Plato clearly asserts, that God had impressed upon the planets “a motion which was the most proper for them.” This could be nothing else than that perpendicular motion, which has a tendency to the centre of the universe, that is, gravity; and what coincides with it, a lateral impulse, rendering the whole circular.
Diogenes Laertius says, that at the beginning, the bodies of the universe were agitated tumultuously, and with a disorderly movement; but that God afterwards regulated their course, by laws natural and proportional.
Anaxagoras being asked what it was that retained the heavenly bodies in their orbit, notwithstanding their gravity, remarkably answered, that “the rapidity of their course preserved them in their stations; and that should the celerity of their motions abate, the equilibrium of the world being broken, the whole machine would fall to ruin.”
Plutarch, who knew almost all the shining truths of astronomy, in explaining what it was that made bodies tend towards the earth, attributes it to “a reciprocal attraction, whereby all terrestrial bodies have this tendency, and which collects into one the parts constituting the sun and moon, and retains them in their spheres.” He afterwards applies these particular phenomena to others more general; and, from what happens in our globe, deduces, according to the same principle, whatever must thence happen respectively in each celestial body; and then considers them in their relative connections one towards another. He illustrates this general relationship and connection, by instancing what happens to our moon in its revolution round the earth, comparing it to “a stone in a sling, which is impressed by two powers at once;” that of projection, which would carry it away, were it not retained by the embrace of the sling; which, like the central force, keeps it from wandering, whilst the combination of the two moves it in a circle. In another place, he speaks “of an inherent power in bodies, that is, in the earth, and other planets, of attracting to themselves whatever is within their reach.” In these two passages, there is a plain reference to the centripetal force, which binds the planets to their proper, or common centres; and to the centrifugal, which makes them roll in circles at a distance.
The ancients, then, attribute to the celestial bodies a tendency towards one common centre, and a reciprocal attractive power. It appears also, that they knew, as well as the moderns, that the cause of gravitation, that attracted all things, did not reside solely in the centre of the earth. Their ideas were even more philosophic; for they taught, that “this power was diffused through every particle of the terrestrial globe, and compounded of the various energy residing in each.”
It remains to inquire, whether they knew the law by which gravity acts upon the celestial bodies, that it was in an inverse proportion of their quantity of matter, and the square of their distance. Certainly they were not ignorant, that the planets in their courses observed a constant and invariable proportion; though some sought for it in the difference of the quantity of matter contained in the masses, of which the planets were composed; and others, in the difference of their distances. Lucretius, after Democritus and Aristotle, thought that “the gravity of bodies was in proportion to the quantity of matter of which they were composed.” It is true, that the penetration and sagacity of a Newton, a Gregory, and a Maclaurin, were requisite to perceive and discover, in the few fragments of the ancients now remaining, the inverse law respecting the squares of the distances, a doctrine which Pythagoras had taught; but they acknowledge that it was contained in those writings; and they avail themselves of the authority of Pythagoras, to give weight to their system.
Plutarch, of all the philosophers who have spoken of Pythagoras, had a better opportunity of entering into the ideas of that great man, and has explained them better than any one besides. Pliny, Macrobius, and Censorinus, have also spoken of the harmony which Pythagoras observed to reign in the course of the planets; but Plutarch makes him say, that it is probable that the bodies of the planets, their distances, the intervals between their spheres, the celerity of their courses and revolutions, are not only proportionable among themselves, but to the whole of the universe. Dr. Gregory declares it to be evident, that Pythagoras understood, that the gravitation of the planets towards the sun was in a reciprocal ratio of their distance from that luminary; and that illustrious modern, followed herein by Maclaurin, makes that ancient philosopher speak thus:—
“A musical string, says Pythagoras, yields the very same tone with any other of twice its length, because the tension of the latter, or the force whereby it is extended, is quadruple to that of the former; and the gravity of one planet is quadruple to that of any other, which is at double the distance. In general, to bring a musical string into unison with one of the same kind, shorter than itself, its tension ought to be increased in proportion as the square of its length exceeds that of the other; and that the gravity of any planet may become equal to that of any other nearer the sun, it ought to be increased in proportion as the square of its distance exceeds that of the other. If, therefore, we should suppose musical strings stretched from the sun to each of the planets, it would be necessary, in order to bring them all to unison, to augment or diminish their tensions, in the very same proportion as would be requisite to render the planets themselves equal in gravity. This, in all likelihood, gave foundation for the reports, that Pythagoras drew his doctrine of harmony from the spheres.”[353]
Galileo duly honours Plato, by acknowledging that he is indebted to him for his first idea of the method of determining, how the different degrees of velocity ought to produce that uniformity of motion discernible in the revolutions of the heavenly bodies. His account is, that “Plato being of opinion that no movable thing could pass from a state of rest to any determinate degree of velocity, so as perpetually and equably to remain in it, without first passing through all the inferior degrees of celerity or retardation; he thence concludes, that God, after having created the celestial bodies, determining to assign to each a particular degree of celerity, in which they should always move, impressed upon them, when he drew them from a state of rest, such a force as made them run through their assigned spaces, in that natural and direct way wherein we see the bodies around us pass from rest into motion, by a continual and successive acceleration. And he adds, that having brought them to that degree of motion, wherein he intended they should perpetually remain, he afterwards changed the perpendicular into a circulary direction, that being the only course that can preserve itself uniform, and make a body without ceasing keep at an equal distance from its proper centre.”
This acknowledgment of Galileo is remarkable. It is a homage to antiquity from an inventive genius, who least of any, owes his eminence to the aid of the ancients. It is the disposition of noble minds to arrogate to themselves as little as possible any merit, but what they have the utmost claim to; and thus Galileo and Newton, the greatest of modern philosophers, set an example, which will never be imitated but by men of distinguished greatness.