Reverting to the dynamical principle, that the product of every particle
of matter in a fluid vortex, moving around a given axis, by its distance
from the centre and angular velocity, must ever be a constant quantity,
it follows that if the ethereal medium be uniformly dense, the periodic
times of the parts of the vortex will be directly as the distances from
the centre or axis; but the angular velocities being inversely as the
times, the absolute velocities will be equal at all distances from the
centre.
Newton, in examining the doctrine of the Cartesian vortices, supposes
the case of a globe in motion, gradually communicating that motion to
the surrounding fluid, and finds that the periodic times will be in the
duplicate ratio of the distances from the centre of the globe. He and
his successors have always assumed that it was impossible for the
principle of gravity to be true, and a Cartesian plenum also;
consequently, the question has not been fairly treated. It is true that
Descartes sought to explain the motions of the planets, by the
mechanical action of a fluid vortex _solely_; and to Newton belongs the
glorious honor of determining, the existence of a centripetal force,
competent to explain these motions mathematically, (but not physically,)
and rashly rejected an intelligible principle for a miraculous virtue.
If our theory be true, the visible creation depends on the existence of
both working together in harmony, and that a physical medium is
absolutely necessary to the existence of gravitation.
If space be filled with a fluid medium, analogy would teach us that it
is in motion, and that there must be inequalities in the direction and
velocity of that motion, and consequently there must be vortices. And if
we ascend into the history of the past, we shall find ample testimony
that the planetary matter now composing the members of the solar system,
was once one vast nebulous cloud of atoms, partaking of the vorticose
motion of the fluid involving them. Whether the gradual accumulation of
these atoms round a central nucleus from the surrounding space, and thus
having their tangential motion of translation converted into vorticose
motion, first produced the vortex in the ether; or whether the vortex
had previously existed, in consequence of conflicting currents in the
ether, and the scattered atoms of space were drawn into the vortex by
the polar current, thus forming a nucleus at the centre, as a necessary
result of the eddy which would obtain there, is of little consequence.
The ultimate result would be the same. A nucleus, once formed, would
give rise to a central force, tending more and more to counteract the
centripulsive power of the radial stream; and in consequence of this
continually increasing central power, the heaviest atoms would be best
enabled to withstand the radial stream, while the lighter atoms might be
carried away to the outer boundaries of the vortex, to congregate at
leisure, and, after the lapse of a thousand years, to again face the
radial stream in a more condensed mass, and to force a passage to the
very centre of the vortex, in an almost parabolic curve. That space is
filled with isolated atoms or planetary dust, is rendered very probable
by a fact discovered by Struve, that there is a gradual extinction in
the light of the stars, amounting to a loss of 1/107 of the whole, in
the distance which separates Sirius from the sun. According to Struve,
this can be accounted for, "by admitting as very probable that space is
filled with an _ether_, capable of intercepting in some degree the
light." Is it not as probable that this extinction is due to planetary
dust, scattered through the pure ether, whose vibrations convey the
light,--the material atoms of future worlds,--the debris of dilapidated
comets? Does not the Scripture teach the same thing, in asserting that
the heavens are not clean?
The theory of vortices has had many staunch supporters amongst those
deeply versed in the science of the schools. The Bernoullis proposed
several ingenious hypothesis, to free the Cartesian system from the
objections urged against it, viz.: that the velocities of the planets,
in accordance with the three great laws of Kepler, cannot be made to
correspond with the motion of a fluid vortex; but they, and all others,
gave the vantage ground to the defenders of the Newtonian philosophy, by
seeking to refer the principle of gravitation to conditions dependent on
the density and vorticose motion of the ether. When we admit that the
ether is imponderable and yet material, and planetary matter subject to
the law of gravitation, the objections urged against the theory of
vortices become comparatively trivial, and we shall not stop to refute
them, but proceed with the investigation, and consider that the ether is
the original source of the planetary motions and arrangements.
On the supposition that the ether is uniformly dense, we have shown that
the periodic times will be directly as the distances from the axis. If
the density be inversely as the distances, the periodic times will be
equal. If the density be inversely as the square roots of the distances,
the times will be directly in the same ratio. The celebrated J.
Bernoulli assumed this last ratio; but seeking the source of motion in
the rotating central globe, he was led into a hypothesis at variance
with analogy. The ellipticity of the orbit, according to this view,
was caused by the planet oscillating about a mean position,--sinking
first into the dense ether,--then, on account of superior buoyancy,
rising into too light a medium. Even if no other objection could be
urged to this view, the difficulty of explaining why the ether should be
denser near the sun, would still remain. We might make other
suppositions; for whatever ratio of the distances we assume for the
density of the medium, the periodic times will be compounded of those
distances and the assumed ratio. Seeing, therefore, that the periodic
times of the planets observe the direct ses-plicate ratio of the
distances, and that it is consonant to all analogy to suppose the
contiguous parts of the vortex to have the same ratio, we find that the
density of the ethereal medium in the solar vortex, is directly as the
square roots of the distances from the axis.
Against this view, it may be urged that if the inertia of the medium is
so small, as is supposed, and its elasticity so great, there can be no
condensation by centrifugal force of rotation. It is true that when we
say the ether is condensed by this force, we speak incorrectly. If in an
infinite space of imponderable fluid a vortex is generated, the central
parts are rarefied, and the exterior parts are unchanged. But in all
finite vortices there must be a limit, outside of which the motion is
null, or perhaps contrary. In this case there may be a cylindrical ring,
where the medium will be somewhat denser than outside. Just as in water,
every little vortex is surrounded by a circular wave, visible by
reflection. As the density of the planet Neptune appears, from present
indications, to be a little denser than Uranus, and Uranus is denser
than Saturn, we may conceive that there is such a wave in the solar
vortex, near which rides this last magnificent planet, whose ring would
thus be an appropriate emblem of the peculiar position occupied by
Saturn. This may be the case, although the probability is, that the
density of Saturn is much greater than it appears, as we shall presently
explain.
In order to show that there is nothing extravagant in the supposition of
the density of the ether being directly as the square roots of the
distances from the axis, we will take a fluid whose law of density is
known, and calculate the effect of the centrifugal force, considered as
a compressing power. Let us assume our atmosphere to be 47 miles high,
and the compressing power of the earth's gravity to be 289 times greater
than the centrifugal force of the equator, and the periodic time of
rotation necessary to give a centrifugal force at the equator equal to
the gravitating force to be 83 minutes. Now, considering the gravitating
force to be uniform, from the surface of the earth upwards, and knowing
from observation that at 18,000 feet above the surface, the density of
the air is only 1/2, it follows, (in accordance with the principle that
the density is as the compressing force,) that at 43 1/2 miles high, or
18,000 feet _below_ the surface of the atmosphere, the density is only
1/8000 part of the density at the surface of the earth. Let us
take this density as being near the limit of expansion, and conceive a
hollow tube, reaching from the sun to the orbit of Neptune, and that
this end of the tube is closed, and the end at the sun communicates with
an inexhaustible reservoir of such an attenuated gas as composes the
upper-layer of our atmosphere; and further, that the tube is infinitely
strong to resist pressure, without offering resistance to the passage of
the air within the tube; then we say, that, if the air within the tube
be continually acted on by a force equal to the mean centrifugal force
of the solar vortex, reckoning from the sun to the orbit of Neptune, the
density of the air at that extremity of the tube, would be greater than
the density of a fluid formed by the compression of the ocean into one
single drop. For the centrifugal force of the vortex at 2,300,000 miles
from the centre of the sun, is equal to gravity at the surface of the
earth, and taking the mean centrifugal force of the whole vortex as
one-millionth of this last force; so that at 3,500,000 miles from the
surface of the sun, the density of the air in the tube (supposing it
obstructed at that distance) would be double the density of the
attenuated air in the reservoir. And the air at the extremity of the
tube reaching to the orbit of Neptune, would be as much denser than the
air we breathe, as a number expressed by 273 with 239 ciphers annexed,
is greater than unity. This is on the supposition of infinite
compressibility. Now, in the solar vortex there is no physical barrier
to oppose the passage of the ether from the centre to the circumference,
and the density of the ethereal ocean must be considered uniform, except
in the interior of the stellar vortices, where it will be rarefied; and
the rarefaction will depend on the centrifugal force and the length of
the axis of the vortex. If this axis be very long, and the centrifugal
velocity very great, the polar influx will not be sufficient, and the
central parts will be rarefied. We see, therefore, no reason why the
density of the ether may not be three times greater at Saturn than at
the earth, or as the square roots of the distances directly.