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344 of the lunar orbit described a circle round the mean pole with a radius of 9′ 30″, so that the inclination reaches its minimum at syzygy and its maximum at quadrature. He applied corrections separately to the latitude for equation of node and for change of inclination, a form which was retained even by Newton and Euler, until Tobias Mayer showed that the two equations can be combined into one, varying with the double distance of the moon from the sun, less the argument of latitude of the moon.

It would lead us too far if we were in this place to enter into a description of Tycho's lunar tables, or of his precepts for finding the longitude from his theory. We shall only mention that he was the first to tabulate the reduction, or the difference between the moon's motion along its orbit, and the same referred to the ecliptic. The table of parallax makes this quantity vary between 66′ 6″ and 56′ 21″, the apparent diameter varying from 32′ to 36′ at full moon, while he believed to have found from his observations of eclipses that the diameter appears less at new moon (25′ 36″ to 28′ 48″), owing to the limb being "extenuated" by the solar rays. He therefore denied the possibility of a total solar eclipse, to some extent also misled by the accounts