Smiling the prayer that on thy lips has hung
While ages traveled. Still thou kneel’st among
The quiet tombs. Impassioned joy or spleen
Moves not thy face—in part to heaven addressed,
In part to the green hills thy feet have clomb.
Image of what is past, and what shall come!
Silent as death, which thou embodiest
Far more than life. Mute sentry! stood between
The crumbled mortal and ascended sprite!
Has thou no sense for what is, or has been?
Can nothing break thy sepulchre of rest?
Once thy heart throbbed with human motion keen,
Thy folded hands with others warmly pressed,
Thy close-sealed lips have sweetly spoke or sung—
Now an eternity is not more dumb!
The organ peels around thee its deep notes;
But thou art deaf to music’s noblest strains.
A glory of rich hues about thee floats;
Thou car’st not for the splendor of bright panes.
What fateful storms and changes hast thou seen!
How little dost thou heed the mad world’s hum!
Our childhood knew thee as doth now our age—
Time stirs not thee. Where art thou all this space,
The part of thee which not in stone remains,
While wondering centuries roll past thy place?
They change and cease: the whole world turns a page—
But thou still wear’st that smile upon thy face.
COMETS.
By RICHARD A. PROCTOR.
During the last two years several comets—some telescopic, others
visible to the naked eye, and even conspicuous objects in the
heavens—have been observed, not only by the older methods, but by some
which have only been available within recent years. It is naturally
expected, therefore, by the general public that some new light should
be thrown on these mysterious objects, whose phenomena still remain
among the unexplained, seemingly the inexplicable problems of the
celestial depths.
We propose to consider here what has thus been learned, and what also
(unfortunately it is much more) remains still to be learned, respecting
comets. But first it will be well to show what are the special
phenomena which present themselves for explanation.
A comet apparently comes out from the remote depths of space in a
condition of comparative calm. It appears as a small round nebulous
object, looking like a tiny cloud of extreme tenuity—the idea of
tenuity being suggested by the exceeding faintness of the comet’s
light. This cloud appears somewhat condensed toward the middle. As the
comet draws nearer to the sun, it usually grows somewhat long in the
direction of the sun; and before long a portion within the part nearest
the sun is seen to be brighter than the rest, and to have a more or
less defined outline. This is the _nucleus_—sometimes seen as a dull
disc of nearly uniform brightness, at others as a mere bright point not
unlike a star. The fainter light around this is the _coma_, or hair,
which resembles a luminous fog round the nucleus, usually brighter on
the side toward the sun, and on the other side growing fainter and
fainter till it can no longer be seen. Later this lengthening of the
comet in directions toward and from the sun becomes more marked, until
at length the comet may fairly be said to have a head directed toward
the sun and a tail directed from him. Nucleus, coma, and tail may be
very different in appearance in different comets, and in particular the
tail may be more or less complicated in structure, being sometimes a
mere straight streak, at others twofold, multiple, curved, with thwart
streaks, and so forth—no two comets, in fine, having tails resembling
each other except in general details.
Dr. Huggins, in a rather disappointing article on comets, recently
communicated to a contemporary, remarks that the nucleus, though an
apparently insignificant speck, “is truly the heart and kernel of the
whole thing—potentially it is the comet.” This has scarcely yet been
proved, though it appears exceedingly probable. It is true, however,
as he adds, that this part only of the comet conforms rigorously to
the laws of gravitation, and moves strictly in its orbit. “If we
could see a great comet,” he proceeds, “during its distant wandering,
when it has put off the gala trappings of perihelion excitement, it
would appear as a very sober object, and consist of little more than
nucleus alone.” This again seems probable, though it has never yet
been proved, and the division of some comets into two or more parts,
each having coma, nucleus, and tail of its own, shows that the nucleus
cannot be, in every case, what Dr. Huggins seems here to suggest.
