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_