HISTORY OF PHYSICAL ASTRONOMY.

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; in magnitude the angle described by her round her axis, and other timesto fall short of the same angle; whence it happened, that the great circleformed by the intersection of the lunar surface with a plane passingthrough the moon’s centre, and perpendicular to the line joining the earthand moon (which great circle determines the lunar hemisphere visible tothe spectator), does not maintain a fixed position, but oscillates continuallyround a mean state. Hence the moon will appear to librate continuallyI to and fro in the plane of her motion. In the same letter Newton ex-| plained the libration in latitude, which arises in consequence of the moon’sj axis of rotation being inclined to her orbit. This phenomenon, like the- two already mentioned, is purely optical.

! Cassini is the next person whose researches contributed to throw light; upon this interesting subject. This astronomer discovered the remark-I able fact, that the nodes of the moon’s equator always coincide with the

■ nodes of her orbit. He also found that a plane drawn through the moon's

■ centre, parallel to the plane of the ecliptic, is always contained between theplanes of her equator and orbit, so that the poles of the latter are con-stantly situated in the same great circle with the pole of the ecliptic, huton opposite sides of it. He fixed the inclination of the lunar equator tothe ecliptic at 2° 30'.

Mayer, about the middle of the last century, undertook an extensiveseries of observations for the purpose of verifying the conclusions of Cas-sini. Tie measured the distance between the nodes of the equator andorbit, and found it to amount to 3° 30'. He remarked, however, that thedisplacement might he considered as absolutely insensible, since its de-termination depended on the inclination of the lunar equator, an error inwhich of only 5' would produce a corresponding error of 20° or 25° in thedistance between the nodes. He fixed the inclination of the lunar equatorat 1° 45', a quantity considerably less than the corresponding estimateof Cassini. Lalande, a short time afterwards, made observations on themoon, and arrived at conclusions which mainly agreed with those ofMayer, but he obtained 2° 9' for the inclination of the lunar equator.Recent observations have, however, completely confirmed the value as-signed to that element by the illustrious astrouomer of Gottingen .

The librations we have hitherto mentioned are apparent, not real; for theydo not depend upon any actual inequality in the motion of the moon roundher axis. Newton, however, did not fail to perceive that the action of theearth would, under certain conditions, affect the figure of the moon, andwould thereby occasion a real variation of her rotatory motion. Proceed-ing upon the supposition that she was originally in a fluid state, lie con-cluded that the terrestrial attraction would draw her into the form of aspheroid, the longer axis of which, when produced, would pass throughthe earth’s centre. Comparing this phenomenon with the tidal spheroid,occasioned by the action of the moon upon the earth, he found that thediameter of the lunar sqheroid, which is directed towards the earth, wouldexceed the diameter at right angles to it by 186 feet. He discovered inthis elongation of the moon the cause why she always turns the same sidetowards the earth, for he remarked that in any other position the actionof the earth would not maintain her in equilibrium, but would constantlydraw her back, until the elongated axis coincided in direction with the linejoining the earth and moon. Now, in consequence of the inequalities ofthe moon in longitude, the elongated axis will not always be directedexactly to the earth. Newton therefore concluded that a real libration of