111. Almost every astronomical quantity of importance was re-determined and generally corrected by him. The annual motion of the sun’s apogee relative to ♈, for example, which Coppernicus had estimated at 24″, Tycho fixed at 45″, the modern value being 61″; the length of the year he determined with an error of less than a second; and he constructed tables of the motion of the sun which gave its place to within 1′, previous tables being occasionally 15′ or 20′ wrong. By an unfortunate omission he made no inquiry into the distance of the sun, but accepted the extremely inaccurate value which had been handed down, without substantial alteration, from astronomer to astronomer since the time of Hipparchus (chapter II., § 41). In the theory of the moon Tycho made several important discoveries. He found that the irregularities in its movement were not fully represented by the equation of the centre and the evection (chapter II., §§ 39, 48), but that there was a further irregularity which vanished at opposition and conjunction as well as at quadratures, but in intermediate positions of the moon might be as great as 40′. This irregularity, known as the =variation=, was, as has been already mentioned (chapter III., § 60), very possibly discovered by Abul Wafa, though it had been entirely lost subsequently. At a later stage in his career, at latest during his visit to Wittenberg in 1598-9, Tycho found that it was necessary to introduce a further small inequality known as the =annual equation=, which depended on the position of the earth in its path round the sun; this, however, he never completely investigated. He also ascertained that the inclination of the moon’s orbit to the ecliptic was not, as had been thought, fixed, but oscillated regularly, and that the motion of the moon’s nodes (chapter II., § 40) was also variable. 112. Reference has already been made to the star catalogue. Its construction led to a study of precession, the amount of which was determined with considerable accuracy; the same investigation led Tycho to reject the supposed irregularity in precession which, under the name of trepidation (chapter III., § 58), had confused astronomy for several centuries, but from this time forward rapidly lost its popularity. The planets were always a favourite subject of study with Tycho, but although he made a magnificent series of observations, of immense value to his successors, he died before he could construct any satisfactory theory of the planetary motions. He easily discovered, however, that their motions deviated considerably from those assigned by any of the planetary tables, and got as far as detecting some regularity in these deviations. CHAPTER VI. GALILEI. “Dans la Science nous sommes tous disciples de Galilée.”—TROUESSART. “Bacon pointed out at a distance the road to true philosophy: Galileo both pointed it out to others, and made himself considerable advances in it.”—DAVID HUME.