Date of Longitude of Longitude of Difference of
Perihelion. Perihelion. nearest Node. Longitude.
1772 110d 14' 54" 74d 0' 1" 36d 14' 53"
1806 109 32 23 71 15 15 38 17 8
1826 109 45 50 71 28 12 38 17 38[43]
1832 110 55 55 68 15 36 41 45 19
1846 109 2 20 65 54 39 43 7 41
Between 1832 and 1846, the increase of the angle is twice as great for
Biela as for Encke, and the angle itself throws the major axis of Biela
10d above the ecliptic, whereas the angle made by Encke's major axis, is
only about 1d; the cosine of the first angle, diminishes much faster
therefore, and consequently the same difference of longitude between the
perihelion and node, will cause a greater acceleration of Biela; and
according to Prof. Encke's theory, Biela would require a resisting
medium twenty-five times greater than the comet of Encke to reconcile
observation with the theory. Halley's comet can scarcely be considered
to have had an orbit with perfect elements before 1835. If they were
known accurately for 1759, we should no doubt find, that the angle
between the node and perihelion _diminished_ in the interval between
1750 and 1835, as according to the calculations of M. Rosenberg, the
comet was six days behind its time--a fact fatal to the common ideas of
a resisting medium; but this amount of error must be received as only
approximate.
No comet that has revisited the sun, has given astronomers more trouble
than the great comet of 1843. Various orbits have been tried,
elliptical, parabolic and hyperbolic; yet none will accord with all the
observations. The day before this comet was seen in Europe and the
United States, it was seen close to the body of the sun at Conception,
in South America; yet this observation, combined with those following,
would give an orbital velocity due to a very moderate mean distance.
Subsequent observations best accorded with a hyperbolic orbit; and it
was in view of this anomaly, that the late Sears C. Walker considered
that the comet came into collision with the sun in an elliptical orbit,
and its _debris_ passed off again in a hyperbola. That a concussion
would not add to its velocity is certain, and the departure in a
hyperbolic orbit would be contrary to the law of gravitation. This
principle is thus stated by Newton:--"In parabola velocitas ubiquo
equalis est velocitati corporis revolventis in circulo ad dimidiam
distantiam; in ellipsi minor est in hyperbola major." (Vid. Prin. Lib.
1. Prop. 6 Cor. 7.)
But as regards the _fact_, it is probable that Mr. Walker's views are
correct, so far as the change from an ellipse to an hyperbola is
considered. The Conception observation cannot be summarily set aside,
and Professor Peirce acknowledges, that "If it was made with anything of
the accuracy which might be expected from Captain Ray, it exhibits a
decided anomaly in the nature of the forces to which the comet was
subjected during its perihelion passage." The comet came up to the sun
almost in a straight line against the full force of the radial stream;
its velocity must therefore necessarily have been diminished. After its
perihelion, its path was directly _from_ the sun, and an undue velocity
would be kept up by the auxiliary force impressed upon it by the same
radial stream; and hence, the later observations give orbits much larger
than the early ones, and there can be no chance of identifying this
comet with any of its former appearances, even should its orbit be
elliptical. This unexpected confirmation of the theory by the
observation of Capt. Ray, cannot easily be surmounted.
