DESCARTES AND HIS THEORY OF VORTICES 136 LECTURE VII SIR ISAAC NEWTON 159 LECTURE VIII NEWTON AND THE LAW OF GRAVITATION 180 LECTURE IX NEWTON'S "PRINCIPIA" 203 _PART II_ LECTURE X ROEMER AND BRADLEY AND THE VELOCITY OF LIGHT 232 LECTURE XI LAGRANGE AND LAPLACE--THE STABILITY OF THE SOLAR SYSTEM, AND THE NEBULAR HYPOTHESIS 254 LECTURE XII HERSCHEL AND THE MOTION OF THE FIXED STARS 273 LECTURE XIII THE DISCOVERY OF THE ASTEROIDS 294 LECTURE XIV BESSEL--THE DISTANCES OF THE STARS, AND THE DISCOVERY OF STELLAR PLANETS 304 LECTURE XV THE DISCOVERY OF NEPTUNE 317 LECTURE XVI COMETS AND METEORS 331 LECTURE XVII THE TIDES 353 LECTURE XVIII THE TIDES, AND PLANETARY EVOLUTION 379 ILLUSTRATIONS FIG. PAGE 1. ARCHIMEDES 8 2. LEONARDO DA VINCI 10 3. COPERNICUS 12 4. HOMERIC COSMOGONY 15 5. EGYPTIAN SYMBOL OF THE UNIVERSE 16 6. HINDOO EARTH 17 7. ORDER OF ANCIENT PLANETS CORRESPONDING TO THE DAYS OF THE WEEK 19 8. PTOLEMAIC SYSTEM 20 9. SPECIMENS OF APPARENT PATHS OF VENUS AND OF MARS AMONG THE STARS 21 10. APPARENT EPICYCLIC ORBITS OF JUPITER AND SATURN 22 11. EGYPTIAN SYSTEM 24 12. TRUE ORBITS OF EARTH AND JUPITER 25 13. ORBITS OF MERCURY AND EARTH 25 14. COPERNICAN SYSTEM AS FREQUENTLY REPRESENTED 26 15. SLOW MOVEMENT OF THE NORTH POLE IN A CIRCLE AMONG THE STARS 29 16. TYCHONIC SYSTEM, SHOWING THE SUN WITH ALL THE PLANETS REVOLVING ROUND THE EARTH 38 17. PORTRAIT OF TYCHO 41 18. EARLY OUT-DOOR QUADRANT OF TYCHO 43 19. MAP OF DENMARK, SHOWING THE ISLAND OF HUEN 45 20. URANIBURG 46 21. ASTROLABE 47