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348 observations of the new star and of the successive comets made Tycho feel the necessity of getting accurate places for his stars of comparison, and when his observatory was complete, he took up the work of forming a new star catalogue with great energy.

By Hipparchus the longitudes of stars had been deduced from the longitude of the sun by using the moon as intermediate link, which method is described by Ptolemy, who gives a full account of the manipulation of the zodiacal armillæ. Unfortunately Ptolemy does not say a word about the manner in which the standard stars (Regulus and Spica) were connected with the other stars, nor does he give any details about the actual observations on which the adopted places of the stars were founded. It is, therefore, not known whether every single star was connected with a standard star, or whether he perhaps also made use of conjunctions of stars with the moon (which had been of great value for the deduction of stellar positions for earlier epochs for the determination of the constant of precession), and nothing but a slight sketch of the method was handed down to posterity. The Arabs, as already remarked, did not observe fixed stars, and here, as in several other branches of practical astronomy, Walther was the first to recommence work. At the Nürnberg observatory he introduced a very important improvement on the method of Hipparchus by substituting Venus for the moon, as the small diameter, slow motion, and very small parallax made the planet far more suitable for the purpose than the moon. Among the