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portion, or even in some rare conjunctures the whole, of its disc is obscured, and, as it were, obliterated, by the superposition of that of the moon, which appears upon it as a circularly-terminated black spot, producing a temporary diminution of daylight, or even nocturnal darkness, so that the stars appear as if at midnight. In other cases, when, at the moment that the moon is centrally superposed on the sun, it so happens that her distance from the earth is such as to render her angular diameter less than the sun's, the very singular phenomenon of an annular solar eclipse takes place, when the edge of the sun appears for a few minutes as a narrow ring of light, projecting on all sides beyond the dark circle occupied by the moon in its center.

(347.) A solar eclipse can only happen when the sun and moon are in conjunction, that is to say, have the same, or nearly the same, position in the heavens, or the same longitude. It will presently be seen that this condition can only be fulfilled at the time of a new moon, though it by no means follows, that at every conjunction there must be an eclipse of the sun. If the lunar orbit coincided with the ecliptic, this would be the case, but as it is inclined to it at an angle of upwards of 5°, it is evident that the conjunction, or equality of longitudes, may take place when the moon is in the part of her orbit too remote from the ecliptic to permit the discs to meet and overlap. It is easy, however, to assign the limits within which an eclipse is possible. To this end we must consider, that, by the effect of parallax, the moon's apparent edge may be thrown in any direction, according to a spectator's geographical station, by any amount not exceeding the horizontal parallax. Now, this comes to the same (so far as the possibility of an eclipse is concerned) as if the apparent diameter of the moon, seen from the earth's center, were dilated by twice its horizontal parallax; for if, when so dilated, it can touch or overlap the sun, there must be an eclipse at some part or other of the earth's surface. If, then, at the moment of the nearest conjunction, the geocentric distance of the

centers of the two luminaries do not exceed the sum of their semidiameters and of the moon's horizontal parallax, there will be an eclipse. This sum is, at its maximum, about 1°34' 27". In the spherical triangle S N M, then, in which S is the sun's center, M the moon's, SN the ecliptic, MN the moon's orbit, and N the node, we may suppose the angle N S M a right angle, S M = 1° 34′ 27′′, and the angle MNS=5° 8′ 48′′, the inclination of the orbit.

N

Hence we calculate S N, which comes out 16° 58'. If, then, at the moment of the new moon, the moon's node is farther from the sun in longitude than this limit, there can be no eclipse; if within, there may, and probably will, at some part or other of the earth. To ascertain precisely whether there will or not, and, if there be, how great will be the part eclipsed, the solar and lunar tables must be consulted, the place of the node and the semidiameters exactly ascertained, and the local parallax, and apparent augmentation of the moon's diameter due to the difference of her distance from the observer and from the center of the earth (which may amount to a sixtieth part of her horizontal diameter), determined; after which it is easy, from the above considerations, to calculate the amount overlapped of the two discs, and their moment of contact.

(348.) The calculation of the occultation of a star depends on similar considerations. An occultation is possible, when the moon's course, as seen from the earth's center, carries her within a distance from the star equal to the sum of her semidiameter and horizontal parallax; and it will happen at any particular spot, when her apparent path, as seen from that spot, carries

her center within a distance equal to the sum of her augmented semidiameter and actual parallax. The details of these calculations, which are somewhat troublesome, must be sought elsewhere.*

(349.) The phenomenon of a solar eclipse and of an occultation are highly interesting and instructive in a physical point of view. They teach us that the moon is an opaque body, terminated by a real and sharply defined surface intercepting light like a solid. They prove to us, also, that at those times when we cannot see the moon, she really exists, and pursues her course, and that when we see her only as a crescent, however narrow, the whole globular body is there, filling up the deficient outline, though unseen. For occultations take place indifferently at the dark and bright, the visible and invisible outline, whichever happens to be towards the direction in which the moon is moving; with this only difference, that a star occulted by the bright limb, if the phenomenon be watched with a telescope, gives notice, by its gradual approach to the visible edge, when to expect its disappearance, while, if occulted at the dark limb, if the moon, at least, be more than a few days old, it is, as it were, extinguished in mid-air, without notice or visible cause for its disappearance, which, as it happens instantaneously, and without the slightest previous diminution of its light, is always surprising; and, if the star be a large and bright one, even startling from its suddenness. The re-appearance of the star, too, when the moon has passed over it, takes place in those cases when the bright side of the moon is foremost, not at the concave outline of the crescent, but at the invisible outline of the complete circle, and is scarcely less surprising, from its suddenness, than its disappearance in the other case. †

