ECLIPSES or THE MOON. It has been said that these are eaused by the moon passing through the (arth's shadow. Before this explanation can be aceepted, it must he shown that that shadow extends as far as the moon. This is easily done. Supposing the earth to no atmosphere, then the shadow is the cone marked in shade in Fig. 1, in which 'I' and S are the eentres of the earth sun. The apex is t C); and the question is, whether the distance UT from the apex to the earth's centre exceeds the moon's distance from the earth. Drawing TB, SA. from the centres of the earth and sun, respectively, perpendicular to the line 011A, tangent to both :There,. :Ind the line TO parallel to the line 011.1, we have from the similar triangles O'I'B TSC, the proportion, OT : 'I'll : : TS : SC. Now, we know that 'I'S, the (mean) distance of the sun, is equal to about 24,000 times TB; also, from the construction. AC = TB; and we know. that SA = 112 times TB; whence it follows that SC = Ill times TB. The above proportion then gives UT = 216 times TB, since = 216 nearly. But the moon's average distance is only 60 times TB (the earth's radius). Hence it appears that the length of the earth's shadow is almost four times the average distance of the moon, and that the moon •an enter it. Further, it is clear that, should it do so. it may be totally obscured; for it must enter at a point much nearer T than half the distance which is 108 times TB; and everywhere within that distance, it might he shown, the breadth of the shadow is much greater than the moon's disk. But one consideration now remains to be stated to com plete the proof of the theory of lunar eclipses. It was mentioned that they only occur at full moon, and we that to be the only time when the earth is between the sun and moon, and se has a chance of throwing her shadow upon it. Why they (In not occur every full moon will he explained in treating of the prediction of eclipses.
In the foregoing explanation, we proceeded on the assumption that the earth has no atmosphere. If the assumption were correct, the earth's shadow would be darker and narrower than it is, and the phenomena of eclipses more sudden. The effeet of atmospheric refraction (see Rr:rit.v• vov) is to bend the rays which fall on the atmosphere in toward the axis of the 'one of the earth's shadow. those which pass through the
lowest strata of the air being refracted through an angle of 1° S'. and converging to a point in the line (IT (Fig. 1) considerably nearer the earth than the point where the moon crosses her shadow. As a result of this, the moon never enters that part of the shadow which is com pletely dark; thus, site never loses her light en tirely. hut appears of a distinet reddish color resembling tarnished copper—an appearance caused by the atmospheric refraction in the same way as the ruddy color of the clouds at sunset. There is another reason why the phenomena of a lunar eclipse are less striking titan might he expected from the explanation given relative to Fig. I. Every shadow cast by the sun's rays necessarily has a penumbra, or envelope, on both sides of the central cone, In the case before us t Fig. 2). suppose a cone having its apex 0' be tween the sun and the earth. and enveloping each of them respectively in its opposite halves CO'C' and AO'A'. It is clear that from every point in the shaded part of the cone CO'C' but without the shadow BUB% a portion of the sun be visible and a portion onl•—the portion increas ing as the point approaches either of the lines CB, Cl)', and diminishing as it approaches the lines BO, B'O. In other words, the ilhunina t ion from the sun's rays is only partial within the space referred to, and diminishes its extreme boundary line toward the lines BO, Ll'O. \\ hen, then, the moon is about to suffer eclipse, it first loses brightness on entering this pe numbra; so that when it enters the real shadow, the contrast is not between one part of it ill shade and the other in full brilliancy, but between a part in shade and a part in par tial shade. On its emersion, the same con trast is presented between the part in the umbra and the part in the penumbra. What we should expect ou this geometrie view of the earth's shadow', actually happens. From the breadth of the penumbra, it happens that the moon may fall wholly within it before immer sion in the umbra commences; and so softly do the degrees of light shade into one another, that it is difficult to tell when a remarkable point on the moon's surface leaves the penumbra to pass into the umbra, or the reverse.