Even Descartes, though he had recourse to physical principles, and tried to fix his system on a firmer basis than the mere abstractions of the mind, left behind him a work which not only could not be improved, but was 'such, that every addition at tempted to be made destroyed the equilibrium of the mass, and pulled away the part to which it was intended that it should be attached. The philosophy of Newton has proved susceptible of continual improvement; its theories have explained facts quite unknown to the author of it; and the exertions of La Grange and La Place, at the dis tance of an hundred years, have perfected a work which it was not for any of the hu man race to begin and to complete.
Newton next turned his attention to the phenomena of the Tides, the dependence of which on the moon, and in part also on the sun, was sufficiently obvious even from . common observation. That the moon is the prime ruler of the tide, is evident from the fact, that the high water, at any given place, occurs always nearly at the moment when the moon is on the same meridian, and that the retardation of the tide from day to day, is the same with the retardation of the moon in her diurnal revolution. That the sun is also concerned in the production of the tides is evident from this, that the highest tides happen when the sun, the moon, and the earth, are all three in the same straight line ; and that the lowest, or neap tides, happen when the lines drawn from the aim and moon to the earth make right angles with one another. The eye of New ton, accustomed to generalize and to penetrate beyond the surface of things, saw that the waters of the sea revolving with the earth, are nearly in the condition of a satelLite revolving about its primary ; and are liable to the same kind of disturbance from the attraction of a third body. The fact in the history of the tides which seems most difficult to be explained, received, on this supposition, a very easy solution. It is known, that high water always takes place in the hemisphere where the moon is, and in the opposite hemisphere where the moon is not, nearly at the same time. This seems, at first sight, very unlike an effect of the moon's attraction; for, though the water in the hemisphere where the moon is, and which, therefore, is near est the moon, may be drawn up toward that body, the same ought not to happen in the opposite hemisphere, where the earth's surface is most distant from the moon. But
if the action of the moon disturb the equilibrium of the ocean, just as the action of one planet disturbs the motion of a satellite moving round another, it is exactly whet might be expected. It had been shown, that the moon, in conjunction with the sun, has her gravitation to the earth diminished, and when in opposition to the sun has it di minished very nearly by, the same quantity. The reason, is, that at the conjunction, or the new moon, the moon is drawn to the sun more than the earth is ; and that at the opposition, or full moon, the earth is drawn toward the sun more than the moon nearly by the same quantity ; the relative motion of the two bodies is therefore affected the same way in both cases, and the gravity of the moon to the earth, or her tendency to descend toward it, is in both cases lessened.
It is plain, that the action of the moon on the waters of the ocean must be regulated by the same principle. In the hemisphere where the moon is, the water is more drawn toward the moon than the mass of the earth is, and its gravity being lessened, the columns toward the middle of the hemisphere lengthen, in consequence of the pres sure of the columns which are at a distance from the middle point, of which the weight is less diminished, and towards the horizon must even be increased. In the oppo site hemisphere, again, the mass of the earth is more drawn to the moon than the waters of that hemisphere, and their relative tendencies are changed in the same direction, and nearly by the same quantity. If the action of the moon on all the parts of the earth, both sea and land, were the same, no tide whatever would be pro duced.
Thus, the same analysis of the force of gravity which explained the inequalities of the moon, were shown by Newton to explain those inequalities in the elevation of the waters of the ocean to which we give the name of tides. On the principle also ex plained in this analysis, it is, that the attraction of the sun and moon conspire to ele vate the waters of the ocean whether these luminaries be in opposition or conjunction. In both cases the solar and lunar tides are added together, and the tide actually ob served is their sum. At the quadratures, or the first and third quarters, these two tides are opposed to one another, the high water of the lunar tide coinciding with the low water of the solar, and conversely, so that the tide actually observed is the differ ence of the two.