It appears, that it was not till some years after this, that his attention was called to the same subject, by a letter from Dr Hooke, proposing as a question, To determine the line in which a body let fall from a height descends to the ground, taking into con sideration the motion of the earth on its axis. This induced him to resume the sub ject of the moon's motion ; and the measure of a degree by Norwood having now fur nished more exact data, he found that his calculation gave the precise quantity for the moon's momentary deflection from the tangent of her orbit, which was deduced from astronomical observation. The moon, therefore, has a tendency to descend toward the earth from the same cause that a stone at its surface has; and if the descent of the stone in a second be diminished in the ratio of 1 to 3600, it will give the quantity by which the moon descends in a second, below the tangent to her orbit, and thus is ob tained an experimental proof of the fact, that gravity decreases as the square of the distance increases. He had already found that the times of the planetary revolutions, supposing their orbits to be circular, led to the same conclusion ; and he now pro ceeded, with a view to the solution of Hooke's problem, to inquire what 'their orbits must be, supposing the centripetal force to be inversely as the square of the distance, and the initial or projectile force to be any whatsoever. On this subject Pemberton says, he composed (as he calls it) a dozen propositions, which probably were the same with those in the beginning of the Principia,—such as the description of equal areas in equal times, about the centre of force, and the ellipticity of the orbits described un. der the 1111111CM of a centripetal force that varied inversely as the square of the dia.
tanees.
What seems very difficult to be explained is, that after having made trial of his strength, and of the power of the instruments of investigation which he was now in pos.
session of, and had entered by means of them on the noblest and most magnificent field of investigation that was ever yet opened to any of the human race, he again de sisted from the pursuit, so that it was not till several years afterwards that the conver sation of Dr Halley, who made him, a visit at Cambridge, induced him to resume and extend his researches.
He then found, that the three great facts in astronomy, which form the laws of Kepler, gave the most complete evidence to the system of gravitation. The first of them, the proportionality of the areas described by the radius vector to the times in which they are described, is the peculiar character of the motions produced by an original impulse impressed on a body, combined with a centripetal force continually urging it to a given centre. The second law, that the planets describe ellipses, having the sun in one of the foci, common to them all, coincides with this propo sition, that a body under the influence of a centripetal force, varying as the square of the distance inversely, and having any projectile force whatever originally im pressed on it, must describe a conic section having one focus in the centre of force, which section, if the projectile force does not exceed a certain limit, will become an ellipse. The third law, that the squares of the periodic times are as the cubes of the distances, is a property which belongs to the bodies describing elliptic orbits under the conditions just stated. Thus the three great truths to which the astronomy of the planets had been reduced by Kepler, were all explained in the most satisfactory man ner, by the supposition that the planets gravitate to the sun with a force which varies in the inverse ratio of the square of the distances. It added much to this evidence,
that the observations of Cassini had proved the same laws to prevail among the satel lites of Jupiter.
But did the principle which appeared thus to unite the great bodies of the universe act only on those bodies ? Did it reside merely in their centres, or was it a force common to 41 the particles of matter? Was it a fact that every particle of matter had a tendency to unite with every other? Or was that tendency directed only to particular centres? It could hardly be doubted that the tendency was common to all the particles of matter. The centres of the great bodies had no properties as mathematical" points, they had none but what they derived from the material particles distributed around them. But the question admitted of being brought to a better test than that of such general reason ing as the preceding. The bodies between which this tendency had been observed to take place were all round bodies, "and either spherical or nearly so, but whether great or small, they seemed to gravitate toward one another according. to the same law.
The planets gravitated to the sun, the moon to the earth, the satellites of Jupiter to ward Jupiter ; and gravity, in all these instances, varied inversely as the squares of the distances. Were the bodies ever • so small—were they mere particles—pro vided only they were round, it was therefore safe to infer, that they would tend to unite with forces inversely as the squares of the distances. It was probable, then, that gra-. vity was the mutual tendency of all the particles of matter toward one another; but this could not be concluded with certainty, till it was found, whether great spherical bodies composed of particles gravitating According to this law, would themselves gravitate according to the same. Perhaps no man of that age but Newton himself was fit to undertake the solution of this problem. His analysis, either in the form of fiwions or in that of prime and ultimate ratios, was able to reduce it to the quadrature of curves, and he then found, no doubt infinitely to his satisfaction, that the law was the same for the sphere as for the particles which composed it ; that the gravitation was directed to the centre of the sphere, and was as the quantity of matter contain ed in it, divided by the square of the distance from its centre. Thus a complete expression was obtained for the law_ of gravity, involving both the conditions on which it must depend, the quantity of matter in the • gravitating bodies, and the distance at which the bodies were placed. There could be no doubt that this tendency was always mutual, as there appeared nowhere any exception to the rule that action and reaction are equal; so that if a stone gravitated to the earth, the earth gravitated equally to the stone ; that is to say, that the two bodies tended to ap proach one another with velocities which were inversely as their quantities of matter.' There appeared to be no limit to the distance to which this action reached ; it was ' a force that united all the parts of matter to one another, and if it appeared to be particularly directed to certain points, such as the centres of the sun or of the planets, it was only on account of the quantity of matter collected and distributed uniformly round those points, through which, therefore, the force resulting from the composition of all those elements must pass either accurately or nearly.