system and the emergent qualities arising at higher levels from their interactions. In his 1937 book Genetics and the Origin of the Species, Theodosius Dobzhansky (1900-1975) shifted the emphasis from individuals to a dynamic population of genes. The gene-pool concept became a giant organism in which genetic variability became as important as mutations, and selection acted upon dynamic complexes rather than atomic units. Furthermore, the enormous complexity of a single gene, to say nothing of the entire human genome consisting of over 100,000 different genes, defies all odds of random processes without severe restraints on the conditions for its formation. Early in the twentieth century, the Ger-man chemist Emil Fischer (1852-1919) showed how amino acids (more than 20) combined to form protein molecules. In the 1920s, chemists developed methods to produce protein crystals whose structure could be analyzed by x-ray dif-fraction techniques. A decade later, the American chemist Linus Pauling (b. 1901) worked out a theory of chemical bonding in protein molecules, in which the amino acids formed a folded chain called an alpha helix, as later confirmed by x-ray crystallography. These amino acid sequences reacted in the cell with protein catalysts called

enzymes to transform matter and energy. In the meantime, two types of nucleic acids known as DNA (deoxyribonucleic acid) and RNA (ribo-nucleic acid), containing the nitrogenous bases adenine (A), guanine (G), thymine (T), cytosine (C) and uracil (U), were identified in the cell. The DNA found in the cell nucleus is a combination of phosphate (acid) and sugar (deoxyribose) with the bases A, G, T and C. The RNA contains a related sugar (ribose) with the bases A, G, U and C. These molecules seemed to offer the possibility of replicating genetic information on the molecular level. In April of 1953 at the Cavendish Labo-ratories, the British biophysicist Francis Crick (b. 1916) and the American molecular biologist James D. Watson (b. 1928) unraveled the struc-ture of DNA and recognized its genetic implica-tions in what Crick called “the secret of life.” Their model of the DNA molecule was a double helix consisting of two phosphate-sugar chains twisted around each other to form a spiraling “ladder” with “rungs” made of paired nucleic bases linking the two chains by weak hydrogen bonds, allowing for the unzipping of the double helix. The pairing sequence of the nucleotide bases allows only adenine with thymine (A-T or T-A) and guanine with cytosine (G-C or C-G), so that the two chains are complementary and a long DNA molecule can contain many permutations of base sequences. In this four-letter system, the order of the bases on one chain determines the order of the complementary bases on the other. Thus when the hydrogen bonds break and the chains unzip, each forms a template for building a new chain, giving two identical DNA double helixes. In this way the genetic code is replicated on the chromosomes in the cell nucleus. When the amount of DNA has doubled, the cell divides in the mitosis process, producing two identical cells. The process for transcribing the genetic code to the amino acids of proteins in the cell was worked out in the 1960s. In protein synthesis, the DNA code for a protein is replicated on single strands of messenger RNA, which carry the genetic information to sites in the cell where


transfer RNA assembles amino acids by translat-ing the 4-letter DNA code into the 20-letter amino acid codes. In the process of replicating itself and building an organism, the gene sometimes makes “typographical errors” that cause mutations and lead to evolutionary changes. Genetic information flows in one direction only, from DNA to DNA, and from DNA to RNA to protein, but not vice versa, and thus there is no inheritance of acquired characteristics. The DNA code appears to be similar in all organisms, revealing the unity of self-regulating life on Earth. 2. THE MIRACLE OF LIFE Although the “secret of life” appears to have been reduced to molecular processes, the odds against the spontaneous assembly of a single gene are huge, and for the human genome to arise by pure chance the odds are beyond comprehen-sion. As many as 90 percent of the amino acids in a protein molecule can be changed by random mutations without altering its biological function, but a minimum of 10 percent is significant in maintaining such functions. Thus at least 180 nucleotide bases of the 1800 in the average gene are significant for the activity of each gene. Since each base in a DNA chain repre-sents one of four “letters” (A, C, G and T), which must be arranged in the proper order to carry the genetic information of a gene, the number of dif-ferent possible orders is equal to 4 raised to the number of significant bases. Thus to assemble a single gene with the required properties, it must be coded from at least 4180 = 2.3 × 10108 possible arrangements of its bases. The 4.5 billion years (1.4 × 1016 seconds) since the formation of the Earth is far too short to try this many combinations by chance. In their 1988 book on The Anthropic Cosmological Principle, John Barrow and Frank Tipler calculated that the total number of possible nucleotide base combinations over the history of the Earth is less than 1048, so the probability for the chance occurrence of a single gene is on the order of 10-108 × 1048 = 10-60. About 100 different specific genes is the minimum number needed for

a viable living organism, so the probability for spontaneous formation is (10-60)100 = 10-6000! For all of these genes to be formed at the same time and place, the probability is much lower. It is estimated that the human genome contains 110,000 different genes. The consensus of many of the leading evolutionists (T. Dobzhansky, G. Simpson, E. Mayr, et al.) is that the evolution of intelligent life is so improbable that it is unlikely to have occurred on any other planet in the uni-verse (some 1022 stars). More than forty different elements must be capable of bonding into molecules for life to be possible. A slight increase in the electromagnetic force would not permit the sharing of electrons required for such bonding, and a slight decrease would not allow atoms to hold electrons at all. If the strong nuclear force were 2% weaker, nucle-ons would not bind together and only hydrogen would exist. If this force were just 0.3% stronger, no nucleons would remain alone and only heavy elements would form, with none of the hydrogen needed for life. A small change in the weak force would have produced too much or too little helium from hydrogen in the big bang. Its precise value is also critical for the possibility of the supernova explo-sions that generate the life-essential heavy ele-ments in the cores of supergiant stars. If the gravitational force were any stronger, stars would burn too quickly to permit life. If it were weaker, stars would not be hot enough to ignite the nuclear fusion reactions that fuel the stars and produce elements heavier than hydrogen and helium. It appears that we live in a “Goldi-locks” universe in which the forces are neither too weak nor too strong, but have been tuned “just right.” The most essential element for life is car-bon, the only element that can hold together a sufficient number of amino acids to support life. After Fred Hoyle found that a 4% change in any one of the nearly equal nuclear energy resonances between helium, beryllium, carbon, and oxygen would prevent the formation of the last two in sufficient quantities for life, he concluded that, “A superintellect has monkeyed with physics, as well as with chemistry and biology.” The same is true


at every level of matter. The slight excess of mat-ter over antimatter (about one in a billion) in the early universe was just enough to form the galax-ies but not too much to prevent star formation. If the neutron were 0.1% more massive, not enough would have formed in the cooling of the big bang to produce heavy elements. If it were 0.1% less massive, so many would have formed that all stars would collapse into neutron stars or black holes. If the number of electrons were not equal to the number of protons to an accuracy of one part in 1037 or better, electromagnetic forces would have exceeded gravity enough to prevent star formation. At every level of matter, the fine tuning of the universe appears to be exactly set for the existence of life. The conditions of the universe at large are even more finely tuned for life. If the expansion rate of the universe differed by more than one part in 1055, matter would either disperse too rapidly to form galaxies and stars, or it would collapse into a black hole. If the age of the universe were much less, heavy elements would not be available from the explosion of earlier giant stars to produce planets. An increase in the electromagnetic force relative to gravity by one part in 1040 would allow only small stars to form, and a similar decrease would only permit large stars. But life requires both large stars to produce heavy elements, and small stars like the Sun that burn long enough to sustain a planet with life. One life-essential element not produced in supernova explosions is fluorine. White dwarf stars in binary systems produce fluorine, and this must happen at the right time and place to be available for use on Earth. In 1966 Iosef Shklovskii and Carl Sagan estimated that just 0.001% of all stars would be the right type and have a planet at the right distance to support life, allowing for over a million such planets in our galaxy. More recent evidence shows that they overestimated such stars and planets and ignored many other significant parameters, which lead to a very much lower probability for any life-supporting planet at all. Only 5% of galaxies are spirals like our Milky Way, in which second generation stars are produced with heavy elements.

