the total and partial obscuration of any one point of the moon's disc in traversing centrally the geometrical shadow.

(423.) Were the earth devoid of atmosphere, the whole of the phenomena of a lunar eclipse would consist in these partial or total obscurations. Within the space Cc the whole of the light, and within KC and ck a greater or less portion of it, would be intercepted by the solid body Bb of the earth. The refracting atmosphere, however, extends from B, b, to a certain unknown, but very small distance B H, bh, which, acting as a convex lens, of gradually (and very rapidly) decreasing density, disperses all that comparatively small portion of light which falls upon it over a space bounded externally by Hg, parallel and very nearly coincident with BF, and internally by a line B z, the former representing the extreme exterior ray from the limb a of the sun, the latter, the extreme interior ray from the limb A. To avoid complication, however, we will trace only the courses of rays which just graze the surface at B, viz: Bz from the upper border, A, and Bv from the lower, a, of the sun. Each of these rays is bent inwards from its original course by double the amount of the horizontal refraction (33') i. e. by 1° 6', because, in passing from B out of the atmosphere, it undergoes a deviation equal to that at entering, and in the same direction. Instead, therefore, of pursuing the courses BD, BF, these rays respectively will occupy the positions Bzy, B v, making, with the aforesaid lines, the angles D Bb, FB v, each 1o 6'. Now we have found DBE 89° 44' 14" and therefore

=

D

FBE(DBE+ angular diam. of O)=90° 17′ 17", consequently the angles E By and E Bv will be respectively 88° 38′ 14′′ and 89° 11' 17" from which we conclude Ez = 42.03 and Ev 88-89, the former falling short of the moon's orbit by 17.07, and the latter surpassing it by 28.89 radii of the earth.

(424.) The penumbra, therefore, of rays refracted at B, will be spread over the space v By, that at H over g H d, and at the intermediate points, over similar intermediate spaces, and through this compound of superposed penumbra the moon passes during the whole of its path through the geometrical shadow, never attaining the absolute umbra Bzb at all. Without going into detail as to the intensity of the refracted rays, it is evident that the totality of light so thrown into the shadow is to that which the earth intercepts, as the area of a circular section of the atmosphere to that of a diametrical section of the earth itself, and, therefore, at all events but feeble. And it is still further enfeebled by actual clouds suspended in that portion of the air which forms the visible border of the earth's disc as seen from the moon, as well as by the general want of transparency caused by invisible vapour, which is especially effective in the lowermost strata, within three or four miles of the surface, and which will impart to all the rays they transmit, the ruddy hue of sunset, only of double the depth of tint which we admire in our glowing sunsets, by reason of the rays having to traverse twice as great a thickness of atmosphere. This redness will be most intense at the points x, y, of the moon's path through the umbra, and will thence degrade very rapidly outwardly, over the spaces x c, y C, less so inwardly, over x y. And at C, c, its hue will be mingled with the bluish or greenish light which the atmosphere scatters by irregular dispersion, or in other words by our twilight (art. 44). Nor will the phenomenon be uniformly conspicuous at all times. Supposing a generally and deeply clouded state of the atmosphere around the edge of the earth's disc visible from the moon (i. e. around that great circle of the earth, in which, at the moment the sun is in the horizon,) little or no refracted light may reach the moon. Supposing that circle partly clouded and partly clear, patches of red light corresponding to the clear portions will be thrown into the umbra, and may give rise to various and changeable distributions of light on the eclipsed disc; while, if entirely clear, the eclipse will be remarkable for the conspicuousness of the moon during the whole or a part of its immersion in the umbra,3

'As in the eclipses of June 5, 1620, April 25, 1642. Lalande, Ast. 1769.

As in the eclipse of Oct. 13. 1837, observed by the author.

As in that of March 19, 1848, when the moon is described as giving "good light" during more than an hour after its total immersion, and some persons even doubted its being eclipsed. (Notices of R. Ast. Soc. viii. p. 132.)

(425.) Owing to the great size of the earth, the cone of its umbra always projects far beyond the moon; so that, if, at the time of a lunar eclipse, the moon's path be properly directed, it is sure to pass through the umbra. This is not, however, the case in solar eclipses. It so happens, from the adjustment of the size and distance of the moon, that the extremity of her umbra always falls near the earth, but sometimes attains and sometimes falls short of its surface. In the former case (represented in the lower figure art. 420) a black spot, surrounded by a fainter shadow, is formed, beyond which there is no eclipse on any part of the earth, but within which there may be either a total or partial one, When the apex of

as the spectator is within the umbra or penumbra. the umbra falls on the surface, the moon at that point will appear, for an instant, to just cover the sun; but, when it falls short, there will be no total eclipse on any part of the earth; but a spectator, situated in or near the prolongation of the axis of the cone, will see the whole of the moon on the sun, although not large enough to cover it, i. e. he will witness an annular eclipse.

(426.) Owing to a remarkable enough adjustment of the periods in which the moon's synodical revolution, and that of her nodes, are performed, eclipses return after a certain period, very nearly in the same order and of the same magnitude. For 223 of the moon's mean synodical revolutions, or lunations, as they are called, will be found to occupy 6585-32 days, and nineteen complete synodical revolutions of the node to occupy 6585-78. The difference in the mean position of the node, then, at the beginning and end of 223 lunations, is nearly insensible; so that a recurrence of all eclipses within that interval must take place. Accordingly, this period of 223 lunations, or eighteen years and ten days, is a very important one in the calculation of eclipses. It is supposed to have been known to the Chaldeans, the earliest astronomers, the regular return of eclipses having been known as a physical fact for ages before their exact theory was understood. In this period there occur ordinarily 70 eclipses, 29 of the moon and 41 of the sun, visible in some part of the earth. Seven eclipses of either sun or moon at most, and two at least (both of the sun,) may occur in a year.

