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144 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, § 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, § 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, § 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.