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 11° 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 calculaLion.

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, 66° out of 360°, in which eclipses of the Sun may happen: in the latter case, there are 210 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 60 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 shad

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.

Sun at the perigee

of the

shadow.

ow in ms.

Sun at his mean distance

Moon at her mean distance

5,799

856,597

871,262

Moon at the perigee

6,365

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 inore 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?

but has not quite accomplished her revolution arcund the Sun: the consequence is, that the Moon's nodes fall back in the ecliptic at the rate of about 1910 annually; so that the eclipses happen sooner every year by about 19 days.

As the Moon passes from one of her nodes to the other in 173 days, there is just this period between two successive eclipses of the Sun, or of the Moon. In whatever time

of the year, then, we have eclipses at either node, we may be sure that in 173 days afterwards, we shall have eclipses at the other node.

As the Moon's nodes fall back, or retrograde in the ecliptic, at the rate of 191 every year, they will complete a backward revolution entirely around the ecliptic to the same point again, in 18 years, 225 days; in which time there would always be a regular period of eclipses, if any complete number of lunations were finished without a remainder. But this never happens; for if both the Sun and Moon should start from a line of conjunction with either of the nodes in any point of the ecliptic, the Sun would perform 18 annual revolutions and 2220 of another, while the Moon would perform 230 lunations, and 85° of another, before the node would come around to the same point of the ecliptic again: so that the Sun would then be 138° froin the node, and the Moon 85° froin the Sun.

But after 223 luuations, or 18 years. 11 days,* 7 hours, 42 minutes, and 31 seconds, the Sun, Moon, and Earth, will return so nearly in the same position with respect to each other, that there will be a regular return of the same eclipses for many ages. This grand period was discovered by the Chaldeans, and by them called Saros. If, therefore, to the mean time of any eclipse, either of the Sun or Moon, we add the Chaldean period of 18 years and 11 days, we shall have the return of the same eclipse. This mode of predict. ing eclipses will hold good for a thousand years. In this period there are usually 70 eclipses; 41 of the Sun, and 29 of the Moon.

The number of eclipses in any one year, cannot be less than two, nor more than seven. In the former case, they will both be of the Sun; and in the latter, there will be five of the Sun, and two of the Moon—those of the Moon will be total. There are sometimes six; but the usual number is four: two of the Sun, and two of the Moon.

The cause of this variety is thus accounted for. Although the Sun usually passes by both nodes only once in a year, he may pass the same node again a little before the end of the year. In consequence of the retrograde motion

*If there are four leap years in this interval, add 11 days; but if there are five, add only ten days.

How far do the Moon's nodes fall back in the ecliptic annually, and how much sooner do the eclipses happen every year? In what time does the Moon pass from one of her nodes to the other? What is the length of the time which elapses between two successive eclipses of the Sun or the Moon? After there have been eclipses at one node, in what time may we be sure that there will be eclipses at the other? In what time do the Moon's nodes complete a backward revolution around the ecliptic? Why is there not always regular period of eclipses in this time? If the Sun and Moon should both start from a line of conjunction with either node, how many revolutions would the Sun erform, and how many lunations the Moon, before the node would come around to he same point again? After how many lunations will the Sun, Moon, and Earth, eturn so nearly to the same position with respect to each other, that there will be a regular return of the same eclipses for many ages? What nation discovered this grand period, and what did they call it? What is the mode of predicting eclipses, with which this fact furnishes us? How many eclipses are there usually in this period? What is the least, and what the greatest number of eclipses, in any one year? In the former case, what eclipses will they be? What, in the latter? What is the usual amber of eclipses in the year, and what eclipses are they? Please explain the cause of this variety.

of the Moon's nodes, he will come to either of them 173 days after passing the other. He may, therefore, return to the same node in about 316 days, having thus passed one node twice and the other once, making each time, at each, an eclipse of both the Sun and the Moon, or, six in all. And, since 12 lunations, or 354 days from the first eclipse in the beginning of the year, leave room for another new Moon before the close of the year, and since this new Moon may fall within the ecliptic limit, it is possible for the sun to be eclipsed again. Thus there may be seven eclipses in the same year. Again: when the Moon changes in either of her nodes, she cannot come within the lunar ecliptic limit at the next full, (though if she be full in one of her nodes, she may come into the solar ecliptic limit at her next change,) and six months afterwards, she will change near the other node; thus mak ing only two eclipses.

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 1838, 1854, 1869, 1875, and 1900, will be very large. In those of 1845, 1858, 1861, 1873, 1875, and 1880, the Sun will rise eclipsed.

In that of 1844, the Sun will set eclipsed. Those of 1838, 1854, and 1975, will be annular. The scholar can continue this table, or extend it backwards, by adding or subtracting the Chaldean period of 18 years, 11 days, 7 hours, 54 minutes, and 31 seconds.

MARS.

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.

Mars appears to the naked eye, of a fine ruddy com plexion; resembling, in colour, and apparent magnitude, the star Antares, or Aldebaran, near which it frequently passes. It exhibits its greatest brilliancy about the time

What is the position of Mars in the solar system? Describe its appearance to the na ked eye. When does it exhibit its greatest brilliancy?

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. Its distance from the Earth at its nearest approach is about 50 millions of miles. Its greatest distance from us is about 240 millions 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.

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. This proves 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.

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 so on.

Mars performs his revolution around the Sun in 1 year and 10 months, at the distance of 145 millions of miles; moving in its orbit at the mean rate of 55 thousand miles an hour. Its diurnal rotation on its axis is performed in 24 hours, 39 minutes, and 21 seconds; which makes its day about 44 minutes longer than ours.

Why is it most brilliant at this time? What are its least and greatest distances from us? How much larger does it appear in the former case than in the latter? Within what limis does the distance of all the planets from the Earth vary? With what does the apparent diameter of a planet vary? What moon-like phases has Mars ? What does the fact, that it never assumes the crescent form at its conjunction, prove, in regard to its situation? How do we know it to be opaque? What is the rate of its motion through the constellations of the zodiac, compared with that of the Earth? How long is it in passing over one sign? At what rate per day is this? How, then, if we know in what constellation it is at any one time, may we determine in what constellation it will be at any subsequent time? In what time does it perform its revolution around the Sun? What is its distance from the Sun? What is the mean rate of its motion in its or bit per hour? In what time does it perform its revolution on its axis ? What, then, is the length of its day, compared with that of the Earth 7