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the moon’s line of nodes regredes, but that the regres-sion is most rapid when the plane of the lunar orbit ismost inclined to the line from the sun.
The plane’s inclination to the ecliptic changes inan oscillatory manner in a mean period equal to one-half the interval of 346" 6 days, between successivereturns of the line of nodes to such a position as isindicated in fig. 45 at n e l ri and n e- a n, or in 173’3days. The variation amounts to about 8', by whichthe inclination is alternately greater and less than themean value,—rather less than 5° 9'.
Such are the chief perturbations to which the moonis subject. Others of lesser importance need not hereoccupy our attention, because their discussion wouldintroduce no new principles to our notice, at leastnone which could be discussed in such a work as thepresent.
This chapter cannot properly be drawn to a con-clusion, however, without dwelling on the singularinterest of the history of the researches made by astro-nomers into the subject of the lunar motions. Thewhole progress of the inquiry has been attended bydifficulties only to be mastered by the most wonderfulexercise of skill and patience. It was only the uniquecombination of powers possessed by Newton that per-mitted the problem to be grappled with in the first in-stance; and even Newton would have failed but forcertain fortunate circumstances by which he wasassisted. Since his day the problem has been dealtwith by the most acute mathematicians, by the most