Chapter VI: Sequel to the Generalization of the Principles of

MECHANICS.--PERIOD OF MATHEMATICAL DEDUCTION.--ANALYTICAL MECHANICS. 362

1. Geometrical Mechanics.--Newton, &c. 363 2. Analytical Mechanics.--Euler. 363 3. Mechanical Problems. 364 4. D'Alembert's Principle. 365 5. Motion in Resisting Media.--Ballistics. 365 6. Constellation of Mathematicians. 366 7. The Problem of Three Bodies. 367 8. Mécanique Céleste, &c. 371 9. Precession.--Motion of Rigid Bodies. 374 10. Vibrating Strings. 375 11. Equilibrium of Fluids.--Figure of the Earth.--Tides. 376 12. Capillary Action. 377 13. Motion of Fluids. 378 14. Various General Mechanical Principles. 380 15. Analytical Generality.--Connection of Statics and Dynamics. 381 {19}

BOOK VII.

HISTORY OF PHYSICAL ASTRONOMY.

CHAPTER I.--PRELUDE TO THE INDUCTIVE EPOCH OF NEWTON. 385

CHAPTER II.--THE INDUCTIVE EPOCH OF NEWTON.--DISCOVERY OF THE UNIVERSAL GRAVITATION OF MATTER, ACCORDING TO THE LAW OF THE INVERSE SQUARE OF THE DISTANCE. 399

1. Sun's Force on Different Planets. 399 2. Force in Different Points of an Orbit. 400 3. Moon's Gravity to the Earth. 402 4. Mutual Attraction of all the Celestial Bodies. 406 5. " " " Particles of Matter. 411 Reflections on the Discovery. 414 Character of Newton. 416

CHAPTER III.--SEQUEL TO THE EPOCH OF NEWTON.--RECEPTION OF THE NEWTONIAN THEORY.

_Sect._ 1. General Remarks. 420 _Sect._ 2. Reception of the Newtonian Theory in England. 421 _Sect._ 3. " " " " Abroad. 429

CHAPTER IV.--SEQUEL TO THE EPOCH OF NEWTON, CONTINUED. VERIFICATION AND COMPLETION OF THE NEWTONIAN THEORY.

_Sect._ 1. Division of the Subject. 433 _Sect._ 2. Application of the Newtonian Theory to the Moon. 434 _Sect._ 3. " " " " Planets, Satellites, and Earth. 438 _Sect._ 4. Application of the Newtonian Theory to Secular Inequalities. 444 _Sect._ 5. " " " " to the new Planets.446 _Sect._ 6. " " " " to Comets. 449 _Sect._ 7. " " " " to the Figure of the Earth. 452 _Sect._ 8. Confirmation of the Newtonian Theory by Experiments on Attraction. 456 _Sect._ 9. Application of the Newtonian Theory to the Tides. 457

CHAPTER V.--DISCOVERIES ADDED TO THE NEWTONIAN THEORY.

_Sect._ 1. Tables of Astronomical Refraction. 462 _Sect._ 2. Discovery of the Velocity of Light.--Römer. 463 {20} _Sect._ 3. Discovery of Aberration.--Bradley. 464 _Sect._ 4. Discovery of Nutation. 465 _Sect._ 5. Discovery of the Laws of Double Stars.--The Two Herschels. 467

CHAPTER VI.--THE INSTRUMENTS AND AIDS OF ASTRONOMY DURING THE NEWTONIAN PERIOD.

_Sect._ 1. Instruments. 470 _Sect._ 2. Observatories. 476 _Sect._ 3. Scientific Societies. 478 _Sect._ 4. Patrons of Astronomy. 479 _Sect._ 5. Astronomical Expeditions. 480 _Sect._ 6. Present State of Astronomy. 481

_ADDITIONS TO THE THIRD EDITION._

INTRODUCTION 489

BOOK I.--THE GREEK SCHOOL PHILOSOPHY.

THE GREEK SCHOOLS.

The Platonic Doctrine of Ideas. 491

FAILURE OF THE GREEK PHYSICAL PHILOSOPHY.

Bacon's Remarks on the Greeks. 494 Aristotle's Account of the Rainbow. 495

BOOK II.--THE PHYSICAL SCIENCES IN ANCIENT GREECE.

Plato's Timæus and Republic. 497 Hero of Alexandria. 501

BOOK III.--THE GREEK ASTRONOMY.

Introduction. 503

EARLIEST STAGES OF ASTRONOMY.

The Globular Form of the Earth. 505 The Heliocentric System among the Ancients. 506 The Eclipse of Thales. 508 {21}

BOOK IV.--PHYSICAL SCIENCE IN THE MIDDLE AGES.

General Remarks. 511

PROGRESS IN THE MIDDLE AGES.

Thomas Aquinas. 512 Roger Bacon. 512

BOOK V.--FORMAL ASTRONOMY.

PRELUDE TO COPERNICUS.

Nicolas of Cus. 523

THE COPERNICAN THEORY.

The Moon's Rotation. 524 M. Foucault's Experiments. 525

SEQUEL TO COPERNICUS.

English Copernicans. 526 Giordano Bruno. 530 Did Francis Bacon reject the Copernican Doctrine? 530 Kepler persecuted. 532 The Papal Edicts against the Copernican System repealed. 534

BOOK VI.--MECHANICS.

PRINCIPLES AND PROBLEMS.

Significance of Analytical Mechanics. 536 Strength of Materials. 538 Roofs--Arches--Vaults. 541