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Since the disturbing action of the sun and moon can only become sensible in a very great extent of water, it is evident that the Pacific Ocean is one of the principal sources of our tides'; but, in consequence of the rotation of the earth, and the inertia of the ocean, high water does not happen till some time after the moon's southing. The tide raised in that world of waters is transmitted to the Atlantic, from which sea it moves in a northerly direction along the coasts of Africa and Europe, arriving later and later at cach place. This great wave, however, is modified by the tide raised in the Atlantic, which sometimes combines with that from the Pacific in raising the sea, and sometimes is in opposition to it, so that the tides only rise in proportion to their difference. This vast combined wave, reflected by the shores of the Atlantic, extending nearly from pole to pole, still coming northward, pours through the Irish and British Channels into the North Sea, so that the tides in our ports are modified by those of another hemisphere. Thus the theory of the tides in each port, both as to their height and the times at which they take place, is really a matter of experiment, and can only be perfectly determined by the mean of a very great number of observations, including several revolutions of the moon's nodes.
The height to which the tides rise is much
greater in narrow channels than in the open sea, on account of the obstructions they meet with. The sea is so pent up in the British Channel, that the tides sometimes rise as much as fifty feet at St. Malo, on the coast of France, whereas, on the shores of some of the South Sea islands, they do not exceed one or two feet. The winds have a great influence on the height of the tides, according as they conspire with or oppose them; but the actual effect of the wind in exciting the waves of the ocean extends very little below the surface: even in the most violent storms, the water is probably calm at the depth of ninety or a hundred feet. The tidal wave of the ocean does not reach the Mediterranean nor the Baltic, partly from their position and partly from the narrowness of the Straits of Gibraltar and of the Categat, but it is very perceptible in the Red Sea and in Hudson's Bay. In high latitudes, where the ocean is less directly under the influence of the luminaries, the rise and fall of the sea is inconsiderable, so that, in all probability, there is no tide at the poles, or only a small annual and monthly tide. The ebb and flow of the sea are perceptible in rivers to a very great distance from their estuaries. In the Straits of Pausis, in the river of the Amazons, more than five hundred miles from the sea, the tides are evident. It requires so many days for the tide to ascend this mighty stream, that the returning tides meet a succession of those which are coming up; so that every possible variety occurs in some part or other of its shores, both as to magnitude and time. It requires a very wide expanse of water to accumulate the impulse of the sun and moon, so as to render their influence sensible ; on that account, the tides in the Media terranean and Black Sea are scarcely perceptible.
These perpetual commotions in the waters are occasioned by forces that bear a very small proportion to terrestrial gravitation : the sun's action in raising the ocean is only yu+T7oo of gravitation at the earth's surface, and the action of the moon is little more than twice as much; these forces being in the ratio of 1 to 2.35333, when the sun and moon are at their mean distances from the earth. From this ratio, the mass of the moon is found to be only is of that of the earth. Had the action of the sun on the ocean been exactly equal to that of the moon, there would have been no neap tides, and the spring tides would have been of twice the height which the action of either the sun or moon would have produced separately; a phenomenon depending upon the interference of the undulations,
A stone plunged into a pool of still water occasions a series of waves to advance along the surface, though the water itself is not carried forward, but only rises into heights and sinks into hollows, each portion of the surface being elevated and depressed in its turn.. Another stone of the same size, thrown into the water near the first, will occasion à similar set of undulations. Then, if an equal and similar wave from each stone arrive at the same spot at the same time, so that the elevation of the one exactly coincides with the elevation of the other, their united effect will produce a wave twice the size of either; but if one wave precede the other by exactly half an undulation, the elevation of the one will coincide with the hollow of the other, and the hollow of the one with the elevation of the other, and the waves will so entirely obliterate one another, that the surface of the water will remain smooth and level. Hence, if the length of each wave be represented by 1, they will destroy one another at intervals of , , , &e, and will combine their effects at the intervals 1, 2, 3, &e. It will be found, according to this principle, when still water is disturbed by the fall of two equal stones, that there are certain lines on its surface of a hyperbolie form, where the water is smooth in consequence of the waves obliterating each other; and that the elevation of the water in the adjacent parts corresponds to both the waves united. Now, in the spring and neap tides, arising from the combination of the
'simple soli-lunar waves, the spring tide is the joint result of the combination when they, coincide in time and place; and the neap tide happens when they succeed each other by half an interval, so as to leave only the effect of their difference sensible. It is therefore evident that, if the solar and lunar tides were of the same height, there would be no difference, consequently no neap tides, and the spring tides would be twice as high as either separately. In the port of Batsha, in Tonquin, where the tides arrive by two channels, of lengths corresponding to half an interval, there is neither high nor low water, on account of the interference of the waves.
The initial state of the ocean has no influence on the tides; for, whatever its primitive conditions may have been, they must soon have vanished by the friction and mobility of the fluid. One of the most remarkable circumstances in the theory of the tides is the assurance that, in consequence of the density of the sea being only one-fifth of the mean density of the earth, and that the earth itself increases in density toward the centre, the stability of the equilibrium of the ocean never can be subverted by any physical cause whatever. A general inundation, arising from the mere instability of the ocean, is therefore impossible. A variety of circumstances, however, tend to produce partial variations in the equilibrium of the seas, which is