Only about 1% of stars are near enough to super-nova eruptions to have formed with enough heavy elements, and yet far enough away to avoid their life threatening radiation. Less than 4% of stars are gravitationally independent and at the right location in a galaxy to avoid stars so close that they would disrupt planetary orbits. Only 0.001% of stars have the right mass and luminosity to provide the right conditions for planetary life. The critical requirements of a planet to support life have been recognized since at least the time of Alfred Russell Wallace (1823-1913). Life requires an environment where liquid water is stable. A change in the distance of the Earth from the Sun as small as 2% would make life impossible. If the Earth’s temperature cools by even a few degrees, snow and ice would build up and reflect more solar energy, producing even lower temperatures and runaway glaciation. A slightly warmer temperature produces more water vapor and carbon dioxide, which trap heat from the Sun and create higher temperatures, causing a runaway greenhouse effect. A decrease of 0.1% in surface gravity would allow water vapor (mol-ecular weight 18) to escape from the Earth, and a similar increase would retain too much methane (16) and ammonia (17) for life to survive. Several other physical conditions of the Earth are critical for life. A 5% decrease in the rotation of the Earth would cause too large a tem-perature difference between night and day, and a similar increase would result in wind velocities too large for advanced life. An increase in light-ning would cause excessive fire, and a decrease would fix insufficient nitrogen from the atmos-phere. A 1% decrease in the Earth’s magnetic field would permit solar particles to break down the ozone shield that protects life from ultraviolet radiation. Even the Moon is critical: if it was closer, tidal effects would be too severe; if it was further, the Earth’s magnetism would be too weak and its axial tilt would be too unstable to keep surface temperature differences small enough. In 1993, a computer simulation at the Bureau of Longitudes in Paris and another at MIT reported that the unusually large size of our Moon relative to the


Earth is necessary to stablilize the angle of the Earth’s spin axis enough to prevent wild climate fluctuations hostile to life. The Moon’s gravity is sufficient to act as an anchor, cancelling other forces on the Earth that would have caused vari-ations in tilt up to 85°. The two parameters of Sagan and Shklovskii in 1966 for a life-supporting planet have now increased to over 40, with a combined probability of less than 10-42, far too small for chance occurrence even if every star among the 1022 stars in the universe had planets. 3. THE VALUE OF LIFE Life appears to depend on extremely un-usual conditions in a very finely tuned universe. But even a universe expanding at exactly the right rate for a long enough time, with just the right balance of basic forces, containing the necessary kinds of elements, and having the right kind of planet and Sun, does not guarantee that it will produce life and intelligence. Ernst Mayr demon-strates the unpredictability of various life forms and the uniqueness of human life by using a cal-endar year to mark the equivalent dates in the fossil record since the formation of the Earth (4.5 billion years) for the origins of different organ-isms:

Origin of Earth 4.5 b.yr. January 1 Prokaryotes (one cell) 3.8 February 27 Eukaryotes (nucleus) 800 m.yr. October 28 Chordates (multicell) 555 November 17 Vertebrates 505 November 21 Mammals 247 December 12 Primates 74 December 26 Hominids 3 Dec. 31, 6 PM Homo Sapiens 30,000 yr. 11:56½ PM

(3½ minutes to present)

Mayr observes that for 3 billion years, about two-thirds of the age of the Earth, no noticeable events occur except for diversification of the eukaryotes. He concludes, “If evolutionists have learned any-thing from a detailed analysis of evolution, it is that the origin of new taxa is largely a chance event.” Given the unpredictability of evolution, the timing for the appearance of human life appears to be extremely precise, during a relatively

brief period of atmospheric stability between ice ages. The miracle of human life has begun to lead science to recognize that our existence must influence the way we understand the universe, rather than the usual argument that the existence of humanity is accidental and insignificant. In 1974 the British physicist Brandon Carter coined the term anthropic principle (from the Greek anthropos for “man”) to describe this kind of rea-soning, which argues that, “If some feature of the natural world is required for our existence, then it must have happened.” The same idea was ex-pressed in different ways by Robert Dicke and John Wheeler. This was the basis for Fred Hoyle’s prediction that the carbon nucleus must have a resonance of 7.7 MeV for sufficient quan-tities to be made in stars from the fusion of helium with a very unstable beryllium isotope, which was then discovered at 7.65 MeV. It was also recog-nized that carbon would have been destroyed by combining with helium to produce oxygen was it not for the fact that the oxygen nucleus has a resonance at 7.1187 MeV, just below the 7.1616 MeV energy of carbon + helium, so that not all carbon would fuse into oxygen. Such “coincidences” were necessary for our existence. In its strong form, the anthropic principle asserts that the universe must have the finely tuned properties that allow life to develop. The weaker form states that, from a range of possible values, physical quantities take on values that are consistent with the emergence of carbon-based life, and that the age of the universe be old enough for this to have happened. The evidence that life requires such fine tuning to beat impossible odds has been compelling enough to lead some to sug-gest the existence of numerous universes, and that ours just happened by chance to have the right conditions for life. Some have suggested that an oscillating universe has finally produced one that supports life, in the same way that enough throws of the dice will eventually give the desired result; but increasing entropy in each oscillation would not permit nearly enough to match the odds. Others have suggested that an inflationary big bang allows for the possibility of generating many uni-


verses, and that ours just happened to beat the odds. The principle of parsimony, that the simplest among equivalent explanations is the best, would seem to argue against the idea of a vast number of other universes, none of which can ever be observed. If our existence determines the design of our universe, it would seem far simpler and more rational to accept the traditional theistic principle that a Creator has designed our finely tuned uni-verse specifically to contain intelligent life that could understand and appreciate his creation. The infinitesimally small probabilities in the micro-cosm of the gene and the macrocosm of the uni-verse suggest that biology and cosmology are mutually intelligible only if the conditions for human existence were specified in advance by a Creator, who continues to pervade and guide the universe with his presence. Only a transcendent God from beyond our universe could establish the right initial con-ditions, and only his continuing immanent pres-ence in the universe could ensure the right selec-tion of events from all the possible options. In his 1988 book The Symbiotic Universe: Life and Mind in the Cosmos, George Greenstein says,

As we survey all the evidence, the thought insistently arises that some supernatural agency–or rather, Agency–must be involved. Is it possible that suddenly, without intending to, we have stumbled upon scien-tific proof of the existence of a Supreme Being? Was it God who stepped in and so providentially crafted the cosmos for our benefit? (p. 27)

Thus the miracle of life can lead us to recognize the value of life as the focus of God’s creation. His immanence in our world makes the human world rational and meaningful.

REFERENCES Barrow, John D. and Frank J. Tipler. The Anthropic

Cosmological Principle. New York: Oxford University Press, 1986.

Collins, Francis. The Language of God: A Scientist Provides Evidence for Belief. New York: Simon and Schuster, 2006

Dyson, Freeman. Infinite in all Directions. New York: Harper and Row, 1988.

Greenstein, George. Symbiotic Universe: Life and Mind in the Cosmos. New York: William Mor-row and Company, 1988.

Harrison, Edward R. Masks of the Universe. New York: Collier Books, Macmillan, 1985.

Hoyle, Fred and Chandra Wickramasinghe. Evo-lution from Space. New York: Simon and Schuster, 1981.

Jastrow, Robert. God and the Astronomers. New York: W. W. Norton, 1978.

Ross, Hugh. The Creator and the Cosmos. Colo-rado Springs: NavPress, 1993.

Shapiro, Robert. Origins. New York: Summit Books, 1986.

Thaxton, Charles B., Walter L. Bradley, and Roger Olsen. The Mystery of Life’s Origin. New York: Philosophical Library, 1984.

Yockey, Hubert P. Information Theory and Mo-lecular Biology. Cambridge: Cambridge Uni-versity Press, 1992.

268

(Primary references for names have boldface numbers.)

A abu Kamil, 59 Académie des Sciences, 179, 185, 186 Académie Royale de Sciences, 129, 130 Academy (Athens), 32-36, 40, 54, 55 Accademia dei Lincei, 89 Accademia del Cimento, 99 Achilles, 29 Adam, 3, 51, 53, 54, 61 Adams, John Couch, 123 Addison, Joseph, 121 Adelard of Bath, 63 Aepinus, Franz, 181, 182 Aether, see Ether Aetius of Antioch, 36 Agassiz, Louis, 167, 171 Air pump, 102, 107, 108 al-Ashari, 59 al-Battani (Albategnius), 58 al-Biruni, 61 al-Bitruji (Alpetrugius), 62 al-Din, Salah (Saladin), 62 al-Farabi, 59, 65 al-Farghani, 58 al-Ghazzali, 62 al-Hakam II, 59 al-Hakim, 59 al-Haytham (Alhazen), 59-61, 64, 87 al-Jabir (Geber), 58, 59 al-Khazini, 62 al-Khwarizmi, 57-58, 59, 63 al-Kindi, 58 al-Ma'mun, 57 al-Mansur, 57 al-Mardini, Masawaih, 60-61 al-Mas'udi, 59 al-Mawsili, 'Ammar, 60-61 al-Rashid, Harun, 57 al-Razi (Rhazes), 58 al-Zarkali, 62 Albertus Magnus, 65, 66 Alchemy, 58, 59, 65, 71, 92, 98, 103,

109, 127 Geber, 57

Alchemy (cont'd) Newton, 112 Paracelsus, 77 Roger Bacon, 64 sources, 50, 51 Zosimus, 51

Alcmaion, 26-27 Alcuin, 55 Aldini, Giovanni, 184 d'Alembert, Jean, 120, 121, 126 Alexander the Great, 36, 38, 40 Alphabet, 7, 17-18 Alpher, Ralph, 250 Ambrose of Milan, 52 American Philosophical Society, 180 Ampère, André-Marie, 186-87, 188, 189,

191, 197, 198 Amyntas II, 36 Anaxagoras, 30-31 Anaximander, 24-25 Anaximenes, 25 Anderson, Carl, 233, 243 Ångström, Anders, 150 Anthony, Saint, 54 Anthropic principle, 264-266 Antiperistasis, 37, 56, 67 Antipodes, 54 Apollonius, 42-43, 46, 47, 48, 84 Aquinas, Thomas, 65-66, 89

medieval synthesis, 66 proofs of God, 65

reactions of Nominalism, 66 Arago, François, 148, 185-86, 188-90 Archimedes, 34, 41-42, 43, 86, 87, 95, 96, 117 Arduino, Giovanni, 167 Aristarchus, 43-44, 46, 72 Aristophanes, 30 Aristotle, 23, 25, 27, 29, 30, 36-39, 40,

