A remarkable inference was deddced from this view of the planetary motions, giv ing a deep insight into the constitution of our system in a matter that seems the most recondite, and the furthest beyond the sphere which necessarily circumscribes human knowledge. The quantity of matter, and even the density of the planets, was determined. We have seen how Newton compared the intensity of gravitation at the surface of the earth, with.its intensity at the moon, and by a computation somewhat similar, he com pared the intensity of the earth's gravitation to the sun, with the moon's gravitation to the earth, each being measured by the contemporaneous and momentary deflexion from a tangent to the small arch of its orbit. A more detailed investigation showed that the intensity of the central force in different orbits, is as the mean distance divided by the square of the periodic time; and the same intensity being also as the quantities of matter divided by the squares of the distances, it follows, that these two quotients are equal to one another, and that, therefore, the quantities of matter are. as the mean distances divided by the squares of the periodic times. Supposing, therefore. in the instance just mentioned, that the ratio of the mean. distance of the sun from the earth to the mean distance of the moon from the earth is given (which it is from , astronomical observation); as the ratio of their periodic lines is also known, the ratio of the quantity of matter in the sun to the quantity of matter in the earth, of consequence, is found, and the same holds good. for all the planets which have satellites moving round them. Nothing certainly can be more unexpected than that the quantities of matter in bodies so remote, should admit of being compared with one another,. and with the earth. Hence also their mean densities, or mean specific gravities, became known. For from their distances and the angles they subtended, both, known from observation, their magnitudes or cubical contents were easily inferred, and the densities of all bodies are, as their quantities of matter, divided by their mag nitude. The Principia Philosophise Naturalis, which contained all these discoveries, and established the principle of universal gravitation, was given to the world in 1687, an era, on that account, for ever memorable in the history of human knowledge.
The principle of gravity which was -thus, fully established, and extensive consequences deduced, was not now mentioned for the first times though for the first time its existence as a fact was ascertained, and the law it observes was dis... covered. Besides some curious references to weight and gravity, contained in the writings of the ancients, we find something_ more precise concerning it in the writings of Copernicus, Kepler, and Hooke.
Anaxagoras is said to have held that " the heavens are kept in their place by the rapidity of their revolution, and would fall down if that rapidity were to cease." Plutarch, in like manner, says, the moon is kept from falling by the rapidity of her motion, just as a stone whirled round in a sling is prevented from falling to the ground.' Lucretius, reasoning probably after Democritus, holds, that the atoms would fall from &ir gravity, have long since in the centre of the universe, if the' universe were notinfinite-so as to have no centre.' An observation of Pythagoras, supposed to 'refer to the doctrine of gravity, though in reality extremely vague, has been abundantly commented on 'by Gregory and Mao • laurin. A musical string, said gives the same sound with another of twice the length, if the latter be straitened by four times the weight that straitens the former ; and the gravity of a planet is four times that of another which is at twice the distance. These are the most precise notices, as far as I know, that exist 'in the writ ings of the ancients concerning gravity as a force acting on terrestrial bodies, or as extending even to those that are more distant. They are the reveries of ingenious men who had no steady principles deduced from experience and observation to direct their inquiries ; and who, even when in their conjectures they hit on the truth, could hardly distinguish it from error.
Copernicus, as might be expected, is considerably more precise. " I do not think," says he, " that gravity is any thing but a natural appetency of the parts (of the earth) given by the providence of the Supreme Being, that, by uniting together, they may as sume the form of a globe. It is probable, that this same affection belongs to the sun,
the moon, and the fixed stars, which all are of a round The power which Copernicus here speaks of has nothing to do, in his opinion, with the revolutions of the earth or the planets in their different orbits. It is merely intend ed as an explanation of their globular forms, and the consideration that does the author most credit is, that of supposing the force to belong, not to the centre, but to all the parts of the earth.
Kepler, in his immortal work on the Motions of Mars, treats of gravity as a force acting naturally from planet to planet, and particularly from the earth to the moon. " If the moon and the earth were not retained by some animal or other equivalent force each in its orbit, the earth would ascend to the moon by a 54th part of the in terra' between them, while the moon moved over the remaining 53 parts, that is sup posing them both of the same density."' This passage is curious, as displaying a singular mixture of knowledge and error on the subject of the planetary motions. The tendency of the earth and moon being mutual, and producing equal quan tities of motion in those bodies, bespeaks an accurate knowledge of the nature of that tendency, and of the equality, at least in this instance, between action and re action. Then, again, the idea of an animal force or some other equally unintelligible power being necessary to carry on the circular motion, and to prevent the bodies from moving directly toward each other, is very strange ; considering that Kepler knew the inertia of matter, and ought, therefore, to have understood the nature of centrifugal force, and its power to counteract the mutual gravitations of the two bo dies. In this respect, the great astronomer who was laying the foundation of all that is known of the heavens, was not so far advanced as Anaxagoras and Plutarch ;—so slow and unequal are the steps by which science advances to perfection. The mutual gravity of the earth and moon is not supposed by Kepler to have any concern in the production of their circular motions ; yet he holds the tides to be produced by the gravitation of the waters of the sea toward the moon.' The length to which Galileo advanced in this direction, and the point at which he stopped, are no less curious to be remarked. Though so well acquainted with the nag ture of gravity on the earth's surface,—the object of so many of his researches and dis coveries, and though he conceived it to exist in all the planets, nay, in all the celes, tial bodies, and to be the cause of their round figure, he did not believe it to be a power that extended from one of those bodies to another. He seems to have thought that gravity was a principle which regulated the domestic economy of each particu. bar body, but had nothing to do with their external relations ; so that he censured Kepler for supposing, that the phenomena of the tides are produced by the gravitation of the waters of the ocean to the moon.' Hooke did not stop short in the same unaccountable manner, but made a nearer ap proach to the truth than any one bad yet done. In his attempt to prove the motion of the earth, published in 1674, he lays it down as the principle on which the celestial notions are to be explained, that the heavenly bodies have an attraction or gravitation toward their own centres, which extends to other bodies within the sphere of their activity ; and that all bodies would move in straight lines, if some force like this did not act on them continually, and compel them to describe circles, ellipses, or other curve lines. The force of gravity, also, he considered as greatest nearest the body, though the law of its variation he could not determine. These are great advances ; though, from his mention of the sphere of activity, from his considering the force as residing in the centre, and from his ignorance of the law which it observed, it is evident, that beside great vagueness, there was much error in his notions about gravity. Hooke, however, whose candour and uprightness bore no proportion to the strength of his understanding, was disingenuous enough, when Newton had de termined that law, to lay claim himself to the discovery.