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321° 0'

16" O'S.

231 0

18 0 S.

1290 19 0 N.
301 0

210 s. 2. At what time did Saturn rise at London, on November 1st, 1828? Ans. 15 min. past 10 p.m.

3. When did Jupiter, Mars, and Venus, set at London, on February 2d, 1837 ?

4. Required the situation of the Planets for November 19th, 1838.

5. Which of the Planets were visible at Newcastle, November 25, 1837, and whether in the evening or morning ?

To find when Jupiter and Venus are Morning, and when

they are Evening Stars.
1. Find their situation, as before directed.

2. If it be to the east of the sun's place, they will be evening stars ; if to the west, they will be morning stars.

EXAMPLES.–1. Were Jupiter and Venus morning or evening stars on Dec. 7th, 1828 ?

Ans. They were W. of the sun, and were morning stars.

2. During what time will Jupiter be a morning star this year, and what time will it be an evening star ?

3. Required the same for Venus.


SECTION IV. PROBLEMS RELATING TO THE MOON. The motion of the moon is very irregular. This irregularity is occasioned by its being attracted both by the sun and by the earth. It does not move in the ecliptic, but its orbit forms with the ecliptic an angle of 532. The

points where its orbit cuts the ecliptic are called its nodes, and are constantly changing..

The course which the moon appears to pursue in the heavens is always varying. Passing in a month through all the signs of the zodiac, its meridian altitude will vary in that time 47'. The full moon that happens in Cancer is the most beneficial to us in the northern hemisphere, for its altitude is then the greatest, and it continues longest above the horizon: but when the full moon happens in Cancer, the sun is in Capricorn; and our days being then at the shortest, we are the most in want of auxiliary light. The full moon that is of the least use to us is in Capricorn, for its altitude is then the least, and its stay the shortest above the horizon : but the sun being then in Cancer, our days are long, and the light of the moon is not needed.

This is a wonderful display of the Divine wisdom and goodness, in apportioning the quantity of light suitable to the various necessities of the inhabitants of the earth, according to their different situations.

The full moon being always opposite to the sun, can never be seen by the inhabitants of the poles whilst the sun is above the horizon; but all the time the sun is below the horizon the full moons never set.


An eclipse of the moon is caused by its entering into the earth's shadow. It can only bappen at the time of full

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moon, or when in opposition to the sun, as the shadow of the earth must lie opposite to the sun.

The preceding figure will illustrate this.

Let A B represent the sun, and C g the earth. The moon, when at a, is just entering the earth's shadow, and the eclipse is then said to commence; at D, the moon is wholly enveloped in the shadow and is totally eclipsed.

When most obscure, the moon's disc is not entirely hid from us, for some of the solar light generally reaches it through the refracting influence of our own atmosphere.

An observer who consults an almanack often expects an eclipse of the moon to begin long before he notices the earth's shadow to strike it. An inspection of the figure will explain the reason of this. Be. fore the moon reaches the line b C it receives rays from the whole of the sun's surface, but after crossing that line, the portion of the sun's

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disc from which it receives light is gradually diminished by the intervention of the earth; a shadow thus gently steals over the moon. It is only after crossing the line C d that all the sun's rays are cut off, and that it enters the dark shadow, and it is then only that an observer unprovided with a telescope detects the commencement of the eclipse. The conical dark shadow C d 9, cast by the earth, is termed the umbra. The partial shadow, which gradually increases in intensity as the umbra is approached, is called the penumbra (almost shade). During the progress of an eclipse the penumbra always precedes and follows the umbra. The appearance of the penumbra, as seen through a telescope, is well depicted in the annexed wood-cut, allowance being made for a little necessary exaggeration in the depths of its shade.

An eclipse of the sun is caused by the interposition of the moon between the earth and sun, and therefore it must happen when the moon is in conjunction with the sun, or at the new moon.

ECLIPSE OF THE SUN. When the sun A B, the moon C, and the earth D, are in the relative position represented in this figure, an eclipse of the sun takes place.

The eclipse may be total, when the whole of the sun's disc is obscure; partial when only a part of his surface is obscured; and annular, when the moon cuts off a circle in the middle, leaving a luminous ring (Latin annulus) around the part obscured

The wood-cut represents the circumstances in which an annular eclipse takes place. The moon's umbra falls short of the earth, and an observer at e, directing his eye along the upper edge of the moon will see the portion of the sun A a, unobscured; directing it past the lower

edge, he will see the portion B b, and so of the whole circumference.

Frequently on the occurrence of an eclipse of the sun, the moon happens to be nearer to the earth than in the case supposed, and the umbra strikes the earth. The sun will then be totally eclipsed to an observer at e, and partially eclipsed to observers on each side of the conical umbra in a degree proportioned to their distance from it.

Lunar eclipses are visible in all parts of the earth which have the moon above their horizon, and are everywhere of the same magnitude and duration; but a solar eclipse is never seen throughout the whole hemisphere of the earth where the sun is visible; as the moon's disc is too small to hide the whole, or any part, of the sun from the whole disc or hemisphere of the earth. Nor does an eclipse of the sun appear the same in all parts of the earth where it is visible, but when in one place it is total in another it is partial.

If the moon moved in the ecliptic, there would be an eclipse of the moon every full moon, and an eclipse of the sun every new moon; but the moon being, in one part of its orbit, 52° to the north of the ecliptic, and in another part 54' to the south, there can be no eclipse except the moon, at full or change, be near its nodes. When the moon is less than 18° from either of the nodes at the time of change, there will be an eclipse of the sun; when it is less than 12° from either node at the time of full, there will be an eclipse of the moon.

These are called the ecliptic limits; and as they are nearly in the proportion of 3 to 2, there will be more solar than lunar eclipses in the same ratio. But more lunar than solar eclipses are seen at any place; because a lunar eclipse is visible to a whole hemisphere,mwhereas a solar eclipse is visible only to a part. The greatest number of eclipses that can happen any year is 7, and of these, 5 will be of the sun, and 2 of the moon—the least number that can happen is 2, and these must be both solar: the mean number is about 4. –The season of eclipses will return at an interval of about 9 or 10 days less than half a year; so that, if there be eclipses about the middle of January, the next will be about the first week of July.

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