50, 54, 55, 58, 59, 61-67, 86- 88, 95, 96, 99, 103, 152

biological classification, 38 physics, 37 planetary spheres, 38 spherical earth, 37

Asclepius, 32 Astrolabe, 58

Astrology, 14-18, 40, 48, 50, 58, 64, 71 Chaldean, 50 Johannes Kepler, 82 opposition by Augustine, 53 Ptolemy, 50 Roman, 49 Tycho Brahe, 79

Astronomy (see also Big bang theory, Cosmology, Planets)

aberration of starlight, 122 atmospheric refraction, 60, 69 Babylonian, 14-16 celestial sphere, 24, 52, 86 comets, 69, 81, 82, 117, 120, 163, 236 concentric spheres, 29, 35, 38 Copernican system, 71-76, 78, 81, 82, 86, 89-91, 100, 152 crystalline spheres, 32, 52, 56, 60- 61, 64, 81 dark matter, 260, 261 distance of the moon, 46 ecliptic angle, 32, 34, 58 Egyptian, 10 epicycle model, 43, 46 galaxies, 123, 236, 237, 238-39, 260, 261 Galileo's discoveries, 86-92 heliocentric theory, 43, 71-76 Herakleides' system, 36 lunar phases and eclipses, 31 MACHOS and WIMPS, 260 meteor, 172 origin of the moon, 172 origin of the solar system, 122 period-luminosity law, 236-38, 248 precession of the equinoxes, 46, 55, 56, 59, 64, 77, 116 Ptolemaic system, 46-48, 65, 75, 89, 90, 91, 100 quasars, 251, 260 red shift, 151, 236, 237, 238-39 size and distance of sun, 44 stars vs. planets, 25, 56 supernova, 80, 86-87, 242, 251, 265 Tychonic system, 81, 89, 90, 91, 100 white dwarf stars, 265

zodiac, 14, 16, 34

INDEX

Index 269

Atomism, 39, 151 (see also Electron, Elementary particles)

atomic bomb, 245, 247 Bacon, 100 Bohr theory, 224-26, 227 Christian view, 98, 102 corpuscular philosophy, 102-3 Dalton's atoms, 131-32 Democritus, 30 Einstein, 209 Epicurean, 30, 39 Faraday, 193 Galileo and Gassendi, 98-99 Herakleides' theory, 35 Islamic view, 59 kinetic theory, 143 Lucretius, 30, 98 nuclear model, 220, 224 plum-pudding model, 216 Prout's hypothesis, 133

Augustine of Hippo, 4, 52-54, 59, 65, 91, 176-77

Avogadro, Amedeo, 132-33, 134

B Baade, Walter, 238 Bacon, Francis, 99-100, 101, 102, 120 atomism, 100

method of induction, 99-100 organized science, 100

Bacon, Roger, 60, 64, 66, 69 Baer, Karl Ernst von, 158-59 Balmer, Johann, 151, 224, 225-26 Barberini (Cardinal), 91 Barometer, 93 Baronius (Cardinal), 90 Barrow, Isaac, 109, 110, 112 Barrow, John, 264 Bartholinus, Erasmus, 106 Basil, Bishop of Caesarea, 52, 54 Bateson, William, 174 Becher, Joachim, 127 Becquerel, Antoine, 215 Becquerel, Edmond, 215 Becquerel, Henri, 204, 215, 216-19 Bede (the Venerable), 54-55 Bell, Alexander Graham, 196 Bell, Charles, 160 Bellarmine, Robert (Cardinal), 91 Beneden, Edouard van, 160 Benedetti, Giovanni, 96 Benedict of Nursia, 54 Berkeley, George, 119 Bernard, Claude, 161, 171 Bernoulli, Daniel, 121, 143 Bernoulli, Jakob, 121 Bernoulli, Johann, 121 Berthollet, Claude, 131 Berzelius, Jakob, 132, 133, 161 Bessel, Friedrich, 76, 235 Bethe, Hans, 248, 249, 250 Bhabha, Homi, 243

Bible, 17-18, 23, 53, 65, 76, 77, 89, 90, 103, 209

Biblical, 3, 4, 5, 12, 14, 52, 163 basis for science, 19-21 cosmology, 51 inerrancy, 171 view of creation, 18-21, 53, 165, 249

Bichat, Xavier, 159 Big bang theory, 235, 249-52, 257-60,

266 background radiation, 250, 251, 259, 260 inflation era, 258-59, 260 lepton era, 258-59 matter era, 250, 260 nucleosynthesis, 251-52, 258-59 particle era, 258-59 quark era, 258-59 quasars, 251 radiation era, 250, 258-59, 260

Biology, 53, 155 (see also Medicine, Physiology)

Aristotelian, 38 bacteria, 109, 162 biochemistry, 263-64 chromosomes, 160, 174 classification, 38-39, 120, 155-57 definition of species, 120 DNA and RNA, 263-64 embryology, 156, 158, 159, 171 genetics, 172-75, 263 human genome, 263, 264 mechanical view, 99, 102, 120, 160, 161, 263 meiosis, 160, 174 microscope discoveries, 108-9 mitosis, 160, 263 parthenogenesis, 153 protozoa, 109

Biot, Jean-Baptiste, 185-86 Black, Joseph, 127-28, 136-37, 138, 146

caloric theory, 137 calorimetry, 137 fixed air (carbon dioxide), 127-28 heat vs. temperature, 137 specific and latent heat, 137

Boethius, Anicius, 54 Bohr, Niels, 224-26, 241

atomic theory, 225-26, 227 complementarity principle, 231, 232 correspondence principle, 224-25, 231 hydrogen atom postulates, 224-25, 229, 230 liquid-drop model, 245

Boltwood, Bertram, 219 Boltzmann, Ludwig, 143 Bondi, Hermann, 249 Bonnet, Charles, 153, 158 Borelli, Giovanni, 99, 108 Born, Max, 231

Boscovich, Roger, 126 Bose, S. N., 256 Boulton, Matthew, 137 Boyle, Robert, 98, 102-3, 107, 108, 125,

130, 131 amber effect, 177 corpuscular philosophy, 103 definition of element, 103 gases, 103 sound, 144

Bradley, James, 122 Bradwardine, Thomas, 67 Bragg, William Henry, 204 Bragg, William Lawrence, 204 Brahe, Tycho, 79-82, 83, 84 Brand, Hennig, 103 Brethren of Purity, 59 Brewster, David, 148 British Association for the Advancement of Science, 142 Broglie, Louis de, 229, 230, 240 Bronze Age, 7 Brown, Robert, 159 Bruno, Giordano, 78-79 Bucherer, Alfred, 218 Buchner, Eduard, 162 Buckland, William Rev., 165, 166 Buffon, George Leclerc, Comte de, 120,

153, 154, 163, 180 Bunsen, Robert, 150 Buridan, John, 67, 87 Burnet, Thomas, 163 Bush, Vannevar, 246 Butler, Joseph, 157

C Cabeo, Niccolò, 177 Caccini,Tommaso, 91 Caesar, Julius, 9 Calcar, Jan Stephen van, 78 Calendar Anno Domini, 55

Gregorian, 77, 109 Julian, 9-10, 34, 64, 69, 77, 109 lunar, 9, 14, 17 luni-solar, 14, 35 solar, 9-10

Callippus, 36, 38 Caloric theory, 130-31, 137-39, 140, 142 Calvin, John, 77, 78, 79, 103 Candolle, Augustin, 156 Cannizzaro, Stanislao, 134 Capella Martianus, 49 Carlisle, Anthony, 184 Carnot, Lazare, 139 Carnot, Sadi, 139-40, 142 Carolingian Renaissance, 55 Carter, Brandon, 266 Cassini, Giovanni, 105, 107 Cassiodorus, Flavius, 49, 54 Cathode-ray tube, 203, 204, 215-16, 219 Cauchy, Augustin, 148

Index 270

Cavendish Laboratory, 199, 215, 224, 263 Cavendish, Henry, 122, 123, 128, 130,

132, 133 combining volumes, 132, 133 electric force, 182 inflammable air (hydrogen), 128 phlogiston theory of water, 128

Caventou, Joseph, 133 Cell theory, 108-9, 158-62, 171 Celsius, Anders, 137 Celsus, Aurelius, 50, 77 Censorinus, 9 CERN accelerator, 256, 259 Chadwick, James, 241 Chambers, Robert, 169 Champollion, Jean, 148 Charlemagne, 55 Charles I, 104 Charles II, 104, 110 Charleton, Walter, 102 Chatelet, Mme de, 120 Chemistry (see also Atomism, Quantum

theory, Radioactivity) catalysts and enzymes, 161-62, 263 conservation of mass, 129-30 electrochemistry, 184-85, 193 element discoveries, 103, 127, 130, 134-36, 150-51, 184, 203, 217-18, 219-21, 243-44, 246 element notation, 132 gases, 127-28 Lavoisier, 129-31 law of definite proportions, 131 molecular theory, 132-34, 228 organic chemistry, 133-35 Periodic Table, 135-36, 228 phlogiston theory, 126-28 pneumatic chemistry, 127-28 structural chemistry, 134-35 theory of valence, 134

