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,
2.213 : 6.593 : : 12 : 5.22,
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.