The tides have been always found to follow, periodically, the course of the sun and moon; and hence it has been suspected, in all ages, that the tides were, some way or other, produced by these bodies.

The celebrated Kepler was the first person who formed any conjectures respecting their true cause. But what Kepler only hinted, has been completely developed and demonstrated by Sir Isaac Newton.

After his great discovery of the law of gravitation, he found it an easy matter to account for the whole phenomena of the tides; for, according to this law of nature, all the particles of matter which compose the universe, however remote from one another, have a continual tendency to approach each other, with a force directly proportional to the quantity of matter they contain, and inversely proportional to the square of their distance asunder. It is therefore evident, from this, that the earth will be attracted both by the sun and moon. But, although the attraction of the sun greatly exceeds that of the moon, yet the sun being nearly 400 times more distant from the earth than the moon, the difference of his attraction upon different parts of the earth, is not nearly so great as that of the moon; and therefore the moon is the principal cause of the tides.

2. There are two tides every 24 hours, 50 minutes, and 28 seconds, agreeing with the mean interval from the moon's leaving the meridian of any place till it returns to the same meridian again. Or, which amounts to the same thing, it is high water at any place every 12 hours, 25 minutes, and 14 seconds.

The mean retardation of the tides, or of the moon's coming to the meridian in 24 hours, is about 48' 45.7"; and the mean interval between two successive tides is 12 hours, 25 minutes, and 14 seconds: hence the mean daily retardation of high water is 50 minutes and 28.4 seconds.

The retardation in the time of high water, or the tide, varies with the phases of the moon.

About the time of new and full moon the interval is least, being only 12 hours, 19 minutes, 29 seconds; and at the quadratures the interval is the greatest, being 12 hours, 30 minutes, and 7 seconds.

If all parts of the earth were equally attracted by the moon, the waters of the ocean would always retain a spherical form, and there would be no tides, except those which would

be produced by the action of the sun. But the action of the moon being unequal on different parts of the earth, those parts being most attracted that are nearest the moon, and those at the greatest distance least, the spherical figure must suffer some change from the moon's action. Now as the waters of the ocean directly under the moon are nearer to her than the central parts of the earth, they will be more attracted by the moon than the central parts. For the same reason the central parts will be more attracted than the waters on the opposite side of the earth, and, therefore, the distance between the earth's centre and the waters on its surface, both under the moon and on the opposite side will be increased; or the waters will rise higher, and it will then be flood or high water at those places.

But this is not the only cause that produces the rise of the waters at these two points; for those parts of the ocean which are 90° from them, will be attracted with nearly the same force as the centre of the earth, the effect of which will be a small increase of their gravity towards the centre of the earth. Hence, the waters of those places will press towards the zenith and nadir, or the points where the gra vity of the waters is diminished, to restore an equilibrium, and thus occasion a greater rise at those places.

But in order to know the real effect of the moon on the ocean, the motion of the earth on its axis must be taken into account. For if it were not for this motion, the longest diameter of the watery spheroid would point directly to the moon's centre; but by reason of the motion of the whole mass of the earth on its axis, from west to east, the most elevated parts of the waters no longer answer precisely to the moon, but are carried considerably to the eastward in the direction of the rotation. The waters also continue to rise after they have passed directly under the moon, though the immediate action begins then to decrease; and they do not reach their greatest height till they have got about 450 farther. After they have passed the point, which is 900 distant from the point below the horizon, they continue to descend, although the force which the moon adds to their gravity, begins there to decrease. For still the action of the moon adds to their gravity, and makes them descend till they have got about 450 farther; the greatest elevations, Therefore, do not take place at the points which are in a Line with the centres of the earth and moon, but about half

a quadrant to the east of these points, in the direction of the motion of rotation.

Thus it appears, if the earth were entirely covered by the ocean, that the spheroidal form which it would assume, would be so situated, that its longest diameter would point to the east of the moon; or, which amounts to the same thing, the moon would always be to the west of the meridian of the parts of greatest elevation. And as the moon apparently shifts her position from east to west in going round the earth every revolution, the longer diameter of the spheroid fol lowing her motions, will occasion two floods and two ebbs in the interval of 24 hours, 48 minutes, 45", as above.

3. The action of the moon in raising the waters of the ocean, is to that of the sun nearly as 4 to 1. Therefore when the actions of the sun and moon are in the same direction as at the time of new and full moon, the tides rise higher than at any other time, and are called spring tides. But when the moon is in the quarters, the action of the sun diminishes that of the moon, because his action is opposed to that of the moon; consequently, the effect must be to depress the waters where the moon's action has a tendency to raise them. These tides are considerably lower than at any other time, and are called neap tides.

The spring tides do not take place on the very day of the new and full moon, nor the neap tides on the very day of the quadratures, but a day or two after; because in this case, as in some others, the effect is neither the greatest nor least when the immediate influence of the cause is greatest or least: as the greatest heat, for instance, is not on the solstitial day, when the immediate action of the sun is greatest, but some time after it. And, although the actions of the sun and moon were to cease, yet the ocean would continue to ebb and flow for some time, as its waves continue in violent motion for some time after a storm.

The high water at a given place does not always answer to the same situation of the moon, but happens sometimes sooner and sometimes later than if the moon alone acted on the ocean This proceeds from the action of the sun not conspiring with that of the moon. The different distances of the moor from the earth also occasion a sensible variation in the tide

When the moon approaches the earth, her action in every part increases, and the differences in that action, upon which the tides depend, likewise increase. For the attraction of any body is in the inverse ratio of the square of its distance; the nearer, therefore, the moon is to the earth, the greater is her attraction, and the more remote, the less. Hence, her action on the nearest parts increases more quickly than it does on the more remote parts, and therefore the tides increase in a higher proportion as the distance of the moon diminishes.

Newton has shown that the tides increase as the cubes of the distances decrease; so that the moon at half her present distance, would produce a tide eight times greater. Now the moon describes an ellipse about the earth, and, of course, must be once in every revolution nearer the earth than in any other part of her orbit; consequently, she must produce a much higher tide when in this point of her orbit than in the opposite point. This is the reason that two great spring tides never take place immediately after each other; for if the moon be at her least distance at the time of new moon, she must be at her greatest distance at the time of full moon, having performed half a revolution in the intervening time, and therefore the spring tide at the full will be much less than that at the preceding change. For the same reason, if a great spring tide happens at the time of full moon, the tide at the following change will be less.

The spring tides are highest, and the neap tides lowest about the beginning of the year; for the earth being nearest the sun about the 1st of January, must be more strongly attracted by that body, than at any other time of the year; hence, the spring tides which happen about that time will be greater than at any other time. And should the moon be new or full in that part of her orbit which is nearest to the earth, at the same time the tides will be considerably higher than at any other time of the year.

When the moon has north declination, the tides are higher in northern latitudes; when she passes the meridian above the horizon, than when she passes the meridian below it; but when the moon has southern declination, the reverse takes place.

Newton has shown that the moon raises the waters 8 feet 7 inches, while the sun and moon together raise them 10 feet, when at their mean distances from the earth; and about 12 feet when the moon is at her least distance. Such

would the tides regularly be, if the earth were all covered with the ocean to a great depth; but as this is not the case. it is only in places situated on the shores of large oceans, where such tides, as above described, take place.

The tides are also subject to very great irregularities from local circumstances; such as meeting with islands, shoals, headlands, passing through straits, &c. In order that they may have their full motion, the ocean in which they are produced ought to extend 90° from east to west, because that is the distance between the greatest elevation, and the greatest depression produced in the waters by the moon. Hence, it is that the tides in the Pacific Ocean exceed those of the Atlantic, and that they are less in that part of the Atlantic which is within the torrid zone, between America and Africa, than in the temperate zones, on either side of it where the ocean is much broader.

In the Baltic, the Mediterranean, and the Black Seas, there are no sensible tides; for they communicate with the ocean by so narrow inlets, and are of so great extent, that they cannot speedily receive, and let out water enough to raise or depress their surfaces in any sensible degree.

At London the spring tide rises 19 feet, at St. Maloes, in France, they rise 45 feet, and in the bay of Fundy, in Nova Scotia, about 60 feet.

CHAPTER XV.

Of Refraction, Parallax, &c.

It fol

1. The density of the atmosphere surrounding the Earth continually decreases, and at a few miles high becomes very small; and a ray of light passing out of a rarer medium into a denser, is always bent out of its course towards the perpendicular to the surface, on which the ray is incident. lows, therefore that a ray of light must be continually bent in its course through the atmosphere, and describe a curve, the tangent to which curve, at the surface of the Earth, is the direction in which the celestial object appears. Consequently the apparent altitude is always greater than the true