_The_ COPERNICAN SYSTEM _demonstrated to be true_.
[Sidenote: Of matter and motion.]
99. Matter is of itself inactive, and indifferent to motion or rest. A
body at rest can never put itself in motion; a body in motion can never
stop nor move slower of itself. Hence, when we see a body in motion we
conclude some other substance must have given it that motion; when we
see a body fall from motion to rest we conclude some other body or cause
stopt it.
100. All motion is naturally rectilineal. A bullet thrown by the hand,
or discharged from a cannon would continue to move in the same direction
it received at first, if no other power diverted its course. Therefore,
when we see a body moving in a curve of whatever kind, we conclude it
must be acted upon by two powers at least: one to put it in motion, and
another drawing it off from the rectilineal course which it would
otherwise have continued to move in.
[Sidenote: Gravity demonstrable.]
101. The power by which bodies fall towards the Earth is called
_Gravity_ or _Attraction_. By this power in the Earth it is, that all
bodies, on whatever side, fall in lines perpendicular to it’s surface.
On opposite parts of the Earth bodies fall in opposite directions, all
towards the centre where the force of gravity is as it were accumulated.
By this power constantly acting on bodies near the Earth they are kept
from leaving it altogether; and those on its surface are kept thereto on
all sides, so that they cannot fall from it. Bodies thrown with any
obliquity are drawn by this power from a straight line into a curve,
until they fall to the Ground: the greater the force by which they are
thrown, the greater is the distance they are carried before they fall.
If we suppose a body carried several miles above the Earth, and there
projected in an horizontal direction, with so great a velocity that it
would move more than a semidiameter of the Earth, in the time it would
take to fall to the Earth by gravity; in that case, if there were no
resisting medium in the way, the body would not fall to the Earth at
all; but continue to circulate round the Earth, keeping always the same
path, and returning to the point from whence it was projected, with the
same velocity as at first.
[Sidenote: Projectile force demonstrable.]
102. We find the Moon moves round the Earth in an Orbit nearly circular.
The Moon therefore must be acted on by two powers or forces; one which
would cause her to move in a right line, another bending her motion from
that line into a curve. This attractive power must be seated in the
Earth; for there is no other body within the Moon’s Orbit to draw her.
The attractive power of the Earth therefore extends to the Moon; and, in
combination with her projectile force, causes her to move round the
Earth in the same manner as the circulating body above supposed.
[Sidenote: The Sun and Planets attract each other.]
103. The Moons of Jupiter and Saturn are observed to move round their
primary Planets: therefore there is such a power as gravity in these
Planets. All the Planets move round the Sun, and respect it for their
centre of motion: therefore the Sun must be endowed with attracting
force, as well as the Earth and Planets. The like may be proved of the
Comets. So that all the bodies or matter in the Solar System are
possessed of this power; and perhaps so is all matter whatsoever.
104. As the Sun attracts the Planets with their Satellites, and the
Earth the Moon, so the Planets and Satellites re-attract the Sun, and
the Moon the Earth: action and re-action being always equal. This is
also confirmed by observation; for the Moon raises tides in the ocean,
the Satellites and Planets disturb one another’s motions.
105. Every particle of matter being possessed of an attracting power,
the effect of the whole must be in proportion to the number of
attracting particles: that is, to the quantity of matter in the body.
This is demonstrated from experiments on pendulums: for, if they are of
equal lengths, whatever their weights be, they always vibrate in equal
times. Now, if one be double the weight of another, the force of gravity
or attraction must be double to make it oscillate with the same
celerity: if one is thrice the weight or quantity of matter of another,
it requires thrice the force of gravity to make it move with the same
celerity. Hence it is certain, that the power of gravity is always
proportional to the quantity of matter in bodies, whatever their bulks
or figures are.
106. Gravity also, like all other virtues or emanations issuing from a
centre, decreases as the square of the distance increases: that is, a
body at twice the distance attracts another with only a fourth part of
the force; at four times the distance, with a sixteenth part of the
force. This too is confirmed from observation, by comparing the distance
which the Moon falls in a minute from a right line touching her Orbit,
with the space which bodies near the Earth fall in the same time: and
also by comparing the forces which retain Jupiter’s Moons in their
Orbits. This will be more fully explained in the seventh Chapter.
