the node, the penumbra is circular on the earth at the middle of the general eclipse, because at that time it falls perpendicularly on the earth's surface; but in every other moment it falls obliquely, and therefore will be elliptical, and the more so, as the time is longer after the middle of the general eclipse; and then much greater portions of the earth are involved in the penumbra. When the penumbra first touches the earth the general eclipse begins, and it ends when it leaves the earth : from the beginning to the end, the Sun appears eclipsed in some part of the earth or other. When the penumbra touches any place, the eclipse begins at that place, and ends when the penumbra leaves it.* When the Moon changes exactly in the node the penumbra goes over the centre of the earth, as seen from the Moon, and consequently by describing the longest line possible on the earth continues the longest upon it; namely at a mean rate five hours and fifty minutes; more, if the Moon be at her greatest distance from the earth, because she then moves slowest, and less if she be at her nearest approach, because of her accelerated motion. The Moon changes at all hours, and as often in one node as in the other, and at all distances from them both, at different times as it happens; the variety of phases of eclipses are therefore almost innumerable, even at the same places, considering also how variously the same places are situated on the enlightened disk of the earth with respect to the motion of the penumbra, at the different hours when eclipses happen. When the Moon changes 17 degrees short of her descending node, the penumbra just touches the northern part of the earth's disk near the north pole, and as seen from that place, the Moon appears to touch the Sun, but hides no part of him from sight. Had the change been as far short of the ascending node, the penumbra would have touched the southern part of the disk near the south pole. When the Moon changes 12 degrees short * Plate 6th, figure 10th, a b c d represent the Moon's penumbra; the arch b d its extent on the earth. of the descending node; more than a third part of the penumbra, falls on the northern parts of the earth at the middle of the general eclipse. Had she changed as far past the same node, as much of the other side of the penumbra would have fallen on the southern parts of the earth; all the rest in open space. When the Moon changes 6 degrees from the node, almost the whole penumbra falls on the earth at the middle of the general eclipse. Plate 6th, figure 2d, represents the number of digits eclipsed up to 12 on the right hand, where the eclipse being at the node, is total at the equator. The further the Moon changes from either node within 17 degrees of it, the shorter is the penumbra's continuance on the earth; because it goes over a less portion of the disk. The nearer the penumbra's centre is to the equator at the middle of the general eclipse, the longer is its duration at places where it is central; because the nearer that any place is to the equator, the greater is the circle it describes by the earth's motion on its axis, and the place moving quick keeps longer in the penumbra, whose motion is the same way with that of the place, though faster as has been mentioned. That eclipses of the Moon can never happen only at the time of full, and the reason why she is not eclipsed at every full, has already been mentioned. The Moon when totally eclipsed, (though a dark opaque body, and shines only by reflection,) is not invisible, if she be above the horizon, and the sky clear; but generally appears of a dusky colour, which some have thought to be her native light. But the true cause of her being visible, is the scattered beams of the Sun, bent into the earth's shadow by going through the atmosphere, which being more dense near the earth than at considerable heights above it, refracts, or bends the rays of the Sun more inward the nearer they are passing by the earth's surface, than those rays which go through higher parts of the atmosphere where it is less dense; according to its height, until it be so thin, or rare as to lose its refractive power. When the Moon goes through the centre of the earth's shadow, she is directly opposite to the Sun, yet the Moon has been often seen totally eclipsed in the horizon, when the Sun was also visible in the opposite part of it; for the horizontal refraction being almost 34 minutes of a degree, and the diameter of the Sun and Moon being each at a mean state but 32 minutes, the refraction causes both luminaries to appear above the horizon, when they are actually below it. When the Moon is full at 12 degrees from either node, she just touches the earth's shadow, but does not enter into it. When she is full at 6 degrees from either node, she is totally, but not centrally immersed in the earth's shadow, and when she passes by the node she takes the longest line possible, which is the diameter through it, and such an eclipse, (being both total and central, see plate 6th, figure 10th,) is of the longest duration, namely, three hours, 57 minutes and 6 seconds from the beginning to the end, if the Moon be at her greatest distance from the earth; and 3 hours, 37 minutes and 26 seconds, if she be at her least distance. The reason of this difference is, that when the Moon is farthest from the earth, her motions are retarded, but when nearest to the earth, her motions are accelerated. INTERROGATIONS FOR SECTION TWELFTH. Are the rays of light proceeding from the Sun, frequently intercepted? By what are they intercepted? What is understood by the penumbra ? What is an eclipse of the Sun ? At what stage of the Moon does an eclipse of the Sun happen? How near to either of the nodes must the Sun be to suffer an eclipse? Does the Moon's orbit differ from the ecliptic ? What is the ecliptic? What are the Moon's nodes? Why cannot the Sun be eclipsed unless he be within 17 degrees of the node? How often is the Moon in the ecliptic ? At what stage of the Moon does this happen? How near must the Sun be to either of the nodes, so that the Moon can suffer an eclipse? What causes it? Should the same distance from either node at the time of full Moon exceed twelve degrees, could the shadow of the earth touch the surface of the Moon? As the Moon passes between the Sun and the earth at every new Moon, why is not the Sun eclipsed at every new Moon? Why is not the Moon eclipsed at every full ? What is the farthest point of each orbit from the earth's centre called ? What the nearest point? How many times a year does the Sun generally pass by the nodes? In what time do the nodes pass through all the signs of the ecliptic ? How many lunations after the Sun, Moon and nodes have been in conjunction, before they return nearly to the same state again? What is a periodical return of an eclipse? Are the motions of the Sun, Moon and nodes the same in every part of their orbits ? How can the mean time of these conjunctions be reduced to the true? How many are the greatest number of eclipses that can possibly happen in one year? How many the least ? What the most usual number? Which is the most frequent, those of the Sun or Moon? What is the reason? Are there more visible eclipses of the Moon than of the Sun? What is the reason? What is a total eclipse of the Sun? How long can the Moon hide the whole face of the Sun from our view? In what part of her orbit must the Moon be to cause a total eclipse ? What is an annular eclipse ? How many miles in diameter would the shadow of the Moon be on the earth, in an eclipse when total darkness continues four minutes? When the Moon changes exactly in the node, what is the form of the shadow, and where does it strike the earth? When does an eclipse begin? When does it begin and end at any particular place? When the Moon changes 17 degrees short of her descending node, where will her shadow touch the earth? If as far short of her ascending node, where on the earth will her shadow fall? Why in total eclipses of the Moon is she not invisible, if she be a dark opaque body? Is it possible for the Moon to be visibly eclipsed while the Sun is in sight? When the Moon is full, within six degrees of either node, will she be totally eclipsed? When she passes by the node in the earth's shadow, how much of the Moon will be eclipsed? What is the longest time that the Moon can suffer an eclipse? What the shortest if she be at her least distance ? What is the time of the longest duration of an eclipse of the Sun? What the shortest, if the eclipse be central? |