No. VII.
In the present stage of the inquiry will be adduced examples of the
knowledge of the ancients, respecting the essential principles that
“uphold the world.”
GRAVITY, ATTRACTION--THE LAW OF SQUARING THE DISTANCES--CENTRIPETAL
AND CENTRIFUGAL FORCE.
The moderns, who imagine that they were the first to discover universal
gravitation, have only trod in the paths of the ancients. It is true,
that they have demonstrated the laws of gravitation, but this is all.
Besides universal gravitation, the ancients knew that the circular
motion described by the planets in their courses, is the result of two
moving forces combined--a rectilinear and a perpendicular; which, united
together, form a curve. They knew also why these two contrary forces
retain the planets in their orbs; and explained themselves, 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; or, which is the same thing, in more modern
terms, they knew the “law of the inverse ratio of the square of the
distance from the centre of the revolution.”
Some have thought, that in Empedocles’s system the foundation of
Newton’s was to be found; imagining, that under the name of “love,” he
intended to intimate a law, or power, which separated the parts of
matter, in order to join itself to them, and to which nothing was
wanting but the name of _attraction_; and that by the term “discord,” he
intended to describe another force, which obliged the same parts to
recede from one another, and which Newton calls a repelling _force_.
The Pythagoreans and Platonics perceived the necessity of admitting the
force of two powers, viz. projection and gravity, in order to account
for the revolution of the planets. Timæus, speaking of the soul of the
world, which animates all nature, says, that “God hath endowed it with
two powers, which, in combination, act according to certain numeric
proportions.”
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.
[353] Gregorii Astronomiæ Elementa; and Maclaurin’s Systems of the
Philosophers, in a discourse prefixed to his philosophy of Newton, p.
32. Wallis, vol. iii. p. 138 and 150.
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