TIDES. It was known, at least as early as the time of Caesar, though probably long before, that the time of high-water, and also the height of the tide, are in some way connected with the age of the moon. And even in the present state of science, what is called the establishment of a port, or the time of high-water at new or full moon (that is, the interval between the moon's crossing the meridian and the full tide), which is prac tically the most important part of the whole question, cannot be predicted by theory, but must be obtained by observation. The first attempt to explain the phenomena of the tides was made by Newton; and, considering the little that has, since his time, been effected, his approximate solution must be pronounced highly creditable, although in many respects unsatisfactory. D. Bernouilli and others have since slightly improved Newton's method; and a complete solution of the problem has been attempted by Laplace. The principles involved in this solution are undoubtedly correct, and the result, so far as it goes, leaves little to be desired. But it does not go far, for two reasons: wo know very little as to the depth of the sea; and, even had we that knowl cdge, the excessive difficulties of the mathematical processes required in taking account of it, and of the forms of continents and islands, would be such as to render Laplace's method inapplicable. .
Newton's approximate method consists in the study of the problem as a statical one, and this we will presently describe. Laplace, on the other hand, treats the problem as one of fluid motion. Airy and others have, more recently, attempted, with success, to simplify Laplace's process. Curiously enough, however, the results of all these theories are very much alike; and, while some of the results agree well with observation, others seem irreconcilable with it. We cannot explain Laplaoe's method without employing high analysis, quite unsuited to this work; so we must be content to describe the faulty theory. In the Newtonian or equilibrium theory, we consider the earth to be spherical, and covered with a layer of water, which would, of course, if left to itself, be uniformly .deep over the whole surface. The attraction of the moon (per unit of mass) on the water immediately below her, is greater than her attraction on the solid earth (per unit of mass), and tends, therefore, to raise the water at that part of the surface. At the point of the surface directly opposite to the moon, the water-layer is further from the moon than the bulk of the earth, and, consequently, the moon attracts the water (per unit of mass) less than it attracts the earth. The tendency is, as it were, to pull the earth away from the water, so that here also the water is raised, though not quite so much as on the other side, as the moon's attraction diminishes with distance. The
effect of the moon's action on the previously uniform layer of water is thus to elongate it both ways in the direction of the line joining the centers of the earth and moon. On account of the very small amount of this elongation, it is found by mathematical pro cesses, which we cannot give here, that the form of the surface will become very nearly a prolate spheroid (a solid formed by the revolution of an ellipse about its longer axis).
Before proceeding further with our explanation, it is necessary to say a few words wit reference to a mistake often fallen into by those whose knowledge of mechanics is scanty; and at times paraded with a show of learning by a class of men who doubt such plain matters of fact as the moon's rotation, the oblateness of the earth, the inertia of matter, and what not. Such people say that, since, if the moon and earth were rigidly fixed to each other, the water would rice only on the side next the moon, this must be the case in nature also. This is the same mistake as those commit (see PERTURBATIONO who allow that at new moon the sun virtually diminishes the moou's gravitation toward the earth, but refuse to allow that the same is true at full moon.] We have next to consider that the moon revolves about the earth, and that the earth also revolves about its axis. Thus, the equilibrium figure has never time to form; but an imperfect form of it travels round the earth in the time of a lunar day (24 hours -54 minutes). If the moon be on the equator, it is obvious that similar portions of the water-spheroid will reach any one spot on the earth at intervals of half a lunar day (12 hours 27 minutes). If the moon's declination be considerable, such will not be the case—a place, for instance, whose latitude is equal to the moon's declination, will be reached by one pole of the wave-spheroid when the moon is on the meridian; but in 12 hours 27 minutes, the other pole of the spheroid will not pass over the place, but at a meridian distance of twice the latitude of the place, or twice the moon's declination. Thus, when the moon's declination is sensible, the two tides of each day are not gener ally equal in height, except for places on the earth's equator. This gives rise to what is called the diurnal tide, which is, as it were, superposed upon the ordinary, or semi diurnal, tide, and ought to be more sensible as the latitude is greater. Owing to fluid friction, and other causes, we should expect that the axis of the tidal spheroid would Jag a little behind the moon, and this is found to be the case.