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toward the east. From the inferior conjunction to the point of greatest elongation, the illuminated part will appear less than a semicircle, and it will be smaller the nearer the planet is to the inferior conjunction ; while, in the other half of its path, the planet will appear more than a semicircle, and greater the nearer it is to the superior conjunction. But as the planet is considerably nearer to the earth in that half of its orbit which is divided by the inferior conjunction than it is in the other half, it does not follow that the planet will shine the most resplendently when the greater portion of it is illuminated.

2. THE SUPERIOR PLANETS,

As the orbits of all the superior planets lie beyond, and therefore include that of the earth, they can have no inferior conjunction, and no transits over the sun; neither will their distances from that luminary be limited by any elongation, like that of Mercury and Venus; but they will, in the course of a certain period of time, appear in every part of the circumference of the heavens; but, in consequence of the earth and them revolving in the same direction, and with different degrees of rapidity, they will appear to move sometimes forward, sometimes backward, and sometimes they will appear to be stationary.

Take, for instance, Mars; and, for the sake of simplification, suppose that instead of the earth's moving, as in reality it does, round the sun, the sun moves round the earth in the plane of the ecliptic, and with the same velocity that the earth does, but on the opposite side of the orbit, After his conjunction with the sun, Mars, like the sun, appears to have an annual motion from west to east; Mars is, therefore, approaching the sun; but as the apparent motion of the sun is more rapid Mars is left behind, The motion of Mars becomes gradually slower, and when, after an interval of nearly one year, his right ascension from the sun is 128°, he appears for some days stationary. Afterwards Mars seems to move in a retrograde direction, from east to west, while the sun moves from west to east. Thus the distance between the bodies increases rapidly till Mars be in opposition to the sun. The retrograde motion continues, but at a rate gradually diminishing, till the difference in right ascension be again 128°, at which time Mars again becomes stationary, but, after a few days, resumes the direct motion from west to east. This direct motion would increase the distance between Mars and the sun, but as the sun moves with more rapidity, be comes up with Mars, and after an interval of about one year, Mars is again in conjugation.

SECTION IV.

PHENOMENA PRODUCED BY THE MOTIONS OF THE EARTH. The earth is a globe, having its mean diameter 7911.73 miles, or, in round numbers, 8000, its mean distance from the sun 95,000,000 miles, and it performs its revolution in the ecliptic, from one point of that orbit

to the same back again, in 365 days, 5 hours, 48 minutes, 49 seconds; or from one star to the same star back again, in 365 days, 6 hours, 9 minutes, 12 seconds. That is to say, in the time of performing one revolution round the sun, it turns round its axis 365 times, and as much of a time as is represented by the first number of hours, minutes, and seconds. The axis round which it turns being inclined to the plane of the ecliptic, at an angle of 66° 32', or the plane of the equator, already described, forming, with the plane of the ecliptic, an angle of 23° 28′.

In the upper diagram, on the second copper-plate, the space in the centre represents the Sun, and the twelve figures around it, which are partially shaded, represent the northern hemisphere of the earth, as it would appear if seen from an immense distance, and by an observer, so placed as that the line of his observation, and the centre of the sun, formed a right angle with the plane of the ecliptic. The motion is in the direction from the right hand, by the top, round to the right hand again. The interior or bright side of each figure shows the illuminated portion of the hemisphere, and the exterior or shaded side, the dark portion. The point round which the circles in each figure are drawn, represents the north pole; and the curves, which cross those circles, represent meridians, which are 15° or 1 hour distance in time, asunder. The figures are placed in the situation which the earth occupies upon entering each of the twelve signs of the ecliptic; and the signs and corresponding months are particularly represented in the diagram. If the blank surface represent the plane of the ecliptic the axis round which the earth turns, is supposed to lean or incline towards the bottom of it, at an angle of 66° 32. Now, a bare inspection of the figure will show, that in the situations at the two sides, and, the illuminated hemisphere is divided from the dark one by a line passing exactly through the poles; but the light of the sun will shine upon an entire half of the globe, and, therefore, if the line dividing the light from darkness in these points were continued round the earth, it would pass through the south pole also; and, therefore, upon whatever part of the earth's surface a place happened to be situated, that place would pass through the light during one half of the revolution, and through the darkness during the other half. In other words, when the earth is in these two points of its orbit, the day and the night must be equal throughout its whole surface.

The reason of this is obvious; for, the axis round which the earth turns being inclined only toward the bottom of the diagram, is neither inclined toward nor from the sun, but stands in such a position as to be at right angles to a line joining the centres of the sun and earth. In this state, therefore, as seen from the earth, the sun will be, in the course of twentyfour hours, directly over head at every successive point of the earth's equator. For this reason the equator is called the equinoctial, or circle of equal day and night.

If, again, the earth be taken as in the position at the top of the diagram, the axis of its rotation will incline or lean toward the sun, at an angle of 23° 28′, and thus a circle round the north pole, of double that diameter, will be brought entirely within the light; and, while the earth turns round, the surface within that circle will be always illuminated by the sun. But, in this case, the sun can shine only upon one half of the earth, the same as in the former case; and, therefore, whatever portion toward the north or visible pole is brought wholly within the light, there must be as much round the south or invisible pole left wholly within the darkness. In this situation, therefore, the days in the northern hemisphere will be longer than the nights; the nights in the southern hemisphere longer than the days; a portion round the north pole will enjoy continual day; a portion round the south pole continual night, while at the equator day and night will be equal; but as the axis of the earth inclines 23° 28' toward the sun, the sun will not appear directly over head at the equator, but over a parallel circle in the northern hemisphere, situate 23° 28′ from the equator.

