involved in the umbra, the former bordering the latter like a smoky haze. At this period of the eclipse, and while yet a considerable part of the moon remains unobscured, the portion involved in the umbra is invisible to the naked eye, though still perceptible in a telescope, and of a dark grey hue. But as the eclipse advances, and the enlightened part diminishes in extent, and grows gradually more and more obscured by the advance of the penumbra, the eye, relieved from its glare, becomes more sensible to feeble impressions of light and colour; and phenomena of a remarkable and instructive character begin to be developed. The umbra is seen to be very far from totally dark; and in its faint illumination it exhibits a gradation of colour, being bluish, or even (by contrast) somewhat greenish, towards the borders for a space of about 4' or 5' of apparent angular breadth inwards, thence passing, by delicate but rapid gradation, through rose red to a fiery or copper-coloured glow, like that of dull red-hot iron. As the eclipse proceeds this glow spreads over the whole surface of the moon, which then becomes on some occasions so strongly illuminated, as to cast a very sensible shadow, and allow the spots on its surface to be perfectly well distinguished through a telescope.

(422.) The cause of these singular, and sometimes very beautiful Fig. 61.

D

our atmosphere, which at the same time becomes coloured with the hues of sunset by the absorption of more or less of the violet and blue rays, as it passes through strata nearer or more remote from the earth's surface, and, therefore, more or less loaded with vapour. To show this, let A D a be a section of the cone of the umbra, and F B Hf of the penumbra, through their common axis DE S, passing through the centres ES of the earth and sun, and let K Mk be a section of these cones at a distance E M from E, equal to the radius of the moon's orbit, or 60 radii of the earth.* Taking this radius for unity, since E S, the distance of the sun, is 23974, and the semidiameter of the sun 111 such units, we readily calculate D E=218, D M=158, for the distances at which the apex of the geometrical umbra lies behind the earth and the moon respectively. We also find for the measure of the angle ED B, 15' 46", and therefore D B E 89° 44' 14", whence also we get M C (the linear semidiameter of the umbra)=0.725 (or in miles 2864), and the angle C E M, its apparent angular semidiameter as seen from E=41' 30". And instituting similar calculations for the geometrical penumbra we get M K=1·005 (3970 miles), and K EM 57'36"; and it may be well to remember that the doubles of these angles, or the mean angular diameters of the umbra and penumbra, are described by the moon with its mean velocity in 2h 43m, and 3h 47m respectively, which are therefore the respective durations of 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 C c the whole of the light, and within K C and c k a greater or less portion of it would be intercepted by the solid body B b 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 H g, parallel and very nearly coincident with B F, and internally by a line B z, the former represent

The figure is unavoidable drawn out of all proportion, and the angles violently exaggerated. The reader should endeavour to draw the figure in its true proportions.

ing 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: B z from the upper border, A, and B v 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 B D, BF, these rays respectively will occupy the positions Bzy, B v, making, with the aforesaid lines, the angles D B b, FB v, each 106'. Now we have found D B E 89° 44' 14" and therefore F BE (=D BE + angular diam. of ) = 90° 17' 17", consequently the angles E By and E B v will be respectively 88° 38′ 14" and 89° 11′ 17", from which we conclude E z 42.03 and Ev=88.89, the former falling short of the moon's orbit by 17.97, 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 penumbræ the moon passes during the whole of its path through the geometrical shadow, never attaining the absolute umbra B z b 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 xc, 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.‡

(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, as the spectator is within the umbra or penumbra. When the apex of 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, * 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.)

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, under the name of the Saros; 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 parts 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 11° 21', meaning by an eclipse the immersion 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