We must now endeavor to explain the physical peculiarities of comets, in
accordance with the principles laid down. The most prominent phenomenon
of this class is the change of diameter of the visible nebulosity. It is
a most singular circumstance, but well established as a fact, that a
comet contracts in its dimensions on approaching the sun, and expands on
leaving it. In 1829, accurate measures were taken on different days, of
the diameter of Encke's comet, and again in 1838. The comet of 1618 was
also observed by Kepler with this very object, and also the comet of
1807; but without multiplying instances, it may be asserted that it is
one of those facts in cometary phenomena, to which there are no
exceptions. According to all analogy, the very reverse of this ought to
obtain. If a comet is chiefly vaporous, (as this change of volume would
seem to indicate,) its approach to the sun ought to be attended by a
corresponding expansion by increase of temperature. When the contrary is
observed, and invariably so, it ought to be regarded as an index of the
existence of other forces besides gravitation, increasing rapidly in the
neighborhood of the sun; for the disturbing power of the sun's
attraction would be to enlarge the diameter of a comet in proportion to
its proximity. Now, the force of the radial stream, as we have shown, is
as the 2.5th power of the distances inversely. If this alternate
contraction and expansion be due to the action of this force, there
ought to be an approximate correspondence of the law of the effect with
the law of the cause. Arago, in speaking of the comet of 1829, states,
"that between the 28th of October and the 24th of December, the volume
of the comet was reduced as 16000 to 1, the change of distance in the
meantime only varying about 3 to 1." To account for this, a memoir was
published on the subject by M. Valz, in which he supposes an atmosphere
around the sun, whose condensation increases rapidly from superincumbent
pressure; so that the deeper the comet penetrates into this atmosphere
the greater will be the pressure, and the less the volume. In this it is
evident, that the ponderous nature of a resisting medium is not yet
banished from the schools. In commenting on this memoir, Arago justly
observes, that "there would be no difficulty in this if it could be
admitted that the exterior envelope of the nebulosity were not permeable
to the ether; but this difficulty seems insurmountable, and merits our
sincere regret; for M. Valz's ingenious hypothesis has laid down the law
of variation of the bulk of the nebulosity, as well for the short-period
comet as for that of 1618, with a truly wonderful exactness." Now, if we
make the calculation, we shall find that the diameter of the nebulosity
of a comet is inversely as the force of the radial stream. This force is
inversely as the 2.5 power of the distances from the axis, and not from
the sun: it will, therefore, be in the inverse ratio of the cosine of
the comet's heliocentric latitude to radius, and to this ratio the
comet's distance ought to be reduced. But, this will only be correct for
the same plane or for equal distances above the ecliptic plane,
considering this last as approximately the central plane of the vortex.
From the principles already advanced, the radial stream is far more
powerful on the central plane than in more remote planes; therefore, if
a comet, by increase of latitude, approaches near the axis, thus
receiving a larger amount of force from the radial stream in that plane
than pertains to its actual distance from the sun, it will also receive
a less amount of force in that plane than it would in the central plane
at the same distance from the axis. Now, we do not know the difference
of force at different elevations above the central plane of the vortex;
but as the two differences due to elevation are contrary in their
effects and tend to neutralize each other, we shall make the calculation
as if the distances were truly reckoned from the centre of the sun.
The following table is extracted from Arago's tract on Comets, and
represents the variations of the diameter of Encke's comet at different
distances from the sun,--the radius of the orbis magnus being taken as
unity.
Times of observation, Distances of the Real diameters
1828. comet from the sun. in radii of the earth.
Oct. 28 1.4617 79.4
Nov. 7 1.3217 64.8
Nov. 30 0.9668 29.8
Dec. 7 0.8473 19.9
Dec. 14 0.7285 11.3
Dec. 24 0.6419 3.1
In order the better to compare the diameters with the force, we will
reduce them by making the first numbers equal.
Distances. Diameters. The 2.5th power Reduced
of the Distances. Diameters.
1.4617 79.4 2.58 2.58
1.3217 64.8 2.10 2.10
0.9668 29.8 0.92 0.97
0.8473 19.9 0.66 0.65
0.7285 11.3 0.45 0.37
0.5419 3.1 0.21 0.10
This is a very close approximation, when we consider the difficulty of
micrometric measurement, and the fact, that as the comet gets nearer to
the sun, as at the last date of the table, the diameter is more than
proportionally diminished by the fainter nebulosity becoming invisible.
But, there may be a reality in the discrepancy apparent at the last
date, as the comet was then very near the plane of the ecliptic, and
was, consequently, exposed to the more violent action of the radial
stream.
To attempt to explain the _modus agendi_ is, perhaps, premature. Our
principal aim is to pioneer the way into the labyrinth, and it is
sufficient to connect this seeming anomaly with the same general law we
have deduced from other phenomena. Still, an explanation may be given in
strict accordance with the general principles of the theory.
Admitting the _nucleus_ of a comet to be gaseous, there is no difficulty
about the solution. According to Sir John Herschel, "stars of the
smallest magnitude remain distinctly visible, though covered by what
appears the densest portion of their substances; and since it is an
observed fact, that the large comets which have presented the appearance
of a nucleus, have yet exhibited no phases, though we cannot doubt that
they shine by the reflected solar light, it follows that even these can
only be regarded as great masses of thin vapor." That comets shine
solely by reflected solar light, is a position that we shall presently
question; but that they are masses of vapor is too evident to dispute.
According to the same authority quoted above, "If the earth were reduced
to the one thousandth part of its actual mass, its coercive power over
the atmosphere would be diminished in the same proportion, and in
consequence the latter would expand to a thousand times its actual
_bulk_." If this were so, and comets composed of the elementary gases,
some of them would have very respectable masses, as the nuclei are
frequently not more than 5,000 miles in diameter, and consequently it
becomes important to examine the principle. From all experiments the
density of an elastic fluid is directly as the compressing force; and if
a cylinder reached to the top of our atmosphere, compressed by the
gravitation of the earth, considered equal at each end of the cylinder,
it would represent the actual compressing force to which it owes its
density. If the gravitation of the earth were diminished one thousand
times this atmospheric column would expand one thousand times,[44]
(taking no account of the decrease of gravitation by increase of
distance;) so that the diameter of the aerial globe would be increased
to 108,000 miles, taking the atmosphere at 50 miles. But the mere
increasing the _bulk_ of the atmosphere 1000 times would increase the
diameter to little more than double. Even giving the correct expansion,
a comet's mass must be much greater than is generally supposed, or the
diameters of the nuclei would be greater if composed of any gas lighter
than atmospheric air.
It is very improbable that a comet is composed of only one elementary
gas, and if of many, their specific gravities will vary; the lighter, of
course, occupying the exterior layers. With such a small mass,
therefore, the upper portion of its atmosphere must be very attenuated.
Now let us remember that the density of the ether at a comet's aphelion,
is greater than at the perihelion, in the direct ratio of the square
roots of the distances from the sun nearly. At the aphelion the comet
lingers through half his period, giving ample time for the nucleus to be
permeated by ether proportionally dense with the surrounding ether of
the vortex at that distance. Thus situated, the comet descends to its
perihelion, getting faster and faster into a medium far less dense, and
there must consequently be an escape from the nucleus, or in common
parlance, the comet is positively electric. This escaping ether, in
passing through the attenuated layers composing the surface of the
nucleus, impels the lighter atoms of cometic dust further from the
centre, and as for as this _doubly_ attenuated atmosphere of isolated
particles extends, so far will the escaping ether be rendered luminous.
It may be objected here, that a contrary effect ought to be produced
when the comet is forsaking, its perihelion; but the objection is
premature, as the heat received from the sun will have the same effect
in increasing the elasticity, as change of density, and the comet will
probably part with its internal ether as long as it is visible to the
earth; and not fully regain it perhaps, until after it arrives at its
aphelion. Suppose that we admit that a comet continues to expand in the
same ratio for all distances, as is laid down for the comet of Encke
when near its perihelion; it would follow, that the comet of 1811, would
have a diameter at its aphelion of fifty millions of millions of miles,
that is, its outside would extend one thousand times further from the
sun, at the opposite side to that occupied by the centre of the comet,
than the distance of the comet's centre from the sun, at its enormous
aphelion distance. Such an absurdity shows us that there is a limit of
expansion due to natural causes, and that if there were no radial stream
the volume of a comet would be greatest when nearest the sun.
