come under the real sun's meridian, sooner than under the fictitious sun's meridian; that is, it will be 12 o'clock by the true sun, before it is 12 o'clock by the false sun, or by a true clock; but were the true sun in place of the false one, the sun and clock would agree. While the true sun is passing through that quarter of his orbit, from a to C, and the fictitious sun from 1 to 3, it will always be noon by the true sun before it is noon by the false sun, and during this period, the sun will be faster than the clock.

When the true sun arrives at C, and the false one at 3, they are both on the same meridian, and the sun and clock agree. But while the real sun is passing from C to B, and the false one from 3 to B, any meridian comes later under the true sun than it does under the false, and then it is noon by the sun after it is noon by the clock, and the sun is then said to be slower than the clock. At B, both suns are again on the same meridian, and then again the sun and clock agree.

We have thus followed the real sun through one half of his true apparent place in the heavens, and the false one through half the celestial equator, and have seen that the two suns, since leaving the point A, have been only twice on the same meridian at the same time. It has been supposed that the two suns passed through equal arcs, in equal times, the real sun through the ecliptic, and the false one through the equator. The place of the false sun may be considered as representing the place where the real sun would be, in case the earth's axis had no inclination, and consequently it agrees with the clock every 24 hours. But the true sun, as he passes round in the ecliptic, comes to the same meridian, sometimes sooner, and sometimes later, and in passing around the other half of the ecliptic, or in the other half year, the same variations succeed each other.

The two suns are supposed to depart from the point A, on the 20th of March, at which time the sun and clock coincide. From this time, the sun is faster than the clock, until the two suns come together at the point C, which is on the 21st of June, when the sun and clock again agree. From this period the sun is slower than the clock, until the 23d of September,

While the suns are passing from A to C, and from 1 to 3, will the sun be faster, or slower than the clock? When the two suns are at C, While the real sun is passing What does the place

and 3, why will the sun and clock agree?
from B to C, which is fastest, the clock, or sun?
of the false sun represent, in fig. 203?

and faster again until the 21st of December, at which time they agree as before.

We have thus seen how the inclination of the earth's axis, and the consequent obliquity of the equator to the ecliptic, causes the sun and clock to disagree, and on what days they would coincide, provided no other cause interfered with their agreement. But although the inclination of the earth's axis would bring the sun and clock together on the above mentioned days, yet this agreement is counteracted by another eause, which is the elliptical form of the earth's orbit, and though the sun and clock do agree four times in the year, it is not on any of the days above mentioned.

It has been shown by fig. 193, that the earth moves more rapidly in one part of its orbit than in another. When it is nearest the sun, which is in the winter, its velocity is greater, than when it is most remote from him, as in the summer. Were the earth's orbit a perfect circle, the sun and clock would coincide on the days above specified, because then the only disagreement would arise from the inclination of the earth's axis. But since the earth's distance from the sun is constantly changing, her rate of velocity also changes, and she passes through unequal portions of her orbit in equal times. Hence on some days, she passes through a greater portion of it than on others, and thus this becomes another cause of the inequality of the sun's apparent motion.

The elliptical form of the earth's orbit would prevent the coincidence of the sun and clock at all times, except when the earth is at the greatest distance from the sun, which happens on the 1st of July, and when she is at the least distance from him, which happens on the 1st of January. As the earth moves faster in the winter than in the summer, from this cause, the sun would be faster than the clock from the 1st of July to the 1st of January, and then slower than the clock from the 1st of January to the 1st of July.

We have now explained, separately, the two causes which prevent the coincidence of the sun and clock. By the first cause, which is the inclination of the earth's axis, they would

The inclination of the earth's axis would make the sun and clock agree in March and the other months above named: why then do they not actually agree at those times? Were the earth's orbit a perfect circle, on what days would the sun and clock agree? How does the form of the earth's orbit interfere with the agreement of the sun and clock on those days? At what times would the form of the earth's orbit bring the sun and clock to agree?

agree four times in the year, and by the second cause, the ir regularity of the earth's motion, they would coincide only twice in the year.

Now these two causes counteract the effects of each other, so that the sun and clock do not coincide on any of the days, when either cause, taken singly, would make an agreement between them. The sun and clock, therefore, are together, only when the two causes balance each other; that is, when one cause so counteracts the other, as to make a mutual agreement between them. This effect is produced four times in the year; namely, on the 15th of April, 15th of June, 31st of August, and 24th of December. On these days, the sun and a clock keeping exact time, coincide, and on no others. The greatest difference between the sun and clock, or between apparent and mean time, is 16 minutes, which takes place about the 1st of November.

