The authority of Tycho Brahe was so great, that the mere fact of his having ignored the phenomenon of trepidation was sufficient to lay this spectre, which had haunted the precincts of Urania for a thousand years, and possibly much longer. Though he had expressed himself somewhat guardedly (promising to discuss the matter further in the great work which he did not live to write), he had done enough by making his contemporaries aware of the vast difference between the accuracy of ancient observations and that of his own, and trepidation was never again heard of.[1]
It would not convey a correct idea of the accuracy which Tycho attained in his observations if we were to compare the positions of stars given in his catalogue with those resulting from modern observations. It would certainly be possible to reconstruct his catalogue from his original observations, but as this considerable labour would not benefit modern astronomy, for which a recurrence to Tycho Brahe's observations would hardly ever be of value except in very special cases, it is not likely to be undertaken. We are, however, able to form a conception of the accuracy of his results in other ways. First, the star of 1572 was, as we have seen, connected by distance measures with nine stars in Cassiopea. Computing the positions of these from modern data, Argelander found the probable error of one distance of the new star (with the sextant of 1572) to be ±18″.2, while the distances between the stars of Cassiopea measured with the arcus bipartitus gave ±41″.0.[2] The first result seems rather too small, but as we do not possess the original individual observations of Nova, we have no way of knowing how many such are embodied in the mean
