CHAPTER V.-GENERALISATION OF THE PRINCIPLES OF

MECHANICS.

Page

Sect. 1. Generalisation of the Second Law of Motion. Central Forces

72

Sect. 2. Generalisation of the Third Law of Motion. Centre of Oscillation. Huyghens.

CHAPTER VI.-SEQUEL OF THE GENERALISATION OF THE PRINCIPLES OF MECHANICS. PERIOD OF MATHEMATICAL DEDUC

4. D'Alembert's Principle

5. Motion in Resisting Media. Ballistics

6. Constellation of Mathematicians.

79

91

92

93

94

96

97

98

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

111

CHAPTER II.-THE INDUCTIVE EPOCH OF NEWTON. DISCO-
VERY OF THE UNIVERSAL GRAVITATION OF MATTER, AC-
CORDING TO THE LAW OF THE INVERSE SQUARE OF THE
DISTANCE

1. Sun's Force on Different Planets .

2. Force in Different Points of an Orbit

127

152

153

154

CHAPTER III.-SEQUEL TO THE EPOCH OF NEWTON. RECEP

TION OF THE NEWTONIAN THEORY.

Sect. 2. Reception of the Newtonian Theory in England. 190 Sect. 3.

abroad

198

CHAPTER IV.-SEQUEL TO THE EPOCH OF NEWTON, CONTI-
NUED. VERIFICATION AND COMPLETION OF THE NEWTO-
NIAN THEORY.

Sect. 1. Division of the Subject

206

Sect. 2. Application of the Newtonian Theory to the Moon 207

Sect. 3.

Sect. 4.

to Secular

Inequalities

225

240

to Comets. 236

to the Figure

Sect. 8. Confirmation of the Newtonian Theory by Experi

245

Sect. 9. Application of the Newtonian Theory to the Tides 246

CHAPTER V.-DISCOVERIES ADDED TO THE NEWTONIAN

Sect. 1. Tables of Astronomical Refraction

THEORY.

254

Sect. 2. Discovery of the Velocity of Light. Römer

257

Sect. 4. Discovery of Nutation

Sect. 3. Discovery of Aberration. Bradley

Sect. 5. Discovery of the Laws of Double Stars. The two

258

CHAPTER VI.-THE INSTRUMENTS AND AIDS OF ASTRONOMY

DURING THE NEWTONIAN PERIOD.

CHAPTER I.-PRELUDE TO THE SOLUTION OF PROBLEMS IN

Page

266

275

278

280

282

283

293

ACOUSTICS

295

CHAPTER II.-PROBLEM OF THE VIBRATIONS OF STRINGS .

302

CHAPTER III.-PROBLEM OF THE PROPAGATION OF SOUND

310

CHAPTER IV.-PROBLEM OF DIFFERENT SOUNDS OF THE

SAME STRING

CHAPTER V.-PROBLEM OF THE SOUNDS OF PIPES

317

321

CHAPTER VI.-PROBLEM OF DIFFERENT MODES OF VIBRATION

OF BODIES IN GENERAL

325

BOOK IX.

HISTORY OF OPTICS, FORMAL AND PHYSICAL.

Introduction

FORMAL OPTICS.

CHAPTER I.-PRIMARY INDUCTION OF OPTICS. RAYS OF

LIGHT AND LAWS OF REFLECTION

CHAPTER II.-DISCOVERY OF THE LAW OF REFRACTION

344

Page

CHAPTER III.-DISCOVERY OF THE LAW OF DISPERSION
BY REFRACTION

349

CHAPTER IV.-DISCOVERY OF ACHROMATISM

362

CHAPTER V.-DISCOVERY OF THE LAWS OF DOUBLE RE

CHAPTER VI.-DISCOVERY OF THE LAWS OF POLARIZATION 372

CHAPTER VII.-DISCOVERY OF THE LAWS OF THE COLOURS

CHAPTER VIII.-ATTEMPTS TO DISCOVER THE LAWS OF

OTHER PHENOMENA

381

CHAPTER IX.-DISCOVERY OF THE LAWS OF PHENOMENA
OF DIPOLARIZED LIGHT

384

PHYSICAL OPTICS.

CHAPTER X.-PRELUDE TO THE EPOCH OF YOUNG AND

FRESNEL

CHAPTER XI.-EPOCH OF YOUNG AND FRESNEL.

Sect. 1. Introduction

390

402

Sect. 2. Explanation of the Periodical Colours of Thin
Plates and Shadows by the Undulatory Theory 404
Sect. 3. Explanation of Double Refraction by the Undu-

CHAPTER XII.-SEQUEL TO THE EPOCH OF YOUNG AND
FRESNEL. RECEPTION OF THE UNDULATORY THEORY

CHAPTER XIII.-CONFIRMATION AND EXTENSION OF THE

UNDULATORY THEORY.

412

415

424

430

1. Double Refraction of Compressed Glass

2. Circular Polarization

ADDITIONAL CORRECTION IN VOL. II.

Page 105, line 14. variation of elements.

Euler was the true author of the method of the The first essay of this method appears in a memoir in 1749; and it was further developed in another memoir in 1756, ten years before that of Lagrange mentioned in the text. See Laplace, Mécanique Céleste, livre xv., page 305, 310.