THEORY OF OLBERS 38 SMALL MASS OF THE ASTEROIDS 38 LIMITS OF PERIHELION DISTANCE 39 DISTRIBUTION OF THE ASTEROIDS IN SPACE 40 LAW OF GAP FORMATION 42 COMMENSURABILITY OF PERIODS WITH THAT OF JUPITER 43 ORDERS OF COMMENSURABILITY 44 ELIMINATION OF VERY ECCENTRIC ORBITS 46 RELATIONS BETWEEN CERTAIN ADJACENT ORBITS 47 THE ECCENTRICITIES 48 THE INCLINATIONS 49 LONGITUDES OF THE PERIHELIA AND OF THE ASCENDING NODES 50 THE PERIODS 51 ORIGIN OF THE ASTEROIDS 52 VARIABILITY OF CERTAIN ASTEROIDS 53 THE AVERAGE ASTEROID ORBIT 54 THE RELATION OF SHORT-PERIOD COMETS TO THE ZONE OF ASTEROIDS 55 APPENDIX 59 PART I. THE ASTEROIDS, OR MINOR PLANETS BETWEEN MARS AND JUPITER. 1. Introductory. PLANETARY DISCOVERIES BEFORE THE ASTEROIDS WERE KNOWN. The first observer who watched the skies with any degree of care could not fail to notice that while the greater number of stars maintained the same relative places, a few from night to night were ever changing their positions. The planetary character of Mercury, Venus, Mars, Jupiter, and Saturn was thus known before the dawn of history. The names, however, of those who first distinguished them as "wanderers" are hopelessly lost. Venus, the morning and evening star, was long regarded as two distinct bodies. The discovery that the change of aspect was due to a single planet's change of position is ascribed to Pythagoras.