Dr. Huggins has done well in saying (though scarcely with sufficient
emphasis, considering how often the mistake is repeated) that “though
many telescopic comets are of extremely small mass, nucleus included—so
small, indeed, that they are unable to perturb such small bodies as
Jupiter’s satellites—yet we should mistake greatly if we were to
suppose that all comets are ‘airy nothings.’ In some large comets the
nucleus may be a few hundred miles in diameter, or even very much
larger, and may consist of solid matter. It is not necessary to say
that the collision of a cometary nucleus of this order with the earth
would produce destruction on a wide scale.”
It is even more necessary to correct the widely-spread misapprehension
as to the relations between meteors and comets. We hear it stated that
the nucleus of a comet is made up of meteoric stones (Professor P. G.
Tait says—for unknown reasons—that they resemble “paving stones or even
bricks”) as confidently as though the earth had at some time passed
through the nucleus of a comet, and some of our streets were now paved
with stones which had fallen to earth on such an occasion. As a matter
of fact, all that has yet been proved is that meteoric bodies follow
in the track (which is very different from the tail) of some known
comets, and that probably all comets are followed by trains of meteors.
These may have come out of the head or nucleus in some way as yet
unexplained; but it is by no means certain that they have done so, and
it is by many astronomers regarded as more than doubtful.
The most important points to be noticed in the behavior of large
comets, as they approach the sun, is that usually the side of the
coma which lies toward the sun is the scene of intense disturbance.
Streams of luminous matter seem to rise continually toward the sun,
attaining a certain distance from the head, when, assuming a cloud-like
appearance, they seem to form an envelope around the nucleus. This
envelope gradually increases its distance from the sun, growing fainter
and larger, while within it the process is repeated, and a new envelope
is formed. This in turn ascends from the nucleus, expanding as it does
so, while within it a new envelope is formed. Meanwhile, the one first
formed has grown fainter, perhaps has disappeared. But sometimes the
process goes on so rapidly (a day or two sufficing for the formation
of a complete new envelope) that several envelopes will be seen at the
same time, the outermost faintest, the innermost most irregular in
shape and most varied in brightness, while the envelope or envelopes
between are the best developed and most regular.
The matter raised up in these envelopes seems to have undergone a
certain change of character, causing it no longer to obey the sun’s
attractive influence, but to experience a strong repulsive action
from him, whereby it is apparently swept away with great rapidity to
form the tail. “It flows past the nucleus,” says Dr. Huggins, “on
all sides, still ever expanding and shooting backward until a tail
is formed in a direction opposite to the sun. This tail is usually
curved, though sometimes rays or extra tails sensibly straight are
also seen.” The description is, however, incomplete in one important
respect. The matter raised from the nucleus to form the envelopes may
be, and probably is, carried past the nucleus on all sides; but the
appearance presented by the tail just behind the nucleus is not exactly
in accordance with our ideas as to what should result from the flowing
past “on all sides.” There is a dark space immediately behind the
nucleus, that is, where the nucleus, if solid, would throw its shadow,
if there were matter to receive the light all around so that the shadow
could be seen. Now it may be thought at first that this corresponds
exactly with what should be seen: when we look just behind the nucleus
there is no light, or very little; when we look on either side of that
dark space there is the luminous matter which has been driven back from
the envelopes in front of the nucleus. But if the luminous matter flows
past the nucleus _on all sides_, it must flow past the nucleus on the
side nearest to the observer, and also on the side farthest away; and
it is just where the line of the sight passes through these two regions
of brightness that a dark streak is seen just behind the nucleus. Let
the reader draw two concentric circles—one an inch in diameter, the
other two inches—and let him then draw two parallel tangents to the
inner circle on opposite sides of it. Supposing now the space between
the two circles to represent in section the luminous matter which flows
all round the nucleus, while the surface of the inner circle represents
the unilluminated part behind the nucleus, the two tangent lines
will represent the lines of sight on either side of the dark region,
where as we might expect, we get plenty of light; and we can also
understand very well why outside of that the line of sight through the
luminous matter (or the chords to our outer circle), getting shorter
and shorter, the light of the luminous streaks bounding this part of
the tail gets fainter and fainter; but if just inside either of the
two tangents, chords are drawn parallel to them, crossing the inner
circle, the parts of these chords which lie between the two circles
are very nearly equal in length to the tangent lines themselves; and
even a common diameter to both circles has, lying between them, two
portions together equal to the radius of the outer. Hence, since the
line of sight even across the middle of the space behind the nucleus,
passes through a considerable range of luminous matter, while a line
within but near the outskirts of that space passes through nearly
as great a range of luminous matter as one just outside that space,
there should be plenty of light where yet to the eye there seems to
be something like absolute darkness. Either then the eye is greatly
deceived, or else we must find some explanation of darkness existing
where considerable brightness might be expected.[D]
The matter which forms the tail, seems, as I have said, to be swept
off from the envelopes raised by the sun’s action on the nucleus.
