Part 19

As another evidence of the necessity of modifying the strict wording of the Newtonian law, it is found that the disturbing action of Jupiter on different bodies, gives different values for the mass of Jupiter. The mass deduced from Jupiter's action on his satellites, is different from that derived from the perturbations of Saturn, and this last does not correspond with that given by Juno: Vesta also gives a different mass from the comet of Encke, and both vary from the preceding values.

In the analytical investigation of planetary disturbances, the disturbing force is usually divided into a radial and tangential force; the first changing the law of gravitation, to which law the elliptic form of the orbit is due. The radial disturbing force, therefore, being directed to or from the centre, can have no influence over the first law of Kepler, which teaches that the radius vector of each planet having the sun as the centre, describes equal areas in equal times. If the radial disturbing force be exterior to the disturbed body, it will diminish the central force, and cause a progressive motion in the aphelion point of the orbit. In the case of the moon this motion is very rapid, the apogee making an entire revolution in 3232 days. Does this, however, correspond with the law of gravitation? Sir Isaac Newton, in calculating the effect of the sun's disturbing force on the motion of the moon's apogee, candidly concludes thus: "Idoque apsis summa singulis revolutionibus progrediendo conficit 1d 31' 28". Apsis lunae est duplo velocior circiter." As there was a necessity for reconciling this stubborn fact with the theory, his followers have made up the deficiency by resorting to the tangential force, or, as Clairant proposed, by continuing the approximations to terms of a higher order, or to the square of the disturbing force.

Now, in a circular orbit, this tangential force will alternately increase and diminish the velocity of the disturbed body, without producing any permanent derangement, the same result would obtain in an elliptical orbit, if the position of the major axis were stationary. In the case of the moon, the apogee is caused to advance by the disturbing power of the radial force, and, consequently, an exact compensation is not effected: there remains a small excess of velocity which geometers have considered equivalent to a doubling of the radial force, and have thus obviated the difficulty. To those not imbued with the profound penetration of the modern analyst, there must ever appear a little inconsistency in this result. The major axis of a planet's orbit depends solely on the velocity of the planet at a given distance from the sun, and the tangential portion of the disturbance due to the sun, and impressed upon the moon, must necessarily increase and diminish alternately the velocity of the moon, and interfere with the equable description of the areas. If, then, there be left outstanding a small excess of velocity over and above the elliptical velocity of the moon, at the end of each synodical revolution, in consequence of the motion impressed on the moon's apogee by the radial force, the legitimate effect would be a small enlargement of the lunar orbit every revolution in a rapidly-increasing ratio, until the moon would at last be taken entirely away. In the great inequality of Jupiter and Saturn, this tangential force is not compensated at each revolution, in consequence of continual changes in the configuration of the two planets at their heliocentric conjunctions, with respect to the perihelion of their orbits, and the near commensurability of their periods; and the effect of the tangential force is, in this case, legitimately impressed on the major axes of the orbits. But why (we may ask) should not this also be expended on the motion of the aphelion as well as in the case of the moon? Astronomy can make no distinctions between the orbit of a planet and the orbit of a satellite. And, we might also ask, why the tangential resistance to the comet of Encke should not also produce a retrograde motion in the apsides of the orbit, instead of diminishing its period? To the honor of Newton, be it remembered, that he never resorted to an explanation of this phenomenon, which would vitiate that fundamental proposition of his theory, in which the major axis of the orbit is shown to depend on the velocity at any given distance from the focus.

Some cause, however, exists to double the motion of the apogee, and that there is an outstanding excess of orbital velocity due to the tangential force, is also true. This excess may tell in the way proposed, provided some other arrangement exists to prevent a permanent dilation of the lunar orbit; and this provision may be found in the increasing density of the ether, which prevents the moon overstepping the bounds prescribed by her own density, and the force of the radial stream of the terral vortex. In the case of Jupiter and Saturn, their mutual action is much less interfered with by change of density in the ether in the enlarged or contracted orbit, and, consequently, the effect is natural. Thus, we have in the law of density of the ethereal medium a better safeguard to the stability of the dynamical balance of the system, than in the profound and beautiful Theorems of La Grange. It will, of course, occur to every one, that we are not to look for the same law in every vortex, and it will, therefore, appear as if the satellites of Jupiter, whose theory is so well known, should render apparent any deviation between their periodic times and the periodic times of the contiguous parts of the vortex, which would obtain, if the density of the ether in the Jovian vortex were not as the square roots of the distances directly. But, we have shown how there can be a balance preserved, if the tangential resistance of the vortex shall be equal and contrary at the different distances at which the satellites are placed; that is, if these two forces shall follow the same law. These are matters, however, for future investigation.

