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The contents of the book are as follows CHAPTER I. GENERAL NOTIONS. THE PRINCIPLE OF CONSERVATION OF EXTENSION-IN-PHASE. CHAPTER II. APPLICATION OF THE PRINCIPLE OF CONSERVATION OF EXTENSION-IN-PHASE TO THE THEORY OF ERRORS. CHAPTER III. APPLICATION OF THE PRINCIPLE OF CONSERVATION OF EXTENSION-IN-PHASE TO THE INTEGRATION OF THE DIFFERENTIAL EQUATIONS OF MOTION. CHAPTER IV. ON THE DISTRIBUTION-IN-PHASE CALLED CANONICAL, IN WHICH THE INDEX OF PROBABILITY IS A LINEAR FUNCTION OF THE ENERGY. CHAPTER V. AVERAGE VALUES IN A CANONICAL ENSEMBLE OF SYSTEMS. CHAPTER VI. EXTENSION-IN-CONFIGURATION AND EXTENSION-IN-VELOCITY. CHAPTER VII. FARTHER DISCUSSION OF AVERAGES IN A CANONICAL ENSEMBLE OF SYSTEMS. CHAPTER VIII. ON CERTAIN IMPORTANT FUNCTIONS OF THE ENERGIES OF A SYSTEM. CHAPTER IX. THE FUNCTION ¿ AND THE CANONICAL DISTRIBUTION. CHAPTER X. ON A DISTRIBUTION IN PHASE CALLED MICROCANONICAL IN WHICH ALL THE SYSTEMS HAVE THE SAME ENERGY. CHAPTER XI. MAXIMUM AND MINIMUM PROPERTIES OF VARIOUS DISTRIBUTIONS IN PHASE CHAPTER XII. ON THE MOTION OF SYSTEMS AND ENSEMBLES OF SYSTEMS THROUGH LONG PERIODS OF TIME. CHAPTER XIII. EFFECT OF VARIOUS PROCESSES ON AN ENSEMBLE OF SYSTEMS. CHAPTER XIV. DISCUSSION OF THERMODYNAMIC ANALOGIES CHAPTER XV. SYSTEMS COMPOSED OF MOLECULES