vi CONTENTS OF THE SECOND VOLUME. 



CHAPTER V. GENERALIZATION OF THE PRINCIPLES OF 

 MECHANICS. 



PAGE 



Sect. 1. Generalization of the Second Law of Motion. Cen- 

 tral Forces 73 



Sect. 2. Generalization of the Third Law of Motion. Cen- 

 ter of Oscillation. Huyghens . 80 



CHAPTER VI. SEQUEL OF THE GENERALIZATION OF THE 

 PRINCIPLES OF MECHANICS. PERIOD OF MATHEMATICAL 



DEDUCTION. ANALYTICAL MECHANICS. . . 92 



1. Geometrieal Mechanics. Newton, c. ... 93 



2. Analytical Mechanics. Euler ..... 94 



3. Mechanical Problems 95 



4. D'Alembert's Principle ...... 97 



5. Motion in Resisting Media. Ballistics ... 98 



6. Constellation of Mathematicians . . . .100 



7. The Problem of Three Bodies . . . . 101 



8. Mecanique Celeste, &c 108 



9. Precession. Motion of Rigid Bodies . . . 109 



10. Vibrating Strings Ill 



11. Equilibrium of Fluids. Figure of the Earth. Tides 113 



12. Capillary Action . . . . . . . 115 



13. Motion of Fluids 116 



14. Various General Mechanical Principles . . 120 



15. Analytical Generality. Connexion of Statics and Dy- 



namics .... . 121 



BOOK VII. 

 HISTORY OF PHYSICAL ASTRONOMY. 



CHAPTER 1. PRELUDE TO THE INDUCTIVE EPOCH OF 



NEWTON . . . .135 



CHAPTER II. THE INDUCTIVE EPOCH OF NEWTON. DIS- 

 COVERY OF THE UNIVERSAL GRAVITATION OF MATTER, 

 ACCORDING TO THE LAW OF THE INVERSE SQUARE OF 

 THE DISTANCE . . . . . . . .160 



1. Sun's Force on Different Planets .... 161 



2. Force in Different Points of an Orbit 162 



