Outlines of a Mechanical Theory of Storms
T >> T. Bassnett >> Outlines of a Mechanical Theory of StormsIf 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.
BODES' LAW OF PLANETARY DISTANCES.
Thus, in the solar vortex, there will be two polar currents meeting at
the sun, and thence being deflected at right angles, in planes parallel
to the central plane of the vortex, and strongest in that central plane.
The velocity of expansion must, therefore, diminish from the divergence
of the radii, as the distances increase; but in advancing along these
planes, the ether of the vortex is continually getting more dense,
which operate by absorption or condensation on the radial stream; so
that the velocity is still more diminished, and this in the ratio of the
square roots of the distances directly. By combining these two ratios,
we find that the velocity of the radial stream will be in the
ses-plicate ratio of the distances inversely. But the force of this
stream is not as the velocity, but as the square of the velocity. The
_force_ of the radial stream is consequently as the cubes of the
distances inversely, from the axis of the vortex, reckoned in the same
plane. If the ether, however, loses in velocity by the increasing
density of the medium, it becomes also more dense; therefore the true
force of the radial stream will be as its density and the square of its
velocity, or directly as the square roots of the distances, and
inversely as the cubes of the distances, or as the 2.5 power of the
distances inversely.
If we consider the central plane of the vortex as coincident with the
plane of the ecliptic, and the planetary orbits, also, in the same
plane; and had the force of the radial stream been inversely as the
square of the distances, there could be no disturbance produced by the
action of the radial stream. It would only counteract the gravitation of
the central body by a certain amount, and would be exactly proportioned
at all distances. As it is, there is an outstanding force as a
disturbing force, which is in the inverse ratio of the square roots of
the distances from the sun; and to this is, no doubt, owing, in part,
the fact, that the planetary distances are arranged in the inverse order
of their densities.
Suppose two planets to have the same diameter to be placed in the same
orbit, they will only be in equilibrium when their densities are equal.
If their densities are unequal, the lighter planet will continually
enlarge its orbit, until the force of the radial stream becomes
proportional to the planets' resisting energy. This, however, is on the
hypothesis that the planets are not permeable by the radial stream,
which, perhaps, is more consistent with analogy than with the reality.
And it is more probable that the mean atomic weight of a planet's
elements tends more to fix the position of equilibrium for each. Under
the law of gravity, a planet may revolve at any distance from the sun,
but if we superadd a centripulsive force, whose law is not that of
gravity, but yet in some inverse ratio of the distances, and this force
acts only superficially, it would be possible to make up in volume what
is wanted in density, and a lighter planet might thus be found occupying
the position of a dense planet. So the planet Jupiter, respecting only
his resisting surface, is better able to withstand the force of the
radial stream at the earth than the earth itself. To understand this, it
is necessary to bear in mind, that, as far as planetary matter is
concerned, the earth would revolve in Jupiter's orbit in the same
periodic time as Jupiter, under the law of gravity: but that, in
reality, the whole of the gravitating force is not effective, and that
the equilibrium of a planet is due to a nice balance of interfering
forces arising from the planet's physical peculiarities. As in a
refracting body, the density of the ether may be considered inversely as
the refraction, and this as the atomic weight of the refracting
material, so, also, in a planet, the density of the ether will be
inversely in the same ratio of the density of the matter approximately.
Hence, the density of the ether within the planet Jupiter is greater
than that within the earth; and, on this ethereal matter, the sun has no
power to restrain it in its orbit, so that the centrifugal momentum of
Jupiter would be relatively greater than the centrifugal momentum of the
earth, were it also in Jupiter's orbit with the same periodic time.
Hence, to make an equilibrium, the earth should revolve in a medium of
less density, that there may be the same proportion between the external
ether, and the ether within the earth, as there is between the ether
around Jupiter and the ether within; so that the centrifugal tendency of
the dense ether at Jupiter shall counteract the greater momentum of the
dense ether within Jupiter; or, that the lack of centrifugal momentum in
the earth should be rendered equal to the centrifugal momentum of
Jupiter, by the deficiency of the centrifugal momentum of the ether at
the distance of the earth.
If then, the diameters of all the planets were the same (supposing the
ether to act only superficially), the densities would be as the
distances inversely;[37] for the force due to the radial stream is as
the square roots of the distance inversely, and the force due to the
momentum, if the density of the ether within a planet be inversely as
the square root of a planet's distance, will also be inversely as the
square roots of the distances approximately. We offer these views,
however, only as suggestions to others more competent to grapple with
the question, as promising a satisfactory solution of Bode's empirical
formula.
If there be a wave of denser ether cylindrically disposed around the
vortex at the distance of Saturn, or between Saturn and Uranus, we see
why the law of densities and distances is not continuous. For, if the
law of density changes, it must be owing to such a ring or wave. Inside
this wave, the two forces will be inverse; but outside, one will be
inverse, and the other direct: hence, there should also be a change in
the law of distances. As this change does not take place until we pass
Uranus, it may be suspected that the great disparity in the density of
Saturn may be more apparent than real. The density of a planet is the
relation between its mass and volume or extension, no matter what the
form of the body may be. From certain observations of Sir Wm.
Herschel--the Titan of practical astronomers--the figure of Saturn was
suspected to be that of a square figure, with the corners rounded off,
so as to leave both the equatorial and polar zones flatter than
pertained to a true spheroidal figure. The existence of an unbroken ring
around Saturn, certainly attaches a peculiarity to this planet which
prepares us to meet other departures from the usual order. And when we
reflect on the small density, and rapid rotation, the formation of this
ring, and the figure suspected by Sir Wm. Herschel, it is neither
impossible nor improbable, that there may be a cylindrical vacant space
surrounding the axis of Saturn, or at least, that his solid parts may be
cylindrical, and his globular form be due to elastic gases and vapors,
which effectually conceal his polar openings. And also, by dilating and
contracting at the poles, in consequence of inclination to the radial
stream, (just as the earth's atmosphere is bulged out sufficiently to
affect the barometer at certain hours every day,) give that peculiarity
of form in certain positions of the planet in its orbit. Justice to Sir
Wm. Herschel requires that _his_ observations shall not be attributed to
optical illusions. This view, however, which may be true in the case of
Saturn, would be absurd when applied to the earth, as has been done
within the present century. From these considerations, it is at least
possible, that the density of Saturn may be very little less, or even
greater than the density of Uranus, and be in harmony with the law of
distances.
It is now apparently satisfactorily determined, that Neptune is denser
than Uranus, and the law being changed, we must look for transneptunean
planets at distances corresponding with the new law of arrangement. But
there are other modifying causes which have an influence in fixing the
precise position of equilibrium of a planet. Each planet of the system
possessing rotation, is surrounded by an ethereal vortex, and each
vortex has its own radial stream, the force of which in opposing the
radial stream of the sun, depends on the diameter and density of the
planet, on the velocity of rotation, on the inclination of its axis, and
on the density of the ether at each particular vortex; but the numerical
verification of the position of each planet with the forces we have
mentioned, cannot be made in the present state of the question. There is
one fact worthy of note, as bearing on the theory of vortices in
connection with the rotation of the planets, viz.: that observation has
determined that the axial rotation and sidereal revolution of the
secondaries, are identical; thus showing that they are without vortices,
and are motionless relative to the ether of the vortex to which they
belong. We may also advert to the theory of Doctor Olbers, that the
asteroidal group, are the fragments of a larger planet which once
filled the vacancy between Mars and Jupiter. Although this idea is not
generally received, it is gathering strength every year by the discovery
of other _fragments_, whose number now amounts to twenty-six. If the
idea be just, our theory offers an explanation of the great differences
observable in the mean distances of these bodies, and which would
otherwise form a strong objection against the hypothesis. For if these
little planets be fragments, there will be differences of density
according as they belonged to the central or superficial parts of the
quondam planet, and their mean distances must consequently vary also.
There are some other peculiarities connecting the distances and
densities, to which we shall devote a few words. In the primordial state
of the system, when the nebulous masses agglomerated into spheres, the
diameter of these nebulous spheres would be determined by the relation
existing between the rotation of the mass, and the gravitating force at
the centre; for as long as the centrifugal force at the equator exceeded
the gravitating force, there would be a continual throwing off of matter
from the equator, as fast as it was brought from the poles, until a
balance was produced. It is also extremely probable, (especially if the
elementary components of water are as abundant in other planets as we
have reason to suppose them to be on the earth,) that the condensation
of the gaseous planets into liquids and solids, was effected in a _brief
period of time_,[38] leaving the lighter and more elastic substances as
a nebulous atmosphere around globes of semi-fluid matter, whose
diameters have never been much increased by the subsequent condensation
of their gaseous envelopes. The extent of these atmospheres being (in
the way pointed out) determined by the rotation, their subsequent
condensation has not therefore changed the original rotation of the
central globe by any appreciable quantity. The present rotation of the
planets, is therefore competent to determine the former diameters of the
nebulous planets, _i.e._, the limit where the present central force
would be balanced by the centrifugal force of rotation. If we make the
calculation for the planets, and take for the unit of each planet its
present diameter, we shall find that they have condensed from their
original nebulous state, by a quantity dependent on the distance, from
the centre of the system; and therefore on the original temperature of
the nebulous mass at that particular distance. Let us make the
calculation for Jupiter and the earth, and call the original nebulous
planets the nucleus of the vortex. We find the Equatorial diameter of
Jupiter's nucleus in equatorial diameters of Jupiter = 2.21, and the
equatorial diameter of the earth's nucleus, in equatorial diameters of
the earth = 6.59. Now, if we take the original temperature of the
nebulous planets to be inversely, as the squares of the distances from
the sun, and their volumes directly as the cubes of the diameters in the
unit of each, we find that these cubes are to each other, in the inverse
ratio of the squares of the planet's distances; for,
2.21^3 : 6.59^3 :: 1^2 : 5.2^2,
showing that both planets have condensed equally, allowing for the
difference of temperature at the beginning. And we shall find, beginning
at the sun, that the diameters of the nebulous planets, _ceteris
paribus_, diminish outwards, giving for the nebulous sun a diameter of
16,000,000 miles,[39] thus indicating his original great temperature.
That the original nebulous planets did rotate in the same time as they
do at present, is proved by Saturn's ring; for if we make the
calculation, about twice the diameter of Saturn. Now, the diameter of
the planet is about 80,000 miles, which will also be the semi-diameter
of the nebulous planet; and the middle of the outer ring has also a
semi-diameter of 80,000 miles; therefore, the ring is the equatorial
portion of the original nebulous planet, and ought, on this theory, to
rotate in the same time as Saturn. According to Sir John Herschel,
Saturn rotates in 10 hours, 29 minutes, and 17 seconds, and the ring
rotates in 10 hours, 29 minutes, and 17 seconds: yet this is not the
periodic time of a satellite, at the distance of the middle of the ring;
neither ought the rings to rotate in the same time; yet as far as
observation can be trusted, both the inner and outer ring do actually
rotate in the same time. The truth is, the ring rotates too fast, if we
derive its centrifugal force from the analogy of its satellites; but it
is, no doubt, in equilibrium; and the effective mass of Saturn on the
satellites is less than the true mass, in consequence of his radial
stream being immensely increased by the additional force impressed on
the ether, by the centrifugal velocity of the ring. If this be so, the
mass of Saturn, derived from one of the inner satellites, will be less
than the same mass derived from the great satellite, whose orbit is
considerably inclined. The analogy we have mentioned, between the
diameters of the nebulous planets and their distances, does not hold
good in the case of Saturn, for the reason already assigned, viz.: that
the nebulous planet was probably not a globe, but a cylindrical ring,
vacant around the axis, as there is reason to suppose is the case at
present.
And now we have to ask the question, Did the ether involved in the
nebulous planets rotate in the same time? This does not necessarily
follow. The ether will undoubtedly tend to move with increasing velocity
to the very centre of motion, obeying the great dynamical principle when
unresisted. If resisted, the law will perhaps be modified; but in this
case, its motion of translation will be converted into atomic motion or
heat, according to the motion lost by the resistance of atomic matter.
This question has a bearing on many geological phenomena. As regards the
general effect, however, the present velocity of the ether circulating
round the planets, may be considered much greater than the velocities of
the planets themselves.
PERTURBATIONS DUE TO THE ETHER.
In these investigations it is necessary to bear in mind that the whole
resisting power of the ether, in disturbing the planetary movements, is
but small, in comparison with gravitation. We will, however, show that,
in the case of the planets, there is a compensation continually made by
this resistance, which leaves but a very small outstanding balance as a
disturbing power. If we suppose all the planets to move in the central
plane of the vortex in circular orbits, and the force of the radial
stream, (or that portion which is not in accordance with the law of
gravitation,) to be inversely as the square roots of the distances from
the sun, it is evident, from what has been advanced, that an equilibrium
could still obtain, by variations in the densities, distances and
diameter of the planets. Supposing, again, that the planets still move
in the same plane, but in elliptical orbits, and that they are in
equilibrium at their mean distances, under the influence or action of
the tangential current, the radial stream, and the density of the ether;
we see that the force of the radial stream is too great at the
perihelion, and too small at the aphelion. At the perihelion the planet
is urged from the sun and at the aphelion towards the sun. The density
and consequent momentum is also relatively too great at the perihelion,
which also urges the planet from the sun, and at the aphelion,
relatively too small, which urges the planet towards sun; and the law is
the same in both cases, being null at the mean distance of the planet,
at a maximum at the apsides; it is, consequently, as the cosine of the
planet's eccentric anomaly at other distances, and is positive or
negative, according as the planet's distance is above or below the mean.