LIGHT AND HEAT.

But will not the admission of a vorticose motion of the ethereal medium, affect the aberration of light? It is well known that the question has been mooted, whether the velocity of reflected light is the same as that of direct light. The value of aberration having been considered 20".25, from the eclipses of Jupiter's satellites, while later determinations, from observations on Polaris, give 20".45. It cannot be doubted that light, in traversing the central parts of the solar vortex, that is, having to cross the whole orbit of the earth, should pass this distance in a portion of time somewhat different to a similar distance outside the earth's orbit, where the density is greater, and consequently induce an error in the aberration, determined by the eclipses of Jupiter's satellites. In the case of Polaris, the circumstances are more equal; still, a difference ought to be detected between the deduced aberration in summer and in winter, as, in the first case, the light passes near the axis of the solar vortex, where (according to the theory) a change of density occurs. This is an important practical question, and the suggestion is worthy attention. Now, the question occurs, will light pass through the rarefied space with greater velocity than through the denser ether beyond? From recent experiments, first instituted by Arago, it is determined that light passes with less velocity through water than through air; and one result of these experiments is the confirmation they give to the theory of Fresnel, that the medium which conveys the action of light partly partakes of the motion of the refracting body. This of itself is a strong confirmation of this theory of an ethereal medium. It may also be remarked, that every test applied to the phenomenon of light, adds additional strength to the undulatory theory, at the expense of the Newtonian theory of emission. As light occupies time in traversing space, it must follow from the theory that it does not come from the radiant point exactly in straight lines, inasmuch as the ether itself is in motion tangentially,--the velocity being in the sub-duplicate ratio of the distances from the sun inversely.

May not that singular phenomenon,--the projection of a star on the moon's disc, at the time of an occultation,--be due to this curvature of the path of a ray of light, by considering that the rays from the moon have less intensity, but more mechanical momentum, and consequently more power to keep a straight direction? Let us explain: we have urged that light, as well as heat, is a mechanical effect of atomic motion, propagated through an elastic medium; that, ceteris paribus, the product of matter by its motion is ever a constant quantity for equal spaces throughout the universe,--in a word, that it is, and must necessarily be, a fundamental law of nature. All departures from this law are consequences of accidental arrangements, which can only be considered of temporary duration. Our knowledge of planetary matter requires the admission of differences in the density, form, and size of ultimate atoms, and, according to the above law, when the atoms are of uniform temperature or motion, the product of the matter of each by its motion, when reduced to the same space, will be constant. The momentum of two different atoms, therefore, we will consider equal, for the sake of illustration; yet this momentum is made up of two different elements,--matter and motion. Let us exaggerate the difference, and assign a ratio of 1000 to 1. Suppose a ball of iron of 1000 lbs., resting upon a horizontal plane, should be struck by another ball of 1 lb., having a motion of 1000 feet in a second, and, in a second case, should be struck by a ball of 1000 lbs., having a velocity of 1 foot per second, the momentum of each ball is similar; but experience proves that the motion impressed on the ball at rest is not similar; the ponderous weight and slow motion is far more effective in displacing this ball, for the reason that time is essential to the distribution of the motion. If the body to be struck be small as, for instance, a nail, a greater motion and less matter is more effective than much matter and little motion. Hence, we have a distinction applicable to the difference of momentum of luminous and calorific rays. The velocity of a wave of sound through the atmosphere, is the same for the deep-toned thunder and the shrillest whistle,--being dependent on the density of the medium, and not on the source from which it emanates. So it is in the ethereal medium.

