because they were found to have no diurnal parallax, so their annual
parallax is a convincing proof of their descending into the regions of the
planets. For all the comets which move in a direct course, according to
the order of the signs, about the end of their appearance become more than
ordinarily slow, or retrograde, if the earth is between them and the sun ;
and more than ordinarily swift if the earth is approaching to a heliocen
tric opposition with them. Whereas, on the other hand, those which move
against the order of the signs, towards the end of their appearance, appear
swifter than they ought to be if the earth is between them and the sun ;
and slower, and perhaps retrograde, if the earth is in the other side of its
crbit. This is occasioned by the motion of the earth in different situa
tions. If the earth go the same way with the comet, with a swifter
motion, the comet becomes retrograde; if with a slower motion, the comet
becomes slower, however ; and if the earth move the contrary way, it be
comes swifter ; and by collecting the differences between the slower and
swifter motions, and the sums of the more swift and retrograde motions,
and comparing them with the situation and motion of the earth from,
whence they arise, I found, by means of this parallax, that the distances
of the comets at the time they cease to be visible to the naked eye are
always less than the distance of Saturn, and generally even less than the
distance of Jupiter.
The same thing may be collected from the curvature of the way of the
comets (p. 462). These bodies go on nearly in great circles while their
motion continues swift ; but about the end of their course, when that part
THE SYSTEM OF THE WORLD. 549
of their apparent motion which arises from the parallax bears a greater
proportion to their whole apparent motion, they commonly deviate from
those circles ; and when the earth goes to one side, they deviate to the
other ; and this deflection, because of its corresponding with the motion
of the earth, must arise chiefly from the parallax ; and the quantity there
of is so considerable, as, by my computation, to place the disappearing
comets a good deal lower than Jupiter. Whence it follows, that, when
they approach nearer to us in their perigees and perihelions, they often de
scend below the orbits of Mars and the inferior planets.
Moreover, this nearness of the cornets is confirmed by the annual paral
lax of the orbit, in so far as the same is- pretty nearly collected by the
supposition that the comets move uniformly in right lines. The method
of collecting the distance of a comet according to this hypothesis from
four observations (first attempted by Kepler, and perfected by Dr. Wallis
and Sir Christopher Wren) is well known and the comets reduced to
this regularity generally pass through the middle of the planetary region.
So the comets of the year 1607 and 1618, as their motions are defined by
Kepler, passed between the sun and the earth : that of the year 16 4 be
low the orbit of Mars; and that in 1680 below the orbit of Mercury, as
its motion was defined by Sir Christopher Wren rind others. By a like
rectilinear hypothesis, Hevelius placed all the comets about which we have
any observations below the orbit of Jupiter. It is a false notion, there
fore, and contrary to astronomical calculation, which some have enter
tained, who, from the regular motion of the comets, either remove them
into the regions of the fixed stars, or deny the motion of the earth : where
as their motions cannot be reduced to perfect regularity, unless we suppose
them to pass through the regions near the earth in motion ; and these are
the arguments drawn from the parallax, so far as it can be determined
without an exact knowledge of the orbits and motions of the comets.
The near approach of the comets is farther confirmed from the light of
their heads (p. 463, 465) ;
for the light of a celestial body, illuminated by
the sun, and receding to remote parts, is diminished in the quadruplicate
proportion of the distance ; to wit, in one duplicate proportion on account
of the increase of the distance from the sun ; and in another duplicate
proportion on account of the decrease of the apparent diameter. Hence it
may be inferred, that Saturn being at a double distance, and having its
apparent diameter nearly half of that of Jupiter, must appear about I (5
times more obscure ; and that, if its distance were 4 times greater, its
light would be 256 times less ; and therefore would be hardly perceivable
to the naked eye. But now the comets often equal Saturn s light, without
exceeding him in their apparent diameters. So the comet of the year
1668, according to Dr. Hooke s observations, equalled in brightness the
light of a fixed star of the first magnitude ; and its head, or the star ID
550 THE SYSTEM OF THE WORLD.
the middle of the coma, appeared, through a telescope oi 15 feet, as lucid
as Saturn near the horizon ; but the diameter of the head was only 25"
that is, almost the same with the diameter of a circle equal to Saturn
and his ring. The coma or hair surrounding the head was about ten times
as broad; namely, 4 min. Again ; the least diameter of the hair of the
comet of the year 1682, observed by Mr. Flamsted with a tube of 16 feet
and measured with the micrometer, was 2 ; but the nucleus, or star in
the middle, scarcely possessed the tenth part of this breadth, and was
therefore only 11 or 12" broad; but the light and clearness of its head
exceeded that of the year 1680, and was equal to that of the stars of the
first or second magnitude. Moreover, the comet of the year 1665, in April,
as Hevelws informs us, exceeded almost all the fixed stars in splendor, arid
even Saturn itself, as being of a much more vivid colour ; for this comet
was more lucid than that which appeared at the end of the foregoing year
and was compared to the stars of the first magnitude. The diameter of
the coma was about 6
; but the nucleus, compared with the planets by
means of a telescope, was plainly less than Jupiter, and was sometime*?
thought less, sometimes equal to the body of Saturn within the ring. To
this breadth add that of the ring, and the whole face of Saturn will be
twice as great as that of the comet, with a light not at all more intense ;
and therefore the comet was nearer to the sun than Saturn. From the
proportion of the nucleus to the whole head found by these observations,
and from its breadth, which seldom exceeds 8 or 12;
,
it appears that thi-
Btars of the comets are most commonly of the same apparent magnitude
as the planets ; but that their light may be compared oftentimes with that
of Saturn, and sometimes exceeds it. And hence it is certain that in their
perihelia their distances can scarcely be greater than that of Saturn. At
twice that distance, the light would be four times less, which besides by its
dim paleness would be as much inferior to the light of Saturn as the light
of Saturn is to the splendor of Jupiter : but this difference would be easily
observed. At a distance ten times greater, their bodies must be greattr
than that of the sun ; but their light would be 100 times fainter than
that of Saturn. And at distances still greater, their bodies would far
exceed the sun ;. but, being in such dark regions, they must be no longer
visible. So impossible is it to place the comets in the middle regions be
tween the sun and fixed stars, accounting the sun as one of the fixed stars:
for certainly they would receive no more light there from the sun than w<?
do from the greatest of the fixed stars.
So far we have gone without considering that obscuration which comets
suffer from that plenty of thick smoke which encompasseth their heads.
and through which the heads always shew dull as through a cloud ; for
by how much the more a body is obscured by this smoke, by so much th.2
more near it must be allowed to come to the sun, that it may vie with the
THE SYSTEM OF THE WORLD. 651
planets in the quantity of light which it reflects : whence it is probable
that the comets descend far below the orbit of Saturn, as we proved before
from their parallax. But, above all, the thing is evinced from their tails,
which must be owing either to the sun s light reflected from a srnoke
arising from them, and dispersing itself through the aether, or to the light
uf their own headt.
In the former case we must shorten the distance of the comets, lest we be
obliged to allow that the smoke arising from their heads is propagated
through such a vast extent of space, and with such a velocity of expansion,
jus will seem altogether incredible; in the latter case the whole light of
both head and tail must be ascribed to the central nucleus. But, then, if
we suppose all this light to be united and condensed within the disk of the
nucleus, certainly the nucleus will by far exceed Jupiter itself in splendor,
especially when it emits a very large and lucid tail. If, therefore, under a less
apparent diameter, it reflects more light, it must be much more illuminated
by the sun, and therefore much nearer to it. So the comet that appeared
Dec. }2 and 15, O.S. Anno 1679, at the time it emitted a very shining
tail, whose splendor was equal to that of many stars like Jupiter, if their
light were dilated and spread through so great a space, was, as to the mag
nitude of its nucleus, less than Jupiter (as Mr. Flawsled observed), and
therefore was much nearer to the sun : nay, it was even less than Mercury.
