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Rh an equation of 1° 14′ 45″ (evection), not differing much from Ptolemy's values, though somewhat more accurate.

So far Tycho had not made much advance, but the discovery of the third and fourth inequalities was a very great step in advance. He probably thought that there were epicycles enough in his theory, and therefore he did not attempt to account for the variation by adding another. He merely let the centre of the first epicycle oscillate (librate) backwards and forwards on the deferent to the extent of 40′.5 on each side of its mean position, the latter moving along the deferent with the moon's mean motion in anomaly, and the centre of the epicycle being in its mean position at the syzygies and quadratures, and farthest from it at the octants, the period of a complete libration being half a synodical revelation. At the same time Tycho's observations showed