Outlines of a Mechanical Theory of Storms Part 11

Year of observation. Groups of spots observed. Number of days.

1826 118 277 1827 161 273 1828 225 282 1829 199 244 1830 190 217 1831 149 239 1832 84 270 1833 33 267 1834 51 273 1835 173 244 1836 272 200 1837 333 168 1838 282 202 1839 162 205 1840 152 263 1841 102 283 1842 68 307 1843 34 324

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 Ura.n.u.s were caused by an exterior planet, he adopted the notion that there were two planets exterior to Ura.n.u.s, 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 outstanding discrepancy 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:

Long. of Planets. Ma.s.ses. Mean distances. Eccentricities. Perihelion.

? 1/1648 494.800.000 0.0481 11 ? 1/3310 907.162.000 0.0561 89 ? 1/23000 1824.290.000 0.0166 167 ? 1/20000 2854.000.000 0.0088 0 ? 1/28000 4464.000.000

No. of spots in Dates. Rad. vector. Sun's long. Ordinates. Schwabe's table.

Jan. 1, 1826 528,000 320 + 84 118 " 1827 480,000 339 + 36 161 " 1828 432,000 352 - 12 Max. 225 Max.

" 1829 397,000 38 - 47 199 " 1830 858,000 71 - 86 190 " 1831 324,000 104 - 120 149 " 1832 311,000 144 - 133 84 " 1833 300,000 183 - 144 Min. 33 Min.

" 1834 307,000 220 - 137 51 " 1835 338,000 263 - 106 173 " 1836 380,000 302 - 55 272 " 1837 419,000 337 + 25 Max. 333 Max.

" 1838 488,000 3 + 44 282 " 1839 651,000 29 + 107 162 " 1840 632,000 51 + 188 152 " 1841 680,000 80 + 236 102 " 1842 730,000 105 + 286 68 " 1843 160,000 128 + 322 34 Min.

" 1844 188,000 152 + 339 Min. 52 " 1845 772,000 174 + 328 114 " 1846 728,000 196 + 284 157 " 1847 660,000 218 + 216 " 1848 563,000 240 + 119 Observed. Max.

" 1849 447,000 261 + 3 Max.

" 1850 309,000 283 - 135 " 1851 170,000 323 - 274 " 1852 53,000 41 - 391 Min.

" 1853 167,000 133 - 277 " 1854 315,000 160 - 129 " 1855 475,000 183 + 31 Max.

" 1856 611,000 203 + 167 " 1857 720,000 225 + 276

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 pa.s.sing judgment on this relation, it must also be borne in mind, that the recognized ma.s.ses of the planets cannot be the true ma.s.ses, 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, _ceteris paribus_, 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 a.s.signed. There may even be a comet of great ma.s.s, capable of producing an effect on the position of the sun's centre (although it follows from the theory that comets have very little ma.s.s). 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 ma.s.s, 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.

Ma.s.sES OF THE SUN AND PLANETS.

We have alluded to the fact of the radial stream of the sun necessarily diminishing the sun's power, and, consequently, diminishing his apparent ma.s.s. The radial stream of all the planets will do the same, so that each planet whose ma.s.s is derived from the periodic times of the satellites, will also appear too 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 ent.i.tle 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 a.n.a.logy 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, a.s.suredly, 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 more _rational_ the 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 trans.m.u.tations, 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 s.p.a.ce, 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 ma.s.s, 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 united _attraction_ of all the atoms of which the earth is composed. The _attraction_ of 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 s.p.a.ce, 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, produce _some_ difference between the gravitating ma.s.s and 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 ma.s.s of the earth is _latent_ may 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 lat.i.tudes and longitudes. The same may also be deduced from the different values of the moon's ma.s.s 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 ma.s.s of the moon comes out much greater by our theory than nutation gives. The ma.s.s deduced from the theory is only dependent on the relative inertiae of the earth and moon. That given by nutation depends on gravity. If, then, a part of the ma.s.s 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 pa.s.s, until suspicions, derived from other sources, induced the author to inquire: Whether the phenomenon did exactly accord 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.

Ma.s.s of the moon 1/80 Mean distance in equatorial radii 59.96435 Sidereal period in seconds 2360591

The vibrations of the pendulum give the force of gravity at the surface of the earth, and it is found to vary in different lat.i.tudes. 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 lat.i.tude the squares of whose sine is ?, it is 16.0697 feet. The effect in this last-named lat.i.tude 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 lat.i.tudes it is diminished in the ratio of the squares of the cosines of the lat.i.tude; it therefore becomes 1/434 in that lat.i.tude the square of whose sine is ?. Hence the 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 John Herschel, 20.923.713 feet. Her mean distance as derived from the parallax is 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 ma.s.ses 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 ma.s.ses 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 circ.u.mference to the radius, gives 7.850.791.736 feet, for the mean circ.u.mference 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 = ---------------- = 0.004426106 feet.

2498984746

This fraction is, however, too small, as the ablat.i.tious action of the sun diminishes the attraction of the earth on the moon, in the ratio of 178 29/40 to 177 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 is 16.1067/3574.595975805625 = 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 princ.i.p.al 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 ma.s.s 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 this reason, 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 ma.s.ses 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 ma.s.s; and if, in addition to this, there be a portion of these ma.s.ses 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.

LAW OF DENSITY IN SOLAR VORTEX.

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 quant.i.ty, 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 a.s.sumed that it was impossible for the principle of gravity to be 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 vortex _solely_; 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 s.p.a.ce be filled with a fluid medium, a.n.a.logy 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 acc.u.mulation of these atoms round a central nucleus from the surrounding s.p.a.ce, 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 s.p.a.ce 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 ma.s.s, and to force a pa.s.sage to the very centre of the vortex, in an almost parabolic curve. That s.p.a.ce 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 s.p.a.ce is filled with an _ether_, capable of intercepting in some degree the light." Is it not as probable that this extinction is due to planetary dust, scattered through the pure ether, whose vibrations convey the light,--the material atoms of future worlds,--the debris of dilapidated comets? Does not the Scripture teach the same thing, in a.s.serting that the heavens are not clean?

The theory of vortices has had many staunch supporters amongst those deeply versed in the science of the schools. The Bernoullis proposed several ingenious hypothesis, to free the Cartesian system from the objections urged against it, viz.: that the velocities of the planets, in accordance with the three great laws of Kepler, cannot be made to correspond with the motion of a fluid vortex; but they, and all others, gave the vantage ground to the defenders of the Newtonian philosophy, by seeking to refer the principle of gravitation to conditions dependent on the density and vorticose motion of the ether. When we admit that the ether is imponderable and yet material, and planetary matter subject to the law of gravitation, the objections urged against the theory of vortices become comparatively trivial, and we shall not stop to refute them, but proceed with the investigation, and consider that the ether is the original source of the planetary motions and arrangements.

On the supposition that the ether is uniformly dense, we have shown that the periodic times will be directly as the distances from the axis. If the density be inversely as the distances, the periodic times will be equal. If the density be inversely as the square roots of the distances, the times will be directly in the same ratio. The celebrated J.

Bernoulli a.s.sumed this last ratio; but seeking the source of motion in the rotating central globe, he was led into a hypothesis at variance with a.n.a.logy. 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 a.s.sume for the density of the medium, the periodic times will be compounded of those distances and the a.s.sumed 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 a.n.a.logy 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 s.p.a.ce 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 Ura.n.u.s, and Ura.n.u.s is denser than Saturn, we may conceive that there is such a wave in the solar vortex, near which rides this last magnificent planet, whose ring would thus be an appropriate emblem of the peculiar position occupied by Saturn. This may be the case, although the probability is, that the density of Saturn is much greater than it appears, as we shall presently explain.

