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mary and secondary, derives its light from the Sun, it must cast a shadow towards that part of the heavens which is opposite to the Sun. This shadow is of course nothing but a privation of light in the space hid from the Sun by the opaque body, and will always be proportioned to the magnitude of the Sun and planet.
If the Sun and planet were both of the same magnitude, the form of the shadow cast by the planet, would be that of a cylinder, and of the same diameter as the Sun or planet. If the planet were larger than the Sun, the shadow would continually diverge, and grow larger and larger; but as the Sun is much larger than any of the planets, the shadows which they cast must converge to a point in the form of a cone; the length of which will be proportional to the size and distance of the planet from the Sun.
The magnitude of the Sun is such, that the shadow cast by each of the primary planets always converges to a point before it reaches any other planet; so that not one of the primary planets can eclipse another. The shadow of any planet which is accompanied by satellites, may, on certain occasions, eclipse its satellites; but it is not long enough to eclipse any other body. The shadow of a satellite, or Moon, may also, on certain occasions, fall on the primary, and eclipse it.
When the Sun is at his greatest distance from the Earth, and the Moon at her least distance, her shadow is sufficiently long to reach the Earth, and extend 19,000 miles beyond. When the Sun is at his least distance from the Earth, and the Moon at her greatest, her shadow will not reach the Earth's surface by 20,000 miles. So that when the Sun and Moon are at their mean distances, the cone of the Moon's shadow will terminate a little before it reaches the Earth's surface.
In the former case, if a conjunction take place when the centre of the Moon comes in a direct line between the centres of the Sun and Earth, the dark shadow of the Moon will fall centrally upon the Earth, and cover a circular area of 175 miles in diameter. To all places lying within this dark spot, the Sun will be totally eclipsed, as illustrated by Fig. 13. In consequence of the Earth's motion during the eclipse, this circular area becomes a continued belt over the earth's surface; being, at the broadest,
In what direction does every planet of the solar system cast a shadow? What is this shadow, and to what is it proportional? If the Sun and planet were both of the same magnitude, what would be the form of the shadow, and its diameter? If the planet were larger than the Sun, what would be the form of the shadow? But as the Sun is much larger than any of the planets, what must be the form of their shadows, and to what are they proportional? Why can no one of the primary planets eclipse another? Explain how, on certain occasions, they may eclipse their satellites, and on others be eclipsed by them. When the Sun is at his greatest distance from the Earth, and the Moon at her least distance, how far will her shadow extend? When the Sun is at his least distance, and the Moon at her greatest? When the Sun and Moon are both at their mean distances? In the first case, in what circumstances will the Moon's shadow fall centrally on the Earth, and what will be its figure and diameter? How will the Sun ap pear to all places lying within this dark spot? Describe the effect of the Earth's motion. during the eclipse, upon this circular area.
175 miles wide. This belt is, however, rarely so broad, and often dwindles to a mere nominal line, without total darkness.
In March, this line extends itself from S. W. to N. E., and in September, from N. W. to S. E. In June, the central line is a curve, going first to the N. E., and then to the S. E.; in December, on the contrary, first to the S. E., and then to the N. E. To all places within 2000 miles, at least, of the central line, the eclipse will be visible; and the nearer the place of observation is to the line, the larger will be the eclipse. In winter, if the central trace be but a little northward of the equator, and in summer, if it be 25° N. latitude, the eclipse will be visible all over the northern hemisphere. As a general rule, though liable to many modifications, we may observe, that places from 200 to 250 miles from the central line, will be 11 digits eclipsed; from thence to 500 miles, 10 digits; and so on, diminishing one digit .n about 250 miles.
ECLIPSES OF THE SUN.
If, in either of the other cases, a conjunction take place when the Moon's centre is directly between the centres of the Sun and Earth, as before, the Moon will then be too distant to cover the entire face of the Sun, and there will be seen, all around her dark body, a slender ring of dazzling light.
This may be illustrated by the adjoining fig. ure. Suppose CD to represent a part of the Earth's orbit, and the Moon's shadow to terniinate at the vertex V. The small space between ef will represent the breadth of the luminous ring which will be visible all around the dark body of the Moon.
