since C D and A B are spheres), there will be a total shadow. This shadow is called the umbra, and a spectator situated within it can see no part of the sun's disc. Beyond the umbra are two diverging spaces (or rather, a portion of a single conical space, having K for its vertex), where if a spectator be situated, as at M, he will see a portion only (A ON P) of the sun's surface, the rest (B O N P) being obscured by the earth. He will, therefore, receive only partial sunshine; and the more, the nearer he is to the exterior borders of that cone which is called the penumbra. Beyond this he will see the whole sun, and be in full illumination. All these circumstances may be perfectly well shown by holding a small globe up in the sun, and receiving its shadow at different distances on a sheet of paper.

(421.) In a lunar eclipse (represented in the upper figure), the moon is seen to enter degrees, get involved in the the latter like a smoky haze.

the penumbra first, and by umbra, the former bordering 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 phænomena 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

* The actual contact with the penumbra is never seen; the defalcation of light comes on so very gradually that it is not till when already deeply immersed, that it is perceived to be sensibly darkened,

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 appearances, is the refraction of the sun's light in passing through 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 Da be a section of the cone of the umbra, and F Bhf

of the penumbra, through their common axis D E S, passing through the centers E S of the earth and sun, and let K M k 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 23984, and the semidiameter of the sun 111 such units, we readily calculate D E=218, D M=158, for the

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

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 E D B, 15′ 46′′, and therefore D-BE 89° 44' 14", whence also we get M C (the linear semidiameter of the umbra)=0·725 (or in miles 2868), and the angle C E M, its apparent angular semidiameter as seen from E=41' 32". And instituting similar calculations for the geometrical penumbra we get M K=1.280 (5064 miles), and K E M 1° 13′ 20′′; 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 46m, and 4h 56m 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 phænomena of a lunar eclipse would consist in these partial or total obscurations. Within the space Ce 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 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 H g, parallel and very nearly coincident with B F, 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.: 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, B F, these rays respectively will occupy

=

the positions B zy, B v, making, with the aforesaid lines, the angles D By, F B v, each 1o 6'. Now we have found DB E 89° 44' 14" and therefore F B E (=D BE+ angular diam. of ©)=90° 16′ 17′′; consequently the angles E By and E B will be respectively 88° 38′ 14′′ and 89° 10′ 17′′, from which we conclude E z=42·04 and E v= 69.14; the former falling short of the moon's orbit by 17.96, and the latter surpassing it by 9·14 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 x C, y c, less so inwardly, over ry. 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 phænomenon 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 disct; 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, a phænomenon to which much interest is attached by reason of some curious optical phænomena first observed by Mr. Baily at the moments of the forming and breaking of the annulus, like beads of light

*As in the eclipses of June 5. 1620, April 25. 1642. Lalande, Ast. 1769. Also December 9. 1601, and June 10. 1816, on which occasions the moon was totally invisible even in telescopes.

† 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.)