[Sidenote: Gravitation and projection exemplified.]
107. The mutual attraction of bodies may be exemplified by a boat and a
ship on the Water, tied by a rope. Let a man either in ship or boat pull
the rope (it is the same in effect at which end he pulls, for the rope
will be equally stretched throughout,) the ship and boat will be drawn
towards one another; but with this difference, that the boat will move
as much faster than the ship as the ship is heavier than the boat.
Suppose the boat as heavy as the ship, and they will draw one another
equally (setting aside the greater resistance of the Water on the bigger
body) and meet in the middle of the first distance between them. If the
ship is a thousand or ten thousand times heavier than the boat, the boat
will be drawn a thousand or ten thousand times faster than the ship; and
meet proportionably nearer the place from which the ship set out. Now,
whilst one man pulls the rope, endeavouring to bring the ship and boat
together, let another man, in the boat, endeavour to row her off
sidewise, or at right Angles to the rope; and the former, instead of
being able to draw the boat to the ship, will find it enough for him to
keep the boat from going further off; whilst the latter, endeavouring to
row off the boat in a straight line, will, by means of the other’s
pulling it towards the ship, row the boat round the ship at the rope’s
length from her. Here, the power employed to draw the ship and boat to
one another represents the mutual attraction of the Sun and Planets, by
which the Planets would fall freely towards the Sun with a quick motion;
and would also in falling attract the Sun towards them. And the power
employed to row off the boat represents the projectile force impressed
on the Planets at right Angles, or nearly so, to the Sun’s attraction;
by which means the Planets move round the Sun, and are kept from falling
to it. On the other hand, if it be attempted to make a heavy ship go
round a light boat, they will meet sooner than the ship can get round;
or the ship will drag the boat after it.
108. Let the above principles be applied to the Sun and Earth; and they
will evince, beyond a possibility of doubt, that the Sun, not the Earth,
is the center of the System; and that the Earth moves round the Sun as
the other Planets do.
[Sidenote: The absurdity of supposing the Earth at rest.]
For, if the Sun moves about the Earth, the Earth’s attractive power must
draw the Sun towards it from the line of projection so, as to bend it’s
motion into a curve; and the Earth being at least 169 thousand times
lighter than the Sun, by being so much less as to it’s quantity of
matter, must move 169 thousand times faster toward the Sun than the Sun
does toward the Earth; and consequently would fall to the Sun in a short
time if it had not a very strong projectile motion to carry it off. The
Earth therefore, as well as every other Planet in the System, must have
a rectilineal impulse to prevent its falling into the Sun. To say, that
gravitation retains all the other Planets in their Orbits without
affecting the Earth, which is placed between the Orbits of Mars and
Venus, is as absurd as to suppose that six cannon bullets might be
projected upwards to different heights in the Air, and that five of them
should fall down to the ground; but the sixth, which is neither the
highest nor the lowest, should remain suspended in the Air without
falling; and the Earth move round about it.
109. There is no such thing in nature as a heavy body moving round a
light one as its centre of motion. A pebble fastened to a mill-stone by
a string, may by an easy impulse be made to circulate round the
mill-stone: but no impulse can make a mill-stone circulate round a loose
pebble, for the heaviest would undoubtedly carry the lightest along with
it wherever it goes.
110. The Sun is so immensely bigger and heavier than the Earth[18], that
if he was moved out of his place, not only the Earth, but all the other
Planets if they were united into one mass, would be carried along with
the Sun as the pebble would be with the mill-stone.
[Sidenote: The harmony of the celestial motions.
The absurdity of supposing the Stars and Planets to move round
the Earth.]
