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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 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 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 50 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, page 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 1" 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.

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 urished; what light docs astronomy shed upon his question? By what means was the retrogradation of the equinoxes determined? Why was it difficu't 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 hackward 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 motion 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 2316 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 van 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? Is 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 pole?

tion of the north polar star in 1836, will be in the 17° of Taurus; when it arrives at the first degree of Cancer, which it will do in about 250 years, it will be at its nearest possible approach to the pole-namely, 29′ 55′′. About 2900 years before the commencement of the Christian era, Alpha Draconis, the third star in the Dragon's tail, was in the first degree of Cancer, and only 10' from the pole; consequently it was then the pole star. After the lapse of 11,600 years, the star Lyra, the brighest in the northern hemisphere, will occupy the position of a pole star, being then about 5o from the pole; whereas now its north polar distance is upwards of 51°.

The mean average precession from the creation (4004 B. C.) to the year 1800, is 49.51455; consequently the equinoctial points have receded since the creation, 2 s. 14° 8' 27'7. The longitude of the star Beta Arietis, was, in 1820, 31° 27' 28" Meton, a famous mathematician of Athens, who flourished 430 years before Christ, says this star, in his time, was in the vernal equinox. If he is correct, then 31° 27' 28", divided by 2250 years, the elapsed time, will give 50 for the precession. Something, however, must be allowed for the imperfection of the instruments used at that day, and even until the sixteenth century.

Since all the stars complete half a revolution about the axis of the ecliptic in about 12,500 years, if the North Star be at its nearest approach to the pole 250 years hence, it will, 12,500 years afterwards, be at its greatest possible distance from it, or about 47° above it :-That is, the star itself will remain immoveable in its present position, but the pole of the Earth will then point as much below the pole of the ecliptic, as now it points above. This will have the effect, apparently, of elevating the present polar star to twice its present altitude, or 47°. Wherefore, at the expiration of half the equinoctial year, that point in the heavens which is now 1° 18' north of the zenith of Hartford, will be the place of the north pole, and all those places which are situated 1° 18' north of Hartford, will then have the present pole of the heavens in their zenith.

OBLIQUITY OF THE ECLIPTIC.

The distance between the equinoctial and either tropic, measured on the meridian, is called the Obliquity of the Ecliptic: or, this obliquity may be defined as the angle form

What is the position, at present, of the north polar star, and when will it make its nearest possible approach to the true pole of the heavens? At what period has any other star been the polar star? When will the star Lyra, which is more than 50° from it, be the north polar star? What was the mean annual precession from the creation to the year 1800, and how much did it amount to in that period? When was Beta Arietis in the equinox, and what is its longitude now? When will our present north star be at its least, and when at its greatest distance from the pole? In this case, is it meant that the star itself will move, or the pole? In what manner? What, then, must be the apparent effect? Illustrate thesc phenomena by a diagram. What is the obliquity of the ecliptic?

ed by the intersection of the celestial equator with the ecliptic. Hitherto, we have considered these great primary circles in the heavens, as never varying their position in space, nor with respect to each other. But it is a remarkable and well ascertained fact, that both are in a state of constant change. We have seen that the plane of the Earth's equator is constantly drawn out of place by the unequal attraction of the Sun and Moon acting in different directions upon the unequal masses of matter at the equator and the poles; whereby the intersection of the equator with the ecliptic is constantly retrograding—thus producing the precession of the equinoxes.

The displacement of the ecliptic, on the contrary, is produced chiefly by the action of the planets, particularly of Jupiter and Venus, on the Earth; by virtue of which the plane of the Earth's orbit is drawn nearer to those of these two planets, and consequently, nearer to the plane of the equinoctial. The tendency of this attraction of the planets, therefore, is to diminish the angle which the plane of the equator makes with that of the ecliptic, bringing the two planes nearer together; and if the Earth had no motion of rotation, it would, in time, cause the two planes to coincide. But in consequence of the rotary motion of the Earth, the inclination of these planes to each other remains very nearly the same; its annual diminution being scarcely more than three fourths of one second of a degree in a year.

The obliquity of the ecliptic, at the commencement of the present century, was, according to Baily, 23° 27′ 56′′, subject to a yearly diminution of 0'' .4755. According to Bessel, it was 23° 27' 54".32, with an annual dimi nution of 0.46. This diminution, however, is subject to a slight semiannual variation, from the same causes which produce the displacement of the plane of the ecliptic, in precession.

The attraction of the Sun and Moon, also, unites win that of the planets, at certain seasons, to augment the dim.nution of the obliquity, and at other times, to lessen it. On this account the obliquity itself is subject to a periodical variation; for the attractive power of the Moon, which tends to produce a change in the obliquity of the ecliptic, is variable, while the diurnal motion of the Earth, which tends to prevent the change from taking place, is constant. Hence the Earth, which is so nicely poised on her centre, bows a

In what light have we hitherto considered the great circles of the heavens? But what is the fact? By what cause is the displacement of the equinoctial, or the plane of the Earth's equator, effected? How is the displacement of the plane of the ecliptic effected? If the planetary attraction tends constantly to draw the planes of the equinoctial and ecliptic nearer together, what is to prevent them from coinciding in one and the same plane? How much is the distance or angle between them diminished every year? What was the obliquity of the ecliptic, or the quantity of this angle, at the commencement of the present century? Is the annual diminution of the obliquity subject to any variation? From what cause? What effect has the attraction of the Sun and Moon on this obliquity 7

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