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points in the Earth's orbit, where it crosses the celestial equator. The first is-in Aries; the other, in Libra. By the precession of the equinoxes is meant, that the intersection of the equator with the ecliptic is not always in the same point :-in other words, that the Sun, in its apparent annual course, does not cross the equinoctial, Spring and Autumn, exactly in the same points, but every year a little behind those of the preceding year.

576. This annual falling back of the equinoctial points, is called by astronomers, with reference to the motion of the heavens, the Precession of the Equinoxes; but it would better accord with fact as well as the apprehension of the learner, to call it, as it is, the Recession of the Equinoxes; for the equinoctial points do actually recede upon the ecliptic, at the rate of about 501" of a degree every year. It is the name only, and not the position, of the equinoxes which remains permanent. Wherever the Sun crosses the equinoctial in the spring, there is the vernal equinox; and wherever he crosses it in the autumn, there is the autumnal equinox; and these points are constantly moving to the west.

To render this subject familiar, we will suppose two carriage roads, extending quite around the Earth; one, representing the equator, running due east and west; and the other representing the ecliptic, running nearly in the same direction as the former, yet so as to cross it with a small angle (say of 23°), both at the point where we now stand, for instance, and in the nadir, exactly opposite; let there also be another road, to represent the prime meridian, running north and south, and crossing the first at right angles, in the common point of intersection, as in the annexed figure.

Let a carriage now start from this point of intersection, not in the road leading directly east, but along that of the ecliptic, which leaves the former a little to the north, and let a person be placed to watch when the carriage comes around again, after having made the circuit of the Earth, and see whether the carriage will cross the equinoctial road again

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precisely in the same track as when it left the goal. Though the person stood exactly in the former track, he need not fear being run over, for the carriage will cross the road 100 rods west of him, that is 100 rods west of the meridian on which he stood. It is to be observed, that 100 rods on the equator is equal to 50% seconds of a degree.

If the carriage still continue to go around the Earth, it will, on completing its second

What meant by their precession? 576. With reference to what is it a precession? Is it really a precession of the equinoxes? Where are the equinoxes spring and fall? Can you illustrate by the two carriage roads, &c.? By the other diagram? Does the Sun



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circuit, cross the equinoctial path 200 rods west of the meridian whence it first set out; on the third circuit, 800 rods west; on the fourth circuit, 400 rods, and so on, continually. After 71% circuits, the point of intersection would be one degree west of its place at the commencement of the route. At this rate it would be easy to determine how many complete circuits the carriage must perform before this continual falling back of the intersecting point would have retreated over every degree of the orbit, until it reached again the point from whence it first departed. The application of this illustration will be manifest when we consider, further, that this interesting phenomenon may be explained in another way by the adjoining diagram. Let the point A represent the vernal equinox, reached, for instance, at 12 o'clock on the 20th of March. The next year the Sun will be in the equinoctial 22 minutes 33 seconds earlier, at which time the Earth will be 50% on the ecliptic, back of the point at which the Sun was in the equinoctial the year before. The next year the same will occur again; and thus the equinoctial point will recede westward little by little, as shown by the small lines from A to B, and from C to D. It is in reference to the stars going forward, or seeming to precede the equinoxes, that the phenomenon is called the Precession of the Equinoxes. But in reference to the motion of the equinoxes themselves, it is rather a recession.


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577. The Sun revolves from one equinox to the same equinox again, in 365d. 5h. 48′ 47′′.81. This constitutes the natural, or tropical year, because, in this period, one revolution of the seasons is exactly completed. But it is, meanwhile, to be borne in mind, that the equinox itself, during this period, has not kept its position among the stars, but has deserted its place, and fallen back a little way to meet the Sun; whereby the Sun has arrived at the equinox before he has arrived at the same position among the stars from which he departed the year before; and, consequently, must perform as much more than barely a tropical revolution, to reach that point again.