Thirdly, if the middle position, at the bottom, be referred to, the north pole and axis will decline 23° 28′ from the sun, and the circumstances of the two hemispheres will, as compared with the opposite situation, be exactly reversed.

From the middle situation on the right hand, to the situation at top the quantity of light in the northern hemisphere and darkness in the southern will continue to increase, and thence to the situation at the left, it will diminish till both hemispheres have an equal quantity of day and night as they had in the situation at the right. From the right-hand side, to the middle at the bottom the light in the northern hemisphere, and the darkness in the southern one will continue to increase; and from the bottom to a complete revolution at the middle at the right-hand side, the light will increase in the north till both have equal illumination the same as at the

commencement.

By this simple arrangement, of the axis of the earth continuing parallel to itself in every position, and always forming with the plane of the ecliptic the same angle of 66° 32′ in the same direction, the whole changes of the seasons are produced. When the earth is situated as at top, the northern hemisphere has spring and the southern one autumn; when the middle position on the left hand is arrived at, the northern hemisphere has midsummer, and the southern mid-winter; when the bottom is arrived at, the northern has autumn and the southern spring; and when the middle at the right is arrived at, the northern has winter and the southern summer. Thus the two hemispheres have opposite seasons; and if two places be situate on opposite sides of the equator, and at the same distance from it, the night at the one place is always of the same length as the day at the other.

Also the surface of the earth is divided into five distinct portions, in each

of which the phenomena of the seasons are different from what they are at the others. Thus a portion in the middle-that is a zone or belt extending 23° 28′ northward and southward of the equator, will have the sun overhead at noon-day, at the same time of the year, and if the place be not situate in the very extremity of this portion, the sun will be directly overhead twice in the year, once in his apparent progress northward, and another time in his apparent progress southward. This portion of the earth is called the torrid zone, and the circles (latitude 23° 28′ north and south), which form its boundaries are called the two tropics, because at them the sun appears to turn back.

A circular portion, measuring 46° 56′ across, and having the pole in its centre, will in each hemisphere be for some portion of the year in continued light, and for an equal and opposite portion in continued darkness. These two portions are called the frigid zones, and the circles by which they are bounded (latitude 66° 32′ north and south) are called the polar circles.

The intermediate portions (from latitude 23° 28′ to latitude 66° 32′ north and south) are called the temperate zones, they have light and darkness every twenty-four hours, and the greater variation of seasons the farther they are from the equator. Thus the influence of the sun is most uniformly exerted upon the earth in the regions of the equator, day and night being equal there throughout the year; while as the latitude increases, the change of seasons becomes more apparent, while at the poles there is only one day, and one night in the year, each of them of six months' duration.

SECTION V.

PHENOMENA ARISING FROM THE MOTION OF THE MOON. The only general motion of the celestial bodies which remains to be explained, is that of a secondary planet round its primary. The secondaries, like the primaries, move in ellipses or ovals, and the planes of their orbits form various angles with the ecliptic and the orbits of the primaries; but making allowance for difference of magnitude, size, and inclination of orbit, and rate of motion, they are all subject to the same laws, and exhibit, generally speaking, the same phenomena, so that from a description of one the appearances of all the others may be inferred.

The one best adapted to this purpose is the earth's satellite, the moon, of the phases or appearances of which, at eight equidistant points of its revolution round the earth, a representation is given in the copper-plate engraving.

The moon is a globe, 2180 miles in diameter, at a mean distance of 240,000 miles from the earth, and revolving round it in 27 days, 7 hours, 43 minutes, in an orbit which makes with the plane of the ecliptic an angle of 5° 9′ 3′′. But though the time stated above be short of the moon's real revolution according to its mean distance from the earth and its velocity,

the apparent time is much greater, because in the course of one revolution of the moon round the earth, the earth itself moves over about onethirteenth part of its orbit. This combination of motions produces a curve of rather angular and complicated form; namely, that kind of epicycloid which is generated by the revolution of one ellipse round the circumference of another.

The following figure will give an idea of the path which the moon describes in free space, and of the relative positions of the earth and moon at every quarter and half-quarter during one month.

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As this figure is a little complicated, and as a perfect understanding of it will save the trouble of much (and not very simple) verbal description, the reader will do well to examine, with much attention, the following

Explanation.

The larger circles, 0, 1, 2, 3, 4, represent the earth at the beginning, first quarter, second quarter, third quarter, and end of a lunation, or lunar month.

The strong curve, passing from the centre of 0, through the intermediate circles, to the centre of 4, is about one-thirteenth part of the earth's annual path, or orbit; and the dotted curve, from the centres of the first and last circles, is that orbit continued.

The dotted lines, AB, CD, are radii of the earth's orbit; that is, lines joining the earth and sun; and, if they were continued till they met, the point of their meeting would be the plane of the sun.

The intermediate points, 1, 1, 2, and 3, in orbit, are the positions of the earth's centre at the half quarters.

The north pole of the earth is supposed to be turned directly toward the reader; and the motion of the earth is from west to east, or from 0 to 4.

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