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The Postscript
By the bye, lest you infer that my views, in detail, are the same with those advanced in the Nebular Hypothesis, I venture to offer a few addenda, the substance of which was penned, though never printed, several years ago, under the head of — A Prediction.
As soon as the next century it will be entered in the books, that the [page 109:] Sun was originally condensed at once (not gradually, according to the supposition of Laplace) into his smallest size; that, thus condensed, he[[2.1]] rotated on an axis; that this axis of rotation was not the centre of his figure, so that he not only rotated, but revolved in an elliptical orbit (the rotation and revolution are one; but I separate them for convenience of illustration); that, thus formed and thus revolving, he was on fire (in the same way that a volcano and an ignited meteoric stone are on fire) and sent into space his substance in the form of vapor, this vapor reaching farthest on the side of the larger hemisphere, partly on account of the largeness, but principally because the force of the fire was greater here; that, in due time, this vapor, not necessarily carried then to the place now occupied by Neptune, condensed into Neptune; that the planet took, as a matter of necessity, the same figure that the Sun had, which figure made his rotation a revolution in an elliptical orbit; that, in consequence of such revolution — in consequence of his being carried backward at each of the daily revolutions — the velocity of his annual revolution is not so great as it would be, if it depended solely upon the Sun's velocity of rotation (Kepler's Third Law);[[2.2]] that his figure, by influencing his rotation — the heavier half, as it turns downward toward the Sun, gains an impetus sufficient to carry it by the direct line of attraction, and thus to throw outward the centre of gravity — gave him power to save himself from falling to the Sun (and, perhaps, to work himself gradually outward to the position he now holds); that he received, through a series of ages, the Sun's heat, which penetrated to his centre, causing volcanic eruptions eventually, and thus throwing off vapor; and which evaporated substances upon his surface, till finally his moons and his gaseous ring[[2.3]] (if it is true that he has a ring) were produced; that these moons took elliptical forms, rotated and revolved “both under one”, were kept in their monthly orbits by the centrifugal force acquired in their daily orbits, and required a longer time to make their monthly revolutions than they would have required if they had had no daily revolutions.
I have said enough, without referring to the other planets, to give you an inkling of my hypothesis, which is all I intended to do. I did not design to offer any evidence of its reasonableness; since I have not, in fact, any collected, excepting as it is flitting, in the shape of a shadow, to and fro within my brain. [page 110:]
You perceived that I hold to the idea that our Moon must rotate upon her[[4.1]] axis oftener than she revolves round her primary, the same being the case with the satellites accompanying Jupiter, Saturn and Uranus.
Since the penning, a closer analysis of the matter contained has led me to modify somewhat my opinion as to the origin of the satellites — that is, I think now that these came, not from vapor sent off in volcanic burnings and by simple diffusion under the solar rays, but from rings of it which were left in the inter-planetary spaces, after the precipitation of the primaries. There is no insuperable obstacle in the way of the conception that aerolites and “shooting-stars” have their source in matter which has gone off from the Earth's surface and from out her bowels; but it is hardly supposable that a sufficient quantity could be produced thus to make a body so large as, by centrifugal force resulting from rotation, to withstand the absorptive power of its parent's rotation. The event implied may take place not until the planets have become flaming suns — from an accumulation of their own Sun's caloric,[[5.1]] reaching from centre to circumference, which shall, in the lonesome latter days,[[5.2]] melt all the elements and dissipate the solid foundations out as a scroll![[5.3]] (Please substitute the idea for that in “Conversation of Eiros and Charmion”).
The Sun forms, in rotating, a vortex in the ether surrounding him. The planets have their orbits lying within this vortex at different distances from its centre; so that their liabilities to be absorbed by it are, other things being equal, inversely just according to those distances, since length, not surface, is the measure of the absorptive power along the lines marking the orbits. Each planet overcomes its liability — i.e., keeps in its orbit — through a counter-vortex generated by its own rotation. The force of such counter-vortex is measured by multiplying together the producing planet's density and rotary velocity; which velocity depends, not upon the length of the planet's equatorial circumference, but upon the distance through which a given point of the equator is carried during a rotary period. Then if Venus and Mercury, for example, have now the orbits in which they commenced their revolutions — the orbit of the former 68 million miles, and that of the latter 37 million miles, from the centre of the Sun's vortex; if the diameter of Venus is 22/3 times the diameter, and [page 111:] her[[6.1]] density is the same with the density, of Mercury; and if the rotary velocity of the equator of Venus is l000 miles per hour, that of Mercury's equator is 1900 miles per hour, making the diameter of his[[6.2]] orbit of rotation 1450 miles — nearly 5 times that of himself. But I pass this point without farther examination. Whether there is or is not a difference in the relative conditions of the different planets, sufficient to cause such diversity in the extents of their peripheries of rotation as is indicated, still each planet is to be considered to have, other things being equal, a vortical resistence bearing the same proportion, inversely, to that of every other planet which its distance from the centre of the solar vortex bears to the distance of every other from the same; so that, if it be removed inward or outward from its position, it will increase or diminish that resistence, accordingly, by adding to or subtracting from its speed of rotation. As the rotary period must be the same in the two cases, the greater or less speed can be produced only by the lengthening or the shortening of the circumference described by the rotation.
