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354 twenty-one standard stars were not sufficient, but that it became necessary to build further on the stars determined by them. Magnitudes were frequently noted, and in the final star catalogue they were entered, occasionally with two dots added or one (.), to show that the star was slightly brighter or fainter than indicated by the figure. But these estimates of magnitude were probably not made with particular care, so that it would be risky to draw conclusions from a comparison of them with the more systematically made observations of relative brightness of Ptolemy, Al Sûfi, and astronomers of the nineteenth century.

In reducing his observations, Tycho adopted 51″ as the value of the constant of precession, which he deduced from a comparison of his own places for Regulus and Spica with those found by Hipparchus, Al Battani, and Copernicus. Although the places of Spica recorded by Timocharis and Ptolemy gave respectively 49$1⁄4$″ and 53$1⁄4$″, he had sense enough to attribute this to the crudeness of earlier observations, and pointed out that these often erred very greatly as to the relative positions of stars which were supposed to have been well observed, so that there was no need of assuming any irregularity in the precession of the equinoxes in order to reconcile discrepancies in the absolute longitudes. The origin of this old idea, that the equinoxes did not recede with uniform velocity on the ecliptic, but were also subject to an oscillating motion, is shrouded in mystery. The name of Tabit ben Korra (who lived in the second half of the ninth century) is usually associated with this trepidatio, but the idea seems to be very old, and is first mentioned by Theon, the commentator of Ptolemy, according to whom "some ancient astrologers" had found that the stars had an oscillating