111. By considering the law of gravitation, which takes place throughout
the Solar System, in another light, it will be evident that the Earth
moves round the Sun in a year; and not the Sun round the Earth. It has
been shewn (§ 106) that the power of gravity decreases as the square of
the distance increases: and from this it follows with mathematical
certainty, that when two or more bodies move round another as their
centre of motion, the squares of their periodic times will be to one
another in the same proportion as the cubes of their distances from the
central body. This holds precisely with regard to the Planets round the
Sun, and the Satellites round the Planets; the relative distances of all
which, are well known. But, if we suppose the Sun to move round the
Earth, and compare its period with the Moon’s by the above rule, it will
be found that the Sun would take no less than 173,510 days to move round
the Earth, in which case our year would be 475 times as long as it now
is. To this we may add, that the aspects of increase and decrease of the
Planets, the times of their seeming to stand still, and to move direct
and retrograde, answer precisely to the Earth’s motion; but not at all
to the Sun’s without introducing the most absurd and monstrous
suppositions, which would destroy all harmony, order, and simplicity in
the System. Moreover, if the Earth is supposed to stand still, and the
Stars to revolve in free spaces about the Earth in 24 hours, it is
certain that the forces by which the Stars revolve in their Orbits are
not directed to the Earth, but to the centres of the several Orbits:
that is, of the several parallel Circles which the Stars on different
sides of the Equator describe every day: and the like inferences may be
drawn from the supposed diurnal motion of the Planets, since they are
never in the Equinoctial but twice, in their courses with regard to the
starry Heavens. But, that forces should be directed to no central body,
on which they physically depend, but to innumerable imaginary points in
the axe of the Earth produced to the Poles of the Heavens, is an
hypothesis too absurd to be allowed of by any rational creature. And it
is still more absurd to imagine that these forces should increase
exactly in proportion to the distances from this axe; for this is an
indication of an increase to infinity: whereas the force of attraction
is found to decrease in receding from the fountain from whence it flows.
But, the farther that any Star is from the quiescent Pole the greater
must be the Orbit which it describes; and yet it appears to go round in
the same time as the nearest Star to the Pole does. And if we take into
consideration the two-fold motion observed in the Stars, one diurnal
round the Axis of the Earth in 24 hours, and the other round the Axis of
the Ecliptic in 25920 years § 251, it would require an explication of
such a perplexed composition of forces, as could by no means be
reconciled with any physical Theory.
[Sidenote: Objections against the Earth’s motion answered.]
112. There is but one objection of any weight that can be made to the
Earth’s motion round the Sun; which is, that in opposite points of the
Earth’s Orbit, it’s Axis which always keeps a parallel direction would
point to different fixed Stars; which is not found to be fact. But this
objection is easily removed by considering the immense distance of the
Stars in respect of the diameter of the Earth’s Orbit; the latter being
no more than a point when compared to the former. If we lay a ruler on
the side of a table, and along the edge of the ruler view the top of a
spire at ten miles distance; then lay the ruler on the opposite side of
the table in a parallel situation to what it had before, and the spire
will still appear along the edge of the ruler; because our eyes, even
when assisted by the best instruments are incapable of distinguishing so
small a change.
113. Dr. BRADLEY, our present Astronomer Royal, has found by a long
series of the most accurate observations, that there is a small apparent
motion of the fixed Stars, occasioned by the aberration of their light,
and so exactly answering to an annual motion of the Earth, as evinces
the same, even to a mathematical demonstration. Those who are qualified
to read the Doctor’s modest Account of this great discovery may consult
the _Philosophical Transactions_, N^o 406. Or they may find it treated
of at large by Drs. SMITH[19], LONG[20], DESAGULIERS[21], RUTHERFURTH,
Mr. MACLAURIN[22], and M. DE LA CAILLE[23].
[Sidenote: Why the Sun appears to change his place.]
114. It is true that the Sun seems to change his place daily, so as to
make a tour round the starry Heavens in a year. But whether the Earth or
Sun moves, this appearance will be the same; for, when the Earth is in
any part of the Heavens, the Sun will appear in the opposite. And
therefore, this appearance can be no objection against the motion of the
Earth.