Then Mercury, at the distance of Venus, would rotate in an orbit only 37/68 as broad as the one in which he does rotate; so his centrifugal force, in that position, would be only 37/68 as great as it is in his own position; so his capability, while there, of resisting the forward pressure of the Sun's vortex, which (pressure) prevents him from passing his full (circle) distance behind his centre of rotation and thus adds to his velocity in his annual orbit, would be but 37/68 what it is in his own place. But this forward pressure is only 37/68 as great at the distance of Venus as it is at that of Mercury. Then Mercury, with his own rotary speed in the annual orbit of Venus, would move in this orbit but 37/68 as fast as Venus moves in it; while Venus, with her rotary speed in Mercury's annual orbit, would move 68/37 as fast as she moves in her own — that is, 68/37 of 68/37as fast as Mercury would move in the same (annual orbit of Venus); it follows that the square root of 68/37 is the measure of the velocity of Mercury in his own annual orbit with his own rotary speed, compared with that of Venus in her annual orbit with her own rotary speed — in accordance with fact.
Such is my explanation of Kepler's first and third laws, which laws cannot be explained upon the principle of Newton's Theory.[[8.1]] [page 112:]
Two planets, gathered from portions of the Sun's vapor into one orbit, would rotate through the same ellipse with velocities proportional to their densities — that is, the denser planet would rotate the more swiftly; since, in condensing, it would have descended farther toward the Sun. For example, suppose the Earth and Jupiter to be the two planets in one orbit. The diameter[[9.1]] of the former is 8000 miles; period of rotation, 24 hours. The diameter of the latter is 88000 miles; period, 9 1/2 hours. The ring of vapor out of which the Earth was formed, was of a certain (perpendicular) width; that out of which Jupiter was formed, was of a certain greater width. In condensing, the springs of ether lying among the particles (these springs having been latent before the condensation began) were let out, the number of them along any given radial line being the number of spaces between all the couples of the particles constituting the line. If the two condensations had gone on in simple diametric proportions, Jupiter would have put forth only 11 times as many springs as the Earth did, and his velocity would have been but 11 times her velocity. But the fact that the falling-downward of her particles was completed when they had got so far that 24 hours were required for her equator to make its circuit; while that of his particles continued till but about 2/5 of her period was occupied by his equator in effecting its revolution; shows that his springs were increased above hers in still another ratio of 2 1/2, making, in the case, his velocity and his vortical force (21/2 x 11 =) 27 times her velocity and force.
Thus the planets’ densities are inversely as their rotary periods; and their rotary velocities and degrees of centrifugal force are, other things being equal, directly as their densities.
Two planets, revolving in one orbit, in rotating would approach the Sun, therefore enlarge their rotary ellipses, therefore accelerate their rotary velocities, therefore increase their powers of withstanding the influence of the solar vortex, inversely according to the products of their diameters into their densities — that is, the smaller and less dense planet, having to resist an amount of influence equal to that resisted by the other, would multiply the number of its resisting springs by the ratios of the other's diameter and density to the diameter and density of itself. Thus, the Earth, in Jupiter's orbit, [page 113:] would have to rotate in an ellipse 27 times as broad as herself, in order to make her power correspond with his.
Then the breadths, in a perpendicular direction, of the rotary ellipses of the planets in their several orbits are inversely as the products obtained by multiplying together the bodies’ densities, diameters and distances from the centre of the solar vortex. Thus, the product of Jupiter's density, diameter and distance being (21/2 times 11 times 51/4 =) 140 times the product of the Earth's density, diameter and distance, the breadth[[12.1]] of the latter's ellipse is about 1.120.000 miles; this upon the foundation, of course, that Jupiter's ellipse coincides, precisely, with his own equatorial diameter.
