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CHAPTER XIII
OF UNIVERSAL
GRAVITY, AND CENTRIPETAL AND CENTRIFUGAL FORCE
Laws of the movement
of the planets, according to their distance from the common centre.
1. IT is here the moderns flatter themselves they have a remark
able advantage, imagining, that they were the first who discovered
the principle of universal gravitation, which they look upon as
a truth
known to the ancients. It is however easy to make it appear, that they
have done nothing but trod in the paths of those ancients. It
the moderns have demonstrated the laws of this universal gravitation,
and explained them with clearness and precision; but this is all
they have done in this respect, and have added nothing.
2. With the least attention to the knowledge of the ancients,
we that they were not unacquainted with universal gravitation;
and knew besides, that the circular motion, by which the planets
describe their course, is the result of the combination of two
moving forces, a rectilinear and a perpendicular, which, united
together, form a curve. They knew the reason why these two movements,
or contrary forces, retain the planets in their orbs; and have
explained themselves on this head, just as the moderns do, excepting
only the terms of centripetal and centrifugal; instead of which,
however, they used what was altogether equivalent. They also knew
the inequality of the course of the planets, ascribing it to’
the variety of their weights reciprocally considered, and of
their proportional distances.
3. I will not expatiate upon Empedocles’ system, in which
some have thought the foundation of Newton’s was to be found;
imagining, that under the name of love, he intended to initiate
a law, or power, which separated the parts of matter, in order
to join himself to them, and to which nothing was wanting but
the name of attraction. One sees also, that by the name discords
be intended to describe another force, which obliged the same
parts to recede from one another, and which Newton calls a repelling
force. But I leave Empedocles, and pass on’ to passages more
deserving notice. -
4. The Pythagoreans and Platonics, treating
of the creation of the world, perceived the necessity of admitting
the force of two powers, viz, projection and gravity, in order
to account for the revolution of the planets. Timoeus, speaking
of the soul of the world, which puts all nature in motion, says,
that God “hath endowed it with two powers, which, in combination,
act according to certain numeric proportions.” Plato, who hath followed Timoeus, in his natural philosophy,
clearly asserts, that God had impressed upon the planets”
a motion which was the most proper for them ; which could be nothing
else than the perpendicular motion, which has a tendency to the
Centre of the universe, that is, gravity ; and what in this case
coincides with it, a lateral impulse, rendering the whole circular.
And Diogenes Laer alluding in all likelihood to this passage
of Plato, says, that at the beginning, the bodies of the universe
were agitated tumultuously, and with a disorderly movement, but
that God afterward regulated their course, by laws natural and
proportional.
5. Anaxagoras cited by Diogenes Laertius, being asked
what it was that retained the heavenly bodies in their orbit,
notwithstanding their gravity ; answered, that” the rapidity
of their course preserved them in their stations ; and should
the celerity of their motions abate,” the equilibrium of
the world being broke, the whole machine would fall to ruin.
6. Plutarch, who knew almost all the shining truths of
astronomy, took notice also of the reciprocal energy, which causes
the planets to gravitate towards one another; and in explaining
what it was that made bodies tend towards the earth, he attributes
it “to a reciprocal attraction, whereby all terrestial bodies
have this tendency, and which collects into one the parts constituting
the sun and moon, and retains them in their spheres. He afterward
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
connexions one towards another. He illustrates this general connexion,
“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.” It is impossible, not to perceive
in all these passages, 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.
7. We have seen that the ancients attribute to the celestial
bodies, a tendency towards one common centre, and a reciprocal
attractive power. Lucretius well perceived this truth, though
he deduced’ from it a very strange consequence, that the
universe had no common centre, but that infinite space was filled
with an infinity of worlds like ours; for, says he, if the celestial
bodies were all of them carried towards one common centre, and
not restrained from that tendency by some exterior active force, they must needs soon diverge
towards one another, by virtue of their attractive power, and
like bodies tumbling from on high, reunite at the common centre
of gravity, and into one infinite, inactive mass.
8. It appears also, that the ancients knew, as well as the
moderns the cause of gravitation, which attracted all things,
did not reside solely in the centre of the earth. Their ideas
were more philosophic; “That this power was diffused through
every particle of the terrestrial globe, and compounded of the
various energy residing in each.”
9. It remains to inquire, whether the ancients 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. Certain it is, that the ancients were not
ignorant, that the planets, in their courses observed a constant
and invariable pro portion; and that they had different opinions
respecting this proportion. Some sought for it in the difference
of the quantity of matter contained in the masses, of which they
were composed; and others, in the differences 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 ;“ and the ablest Newtonians,
even such as ought to be the most interested to preserve to their
master the glory of having first discovered those truths, which
are ‘the principal ornaments of his system, have been the
first to point at the sources whence they seem to have been drawn.
It is true the penetration and sagacity of a Newton, a Gregory,
and a Maclauren, were requisite to discover, in the few fragments
now remaining, the inverse’ law respecting the squares of
the distances, a doctrine which Pythagoras had taught ; but it
is no less true, that it was contained in those writings. This
the Newtonians acknowledge, and are the first to avail themselves
of the authority of Pythagoras, to give weight to their system.
10. Plutarch, of all the philosophers who have spoken of Pythagoras,
is he, who, as be had a better opportunity of entering into the
ideas of that great man, bath explained them better than any one
besides. Pliny, Macrobrius, and Censorinus, have also spoken of
the harmony which Pythagoras observed to reign in the course of
the planets. Plutarch makes him say, it is probable that the bodies
of the planets, their distances, the intervals between their spheres,
and the celerity of their courses and revolutions, are not only
proportionable among themselves, but to the whole of the universe.
And Gregory bath been led to declare, it was evident to any attentive
mind, that this great man 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 Naclaurin, makes that ancient philosopher speak thus:
11. “ 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 to 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.” And this, in all likelihood,
gave foundation for the reports, that Pythagoras drew his doctrine
of harmony from the spheres.
12. Before I finish this chapter, 1 must not neglect to insert
a passage of Galileo’s, wherein he acknowledges, that he
owes to Plato his first idea of the method of determining, how
the different degrees of velocity, ought to produce that uniformity
of motion discernable in the revolutions of the heavenly bodies.
His account is, “Plato being of opinion, that no moveable
thing could pass from a state of rest’ to any determinate
degree of velocity, so as perpetually and equally to remain in
it, without first passing through all the inferior degrees of
celerity or retardation; concludes thence, 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 afterward
changed the perpendicular into a circular direction, that being
the only course that can preserve itself uniform, and make a
body without ceasing to keep at an equal distance from its proper
centre.” This acknowledgment of Galileo is the more remarkable,
as it comes from an inventive genius, who least of any owes his
eminence to the aid of the ancients ; for 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. Thus do Galileo
and Newton, the greatest of all modern philosophers, set an example
which will never be imitated but by those of their own class.
Chapter 14
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