Photograph taken October 10, 1858, at Harvard College Observatory
]
“Suppose we could take a comet, head, tail and all, and put it in
one pan of a balance, and we could carve out from the air which
surrounds us an object of the same size to put in the other pan, we
should find that our aërial body weighed four or five thousand times
more than the comet. But though a comet as a whole is lighter than
air, it must not be concluded that comets consist solely of gases in
a state of extreme tenuity. The head may be, and very probably is,
composed of a large number of small but solid bodies; nevertheless,
when a comet is taken in its entirety, the mean density is extremely
low.”
By October 10, the comet was receding from the neighborhood of Ursa
Major, drifting across the constellation of Boötes. On this date the
comet made its nearest approach to the earth. Its train now resembled
that of a widely opened fan, but its outline was already growing dim. It
showed strange alterations of dark and bright bands, resembling the
streamers which are sometimes seen to break up the continuous outline of
an auroral arch. The extreme length of the tail was nearly 64°, the
greatest extent observed during the apparition of the comet. The
secondary tail was still visible, but extremely faint.
October 11, the dark stripe in the tail had almost vanished, the
secondary tail was no longer to be seen, and the main tail was curved
like an ostrich plume. Its length was now judged to be about 30°, and
the nucleus had somewhat diminished in brightness. By October 15 the
comet was considerably fainter and smaller, as seen with the naked eye,
and it was bent southward like a sail wafted by a celestial breeze.
After the middle of October, the comet was best seen from the southern
hemisphere, and the last glimpse obtained in the northern hemisphere was
on October 25, when it was at an altitude of 3°, the sky fortunately
being very clear. The nucleus was still bright, but the tail was only 1°
long.
Its course was then followed by Maclear, Royal Astronomer at the Cape of
Good Hope, who reported that on December 23 the comet was merely a faint
nebulous body, about 90″ in diameter, with a slight central condensation
of light and no trace of a tail. Thus, it vanished in the remote depths
of space, in the same undecorated condition as when it first made its
eventful début to gladden the eyes of mortals on planet earth. Its visit
lasted but one hundred and seventy-seven days, from the time of its
first appearance until it took its departure along a track which will
not bring it within our ken again until nearly two thousand years have
rolled away.
BIOGRAPHICAL NOTE.—G. B. Donati, the Italian astronomer, was born at
Pisa, in 1826. At the age of twenty-six, he obtained a post in the
observatory at Florence, and there by his superior abilities,
acquirements, and unwearied application to duty soon gained a high
reputation among the men of science of his native country. He became
known to the world in 1858, by his discovery of the magnificent comet
called by his name. In 1864 he was appointed director of the observatory
in which he had worked so efficiently for twelve years. He then
undertook the arduous task of superintending the erection of a new and
more convenient observatory on the site of Arcetri, near Florence. All
difficulties were conquered, the new observatory was in working
condition, and the director had entered upon a new series of
observations when his labors were suddenly cut short by death. He died
at his home in Arcetri, September 29, 1873.
CHAPTER FOUR
COMETS IN DISTRESS
“Thou comest whence no mortal seer can know,
Thou goest whither nothing human dreams.”
—ANON.
Until the photographic eyes of Science detected the peculiarities of
comets, and mathematicians calculated with unerring accuracy their
comings and goings, they were looked upon, as we have already seen, with
more or less suspicion and dread. Nowadays, we know that these “airy
nothings,” as Sir John Herschel termed them, have been unjustly
maligned. Were they given the power of speech, they could a tale unfold
of adventurous thrills and overwhelming disasters encountered during
their voyages in space, far exceeding in interest any story of
terrestrial adventure. It would take the pen of a Jules Verne and an
author gifted with his vivid imagination to describe the erratic career
of a comet.
Take for instance the tragic fate of the headless comet of 1887, which
was described by Dr. Thomé of the Cordoba University as:
“a beautiful object with a narrow, straight, sharply defined
graceful tail over fifty degrees long. It was shining with a soft
starry light against a dark sky, beginning apparently without a
head, and gradually widening and fading as it extended upwards.”[4]
Now the popular idea of a well-regulated comet is a star with a tail,
but a tail without an accompanying star seems preposterous, yet a
headless comet this object remained as viewed with the naked eye. The
why and the wherefore of the tragedy is unknown, and whether it ever had
a head and what became of it remains one of the many unsolved problems
of the sky.
