vi CONTENTS OF THE SECOND VOLUME. 



CHAPTER V. GENERALIZATION OF THE PRINCIPLES OF 

 MECHANICS. 



PACK 



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. Geometrical 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 OP 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 