In order to show that there is nothing extravagant in the supposition of the density of the ether being directly as the square roots of the distances from the axis, we will take a fluid whose law of density is known, and calculate the effect of the centrifugal force, considered as a compressing power. Let us a.s.sume 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 , it follows, (in accordance with the principle that the density is as the compressing force,) that at 43 miles high, or 18,000 feet _below_ the surface of the atmosphere, the density is only 1/8000 part of the density at the surface of the earth. Let us take this density as being near the limit of expansion, and conceive a hollow tube, reaching from the sun to the orbit of Neptune, and that this end of the tube is closed, and the end at the sun communicates with an inexhaustible reservoir of such an attenuated gas as composes the upper-layer of our atmosphere; and further, that the tube is infinitely strong to resist pressure, without offering resistance to the pa.s.sage of the air within the tube; then we say, that, if the air within the tube be continually acted on by a force equal to the mean centrifugal force of the solar vortex, reckoning from the sun to the orbit of Neptune, the density of the air at that extremity of the tube, would be greater than the density of a fluid formed by the compression of the ocean into one single drop. For the centrifugal force of the vortex at 2,300,000 miles from the centre of the sun, is equal to gravity at the surface of the earth, and taking the mean centrifugal force of the whole vortex as one-millionth of this last force; so that at 3,500,000 miles from the surface of the sun, the density of the air in the tube (supposing it obstructed at that distance) would be double the density of the attenuated air in the reservoir. And the air at the extremity of the tube reaching to the orbit of Neptune, would be as much denser than the air we breathe, as a number expressed by 273 with 239 ciphers annexed, is greater than unity. This is on the supposition of infinite compressibility. Now, in the solar vortex there is no physical barrier to oppose the pa.s.sage of the ether from the centre to the circ.u.mference, and the density of the ethereal ocean must be considered uniform, except in the interior of the stellar vortices, where it will be rarefied; and the rarefaction will depend on the centrifugal force and the length of the axis of the vortex. If this axis be very long, and the centrifugal velocity very great, the polar influx will not be sufficient, and the central parts will be rarefied. We see, therefore, no reason why the density of the ether may not be three times greater at Saturn than at the earth, or as the square roots of the distances directly.

BODES' LAW OF PLANETARY DISTANCES.

Thus, in the solar vortex, there will be two polar currents meeting at the sun, and thence being deflected at right angles, in planes parallel to the central plane of the vortex, and strongest in that central plane.

The velocity of expansion must, therefore, diminish from the divergence of the radii, as the distances increase; but in advancing along these planes, the ether of the vortex is continually getting more dense, which operate by absorption or condensation on the radial stream; so that the velocity is still more diminished, and this in the ratio of the square roots of the distances directly. By combining these two ratios, we find that the velocity of the radial stream will be in the ses-plicate ratio of the distances inversely. But the force of this stream is not as the velocity, but as the square of the velocity. The _force_ of the radial stream is consequently as the cubes of the distances inversely, from the axis of the vortex, reckoned in the same plane. If the ether, however, loses in velocity by the increasing density of the medium, it becomes also more dense; therefore the true force of the radial stream will be as its density and the square of its velocity, or directly as the square roots of the distances, and inversely as the cubes of the distances, or as the 2.5 power of the distances inversely.

If we consider the central plane of the vortex as coincident with the plane of the ecliptic, and the planetary orbits, also, in the same plane; and had the force of the radial stream been inversely as the square of the distances, there could be no disturbance produced by the action of the radial stream. It would only counteract the gravitation of the central body by a certain amount, and would be exactly proportioned at all distances. As it is, there is an outstanding force as a disturbing force, which is in the inverse ratio of the square roots of the distances from the sun; and to this is, no doubt, owing, in part, the fact, that the planetary distances are arranged in the inverse order of their densities.

Suppose two planets to have the same diameter to be placed in the same orbit, they will only be in equilibrium when their densities are equal.

If their densities are unequal, the lighter planet will continually enlarge its...o...b..t, 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 a.n.a.logy 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...o...b..t 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...o...b..t, so that the centrifugal momentum of Jupiter would be relatively greater than the centrifugal momentum of the earth, were it also in Jupiter's...o...b..t 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.