Such was the eclipse of February 12, 1831, which passed over the southern states from S. W. to N. E. It was the only annular eclipse ever visible in the United States. Along the path of this eclipse, the luminous ring remained perfect and unbroken for the space of two minutes. The next annular eclipse which will be visible to any considerable portion of the United States, will take place Sept. 18th, 1838.
From the most elaborate calculations, compared with a long series of observations, the length of the Moon's shadow in eclipses, and her distance from the Sun at the same time, vary within the limits of the following table:
In either of the other cases, the same circumstances occurring as before, what will be the appearance of the Sun? Why does not the Moon, in this case, cause a total eclipse? When did the only eclipse of this kind, ever visible in the United States, happen? How long did the luminous ring, along its path, remain unbroken? When will the next annular eclipse, visible to any considerable portion of the United States, happen?
Thus it appears that the length of the cone of the Moon's shadow, in eclipses, varies froin 228,499 to 236,292 miles; being 7.793 miles longer in the one case, than in the other. The inequality of her distances from the Earth is much greater; they vary from /221,148 to 252,638 miles, making a difference of 31,490 miles.
Although a central eclipse of the Sun can never be total to any spot on the Earth more than 175 miles broad; yet the space over which the Sun will be more or less partially eclipsed, is nearly 5000 miles broad.
The section of the Moon's shadow, or her penumbra, at the Earth's sur face, in eclipses, is far from being always circular. If the conjunction happen when the centre of the Moon is a little above or a little below the line joining the centres of the Earth and Sun, as is most frequently the case, the shadow will be projected obliquely over the Earth's surface, and thus cover a much larger space.
To produce a partial eclipse, it is not necessary that the shadow should reach the Earth; it is sufficient that the apparent distance between the Sun and Moon be not greater than the sum of their semidiameters.
If the Moon performed her revolution in the same path in which the Sun appears to move; in other words, if her orbit lay exactly in the plane of the Earth's orbit, the Sun would be eclipsed at the time of every new Moon, and the Moon at the time of every full. But one half of the Moon's orbit lies about 50 on the north side of the ecliptic, and the other half as far on the south side of it; and, consequently, the Moon's orbit only crosses the Earth's orbit in two opposite points, called the Moon's nodes.
When the Moon is in one of these points, or nearly so, at the time of new Moon, the Sun will be eclipsed. she is in one of them, or nearly so, at the time of full Moon, the Moon will be eclipsed. But at all other new Moons, the Moon either passes above or below the Sun, as seen from the Earth; and, at all other full Moons, she either passes above or below the Earth's shadow; and consequently there can be no eclipse.
What are the limits between which the Moon's shadow varies in eclipses? What is the difference between these two limits? What are the limits of her distances from the Earth? What is the difference between them? What is the greatest breadth of any spot on the Earth's surface, to which a central eclipse of the Sun can be total? What is the breadth of the greatest space over which the Sun can be more or less partially eclipsed? Is the penumbra of the Moon at the Earth's surface in eclipses always circular? In what circumstances will the shadow be projected obliquely over the Earth's surface? Must the shadow reach the Earth, to produce a partial eclipse? What is the greatest apparent distance between the Sun and Moon, within which such a result will take place? Why is not the Sun eclipsed at the time of every new Moon, and the Moon at every full? In what circumstances will an eclipse of the Sun, and in what an eclipse of the Moon, happen?
If the Moon be exactly in one of her nodes at the time of her change, the Sun will be centrally eclipsed. If she be 14° from her node at the time of her change, the Sun will appear at the equator to be about 11 digits eclipsed. If she be 3° from her node at the time of her change, the Sun will be 10 digits eclipsed, and so on ; a digit being the twelfth part of the Sun's diameter. But when the Moon is about 18° from her node, she will just touch the outer edge of the Sun, at the time of her change, without, producing any eclipse. These are called the ecliptic limits. Between these limits, an eclipse is doubtful, and requires a more exact calculation.