Cheops, see Khufu Chladni, Ernst, 145 Christian IV of Denmark, 82 Christina (Grand Duchess), 90 Chromosomes, 160, 174 Clairaut, Alexis-Claude, 121 Clapeyron, B. P. E., 140, 142 Clarke, Samuel, 119 Clausius, Rudolf, 142-43

entropy, 142-43 kinetic theory, 143

Clavius, Christopher, 87-88 Cleanthes the Stoic, 43 Clement IV (Pope), 64 Clement of Alexandria, 51 COBE satellite, 251, 260, 261 Cohn, Ferdinand, 162 Colbert, Jean, 104 Collinson, Peter, 179, 180 Columbus, Christopher, 45, 69 Compton, Arthur H., 228-29, 246 Comte, Auguste, 151

Conant, James, 246 Constantine the African, 63 Constellations, 10, 14 Copernicus, Nicolaus, 43, 71-76, 78, 83,

91, 94, 170 motions of the earth, 73 planetary distances, 74 sources, 72 use of circles, 72, 75 view of the universe, 76

Cosimo II de' Medici, 89, 90 Cosmas of Alexandria, 54 Cosmology (see also Big bang theory)

age of the universe, 239, 240, 265 anthropic principle, 264, 266 Aristotelian, 38, 66 birth of galaxies, 261 creation of the universe, 239-40, 257-60 expanding universe, 234, 237, 238- 40, 265 hesitation universe, 240 infinite universe, 29-30, 35, 67, 71, 76, 78, 82, 86, 88, 92-93, 262 many universes, 267 mechanical universe, 95, 98, 101, 109, 119, 143, 176, 206 oscillating universe, 240, 266

Plato's problem, 34 relational universe, 206, 212 relativisitic, 237-38 steady-state theory, 249 system of Philolaus, 28-29 Thales, 24 unsupported earth, 25

Coulomb, Charles, 182-83, 185, 198, 225, 244

Counter-Reformation, 79, 82, 86 Cowan, Clyde, 242 Creation, 3-5, 51, 65

Biblical view, 18-21, 53 continuous, 249 evidence from thermodynamics, 143 ex nihilo, 249 Islamic view, 59, 62 meaning, purpose, 20-21 myths, 8, 16 ordered, intelligible, 20 real and good, 20 six days, 3-4, 19, 52, 120, 163, 165

Creationism, 3-4, 167 apparent-age theory, 3-4 day-age theory, 4, 165 flood geology, 4, 165 gap theory, 3, 165 progressive creation, 4 revelatory-day theory, 4

Cremonini, Cesare, 87 Crick, Francis, 263 Crô-Magnon, 7 Cromwell, Oliver, 104 Cronin, James, 259

Crookes, William, 150, 203, 219 Curie, Irène, 218, 244 Curie, Jacques, 216 Curie, Marie, 216-18

polonium and radium, 217 properties of radium, 218

Curie, Pierre, 216-18 energy of radioactivity, 218 piezoelectricity, 216

Curtis, Heber, 236 Cuvier, Georges, 153, 156-57, 165, 166,

167, 171 catastrophism, 157, 165 classification, 156 paleontology, 157

Cyclotron, 234, 246, 252 Cyril of Jerusalem, 52 Cyrus the Persian, 26

D d'Ailly (Cardinal), 69 da Vinci, Leonardo, 69 Dalton, John, 131-32, 133, 151

atomic theory, 132 caloric theory, 131 law of multiple proportions, 131 law of partial pressures, 131

Dante Alighieri, 66 Darwin, Charles, 4, 154, 167-70, 172, 206

Darwin's finches, 168 Descent of Man, 170 H.M.S. Beagle voyage, 168 natural selection, 168-69, 170, 173 Origin of Species, 169, 170 sexual selection, 169, 170 theory of coral reefs, 168

Darwin, Erasmus, 138, 154, 170 Darwin, George, 172 Davenport, Thomas, 191 Davisson, Clinton, 229 Davy, Humphry, 130,140,184-85,188, 189 Debierne, André, 217 Dee, John, 78 Defoe, Daniel, 121 Deforest, Lee, 203 Deism, 120, 143, 153, 158, 179 Demarçay, Eugéne, 217 Democritus, 29-30 Dempster, Arthur, 243 Derham, William, 144 Descartes, René, 92, 100-102, 106, 109

analytic geometry, 101 deductive method, 100 individualism, 102 mechanical universe, 101, 119 mind and matter, 101, 113 momentum, 101, 125 theory of colors, 110 vortex theory, 101-2, 111, 114, 178

Desmarest, Nicolas, 163 Determinism, 121, 154, 221, 222, 231,

232, 262, 263

Index 271

DeVries, Hugo, 174 Dicke, Robert, 251, 266 Diderot, Denis, 120, 152 Diego de Zuñiga, 79 Digges, Leonard, 78 Digges, Thomas, 78 Diodorus, Bishop of Tarsus, 52 Dionysius (pseudo), 55 Dionysius the Areopagite, 55 Diophantus, 48 Dirac, Paul, 232-33, 234, 256

antimatter, 233, 234, 241 electron-spin theory, 233 photon-exchange theory, 232, 241- 242

Dobzhansky, Theodosius, 263, 264 Domenico Maria da Novara, 72 Donne, John, 94 Doppler effect, 151, 238 Doppler, Christian, 151 Dorn, Friedrich, 218 Dryden, John, 121 Du Bois-Reymond, Emil, 161 Dufay, Charles, 179 Dumas, J. B., 134

E Earth (see also Geology)

circumference, 44-45, 47, 58, 69 climate fluctuations, 266 equatorial bulge, 106, 115-16 estimated age, 120, 142, 163, 165, 171, 220 flat, 24, 31, 52, 54 greenhouse effect, 265 ionosphere, 203 magnetic field, 265 mapping, 25, 45, 163 mass, 122 motion, 28, 43, 68, 72, 73, 76, 81, 82, 84, 91, 94, 98, 122, 207 nutation, 122 rotation, 35, 44, 61, 67, 82, 112, 172, 265 seasonal variations, 75 spherical, 27, 29, 33, 37, 52, 54, 64

Eclipses, 16, 31, 35, 69 lunar, 24, 37, 43, 46 solar, 23-24, 79

Ecliptic, 14-15, 16, 35 Ecphantos, 29, 36, 72 Eddington, Arthur, 214, 239, 248 Einstein, Albert, 209-15, 218, 230, 245

general relativity,123,212-15,237, 239 Jewish background, 209, 214 mass-energy equivalence, 212 molecular theory, 220 photoelectric effect, 223-24 photon concept, 223-24, 228 quantum probability, 232 special relativity, 119,206,210-12,218

Einstein, Albert (cont'd) static universe, 237 stimulated emission, 227 time dilation, 211-12

Einstein, Mileva Maric, 209 Electricity (see also Electron)

action at a distance, 181 amber effect, 176, 177 animal electricity, 183 conduction, 178 conservation of charge, 180 effluvia theory, 177, 178, 181 electric battery, 184, 186-87, 195 electric charge, 176, 177-83 electric circuit laws, 195 electric current, 183 electric force, 176-79, 181-83 electric voltage, 185, 186-87, 195 electrolysis, 184-85, 188, 193 Leyden jar, 179, 180, 181, 183 lightning, 176, 179, 180-81, 183 one-fluid theory, 180, 183 resistance, 187 telephone, 196 two-fluid theory, 179, 180 vacuum tubes, 203 vitreous and resinous, 179, 180

Electromagnetism, 185-91 action at a distance, 188, 200 displacement current, 197 electric generator, 190-92, 195 electric motor, 188, 191 electromagnet, 186-88, 190, 191 electromagnetic force, 186,187, 188 electromagnetic spectrum, 203-4 electromagnetic waves, 194-95, 197-200, 204, 207, 209, 210, 218, 223, 228, 229 field, 176, 187, 188, 191-94, 205, 206, 209, 262 induction, 188, 189-92, 196, 197 magnetic oscillator, 200 Maxwell's equations, 198 Oersted effect, 185 radio waves, 201-4, 209 transformer, 194

Electron, 203, 204, 208, 223, 253 beta rays, 218, 220 charge and mass, 216-17 discovery by J. J. Thomson, 215-16 exclusion principle, 227 orbiting nucleus, 220 photoelectrons, 223-24 positron, 233 quantum jump, 225, 226 spin, 227, 230, 233

Electron-volt (defined), 225 Electrophorus, 183 Electroscope, 177, 183 Elementary particles, 235, 257-60

anti-proton, 234 axions, 260 baryon, 252, 253, 254, 259

Elementary particles (cont'd) boson, 256 gluon, 257 hadron, 253, 257 lepton, 253, 255, 257, 259 magnetic monopole, 259 meson, 243, 252-54, 259 muon, 243, 253, 255 neutrino, 241-42, 249, 253, 255 neutron, 240-41 photon, 223-34, 240-42, 258-59 pion, 243, 252, 254, 257 positron, 233, 241, 243 resonances, 252, 254 W and Z particles, 256-57, 259 W-particle, 243 X-particle, 257, 258-59

Elizabeth I, 99, 177 Empedocles, 30, 31-32, 152 Encyclopedias, 49-50, 51, 54, 59, 120 Enuma Elish, 15-16 Epicureans, 30, 40, 51 Epicurus, 30, 39, 98 Epicycle, 42-43, 46 Epigenesis theory, 158 Equant, 47 Erasistratus, 50 Eratosthenes, 44-45 Ether, 33, 37, 106, 110, 111, 113, 223

Lorentz-Fitzgerald contraction, 208 luminiferous, 148, 206-8

Maxwell's theory, 197 Michelson-Morley experiment, 208

Newtonian gravity, 119 Euclid, 24, 27, 32, 34, 40-41, 57, 58, 63,

86, 100 Eudemos of Rhodes, 34 Eudoxus, 34-35, 38, 41, 62 Euler, Leonhard, 121, 146 Evolution, 4 Evolutionary theories, 153, 262

Alfred Russell Wallace, 169 Anaximander, 24 Buffon, 163 Charles Lyell, 167, 170 Darwinian Synthesis, 167-70 George Darwin, 172 Erasmus Darwin, 154 human evolution, 170 Lamarck, 154-55 Laplace, 154 mutations, 156, 173, 174, 263 neo-Darwinism, 172-75 recapitulation, 156, 171 Robert Chambers, 169 survival of the fittest, 170 theistic evolution, 4, 171

Evolutionism, 4

F Fabricius Johann, 89 Fahrenheit, Daniel, 137

Index 272

Faraday, Michael, 188-95, 191, 198 capacitor, 194 electric motor, 188-89 electro-optical effect, 195 electromagnetic induction, 189, 192 field concept, 191-94 influence on Maxwell, 196 laws of electrolysis, 193 Sandemanian church, 189

Faraday, Sarah Barnard, 189 Fatima, 59 Feddersen, William, 195 Ferdinand III, 64 Fermi, Enrico, 241-43, 250, 256

neutrino theory, 241-42, 243 neutron studies, 243 particle resonances, 252

Fermilab, 255, 256, 257, 259 Fertile Crescent, 7 Fessenden, Reginald, 203 Feyerbend, Paul, 3 Feynman, Richard, 256 Fibonacci, Leonardo, 64 Fichte, Johann, 185 Field, John, 78 Fischer, Emil, 263 Fitch, Val, 259 FitzGerald, Edward, 62 Fitzgerald, George, 200, 208, 210 Fizeau, Armand, 148, 198 Flamsteed, John, 117 Fleming, John, 203 Flemming, Walther, 160, 174 Fontenelle, Bernard de, 262 Foucault, Jean, 148, 150 Fourier, Joseph, 139, 186 Francis of Assisi, 64 Frankland, Edward, 134 Franklin, Benjamin, 179-82 lightning, 180-81

Newtonian views, 121 one-fluid theory, 180, 183 wave-theory of light, 146 Fraunhofer, Joseph von, 150 Frederick II, 64 Frederick II of Denmark, 80 Frederick the Great, 120 Fresnel, Augustin, 148 Freud, Sigmund, 206 Friedmann, Alexander, 237-38, 239, 250 Frisch, Otto, 245, 247 Füchsel, Georg, 164

G Galen, 32, 50, 57, 58, 61, 63, 77 Galilean-Newtonian transformations, 208 Galilei, Galileo, 56, 67, 86-92, 95-98, 99,

102, 105, 109, 111, 113, 126, 191 acceleration of gravity, 97, 115 Copernicanism, 89-91 mechanics, 87, 91 microscope, 108

Galilei, Galileo (cont'd) motion, 92, 95-98 projectile motion, 97 sound, 144 telescope, 87 telescopic discoveries, 88-89, 94 conflict with the Church, 89-91 the pendulum, 95 thermoscope, 137

Galilei, Vincenzio, 87 Galle, Johann, 123 Galvani, Lucia Galeazzi, 183 Galvani, Luigi, 183, 184 Galvanometer, 186, 187, 189 Gamow, George, 250, 251 Gassendi, Pierre, 98-99, 102, 144 Gay-Lussac, Joseph, 131, 132, 133 Geiger, Hans, 220 Gell-Mann, Murray, 252

eight-fold way, 253 quark theory, 253 weak interactions, 256

Geology (see also Earth) al-Biruni, 61 catastrophism, 153, 157, 167 continental drift, 172 fossils, 26, 102, 152-153, 155-157, 163-164, 166-67, 169, 266 glacial action, 165, 167 plate tectonics, 172 Plutonist school, 164-65 standard geologic column, 167 Steno's principles, 162 stratification, 166-67 uniformitarianism, 164-65, 167 Vulcanism and Neptunism, 163-64

George III, 123 Georgi, Howard, 257 Gerard of Cremona, 63 Gerbert (Pope Sylvester II), 59 Gibbs, Josiah Willard, 209 Gilbert, William, 86, 99, 111, 177 Gilgamesh, Epic of, 12 Glashow, Sheldon, 254, 255, 256, 257 Gnosticism, 51 God-of-the-gaps, 122 Goethe, Johann von, 146 Gold, Thomas, 249 Gosse, Philip Henry, 4 Goudsmit, Sam, 227 Gould, John, 168 Gray, Asa, 171 Gray, Stephen, 178-79 Great Chain of Being, 38, 55, 61, 76,

152- 53, 157 Greenberg, Oscar, 257 Greenstein, George, 267 Gregory of Nyssa, 52 Grimaldi, Francesco, 119 Grosseteste, Robert, 64 Grossmann, Marcell, 214 Groves, Leslie (General), 247

Guericke, Otto von, 102, 107-8, 177, 179 Guettard, Jean, 163 Gundisalvo, Domingo, 63 Guth, Alan, 259

H Habert de Montmor, 104 Haeckel, Ernst, 171 Hahn, Otto, 244 Hales, Stephen, 127 Hall, James, 165 Halley, Edmund, 116

comet, 69 117, 121 gravitation, 111, 112 Newton's Principia, 112

Hamilton, William, 164 Hammurabi, 12-13, 14, 15 Hanson, N. R., 3 Harriot, Thomas, 87, 89 Harvey, William, 92, 108, 158 Hauksbee, Francis, 178 Heaviside, Oliver, 203 Heisenberg, Werner, 229-30

matrix mechanics, 230 nuclear model, 242 uncertainty principle, 231, 232

Helmholtz, Hermann von, 142, 161, 201, 207

conservation of energy, 140-41, 200 electrodynamics, 200 resonance theory of hearing, 145 solar energy, 141, 248

Helmont, Jan van, 92, 129 Henry, Joseph, 190-91

electric relay and transformer, 191 electromagnet, 191 mutual and self-induction, 190, 194 oscillator, 194-95 telegraph, 190

Heraclitus of Ephesus, 25, 29 Heraclides of Pontus, 35-36, 42, 72 Herman, Robert, 250 Hermes Trismegistus, 71, 74 Hermeticism, 71, 74, 78, 109, 113 Herodotus, 11, 23 Herophilus, 50 Herschel, Caroline, 122-23, 236 Herschel, John, 150, 236 Herschel, William, 122-23, 150, 236

discovery of Uranus, 122 double stars, 122 infrared radiation, 149, 203 Milky Way galaxy, 123, 235

Hertz, Heinrich, 200, 201-2, 203, 209 discovery of radio waves, 201-2 Maxwell's theory, 201, 202 photoelectric effect, 202, 223 speed of radio waves, 201-2

Hesiod, 23 Heytesbury, William, 67 Hicetas, 29 Hieron (King), 42

Index 273

Higgs, Peter, 256 Hilaire, Geoffroy St., 156 Hipparchus, 43, 46, 47, 55, 73 Hippocrates of Chios, 32 Hippocrates of Cos, 32, 63 Hobbes, Thomas, 102 Hodge, Charles, 4, 171 Homer, 23, 24, 25 Hominids, 4

Crô-Magnon, 7 Neanderthal, 6

Hooke, Robert, 102, 107, 108-9, 110, 111, 118, 159

gravitation, 112 microscope discoveries, 108-9 Newton's Rings, 118 Royal Society, 104, 112 sound, 144 spring force, 108

Hooykaas, R., 76 Hoyle, Fred, 249, 250, 264, 266 Hubble, Edwin, 236-37

expanding universe, 238-39, 249 galaxy distances, 236-37 velocity-distance law, 238-39

Huggins, William and Margaret, 151 Humason, Milton, 238-39 Hunain ibn Ishaq, 57 Hutton, James, 164-65

geological processes, 165 Plutonist school, 164 uniformitarianism, 164

Huxley, Thomas, 170, 171 Huygens, Christiaan, 92, 95, 104-7, 109,

113 astronomy, 104-5 centrifugal force, 105, 111, 112 clock inventions, 105, 108 collisions, 106, 126 electric charge, 178 microscope optics, 108 pendulum, 105

telescope discoveries: Saturn, 104-5 speed of light, 107 wave theory of light, 106, 146, 148