Still more remarkable is the career of the famous comet of Biela, from
its first appearance as viewed by mortal eyes on March 8, 1772, until
its final disappearance, a century later, in a veritable blaze of
celestial fireworks. Its story reads like a novel, and is far more
fascinating because it is fact and not fiction. The hero is a faint,
insignificant-looking object which was discovered by Montaigne of
Limoges, already referred to as the comet-hunter who so indiscreetly
found the thirteenth comet for which his colleague Messier was
industriously searching. Little did Montaigne guess that this foggy
speck of light which was so faint that it could only be seen with the
aid of his small telescope would one day attract worldwide attention.
Its nondescript appearance, with a tail only one-eighth the diameter of
the moon, made it apparently scarcely worthy of more than passing
notice. Had Montaigne concentrated his efforts on finding out its
peculiarities and tracing its path, his name would have been forever
connected with the little wanderer, instead of being entered in the
annals of astronomy as merely the first to see it.
The introductory chapter in its story is connected with a letter written
by Montaigne to the director of the observatory at Paris, announcing his
discovery. This arrived in time to give the astronomers an opportunity
for seeing the comet three or four times ere it vanished on its way
outward bound. Little more was thought of the celestial visitor until it
was glimpsed again thirty-three years later, in November, 1805, by Pons,
who, as we have already seen, shared honors with Messier and Montaigne
in the “eccentric vocation” of comet-hunting. The comet remained visible
in the northern heavens for only a month, when it sank below the horizon
and was no longer visible to observers in the northern hemisphere.
However, on this occasion the comet came very close to the earth, for we
are told that it was visible to the naked eye, even in the strong
twilight. Then it remained hidden from view until twenty years later,
when it was again rediscovered, this time by an Austrian officer named
Biela, in February, 1826. He was determined that the wily object should
not be lost sight of again, as far as its orbit was concerned, and by
means of careful observations and calculations he was enabled to
announce that it was traveling along the same route as the comet seen by
Montaigne in 1772, and that seen by Pons in 1805. Therefore, he
concluded that it was one and the same comet, and predicted its return
in 1832.
However, when it was announced by the great French astronomer, Arago,
that the comet at this return would cross the orbit of the earth,
widespread was the consternation among those who did not know what an
orbit was. Possibly, imagining that it was something tangible, we can
picture them looking at one another in dismay, and whispering in awed
tones, “Does this mean the comet will hit the earth, and if so what will
happen to us?” A possible collision with the comet was an alarming
thought to the ignorant and superstitious, and the fear caused by
Arago’s announcement was so great that it resulted in the first of the
many comet-scares. People in dread of the threatened calamity sold their
goods and chattels, and thronged the churches as a fit preparation for
the end of the world. There they awaited the expected crash and
doubtless were surprised when nothing unusual happened. The earth still
continued to roll on its appointed path, without jolt or jar to disturb
the “even tenor of its way.” The nervous gave a sigh of relief when the
comet withdrew once more into the obscurity of space, and those who had
parted with their belongings must have felt somewhat annoyed.
The so-called devout astrologers who had made use of Arago’s
announcement to their own advantage, when upbraided by those whom they
had warned, did a skillful kind of “hedging,” by stating that events
announced by a comet might be postponed for one or more periods of forty
years or even as many years as the comet had appeared days.
Consequently, one which had appeared for six months would not produce
any effect, evil or otherwise, for 180 years.[5] Thus these wise
soothsayers allowed a wide margin for possible results.
To give an idea of the filmy structure of the comet, the cause of such
unnecessary alarm, it was described by Sir John Herschel, who observed
it on September 23, 1832, as a round hazy-looking object without a tail.
It was moving in the direction of a small group of faint stars, which
were undimmed when overtaken by the comet, so that it resembled a
fog-like mist sprinkled with stars, this veil of cometary matter being
estimated by Herschel as fifty thousand miles thick. Yet, only a month
later, the remote prospect of a collision with this celestial cobweb
caused a panic in Europe!
The comet was first seen on August 23, 1832, but owing to its excessive
faintness was not generally observed till two months later, when at its
nearest to the sun. This occurred during the month of November, within
twelve hours of the time predicted by an astronomer named Santini. At
its next return, in 1839, the comet was not well placed for observation,
as it was too near the sun, and therefore lost in the glare of its
light. As computations had shown that the comet was traveling in an
orbit requiring six and two-thirds of a year, it was due to return in
1845.
The first to bid it welcome was an astronomer at Rome named De Vico, on
November 28 of that year. Two days later it was observed by Dr. Gallé at
Berlin, but it was not generally seen until December. It appeared as a
single comet on November 28, but on December 19 it was seen distinctly
pear-shaped, and ten days later it amazed all observers by splitting in
two. This marvelous transformation was first detected by two Americans,
Mr. Herrick, then librarian at Yale College, and Mr. Francis Bradley, a
clerk in the New Haven City Bank. The two were watching the comet on
January 29, 1845, taking turns in looking through a telescope which had
been erected in the Athenæum tower.
Suddenly one of the observers exclaimed that he could see a small comet
accompanying the larger one, and we can imagine his friend making some
remark concerning defective eyesight. However, when both saw the
duplicity of the comet, all doubts were dispersed. But what did it mean?
Had the comet a satellite, just as the earth has its accompanying moon,
or had the comet actually split in two? However, the twin comets were
seen two weeks later by Lieutenant Maury and Professor Hubbard at
Washington, D. C., and two days later it came within the ken of European
astronomers. Incidentally, three weeks before the twin comets were
observed, Mr. J. Russell Hind (England) noticed a peculiar lump near the
upper part of the nucleus of the main comet, which may be regarded as
the first symptom indicating that something was amiss.
On January 15, Professor Challis, then director of Cambridge Observatory
(England), had his suspicions aroused when he saw the complete severance
of the little comet from the big one, and the description of his
experience is best given in a letter he wrote to the president of the
Royal Astronomical Society:
“On the evening of January 15, when I sat down to observe it
[Biela’s comet], I said to my assistant, ‘I see _two_ comets.’
However, on altering the focus of the eyeglass and letting in a
little illumination, the smaller of the two comets appeared to
resolve itself into a minute star, with some haze about it. I
observed the comet that evening but a short time, being in a hurry
to proceed to observations of the new planet.”
Presumably he here refers to the search for Neptune. Alas! had he but
given his whole attention to that task, instead of dispersing his
energy—as it were—by pursuing a flimsy comet, England might have been
acknowledged as first in the actual discovery of that planet.
Resuming his observations of the comet on January 23, Professor Challis
again saw two comets, but clouds hid them from view for the next
half-hour, and when they had cleared away he was convinced that the
comets had moved during the interval. This suspicion was afterward
confirmed, and, moreover, Professor Challis found that they had moved in
unison, retaining their relative positions meanwhile. He wondered what
could be the meaning of this strange procedure, and whether they were
two independent comets, a double comet, or that his glass was deceiving
him.
“But I never heard of such a thing,” wrote Professor Challis.
“Kepler supposed that a certain comet separated in two, and for this
Pingré said of him, ‘_Aligreando bonus dormitat Homerus._’ I am
anxious to know whether other observers have seen the same thing.”
In a subsequent letter he shows by his remarks that “the two comets are
not only apparently, but really near each other, and that they are
physically connected.”[6]
The comets continued traveling along in this sociable manner for four
months, at an almost unvarying distance of about 165,000 miles, each
developing meanwhile a very bright nucleus and diminutive tail half a
degree in length, or one tenth the distance separating the pointers in
Ursa Major. Sometimes one comet would be devoid of a tail, sometimes the
other, so that one might almost imagine the tail exchanging owners, for
the comets were rarely both adorned therewith at the same time.
During the latter part of February, Lieutenant Maury, at Washington, D.
C., saw an arc of light extending from the large comet to the small one,
forming a sort of bridge between the two, this occurring when the small
comet was at its brightest. When the large comet had regained its
superiority it threw out new rays, which gave it the appearance of
having three tails, each adjacent tail making an angle of 120 degrees
with its neighbor, one of the tails being the bridge to the new comet.
This produced the effect of an arch in the heavens, through which the
stars were seen to pass.
One can imagine messages passing to and fro along this bridge of light
between the twin comets, and a possible farewell as they drifted further
apart. At their return in August, 1852, they were separated by about one
million five hundred thousand miles, and as so often happens in the case
of twins it was impossible to tell which was which. The comets were not
seen at their next return, in May, 1859, because they were lost in the
glare of sunlight, for the same reason that we are unable to see stars
in the daytime.
At the next expected visit when the comets were looked for, in January,
1866, they were nowhere to be seen. What had happened in the interval no
one knows, but in 1872 the whole astronomical world was startled by a
telegram from an astronomer named Klinkerfues of Göttingen, on November
30, to Pogson, the government astronomer at Madras, which read as
follows:
Biela touched earth on 27th, search near Theta Centauri.
Accordingly, a search was made, with the extraordinary result that a
comet _was_ found, but not _the_ comet. Observations were obtained of it
on December 2 and 3, but bad weather and the advance of twilight made
further search impossible. When the track of the new comet, for such it
proved to be, was eventually followed, it was found to be moving along a
different route from the one previously followed by the comet of Biela.
Nevertheless, by a remarkable coincidence it happened to be passing by
or near the place where this comet was wont to wander, until he took
unto himself a companion comet, which seems to have led him astray.
To be lost is interesting, especially for a comet, when one considers
the vast expanse of highways and byways in starland, but the climax of
the tragedy in connection with this special comet was not reached until
its orbit crossed that of the earth on November 27, 1872. On that
eventful night the sky seemed to be literally ablaze with meteors, which
fell in swarms and showers of dazzling gleams of light, the downpour
lasting from seven o’clock in the evening until one o’clock next
morning, the maximum being attained at nine o’clock. We are told that
the total number observed in England was estimated at a hundred and
sixty thousand. They all came from the same part of the sky, radiating
from a point near the beautiful double star Gamma in the constellation
of Andromeda. But what was the meaning of the display? Had it been
caused by an encounter of the earth with the scattered fragments of the
lost comet? It certainly could not have had any connection with the
comet itself, which, providing it still existed, had passed that way
three months before. It was more likely the débris of its train
scattered along its path after its breaking up in 1846.
There seems to be no doubt of the identity of this swarm of meteors with
the comet of Biela, for on November 27, 1885, a similar encounter took
place, providing a magnificent display of meteors observed all over
Europe, just at the moment when the earth was due at a crossing in the
former path of the comet. On that same evening, a piece of meteoric iron
fell at Mazapil, in northern Mexico, during the course of the shower,
and according to Professor Young, “the coincidence may be accidental,
but is certainly interesting. Some high authorities speak confidently of
this piece of iron _as a piece of Biela’s comet itself_.” (_General
Astronomy_, C. A. Young.)
In 1892 and 1898, when the earth again crossed the former path of the
comet, a similar display occurred, though on a minor scale, and some of
the scattered cometary fragments may still be looked for on the evenings
from November 17 to 27. They are recognizable from their slow motion,
short trains, and from the fact that they all radiate from the
second-magnitude star Gamma in Andromeda. (Incidentally, this is the
star so charmingly dealt with by Dr. Holmes, in the _Poet at the
Breakfast Table_, really the astronomer of the breakfast table, as
suggested by conversations and correspondence between my father and
Oliver Wendell Holmes.)
The star Gamma in Andromeda is easily located, as it is almost overhead
between the dates November 17–27, at a convenient hour in the evening.
It is in a line with Epsilon, the star at the left-hand corner of the
W-shaped group in the constellation, Cassiopeia, and with Polaris, the
Pole Star. The meteors radiating from this point are variously referred
to as the Andromedæ, Andromedids, and the Bielids, on account of their
supposed connection with the Comet of Biela. As a matter of fact it
matters little what they are called, as long as we know their appearance
and when and where to look for them. They may be looked upon as
supplementary to the story of the comet, and possibly some of the
particles may eventually find a resting-place on planet earth.
According to Dr. Crommelin of the Greenwich Observatory:
“the career of a comet may be said to be over when its meteors have
lost all their gas, or when they have been scattered by
perturbations over so wide a space that its unity and visibility are
lost. These disrupting causes are most effective when a comet is
fairly near the sun; therefore the oftener that a comet approaches
the sun, the shorter the period of its existence as a comet. I
think, therefore, that we can ascribe the great prevalence of
long-period comets to the principle of the survival of the fittest.”
