FOOTNOTES:

FOOTNOTES:[22]Hum. Cosmos, art Aerolites.[23]We shall in all cases use this abbreviation for the extremely awkward word zodiacal.[24]It is here assumed, that all the vortices are at their apogee at the same time, and, consequently, they lie in different longitudes, but the central being between, its position is taken for the average position of the three.[25]It is far from improbable that the effect produced in one zone of climate, may be reversed in another, from the nature of the cause.[26]That the 11th, 12th, and 13th of May should recede 2° in temperature as determined by Mædler from observations of 86 years, at a time when the power of the sun so rapidly augments, is strongly confirmatory of the theory. SeeCosmos, p. 121.[27]Plucker first discovered that a plate of tourmaline suspended with its axis vertical, set axial.[28]Silliman’s Journal for March and April, 1853.[29]Humboldt,Cosmosp. 193, London ed.[30]See Silliman’s Journal for September, 1853.[31]See Silliman’s Journal for September, 1853.[32]This was the central vortex ascending.[33]Reid’s Law of Storms, p. 350.[34]Humboldt,Cosmos, p. 203.

[22]Hum. Cosmos, art Aerolites.

[23]We shall in all cases use this abbreviation for the extremely awkward word zodiacal.

[24]It is here assumed, that all the vortices are at their apogee at the same time, and, consequently, they lie in different longitudes, but the central being between, its position is taken for the average position of the three.

[25]It is far from improbable that the effect produced in one zone of climate, may be reversed in another, from the nature of the cause.

[26]That the 11th, 12th, and 13th of May should recede 2° in temperature as determined by Mædler from observations of 86 years, at a time when the power of the sun so rapidly augments, is strongly confirmatory of the theory. SeeCosmos, p. 121.

[27]Plucker first discovered that a plate of tourmaline suspended with its axis vertical, set axial.

[28]Silliman’s Journal for March and April, 1853.

[29]Humboldt,Cosmosp. 193, London ed.

[30]See Silliman’s Journal for September, 1853.

[31]See Silliman’s Journal for September, 1853.

[32]This was the central vortex ascending.

[33]Reid’s Law of Storms, p. 350.

[34]Humboldt,Cosmos, p. 203.

We have yet many phenomena to investigate by the aid of the theory, and we will develop them in that order which will best exhibit their mutual dependence. The solar spots have long troubled astronomers, and to this day no satisfactory solution of the question has been proposed; but we shall not examine theories. It is sufficient that we can explain them on the same general principles that we have applied to terrestrial phenomena. There can be but little doubt about the existence of a solar atmosphere, and, reasoning from analogy, the constituent elements of the sun must partake of the nature of other planetary matter. That there are bodies in our system possessing the same elements as our earth, is proved by the composition of meteoric masses, which, whether they are independent bodies of the system, or fragments of an exploded planet, or projected from lunar volcanoes, is of little consequence; they show that the same elements are distributed to other bodies of the system, although not necessarily in the same proportions. The gaseous matter of the sun’s atmosphere may, therefore, be safely considered as vapors condensable by cold, and the formation of vortices over the surface of this atmosphere, brings down the ether, and causes it to intermingle with this atmosphere. But, from the immensely rapid motion of the polar current of the solar vortex, this ether may beconsidered to enter the atmosphere of the sun with the temperature of space.

Sir John Herschel, in commenting on the theory of Mr. Redfield before the British Association, convened at Newcastle in 1838,[35]suggested an analogy to terrestrial hurricanes, from a suspected rotation and progressive motion in these spots. From their rapid formation, change of shape, and diameter, this view is allowable, and, taken in conjunction with the action of the ethereal currents, will account for all the phenomena. The nucleus of the spot is dense, like the nucleus of a storm on the earth, and surrounded by a penumbon precisely as our storms are fringed with lighter clouds, permitting the light of the sun to penetrate. And, it has been observed, that these spots seem to follow one another in lines on the same parallel of solar latitude (or nearly the same), exactly as we have determined the action of the vortices on the surface of the earth from observation. These spots are never found in very high latitudes—not much above 30° from the solar equator. If we consider this equator to be but slightly inclined to the plane of the vortex, this latitude would be the general position of the lateral solar vortices, and, in fact, be confined principally to a belt on each side of the equator, between 15° and 30° of solar latitude, rather than at the equator itself. This, it is needless to say, is actually the case. But, a more capital feature still has been more recently brought to light by observation, although previously familiar to the author, who, in endeavoring to verify the theory, seriously injured his sight, by observing with inadequate instrumental means. This is the periodicity of the spots.

We have already observed, that there is reason to suppose that the action of the inner vortex of the earth is probably greater than that of the outer vortex, on account of the conflicting currents by which it is caused. And the full development of this vortex requires, that the central vortex ormechanical axis of the system shall be nearly tangential to the surface. In this position, the action of the central vortex is itself at a maximum; and, when the planets of the system are so arranged as to produce this result, we may expect the greatest number of spots. If the axis or central vortex approaches to coincidence with the axis of the sun, the lateral vortices disappear, and the central vortex being then perpendicular to the surface, is rendered ineffective. Under these circumstances, there will be no spots on the sun’s disc. When, on the other hand, all the planets conspire at the same side to force the sun out from the mechanical centre of the system, the surface is too distant to be acted on by the central vortex, and the lateral vortices are also thrown clear of the sun’s surface, on account of the greater velocity of the parts of the vortex, in sweeping past the body of the sun. In this case, there will be but few spots. The case in which the axis of the vortex coincides with the axis of the sun, is much more transient than the first position, and hence, although the interval between the maxima will be tolerably uniform, there will be an irregularity between a particular maximum, and the preceding and subsequent minimum.

The following table exhibits the solar spots, as determined by Schwabe, of Dessau:

Previous to the publication of this table, the author had inferred the necessity of admitting the existence of another planet in the solar system, from the phenomenon of which we are speaking. He found a sufficient correspondence between the minima of spots to confirm the explanation given by the theory, and this was still more confirmed by the more exact determination of Schwabe; yet there was a little discrepancy in the synchronous values of the ordinates, when the theory was graphically compared with the table. Previous to the discovery of Neptune, the theory corresponded much better than afterwards, and as no doubt could be entertained that the anomalous movements of Uranus were caused by an exterior planet, he adopted the notion that there were two planets exterior to Uranus, whose positions at the time were such, that their mechanical affects on the system were about equal and contrary. Consequently, when Neptune became known, the existence of another planet seemed a conclusion necessary to adopt. Accordingly, he calculated the heliocentric longitudes and true anomalies, and the values of radius vector, for all the planets during the present century, but not having any planetary tables, he contented himself with computing for the nearest degree of true anomaly, and the nearest thousand miles of distance. Then by a composition and resolution of all the forces, he deduced the radius vector of the sun, and the longitude of his centre, for each past year of the century. It was in view of a little outstandingdiscrepancy in the times of the minima, as determined by theory and observation, that he was induced to consider as almost certain the existence of a theoretical planet, whose longitude, in 1828, was about 90°, and whose period is from the theory about double that of Neptune. And for convenience of computation and reference, he has been in the habit of symbolizing it by a volcano. The following table of the radii vectores of the sun, and the longitude of his centre, for the years designated in Schwabe’s table, is calculated from the following data for each planet:

It is necessary to observe here, that the values of the numbers in Schwabe’s table are the numbers for the whole year, and, therefore, the 1st of July would have been a better date for the comparison; but, as the table was calculated before the author was cognizant of the fact, and being somewhat tedious to calculate, he has left it as it was, viz., for January 1st of each year. Hence, the minimum for 1843 appears as pertaining to 1844. The number of spots ought to be inversely as the ordinates approximately—these last being derived from the Radii Vectores minus, the semi-diameter of the sun = 444,000 miles.

In passing judgment on this relation, it must also be borne in mind, that the recognized masses of the planets cannot be the true masses, if the theory be true. Both sun and planets are under-estimated, yet, as they are, probably, all to a certain degree proportionally undervalued, it will not vitiate the above calculation much.

The spots being considered as solar storms, they ought also to vary in number at different times of the year, according to the longitude of the earth and sun, and from their transient character, and the slow rotation of the sun, they ought,ceterisparibus, to be more numerous when the producing vortex is over a visible portion of the sun’s surface.

