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 do for many ages. Thus the mean distance of the moon and the consequent minute increase in the height of the tides will oscillate between fixed limits for ever.
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, near the centre of the Pacific, they do not exceed one or two feet. The winds have 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 fathoms. 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. The ebb and flow of the sea are perceptible in rivers to a very great distance from their estuaries. In the Narrows 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 at 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 is only the 1/38448000 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 the 1/75 part 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 waves or undulations.