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darkest portion is called the umbra, and the partial shadow the penumbra.
UMBRA AND PENUMBRA OF THE EARTH AND MOON.
Penumbra is from the Latin pene, almost, and umbra, a shadow. In this cut, the Earth's umbra and penumbra will be readily found by the lettering; while A is the umbra, and B B the penumbra, of the Moon. The latter is more broad than it should be, owing to the nearness of the Sun in the cut, as it never extends to much over half the Earth's diameter. The student will see at once that solar eclipses can be total only to persons within the umbra; while to all on which the penumbra falls, a portion of the Sun's disc will be obscured.
448. The average length of the Earth's umbra is about 860,000 miles; and its breadth, at the distance of the Moon, is about 6000 miles, or three times the Moon's diameter.
As both the Earth and Moon revolve in elliptical orbits, both the above estimates are subject to variations. The length of the Earth's umbra varies from 842,217 to 871,262 miles; and its diameter, where the moon passes it, varies from 5235 to 6365 miles.
449. The average length of the Moon's umbra is about 239,000 miles. It varies from 221,148 to 252,638 miles, according to the Moon's distance from the Sun. Its greatest diameter, at the distance of the Earth, is 170 miles; but the penumbra may cover a space on the Earth's surface 4393 miles in diameter.
When the Moon but just touches the limb of the Sun, or the umbra of the Earth, it is called an appulse (see C and J in the cut on the opposite page).
450. A partial eclipse is one in which only part of the Sun or Moon is obscured. A solar eclipse is partial to all places outside the umbra; but within the umbra, where the whole disc is obscured, the eclipse is said to be total. A central eclipse is one taking place when the Moon is exactly at one of her nodes. If lunar, it is total, as the Earth's umbra is always broad enough, at the Moon's distance, if centrally passed, to obscure her whole disc. But a solar eclipse may be central and not total, as the Moon is not always of sufficient apparent diameter to cover the
penumbra? Derivation? Within which are solar eclipses total? 448. The average length of the Earth's shadow? Breadth at the Moon's distance? Do they vary? Why? 449. Average length of the Moon's umbra? Does it vary? Why? Greatest diameter at the Earth's surface? Of penumbra? What is an appulse? 450. A partial eclipse? A total? A central? Are all central eclipses total? Why not? What called then? Why?
whole disc of the Sun. In that case, the eclipse would be annular (from annulus, a ring), because the Moon only hides the center of the Sun, and leaves a bright ring unobscured.
PROGRESS OF A CENTRAL ECLIPSE.
451. It has already been shown that the apparent magnitudes of bodies vary as their distances vary; and as both the Earth and Moon revolve in elliptical orbits, it follows that the Moon and Sun must both vary in their respective apparent magnitudes. Hence some central eclipses of the Sun are total, while others are partial and annular.
At A, the Earth is at her aphelion, and the Sun being at his most distant point, will have his least apparent magnitude. At the same time, the Moon is in perigee, and appears larger than usual. If, therefore, she pass centrally over the Sun's disc, the eclipse will be total.
At B, this order is reversed. The Earth is at her perihelion, and the Moon in apogee; so that the Sun appears larger, and the Moon smaller than usual. If, then, a central eclipse occur under these circumstances, the Moon will not be large enough to eclipse the whole of the Sun, but will leave a ring, apparently around herself, unobscured. Such eclipse will be annular.
452. 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.
553. As the solar ecliptic's limits are further from the Moon's nodes than the lunar, it results that we have more eclipses of the Sun than of the Moon. There may be seven in all in one
451. Why are some central eclipses total, and others partial and annular? How long may an annular eclipse continue? A total eclipse of the Sun? Of the Moon? 458. Which kind of eclipses is most frequent? Why? The greatest number in a year?
year, viz., five solar and two lunar; but the most usual number is four. There can never be less than two in a year; in which case, both must be of the Sun. Eclipses both of the Sun and Moon recur in nearly the same order, and at the same intervals, at the expiration of a cycle of 223 lunations, or 18 years of 365 days and 15 hours. This cycle is called the Period of the Edipses. At the expiration of this time, the Sun and the Moon's nodes will sustain the same relation to each other as at the beginning, and a new cycle of eclipses begins.
454. In a total eclipse of the Sun, the heavens are shrouded in darkness, the planets and stars become visible, the temperature declines, the animal tribes become agitated, and a general gloom overspreads the landscape. Such were the effects of the great eclipse of 1806. In a lunar eclipse, the Moon begins to lose a portion of her light and grows dim, as she enters the Earth's penumbra, till at length she comes in contact with the umbra, and the real eclipse begins.