115. It is well known to every person who has sailed on smooth Water, or
been carried by a stream in a calm, that however fast the vessel goes he
does not feel its progressive motion. The motion of the Earth is
incomparably more smooth and uniform than that of a ship, or any machine
made and moved by human art: and therefore it is not to be imagined that
we can feel it’s motion.
[Sidenote: The Earth’s motion on it’s Axis demonstrated.]
116. We find that the Sun, and those Planets on which there are visible
spots, turn round their Axes: for the spots move regularly over their
Disks[24]. From hence we may reasonably conclude that the other Planets
on which we see no spots, and the Earth which is likewise a Planet, have
such rotations. But being incapable of leaving the Earth, and viewing it
at a distance; and it’s rotation being smooth and uniform, we can
neither see it move on it’s Axis as we do the Planets, nor feel
ourselves affected by it’s motion. Yet there is one effect of such a
motion which will enable us to judge with certainty whether the Earth
revolves on it’s Axis or not. All Globes which do not turn round their
Axes will be perfect spheres, on account of the equality of the weight
of bodies on their surfaces; especially of the fluid parts. But all
Globes which turn on their Axes will be oblate spheroids; that is, their
surfaces will be higher, or farther from the centre, in the equatoreal
than in the polar Regions: for, as the equatoreal parts move quickest,
they will recede farther from the Axis of motion, and enlarge the
equatoreal diameter. That our Earth is really of this figure is
demonstrable from the unequal vibrations of a pendulum, and the unequal
lengths of degrees in different latitudes. Since then, the Earth is
higher at the Equator than at the Poles, the sea, which naturally runs
downward, or towards the places which are nearest the centre, would run
towards the polar Regions, and leave the equatoreal parts dry, if the
centrifugal force of these parts did not raise and carry the waters
thither. The Earth’s equatoreal diameter is 35 miles longer than its
Axis.
[Sidenote: All bodies heavier at the Poles than they would be at the
Equator.]
117. Bodies near the Poles are heavier than those towards the Equator,
because they are nearer the Earth’s centre, where the whole force of the
Earth’s attraction is accumulated. They are also heavier because their
centrifugal force is less on account of their diurnal motion being
slower. For both these reasons, bodies carried from the Poles toward the
Equator, gradually lose of their weight. Experiments prove that a
pendulum, which vibrates seconds near the Poles vibrates slower near the
Equator, which shews that it is lighter or less attracted there. To make
it oscillate in the same time, ’tis found necessary to diminish it’s
length. By comparing the different lengths of pendulums swinging seconds
at the Equator and at _London_, it is found that a pendulum must be
2-169/1000 lines shorter at the Equator than at the Poles. A line is a
twelfth part of an inch.
[Sidenote: How they might lose all their weight.]
118. If the Earth turned round it’s Axis in 84 minutes 43 seconds, the
centrifugal force would be equal to the power of gravity at the Equator;
and all bodies there would entirely lose their weight. If the Earth
revolved quicker they would all fly off, and leave it.
[Sidenote: The Earth’s motion cannot be felt.]
119. One on the Earth can no more be sensible of it’s undisturbed motion
on it’s Axis, than one in the cabin of a ship on smooth Water can be
sensible of her motion when she turns gently and uniformly round. It is
therefore no argument against the Earth’s diurnal motion that we do not
feel it: nor is the apparent revolutions of the celestial bodies every
day a proof of the reality of these motions; for whether we or they
revolve, the appearance is the very same. A person looking through the
cabin windows of a ship as strongly fancies the objects on land to go
round when the ship turns, as if they were actually in motion.
[Sidenote: To the different Planets the Heavens appear to turn round on
different Axes.]