It seems as though the matter thus raised had undergone in some way
a change of character, which caused it no longer to obey the law of
gravity as it had done when forming part of the nucleus, but instead
of yielding to the sun’s attraction, to submit rather to an intense
repulsive action, carrying it at a much greater rate from the sun
than, under the action of gravity—starting from rest and free from all
perturbing influences—it could have been drawn toward him. Dr. Huggins
thus words his account of what seems to happen: “Now is seen to take
place a change which is most puzzling—namely, these envelopes of light
appear to give up their substance under the influence of a strong
repulsive force exerted from the sun, and to be forced backwards.” Sir
John Herschel, after his long and careful study of the comet of 1830
(Halley’s at its second return) came to the conclusion that repulsive
action exerted by the sun on the matter raised in these envelopes had
been distinctly proved.
Yet here, where we seem to have our first firm ground for hypothesis
respecting these mysterious objects—comets’ tails—we meet with
stupendous difficulties. Consider, for instance, the phenomena
presented by Newton’s comet. That comet had traversed the last ninety
millions of miles of its approach toward the sun in four weeks. At
the end of that time it passed out of view for a few days, having
then a tail ninety millions of miles, at least, in length. Four days
passed, and it reappeared on the other side of the sun—having in the
interval traversed nearly a semi-circle—in reality, of course, the
perihelion end of its long oval path. At its reappearance, it had a
tail still ninety millions of miles in length, but the tail with which
it reappeared had, of course, a direction entirely different from that
of the tail which had been seen before—the two directions were inclined
about one hundred and sixty degrees to each other. Now, as Sir John
Herschel remarks, we can not look on the tail of a comet as something
whirled round like a stick, as the comet circles round its perihelion
sweep. The tail with which the comet reappeared must have been an
entirely new formation. Nor can we doubt that if the comet had been
watched as it swept around the sun, the changes in the tail’s position
which had been observed to the time of disappearance, would have been
observed to progress continuously, the tail passing by a uniform motion
from the position it then had to that which it was observed to have
at the time of reappearance. So that we may fairly suppose the tail
with which the comet reappeared to have been formed in much less than
the time during which the comet had been out of sight. Probably its
farthest part had been formed in much less than a day, the part near
the head being, of course, formed later. But if the matter repelled
from the head was thus driven over a distance of ninety million miles
in twenty-four hours, at the outside, the average velocity of its
motion was about a thousand miles per second, or nearly three times as
great as the greatest velocity which the sun _can_ communicate by his
attractive energy to matter approaching him from without, even though
such matter come to him from an almost infinite distance, and in a
perfectly straight line—the conditions most favorable for giving a
high rate of final velocity. Such velocity as the sun can thus give by
his attractive energy is only given to matter which has been exposed a
long time to his influence; but here, in the tail of the great comet of
1680, matter seems to have acquired almost instantaneously a velocity
sufficing to carry it over ninety million miles with an average
speed three times as great as the sun can thus, after long effort,
communicate by means of his attractive power!
The difficulty is so great that many efforts—some bold and daring,
others positively wild in the unscientific absurdity of their
nature—have been made to overcome it.