But while the comet is shortening its distance and hastening to the sun
in the form of a huge globular mass of diffuse light, it is continually
encountering another force, increasing in a far more rapid ratio than
the law of gravitation. At great distances from the sun, the force of
the radial stream was insufficient to detach any portion of the comet's
atmosphere; presently, however, the globular form is changed to an
ellipsoid, the radial stream begins to strip the comet of that doubly
attenuated atmosphere of which we have spoken, and the diameter of the
comet is diminished, merely because the luminosity of the escaping ether
is terminated at the limit of that atmosphere. Meanwhile the mass of the
comet has suffered only an infinitely small diminution; but if the
perihelion distance be small, the force may become powerful enough to
detach the heavier particles of the nucleus, and thus a comet may suffer
in mass by this denudating process. We regard, therefore, the nucleus of
a comet to represent the mass of the comet and the coma, as auroral rays
passing through a very attenuated envelope of detached particles. The
individual gravitating force of these particles to the comet's centre,
may be therefore considered as inversely as the squares of the
distances, and directly as the density of the particles; and this
density will, according to analogical reasoning, be as the distances or
square roots of the distances;--grant the last ratio, and the
gravitating force of the particles composing the exterior envelope of a
comet, becomes inversely as the 2.5th power of the distances from the
comet's centre.[45] This being the law of the radial stream, it follows,
of course, that a comet's diameter is inversely as the force of the
radial stream. It must, however, be borne in mind, that we are speaking
of the atomic density, and not of density by compression; for this
cometary dust, which renders luminous the escaping ether of the nucleus,
must be far too much diffused to merit the name of an elastic fluid. May
not the concentric rings, which were so conspicuous in the comet of
1811, be owing to differences in the gravitating forces of such
particles, sifted, as it were, and thus arranged, according to some
ratio of the distances, by the centripulsive force of the electric coma,
leaving vacant intervals, through which the ether passed without
becoming luminous? This at least is the explanation given by our theory.
We may, indeed, consider it possible that the escaping ether, when very
intense, might be rendered luminous by passing into the surrounding
ether, and, as it became more diffused by radiation, at last become
invisible. In this case, as the law of radiation is as the squares of
the distances from the centre inversely, the rays would be more and more
bent at right angles, or apparently shortened, as the power of the
radial stream increased, and the apparent diameters of the coma would
be diminished faster than the ratio of the 2.5th power of the distances.
But whichever view we adopt, the diameter would again increase in the
same ratio on leaving the sun, if we make allowance for increase of
temperature, as well as for diminution of density, for the ordinary
distance of a comet's visibility. We, however, regard the change of
diameter, as due to both these nodes of action, as best agreeing with
the indications afforded by their tails.
From the preceding remarks, it results that the density of the particles
producing the nebulous envelope of a comet, renders the variations of
diameter only approximate to the law of the radial stream; a comet's own
electric energy, or the intensity of the escaping ether, may also modify
this expression, and many other causes may be suggested. That the radial
stream is the cause, in the way we have pointed out, is proved by the
positions of the major axis of the short-period comet, making frequently
nearly a right angle with the radius vector of the orbit in 1828. A soap
bubble gently blown aside, without detaching it from the pipe, will
afford a good illustration of the mode, and a confirmation of the cause.
The angles measured by Struve, reckoned from the radius vector,
prolonged towards the sun, are subjoined:
November 7 99d.7 | December 7 154d.0
November 30 145 .3 | December 14 149 .4
At this last date, the comet was getting pretty close to the sun. When
the angle was greater, as on November 7th, the comet appeared to make
almost a right angle with the radius vector; and in this position of the
earth and comet, the longer axis of the elliptical comet was directed to
the axis of the vortex, as may be verified by experiment. At the later
dates, the comet was more rapidly descending, and, at the same time, the
axis of the comet was getting more directed towards the earth; so that
the angle increased between this axis and the radius vector, and
consequently became more coincident with it. We have now to consider the
luminous appendage of a comet, commonly called a tail.
The various theories hitherto proposed to account for this appendage are
liable to grave objections. That it is not refracted light needs not a
word of comment. Newton supposes the tail to partake of the nature of
vapor, rising from the sun by its extreme levity, as smoke in a chimney,
and rendered visible by the reflected light of the sun. But, how vapor
should rise towards opposition in a vacuum, is utterly inexplicable. In
speaking of the greater number of comets near the sun than on the
opposite side, he observes: "Hinc etiam manifestum est quod coeli
resistentia destituuntur."[46] And again, in another place, speaking of
the tail moving with the same velocity of the comet, he says: "Et hinc
rursus colligitur spatia coelestia vi resistendi destitui; utpote in
quibus non solum solida planetarum et cometarum corpora, sed etiam
rarissimi candarum vapores motus suos velocissimos liberrime peragunt ac
diutissime conservant." On what _principle_, therefore, Newton relied to
cause the vapors to ascend, does not appear. Hydrogen rises in our
atmosphere because specifically lighter. If there were no atmosphere,
hydrogen would not rise, but merely expand on all sides. But, a comet's
tail shoots off into space in a straight line of one hundred millions of
miles, and frequently as much as ten millions of miles in a single day,
as in the case of the comet of 1843. Sir John Herschel observes, that
"no rational or even plausible account has yet been rendered of those
immensely luminous appendages which they bear about with them, and which
are known as their tails." Yet, he believes, and astronomers generally
believe, that a comet shines by reflected light. This theory of
reflexion is the incubus which clogs the question with such formidable
difficulties; for, it follows, that the reflecting matter must come
from the comet. But, what wonderful elements must a comet be made of, to
project themselves into space with such immense velocity, and in such
enormous quantities as to exceed in volume the body from which they
emanate many millions of times. This theory may be, therefore, safely
rejected.