Long-period comets are those which sometimes require hundreds of years
before they return sunward, as, for instance, Donati’s comet with its
period of about two thousand years. Others of short period, like Encke’s
comet, are regular visitors to the sun, returning after a short interval
of a few years along a well-known path. Once upon a time they may have
been long-period comets, which have had their paths restricted, owing to
the strong attractive pull of the giant planets Jupiter, Saturn, Uranus,
and Neptune. As a result of the disturbances (or perturbations, as they
are technically called) thus caused, according to the so-called capture
theory, Jupiter has annexed fifty comets, including the Comet of Biela.
Uranus and Saturn, according to the same theory, own a limited family of
two, while Neptune has four, including Halley’s famous comet. Its least
distance from the sun is 56 million miles at its point of nearest
approach, and 3,200 million miles when at the opposite end of its orbit.
But the great majority of these strange bodies appear to travel in
parabolas, open curves leading from infinite space to and around the
sun, and thence back into the region of the fixed stars.
There is a notable instance of a comet traveling about the sun in an
immense ellipse, but, like the moth, hovering around a flame which
finally causes its destruction, this comet returned once too often to
the neighborhood of the giant planet Jupiter, and in an encounter
between a large and a small body, the latter usually comes to grief. Its
path was curtailed at first, and subsequently it was shunted on to
another line. Jupiter, acting as pointsman on the cometary railway, is
suspected of opening the branch of the ellipse along which the comet had
formerly traveled in peace and quiet, with the result that it was
ignominiously sidetracked and sought for in vain.
The comet was first discovered in June, 1770, by Messier, who described
it as a rather insignificant object without a tail, but resembling a
nebula with a star-like nucleus. Early in July it had greatly increased
in size, the nucleus and surrounding haze extending over a space more
than five times the diameter of the moon. At this time it came very near
the earth, remaining visible until October, when it grew small and
faint, and finally faded away. Meanwhile, astronomers did their best to
determine its path, notably Mr. Lexell, of the Academy of Sciences at
St. Petersburg. He became so interested in clearing up the past history
of this quaint little comet, that it is usually referred to as Lexell’s
comet. He came to the conclusion that the comet of 1770 required five
years and seven months for its elliptic tour, but he was such a long
time in getting at this result, that by the time he obtained it in 1778
the comet was two years overdue. Messier made a careful search for it,
but without success.
Lexell was of the opinion that at the end of May, 1776, the comet came
so close to Jupiter that the attractive pull of that planet was three
times greater than that of the sun. When a comet rushes around the sun
it has to go full speed ahead, so as to resist being drawn upon its
surface, but as it recedes from the danger zone it gradually slackens
its pace, with the result that by the time it is crossing the orbit
along which Jupiter travels, it is going at reduced speed. Probably
Jupiter was not far from the part of its orbit crossed by the comet in
1776, with the result that the unfortunate wanderer was exposed for a
longer period to the powerful attraction of the giant planet. This may
have caused an important change in the comet’s path, with the result
that it escaped from what has been termed the _sphere of activity_ early
in October, 1779.
At this period, according to Lexell, the comet was moving in an ellipse
with a period of more than sixteen years, and at such a distance there
would be no hope of our seeing it again. He finally considered the comet
of 1770 as definitely lost. However, when Brooks, the famous
comet-hunter of Geneva, New York, discovered a comet in 1889, which is
known as Comet 1889 V, as it was the fifth comet discovered that year,
it was supposed to be the long-lost Lexell comet of 1770. For that
reason it is known as the Lexell-Brooks comet.
Previous to 1886, the comet discovered in 1889 was traveling around the
sun in an immense ellipse, taking it out beyond the planet Uranus.
Around and around the sun it went, as a moth flutters around a lamp,
until in the year 1886 it came under the magic spell of Jupiter. Unable
to resist this planet’s persuasive influence, the path of the comet was
reduced to a smaller one requiring only seven years for its completion.
Apparently on this occasion the comet passed too near Jupiter for
safety, and was reduced to four fragments in consequence. When it
approached the sun in 1889, and was discovered by Brooks, it may
probably have been one of the four fragments; at any rate, this is the
opinion of Dr. Charles Lane Poor, of New York, who made a careful and
most exhaustive study of the comet and its eccentricities. It remained
visible with telescopes of ordinary power until March, 1890, after which
date it could only be seen with the great telescope at the Lick
Observatory, at Mount Hamilton, California. With this magnificent
instrument Professor Barnard followed the comet until January, 1891.
The path of its next return was calculated so accurately that when it
was rediscovered on June 20, 1896, by Javelle, it was seen within a
distance less than one quarter the diameter of the moon from its
predicted place. By this time the comet had grown fainter, as though
enfeebled by its long wanderings and the vicissitudes of its career, and
it remained visible for only a few months, finally disappearing in
February, 1897. For a third time the comet came near enough for us to
see it, and this occurred during the summer of 1903, when it remained
visible until the following January. It was then so faint, it could only
be observed with the largest telescopes. The future of the comet seems
as likely to be as interesting as its past.
“Unless it become wholly disintegrated by the pulling and hauling of the
sun and planets, it will be seen again in 1910, and yet again in 1917,”
wrote Dr. Poor in 1908, but as a matter of fact it was not observed on
either occasion. Dr. Poor also predicted that early in 1921 it would
again come into close approach with Jupiter, “and beyond that point its
history cannot be predicted. This collision will probably end its story
as far as the earth is concerned, for it will undoubtedly be still
further broken up, and its orbit may be so changed that it will never
afterwards be seen.” And we must leave it with this unsatisfactory
conclusion, as it did not reappear in 1921, and nothing more has been
seen or heard of this comet. By now (1925) it may be merely a derelict
in space, at the mercy of any disturbing planet it may happen to pass on
the way.
These instances give some idea of the dangers to which comets are
subjected as they drift like frail barks on the ocean of space. Whence
they have come and whither they vanish, no one knows, but it has been
suggested that there is a home of comets. This has been described as a
shell of nebulous matter accompanying the sun and planets, though at a
distance some thousands of times greater than that of the earth from the
sun, yet much closer than the nearest star. “However, we have no direct
evidence of any such comet-dropping envelope,” according to Professor C.
A. Young.
Yet supposing it does exist, we see in imagination baby comets cradled
therein in nebulous mist until they are able to take care of themselves.
Then they are presumably launched forth on their perilous career, as
they make their way towards their ruler, the sun, to pay their respects.
Woe betide them should they cross the path of one of the giant planets
at an inauspicious moment, or approach too near the sun, which would
prove equally disastrous.
CHAPTER FIVE
PHOTOGRAPHY AS APPLIED TO COMETS
“With its three eyes—the eye of keenness, the eye of patient
watchfulness, and the eye of artistic truth, photography promises to
be a Cerberus to the science of the future, whose watchfulness will
prevent the admission of error and detect truths which would otherwise
escape us.”
—R. A. PROCTOR.
These words written by my father, in his book entitled _The Universe of
Suns_, shortly after the appearance of the comet of 1882, have since
been amply confirmed, not only in connection with the sun, moon, and
stars, but still more so regarding the hitherto unknown peculiarities of
comets. So far we have gained some idea of the appearance of a comet as
seen with the naked eye, or with the aid of a telescope, but it now
remains to be shown what can be accomplished by means of photography.
Pictures of the ever-varying transformations, for instance, which took
place in the appearance of the celebrated Morehouse comet of 1908,
opened out new vistas in cometary wonders, hitherto beyond our ken.
Successive photographs taken during the course of a night, pictured for
us the unfolding of the comet’s train, its spreading outward like a
gigantic fan of gauze-like texture, and eventual closing up till it
resembled a sheaf. By means of the revelations thus made by the camera,
we became aware of the marvelous quick-change effects produced in the
appearance of this comet not only from night to night, but sometimes
during the brief interval of less than an hour. Nevertheless, as seen
with a telescope, the Morehouse comet appeared inconspicuous and was
invisible to the naked eye.
The first attempt at taking a photograph of a comet was made by Bond at
Harvard College Observatory in 1858, in connection with the magnificent
comet of that year, but his efforts only met with partial success. The
next venture was made in 1881, by Sir William Huggins, in our country,
and Dr. Henry Draper, of New York, but entirely satisfactory photographs
of a comet were not obtained until 1882, when the great Daylight comet
became a conspicuous object in southern skies.
This comet was first seen on September 3, by some employees of the
railroad in Auckland, New Zealand, and by other persons whose duties
required them to rise before daylight. The names of these fortunate
observers are unknown, but what a privilege to obtain the first glimpse
of the comet.
[Illustration: