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 row 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 23 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.

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 dimi nish 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 Buily, 23° 27′ 561⁄2", subject to a yearly diminution of 0.4755. According to Bessel, it was 23° 27′ 54′′.32, 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? 598. 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.

A

It is important, however, to observe, that this diminution will not always continue. 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 oscilla tion, 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.

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 cliptic? 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 And flow?

597. The tides are not uniform, either as to time or amount. They occur about 50 minutes later every day (as we shali explain hereafter), and sometimes rise much higher and sink much lower than the average. These extraordinary high and low tides are called, respectively, spring and neap tides.

598. The cause of the tides is the attraction of the Sun and Moon upon the water of the ocean. But for this foreign influence, as we may call it, the waters having found their proper level, would cease to heave and swell, as they now do, from ocean to ocean, and would remain calm and undisturbed, save by their own inhabitants and the winds of heaven, from age to age.

In this figure, the Earth is represented as surrounded by water, in a state of rest or equilibrium, as it would be were it not acted upon by the Sun and Moon.

NO TIDE.

599. To most minds, it would seem that the natural effect of the Moon's attraction would be to produce a single tide-wave on the side of the Earth toward the Moon. It is easy, therefore, for students to conceive how the Moon can produce one flood and one ebb tide in twenty four hours.

In this cut, the Moon is shown at a distance above the Earth, and ONE TIDE-WAVE. attracting the waters of the ocean, so as to produce a high tide at A. But as the moon makes her apparent westward revolution around the Earth but once a day, the simple rising of a flood tide on the side of the Earth toward the moon, would give give us but one flood and one ebb tide in twenty-four hours; whereas it is known that we have two of each.

"The tides," says Dr. Herschel, "are a subject on which many persons find a strange difficulty of conception. That the Moon by her attraction, should heap up the waters of the ocean under her, seems to many persons very natural. That the same cause should, at the same time, heap them up on the opposite side of the Earth (viz., at B in the figure), seems to many palpably absurd. Yet nothing is more true."

B

B

M

600. Instead of a single tide-wave upon the waters TWO TIDE-WAVES. of the globe, directly under the Moon, it is found that on the side of the Earth directly opposite, there is another high tide; and that half-way between these two high tides are two low tides. These four tides, viz., two high and two low, traverse the ocean from east to west every day, which accounts for both a flood and an ebb tide every twelve hours.

D

597 Are the tides uniform? What variation of time? As to amount? What are these extraordinary high and low tides called? 598. The cause of tides? How but for this influence? 599. What most obvious effect of the Moon's attraction? Substance of note? Remark of Dr. Herschel? 600. How many tide-waves are there on the globe. and how situated?

In this cut, we have a representation of the tide-waves as they actually exist, excy? that their height, as compared with the magnitude of the Earth, is vastly too great. It is designedly exaggerated, the better to illustrate the principle under consideration. While the Moon at A attracts the waters of the ocean, and produces a high tide at B, we see another high tide at C on the opposite side of the globe. At the same time it is low tide at D and E.

601. The principal cause of the tide-wave on the side of the Earth opposite the Moon is the difference of the Moon's attrac tion on different sides of the Earth.

30

If the student well understands the subject of gravitation, he will easily perceive how a difference of attraction, as above described, would tend to produce an elongation of the huge drop of water called the Earth. The diameter of the Earth amounts to about 1th of the Moon's distance; so that, by the rule (558), the difference in her attraction on the side of the Earth toward her, and the opposite side, would be aboutth. The attraction being stronger at B (in the last cut) than at the Earth's center, and stronger at her center than at C, would tend to separate these three portions of the globe, giving the waters an elongated form, and producing two opposite tide-waves, as shown in the cut.

602. A secondary cause of the tide-wave on the side of the Earth opposite the Moon, is the revolution of the Earth around the common center of gravity between the Earth and Moon, thereby generating an increased centrifugal force on that side of the Earth.

The center of gravity between the Earth and Moon is the point where they would exactly balance each other, if connected by a rod, and poised upon a fulcrum.

Earth.

CENTER OF GRAVITY BETWEEN THE EARTH AND MOON.

Moon.

This point which, according to Ferguson, is about 6000 miles from the Earth's center, is represented at A in the above, and also in the next cut.

SECONDARY CAUSE OF HIGH TIDE OPPOSITE THE MOON.

The point A represents the center of gravity between the Earth and Moon; and as it this point which traces the regular curve of the Earth's orbit, it is represented in the arc of that orbit, while the Earth's center is 6000 miles one side of it. Now, the law of gravitation requires that while both the Moon and Earth revolve around the Sun, they should also revolve around the common center of gravity between them, or around the point A. This would give the Earth a third revolution, in addition to that around the

601. State the principal cause of the wave opposite the Moon? Demonstrate by dia. gram. 602. What other cause operates with the one just stated to produce the tide wave opposite the Moon? What is the center of gravity between the Earth and the Moon? Where is it situated? Illustrate the operation of this secondary cause.