It will be observed that that process, in its last analysis, presents the point that rotary speed (hence that vortical force) is in exact inverse proportion to distance. Then, since the movement in orbit is a part of the rotary movement — being the rate at which the centre of the rotary ellipse is carried along the line marking the orbit — and since that centre and the planet's centre are not identical, the former being the point around which the latter revolves, causing, by the act, a relative loss of time in the inverse ratio of the square root of distance (as I have shown, back); the speed in orbit is inversely according to the square root of distance. Demonstration — The Earth's orbital period contains 3651/4 of her rotary periods. During these periods, her equator passes through a distance of (1.120.000 x 22/7 x 3651/4 =) about 1286 million miles; and the centre of her rotary ellipse through a distance of (95.000.000 x 2 X 22/7 =) about 597 million miles. Jupiter's orbital period has (365 1/4 x 21/2 x 12 years =) about 10.957 of his rotary periods, during which his equator courses (88.000 x 22/7 x 10.957 =) about 3.050 million miles; and the centre of his rotary ellipse, about the same number of miles (490.000.000 x 2 X 22/7). Dividing this distance by 12 years (3.050.000.000/i 2 / =) gives the length of Jupiter's double journey during one of the Earth's orbital periods = 254 million miles — Relative velocities in ellipse (1286/254 =), 5 to 1, which is inversely as the distances; and relative velocities in orbit (597/254 =), 2 to 1, inversely as the square roots of the distances.
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The Sun's period of rotation being 25 days, his density is only 1/25 of that of a planet having a period of 24 hours — that of Mercury, for [page 114:] instance. Hence Mercury has, for the purpose now in view, virtually, a diameter equal to a little more than 712 of that of the Sun (888.000 / 25 = 35.520, 35.520 / 3000 = 11.84; 888.000 / 11.84 =) — say, 75 thousand miles.
Here, we have a conception of the planet in the mid-stage, so to speak, of its condensation — after the breaking-up of the vaporous ring which was to produce it, and just at the taking-on of the globular form. But before the arrival at this stage, the figure was that of a truck,[[15.1]] the vortical diameter of which is identifiable in the periphery of the globe (75.000 x 2 2 / 7 =)-236 thousand miles. Half-way down this diameter, the body settled into its (original) orbit — would have settled, had it been the only body, besides its parent, in the Solar System — an orbit distant from the Sun's equator (236.000 / 2 =) 118 thousand miles; and from the centre of the solar vortex (1 18.000 + 888.000 / 2 =), 562 thousand miles. To this last are to be added, successively, the lengths of the semi-diameters of the trucks of Venus, of the Earth — and so on outward.
There, the planets’ original distances rather, speaking strictly, the widths from the common centre to the outer limits of their rings of vapor — are pointed at. From them, as foundations, the present distances may be deduced. A simple outline of the process to the deduction is this: — Neptune took his orbit first; then Uranus took his. The effect of the coming into close conjunction of the two bodies was such as would have been produced by bringing each so much nearer the centre of the solar vortex. Each enlarged its rotary ellipse and increased its rotary velocity in the ratio of the decrease of distance. A secondary result — the final consequence — of the enlargement and of the increase was the propulsion of each outward, the square root of the relative decrease being the measure of the length through which each was sent. The primary result of course was the drawing of each inward; and it is fairly presumable that there were oscillations inward and outward, outward and inward, during several successive periods of rotation. It is probable — at any rate, not glaringly improbable — that, in the oscillations across the remnants of the rings of vapor (the natural inference is that these were not completely gathered into the composition of the bodies), portions of the vapor were whirled into satellites, which followed in the last passage outward.
Saturn's ring (I have no allusion to the rings now existing), as well [page 115:] as that of each of the other planets after him, while it was gradually being cast off from the Sun's equator, was carried along in the track of its next predecessor, the distance, here, being the full quotient (not the square root of the quotient) found in dividing by the breadth to its own periphery that to the periphery of the other. Thus, reckoning for Uranus a breadth of 17 million miles, and for Saturn one of 14 million miles, the latter (still in his vaporous state) was conducted outward (through a sort of capillary attraction) 14/17 as far as the former (after condensation) was driven by means of the vortical influence of Neptune. The new body and the two older bodies interchanged forces, and another advance outward (of all three) was made. Combining all of the asteroids into one of the Nine Great Powers (assuming that there is no planet inside of Mercury), there were eight stages of the general movement away from the centre; and, granting that we have, exact, the diameters and the rotary periods (i.e., the densities) of all of the participants in the movement, the measurement of each stage, by itself, and of all the stages together can be calculated exactly.
How will that do for a postscript?
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Notes:
None.
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[S:0 - SSLER, 2004] - Edgar Allan Poe Society of Baltimore - Editions - EAP: Eureka (S. and S. Levine) (Appendix)