The difficulty of reconciling the solar spots, and their periodicity to any known principle of physics, ought to produce a more tolerant spirit amongst the scientific for speculations even which may afford the slightest promise of a solution, although emanating from the humblest inquirer after truth. The hypothesis of an undiscovered planet, exterior to Neptune, is of a nature to startle the cautions timidity of many; but, if the general theory be true, this hypothesis becomes extremely probable. We may not have located it exactly. There may be even two such planets, whose joint effect shall be equivalent to one in the position we have assigned. There may even be a comet of great mass, capable of producing an effect on the position of the sun’s centre (although it follows from the theory that comets have very little mass). Yet, in view of all these suppositions, there can be but little doubt that the solar spots are caused by the solar vortices, and these last made effective on the sun by the positions of the great planets, and, therefore, we have indicated a new method of determining the existence and position of all the planets exterior to Neptune. On the supposition that there is only one more in the system, from its deduced distance and mass, it will appear only as a star of the eleventh magnitude, and, consequently, will only be recognizable by its motion, which, at the greatest, will only be ten or eleven seconds per day.

We have alluded to the fact of the radial stream of the sun necessarily diminishing the sun’s power, and, consequently, diminishing his apparent mass. The radial stream of all the planets will do the same, so that each planet whose mass is derived from the periodic times of the satellites, will also appeartoo small. But, there is also a great probability that some modification must be made in the wording of the Newtonian law. The experiments of Newton on the pendulum, with every variety of substance, was sufficient justification to entitle him to infer, that inertia was as the weight of matter universally. But, there was one condition which could not be observed in experimenting on these substances, viz., the difference of temperature existing between the interior and surface of a planet.

We have already expressed the idea, that the cause of gravity has no such mysterious origin as to transcend the power of man to determine it. But that, on the contrary, we are taught by every analogy around us, as well as by divine precept, to use the visible things of creation as stepping stones to the attainment of what is not so apparent. That we have the volume of nature spread out in tempting characters, inviting us to read, and, assuredly, it is not so spread in mockery of man’s limited powers. As science advances, strange things, it is true, are brought to light, but the morerationalthe queries we propound, in every case the more satisfactory are the answers. It is only when man consults the oracle in irrational terms that the response is ambiguous. Alchemy, with its unnatural transmutations, has long since vanished before the increasing light. Why should not attraction also? Experience and experiment, if men would only follow their indications, are consistently enforcing the necessity of erasing these antiquated chimeras from the book of knowledge; and inculcating the great truth, that the physical universe owes all its endless variety to differences in the form, size, and density of planetary atoms in motion, according to simple mechanical principles. These, combined with the existence of an all-pervading medium filling space, between which and planetary matter no bond of union subsists, other than that which arises from a continual interchange of motion, are the materials from which the gems of nature are elaborated. But, simplicity of means is what philosophy has ever been reluctant to admit, preferring rather the occult and obscure.

If action be equal to reaction, and all nature be vibrating with motion, these motions must necessarily interfere, and some effect should be produced. A body radiating its motion on every side into a physical medium, produces waves. These waves are a mechanical effect, and the body parts with some of its motion in producing them; but, should another body be placed in juxtaposition, having the same motion, the opposing waves neutralize each other, and the bodies lose no motion from their contiguous sides, and, therefore, the reaction from the opposite sides acts as a propelling power, and the bodies approach, or tend to approach each other. If one body be of double the inertia, it moves only half as far as the first; then, seeing that this atomic motion is radiated, the law of force must be directly as the mass, and inversely as the squares of the distances. There may be other atomic vibrations besides those which we call light, heat, and chemical action, yet the joint effect of all is infinitesimally small, when we disregard the unitedattractionof all the atoms of which the earth is composed. Theattractionof the whole earth at the surface causes bodies to fall 16 feet the first second of time; but, if two spheres of ice of one foot diameter, were placed in an infinite space, uninfluenced by other matter, and only 16 feet apart, they would require nearly 10,000 years to fall together by virtue of their mutual attraction. Our conceptions, or, rather, our misconceptions, concerning the force of gravity, arises from our forgetting that every pound of matter on the earth contributes its share of the force which, in the aggregate, is so powerful. Hence, the cause we have suggested, is fully adequate to account for the phenomena. Whether the harmony of vibrations between two bodies may not have an influence in determining the amount of interference, and, consequently, producesomedifference between the gravitating massand its inertia, is a question which, no doubt, will ultimately be solved; but this harmony of vibrations must depend, in some degree, on the atomic weight, temperature, and intensity of atomic motion.