120. If we could translate ourselves from Planet to Planet, we should
still find that the Stars would appear of the same magnitudes, and at
the same distances from each other, as they do to us here; because the
width of the remotest Planet’s Orbit bears no sensible proportion to the
distance of the Stars. But then, the Heavens would seem to revolve about
very different Axes; and consequently, those quiescent Points which are
our Poles in the Heavens would seem to revolve about other points,
which, though apparently in motion to us on Earth would be at rest as
seen from any other Planet. Thus, the Axis of Venus, which lies almost
at right Angles to the Axis of the Earth, would have it’s motionless
Poles in two opposite points of the Heavens lying almost in our
Equinoctial, where the motion appears quickest because it is performed
in the greatest Circle. And the very Poles, which are at rest to us,
have the quickest motion of all as seen from Venus. To Mars and Jupiter
the Heavens appear to turn round with very different velocities on the
same Axis, whose Poles are about 23-1/2 degrees from ours. Were we on
Jupiter we should be at first amazed at the rapid motion of the Heavens;
the Sun and Stars going round in 9 hours 56 minutes. Could we go from
thence to Venus we should be as much surprised at the slowness of the
heavenly motions: the Sun going but once round in 584 hours, and the
Stars in 540. And could we go from Venus to the Moon we should see the
Heavens turn round with a yet slower motion; the Sun in 708 hours, the
Stars in 655. As it is impossible these various circumvolutions in such
different times and on such different Axes can be real, so it is
unreasonable to suppose the Heavens to revolve about our Earth more than
it does about any other Planet. When we reflect on the vast distance of
the fixed Stars, to which 162,000,000 of miles is but a point, we are
filled with amazement at the immensity of their distance. But if we try
to frame an idea of the extreme rapidity with which the Stars must move,
if they move round the Earth in 24 hours, the thought becomes so much
too big for our imagination, that we can no more conceive it than we do
infinity or eternity. If the Sun was to go round the Earth in a day, he
must travel upwards of 300,000 miles in a minute: but the Stars being at
least 10,000 times as far as the Sun from us, those about the Equator
must move 10,000 times as quick. And all this to serve no other purpose
than what can be as fully and much more simply obtained by the Earth’s
turning round eastward as on an Axis, every 24 hours, causing thereby an
apparent diurnal motion of the Sun westward, and bringing about the
alternate returns of day and night.
[Illustration: Pl. II.]
[Sidenote: Objections against the Earth’s diurnal motion answered.]
121. As to the common objections against the Earth’s motion on it’s
Axis, they are all easily answered and set aside. That it may turn
without being seen or felt to do so, has been already shewn, § 119. But
some are apt to imagine that if the Earth turns eastward (as it
certainly does if it turns at all) a ball fired perpendicularly upward
in the air must fall considerably westward of the place it was projected
from. This objection, which at first seems to have some weight, will be
found to have none at all when we consider that the gun and ball partake
of the Earth’s motion; and therefore the ball being carried forward with
the air as quick as the Earth and air turn, must fall down again on the
same place. A stone let fall from the top of a main-mast, if it meets
with no obstacle, falls on the deck as near the foot of the mast when
the ship sails as when it does not. And if an inverted bottle, full of
liquor, be hung up to the cieling of the cabin, and a small hole be made
in the cork to let the liquor drop through on the floor, the drops will
fall just as far forward on the floor when the ship sails as when it is
at rest. And gnats or flies can as easily dance among one another in a
moving cabin as in a fixed chamber. As for those scripture expressions
which seem to contradict the Earth’s motion, this general answer may be
made to them all, _viz._ ’tis plain from many instances that the
Scriptures were never intended to instruct us in Philosophy or
Astronomy; and therefore, on those subjects, expressions are not always
to be taken in the strictest sense; but for the most part as
accommodated to the common apprehensions of mankind. Men of sense in all
ages, when not treating of the sciences purposely, have followed this
method: and it would be in vain to follow any other in addressing
ourselves to the vulgar, or bulk of any community. _Moses_ calls the
Moon A GREAT LUMINARY (as it is in the Hebrew) as well as the Sun: but
the Moon is known to be an opaque body, and the smallest that
Astronomers have observed in the Heavens and shines upon us not by any
inherent light of it’s own, but by reflecting the light of the Sun. If
_Moses_ had known this, and told the _Israelites_ so, they would have
stared at him; and considered him rather as a madman than as a person
commissioned by the Almighty to be their leader.