Hypatia, 48

I Iatrochemistry, 77, 92, 127, 140 Iatrochemists, 102 Iatrophysics, 99 ibn Aflah, Jabir, 62 ibn Al-Nafis, 62-63, 78 ibn Bajja (Avempace), 62 ibn Rushd (Averroes), 62, 65 ibn Sina (Avicenna), 61, 77 ibn Yunis, 59 Ice Age theory, 167 Imhotep, 9 Impetus, 67, 69, 87, 96 Industrial Revolution, 125, 137, 168 Infrared radiation, 149, 203-4, 223

Infrared spectra, 151, 226 Invisible College, 103 Iron Age, 7 Ishaq ibn Hunain, 57 Isidore, Archbishop of Seville, 54 Isotope (defined), 220

J Jabir ibn Hayyan (Geber), 57 James I, 99 James II, 118 Jameson, Robert, 165 Jansky, Karl, 251 Janssen, Pierre, 150 Jeans, James, 223 Jefferson, Thomas, 121 Jenner, Edward, 162 Jesus, 51, 52 John of Holywood (Sacrobosco), 64 John of Seville, 63 Joliot-Curie, Frédéric, 218, 244 Joliot-Curie, Irène and Frédéric, 241 Joule, James, 141-42

kinetic theory, 143 mechanical equivalence of heat, 141-42 potential and electric energy, 141

Joyce, James, 253 Julius Caesar, 34 Justinian, 55

K Kant, Immanuel, 118, 123, 126, 140, 199 Kekulé, Friedrich, 134-35 Kelvin, Lord (William Thomson), 142,

196, 198 absolute temperature, 142 age of the earth, 142, 171, 219 electric oscillations, 195-96 field concept, 196 mechanical models, 200 telegraphy equation, 196 thermodynamics, 140, 142

Kennelly, Arthur, 203 Kepler, Johannes, 60, 77, 82-86, 95, 98,

99, 109, 112 microscope optics, 108 optics of the eye, 87 planetary laws, 84, 113 planetary moons, 89 telescope optics, 87

Khayyam, 'Omar, 61-62 Khufu (Cheops), 8 Kidinnu, 16 Kierkegaard, Sören, 232 Kirchhoff, Gustav, 150, 196, 201

black-body radiation, 222 circuit laws, 195 spectroscopy, 150

Kohlrausch, Rudolph, 196, 198 Koran, 57, 61, 63 Kuhn, Thomas, 3

L Lagrange, Joseph-Louis, 121 Lamarck, Jean Baptiste, 153, 154-55,

168, 169, 170 Langmuir, Irving, 228 Laplace, Pierre Simon, 121-22

determinism, 122, 154, 232 nebular hypothesis, 122, 154 speed of sound, 144-45 stability of the solar system, 122 work with Lavoisier, 130

Larmor, J., 208 Laser, 227 Laurent, Auguste, 134 Lavoisier, Antoine, 128, 129-31, 163

caloric theory, 130, 139 chemical nomenclature, 130 conservation of mass, 130 elements, 130

Lavoisier, Madame, 130, 139 Lawrence, Ernest, 234, 246 Leap year, 10, 34 Leavitt, Henrietta, 236 Lederman, Leon, 255 Lee, T. D., 256 Leeuwenhoek, Antoni van, 109, 158 Leibniz, Gottfried, 118, 125-26, 140,

154, 262 Academy of Sciences, 118 calculus, 118, 121 pre-established harmony, 126 principle of plenitude, 152 relative space and time, 119 vis viva, 125

Lemaître, Georges, 239-40, 249 Lenard, Philipp, 223-24 Lenz, Heinrich, 190-91 Leucippus, 29 Leverrier, Urbain, 123, 215 Lewis, Gilbert, 228 Leyden jar, 194, 195, 196, 201 Liebig, Justus von, 133, 134, 140, 161 Lining, John, 182 Linnaeus, Carolus, 120, 154, 156 Lippershey, Hans, 87 Lister, Joseph, 162 Livingstone, M. S., 246 Locke, John, 119-20, 121

deism, 120 theory of democracy, 120 theory of mind, 120

Lockyer, Joseph, 150-51 Lodge, Oliver, 203 Logos (reason), 25, 51, 52 Lorentz transformations, 208, 210 Lorentz, Hendrik, 208, 213 Louis the Pious, 55 Louis XIV, 104, 105 Louis XV, 120 Lucretius, 30, 98 Lunar Society, 138, 154

Index 274

Luther, Martin, 72, 77, 79, 103 Lyceum, 36, 38, 39, 40 Lyell, Charles, 166-67, 168, 169, 170 Lyman, Theodore, 226

M Mach, Ernst, 209 MacMillan, William, 237 Maestlin, Michael, 82 Magendie, François, 160-61 Magic, 7, 64, 92, 99, 100 Maimonides, Moses, 62, 65 Malpighi, Marcello, 108, 158 Malthus, Thomas Rev., 168, 169 Malus, Étienne, 147-48 Manhattan Project, 247 Marat, Jean Paul, 131 Marcellus, 41 Marconi, Guglielmo, 203 Maskelyne, Nevil, 122 Mathematics

algebra, 57, 59, 62 analytic geometry, 101 arithmetic, 57, 63, 64 Athenian, 32 Babylonian, 13 calculus, 110, 111, 117-18, 117 conic sections, 42 differential equations, 121 Diophantine equations, 48 Egyptian, 10-12 Euclidean, 40-41 Fourier theorem, 139 graphical representations, 67-68, 96 logarithms, 86 method of exhaustion, 34, 41-42 non-Euclidean, 40-41, 214 Pythagorean, 26-28 regular solids, 33, 82-83 tensor calculus, 214 Thales' geometry, 24 trigonometry, 46, 58, 59, 69 value of pi, 11, 13, 41 Zeno's paradoxes, 29

Maxwell, James Clerk, 188, 196-200, 202, 203, 206, 221, 255, 256

Christian piety, 197 displacement current, 197 electromagnetic waves, 199 field definition, 196 field equations, 198, 208-210, 232 kinetic theory, 143 light prediction, 198 mechanical model for fields, 197 Saturn's rings, 196

Maxwell, Katherine Mary Dewar, 196 Mayer, Julius Robert, 140, 142 Mayr, Ernst, 264, 266 Mays, Herbert, 190 McCosh, James, 171 McKinley, William (President), 205 Mean Speed Rule, 67, 68

Medicine (see also Physiology) Alexandrian, 50 Asclepius, 32 Egyptian, 9 Galenic, 50 germ theory of disease, 162 Hippocratic corpus, 32, 77 Imhotep, 9 Islamic, 58, 61 Paracelsus, 77 vaccination, 162

Meitner, Lise, 244 Melanchthon, Philipp, 77 Melvill, Thomas, 149 Mendel, Gregor, 173, 174 Mendeléev, Dmitri, 135-36 Mersenne, Marin, 92, 104, 144 Mertonians, 66-67 Messier, Charles, 236 Meton of Athens, 14, 35 Meyer, Lothar, 136 Michael (Byzantine Emperor), 55 Michelangelo, 87 Michell, John Rev., 122, 182 Michelson, Albert, 200, 205, 207-8

ether experiment, 208 interferometer, 207 opposition to relativity, 213 speed of light, 208

Microscope, 108-9, 158, 159, 160 Microwaves, 204, 251 Millikan, Robert, 216, 233

oil-drop experiment, 216-17 perpetual universe, 237 Planck's constant, 224

Milton, John, 94 Minkowski, Hermann, 212, 213, 214 Monasticism, 54, 56, 69 Montesquieu, Charles, 120, 121 Montmor Academy, 104 More, Henry, 113 Morgan, Thomas, 174 Moritz, Jacobi von, 191 Morley, Edward, 208 Moro, Anton, 163 Morris, Henry, 4 Morse, Samuel, 191 Moseley, Henry, 220-21 Moses, 4 Muhammad (the Prophet), 56, 59 Müller, Johannes, 160-61 Muller, John (Regiomontanus), 69 Murchison, Roderick, 166 Museum (Alexandria), 39-40, 43-44, 48 Music, 26, 59, 84, 85, 87, 121, 145 Myth, 24, 40

Babylonian, 14-16, 24 Egyptian, 8 Greek, 22, 23

N Nägeli, Karl, 160, 172-73

Nakano, T., 252 Napier, John, 86 Napoleon Bonaparte, 121, 122, 148 Natural theology, 157-58, 175 Nature philosophy, 126, 140, 143, 146,

156, 158, 159, 161, 164, 171, 185, 188

Ne'eman, Yuval, 253 Neanderthal hominids, 6 Neddermeyer, S., 243 Nemorarius, Jordanus, 64 Neolithic period, 7 Neoplatonism, 51, 52, 55, 58, 59, 61, 62,

