little to the influence of the Moon, and rises again, alternately, like the gentle oscillations of a balance. This curious phenomenon, is called Nutation.

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 three fourths 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.

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 ancient astronomers, were situated south of the ecliptic, near the summer solstice, have ap proached 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 situ ated near the winter solstice. All the stars, indeed, participate 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 exceed ing 2o 42'. If we consider the effect of this ever varying attribute in the system of the universe, it may be affirmed

What results from this alternate and opposite influence? By what token does the Earth show her respect to this influence of the Moon? What is this phenomenon called? What is the consequence of the yearly diminution of the obliquity of the ecliptic in respect to the position of the tropics, and the declination of the Sun? What other obvious effects result from this diminution? How does it affect the declination of the stars near the solstices? Do all the stars partake, more or less. in this motion? Will this diminution of the obliquity always continue? What are the limits of its alternate variation? What would be the consequence, in respect to the seasons, should the plane of the ecliptic ever suincide with the plane of the equator ?

that the plane of the ecliptic never has coincided with the plane of the equator, and never will coincide with it. Such à coincidence, could it happen, would produce upon the Earth perpetual spring.

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.

THE Oceans, and all the seas, are observed to be incessantly agitated for certain periods of time, first from the east towards the west, and then again from the west towards the east. In this motion, which lasts about six hours, the sea gradually swells; so that entering the mouths of rivers, it drives back the waters towards their source. After a continual flow of six hours, the seas seem to rest for about a quarter of an hour; they then begin to ebb, or retire back again from west to east for six hours more; and the rivers again resume their natural courses. Then after a seeming pause of a quarter of an hour, the seas again begin to flow, as before, and thus alternately. This regular alternate motion of the sea constitutes the tides, of which there are two in something less than twenty-five hours.

The ancients considered the ebbing and flowing of the tides as one of the greatest mysteries in nature, and were utterly at a loss to account for them. Galileo and Descartes, and particularly Kepler, made some successful advances towards ascertaining the cause; but Sir Isaac Newton was the first who clearly showed what were the chief agents in producing these

motions.

The cause of the tides, is the attraction of the Sun and Moon, but chiefly of the Moon, upon the waters of the

What is the method used by astronomers for determining the obliquity of the ecliptic! What regular motion is observed in the great body of waters upon the globe? In what periods of time is this alternate ebbing and flowing accomplished? What is it called? How were these phenomena regarded by the ancients? Who ascertained their trus cause? What is the cause of the tides)

ocean. In virtue of gravitation, the Moon, by her attraction, draws, or raises the water towards her; but because the power of attraction diminishes as the squares of the distance increase, the waters on the opposite side of the Earth, are not so much attracted as they are on the side nearest the Moon.

That the Moon, says Sir John Herschel, should, by her attraction, heap up the waters of the ocean under her, seems to most persons very natural; but that the same cause should, at the same time, heap them up on the oppo site side, seems, to many, palpably absurd. Yet nothing is more true, nor indeed more evident, when we consider that it is not by her whole attraction, but by the differences of her attractions at the opposite surfaces and at the centre, that the waters are raised.

That the tides are dependent upon some known and determinate laws, is evident from the exact time of high water being previously given in every ephemeris, and in many of the common almanacks.

The Moon comes every day later to the ineridian than on the day preceding, and her exact time is known by calculation; and the tides in any and every place, will be found to follow the same rule; happening exactly 0 much later every day as the Moon comes later to the meridian. From this exact conformity to the motions of the Moon, we are induced to look to her as the cause; and to infer that these phenomena are occasioned principally by the Moon's attraction.

THE TIDES.

Fig. 24.

Fig. 25.

Fig. 26.

M

If the Earth were at rest, and there were no attractive influence from either the Sun or Moon, it is obvious from the principles of gravitation, that the waters in the ocean would be truly spherical; (as represented by Fig. 24;) but daily observation proves that they are in a state of continual agitation.

If the Earth and Moon were without motion, and the Earth covered all over with water, the attraction of the Moon would raise it up in a heap, in that part of the ocean to which the Moon is vertical, as in Figure 25, and there it would, prob

How does the attraction of the Sun and Moon produce tides upon both sides of the earth at the same time? What is Sir John Herschel's remark upon this theory? How is it known that the tides are governed by any ascertained law? What coinci dence is observed between the meridian passage of the Moon, and the time of high water? What conclusion may we derive from this coincidence? If the Earth were at rest, and under no influence from the attraction of the Sun or Moon, what shape would the waters assume? Suppose the attractive power of the Moon upon the Earth to be as it is, and neither the Earth or Moon to have any motion, what would be the result? How would this condition of things be affected by the Earth's rotation?

ably, always continue; but by the rotation of the Earth upon its axis, each part of its surface to which the Moon is vertical is presented to the action of the Moon: wherefore, as the quantity of water on the whole Earth remains the same, when the waters are elevated on the side of the Earth under the Moon, and on the opposite side also, it is evident they must recede from the intermediate points, and thus the attraction of the Moon produce high water at two opposite places, and low water at two opposite places, on the Earth, at the same time, as represented by Figure 26.