455. In order to measure and record the extent of eclipses, the apparent diameters of the Sun and Moon are divided into twelve equal parts, called digits; and in predicting eclipses, astronomers usually state which "limb" of the body is to be eclipsed-the southern or northern-the time of the first contact, of the nearest approach of centers, direction, and number of digits eclipsed.
FIVE DIGITS ECLIPSED.
456. The last annular eclipse visible in the United States, occurred May 26, 1854. The next total eclipse of the Sun will be August 7, 1869.
Some of the ancients, and all barbarous nations, formerly regarded eclipses with amazement and fear, as supernatural events, indicating the displeasure of the gods. Columbus is said
How many of each? Least number, and which? Usual number? What said of the order of eclipses? Time of cycle? 454. Describe the effects of a total eclipse of the Sun. The process of a lunar eclipse? 455. How are eclipses measured and recorded? 456. When the next annular eclipse visible in this country? The next total? How have
to have made a very happy use of this superstition, as already stated on a previous page. (Art. 433.)
457. Eclipses can be calculated with the greatest precision, not only for a few years to come, but for centuries and ages either past or to come. This fact demonstrates the truth of the Copernican theory, and illustrates the order and stability that everywhere reign throughout the planetary regions.
The following is a list of all the solar eclipses that will be visible in Europe and America during the remainder of the present century. To those which will be visible in New England, the number of digits is annexed.
The eclipses of 1869, 1875, and 1900 will be very large. In those of 1858, 1861, 1873, 1875, and 1880, the Sun will rise eclipsed.
That of 1875 will be annular. The scholar can continue this table, or extend it backwards, by adding or substracting the Chaldean period of 18 years, 11 days, 7 hours, 54 minutes, and 31 seconds.
PRIMARY PLANETS CONTINUED-MARS AND THE
458. MARS is the first of the exterior planets, its orbit lying immediately without, or beyond, that of the Earth, while those of Mercury and Venus are within. He appears, to the naked eye, of a fine ruddy complexion; resembling, in color, and appa
the ignorant and superstitious regarded eclipses? 457. What said of the calculation of eclipses? What does this demonstrate and illustrate? 458. Position of Mars' orbit? How does he appear to the naked eye? When most brilliant? When least?
rent magnitude, the star Antares, or Aldebaran, near which it frequently passes. It exhibits its greatest brilliancy about the time that it rises when the Sun sets, and sets when the Sun rises; because it is then nearest the Earth. It is least brilliant when it rises and sets with the Sun; for then it is five times farther removed from us than in the former case.
459. Its distance from the Earth at its nearest approach is about 50,000,000 of miles. Its greatest distance from us is about 240,000,000 of miles. In the former case, it appears nearly 25 times larger than in the latter. When it rises before the Sun, it is our morning star; when it sets after the Sun, it is our evening star.
The distance of all the planets from the Earth, whether they be interior or exterior planets, varies within the limits of the diameters of their orbits; for when a planet is in that point of its orbit which is nearest the Earth, it is evidently nearer by the whole diameter of its orbit, than when it is in the opposite point, on the other side of its orbit. The apparent diameter of the planet will also vary for the same reason, and to the same degree.
460. Mars is sometimes seen in opposition to the Sun, and sometimes in superior conjunction with him; sometimes gibbous, but never horned. In conjunction, it is never seen to pass over the Sun's disc, like Mercury and Venus. These prove not only that its orbit is exterior to the Earth's orbit, but that it is an opaque body, shining only by the reflection of the Sun.
461. The motion of Mars through the constellations of the zodiac is but little more than half as great as that of the Earth; it being generally about 57 days in passing over one sign, which is at the rate of a little more than half a degree each day. Thus, if we know what constellation Mars enters to-day, we may conclude that two months hence it will be in the next constellation ; four months hence, in the next; six months, in the next, and
Its mean sidereal revolution is performed in 686.9796458 solar days; or in 686 days, 23 hours, 30 minutes, 41.4 seconds. Its synodical revolution is performed in 779.936 solar days; or in 779 days, 22 hours, 27 minutes, and 50 seconds.
462. Mars performs his revolution around the Sun in one year and 10 months, at the distance of 145,000,000 of miles; moving in its orbit at the mean rate of 55,000 miles an hour. Its diurnal rotation on its axis is performed in 24 hours, 39
459. Its distance from the Earth? What effect upon its apparent magnitude? When morning and evening star? How do the distances of the planets from the Earth vary? Their apparent diameters? 460. Is Mars ever in opposition to the Sun? In conjunction? Its phases? Does it ever transit the Sun? What do these facts prove? 461. What is his rate of motion through the constellations? What calculation based upon it? 462. His periodic time? Distance from the Sun? Mean rate of motion per hour? Time of rotation on his axis? How does his day compare with ours?