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The periodic motions of the waters of the ocean, on the hypothesis of an ellipsoid of revolution, entirely covered by the sea, are, however, very far from according with observation. This arises from the great irregularities in the surface of the earth, which is but partially covered by the sea, from the variety in the depths of the ocean, the manner in which it is spread out on the earth, the position and inclination of the shores, the currents, and the resistance which the waters meet with : causes impossible to estimate generally, but which modify the oscillations of the great mass of the ocean. However, amidst all these irregularities, the ebb and flow of the sea maintain a ratio to the forces producing them sufficient to indicate their nature, and to verify the law of the attraction of the sun and moon on the sea. La Place observes, that the investigation of such relations between cause and effect is no less useful in natural philosophy than the direct solution of problems, either to prove the existence of the causes or to trace the laws of their effects. Like the theory of probabilities, it is a happy supplement to the ignorance and weakness of the human mind.

Since the disturbing action of the sun and moon can only become sensible in a very great extent of deep water, the Antarctic Ocean is the origin and birthplace of our tides. A succession of tidal waves from that source follow one another in a north-westerly direction down the Pacific and Atlantic Oceans, modified as they proceed by the depth of the water and the form of the coasts. For when the sun and moon are in the same meridian, and pass over the mass of waters lying east from Van Diemen's Land, New Zealand, and the South Pole, the resulting force of their combined attraction, penetrating to the abyss of the deep and boundless circuit of the Southern Ocean, raises a vast wave or ridge of water, which tends to follow the luminaries to the north and west, and continues to flow in that direction long after the bodies cease to act upon it; but it is so retarded by the rotation of the earth and by the inertia of the water, that it does not arrive at the different parts of the coasts till after the moon's southing (N. 156). When this tidal wave leaves the Antarctic Ocean and enters the Pacific, it rushes along the western coast of America to its farthest end, but it is so much obstructed by the number of islands in the middle of that ocean that it is hardly perceptible among them ; while on the east it



enters the Indian Ocean, strikes with violence on the coasts of Hindostan and the shores at the mouths of the Ganges, and causes the terrific bore in the Hoogly. The part of this tidal wave that enters the Atlantic passes impetuously along the coasts of Africa and America, arriving later and later at each place. It is modified, however, by a tide raised in the Atlantic, which is deep and free from islands; and this combined tidal wave, still coming northward, pours its surge into the Gulf of Fundy to the height of fifty feet; then being deflected by the coast of America at right angles, it rushes eastward, bringing high water to the western coasts of Ireland and England. It then goes round Scotland, brings high water to Aberdeen and the opposite coasts of Norway and Denmark, and, continuing its course to the south, arrives at the mouth of the Thames and fills the channels of that river on the morning of the third day after leaving the Antarctic Ocean.

Thus the tides in our ports are owing to an impulse from the waters of the Antarctic seas raised by the action of the sun and

No doubt a similar action raised that tide in the North Polar Ocean which Dr. Kane saw rolling on the northern coast of Greenland in 82° N. latitude, but which, in the present state of the globe, is imprisoned by bars of ice and ice-bound lands.

The tidal wave extends to the bottom of the ocean, and moves uniformly and with great speed in very deep water, variably and slow in shallow water; the time of propagation depends upon the depth of the sea, as well as on the nature and form of the coasts. It varies inversely as the square of the depth—a law which theoretically affords the means of ascertaining the proportionate depth of the sea in different parts. It is one of the great constants of nature, and is to fluids what the pendulum is to solids—a connecting link between time and force.

For example: the tidal wave moves across the Southern Ocean with the velocity of 1000 miles an hour, and in the Atlantic it is scarcely less on account of the deep trough which runs through the centre of that ocean; but the sea is so shallow on the British coast that it takes more time to come from Aberdeen to London than to travel over an arc of 1200, between 600 S. lat. and 600 N. lat.

In deep water the tidal wave is merely a rise and fall of the surface; the water does not advance, though the wave does. Indeed, if so heavy a body as water were to move at the rate of 1000 miles an hour, it would cause universal destruction, since in the most violent hurricanes the velocity of the wind is little more than 100 miles an hour. Besides, it is evident that no ship could either sail or steam against it. When the water is shallow, however, there is a motion of translation in the water along with the tide.

