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340 the existence of another inequality, the fourth one in longitude, of which the solar year was the period, so that the observed place was behind the computed one, while the sun moved from perigee to apogee, and before it during the other six months. We have already mentioned that the solar and lunar eclipses continued to be carefully observed by Tycho, and at the latest during his stay at Wittenberg, he had clearly grasped the peculiarity in the lunar motion just described, since Herwart von Hohenburg wrote to Kepler (in July 1600) that he had probably heard from Brahe himself how the latter in the paper he had printed at Wittenberg had introduced a "circellum annuæ variationis, cujus initium statuitur sole versante in principio Cancri, ita ut in priori semicirculo hujus circelli verus locus Lunæ promoveatur in consequentia, et in posteriori retrotrahatur in præcedentia." Kepler also bears witness to the introduction of this circellus during Tycho's stay at Wittenberg. But the representation of the lunar motion had become so complicated that Tycho shrank from introducing more circles (for which reason he had adopted a mere libratory motion to account for the variation), and the idea of a really unequal motion was too much opposed to the time-honoured conception of uniform circular motion. He (or rather Longomontanus) therefore ultimately allowed for the annual equation by using a separate equation of time for the moon, differing by 8m. 13s. multiplied by sine of the solar anomaly from the ordinary one, even though this left 5′ or 6′ of the irregularity unaccounted for. The correct amount of the equation (11′,