This is evident from the figure. The waters cannot rise in one place, without falling in another; and therefore they must fall as low in the horizon, at C and D, as they rise in the zenith and nadir, at A and B. Fig. 27.

THE TIDES.

Fig. 27.

It has already been shown, under the article gravitation, that the Earth and Moon would fall towards each other, by the power of their mutual attraction, if there were no centrifugal force to prevent them; and that the Moon would fall as much faster towards the Earth than the Earth would fall towards the Moon, as the quantity of matter in the Earth is greater than the quantity of matter in the Moon. The same law determines also the size of their respective orbits around their common centre of gravity.

If follows then, as we have seen, that the Moon does not revolve, strictly speaking, around the Earth as a centre, but around a point between them, which is 80 times nearer the Earth than the Moon, and consequently is situ ated about 3000 miles from the Earth's centre. It has also been shown, that all bodies moving in circles acquire a centrifugal force proportioned to their respective masses and velocity. From these facts, soine philosophers account

If the Earth and the Moon mutually attract each other with so much force, what prevents their coming together? But centrifugal force results only from circular motion, does the Farth then circulate around the Moon to acquire the centrifugal force by which it is kept from falling upon the Moon? Ans. The Earth does not circulate around the Moon, but around the cominon centre of gravity between it and the Moon. Where is this centre situated, and in what time does the ath revolve about it? Ans. The certre of gravity, between the Earth and Moon, is about 3000 miles from the Earth's centre, around which it revolves every lunar month, or as often as the Moon revolves around the Earth.] Fom the fact of the Earth's motion, as in the case described, how do some philoso phers account for high water on the side of the Earth, opposite to the Moon?

for bigh water on the side of the Earth opposite to the Moon, in the following

manner:

As the Earth and Moon move around their common centre of gravity, that pari of the Earth which is at any time turned from the Moon, being about 7000 les farther from the centre of gravity, than the side next the Moon, would have a greater centrifugal force than the side next her. At the Earth's centre, the centrifugal force will balance the attractive force; therefore as much water is thrown off by the centrifugal force on the side which is turned from the Moon, as is raised on the side next her by her attraction.

From the universal law, that the force of gravity diminishes as the square of the distance increases, it results, that the attractive power of the Moon decreases in intensity at every step of the descent from the zenith to the nadir; and consequently that the waters on the zenith, being more attracted by the Moon than the Earth is at its centre, move faster towards the Moon than the Earth's centre does: And as the centre of the Earth moves faster towards the Moon than the waters about the nadir do, the waters will be, as it were, left behind, and thus, with respect to the centre, they will be raised.

The reason why the Earth and waters of our globe do not seem to be af fected equally by the Moon's attraction. is, that the earthy substance of the globe, being firmly united. does not yield to any difference of the Moon's at tractive force; insomuch that its upper and lower surface must move equally fast towards the Moon; whereas the waters, cohering together but very lightly, yield to the different degrees of the Moon's attractive force, at different distances from her.

The length of a lunar day, that is, of the interval from one meridian passage of the Moon to another, being, at a mean rate, 24 hours, 48 minutes and 44 seconds, the interval between the flux and the reflux of the sea is not, at a mean rate, precisely six hours, but twelve minutes and eleven seconds more, so that the time of high water does not happen at the same hour, but is about 49 minutes later every day.

The Earth revolves on its axis in about twenty-four hours; if the Moon, therefore, were stationary, the same part of our globe would return beneath it, and there would be two tides every twenty-four hours; but while the Earth is turning once upon its axis, the Moon has gone forward 13° in her orbitwhich takes forty-nine minutes more before the same meridian is brought again directly under the Moon. And hence every succeeding day the time of high water will be fortynine minutes later than the preceding.

For example:-Suppose at any place it be high water at 3 o'clock in the afternoon, upon the day of new Moon; the following day it will be high water about 49 minutes after 3; the day after, about 33 minutes after 4; and so on,

How is this phenomenon otherwise explained, by the laws of gravity, merely? Are the Earth and waters of the globe affected equally, by the Moon's attraction? Why not? What is the average interval between the flux and reflux of the sea? What is the length of a lunar day, and of the interval of the flux and reflux of the sea? How is this daily "etardation of the tides accounted for? Give an example?