(427.) The commencement, duration, and magnitude of a lunar eclipse are much more easily calculated than those of a solar, being independent of the position of the spectator on the earth's surface, and the same as if viewed from its centre. The common centre of the umbra and penumbra lies always in the ecliptic, at a point opposite to the sun, and the path described by the moon in passing through it is its true orbit as it stands at the moment of the full moon. In this orbit, its position, at every

instant, is known from the lunar tables and ephemeris; and all we have, therefore, to ascertain, is, the moment when the distance between the moon's centre and the centre of the shadow is exactly equal to the sum of the semidiameters of the moon and penumbra, or of the moon and umbra, to know when it enters upon and leaves them respectively. No lunar eclipse can take place, if, at the moment of the full moon, the sun be at a greater angular distance from the node of the moon's orbit than 11o 21', meaning by an eclipse the inmersion of any part of the moon in the umbra, as its contact with the penumbra cannot be observed (see note to art. 421).

(428.) The dimensions of the shadow, at the place where it crosses the moon's path, require us to know the distances of the sun and moon at the time. These are variable; but are calculated and set down, as well as their semidiameters, for every day, in the ephemeris, so that none of the data are wanting. The sun's distance is easily calculated from its elliptic orbit; but the moon's is a matter of more difficulty, by reason of the progressive motion of the axis of the lunar orbit. (Art. 409.)

(429.) The physical constitution of the moon is better known to us than that of any other heavenly body. By the aid of telescopes, we discern inequalities in its surface which can be no other than mountains and valleys, for this plain reason, we see the shadows cast by the former in the exact proportion as to length which they ought to have, when we take into account the inclination of the sun's rays to that part of the moon's surface on which they stand. The convex outline of the limb turned towards the sun is always circular, and very nearly smooth; but the opposite border of the enlightened part, which (were the moon a perfect sphere) ought to be an exact and sharply defined ellipse, is always observed to be extremely ragged, and indented with deep recesses and prominent points. The mountains near this edge cast long black shadows, as they should evidently do, when we consider that the sun is in the act of rising or setting to the parts of the moon so circumstanced. But as the enlightened edge advances beyond them, i. e. as the sun to them gains altitude, their shadows shorten; and at the full moon, when all the light falls in our line of sight, no shadows are seen on any part of her surface. From micrometrical measures of the lengths of the shadows of the more conspicuous mountains, taken under the most favourable circumstances, the heights of many of them have been calculated. Messrs. Beer and Maedler in their elaborate work, entitled "Der Mond," have given a list of heights resulting from such measurements, for no less than 1095 lunar mountains, among which occur all degrees of elevation up to 3569 toises, (22823 British feet), or about 1400 feet higher than Chimborazo in the

Andes. The existence of such mountains is further corroborated by their appearance, as small points or islands of light beyond the extreme edge of the enlightened part, which are their tops catching the sun-beams before the intermediate plain, and which, as the light advances, at length connect themselves with it, and appear as prominences from the general edge.

(430.) The generality of the lunar mountains present a striking uniformity and singularity of aspect. They are wonderfully numerous, especially towards the Southern portion of the disc, occupying by far the larger portion of the surface, and almost universally of an exactly circular or cup-shaped form, foreshortened, however, into ellipses towards the limb; but the larger have for the most part flat bottoms within, from which rises centrally a small, steep, conical hill. They offer, in short, in its highest perfection, the true volcanic character, as it may be seen in the crater of Vesuvius, and in a map of the volcanic districts of the Campi Phlegræi or the Puy de Dôme, but with this remarkable peculiarity, viz. that the bottoms of many of the craters are very deeply depressed below the general surface of the moon, the internal depth being often twice or three times the external height. In some of the principal ones, decisive marks of volcanic stratification, arising from successive deposits of ejected matter, and evident indications of lava currents streaming outwards in all directions, may be clearly traced with powerful telescopes. (See Pl. V. fig. 2.) In Lord Rosse's magnificent reflector, the flat bottom of the crater called Albategnius is seen to be strewed with blocks not visible in inferior telescopes, while the exterior of another (Aristillus) is all hatched over with deep gullies radiating towards its centre. What is, moreover, extremely singular in the geology of the moon is, that, although nothing having the character of seas can be traced, (for the dusky spots, which are commonly called seas, when closely examined, present appearances incompatible with the supposition of deep water,) yet there are large regions perfectly level, and apparently of a decided alluvial cha

racter.

(431.) The moon has no clouds, nor any other decisive indications of an atmosphere. Were there any, it could not fail to be perceived in the occultations of stars and the phænomena of solar eclipses, as well as in a great variety of other phænomena. The moon's diameter, for example, as measured micrometrically, and as estimated by the interval between the disappearance and reappearance of a star in an occultation, ought to differ by twice the horizontal refraction at the moon's surface. No appre

See Breislak's map of the environs of Naples, and Desmarest's of Auvergne. "From a drawing taken with a reflector of twenty feet focal length (h.)