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moon's though greatly less in degree, on account of his distance; he therefore only modifies the form of this spheroid a little. If the waters were capable of assuming the form of equilibrium instantaneously, that is, the form of the spheroid, its summit would always point to the moon, notwithstanding the earth's rotation; but on account of their resistance the rapid motion produced in them by rotation, prevents them from assuming at every instant the form which the equilibrium of the forces acting upon them requires. Hence, on account of the inertia of the waters, if the tides be considered relatively to the whole earth, and open sea, there is a meridian about 30° eastward of the moon, where it is always high water both in the hemisphere where the moon is and in that which is opposite. On the west side of this circle the tide is flowing, on the east it is ebbing, and on every part of the meridian at 90° distant, it is low water. These tides must necessarily happen twice in a day, since the rotation of the earth brings the same point twice under the meridian of the moon in that time, once under the superior, and once under the inferior, meridian.
In the semi-diurnal tides there are two phenomena particularly to be distinguished, one occurring twice in a month, and the other twice in a year.
The first phenomenon is, that the tides are much increased in the syzigies, 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 these points that are 90° distant. It is obvious 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. The spring tides are much increased when the moon is in perigee, because she is then nearest to the earth. 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.
The second phenomenon in the tides is the augmentation, which occurs at the time of the equinoxes, when the sun's declination is zero, which happens twice every year. The greatest tides take place when a new or full moon happens near the equinoxes while the moon is in perigee. The inclination of the moon's orbit on the ecliptic is 5° 8' 479; hence, in the equinoxes, the action of the moon would be increased if her node were to coincide with her perigee. The equinoctial gales often raise these tides to a great height. Besides these remarkable variations, there are others arising from the declination of the sun and moon, which have a great influence on the ebb and flow of the waters. The moon takes about twenty-nine days and a half to vary through all her declinations, which sometimes extend about 28 degrees on each side of the equator, while the sun requires about 365 days to accomplish his motion from tropic to tropic through about 232 degrees, so that their combined motion causes great irregularities, and, at times, their attractive forces counteract each other's effects to a certain extent; but, on an average, the mean monthly range of the moon's declination is nearly the same as the annual range of the declination of the sun; consequently the highest tides take place within the tropics, and the lowest towards the poles.
Both the height and time of high water are thus perpetually changing; therefore, in solving the problem, it is required to determine the heights to which the tides rise, the times at which they happen, and the daily variations. Theory and observation show, that each partial tide increases as the cube of the apparent diameter or of the parallax of the body which produces it, and that it diminishes as the square of the cosine of the declination of that body.
The periodic motions of the waters of the ocean, on the hypothesis of an ellipsoid of revolution entirely covered by the sea, are very far from according with observation; this arises from the very 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 the waters meet with, causes it is impossible to estimate, 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. Thus the problem of the tides does not adınit of a general solution; it is certainly necessary to analyze the general phenomena which ought to result from the attrac
tion of the sun and moon, but these must be corrected in each particular case by local observations modified by the extent and depth of the sea, and the peculiar circumstances of the place.
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 coast of Africa and Europe, arriving later and later at each 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 Gibralter 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 Pauxis, 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 Mediterranean 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