For on the 17th of that month, when it was nearer to the earth, it ap
peared to Cassini through a telescope of 35 feet a little less than the globe
of Saturn. On the 8th of this month, in the morning, Dr. ffalfey saw the
tail, appearing broad and very short, and as if it rose from the body of the
sun itself, at that time very near its rising. Its form was like that of an
extraordinary bright cloud ; nor did it disappear till the sun itself began
to be seen above the horizon. Its splendor, therefore, exceeded the light of
the clouds till the sun rose, and far surpassed that of all the stars together,
as yielding only to the immediate brightness of the sun itself. Neither
Mercury, nor Venus, nor the moon itself, are seen so near the rising sun.
Imagine all this dilated light collected together, and to be crowded into
the orbit of the comet s nucleus which was less than Mercury ; by its
splendor, thus increased, becoming so much more conspicuous, it will vastly
exceed Mercury, and therefore must be nearer to the sun. On the 12th
and 15th of the same month, this tail, extending itself over a much greater
space, appeared more rare; but its light was still so vigorous as to become
visible when the fixed stars were hardly to be seen, and soon after to appear
like a fiery beam shining in a wonderful manner. From its length, which
was 40 or 50 degrees, and its breadth of 2 degrees, we may compute what
the light of the whole must be
This near approach of the comets to the sun is confirmed from the sitution
they are seen in when their tails appear most resplendent; for when
THE SYSTEM OF THE WORLD.
the head passes by the sun, and lies hid under the solar rays, very bright
and shining ta Is, like fiery beams, are said to issue from the horizon; but
afterwards, when the head begins to appear, and is got farther from the
sun, that splendor always decreases, and turns by degrees into a paleness
like to that of the milky way, but much more sensible at first
;
after that
vanishing gradually. Such was that most resplendent comet described by
Aristotle, Lib. 1, Meteor. 6. " The head thereof could not be seen, because
it set before the sun, or at least was hid under the sun s rays ; but the next
day it was seen as well as might be ; for, having left the sun but a very
little way, it set immediately after it
; and the scattered light of the head
obscured by the too great splendour (of the tail) did not yet appear. But
afterwards (says Aristotle), when the splendour of the tail was now dimin
ished (the head of), the comet recovered its native brightness. And the
splendour of its tail reached now to a third part of the heavens (that is, to
60). It appeared in the winter season, and, rising to Orion s girdle, there
vanished away." Two comets of the same kind are described by Justin,
Lib. 37, which, according to his account,
" shined so bright, that the whole
heaven seemed to be on fire
; and by their greatness filled up a fourth part
of the heavens, and by their splendour exceeded that of the sun." By
which last words a near position of these bright comets and the rising or
setting sun is intimated (p. 494, 495). We may add to these the comet of
the year 1101 or 1106, " the star of which was small and obscure (like that
of ] 6SO) ; but the splendour arising from it extremely bright, reaching like
a fiery beam to the east and north," as Hevelius has it from Simeon, the
monk of Durham. It appeared at the beginning of February about the
evening in the south-west. From this and from the situation of the tail
we may infer that the head was near the sun. Matthew Paris says, "it
was about one cubit from the sun ; from the third [or rather the sixth] to
the ninth hour sending out a long stream of light." The comet of 1264,
in July, or about the solstice, preceded the rising sun, sending out its beams
with a great light towards the west as far as the middle of the heavens ;
and at the beginning it ascended a little above the horizon : but as the sun
went forwards it retired every day farther from the horizon, till it passed
by the very middle of the heavens. It is said to have been at the beginning
large and bright, having a large coma, which decayed from day to day. It
is described in Append. Matth, Paris, Hist. Aug. after this manner : ^Au.
Christi 1265, there appeared a comet so wonderful, that none then living
had ever seen the like
; for, rising from the east with a great brightness, it
extended itself \uth a great light as far as the middle of the hemisphere
towards the west." The Latin original being somewhat barbarous and obgcure,
it is here subjoined. Ah oriente enim cum tnaguo fulgore sur-
" :i
s, usque ad medium hcmisp]icerii versus occideutcm, omuia per lucid*
pertrahcbai.
