103. In 1577 appeared a brilliant comet, which Tycho observed with his customary care; and, although he had not at the time his full complement of instruments, his observations were exact enough to satisfy him that the comet was at least three times as far off as the moon, and thus to refute the popular belief, which he had himself held a few years before (§ 100), that comets were generated in our atmosphere. His observations led him also to the belief that the comet was revolving round the sun, at a distance from it greater than that of Venus, a conclusion which interfered seriously with the common doctrine of the solid crystalline spheres. He had further opportunities of observing comets in 1580, 1582, 1585, 1590, and 1596, and one of his pupils also took observations of a comet seen in 1593. None of these comets attracted as much general attention as that of 1577, but Tycho’s observations, as was natural, gradually improved in accuracy. 104. The valuable results obtained by means of the new star of 1572, and by the comets, suggested the propriety of undertaking a complete treatise on astronomy embodying these and other discoveries. According to the original plan, there were to be three preliminary volumes devoted respectively to the new star, to the comet of 1577, and to the later comets, while the main treatise was to consist of several more volumes dealing with the theories of the sun, moon, and planets. Of this magnificent plan comparatively little was ever executed. The first volume, called the _Astronomiae Instauratae Progymnasmata_, or Introduction to the New Astronomy, was hardly begun till 1588, and, although mostly printed by 1592, was never quite finished during Tycho’s lifetime, and was actually published by Kepler in 1602. One question, in fact, led to another in such a way that Tycho felt himself unable to give a satisfactory account of the star of 1572 without dealing with a number of preliminary topics, such as the positions of the fixed stars, precession, and the annual motion of the sun, each of which necessitated an elaborate investigation. The second volume, dealing with the comet of 1577, called _De Mundi aetherei recentioribus Phaenomenis Liber secundus_ (Second book about recent appearances in the Celestial World), was finished long before the first, and copies were sent to friends and correspondents in 1588, though it was not regularly published and on sale till 1603. The third volume was never written, though some material was collected for it, and the main treatise does not appear to have been touched. [Illustration: FIG. 52.—Tycho’s system of the world. From his book on the comet of 1577.]