Ptolemy, we know, was universely acknowledged at the time to be “Master of Astronomy,” as Brunetto Latini calls him. His _Almagest_ was only known indirectly, but it was believed to contain all that could be known about the movements and the nature of the heavens. Some minor additions and corrections had been made, as we have seen, by the Arab astronomers, but the system was accepted as a complete and satisfactory explanation of all celestial phenomena. Hence no professional astronomer was expected to make discoveries; he was simply well versed in the work of those who went before him, skilful in the use of a few simple instruments and tables, and practised in applying the principles of astrology. A general notion of the Ptolemaic system was widely diffused. For those who could not read Latin there were encyclopædic works written in the vernacular and in a popular style, such as the _Trésor_ of Brunetto Latini, and these always contained a section on astronomy. The average educated man probably had only vague ideas about epicycles and eccentrics, and perhaps had never heard of the Arab estimates of the sizes of the planets; but he would know that astronomy taught that Earth is a globe, motionless at the centre of the universe, and smaller than any of the stars; he would know the names of the seven planets (including among these the sun and moon), and probably also their colours, their periods, and their astrological significance; the zodiacal constellations would be familiar, especially as they were often used decoratively; and he would believe that stars and planets are set in crystalline transparent spheres. Moreover, he would often be more of an astronomer than he knew, for he would learn almost unconsciously many things of which modern men are ignorant. The ill-lighted streets and the dangers of night journeys would force him to be better acquainted with the motions and phases of the moon than most of us are to-day; he would know when and where to look for different stars; and the want of a watch would make it necessary for him to be able to take his time from the sun at any season of the year. He could, however, sometimes consult a sundial on a church wall or in a private garden, and the church chimes rang out at tierce, and nones, and vespers. These were heard at intervals which were much longer in summer than in winter, for the system of “temporary hours” was used by the Church, and the service of tierce was held halfway between sunrise and noon (or nones), and vespers was halfway between noon and sunset. _II. DANTE’S STUDIES._ DANTE’S STUDIES.