CONTENTS. 



CHAPTER I. 



GENERAL NOTIONS. THE PRINCIPLE OF CONSERVATION 



OF EXTENSION-IN-PHASE. 



PAGE 



Hamilton's equations of motion 3-5 



Ensemble of systems distributed in phase 5 



Extension-in-phase, density-in-phase 6 



Fundamental equation of statistical mechanics 6-8 



Condition of statistical equilibrium 8 



Principle of conservation of density-in-phase 9 



Principle of conservation of extension-in-phase 10 



Analogy in hydrodynamics 11 



Extension-in-phase is an invariant 11-13 



Dimensions of extension-in-phase 13 



Various analytical expressions of the principle 13-15 



Coefficient and index of probability of phase 16 



Principle of conservation of probability of phase 17, 18 



Dimensions of coefficient of probability of phase 19 



CHAPTER II. 



APPLICATION OF THE PRINCIPLE OF CONSERVATION OF 

 EXTENSION-IN-PHASE TO THE THEORY OF ERRORS. 



Approximate expression for the index of probability of phase . 20, 21 

 Application of the principle of conservation of probability of phase 

 to the constants of this expression 21-25 



CHAPTER III. 



APPLICATION OF THE PRINCIPLE OF CONSERVATION OF 

 EXTENSION-IN-PHASE TO THE INTEGRATION OF THE 

 DIFFERENTIAL EQUATIONS OF MOTION. 



Case in which the forces are function of the coordinates alone . 26-29 

 Case in which the forces are functions of the coordinates with the 

 time 30, 31 



