The other phenomena of the tides were explained in a manner no less satisfactory, and it only remained to inquire, Whether the quantity of the solar and lunar forces were adequate to the effect thus ascribed to them ? The lunar force there were yet no data for measuring, but a measure of the solar force, as it acts on the moon, had been obtained, and it had been shown that in its mean quantity it amounted of the force which retains the moon in her orbit. This last is of the force of gravity at the earth's surface, and therefore, the force with which the sun disturbs the moon's motion Thro of gravity at the earth's surface. This is the solar disturbing force on the moon when distant sixty semidiameters from the earth's centre, but on a body only one semidiameter distant from that centre, that is, on the water of the ocean, the disturb ing force would be sixty times less, and thus is found to be no more than 58448000 of gravity at the earth's surface.
Now, this being the mean force of the sun, is that by which he acts on the waters, 90 degrees distant from the point to which he is vertical, where it is added to the force of gravity, and tends to increase the weight and lower the level of the waters. At the point where the sun is vertical, the force to raise the water is about double of this, and, therefore, the whole force tending to raise the level of the high, above that of the low water, is three times the preceding, or about the 128110000 of gravity. Small as this force is, when it is applied to every particle of the ocean, it is capable of pro- . ducing a sensible effect. The manner in which Newton estimates this effect can only be considered as affording an approximation to the truth. In treating of the figure of the earth, he had shown that the centrifugal force, amounting to of gra vity, was able to raise the level of the ocean more than seventeen miles, or, more ex actly, 85,472 French feet. Hence, making the effect proportional to the forces, the elevation of the waters produced by the solar force will come out 1.92 feet.
But, from the comparison of the neap and spring tides, that is, of the difference and the sum of the lunar and solar forces, it appears, that the force of the moon is to that of the sun as 4.48 to 1. As the solar force raises the tide 1.92 feet, the lunar will raise it 8.63 feet, so that the two together will produce a tide of 10.1 'French feet, which agrees not ill with what is observed in the open sea, at a distance from land.
The calculus of Newton stopped not here. From the force that the moon exerts on the waters of the ocean, he' found the quantity of matter in the moon to that in the earth as 1 to 39.78, or, in round numbers, as 1 to 40. He also found the density of the moon to the density of the earth as 11 to 9.
Subsequent investigations, as we shall have occasion to remark, have shown that much.was yet wanting to a complete theory of the tides; and that even after Mac
laurin, Bernoulli, and had added their efforts to those of Newton, there re mained enough to give full employment to the calculus of Laplace. As an original deduction, and as a first approximation, that of which I have now given an account will be for ever memorable.
The motion of Comets yet remained to be discussed. They had only lately been acknowledged to belong to the heavens, and to be placed beyond the region of the earth's atmosphere ; but with regard to their motion, astronomers were not agreed. Kepler believed them to move in straight lines; Cassini thought they moved in the planes of great circles, but with little curvature. Hevelius had come much nearer the truth; he had shown the curvature of their paths to be different in different parts; and to be greatest when they were nearest the sun ; and a parabola having its vertex in that point seemed to him to be the line in which the comet moved. Newton, con vinced of the universality of the principle of gravitation, had no doubt that the orbit of the comet must be a conic section, having the sun in one of its foci, and might either be an ellipse, a parabola, or even an hyperbola, according to the relation be tween the force of projection and the force tending to the centre. As the eccentri city of the orbit on every supposition must be great, the portion of it that fell within our view could not differ much from a parabola, a circumstance which rendered the calculation of the comet's place, the position of the orbit was once ascertained, more easy than in the case of the planets. Thus far theory proceeded, and observa tion must then determine with what degree of accuracy this theory represented the phenomena. From three observations of the comet, the position of the orbit could be determined, though the geometric problem was one of great difficulty. New ton gave a solution of it; and it was by this that his theory was to be brought to the test of experiment. If the orbit thus determined was not the true one, the places of the comet calculated on the supposition that it was, and that it described equal areas in equal times about the sun, could not agree with the places actually ob served. Newton showed, by the example of the remarkable comet then visible (1680), that this agreement was as great as could reasonably be expected; thus adding another proof to the number of those already brought to support the principle of universal gravitation. The comets descend into our system from all different quar tos in the heavens, and, therefore, the proofs that they afforded went to show, that the action of gravity was confined to no particular region of the heavens.