Copernicus demonstrates clearly how his system explains the retrograde motion of the planets and their stationary points, no matter whether they are within the orbit of the earth, as Mercury and Venus, or outside of it, as Mars, Jupiter, and Saturn. His system provides also the means of ascertaining with accuracy the proportions of the solar system, or the relative distances of the planets from the sun and from each other. In this respect also his system possessed a vast advantage over that of Ptolemy, and the planetary distances which Copernicus computed are very close approximations to the measures of the present day. Reinhold revised the calculations of Copernicus and prepared the "Tabulæ Prutenicæ," based on the "De Revolutionibus," which proved far superior to the Alfonsine Tables, and were only supplanted by the Rudolphine Tables of Kepler. On the whole we may regard the lifework of Copernicus as fundamentally the most significant in the history and progress of astronomy. CHAPTER IX TYCHO, THE GREAT OBSERVER Clear as Copernicus had made the demonstration of the truth of his new system, it nevertheless failed of immediate and universal acceptance. The Ptolemaic system was too strongly intrenched, and the motions of all the bodies in the sky were too well represented by it. Accurate observations were greatly needed, and the Landgrave William IV. of Hesse built the Cassel Observatory, which made a new catalogue of stars, and introduced the use of clocks to carry on the time as measured by the uniform motion of the celestial sphere. Three years after the death of Copernicus, Tycho Brahe was born, and when he was 30 the King of Denmark built for him the famous observatory of Uraniborg, where the great astronomer passed nearly a quarter of a century in critically observing the positions of the stars and planets. Tycho was celebrated as a designer and constructor of new types of astronomical instruments, and he printed a large volume of these designs, which form the basis of many in use at the present day. Unfortunately for the genius of Tycho and the significance of his work, the invention of the telescope had not yet been made, so that his observations had not the modern degree of accuracy. Nevertheless, they were destined to play a most important part in the progress of astronomy. Tycho was sadly in error in his rejection of the Copernican system, although his reasons, in his day, seemed unanswerable. If the outer planets were displaced among the stars by the annual motion of the earth round the sun, he argued, then the fixed stars must be similarly displaced--unless indeed they be at such vast distances that their motions would be too slight to be visible. Of course we know now that this is really true, and that no instruments that Tycho was able to build could possibly have detected the motions, the effects of which we now recognize in the case of the nearer fixed stars in their annual, or parallactic, orbits.