That a part of the mass of the earth islatentmay be inferred from certain considerations: 1st, from the discrepancies existing in the results obtained for the earth’s compression by the pendulum and by actual measurement; and, 2d, from the irregularity of that compression in particular latitudes and longitudes. The same may also be deduced from the different values of the moon’s mass as derived from different phenomena, dependent on the law of gravitation. Astronomers have hitherto covered themselves with the very convenient shield of errors of observation; but, the perfection of modern instruments now demand a better account of all outstanding discrepancies. The world requires it of them.

The mass of the moon comes out much greater by our theory than nutation gives. The mass deduced from the theory is only dependent on the relative inertiæ of the earth and moon. That given by nutation depends on gravity. If, then, a part of the mass be latent, nutation will give too small a value. But, in addition to this, we are justified in doubting the strict wording of the Newtonian law, deriving our authority from the very foundation stone of the Newtonian theory.

It is well known that Newton suspected that the moon was retained in her orbit by the same force which is usually called weight upon the surface, sixteen years before the fact was confirmed, by finding a correspondence in the fall of the moon and the fall of bodies on the earth. Usually, in all elementary works, this problem is considered accurately solved. Having formed a different idea of the mechanism of nature, this fact presented itself as a barrier beyond which it was impossible to pass, until suspicions, derived from other sources, induced the author to inquire: Whether the phenomenon did exactlyaccord with the theory? We are aware that it is easy to place the moon at such a distance, that the result shall strictly correspond with the fact; but, from the parallax, as derived from observation (and if this cannot be depended on certainly, no magnitudes in astronomy can), we find,that the moon does not fall from the tangent of her orbit, as much as the theory requires. As this is of vital importance to the integrity of the theory we are advocating, we have made the computation on Newton’s own data, except such as were necessarily inaccurate at the time he wrote; and we have done it arithmetically, without logarithmic tables, that, if possible, no error should creep in to vitiate the result. We take the moon’s elements from no less an authority than Sir John Herschel, as well as the value of the earth’s diameter.

The vibrations of the pendulum give the force of gravity at the surface of the earth, and it is found to vary in different latitudes. The intensity in any place being as the squares of the number of vibrations in a given time. This inequality depends on the centrifugal force of rotation, and on the spheroidal figure of the earth due to that rotation. At the equator the fall of a heavy body is found to be 16.045223 feet, per second, and in that latitude the squares of whose sine is ⅓, it is 16.0697 feet. The effect in this last-named latitude is the same as if the earth were a perfect sphere. This does not, however, express the whole force of gravity, as the rotation of the earth causes a centrifugal tendency which is a maximum at the equator, and there amounts to 1 ⁄ 289 of the whole gravitating force. In other latitudes it is diminished in the ratio of the squares of the cosines of the latitude; it therefore becomes 1 ⁄ 434 in that latitude the square of whose sine is ⅓. Hencethe fall per second becomes 16.1067 feet for the true gravitating force of the earth, or for that force which retains the moon in her orbit.

The moon’s mean distance is 59.96435 equatorial radii of the earth, which radius is, according to Sir JohnHerschel, 20.923.713 feet. Her mean distance as derived from theparallaxis not to be considered the radius vector of the orbit, inasmuch as the earth also describes a small orbit around the common centre of gravity of the earth and moon; neither is radius vector to be considered as her distance from this common centre; for the attracting power is in the centre of the earth. But the mean distance of the moon moving around a movable centre, is to the same mean distance when the centre of attraction is fixed, as the sum of the masses of the two bodies, to the first of two mean proportionals between this sum and the largest of the two bodies inversely. (Vid. Prin. Prop. 60 Lib. Prim.) The ratio of the masses being as above 80 to 1 the mean proportional sought is 80.666 and in this ratio must the moon’s mean distance be diminished to get the force of gravity at the moon. Therefore as 81 is to 80.666, so is 59.96435 to 59.71657 for the moon’s distance in equatorial radii of the earth. Multiply this last by 20.923.713 to bring the semi-diameter of the lunar orbit into feet = 1.249.492.373, and this by 6.283185, the ratio of the circumference to the radius, gives 7.850.791.736 feet, for the mean circumference of the lunar orbit.