*Woodhouse's Astronomy, vol. i. See also Trans. Ast. Soc. vol. i. p. 325. There is an optical illusion of a very strange and unaccountable nature which has often been remarked in occultations. The star appears to advance actually upon and within the edge of the disc before it disappears, and that sometimes to a considerable depth. I have never myself witnessed this singular effect, but it rests on most unequivocal testimony. I have called it an optical illusion; but it is barely possible that a star may shine on such occasions through deep fissures in the substance of the moon. The

It

(350.) The existence of the complete circle of the disc, even when the moon is not full, does not, however, rest only on the evidence of occultations and eclipses. may be seen, when the moon is crescent or waning, a few days before and after the new moon, with the naked eye, as a pale round body, to which the crescent seems attached, and somewhat projecting beyond its outline (which is an optical illusion arising from the greater intensity of its light). The cause of this appearance will presently be explained. Meanwhile the fact is sufficient to show that the moon is not inherently luminous like the sun, but that her light is of an adventitious nature. And its crescent form, increasing regularly from a narrow semicircular line to a complete circular disc, corresponds to the appearance a globe would present, one hemisphere of which was black, the other white, when differently turned towards the eye, so as to present a greater or less portion of each. The obvious conclusion from this is, that the moon is such a globe, one half of which is brightened by the rays of some luminary sufficiently distant to enlighten the complete hemisphere, and sufficiently intense to give it the degree of splendour we see. Now, the sun alone is competent to such an effect. Its distance and light suffice; and, moreover, it is invariably observed that, when a crescent, the bright edge is towards the sun, and that in proportion as the moon in her monthly course becomes more and more distant from the sun, the breadth of the crescent increases, and vice versa.

(351.) The sun's distance being 23984 radii of the earth, and the moon's only 60, the former is nearly 400 times the latter. Lines, therefore, drawn from the sun to every part of the moon's orbit may be re

occultations of close double stars ought to be narrowly watched, to see whether both individuals are thus projected, as well as for other purposes connected with their theory. I will only hint at one, viz. that a double star, too close to be seen divided with any telescope, may yet be detected to be double by the mode of its disappearance. Should a considerable star, for instance, instead of undergoing instantaneous and complete extinction, go out by two distinct steps, following close upon each other; first losing a portion, then the whole remainder of its light, we may be sure it is a double star, though we cannot see the individuals separately. — Author.

garded as parallel. Suppose, now, O to be the earth, A B C D, &c. various positions of the moon in its orbit, and S the sun, at the vast distance above stated; as is shown, then, in the figure, the hemisphere of the lunar globe turned towards it (on the right) will be bright, the opposite dark, wherever it may stand in its orbit. Now, in the position A, when in conjunction with the sun, the dark part is entirely turned towards O, and the bright from it. In this case, then, the moon is not seen, it is new moon. When the moon has come to C, half the bright and half

S

B

Η

the dark hemisphere are presented to O, and the same in the opposite situation G: these are the first and third quarters of the moon. Lastly, when at E, the whole bright face is towards the earth, the whole dark side from it, and it is then seen wholly bright or full moon. In the intermediate positions B D F H, the portions of the bright face presented to O will be at first less than half the visible surface, then greater, and finally less again, till it vanishes altogether, as it comes round again to A.

(352.) These monthly changes of appearance, or phases, as they are called, arise, then, from the moon, an opaque body, being illuminated on one side by the sun, and reflecting from it, in all directions, a portion of the light so received. Nor let it be thought surprising that a solid substance thus illuminated should appear to shine

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