From what we have already advanced concerning the coma or nebulosity of
the comet, we pass by an easy path to an explanation of the tail. In the
short-period comets, the density of the elementary atoms is too great to
be detached in the gross from the nucleus, or, rather, the density of
the atoms composing the nucleus is too great to permit the radiating
stream of the comet carrying them to a sufficient distance to be
detached by the radial stream of the sun. Hence, these comets exhibit
but very little tails. We may also conceive, that the continual siftings
which the nucleus undergoes at each successive perihelion passage, have
left but little of those lighter elements in comets whose mean distances
are so small. Yet, again, if by any chance the eccentricity is
increased, there are two causes--the density of the ether, and the heat
of the sun--which may make a comet assume quite an imposing appearance
when apparently reduced to the comparatively passive state above
mentioned.
According to our theory, then, the coma of a comet is due to the
elasticity of the ethereal medium within the nucleus, caused both by the
diminished pressure of the external ether near the sun, and also by the
increased temperature acting on the nucleus, and thus on the involved
ether. The tail, on the contrary, is caused by the lighter particles of
the comet's attenuated atmosphere being blown off by the electric blast
of the radial stream of the solar vortex, in sufficient quantities to
render its passage visible. It is not, therefore, reflected light, but
an ethereal stream rendered luminous by this detached matter still held
in check by the gravitating force of the sun, whose centre each
particle still respects, and endeavors to describe such an orbit as
results from its own atomic density, and the resultant action of both
the acting forces. From the law of density of the ether, the coma ought
to be brightest and the radiating stream of the comet's nucleus
strongest on the side of least pressure: from this cause, and the fact
that the body of the comet affords a certain protection to the particles
immediately behind it, there will be an interval between the comet and
the tail less luminous, as is almost invariably observed. We thus have
an explanation of the fact noticed by Sir John Herschel, "that the
structure of a comet, as seen in section in the direction of its length,
must be that of a hollow envelope of a parabolic form, enclosing near
its vertex the nucleus or head." We have, also, a satisfactory
explanation of the rapid formation of the tail; of its being wider and
fainter at its extremity; of its occasional curvature; and of its
greater length after perihelion than before. But, more especially may we
point to the explanation which this theory gives of the fact, that,
_ceteris paribus_, the long-period comets, when their perihelion
distances are small, have tails of such exaggerated dimensions.
A comet, whose mean distance is considerable, is supposed by the theory
to be composed of elements less dense, and, during its long sojourn at
its aphelion, it may be also supposed that it there receives continual
accessions to its volume from the diffused siftings of the system, and
from the scattered debris of other comets. On approaching the
perihelion, the rapidity of the change in the density of the ether in a
given time, depends on the eccentricity of the orbit, and so does the
change of temperature; so that, from both causes, both the length of the
tail and the brilliancy of the comet measurably depends on the magnitude
of the period and of the eccentricity.
If the nuclei of comets be gaseous as we suppose, and that the smallest
stars are visible through them, it is an outrage on common sense, to
refer that light, which renders a comet visible at noon-day, within six
minutes of space of the sun itself, to the reflected light of the sun.
When a small star has been seen through the nucleus of a comet, without
any perceptible diminution of light, it indicates perfect transparency;
but there can be no reflection from a perfectly transparent body, and
therefore, a comet does not shine by reflected light. It is true that
Arago discovered traces of polarized light in the comet of 1819, and
also in more recent comets, but they are mere traces, and Arago himself
admits, that they do not permit "the conclusion decidedly that these
stars shine only with a borrowed light." But it still does not follow
that a comet (even if independent of reflected light) is in an
incandescent state. The auroral light is not polarized, nor any other
electric light, neither is it owing to a state of incandescence, yet it
is luminous. The intense light of a comet at perihelion is analogous to
the charcoal points of a galvanic battery, caused by a rapid current of
ether from the nucleus, and assisted by the radial stream of the vortex.
This will account for the phenomenon in all its shades of intensity, as
well as for the absence of any perceptible phase. It will also account
for the non-combustion of such comets as those of the years 1680 and
1843. We shall also be at no loss to understand, why there is no
refraction when a ray of light from a star passes through the nebulosity
of a comet; and if, as we may reasonably suppose, the gaseous matter
composing the nucleus be very attenuated, instruments are yet too
imperfect to determine whether these also have any refracting power. On
this point, however, it is safest to suspend our judgment, as there may
be comets not belonging to our system, with even liquid or solid nuclei,
or of matter widely different to those elements composing the members of
the solar system.
In addition to what has been already advanced on this subject of a
comet's light, we may appeal to the well-known fact that the visibility
of a comet is not reciprocally as the squares of the distances from the
earth and sun as it ought to be, if shining by reflected light. In
Mr. Hind's late work on comets, the fact is stated that "Dr. Olbers
found that the comet of 1780 attained its greatest brightness on the 8th
of November, thirteen days subsequent to its discovery, whereas
according to the law of reflected light, it should have become gradually
fainter from the day of its discovery; and supposing the comet
self-luminous, the intensity of light should have increased each day
until November 26th; yet in the interval between the 8th and 26th of
that month, it grew rapidly less." Now this theory teaches, that a comet
is neither self-luminous nor dependent on the sun, but on its distance
from the axis of the vortex, and a certain amount of elapsed time from
the perihelion, varying somewhat in each particular case. This fact is
therefore a very strong argument in favor of our theory.
Amidst the many anomalous peculiarities of comets, it has been noticed
that a short tail is sometimes seen at right angles to the principal
tail, and in a few cases pointing directly towards the sun. Much of this
may be owing to perspective, but granting the reality of the fact, it is
still explicable on the same general principles.
In speaking of the modifying causes which influence the weather, we
mentioned the effect due to the position of the sun with respect to the
axis of the vortex. This will be found to have a sensible effect on the
action of the radial stream. The natural direction of a comet's electric
stream is _towards_ the axis of the vortex, and in the central plane of
the vortex it will be also towards the sun. But this stream is met by
the stronger radial stream from the axis, and as Mr. Hind describes it,
"is driven _backward_ in two streams passing on either side of the head,
and ultimately blending into one to form the tail." Now, if the body of
the sun be situated between the comet and the axis of the vortex, it
will shield the comet from the action of the radial stream, and thus a
tail may really point towards the sun.
In 1744 a brilliant comet exhibited six distinct tails spread out like a
fan, some seven days after its perihelion passage; its distance from
the sun at the time not being more than a third of the earth's distance.
The comet was then rapidly approaching the plane of the ecliptic, and if
we make the calculation for the position of the sun, we shall find that
the body of the sun was on the same side of the axis of the vortex as
the comet, and that the comet was then situated at the boundaries of the
conical space, enclosed by the radial stream in its deflected passage
round the body of the sun. In this position there are numerous cross
currents of the stream, and hence the phenomenon in question. As this
fact rests on the testimony of one individual, and is an occurrence
never recorded before or since, many are disposed to doubt the fact, yet
our theory explains even this peculiarity, and shows that there is no
necessity for impugning the statement of Cheseaux.
Another unexplained phenomenon is the corruscation of the tail. It has
been attempted to explode this fact also, by referring it to conditions
of our own atmosphere; and it is generally considered the argument of
Olbers, founded on the great length of the tail and the velocity of
light, is sufficient to prove that these corruscations are not actually
in the tail. Now, it is undoubtedly true, that as light travels less
than two hundred thousand miles in a second, and a comet's tail is
frequently one hundred millions long, it is impossible to see an
instantaneous motion along the whole line of the tail; but granting that
there are such flickerings in the tail as are described by so many, it
must necessarily be, that these flickerings will be _visible_. It would
be wonderful indeed, if a series of waves passing from the comet to the
extremity of the tail, should have their phases so exactly harmonizing
with their respective distances as to produce a uniform steady light
from a light in rapid motion. The argument, therefore, proves too much,
and as it is in the very nature of electric light thus to corruscate, as
we see frequently in the northern lights, we must be permitted still to
believe that not only the tails, but also the heads of comets do really
corruscate as described.
With respect to the direction of the tail, astronomers have been forced
to abandon the antiquated notion, that the tail always pointed directly
from the sun; yet they still pertinaciously cling to the idea, that
although this is not always the case, the tail only deviates from this
direction _in the plane of the orbit_. As this is a most important
question, it is necessary formally to protest against such a conclusion.
If the earth should happen to be in the plane of the comet's orbit and
the tail appears in that plane, it must of course be in that plane
_really_; but if the earth is not in the plane of the comet's orbit, the
tail is not _necessarily_ in the same plane, whatever its apparent
direction may indicate. It is true there is a tendency of every particle
of the tail, moving under the restraining influence of the sun's
attraction, to continue in the plane of the orbit; and in certain
positions there is no oblique action arising from the force of the
radial stream to cause it to deviate from that plane; yet in other
positions of the comet, the action of the radial stream may be oblique,
forcing it out of that plane, and still such a direction might be
assigned to it as to make it conform. In the comet of 1843, P. Smythe
observed a forked tail 25d long on March 3d, and from the end of the
forked tail, and from its _north_ side, a streamer diverged at an angle
of 6d or 7d to the _north_. As this was contrary to the _direction_ of
the curvature, if the tail had been curved, it could only arise from a
portion being driven off by the radial stream, or bent towards the plane
of the ecliptic. The curvature observed by others at a later date, was
concave to the south. Towards the middle and close of March, the tail
became straight, and with the above exception, might be considered to
move in the plane of the orbit.
The celebrated comet of Halley, as observed by Dr. Bessel in 1835,
showed that a more or less well-defined tuft of rays emanated from that
part of the nucleus which was turned towards the sun; and the rays being
_bent backward_ formed a part of the tail. The nucleus, with its
emanations, presented the appearance of a burning rocket, the end of
which was turned sideways by the force of the wind. And, Bessel
concludes: "That the cone of light issuing from the comet deviated
considerably both to the right and left of the true direction of the
sun, but that it always returned to that direction, and passed over to
the opposite side; so that the cone of light, and the body of the comet
from whence it emanated, experienced a rotatory, or, rather, a vibrating
motion _in the plane of the orbit_." It is impossible that Bessel should
here mean that this motion was certainly in the plane of the orbit; for
the orbit was then viewed sideways, and he had no means of ascertaining
the fact. His meaning must be that it was apparently in the plane of the
orbit. If a plane be made to pass through the earth, the comet, and the
sun, the tail might be placed in any position in that plane, and yet
appear to be at the intersection of the two; that is, in the plane of
the comet's orbit. The vibration of the tail, in this case, is another
strong proof of the correctness of our theory. To make it more
intelligible, we shall resort to a diagram.
In the following diagram, the comet's orbit, represented by the dotted
line, is drawn on the plane of the ecliptic; it is, therefore, necessary
to bear in mind, that it is tilted up from the line of nodes SN, at an
angle of 17d 45'. The position of the comet, October 9th, is at C,
approaching its perihelion; that of the earth at the same time at T;
while S represents the sun, and SQ the line of equinoxes. Now, from a
cause already explained, the tail always tends to lay behind the comet,
in the direction indicated by the lower tail in the diagram at 1, and,
if produced, would pass to the left of the sun, as seen from the earth:
the force of the radial stream, however, will not allow this lagging of
the tail, and it is straightened out by this force; but, being directed
to the axis of the vortex, and not to the sun, it is not really in the
plane of the orbit, but is seen in the direction of the upper tail
depicted in the diagram at 3, and, if produced, would pass to the right
of the sun, as seen from T. Now, there is an intermediate position of
the tail, in which it will appear in the prolongation of the radius
vector SC; this position is represented by the middle or central tail of
the comet at 2, yet this is not in the plane of the orbit, it only
appears to be, as may be readily understood by remembering that the
earth at this time is under this plane, and the comet is seen at a
considerable elevation above the plane of the ecliptic. When the comet's
tail becomes directed to the axis of the vortex, or in the _apparent_
position of No. 3, the comet, rapidly careering on its way to the sun,
again leaves the tail behind, and again it is strengthened out by the
radial stream oscillating about the mean position at 2, as observed by
Bessel. From this, it appears, that there is no necessity to make
confusion worse confounded, by resorting to polar forces, which are
about as intelligible as the foundations of the pillars of Atlas.
[Illustration: Fig. 25]
It may be objected that the continued action of the radial stream with
that velocity we have contended for, ought to keep the tail invariably
directed from the axis of the vortex; but, where there are two forces or
tendencies, as in this case, analogy would teach us that a certain
degree of oscillation is a necessary result. There may, also, be slight
and transient changes in the direction of the radial stream. In the
hurricane there are short and fitful blasts inclined to the general
direction of the wind, which must arise from the inertia of the moving
mass of atmosphere, causing temporary condensations and rarefactions. Be
this as it may, we have assigned a cause which satisfies the phenomenon,
without coming into collision with a single principle of celestial
mechanics.
Prof. Struve compared the tail of this comet to a flame, or "ray of fire
shot out from the nucleus, as from some engine of artillery, and driven
on one side by the wind." At the same time, he saw a second emanation
nearly in the opposite direction. This last might arise from a momentary
fluctuation in the relative intensities of the electric radiation of the
comet, and of the radial stream, owing to the probable irregularities
just alluded to. Such and kindred phenomena are utterly inexplicable,
without we adopt the theory we are advocating. One other feature, and we
will leave the subject.
From our explanation of the solar spots, we inferred the existence of
another large planet in the system. Might not the same effect be
produced by a comet? Or may there not be so many comets, whose great
elongation, combined with even a moderate mass, may render it impossible
to calculate the position of the sun with respect to the central axis of
the vortex,--always considering this last as the axis of equilibrium? In
a general way, we might say that the very number of comets in all
directions and all distances, would tend to neutralize each other's
effects; but we are not under this necessity. A comet, moving in a
parabola, does not belong to the system or to the rotating vortex; and
the periodic comets, if of gaseous elements, (as seems so probable,)
must, from the size of their nuclei, which the theory considers the only
part constituting their mass, have far less mass than the very smallest
of the asteroids, and consequently could have very little effect on the
mechanical balance of the vortex, even if elongated as far as the orbit
of Neptune. Did we know the influence of cold in limiting the
expansibility of the elementary gases, we might approximately determine
the mass of a comet, from the size of its nucleus; but this is a problem
that has never yet been solved; and astronomers ought to avail
themselves of every indication which promises to realize this great
desideratum. The grand comet of 1556 is now probably approaching, and,
from recent investigations, it appears that it will arrive at its
perihelion in 1858,--subject to an error either way of about two years.
An opportunity may thus be presented of determining the mass of one of
the largest comets on record, which may not again occur. This arises
from the possible appulse of the comet to the planet Pallas, whose mass,
being so small, would more sensibly be disturbed by such an appulse than
the earth. As the inclinations and ascending nodes of the two orbits
approximately coincide, and as Pallas will be near the comet's path, on
the approach of the latter to the sun, at the beginning of the year
1857, should the comet become visible about that time, a very close
appulse is possible. It is not unlikely, also, that if the elements of
Pallas were so far perfected as to afford reliable indications, that the
near approach of the comet might thus be heralded in advance, and lead
to an earlier detection of its presence. Would it not be a worthy
contribution to science, for some one possessing the necessary leisure,
to give an ephemeris of the planet for that epoch; as a very slight
change in Mr. Hind's elements of the comet, would cause an actual
intersection of the two orbits in about heliocentric longitude 153d? The
subsequent nodal passage of Pallas will take place near opposition, and
be very favorably situated for determining the instant of its passage;
and, of all the elements, this would be more likely to be affected than
any other.[47]