In the deep ocean the undulating motion consists of two distinct things—an advancing form and a molecular movement. The motion of each particle of water is in an ellipse lying wholly in the vertical plane; so that, after the momentary displacement during the passage of the wave, they return to their places again. The resistance of the sea-bed is insensible in deep water; but when the tidal wave, which extends to the very bottom of the ocean, comes into shallow water with diminished velocity, the particles of water moving in vertical ellipses strike the bottom, and by reaction the wave rises higher; and that being continually repeated, as the form moves on the wave rises higher and higher, bends more and more forward, till at last it loses its equilibrium, and then both form and water roll to the shore, and the elliptical trajectories of the particles, which in deep water were vertical, incline more and more, till at length they become horizontal. The distance from the shore at which the water begins to be translated depends upon the depth, the nature of the coast, and the form of the shore. Mr. Scott Russell has demonstrated that in shallow water the velocity of the wave is equal to that which a heavy body falling freely by its gravity would acquire in descending through half the depth of the fluid.

It is proved by daily experience, as well as by strict mathematical reasoning, that, if a number of waves or oscillations be excited in a fluid by different forces, each pursues its course and has its effect independently of the rest. Now, in the tides there are three kinds of oscillations, depending on different causes, and producing their effects independently of each other, which may therefore be estimated separately. The oscillations of the first kind, which are very small, are independent of the rotation of the earth, and, as they depend upon ihe motion of the disturbing body in its orbit, they are of long periods. The second kind of oscillations depend upon the rotation of the earth, therefore their period is nearly a day. The oscillations of the third kind vary


with an angle equal to twice the angular rotation of the earth, and consequently happen twice in twenty-four hours (N. 157). The first afford no particular interest, and are extremely small ; but the difference of two consecutive tides depends upon the second. At the time of the solstices this difference, which ought to be very great according to Newton's theory, is hardly sensible on our shores. La Place has shown that the discrepancy arises from the depth of the sea, and that if the depth were uniform there would be no difference in the consecutive tides but that which is occasioned by local circumstances. It follows, therefore, that, as this difference is extremely small, the sea, considered in a large extent, must be nearly of uniform depth, that is to say, there is a certain mean depth from which the deviation is not great. The mean depth of the Pacific Ocean is supposed to be about four or five miles, that of the Atlantic only three or four, which, however, is mere conjecture. Possibly the great extent and uniformly small depth of the Atlantic over the telegraphic platform may prevent the difference of the oscillations in question from being perceptible on our shores. From the formulæ which determine the difference of these consecutive tides it is proved that the precession of the equinoxes and the nutation of the earth's axis are the same as if the sea fornied one solid mass with the earth.

The oscillations of the third kind are the semi-diurnal tides so remarkable on our coasts. In these there are two phenomena particularly to be distinguished, one occurring twice in a month, the other twice in a year.

The first phenomenon is, that the tides are much increased in the syzigies (N. 158), or at the time of new and full moon : in both cases the sun and moon are in the same meridian ; for when the moon is new they are in conjunction, and when she is full they are in opposition. In each of these positions their action is combined to produce the highest or spring tides under that meridian, and the lowest in those points that are 90° distant. It is observed that the higher the sea rises in full tide, the lower it is in the ebb. The neap tides take place when the moon is in quadrature. They neither rise so high nor sink so low as the spring tides. It is evident that the spring tides must happen twice in a month, since in that time the moon is once new and once full. Theory proves that each partial tide increases as the cube of the parallax or apparent diameter of the body producing it, for the greater the apparent diameter the nearer the body and the more intense its action upon the sea; hence the spring tides are much increased when the moon is in perigee, for then she is nearest to the earth.

The second phenomenon in the tides is the augmentation occurring at the time of the equinoxes, when the sun's declination is zero (N. 159), which happens twice in every year. The spring tides which take place at that time are often much increased by the equinoctial gales, and, on the hypothesis of the whole earth covered by the ocean, would be the greatest possible if the line of the moon's nodes coincided with that of her perigee, for then the whole action of the luminaries would be in the plane of the equator. But since the Antarctic Ocean is the source of the tides, it is evident that the spring tide must be greatest when the moon is in perigee, and when both luminaries have their highest southern declination, for then they act most directly upon the great circuit of the south polar seas.

The sun and moon are continually making the circuit of the heavens at different distances from the plane of the equator, on account of the obliquity of the ecliptic and the inclination of the lunar orbit. The moon takes about 292 days to vary through all her declinations, which sometimes extend 281° on each side of the equator, while the sun requires nearly 3654 days to accomplish his motions through 231° on each side of the same plane, so that their combined action causes great variations in the tides. Both the height and time of high water are perpetually changing, and, although the problem does not admit of a general solution, it is necessary to analyse the phenomena which ought to arise from the attraction of the sun and moon, but the result must be corrected in each particular case for local circumstances, so that the theory of the tides in each port becomes really a matter of experiment, and can only be determined by means of a vast number of observations, including many revolutions of the moon's nodes.

The mean height of the tides will be increased by a very small quantity for ages to come, in consequence of the decrease in the mean distance of the moon from the earth; the contrary effect will take place after that period has elapsed, and the moon's mean distance begins to increase again, which it will continue to



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