Among the most ingenious of these is (or rather was, for I think it
is no longer maintained even by its eminent author), Prof. Tyndall’s
theory of a comet’s tail as an actinic cloud, generated by the
passage of the solar rays through exceedingly tenuous matter after
those rays had been in part deprived of their heating power, during
their passage through the comet’s head. According to this theory the
actinic cloud can not be formed under the heating rays, but so soon
as the actinic rays fall on the tenuous matter alone, the cloud is
formed,—so that all round the region in which would be the comet’s
shadow, there is no luminous cloud, while along that region the cloud
exists. The rapidity with which light travels would of course make
this explanation absolutely perfect in explaining cometic tails lying
always exactly in a straight line directed from the sun, or with their
axis so situated. But unfortunately this exceedingly rapid formation of
the tail (a tail of ninety million miles in length would be formed in
about eight minutes) is more than observation requires or can explain.
Prof. Tyndall made a slight oversight in dealing with this part of his
theory. Noticing that the actinic cloud, as he called it, is not formed
instantly, but after a delay of a few seconds, in his experiments, he
reasoned as though it would follow from this that the formation of
the actinic cloud behind a comet’s head in space might be a process
extending its action in distance from the head at a rate considerably
less than that at which light travels, yet still fast enough to account
for the exceedingly rapid formation of the tail of Newton’s comet,
and of other similar tails. But a little consideration will show that
the few seconds following the fall of light on the vapors dealt with
by Tyndall, before the luminous cloud appeared, would produce no such
effect as he imagined. The rate of formation of the tail would still
be that at which light travels. Imagine the head at A, for the sake of
argument, and the sun’s light after reaching A, passing on to B, C, D,
E, etc., to Z, a distance say of one hundred million miles, in nine
minutes:
A ... B ... C ... D ... E ... ... Z.
Suppose that, when the light has reached the vaporous matter lying at
B, an interval of one full minute (much greater than any noticed in
Tyndall’s experiments), occurs before the actinic cloud comes into
view, a similar interval after the light has passed C before the
cloud is seen there, and so on, up to the time of the arrival of the
light at Z. Professor Tyndall’s reasoning implied that all the time
intervals thus occurring at B, C, D, E, etc., up to Z, had to be added
together, to give the total time of the formation of the tail from A to
Z, and hence naturally a long time might elapse, and the head having
at the end of this time reached a different position from that which
it had occupied at the beginning, the divergence of the tail from
the direction exactly opposite to the sun, and the curvature of the
tail, would be alike readily accounted for. But what are the actual
facts of the case. The part of the tail formed latest by the supposed
solar actinic action, namely, the part at Z, would be formed just nine
minutes after the light had left A, and ten minutes after the part
nearest to A had been formed (by the same light waves), for, nine
minutes after leaving A, the light would be at Z, and a minute after
each epoch (according to our supposition) the actinic cloud would be
formed respectively at A and at Z. We get just the same interval—nine
minutes—whether the actinic cloud appears immediately after light has
traversed the vapour which is to form the cloud, or a minute after, or
an hour after. In every case the tail would be formed outwards from
A, at the rate at which light travels. This does not accord with the
phenomena—in fact, the supposition that a tail could be formed at the
rate at which light travels, will be found, on examination, to lead
to many most manifest absurdities, which Professor Tyndall doubtless
recognized when he sought escape from the supposition of such rapid
tail formation, through the effects he attributed to the delayed
appearance of the actinic cloud.
Another theory in explanation of the rapid formation of such a tail
as that of Newton’s comet is worthy of far less notice. Professor
Tyndall’s theory was based on an interesting physical fact, which he
had himself discovered, and which was also manifestly akin in character
to the formation of a comet’s tail. The one to be now noticed was
suggested to a mathematician by a rather familiar phenomenon, the
effects of which on his imagination he seems to have been never able to
entirely overcome—at any rate no amount of evidence against the theory
seems to counterbalance in his mind the notion once conceived that the
theory might be true. (It is a way some theorists have.)