Precession of the Equinoxes.

A tropical year is the time it takes the sun to pass from one equinox, or tropic, to the same tropic, or equinox again. A siderial year is the time it takes the sun to perform his apparent annual revolution, from a fixed star, to the same fixed star again.

Now it has been found that these two complete revolutions are not finished in exactly the same time, but that it takes the sun about 20 minutes longer to complete his apparent revolution in respect to the star, than it does in respect to the equinox, and hence the siderial year is about 20 minutes longer than the tropical year. The revolution of the earth from equinox to equinox, again, therefore precedes its complete revolution in the ecliptic by about 20 minutes, for the absolute revolution of the earth is measured by its return to the fixed star, and not by the return of the sun to the same equinoctial point. This apparent falling back of the equinoctial point, so as to make the time when it meets the sun precede the time

The inclination of the earth's axis would make the sun and clock agree four times in the year, and the form of the earth's orbit would make them agree twice in the year, now show the reason why they do not agree from these causes, on the above mentioned days, and why they do agree on other days. On what days do the sun and clock agree? What is a tropical year? What is a siderial year? What is the difference in the time which it takes the sun to complete his revolution in respect to a star, and in respect to the eqninox? Explain what is meant by the precession of the equinoxes.

1

when the earth makes its complete revolution in respect to the star, is called the precession of the equinoxes.

The distance which the sun thus gains upon the fixed star, or the difference between the sun and star, when the sun has arrived at the equinoctial point, amounts to 50 seconds of a degree, thus making the équinoctial point recede 50 seconds of a degree, (when measured by the signs of the zodiac,) westward, every year, contrary to the sun's anual progressive motion in the ecliptic.

To illustrate this by a figure, suppose S, fig. 204, to be the sun, E the earth, and o a fixed star, all in a straight line with respect to each other. Let it be supposed that this opposition takes place on the 21st of March, at the vernal exquinox, and that at that time the earth is exactly between the sun and the star. Now when the earth has performed a complete revolution around its orbit b, a, as measured by the star, she will arrive at precisely the same point where she now is. But it is found that when the earth comes to the same equinoctial point, the next year, she has not gone her complete revolution in respect to the star; the equinoctial point having fallen back with respect to the star, during the year, from E to e, so that the earth, after having completed her revolution, in respect to

How many seconds of a degree does the equinox recede every year, when the sun's place is compared with a star? How does fig. 204, illustrate the precession of the equinoxes? Explain fig. 204, and show from what points the equinoxes fall back from year to year:

the equinox, has yet to pass the space from e to E, to complete her revolution in respect to the star.

The space from e to E being 50 seconds of a degree, and the equinoctial point falling this space every year short of the place where the sun and this point agreed the year before, it is obvious, that on the next revolution of the earth, the equinox will not be found at e, but at i, so that the earth, having completed her second revolution in respect to the sun when at i, will still have to pass from i to E, before she completes an. other revolution in respect to the star.

The precession of the equinoxes, being 50 seconds of a de gree, every year, contrary to the sun's apparent motion, or about 20 minutes in time, short of the point where the sun and equinoxes coincided the year before, it follows, that the fixed stars, or those in the signs of the zodiac, move forward every year 50 seconds, with respect to the equinoxes.

In consequence of this precession, in 2160 years, those stars which now appear in the beginning of the sign Aries, for instance, will then appear in the beginning of Taurus, having moved forward one whole sign, or 30 degrees, with respect to the equinoxes, or the equinoxes having gone backwards 30 degrees, with respect to the stars. In 12,960 years, or 6 times 2160 years, therefore, the stars will appear to have moved forward one half of the whole circle of the heavens, so that those which now appear in the first degree of the sign Aries, will then be in the opposite point of the zodiac, and therefore, in the first degree of Libra. And in 12,690 years more, because the equinoxes will have fallen back the other half of the circle, the stars will appear to have gone forward, from Libra to Aries, thus completing the whole circle of the zodiac.

Thus in about 26,000 years the equinox will have gone back. wards a whole revolution around the axis of the ecliptic, and the stars will appear to have gone forward the whole circle of the zodiac.

The discovery of the precession of the equinoxes has thrown much light on ancient astronomy and chronology, by showing an agreement between ancient and modern observations, con

How many minutes, in time, is the precession of the equinoxes per year? What effect does this precession produce on the fixed stars? How many years is a star in going forward one degree, in respect to the equinoxes? In how many years will the stars appear to have passed half around the heavens? In what period will the earth appear to have gone backwards one whole revolution? In what respect is the precession of the equinoxes an important subject?