To pass over this interval, which completes the Sun's sidereal revolution, takes (20′ 22′′.94) about 22 minutes and 23 seconds longer. By adding 22 minutes and 23 seconds to the time of a tropical revolution, we obtain 365d. 6h. 9m. 103s. for the length of a sidereal revolution; or the time in which the Sun revolves from one fixed star to the same star again.

Though we speak of the revolution of the Sun, we mean simply his apparent revolution eastward around the heavens, caused wholly by the actual revolution of the Earth in her

actually revolve? Why, then, speak of his revolution?

577. What is the length of a tropical year? How different from a sidereal year? Difference of time? Length of a sidereal year?

orbit, as a distant object would appear to sweep around the horizon if we were walking or sailing around it. This may be illustrated by the cut, page 288, where the passage of the Earth from A to B would cause the Sun to appear to move from C to D; and so on around the whole circle of the Zodiac.

578. As the Sun describes the whole ecliptic, or 360°, in a tropical year, he moves over 59' 8" of a degree every day, at a mean rate, which is equal to 501" of a degree in 20 minutes and 23 seconds of time; consequently he will arrive at the same equinox or solstice when he is 504′′ of a degree short of the same star or fixed point in the heavens, from which he set out the year before. So that, with respect to the fixed stars, the Sun and equinoctial points fall back, as it were, 1° in 71 years. This will make the stars appear to have gone forward 1°, with respect to the signs in the ecliptic, in that time; for it must be observed, that the same signs always keep in the same points of the ecliptic, without regard to the place of the constellations. Hence it becomes necessary to have new plates engraved for celestial globes and maps, at least once in 50 years, in order to exhibit truly the altered position of the stars. At the present rate of motion, the recession of the equinoxes, as it should be called, or the precession of the stars, amounts to 30°, or one whole sign, in 2140 years.

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To explain this by a figure: Suppose the Sun to have been in conjunction with a fixed star at S, in the first degree of Taurus (the second sign of the ecliptic), 340 years before the birth of our Saviour, or about the seventeenth year of Alexander the Great; then having made 2140 revolutions through the ecliptic, he would be found again at the end of so many sidereal years at S; but at the end of so many Julian years, he would be found at J, and at the end of so many tropical years, which would bring it down to the beginning of the present century, he would be found at T, in the first degree of Aries, which

578. Daily progress of the Sun? What is the amount of the annual recession of the equinoxes? What effect will this have upon the apparent positions of the stars? Hence what becomes necessary? How long does it require for the equinoxes to recede a whole sign? Do you understand the diagram, and the reference to the sidereal, Julian, and Tropical years? Explain the difference in these three kinds of years.

has receded from 8 to T in that time by the precession of the equinoctial points Aries and Libra. The arc S T would be equal to the amount of the precession (for precession we must still call it) of the equinox in 2140 years, at the rate of 50".23572 of a degree, or 20 minutes and 23 seconds of time annually, as above stated.

579. From the constant retrogradation of the equinoctial points, and with them of all the signs of the ecliptic, it follows that the longitude of the stars must continually increase. The same cause affects also their right ascension and declination. Hence, those stars which, in the infancy of astronomy, were in the sign Aries, we now find in Taurus; and those which were in Taurus, we now find in Gemini, and so on. Hence likewise it is, that the star which rose or set at any particular time of the year, in the time of Hesiod, Eudoxus, Virgil, Pliny, and others, by no means answers at this time to their descriptions.

Hesiod, in his Opera et Dies, lib. ii. verse 185, says:

"When from the solstice sixty wintry days

Their turns have finished, mark, with glitt'ring rays,
From Ocean's sacred flood, Arcturus rise,
Then first to gild the dusky evening skies."

But Arcturus now rises acronically in latitude 37° 45' N. the latitude of Hesiod, and nearly that of Richmond, in Virginia, about 100 days after the winter solstice. Supposing Hesiod to be correct, there is a difference of 40 days arising from the precession of the equinoxes since the days of Hesiod. Now, as there is no record extant of the exact period of the world when this poet flourished, let us see to what result astronomy will lead us.

As the Sun moves through about 89° of the ecliptic in 40 days, the winter solstice, in the time of Hesiod, was in the 9th degree of Aquarius. Now, estimating the precession of the equinoxes at 50" in a year, we shall have 504": 1 year:: 39: 2814 years since the time of Hesiod: if we subtract from this our present era, 1855, it will give 958 years before Christ. Lempriere, in his Classical Dictionary, says Hesiod lived 907 years before Christ. See a similar calculation for the time of Thales, page 89.

580. The retrograde movement of the equinoxes, and the annual extent of it, were determined by comparing the longitude of the same stars, at different intervals of time. The most care ful and unwearied attention was requisite in order to determine the cause and extent of this motion-a motion so very slow as scarcely to be perceived in an age, and occupying not less than 25,000 years in a single revolution. It has not yet completed one quarter of its first circuit in the heavens since the creation of Mars.

581. This observation has not only determined the absolute motion of the equinoctial points, but measured its limit; it has also shown that this motion, like the causes which produce it, is not uniform in itself; but that it is constantly accelerated by a

579. What effect has the recession of the equinoxes upon the longitude of the stars, and their right ascension and declination? Hence what results? What interesting calculation in reference to Hesiod? 580. How were this recession and its extent determined?

What necessary? Time of complete revolution? Amount since creation? 581. Is this retrogression uniform? Amount of acceleration? What illustration given?

slow arithmetical increase of 1" of a degree in 4100 years. A quantity which, though totally inappreciable for short periods of time, becomes sensible after a lapse of ages.

For example: The retrogradation of the equinoctial points is now greater by nearly than it was in the time of Hipparchus, the first who observed this motion; consequently, the mean tropical year is shorter now by about 12 seconds than it was then. For, since the retrogradation of the equinoxes is now every year greater than it was then, the Sun has, each year, a space of nearly " less to pass through in the ecliptic, in order to reach the plane of the equator. Now the Sun is 12 seconds of time in passing over " of space.

582. At present, the equinoctial points move backwards, or from east to west along the path of the ecliptic at the rate of 1° in 71 years, or one whole sign in 2140 years. Continuing at this rate, they will fall back through the whole of the 12 signs of the ecliptic in 25,680 years, and thus return to the same position among the stars, as in the beginning.

But in determining the period of a complete revolution of the equinoctial points, it must be borne in mind that the motion itself is continually increasing; so that the last quarter of the revolution is accomplished several hundred years sooner than the first quarter. Making due allowance for this accelerated progress, the revolution of the equinoxes is completed in 25,000 years; or, more exactly, in 24,992 years.

Were the motion of the equinoctial points uniform; that is, did they pass through equal portions of the ecliptic in equal times, they would accomplish their first quarter, or pass through the first three signs of the ecliptic, in 6250 years. But they are 6575 years in passing through the first quarter; about 218 years less in passing through the second quarter; 218 less in passing through the third, and so on.

583. The immediate consequence of the precession of the equinoxes, as we have already observed, is a continually progressive increase of longitude in all the heavenly bodies. For the vernal equinox being the initial point of longitude, as well as of right ascension, a retreat of this point on the ecliptic tells upon the longitude of all alike, whether at rest or in motion, and produces, so far as its amount extends, the appearance of a motion in longitude common to them all, as if the whole heavens had a slow rotation around the poles of the ecliptic in the long period above mentioned, similar to what they have in every twenty-four hours around the poles of the equinoctial. As the Sun loses one day in the year on the stars, by his direct motion in longitude; so the equinox gains one day on them in 25,000 years, by its retrograde motion.

582. Present rate of motion? Exact period at s rate? Period making allowance for acceleration? Time of passing over the first quarter of the ecliptic? The second? Third? 583. What immediate consequences of the precession of the equinoxes? Why does it affect the longitude of the stars? What resemblance between the motion of the celestial sphere and that of the Earth? Between the Sun and equinoxes?

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