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.