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584. 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 wabbling motion of the poles of the Earth around those of the ecliptic, like the pin of a top about its center of motion, when it spins a little bliquely to the base.
585. 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 center, keeping constantly at its present distance of nearly 234° 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.
Let the line A A in the figure represent the plane of the ecliptic; B B, the poles of the ecliptic; O C, the poles of the Earth; and D D, the equinoctial. EE is the obliquity of the ecliptic. The star C, at the top, represents the pole star, and the curve line passing to the right from it, may represent the circular orbit of the north pole of the heavens around the north pole of the ecliptic.
NUTATION OF THE EARTH'S AXIS.
#586. 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 con
584. What said of the cause of this recession? 585. Of what, then, does it consist? What said of the pole of the ecliptic, and the aspects of the heavens during this revolu tion? 585. How is the effect of this motion manifested? How with the Pole star?
struction of the earliest catalogue, 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 vanishing point of the Earth's axis; or that point in the concave sphere which is always opposite the terrestial pole, and which consequently must move as that moves.
587. 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°.
588. The position of the north polar star in 1855, was 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 of 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 brightest in the northern hemisphere, will occupy the position of a pole star, being then about 5 degrees from the pole; whereas now its north polar distance is upward 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, 2s. 14° 8' 27". The longitude of the star Beta Arietis, was in 1820, 81° 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.
589. 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,
What, then, is the real pole of the heavens? 587. Where is the precession of the stars most apparent? Where least? When are the circumpolar stars nearest the tropic of Cancer, and why? 588. Where was the pole star in 1855? When will it be nearest the true pole? How near then? What said of Alpha Draconis? Of Lyra? Mean average recession for 5800 years? Amount? Longitude of Beta Arietis in 1820? Before Christ 430 years, where? Average of precession for these 2250 years? 589. What further result of the revolution of the pole of the heavens? What effect? Where, then,
12,500 years afterwards, be at its greatest possible distance from it, or about 47° above it :-That is, the star itself will remain immovable 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 of 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.
590. The inclination of the Earth's axis to the plane of the ecliptic causes the equinoctial to depart 23° 28' from the ecliptic. This angle made by the equinoctial and the ecliptic is called the Obliquity of the Ecliptic.
Let the line A A represent the axis of the Earth, and BB the poles or axis of the ecliptic. Now if the line A A inclines toward the plane of the ecliptic, or, in other words, departs from the line B B, to the amount of 28° 28', it is obvious that the plane of the equator, or equinoctial, will depart from the ecliptic to the same amount. This departure, shown by the angles C C, constitute the obliquity of the ecliptic.
OBLIQUITY OF THE ECLIPTIC.
PLANE OF THE
591. 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.
will the north pole be 12,500. years hence? 590. What is the Obliquity of the Ecliptic? 591. Is this angle always the same? What variation of the equinoctial?
592. 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.
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′′.82, with an annual diminution of 0".46. At this date (1855), it is only about 23° 27' 29". Consequently, the angle is diminished about 27" in 55 years. This diminution, however, is subject to a slight semi-annual variation, from the same causes which produce the displacement of the plane of the ecliptic, in precession.
593. The attraction of the Sun and Moon, also, unites with that of the planets, at certain seasons, to augment the diminution 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 center, bows a little to the influence of the Moon, and rises again, alternately, like the gentle oscillations of a balance. This curious phenomenon is called Nutation (589).
In consequence of the yearly diminution of the obliquity of the ecliptic, the tropics are slowly and steadily approaching the equinoctial, at the rate of little more than threefourths of a second every year; so that the Sun does not now come so far north of the equator in summer, nor decline so far south in winter, by nearly a degree, as it must have done at the Creation.
594. The most obvious effect of this diminution of the obliquity of the ecliptic, is to equalize the length of our days and nights; but it has an effect also to change the position of the stars near the tropics. Those which were formerly situated north of the ecliptic, near the summer solstice, are now found to be still farther north, and farther from the plane of the ecliptic. On the contrary, those which, according to the testimony of the
592. What displacement of the ecliptic, and by what caused? Effect of these causes? Amount of change annually? Obliquity of the ecliptic in 1800? In 1855? 593. Diminution in 55 years? What is Nutation? Its cause? What effect from this annual diminu. tion of obliquity? 594. What other effect? Will this diminution continue? What
ancient astronomers, were situated south of the ecliptic, near the summer solstice, have approached this plane, insomuch that some are now either situated within it, or just on the north side of it. Similar changes have taken place with respect to those stars situated near the winter solstice. All the stars, indeed, participated more or less in this motion, but less, in proportion to their proximity to the equinoctial.
It is important, however, to observe, that this diminution will not always continue. A time will arrive when this motion, growing less and less, will at length entirely cease, and the obliquity will, apparently, remain constant for a time; after which it will gradually increase again, and continue to diverge by the same yearly increment as it before had diminished. This alternate decrease and increase will constitute an endless oscillation, comprehended between certain fixed limits. Theory has not yet enabled us to determine precisely what these limits are, but it may be demonstrated from the constitution of our globe, that such limits exist, and that they are very restricted, probably not exceeding 2° 42'. If we consider the effect of this ever-varying attribute in the system of the universe, it may be affirmed that the plane of the ecliptic never has coincided with the plane of the equator, and never will coincide with it. Such a coincidence, could it happen, would produce upon the Earth perpetual spring.
595. The method used by astronomers to determine the obliquity of the ecliptic is, to take half the difference of the greatest and least meridian altitudes of the Sun.
The following table exhibits the mean obliquity of the ecliptic for every ten years during the present century.
PHILOSOPHY OF THE TIDES.
596. TIDES are the alternate rising and falling of the waters of the ocean, at regular intervals. Flood tide is when the waters are rising; and ebb tide, when they are falling. The highest and lowest points to which they go are called, respectively, high and low tides. The tides ebb and flow twice every twenty-four hours-i. e., we have two flood and two ebb tides in that time.
cycle of oscillation? Its probable limits? What conclusion from this oscillation of the ecliptic? 595. By what method do astronomers determine the obliquity of the ecliptic? 596. What are tides? Flood and ebb tides? High and low? How often do they ebb