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THE HOON^S MOTIONS.

difference of these two advances. Since the sun’smean advance during a lunar revolution is about27°, and the maximum advance of the perigee in thesame time is about 11°, the displacement of theperigee from the sun may amount to so little as16° in a revolution. This happens when the perigeeis advancing most rapidly, and tends to keep theperigee longer near that position with respect to thesun which is favourable to perigeal advance. Nowwhen the perigee is regreding most rapidly, or at therate of about 9° in a revolution, the displacementof the perigee from the sun is due to the sum ofits regression and the sun’s advance. It amountstherefore to 36° per revolution. Thus the perigeedoes not remain long in that position with respectto the sun which is favourable to perigeal regression.Hence the balance of perigeal advance is importantlyincreased. This reasoning is strengthened by theconsideration that the rate of perigeal advancededuced from the maximum advance per month, isa less rate considerably than the rate deduced fromthe advance per hour, (say) when the apogee isadvancing most rapidly (even in a month when onthe whole the perigee regredes); and a similar con-sideration applies to the perigeal regression, (even mmonths, when, on the whole, the perigee advances).

But it will be obvious that any cause which tendsto encourage either the lingering of the lunar orbitin positions favourable to perigeal advance, or therapidity with which it shifts from positions favourable