Chapter XIII: Electrodynamics 184

Ampère's Theory 184
Closed Currents 185
Action of a Closed Current on a Portion of Current 186
Continuous Rotations 187
Mutual Action of Two Open Currents 189
Induction 190
Theory of Helmholtz 191
Difficulties Raised by these Theories 193
Maxwell's Theory 193
Rowland's Experiment 194
The Theory of Lorentz 196

THE VALUE OF SCIENCE

Translator's Introduction 201
Does the Scientist Create Science? 201
The Mind Dispelling Optical Illusions 202
Euclid not Necessary 202
Without Hypotheses, no Science 203
What Outcome? 203
Introduction 205

PART I. _The Mathematical Sciences_

CHAPTER I.--Intuition and Logic in Mathematics 210

CHAPTER II.--The Measure of Time 223

CHAPTER III.--The Notion of Space 235
Qualitative Geometry 238
The Physical Continuum of Several Dimensions 240
The Notion of Point 244
The Notion of Displacement 247
Visual Space 252

CHAPTER IV.--Space and its Three Dimensions 256
The Group of Displacements 256
Identity of Two Points 259
Tactile Space 264
Identity of the Different Spaces 268
Space and Empiricism 271
Rôle of the Semicircular Canals 276

PART II. _The Physical Sciences_

CHAPTER V.--Analysis and Physics 279

CHAPTER VI.--Astronomy 289

CHAPTER VII.--The History of Mathematical Physics 297
The Physics of Central Forces 297
The Physics of the Principles 299

CHAPTER VIII.--The Present Crisis in Physics 303
The New Crisis 303
Carnot's Principle 303
The Principle of Relativity 305
Newton's Principle 308
Lavoisier's Principle 310
Mayer's Principle 312

CHAPTER IX.--The Future of Mathematical Physics 314
The Principles and Experiment 314
The Rôle of the Analyst 314
Aberration and Astronomy 315
Electrons and Spectra 316
Conventions preceding Experiment 317
Future Mathematical Physics 319

PART III. _The Objective Value of Science_

CHAPTER X.--Is Science Artificial? 321
The Philosophy of LeRoy 321
Science, Rule of Action 323
The Crude Fact and the Scientific Fact 325
Nominalism and the Universal Invariant 333

CHAPTER XI.--Science and Reality 340
Contingence and Determinism 340
Objectivity of Science 347
The Rotation of the Earth 353
Science for Its Own Sake 354

SCIENCE AND METHOD

Introduction 359

BOOK I. _Science and the Scientist_

CHAPTER I.--The Choice of Facts 362

CHAPTER II.--The Future of Mathematics 369

CHAPTER III.--Mathematical Creation 383

CHAPTER IV.--Chance 395

BOOK II. _Mathematical Reasoning_

CHAPTER I.--The Relativity of Space 413

CHAPTER II.--Mathematical Definitions and Teaching 430

CHAPTER III.--Mathematics and Logic 448

CHAPTER IV.--The New Logics 460

CHAPTER V.--The Latest Efforts of the Logisticians 472

BOOK III. _The New Mechanics_

CHAPTER I.--Mechanics and Radium 486

CHAPTER II.--Mechanics and Optics 496

CHAPTER III.--The New Mechanics and Astronomy 512

BOOK IV. _Astronomic Science_

CHAPTER I.--The Milky Way and the Theory of Gases 523