This view is in accordance with the experiments of M. Delaroche and Melloni, on the transmission of light and heat through diaphanous bodies--the more calorific rays feeling more and more the influence of thickness, showing that more motion was imparted to the particles of the diaphanous substance by the rays possessing more material momentum, and still more when the temperature of the radiating body was low, evidently analogous to the illustration we have cited. Light may therefore be regarded as the effect of the vibration of atoms having little mass, and as this mass increases, the rays become more calorific, and finally the calorific effect is the only evidence of their existence; as towards the extreme red end of the spectrum they cease to be visible, owing to their inability to impart their vibrations to the optic nerve. This may also influence the law of gravitation. In this we have also an explanation of the dispersion of light. The rays proceeding from atoms of small mass having less material momentum, are the most refrangible, and those possessing greater material momentum, are the least refrangible; so that instead of presenting a difficulty in the undulatory theory of light, this dispersion is a necessary consequence of its first principles.

It is inferred from the experiments cited, and the facts ascertained by them, viz.: that the velocity of light in water is less than its velocity in air; that the density of the ether is greater in the first case; but this by no means follows. We have advocated the idea, that the ethereal medium is less dense within a refracting body than without. We regard it as a fundamental principle. Taking the free ether of heaven; the vibrations in the denser ether will no doubt be slowest; but within a refracting body we must consider there is motion lost, or light absorbed, and the time of the transmission is thus increased.

There has been a phenomenon observed in transits of Mercury and Venus across the sun, of which no explanation has been rendered by astronomers. When these planets are visible on the solar disc, they are seen surrounded by rings, as if the light was intercepted and increased alternately. This is no doubt due to a small effect of interference, caused by change of velocity in passing through the rarefied nucleus of these planetary vortices, near the body of the planet, and through the denser ether beyond, acting first as a concave, and secondly as a convex refracting body; always considering that the ray will deviate towards the side of least insistence, and thus interfere.

That heat is simply atomic motion, and altogether mechanical, is a doctrine which ought never to have been questioned. The interest excited by the bold experiments of Ericson, has caused the scientific to suspect, that heat can be converted into motion, and motion into heat--a fact which the author has considered too palpable to deny for the last twenty years. He has ever regarded matter and motion as the two great principles of nature, ever inseparable, yet variously combined; and that without these two elements, we could have no conception of anything existing.

It may be thought by some, who are afraid to follow truth up the rugged precipices of the hill of knowledge, that this theory of an interplanetary plenum leads to materialism; forgetting, that He who made the world, formed it of matter, and pronounced it "very good." We may consider ethereal matter, in one sense, purer than planetary matter, because unaffected by chemical laws. Whether still purer matter exists, it is not for us to aver or deny. The Scriptures teach us that "there is a natural body and there is a spiritual body." Beyond this we know nothing. We, however, believe that the invisible world of matter, can only be comprehended by the indications of that which is visible; yet while humbly endeavoring to connect by one common tie, the various phenomena of matter and motion, we protest against those doctrines which teach the eternal duration of the present order of things, as being incompatible with the analogies of the past, as well as with the revelations of the future.

FOOTNOTES:

Silliman's Journal, vol xxxv., page 283.

The real diameter of the earth in that latitude, whose sine is one-third, is a little greater than this; but the true mean is more favorable for the Newtonian law.

This is, perhaps, the nearest ratio of the densities and distances.

This is an important consideration, as bearing on the geology of the earth.

It is not as likely that the condensation of the sun was so sudden as that of the planets, and therefore in this case this distance is only approximate.

Mechanique Celeste. Theory of the Moon.

Mechanique Celeste. Masses of the planets.

SECTION FIFTH.

COMETARY PHENOMENA.