65, 66, 71, 86 Neumann, Franz, 188 Newcomen, Thomas, 108, 137 Newlands, John, 135 Newton, Humphrey, 112 Newton, Isaac, 86, 87, 92, 99, 101, 102,

109-19, 120-25, 129, 131, 146-47, 163, 170, 178, 182, 187, 189, 191

absolute space, 113, 119, 207 centripetal acceleration, 113 centripetal force, 111, 112 comets, 117 equatorial bulge, 115 falling apple and moon, 111 fluxions, 110, 111, 117-18 laws of motion, 113, 125, 126 mechanical universe, 119 Opticks, 118, 119 planetary perturbations, 116 precession of the equinoxes, 116 Principia, 112, 113, 115, 117, 118, 144, 207 Royal Society, 110, 118 sound, 144 theory of colors, 110, 118 theory of gravity, 111 thermometer, 137 theory of tides, 116 universal gravitation, 112, 114-16

Nicholson, William, 184 Nichomachus, 36 Nicolas of Cusa (Cardinal), 68 Nietzsche, Friedrich, 206 Nishijima, K., 252 Noah's Flood, 4, 12, 157, 162-65 Nobel prize, 204, 205, 216, 217, 218,

224, 231, 243 Noddack, Ida Tacke, 243-44 Noddack, Walter, 243 Nollet, Jean-Antoine Abbé, 179 Nominalism, 66, 68 Nonconformists, 138, 181

O Ockham's razor, 66, 67 (see William of) Oersted, Hans Christian, 185, 188 Ohm, Georg Simon

law of acoustics, 145 electric resistance, 186-87, 195

Index 275

Oil-drop experiment, 216-17 Oinopides of Chios, 32 Oken, Lorenz, 158 Olbers, Heinrich, 237 Oldenburg, Henry, 104, 112 Oppenheimer, J. Robert, 247 Oresme, Nicole, 67, 96 Origen of Alexandria, 52 Orr, James, 4, 171 Osiander, Andreas, 77 Owen, Richard, 171

P Pachomios, 54 Paleolithic period, 6-7 Paley, William, 158 Pantheism, 143, 158 Papin, Denis, 108 Papyrus, 7

mathematical, Rhind, 11 medical, Ebers, 9 surgical, Edwin Smith, 9

Paracelsus, 77, 92, 99 Parallax comet, 80-81

lunar, 46, 81 stellar, 43, 76, 78, 80, 81, 88, 91, 122, 235

Paris Academy, 104, 105, 107, 109, 121 Paris Museum of Natural History, 153,

156 Parmenides, 26, 29, 30 Pascal, Blaise, 93, 262 Paschen, L. C., 226 Pasteur, Louis, 161-62

germ theory of disease, 162 opposition to evolution, 171

pasteurization, 161 vaccination, 162

Paul (Apostle), 51, 55 Paul III (Pope), 72 Paul V (Pope), 89 Pauli, Wolfgang, 227, 230, 241, 257 Pauling, Linus, 263 Payne, Cecelia, 248 Peckham, John, 66 Peebles, James, 251 Peierls, Rudolf, 245 Pelletier, Pierre, 133 Penzias, Arno, 251 Peregrinus, 64-65, 177 Pericles, 31 Periodic Table, 135-36, 228 Perl, Martin, 255 Perrin, Jean, 220 Peurbach, George, 69 Philip of Macedon, 22, 36, 40 Philo of Alexandria, 51 Philolaus, 28-29, 72 Philoponus, John, 55-56, 61, 67 Philosophical College, 104 Phlogiston theory, 126-27, 128

Physics (see also Electricity, Electro- magnetism, Elementary

particles,Quantum theory, Radioactivity)

Archimedes, 42 Aristotelian, 37 Boyle's law, 103, 127 caloric theory, 130, 131, 137, 138- 39, 140, 142 collisions, 106, 126, 143 conservation of energy, 130, 140- 43, 152, 241 energy, 126, 140, 143, 152 entropy, 142-43, 240 gas laws, 131, 143 gases, 103 heat, 127, 130, 134, 136-43, 141- 42, 145, 152 heat engines, 139, 140 Hooke's law, 108 kinetic theory, 143 magnetism, 24, 64, 86, 99, 102, 111, 176-177, 182, 185-188, 200 mechanics, 62, 64, 69, 105 motion, 67, 92, 95-98 Newton's laws of motion, 113, 232 nuclear energy, 244, 245-48 nuclear fission, 243-48 nuclear fusion, 247-49, 266 optics, 47, 58, 60, 64, 66, 87, 106, 108, 110, 118, 146-48, 199 rotation, 121 sound, 92, 102, 114, 143-45, 146 spectroscopy, 149-51 speed of light, 196, 198, 199, 202, 203, 204, 208, 209 temperature, 137, 140 thermal radiation, 222-23 thermodynamics, 140, 142-43 universal gravitation, 110, 111, 114-16, 121, 122 waves, 143-44, 152

Physiocrats, 121 Physiology (see also Biology, Medicine)

Alexandrian, 50 anatomy, 78 blood circulation, 63, 92, 108, 140 blood pressure, 127 electrophysiology, 183 experimental, 160, 161 four humors, 32 Galenic, 50 hearing, 145 mechanical view, 99, 161 respiration, 103

sight, see Vision Pixii, Hippolyte, 191 Planck, Max, 200, 223, 225, 227, 231 Planets, 16-17, 26-28, 34

concentric spheres, 34-35, 38-39, 55 discovery of new planets, 123 epicycle theory, 42-43, 46, 47, 62, 72, 74

Planets (cont'd) Kepler's laws, 84-86, 113,123, 196, 208, 214 orbit of Mercury, 214-15 perturbations, 116, 122, 123 planetary distances, 55, 58, 74, 76, 82-83, 85 planetary orbits, 79, 83-86 retrograde motions, 16, 27, 34, 35, 38, 43, 75 rings and moons of Saturn, 104-5, 196 system of Philolaus, 28 vortex theory, 101-2, 105, 111, 114

Plato, 23, 29-32, 34, 35, 36, 46, 47, 50, 51-55, 63, 71, 91, 176

four elements, 31, 33 planetary theory, 34 regular solids, 33 theory of ideas, 33, 95

Playfair, John, 165 Pliny the Elder, 49-50, 54, 100 Plotinus, 51 Plutarch, 41, 72 Poincaré, Henri, 208-9, 213 Poisson, Siméon-Denis, 185 Polo, Marco, 68 Polycrates, 26 Pope, Alexander, 121 Popov, Alexander, 203 Posidonius, 45, 47, 50 Positional number system, 13 Positivism, 3, 209, 228, 263 Powell, Cecil, 243 Precession of the equinoxes, 46 Preformation theories, 153, 158 Prévost, Pierre, 149 Price, George McCready, 4 Priestley, Joseph, 128, 129, 130, 131,

138, 181-82, 183 Proclus, 55, 58 Proust, Joseph, 131 Prout, William, 133 Ptolemy, 43, 45, 46-48, 50, 55, 58, 63,

69, 72, 73, 74, 76, 77, 81, 83, 94 Ptolemy I (Soter), 40 Ptolemy II, 40 Puritanism, 78, 79, 103-4, 138 Purkinje, Jan, 159 Pyramids, 7-9 Pythagoras, 26-28, 71, 210, 212 Pythagoreans, 26, 28, 29, 36 Pythias, 36

Q Quantum theory, 202, 205, 206, 209, 235,

239, 263 (see also Atomism) antimatter, 233-34, 259, 265 Bohr model of the atom, 224-26 Copenhagen Interpretation, 231, 232

electromagnetic force, 241-243, 255, 256, 259

Index 276

Quantum theory (cont'd) electroweak theory, 256, 257 grand unification, 257, 258-59 matter wavelength, 229 nuclear force, 242-43, 264 Pauli exclusion principle, 227, 230 photoelectric effect, 223-24 Planck's law, 221-24 principle of uncertainty, 207, 231- 32, 259 probability interpretation, 231 quantum chromodynamics (QCD), 257 quantum electrodynamics (QED), 232-33, 256 quantum numbers, 227, 230, 233, 252, 253, 254, 255 relativistic wave equation, 233 Schrödinger equation, 230, 231 supersymmetry, 260 thermal radiation, 222-23 wave-particle duality, 228-29 weak force, 241, 264

Quarks, 253-55, 257-59 Quesnay, François, 121 Quintessence, see Ether

R Radar, 204 Radioactivity, 204, 212, 222

analysis of rays, 218-19 artificial radioactivity, 241 beta decay energies, 241 decay half-life, 219 discovery by Becquerel, 215 displacement rules, 220 energy, 218 radioactive elements, 217-18 transmutation, 218 weak force, 241-42

Ramsay, William, 151 Ray, John, 120, 157 Rayleigh, Lord (J. W. Strutt), 223 Reber, Grote, 251 Reformation (Protestant), 3, 76-77, 79,

82, 103, 105 Regular solids, 33, 82-83 Reich, Ferdinand, 150 Reines, Frederick, 242 Reinhold, Erasmus, 77, 78 Relativity, general, 210, 212-15, 235, 257

bending of light, 213-14 cosmologies, 237 gravitational field theory, 214-15 principle of equivalence, 213 space curvature, 214-15

Relativity, special, 200, 205, 206, 208, 222, 235, 262

invariant speed of light, 210 length contraction, 210 Lorentz-Fitzgerald contraction, 208 mass-energy equivalence, 212

Relativity, special (cont'd) Michelson-Morley experiment, 208, 209, 210 postulates, 210 relativistic mass, 212, 218 simultaneity, 211 time dilation, 210, 212 twin paradox, 211

Religion, 2-3, 6 Babylonian, 14-17 Christianity, 3-5, 51-56, 63-69, 79 Darwinism, 170-71 Egytian, 7-8 Greco-Roman, 26, 38, 39, 50-51 Hebrew, 18-21 Islamic, 56-63

Remak, Robert, 160 Rheticus, Georg Joachim, 76 Richer, Jean, 107, 116 Richmann, G. W., 180-81 Richter, Burton, 254 Richter, Hieronymus, 150 Riemann, Bernard, 214 Ritter, Johann, 149, 203 Robert of Chester, 63 Robinet, Jean Baptiste, 153, 155 Robison, John, 182, 183 Roemer, Ole, 107, 118 Roentgen, Wilhelm, 204, 215 Romanticism, 125, 126, 143, 185 Roosevelt, Franklin (President), 245 ROSAT (Roentgen) satellite, 260 Rothmann, Christopher, 81 Rowland, Henry, 200 Royal Institution, 139, 188 Royal Society, 100, 104-5, 109-10, 112,

118-19, 127, 142, 146, 158, 162, 164, 178-80, 184, 187, 189, 192

Rubbia, Carlo, 256 Rudolph II, 82, 84, 86 Rumford, Count (Benjamin Thompson),

138-39, 140 Rutherford, Daniel, 128 Rutherford, Ernest, 218-21, 241

alpha and beta rays, 218 alpha rays identified, 219 neutron proposal, 240 nuclear model, 220-21, 224 radioactive decay, 219-20

Rydberg, Johannes, 225-26

S Sagan, Carl, 265, 266 Sakharov, Andrei, 259 Salam, Abdus, 256 Sandage, Allan, 238, 251 Sandeman, Robert, 189 Sargon II, 16 Sauveur, Joseph, 145 Savart, Félix, 185 Scheele, Carl, 128 Scheiner, Christopher, 89

Schelling, Friedrich, 140, 185 Schiaparelli, Giovanni, 34 Schleiden, Matthias, 159, 171 Schmidt, Maarten, 251 Schramm, David, 255 Schrödinger, Erwin, 230-31, 242 Schwann, Theodor, 159, 161 Schwinger, Julian, 256 Science (see also Positivism)

applied, 20-21, 49 Aristotelian, 36, 65 Baconian, 99-100, 104, 118, 120, 168 Biblical basis, 19 Byzantine, 55-56 Cartesian, 100-102 Christian view, 56, 79, 119, 184 definition, 1 experimental, 19-20, 64 Islamic, 56 Islamic after AD 1000, 59-63 Islamic before AD 1000, 57-59 Platonic, 32-34 rational basis, 25, 53 Roman, 49 theoretical, 20

Scofield Reference Bible, 3 Scotus, John (Erigena), 55 Sedgwick, Adam Rev., 166, 167, 168 Seleucus the Babylonian, 43 Servetus, Michael, 78 Seti I, 10 Seven liberal arts, 49, 54 Seven-day week, 17, 18 Shakespeare, 87 Shapley, Harlow, 236, 239 Shklovskii, Iosef, 265, 266 Simplicius, 55, 56 Simpson, Gaylord, 264 Sitter, Willem de, 237 Sizzi, Francesco, 89 SLAC accelerator, 254, 255 Slipher, Vesto, 236, 237 Smith, Adam, 121 Smith, William, 166 Smithsonian Institution, 195 Snell, Willebrord, 87, 118 Socrates, 23, 30, 32 Soddy, Frederick, 219-20 Sommerfeld, Arnold, 227, 230 Sophism, 30 Sophocles, 74 Sosigenes, 9 Space (see also Cosmology)

absolute, 119, 207, 210, 262 expanding, 238-240

Cartesian plenum, 101 contraction, 210 curved, 41, 214, 237-38 ether theory, 197, 206-208 finite, 29, 37 finite and closed, 237

Index 277

Space (cont'd) flat and static, 237 infinite, 30, 67, 71, 76, 78, 86, 113, 119 open and expanding, 238 reality, 20 relative, 119 relativistic, 212, 214 sensorium of God, 113 subjective, 123

Spallanzani, Lazzaro, 161 Spectroscope, 150, 227, 248 Spence, Mr., 179 Spencer, Herbert, 170 Spontaneous generation, 92, 155, 161,

167, 171 St. Petersburg Academy of Sciences, 180 Stahl, Georg Ernst, 127 Steam engine, 108, 137, 139, 142 Steno, Nicolaus, 102, 162, 167 Stevin, Simon, 96 Stoicism, 43, 50, 51, 53 Stoics, 39, 40, 49, 51 Stokes, George, 148 Stonehenge, 7 Strato of Lampsacus, 39, 40, 50 Strong, A. H., 171-72 Strong, Augustus, 4 Sturgeon, William, 187-88 Swammerdam, Jan, 158 Swift, Jonathan, 109 Sylvius, Franciscus, 99 Szilard, Leo, 245

T Tartaglia, Niccolo, 97 Teleology, 36, 66 Telescope, 86-89, 92, 104, 108, 110, 122,

151, 236, 238, 260 Teller, Edward, 247 Tempier (Bishop of Paris), 65 Thales, 23-24, 26, 176 Theano, 26 Theaetetus, 33 Theodoric the Ostrogoth, 54 Theodoric of Freiberg, 66 Theon of Alexandria, 48 Theophrastus, 25, 38-39 Thomas, St., see Aquinas Thomism, 66 Thomson, George P., 229 Thomson, J. J., 215-16, 218, 224, 229 Tides, 45, 50, 53, 55, 64, 91, 116, 172

Time, 34 absolute, 119, 207, 209, 210, 262 cyclical, 21, 56 gravitational effect, 213 infinite, 37 linear, 53 measurement, 105 relative, 119 relativistic, 206, 208, 212, 214 subjective, 123 thermodynamic, 143, 152 time dilation, 211-12

Ting, Samuel, 254 Tipler, Frank, 264 Titian, 78 Tolman, Richard, 240 Tomonaga, Shin'ichiro, 256 Torricelli, Evangelista, 92, 98, 108 Toscanelli, Paolo, 69 Toulmin, Stephen, 3 Turkevich, A., 250

U Uhlenbeck, George, 227 Ultraviolet catastrophe, 223 Ultraviolet radiation, 149, 202-4, 223 Ultraviolet spectra, 151, 226 Urban VIII (Pope), 91 Urey, Harold, 241, 246

V Varro, Marcus Terentius, 49 Vasco da Gama, 69 Vesalius, Andreas, 77-78 Villard, Paul, 204, 218 Virchow, Rudolf, 160 Vis mortua, 125 Vis viva, 106, 125-26, 140 Vision, 32

accomodation and astigmatism, 146 extramission theory, 41, 47 intromission theory, 60, 64, 87 optic nerve, 161 three-color theory, 146, 196

Vitalism, 133, 134, 140, 141, 158, 160-62 Volta, Alessandro, 183-84, 188, 190 Voltaire, Jean François de, 120, 152

W W-particle, see Elementary particles Wallace, Alfred Russell, 169, 170, 265 Wallis, John, 106 Warfield, Benjamin, 4, 171

Watson, James D., 263 Watt, James, 137-38 Weber, Wilhelm, 188, 196, 198, 200 Wedgwood, Josiah, 154 Wegener, Alfred, 172 Weinberg, Steven, 256 Weismann, August, 173-74 Werner, Abraham, 164 Wheatstone, Charles, 191, 195 Wheeler, John, 245, 266 Whitcomb, John, 4 White, Ellen G., 4 Wien, Wilhelm, 222-23 Wigner, Eugene, 245 Wilberforce, Samuel, 171 Wilkins, John, 104 William of Ockham, 66 Wilson, Robert W., 251 Wöhler, Friedrich, 133-34 Wolff, Caspar Friedrich, 158 Wollaston, William, 150, 188 Woodward, John, 163 Wren, Christopher, 106, 111, 112 Wright, George Frederick, 171 Wright, Thomas, 123 Wu, C. S., 256

X X-particle, see Elementary particles X-rays, 204, 215, 218, 228 Xenophanes, 25-26, 29

Y Yang, C. N., 256 Young, Thomas, 126, 146-48

Egyptian hieroglyphics, 148 energy, 126, 140 light a transverse wave, 148 theories of vision, 146 wavelength of light, 146

Yukawa, Hideki, 242-43, 252, 256

Z Z-particle, see Elementary particles Zeeman, Pieter, 227 Zeno of Cition, 39 Zeno of Elea, 29 Zeno's paradoxes, 118 Ziggurats, 14 Zodiac, 14, 16, 34 Zoser, 9 Zosimos, 51 Zweig, George, 253

Index 269

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