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a b c d represent the Moon's penumbra; the arch b d, its extent on the Earth. The darkness of the penumbra decreases, as it diverges from the dark shadow of the Moon. The motion of the dark shadow and penumbra over the Earth is nearly from west to east; except at the polar regions, when they sometimes pass in an opposite direction.

The whole number of eclipses in any one year is never less than two, nor more than seven: when two, both are of the Sun; when seven, four are of the Sun, three of the Moon.*

The line of the Moon's nodes has a constant motion from east to west, or backwards in the ecliptic; making a complete revolution in 18 y. 223 d. 20 h. 13 m. 32 s. In a year of 365 days, its motion is 19° 19′ 43′′, completing a revolution in 18 y. 224 d. 4 h. 53 m. when leap year is four times taken; in 18 y. 223 d. 4 h. 53 m. when leap year is five times included. By the retrograde motion of the nodes, either of them is brought round to the Sun, or passes from the Sun to the Sun again, in 346 d. 14 h. 52 m. 14 s. on a mean. Half of this time only intervenes between one node and the other passing the Sun. When eclipses happen at the ascending node, other eclipses may be expected at the descending node in about 173 d.; and, after a lapse of the same time, at the ascending node, thus continuing in rotation.

When the Sun and Moon have been in conjunction with the Moon's ascending or descending node, they will be in conjunction again within 28′ 12′′ of the same node, after 223 mean lunations. Thus is formed a regular period of eclipses. It is completed in 18 y. 11 d. 7 h. 43m. 19 s. when leap year is four times included; 18 y. 10 d. 7 h. 43 m. 19 s. when leap year is

* In some books it is stated, that, when there are seven eclipses in a year, five are of the Sun. Such an event seems barely possible. Should it ever happen, two of them must be very slight, the penumbra just touching the pole.

five times included. There is a regular series of returns to each eclipse. Eclipses at the ascending node first strike the Earth at the north, and pass off at the south pole, moving a little southward at each return. Eclipses at the descending node commence at the south, and retire at the north pole. After an eclipse has completed a series, and left the Earth, it will not again return and commence a new series at the same node, till after an absence of more than 12,000 years. The eclipses commencing at one pole are equal in number to those commencing at the other. The irregular motion of the Earth and Moon may accelerate or retard the commencement of a series about one hundred years. In one series an eclipse may visit the Earth but seventy times; it will not surpass seventy-seven times. When an eclipse returns but seventy times, it will occupy about 1,262 years; when it returns seventy-seven times, it will require 1,388 years. The memorable eclipse of June 16, 1806, was total to a large part of New England. It happened at the Moon's descending node. Having traversed the mighty void from the creation, it first met the south pole on the morning of the 6th of March, O. S. 1049, at 10 h. 11 m. 39 s. Each visit has shown it a little farther north. The last return was June 24, 1824. It happened in the evening) the Sun going down a little eclipsed at Washington. It will again visit the Earth, July 8th, 1842 But, being at 2 h. 2 m. 2 s. in the morning, at Washington, it will be invisible in the United States; but will be large and total over a wide extent of the eastern continent. This eclipse will leave the Earth at the north pole on the 11th of May, in the year 2347, N. S. of the Christian era..

The dark shadow of the Moon, when longest, and falling directly on the Earth, extends about 107 miles. In most cases, however, it falls obliquely; in some, very obliquely, when it may cover an extent of more than 900 miles.

The tables make the extent of the penumbra, when least, about 4,500 miles; when greatest, a little more than 7,000 miles. It is very different at different times, varying on account of the distance of the Sun and Moon, but more from the oblique manner in which it often strikes the Earth.

According to the tables in the author's larger work, total darkness in a solar eclipse will never continue in one place more than 5 m. 32 s. The duration will be a little longer, according to the tables of Enfield. Several authors state this duration short of the truth, making it three minutes, or about three minutes. In the June eclipse of 1806, total darkness was considerably short of the greatest possible duration; yet in the southern part of New Hampshire, the author, by the most careful observation, made it 4 m. 20 s At Sterling, Massachusetts, Robert B. Thomas, the author of the Farmer's Almanac, probably nearer the centre of the shadow as it passed, found the time of total darkness 4 m. 45 s.

The beginning of a general eclipse is when the penumbra first touches the Earth; the ending, when it leaves the Earth. In the same manner, the commencement and end of an eclipse at any particular place, is marked by the approach, or first touching and departure of the penumbra. When the Moon changes in one of her nodes, the penumbra and dark shadow pass over the centre of the Earth, making the longest general eclipse. The duration varies a little with the distance of the Sun; more with the distance of the Moon from the Earth. When the Moon is in apogee, and the Earth in perihelion, it is longest, being then about 6 h. 13 m. The mean duration of a general eclipse is 5 h. 46 m.

The position of the Earth's axis, as seen from the Moon or the Sun, (greatly affects solar eclipses. The eclipse of 1806 will make a return in 1860, visible in the United States. But the position of the Earth's

axis being different, it will be to us far less than it was in its former visit. See this eclipse of 1860, as projected by the author in his larger astronomical work.

What is an eclipse? What heavenly body shines by its own light? What is the form of a planet's dark shadow? Are the shadows of the planets coextensive with the Sun's light? Do the primary planets ever eclipse each other? What do eclipse? What is the greatest length of the Earth's shadow? What is its mean length? Why have we not eclipses at every change and full? Where must the Moon be in order that there may be an eclipse? What is the limit of solar, and what of lunar eclipses? When are lunar eclipses partial? When are they total? and when central ? What causes the Moon to be visible when she is eclipsed? Which are the most frequent, solar or lunar eclipses? Why is a solar eclipse sometimes total and sometimes annular According to calculation, how many annular, and how many total eclipses will be visible in the United States in the present century? At what times will they happen? What is the Moon's penumbra? What is the greatest number of eclipses in a year? What is the least? When two, are they lunar or solar? How are they when seven? In what direction does the line of the Moon's nodes move? In what time does it complete a revolution? When eclipses happen at one node, how long before they may be expected at the other When the Sun and Moon have been in conjunction at one of the Moon's nodes, how long before they will be in conjunction again near the same node? Is there a regular period of eclipses? How long is it? Where do eclipses at the ascending node first strike the Earth? Where do they pass off? Where do eclipses at the descending node commence and retire? After an eclipse has completed a series, and left the Earth, how long before it will commence a new series at the same node? How many times may an eclipse visit the Earth in one series? In what number of years is a series completed? At what node was the memorable eclipse of June 16, 1806? When did this eclipse first meet the south pole? When was its last return? Why did it not attract notice? When will be its next return? Where will it be visible and total? When, and at what pole, will this eclipse leave the Earth? How many miles does the dark shadow of the Moon extend on the Earth? What is the extent of the penumbra? Why is the extent different at different times? How long will total darkness continue in a solar eclipse? What was the duration of total darkness in the June eclipse of 1806? When does a general eclipse begin and end? When does an eclipse begin and end at a particular place? What varies a little the duration? What is the longest continuance of a general eclipse? What is its mean duration? Has the position of the Earth's axis any effect on solar eclipses?

9 Catalogue of Eclipses visible at Washington, and generally throughout the United States, extracted from the Author's larger Work. Commencing with the Year 1831, it is continued through the 19th Century.

The time set to solar eclipses is the middle of each eclipse, as seen at Washington; to lunar, the minute of opposition. Both are reduced to apparent time.

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