The planetary arrangements of the solar system are all a priori indications of the theory of vortices, not only by the uniform direction of the motions, the circular orbits in which these motions are performed, the near coincidence of the planes of these orbits, and the uniform direction of the rotation of the planets themselves; but, also, by the law of densities and distances, which we have already attempted to explain. In the motions of comets we find no such agreement. These bodies move in planes at all possible inclinations in orbits extremely eccentrical and without any general direction--as many moving contrary to the direction of the planets as in the opposite direction; and when we consider their great volume, and their want of mass, it appears, at first sight, that comets do present a serious objection to the theory. We shall point out, however, a number of facts which tend to invalidate this objection, and which will ultimately give the preponderance to the opposite argument.

Every fact indicative of the nature of comets proves that the nuclei are masses of material gases, similar, perhaps (at least in the case of the short-period comets), to the elementary gases of our own planet, and, consequently, these masses must be but small. In the nascent state of the system, the radial stream of the vortex would operate as a fan, purging the planetary materials of the least ponderable atoms, and, as it were, separating the wheat from the chaff. It is thus we conceive that the average atomic density of each planet has been first determined by the radial stream, and, subsequently, that the solidification of the nebulous planets has, by their atomic density, assigned to each its position in the system, from the consequent relation which it established between the density of the ether within the planet, and the density of the ether external to it, so that, according to this view, a single isolated atom of the same density as the mean atomic density of the earth could (ceteris paribus) revolve in an orbit at the distance of the earth, and in the same periodic time. This, however, is only advanced by way of illustration.

The expulsive force of the radial stream would thus drive off this cometary dust to distances in some inverse ratio of the density of the atoms; but, a limit would ultimately be reached, when gravitation would be relatively the strongest--the last force diminishing only as the squares of the distances, and the first diminishing in the compound ratio of the squares and the square roots of the distances. At the extreme verge of the system, this cometary matter would accumulate, and, by accumulation, would still further gather up the scattered atoms--the sweepings of the inner space--and, in this condensed form, would again visit the sun in an extremely elongated ellipse. It does not, however, follow, that all comets are composed of such unsubstantial materials. There may be comets moving in parabolas, or even in hyperbolas--bodies which may have been accumulating for ages in the unknown regions of space, far removed from the sun and stars, drifting on the mighty currents of the great ethereal ocean, and thus brought within the sphere of the sun's attraction; and these bodies may have no analogy to the periodical comets of our system, which last are those with which we are more immediately concerned.

The periodical comets known are clearly arranged into two distinct classes--one having a mean distance between Saturn and Uranus, with a period of about seventy-five years, and another class, whose mean distance assigns their position between the smaller planets and Jupiter, having periods of about six years. These last may be considered the siftings of the smaller planets, and the first the refuse of the Saturnian system. In this light we may look for comets having a mean distance corresponding to the intervals of the planets, rather than to the distances of the planets themselves. One remarkable fact, however, to be observed in these bodies is, that all their motions are in the same direction as the planets, and, with one exception, there is no periodical comet positively known whose motion is retrograde.

The exception we have mentioned is the celebrated comet of Halley, whose period is also about seventy-five years. In reasoning on the resistance of the ether, we must consider that the case can have very little analogy with the theory of projectiles in air; nor can we estimate the inertia of an infinitely divisible fluid, from its resisting influence on atomic matter, by a comparison of the resistance of an atomic fluid on an atomic solid. Analogy will only justify comparisons of like with like. The tangent of a comet's orbit, also, can only be tangential to the circular motion of the ether at and near perihelion, which is a very small portion of its period of revolution. As far as the tangential resistance is concerned, therefore, it matters little whether its motion be direct or retrograde. If a retrograde comet, of short period and small eccentricity, were discovered moving also near the central plane of the vortex, it would present a very serious objection, as being indicative of contrary motions in the nascent state of the system. There is no such case known. So, also, with the inclinations of the orbits; if these be great, it matters little whether the comet moves in one way or the other, as far as the tangential current of the vortex is concerned. Yet, when we consider the average inclination of the orbit, and not of its plane, we find that the major axes of nearly all known cometary orbits are very little inclined to the plane of the ecliptic.

In the following table of all the periodical comets known, the inclination of the major axis of the orbit is calculated to the nearest degree; but all cometary orbits with very few exceptions, will be found to respect the ecliptic, and never to deviate far from that plane: