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He communicated to that society in 1847 an able paper on a long-period lunar inequality (Memoirs Roy.
For a selected few of the lunar inequalities, Newton showed in some quantitative detail how they arise from the solar perturbing force.
The basis of these systems appears to have been arithmetical rather than geometrical, but they did approximately account for the main lunar inequality now known as the equation of the center.
Tycho's lunar theory doubled the number of distinct lunar inequalities, relative to those anciently known, and reduced the discrepancies of lunar theory to about 1/5 of their previous amounts.
Słownik astronomiczny