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 the 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 formed 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.