Professor Tait was once looking at a part of the sky which seemed
clear. As he looked, a long streak rapidly formed, which presently
disappeared (if I remember his original description aright) almost as
rapidly as it had formed. At any rate, the appearance of the streak
was rapid enough to remind him of what astronomers said about the
rapid (apparent) development of comets’ tails. The phenomenon itself
was easily explained. There had been a flight of seabirds, traveling
after their wont in a widely extended layer, which when he began his
observations had been looked at somewhat aslant, so that—the distance
being too great for the birds to be seen individually—nothing of the
flight could be discerned at all. But it is evident that in such a
case a very slight movement on the part of each bird would suffice
so to shift the position of the layer in which they were traveling,
that it would be seen edgewise, and then the birds, being so situated
that the range of sight toward any part of the layer passed athwart
a great number of them, would of course be seen, not individually but
as a cloud, or long straight streak, a side view in fact of the layer
in which they were traveling. _Eureka!_ shouted Professor Tait; and
presently announced to the world the marvelous theory that the rapid
formation of comets’ tails may be accounted for on the same general
principle. Astronomers have found that along the tracks of some comets
(where the tails never lie, by the way, but that is a detail) are
countless millions of meteoric bodies separately undiscernable (and
never yet discerned as a cloud—another detail); therefore it follows
that the tails of all comets are formed by movements of “brickbats and
paving stones” in them (Professor Tait’s own description of meteors),
after the manner of the seabirds he saw from Arthur’s Seat. Professor
Thomson at the Edinburgh meeting of the British Association endorsed
this theory with special reference to the value of the “seabird
analogy” in explaining the phenomena of Newton’s comet. Dr. Huggins,
who, as he does not claim to be a mathematician (or to speak more
correctly, as his labors in physical research have not given him time
for profound mathematical research), may be more readily excused, also
speaks of the seabird theory as if it had some legitimate standing.
“The tail, he conceives,” he says, referring to Dr. Tait, “to be a
portion of the less dense part of the train illuminated by sunlight,
and visible or invisible to us, according, not only to circumstances of
density, illumination, and nearness, but also of tactic arrangement,
as of a flock of birds under different conditions of perspective.”
Of course, the theory is utterly untenable—by astronomers who know
something of the actual facts, and have enough mathematics to consider
simple geometrical relations. Bodies moving in a plane surface like
birds, if they individually travel in the same plane, keep its position
unchanged. But if they move individually at an angle to that plane
(as they occasionally do), they change its position—the surface,
however, in which they collectively are at any moment, still remaining
plane. In such a case only could such a phenomenon as was observed
by Professor Tait be seen. But in such a case the visibility of the
streak formed by the flight of birds would last but a few minutes, for
the same motion which had in a few minutes brought the streak into
view would in the next few minutes take it out of view. During the
short time that a flight is visible in this way, it has an unchanging
position, or a scarcely changing one. If the tail of Newton’s comet
had rapidly formed and as rapidly vanished, remaining, while visible,
in an almost unchanging position, the “seabird analogy” might explain
that particular phenomenon, however inadequate to explain multitudes
of others. But the phenomena to be explained are entirely different.
Leaving out of the question the varying position and length of the tail
as it approached the sun, and after it left the sun’s neighborhood,
all of which were entirely inconsistent with the seabird analogy, what
we are called upon to explain is that a visible tail ninety millions
of miles in length, seen in position 1A on one day, was seen three
days later in position 3A (having manifestly in the meanwhile passed
through all the intermediate positions, including 2A). If Professor
Tait, profound mathematician though he be, though he may “differentiate
and integrate like Harlequin,” can show how any flight of bodies,
like or unlike seabirds, can accomplish such a feat as the above,
appearing first to form a thin streak A1, and in less than four days
a thin streak A3, each ninety millions of miles long, without _some_
of them having had to travel a distance nearly equal to the line 1 to
3—or some one hundred and fifty millions of miles long, instead of the
trifling journeys he assigned them, he should take a rank above Newton
and Laplace as a mathematician. But there is another feat, apparently
equally difficult to him, which he might achieve very readily with
great advantage to those non-mathematicians among astronomers whom his
name—well deserved, too—as a mathematician has hitherto misled, and
with not less advantage to his own reputation: he might frankly admit
that the idea which occurred to him while watching those unfortunate
seabirds, had not quite the value which at the moment he mistakenly
attached to it, and has since _seemed_ to do.
[Illustration]
1 2 3
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A