The mean ecliptic limit for the Sun is 1610 on each side of the node; the mean ecliptic limit for the Moon is 101 on each side of the node. In the former case, then, there are 33° about each node, making, in all, 660 out of 360°, in which eclipses of the Sun may happen in the latter case, there are 21° about each node, making, in all, 42° out of 360° in which eclipses of the Moon usually occur. The proportion of the solar, to the lunar eclipses, therefore, is as 66 to 42, or as 11 to 7. Yet, there are more visible eclipses of the Moon, at any given place, than of the Sun; because a lunar eclipse is visible to a whole hemisphere, a solar eclipse only to a small portion of it.
The greatest possible duration of the annular appearance of a solar eclipse, is 12 minutes and 24 seconds; and the greatest possible time during which the Sun can be totally eclipsed, to any part of the world, is 7 minutes and 58 seconds. The Moon may continue totally eclipsed for one hour and three quarters.
Eclipses of the Sun always begin on his western edge, and end on his eastern but all eclipses of the Moon commence on her eastern edge, and end on her western.
If the Moon, at the time of her opposition, be exactly in her node, she will pass through the centre of the Earth's shadow, and be, totally eclipsed. If, at the time of her opposition, she be within 6° of her node, she will still pass through the Earth's shadow, though not centrally, and be totally eclipsed: but if she be 12° from her node, she will only just touch the Earth's shadow, and pass it without being eclipsed.
The duration of lunar eclipses, therefore, depends upon the difference between the diameter of the Moon and that section of the Earth's shadow
In what circumstances is the Sun centrally eclipsed? What is the ratio between the Moon's distance from her node, and the number of digits that the Sun is eclipsed? What are these limits called? Will there always be eclipses when the Moon is within these limits? What is the ecliptic limit for the Sun? What is it for the Moon? What number of degrees, then, are there about each node, and how many out of 360°, in which solar eclipses can happen? How many in which lunar eclipses usually hap pen? What then is the proportion of the solar to the lunar eclipses? Why then are there more eclipses of the Moon visible at any given place than of the Sun? What is the greatest possible duration of the annular appearance of a solar eclipse? What is the greatest possible duration of a total solar eclipse to any part of the world? What is the greatest duration of a total lunar eclipse? On which side of the Sun do solar eclipses always begin, and on which do they end? On which side of the Moon do lunar eclipses always begin, and on which do they end? In what circumstances is the Moon totally eclipsed? Beyond what distance from her node, if she be, will she only touch the Earth's shadow, and not be eclipsed? On what then does the duration of lunar eclipses depend?
through which she passes When an eclipse of the Moon is both total and central, its duration is the longest possible, amounting nearly to 4 hours but the duration of all eclipses not central, varies with her distance from the node..
The diameter of the Earth's shadow, at the distance of the Moon, is nearly three times as large as the diameter of the Moon; and the length of the Earth's shadow is nearly four times as great as the distance of the Moon exceeding it in the same ratio that the diameter of the Earth does the diameter of the Moon, which is as 3.663 to 1.
The length of the Earth's shadow, and its diameter at | Diameter | Length of the distance of the Moon, are subject to the variations exhibited in the following table.
the shadow in ms.
The first column of figures expresses the diameter of the Earth's shadow at the Moon and as the diameter of the Moon is only 2162 miles, it is evident that it can always be comprehended by the shadow, which is more than twice as broad as the disc of the Moon.
The time which elapses between two successive changes of the Moon is called à Lunation, which, at a mean rate, is about 29 days. If 12 lunar months were exactly equal to the 12 solar months, the Moon's nodes would always occupy the same points in the ecliptic, and all eclipses would happen in the same months of the year, as is the case with the transits of Mercury and Venus: but, in 12 lunations, or lunar months, there are only 354 days; and in this time the Moon has passed through both her nodes,
In what circumstances is the duration of the lunar eclipse the longest possible? What is the length of the greatest duration of a lunar eclipse? With what does the duration of eclipses, not central, vary? What is the diameter of the Earth's shadow at the distance of the Moon? What is the length of the Earth's shadow? What is their ratio to each other? Between what limits does the length of the Earth's shadow, and its diameter at the distance of the Moon, vary? What is the breadth of the Earth's shadow compared with that of the disc of the Moon? What is a lunation? How many days does a lunation embrace? Why do not all eclipses happen in the same months of the year?