COMETARY PHENOMENA._Outlines of a mechanical theory of storms

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:

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|De Vico | 1814 | | 2 | Direct | |

|Brorsen | 1846 | five | 7 | Direct | and |

|Messier | 1766 | to | 0 | Direct | |

|Clausen | 1743 | six | 0 | Direct | Jupiter. |

|Pigott | 1783 | or | 4 | Direct | |

|Blaupain | 1819 | | 2 | Direct | |

|Lexell | 1770 | | 1 | Direct | |

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|Pous | 1812 | | 17 | Direct | |

|De Vico | 1846 | 75 | 13 | Direct | and |

|Westphal | 1852 | | 21 | Direct | |

|Halley | 1682 | | 16 | Retrograde| |

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From which it appears, that the objection arising from the great

inclination of the _planes_ of these orbits is much less important than

at first it appears to be.

Regarding then, that a comet's mean distance depends on its mean atomic

density, as in the case of the planets, the undue enlargement of their

orbits by planetary perturbations is inadmissible. In 1770 Messier

discovered a comet which approached nearer the earth than any comet

known, and it was found to move in a small ellipse with a period of five

and a half years; but although repeatedly sought for, it was the

opinion of many, that it has never been since seen. The cause of this

seeming anomaly is found by astronomers in the disturbing power of

Jupiter,--near which planet the comet must have passed in 1779, but the

comet was not seen in 1776 before it passed near Jupiter, although a

very close search was kept up about this time. Now there are two

suppositions in reference to this body: the comet either moved in a

larger orbit previous to 1767, and was then caused by Jupiter to

diminish its velocity sufficiently to give it a period of five and a

half years, and that after perihelion it recovered a portion of its

velocity in endeavoring to get back into its natural orbit; or if moving

in the natural orbit in 1770, and by passing near Jupiter in 1779 this

orbit was deranged, the comet will ultimately return to that mean

distance although not necessarily having elements even approximating

those of 1770. In 1844, September 15th, the author discovered a comet in

the constellation Cetus, (the same previously discovered by De Vico at

Home,) and from positions _estimated with the naked eye_ approximately

determined the form of its orbit and its periodic time to be very

similar to the lost comet of 1770. These conclusions were published in a

western paper in October 1844, on which occasion he expressed the

conviction, that this was no other than the comet of 1770. As the

question bore strongly on his theory he paid the greater attention to

it, and had, previously to this time, often searched in hopes of finding

that very comet. Since then, M. Le Verrier has examined the question of

identity and given his decision against it; but the author is still

sanguine that the comet of 1844 is the same as that of 1770, once more

settled at its natural distance from the sun. This comet returns to its

perihelion on the 6th of August, 1855, according to Dr. Brunnow, when,

it is hoped, the question of identity will be reconsidered with

reference to the author's principles; and, that when astronomers become

satisfied of this, they will do him the justice of acknowledging that

he was the first who gave publicity to the fact, that the "Lost Comet"

was found.

That comets do experience a resistance, is undeniable; but not in the

way astronomers suppose, if these views be correct. The investigations

of Professor Encke, of Berlin, on the comet which bears his name, has

determined the necessity of a correction, which has been applied for

several returns with apparent success. But there is this peculiarity

about it, which adds strength to our theory: "The Constant of

Resistance" requires a change after perihelion. The necessity for this

change shows the action of the radial stream. From the law of this

force, (reckoning on the central plane of the vortex,) there is an

outstanding portion, acting as a disturbing power, in the sub-duplicate

ratio of the distances inversely. If we only consider the mean or

average effect in orbits nearly circular, this force may be considered

as an ablatitious force at all distances below the mean, counterbalanced

by an opposite effect at all distances above the mean. But when the

orbits become very eccentrical, we must consider this force as

momentarily affecting a comet's velocity, diminishing it as it

approaches the perihelion, and increasing it when leaving the

perihelion. A resolution of this force is also requisite for the comet's

distance above the central plane of the vortex, and a correction,

likewise, for the intensity of the force estimated in that plane. There

is also a correction necessary for the perihelion distance, and another

for the tangential current; but we are only considering here the general

effect. By diminishing the comet's proper velocity in its orbit, if we

consider the attraction of the sun to remain the same, the general

effect _may_ be (for this depends on the tangential portion of the

resolved force preponderating) that the absolute velocity will be

increased, and the periodic time shortened; but after passing the

perihelion, with the velocity of a smaller orbit, there is also

superadded to this already undue velocity, the expulsive power of the

radial stream, adding additional velocity to the comet; the orbit is

therefore enlarged, and the periodic time increased. Hence the necessity

of changing the "Constant of Resistance" after perihelion, and this will

generally be found necessary in all cometary orbits, if this theory be

true. But this question is one which may be emphatically called the most

difficult of dynamical problems, and it may be long before it is fully

understood.

According to the calculations of Professor Encke, the comet's period is

accelerated about 2 hours, 30 minutes, at each return, which he

considers due to a resisting medium. May it not rather be owing to _the

change of inclination of the major axis of the orbit, to the central

plane of the vortex_? Suppose the inclination of the _plane_ of the

orbit to remain unchanged, and the eccentricity of the orbit also, if

the longitude of the perihelion coincides with that of either node, the

major axis of the orbit lies in the ecliptic, and the comet then

experiences the greatest mean effect from the radial stream; its mean

distance is then, _ceteris paribus_, the greatest. When the angle

between the perihelion and the nearest node increases, the mean force of

the radial stream is diminished, and the mean distance is diminished

also. When the angle is 90d, the effect is least, and the mean distance

least. This is supposing the ecliptic the central plane of the vortex.

When Encke's formula was applied to Biela's comet, it was inadequate to

account for a tenth part of the acceleration; and although Biela moves

in a much denser medium, and is of less dense materials, even this taken

into account will not satisfy the observations,--making no other change

in Encke's formula. We must therefore attribute it to changes in the

elements of the orbits of these comets. Now, the effect of resistance

should also have been noticed, as an acceleration of Halley's comet in

1835, yet the period was prolonged. To show, that our theory of the

_cause_ of these anomalies corresponds with facts, we subjoin the

elements in the following tables, taken from Mr. Hind's catalogue: