while, 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.

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 504" of a degree in 20 minutes and 23 seconds of time; consequently he will arrive at the same equinox or solstice when he is 501′′ of a degree short of the same star or fixed poin 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 713 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 engraed 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.

Why is it so called? Does the equinox remain stationary during this period? What results from this? How long does it take the Sun to pass over the interval through which the equinox has thus retreated? What is the length of a sidereal revolution, and how is it determined? What portion of the ecliptic does the Sun describe, at a mean rate, every day? What portion does it describe in 20 minutes and 23 seconds? If the Sun and equinoctial points fall back in the ecliptic 50 1-4" of a degree every year, how many years before this regression will amount to a degree? How will this affect the appearance of the stars What practical inconvenience results from this fact? In what period of time does the precession of the stars amount to 30°, or one whole sign?

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 17th 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 has receded from S to T in that time by the precession of the equinoc• tial 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.

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 tame 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.

Explain this by a diagram. How does the retrogradation of the equinoctial points affect the longitude of the stars? Does the same cause extend to their right ascension and declination also? How is this rendered apparent?

Hesiod, in his Opera et Dies, lib. ii. verse 185, says:
When from the solstice sixty wintry days

Their turns have finish'd, mark, with glitt'ring rays,
From Ocean's sacred flood, Arcturus rise,

Then first to gild the dusky evening skies.

But Arcturus now rises acronycally in latitude 37° 45′ N. the latitude e 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 thi poet flourished, let us see to what result astronomy will lead us.

As the Sun moves through about 39° of the ecliptic in 40 days, the winter solstice, in the time of Hesiod, was in the 9th degree of Aquarius. Now es timating the precession of the equinoxes at 504 in a year; we shall have 50: 1 year: 39°: 2791 years since the time of Hesiod; if we substract from this our present era, 1836, 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., age 54.

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 careful 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.

Thus 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 slow arithmetical increase of 1′′ of a degree in 4,100 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 1" of space.

At present, the equinoctial points move backwards, or from east to west along the path of the ecliptic at the rate of

Mention an example. History does not enable us to fix the precise age of the world in which Hesiod flourished; what light does astronomy shed upon this question? By what means was the retrogradation of the equinoxes determined? Why was it diffi cult to determine the cause and extent of this motion? Not to specify particular cases, what has observation at length determined, with respect to the limit and uniformity of this backward movement of the equinoctial points? Give an example. Why should the tropical year, on this account, be shorter now than it was then! What is the present rate of motion of the equinoctial points }

1o 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 6,250 years. But they are 6,575 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.

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 longitudes 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.

The cause of this motion was unknown, until Newton proved that it was a necessary consequence of the rotation of the Earth, combined with its elliptical figure, and the unequal attraction of the Sun and Moon on its polar and equatorial regions. There being more matter about the Earth's equator than at the poles, the former is more strongly attracted than the latter, which causes a slight gyratory or

In what time, continuing at the same rate, will they fall back through the twelve signs of the ecliptic? In determining the exact period of a complete revolution of the equinoctial points, what important circumstance must be borne in mind? Making due allowance for their accelerated progress, in what time is a revolution of the equinoxes completed? Is this motion as quick in the first quarter of their revolution as in the last? What is the time and difference, of describing each quarter? What is the immediate consequence of the precession of the equinoxes upon the position of the heavenly bodies? Explain how this takes place. How does this resemble the annual loss of a sidereal day by the Sun? What is the cause of this motion?

wabbling notion of the poles of the Earth around those of the ecliptic, like the pin of a top about its centre of motion, when it spins a little obliquely to the base.

The precession of the equinoxes, thus explained, consists in a real motion of the pole of the heavens among the stars, in a small circle around the pole of the ecliptic as a centre, keeping constantly at its present distance of nearly 231 from it, in a direction from east to west, and with a progress so very slow as to require 25,000 years to complete the circle. During this revolution it is evident that the pole will point successively to every part of the small circle in the heavens which it thus describes. Now this cannot happen without producing corresponding changes in the apparent diurnal motion of the sphere, and in the aspect which the heavens must present at remote periods of time.

The effect of such a motion on the aspect of the heavens, is seen in the apparent approach of some stars and constellations to the celestial pole, and the recession of others The bright star of the Lesser Bear, which we call the pole star, has not always been, nor will always continue to be, our polar star. At the time of the construction of the earliest catalogues, this star was 12° from the pole; it is now only 1° 34 from it, and it will approach to within half a degree of it; after which it will again recede, and slowly give place to others, which will succeed it in its proximity to the pole.

The pole, as above considered, is to be understood, merely, as the var ishing point of the Earth's axis; or that point in the concave sphere which is always opposite the terrestrial pole, and which consequently must move as that moves.

The precession of the stars in respect to the equinoxes, is less apparent the greater their distance from the ecliptic; for whereas a star in the zodiac will appear to sweep the whole circumference of the heavens, in an equinoctial year, a star situated within the polar circle will describe only a very small circle in that period, and by so much the less, as it approaches the pole. The north pole of the earth being elevated 23° 27′ towards the tropic of Cancer, the circumpolar stars will be successively, at the least distance from it, when their longitude is 3 signs, or 90°. The posi

Admitting this explanation, in what does the precession of the equinoxes really consist? To what point in the heavens will the pole of the Earth be directed, during the revolution? How must this affect the diurnal motion and aspect of the heavens, in remote ages? Wherein will the effects of such a motion be particularly visible? Give an instance. When you speak of the POLE as in motion, what is to be understood by that term? In the precession of the stars, with respect to the equinoxes, equally apparent in every part of the heavens? At what longitude do the circumpolar stars approach nearest the Dole?