HISTORY OF PHYSICAL ASTRONOMY.

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disclosed to astronomers any traces of a libratory motion of this character ;whence we may conclude that the motions of rotation and revolution didnot originally differ by a sensible quantity*.

Lagrange next considered the libration of the moon in latitude. Inthis memoir he did not succeed in explaining the singular fact discoveredby Cassini relative to the coincidence of the nodes of the lunar orbit andequator. When he assumed this coincidence in the outset of his re-searches, he found that the lunar equator, instead of being fixed withrespect to the ecliptic, continually approached towards that plane, whileobservation on the other hand went to prove that it was inclined to it atnearly an invariable angle. This portion of his researches being imper-fect, lie resumed the subject fifteen years afterwards, and in the volumeof the Berlin Academy for 1780, he published an admirable memoir, inwhich he completed the theory of the moon’s motion about her centre ofgravity. On this occasion he was conducted to the remarkable conclusion,that if the mean nodes of the lunar equator and orbit be supposed tohave originally coincided, the action of the earth upon the lunar ellipsoidwould constantly maintain this coincidence. He also determined the lawsof the small oscillations, by which the true node of the lunar equatordeviates from the mean node.

The only question connected with this subject which still remained tobe examined was the effect which the secular inequalities in the'meanmotion of the moon might produce upon the appearance of the lunarsurface. These inequalities will one day derange the mean place of themoon to the extent of several circumferences of the circle, and if therotatory motion of the moon remained constant during the whole periodof their developement, the inevitable consequence would be, that the moonwould present the whole of her surface in gradual succession towards the

* Several writers on astronomy, when describing the various librations of the moon,affirm that the fourth, or physical libration, was discovered by Lagrange. If this refersto the libratory motion mentioned in the text, it cannot be called a discovery, since itsactual existence has not yet been established by astronomers. The only real librationwhich observation has detected is that depending on the lunar inequalities in longitude(chiefly the annual equation ; see Chapter XI.), and this phenomenon was first remarkedas a theoretical truth by the great founder of Physical Astronomy, who unfolded the wholemechanism of the planetary system, and by bis unrivalled sagacity anticipated those resultswhich his successors, by the aid of a refined analysis, have been enabled only to confirmand extend. Laplace is surprised that Newton should have failed to notice that, in orderto assure the constant equality of the motions of rotation and revolution, it was not abso-lutely necessary that at the origin they should have been exactly equal. This, however,might be considered as a natural corollary to the remark of Newton, that any disturbanceof the elongated axis of the moon would merely result in an oscillatory motion on eachside of its mean place ; for the possibility of allowing the arbitrary constants of anysystem to vary a little on each side of a mean state, without occasioning any permanentderangement of the system, is a manifest attribute of the condition of stable equilibrium,and such a condition is clearly implied in Newton’s words:—“Unde ad hunc situmsemper oscillando redibit.”—Princip., lib. iii. prop, xxxviii. If the motions of rotationand revolution had differed a little at the origin, as Laplace conceived they might, it isclear that the elongated axis would not have coincided exactly with the line joining theearth and moon; and hence, according to Newton’s statement, it would oscillate con-tinually on each side of that line. Newton, however, evidently refers to the difference inthe two motions occasioned by the inequalities in the moon’s longitude. It is naturalenough, indeed, to suppose that the illustrious author of the Prineipia did not feel anyanxiety to repudiate the original equality of the motions of rotation and revolution—arelation which, although perhaps difficult to explain by the doctrine of chances, becomesvery interesting and suggestive when it is considered as the result of Supreme Intel-ligence.