Further, the mean sidereal period of the moon is 2360591 seconds and the 1 ⁄ 2360591th part of 7.850.791.736 is the arc the moon describes in one second = 3325.77381 feet, the square of which divided by the diameter of the orbit, gives the fall of the moon from the tangent or versed size of that arc. =1106771.36876644 ⁄ 2498984746= 0.004426106 feet.

This fraction is, however, too small, as the ablatitious actionof the sun diminishes the attraction of the earth on the moon, in the ratio of178 29 ⁄ 40to177 29 ⁄ 40. So that we must increase the fall of the moon in the ratio of 711 to 715, and hence the true fall of the moon from the tangent of her orbit becomes 0.00451 feet per second.

We have found the fall of a body at the surface of the earth, considered as a sphere, 16.1067 feet per second, and the force of gravity diminishes as the squares of the distances increases. The polar diameter of the earth is set down as 7899.170 miles, and the equatorial diameter 7925.648 miles; therefore, the mean diameter is 7916.189 miles.[36]So that, reckoning in mean radii of the earth, the moon’s distance is 59.787925, which squared, is equal to 3574.595975805625. At one mean radius distance, that is, at the surface, the force of gravity, or fall per second, is as above, 16.1067 feet. Divide this by the square of the distance, it is16.1067 ⁄ 3574.595975805625= 0.0045058 feet for the force of gravity at the moon. But, from the preceding calculation, it appears, that the moon only falls 0.0044510 feet in a second, showing a deficiency of 1 ⁄ 82d part of the principal force that retains the moon in her orbit, being more than double the whole disturbing power of the sun, which is only 1 ⁄ 178th of the earth’s gravity at the moon; yet, on this 1 ⁄ 178th depends the revolution of the lunar apogee and nodes, and all those variations which clothe the lunar theory with such formidable difficulties. The moon’s mass cannot be less than 1 ⁄ 80, and if we consider it greater, as it no doubt is, the results obtained will be still more discrepant. Much of this discrepancy is owing to the expulsive power of the radial stream of the terral vortex; yet, it may be suspected that the effect is too great to be attributed to this, and, for thisreason, we have suggested that the fused matter of the moon’s centre may not gravitate with the same force as the exterior parts, and thus contribute to increase the discrepancy.

As there must be a similar effect produced by the radial stream of every vortex, the masses of all the planets will appear too small, as derived from their gravitating force; and the inertia of the sun will also be greater than his apparent mass; and if, in addition to this, there be a portion of these masses latent, we shall have an ample explanation of the connection between the planetary densities and distances. We must therefore inquire what is the particular law of force which governs the radial stream of the solar vortex. It will be necessary to enter into this question a little more in detail than our limits will justify; but it is the resisting influence of the ether, and its consequences, which will appear to present a vulnerable point in the present theory, and to be incompatible with the perfection of astronomical science.

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 tobe 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 vortexsolely; 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 anether, 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, theperiodic 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 withanalogy. 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 issuch 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 ½, it follows, (in accordance with the principle that the density is as the compressing force,) that at 43½ miles high, or 18,000 feetbelowthe 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 begreater 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.

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, whichoperate 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. Theforceof 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 theplanets’resisting energy. This, however, is on the hypothesis that the planets are not permeable by the radial stream, which, perhaps, is moreconsistent 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 thedense 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 usualorder. 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 thathisobservations 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 withthe 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 theasteroidalgroup, 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 otherfragments, 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 abrief period of time,[38]leaving the lighter and more elastic substances as a nebulousatmosphere 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 findthe Equatorialdiameter 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 notnecessarily 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.

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 theperihelion, 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 theplanet’seccentric anomaly at other distances, and is positive or negative, according as the planet’s distance is above or below the mean.

At the planet’s mean distance, the circular velocity of the vortex is equal to the circular velocity of the planet, and, at different distances, is inversely in the sub-duplicate ratio of those distances. But the circular velocity of a planet in the same orbit, is in the simple ratio of the distances inversely. At the perihelion, the planet therefore moves faster than the ether of the vortex, and at the aphelion, slower; and the difference is as the square roots of the distances; but the force of resistance is as the square of the velocity, and is therefore in the simple ratio of the distances, as we have already found for the effect of the radial stream, and centrifugal momentum of the internal ether. At the perihelion this excess of tangential velocity creates a resistance, which urges the planet towards the sun, and at the aphelion, the deficiency of tangential velocity urges the planet from the sun,—the maximum effect being at the apsides of the orbit, and null at the mean distances. In other positions it is, therefore, as the cosines of the eccentric anomaly, as in the former case; but in this last case it is an addititious force at the perihelion, and an ablatitious force at the aphelion, whereas the first disturbing force was an ablatitious force at the perihelion, and an addititious force at the aphelion; therefore, as we must suppose the planet to be in equilibrium at its mean distance, it is in equilibrium at all distances. Hence, a planet moving in the central plane of the vortex, experiences no disturbance from the resistance of the ether.

As the eccentricities of the planetary orbits are continually changing under the influence of the law of gravitation, wemust inquire whether, under these circumstances, such a change would not produce a permanent derangement by a change in the mean force of the radial stream, so as to increase or diminish the mean distance of the planet from the sun. The law of force deduced from the theory for the radial stream is as the 2.5 power of the distances inversely. But, by dividing this ratio, we may make the investigation easier; for it is equivalent to two forces, one being as the squares of the distances, and another as the square roots of the distances. For the former force, we find that in orbits having the same major axis the mean effect will be as the minor axis of the ellipseinversely, so that two planets moving in different orbits, but at the same mean distance, experience a less or greater amount of centripulsive force from this radial stream, according as their orbits are of less or greater eccentricity, and this in the ratio of the minor axis. On the other hand, under the influence of a force acting centripulsively in the inverse ratio of the square roots of the distances, we find the mean effect to be as the minor axis of the ellipsedirectly, so that two planets in orbits of different eccentricity, but having the same major axis, experience a different amount from the action of this radial stream, the least eccentric orbit being that which receives the greatest mean effect. By combining these two results, we get a ratio of equality; and, consequently, the action of the radial stream will be the same for the same orbit, whatever change may take place in the eccentricity, and the mean distance of the planet will be unchanged. A little consideration will also show that the effect of the centrifugal momentum due to the density of ether will also be the same by change of eccentricity; for the positive will always balance the negative effect at the greatest and least distances of the planet. The same remark applies to the effect of the tangential current, so that no change can be produced in the major axes of the planetary orbits by change of eccentricity, as an effect of the resistance of the ether.

We will now suppose a planet’s orbit to be inclined to the central plane of the vortex, and in this case, also, we find, that the action of the radial stream tends to increase the inclination in one quadrant as much as it diminishes it in the next quadrant, so that no change of inclination will result. But, if the inclination of the orbit be changed by planetary perturbations, the mean effect of the radial stream will also be changed, and this will tell on the major axis of the orbit, enlarging the orbit when the inclination diminishes, and contracting it when it increases. The change of inclination, however, must be referred to the central plane of the vortex. Notwithstanding the perfection of modern analysis, it is confessed that the recession of the moon’s nodes does yet differ from the theory by its 350th part, and a similar discrepancy is found for the advance of the perigee.[40]This theory is yet far too imperfect to say that the action of the ethereal medium will account for these discrepancies; but it certainly wears a promising aspect, worthy the notice of astronomers. There are other minute discordancies between theory and observation in many astronomical phenomena, which theoryiscompetent to remove. Some of these we shall notice presently; and, it may be remarked, that it is in those minute quantities which, in astronomy, are usually attributed to errors of observation, that this theory will eventually find the surest evidence of its truth.

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