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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. *
(415.) 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. It may be seen, when the moon is crescent or waning, a few days before and after the new moon, with the naked eye, às 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
* 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 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. Note to the edit, of 1833.
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.
(416.) 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 regarded as very nearly 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 0, 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 the dark hemisphere are presented to 0, 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.
* The angle subtended by the moon's orbit, as seen from the sun (in the incan state of things ), is only 17' 12''.
(417.) 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 and again illuminate the earth. It is no more than a white cloud does standing off upon the clear blue sky. By day, the moon can hardly be distinguished in brightness from such a cloud; and, in the dusk of the evening, clouds catching the last rays of the sun appear with a dazzling splendour, not inferior to the seeming brightness of the moon at night.* That the earth sends also such a light to the moon, only probably more powerful by reason of its greater apparent sizet, is agreeable to optical principles, and explains the appearance of the dark portion of the young or waning moon completing its crescent (art. 413). For, when the moon is nearly new to the earth, the latter (so to speak) is nearly full to the former; it then illuminates its dark half by strong earth-light; and it is a
The actual illumination of the lunar surface is not much superior to that of weathered sandstone rock in full sunshine. I have frequently compared the moon setting behind the grey perpendicular façade of the Table Mountain, illuminated by the sun just risen in the opposite quarter of the horizon, when it has been scarcely distinguishable in brightness from the rock in contact with it. The sun and moon being nearly at equal altitudes and the atmosphere perfectly free from cloud or vapour, its effect is alike on both luminaries. (H: 1848).
† The apparent diameter of the moon is 32' from the earth ; that of the earth seen from the moon is twice her horizontal parallax, or 1° 54'. The apparent surfaces, therefore, are as (114) : (32), or as 13:1 nearly.
portion of this, reflected back again, which makes it visible to us in the twil.ght sky. As the moon gains age, the earth offers it a less portion of its bright side, and the phenomenon in question dies away.
(418.) The lunar month is determined by the recurrence of its phases : it reckons from new moon to new moon; that is, from leaving its conjunction with the sun to its return to conjunction. If the sun stood still, like a fixed star, the interval between two conjunctions would be the same as the period of the moon's sidereal revolution (art. 401.); but, as the sun apparently advances in the heavens in the same direction with the moon, only slower, the latter has more than a complete sidereal period to perform to come up with the sun again, and will require for it a longer time, which is the lunar month, or, as it is generally termed in astronomy, a synodical period. The difference is easily calculated by considering that the superfluous arc (whatever it be) is described by the sun with the velocity of 0°.98565 per diem, in the same time that the moon describes that arc plus a complete revolution, with her velocity of 13°:17640 per diem ; and, the times of description being identical, the spaces are to each other in the proportion of the velocities. Let V and v be the mean angular velocities, x the superfluous arc; then V:v::1+x: 2; and V-0:0::1: x, whence x is found, and 2 = the time of describing x, or the difference of the sidereal and synodical periods. From these data a slight knowledge of arithmetic will suffice to derive the arc in question, and the time of its description by the moon; which being the excess of the synodic over the sidereal period, the former will be had, and will appear to be 290 12h 44m 28.87.
(419.) Supposing the position of the nodes of the moon's orbit to permit it, when the moon stands at A (or at the new moon), it will intercept a part or the whole of the sun's rays, and cause a solar eclipse. On the other hand, when at E (or at the full moon), the earth O will intercept the rays of the sun, and cast a shadow on the moon, thereby causing a lunar eclipse. And this is perfectly consonant to fact, such
eclipses never happening but at the exact time of the full moon. But, what is still more remarkable, as confirmatory of the position of the earth's sphericity, this shadow, which we plainly see to enter upon and, as it were, eat away the disc of the moon, is always terminated by a circular outline, though, from the greater size of the circle, it is only partially seen at any one time. Now, a body which always casts a circular shadow must itself be spherical.
(420.) Eclipses of the sun are best understood by regarding the sun and moon as two independent luminaries, each moving according to known laws, and viewed from the earth; but it is also instructive to consider eclipses generally as arising from the shadow of one body thrown on another by a luminary much larger than either. Suppose, then, A B to represent the sun, and C D a spherical body, whether earth or moon, illuminated by it. If we join and prolong A C, BD; since A B is greater than C D, these lines will meet in a point E, more or less distant from the body C D, according to its size, and within the space CED (which represents a cone,
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 (AO NP) 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