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Rh admissible). There was another important matter in which Kepler's suggestion was acted upon. Soon after his arrival at Benatky, he found that Tycho, like his predecessors, referred all the planetary motions to the mean place of the sun, while he had himself in his Mysterium Cosmographicum referred them to the actual place of the sun. He gave the impulse to this being done in the lunar theory by Longomontanus, and he mentions in the Appendix to the Progymnasmata that the necessity of this step had also become evident in the case of Mars.

With regard to Tycho's observations and researches on comets, we need only refer to Chapter VII., where they have been examined in sufficient detail. It is not among the least of Tycho's scientific merits that he finally proved comets to be celestial bodies.

That a new catalogue of accurate positions of fixed stars was urgently needed had early been felt by Tycho Brahe. The Ptolemean catalogue of stars was fourteen hundred years old, and was probably little more than a reproduction of the still older catalogue of Hipparchus. None of the Arabian astronomers had observed fixed stars, but had contented themselves with adding the precession to the longitudes of Ptolemy; and the only independent catalogue, that of Ulugh Beg, was not yet known in Europe. The co-ordinates of stars given in Ptolemy's catalogue were known at Tycho's time through the two Latin editions of the Almegist of 1515 and 1528 and the Greek edition of 1538; but to the original errors of observation had been added a goodly number of errors of copying, so that the discrepancies of the various editions inter se were numerous and large. The