THE SYSTEM OF THE WORLD. 553
"In the year 1401 or 1402, the sun being got below the horizon, there
appeared in the west a bright and shining comet, sending out a tail up
wards, in splendor like a flame of fire, and in form like a spear, darting its
rays from west to east. When the sun was sunk below the horizon, by the
lustre of its own rays it enlightened all the borders of the earth, not per
mitting the other stars to shew their light, or the shades of night to darken
the air, because its light exceeded that of the others, and extended itself to
the upper part of the heavens, flaming," &c., Hist. Byzaut. Due. Mich.
Nepot. From the situation of the tail of this comet, and the time of its
first appearance, we may infer that the head was then near the sun, and
went farther from him every day ; for that comet continued three months.
In the year 1527, Aug. 11, about four in the morning, there was seen al
most throughout Europe a terrible comet in Leo, which continued flaming
an hour and a quarter every day. It rose from the east, and ascended to
the south and west to a prodigious length. It was most conspicuous to the
north, and its cloud (that is, its tail) was very terrible ; having, according
to the fancies of the vulgar, the form of an arm a little bent holding a
sword of a vast magnitude. In the year 1618, in the end of November,
there began a rumour, that there appeared about sun-rising a bright beam,
which was the tail of a comet whose head was yet concealed within the
brightness of the solar rays. On Nov. 24, and from that time, the comet
itself appeared with a bright light, its head and tail being extremely re
splendent. The length of the tail, which was at first 20 or 30 dog., in
creased till December 9, when it arose to 75 deg,, but with a light much
more faint and dilute than at the beginning. In the year 1668, March 5,
N. S., about 7 in the evening, P. Volent. Estaucius, being in Brazil, saw
a comet near the horizon in the south-west. Its head was small, and
scarcely discernible, but its tail extremely bright and refulgent, so that the
reflection of it from the sea was easily seen by those who stood upon the
shore. This great splendor lasted but three days, decreasing very remark
ably from that time. The tail at the beginning extended itself from west
to south, and in a situation almost parallel to the horizon, appearing like
a shining beam 23 deg. in length. Afterwards, the light decreasing, its
magnitude increased till the comet ceased to be visible; so that Cassiid,
at Bologna^ saw it (Mar. 10, 11, 12) rising from the horizon 32 deg. in
length. In Portugal it is said to have taken up a fourth part of the
heavens (that is, 45 deg.), extending itself from west to east with a notable
brightness ; though the whole of it was not seen, because the head in this
part of the world always lay hid below the horizon. From the increase of
the tail it is plain that the head receded from the sun. and was nearest to
it at the beginning, when the tail appeared brightest.
To all these we may add the comet of 1680, whose wonderful splendor
at the conjunction of the head with the sun was above described. Hut so
554 THE SYSTEM OF THE WORLD.
great a splendor argues the comets of this kind to have really passed near
the fountain of light, especially since the tails never shine so much in
their opposition to the sun j
nor do we read that fiery beams have ever ap
peared there.
Lastly, the same thing is inferred (p. 466; 407) from the light of the
heads increasing in the recess of the comets from the earth towards the
sun, and decreasing in their return from the sun towards the earth ; for so
the last comet of the year 1 665 (by the observation of Hevelius]^ from the
time that it was first seen, was always losing of its apparent motion, and
therefore had already passed its perigee : yet the splendor of its head was
daily increasing, till, being hid by the sun?
s rays, the comet ceased to ap
pear. The comet of the year (683 (by the observation of the same Hejelius),
about the end of July, when it first appeared, moved at a very
slow rate, advancing only about 40 or 45 minutes in its orbit in a day s
time. I3ut from that time its diurnal motion was continually upon the
increase till Septe/uber 4, when it arose to about 5 degrees ; and therefore
in all this interval of time the comet was approaching to the earth. Which
is likewise proved from the diameter of its head measured with a microme
ter ; for, August the 6th, Hevelius found it only 6 5", including the
coma ; which, September 2, he observed 9 7". And therefore its head
appeared far less about the beginning than towards the end of its motion,
though about the beginning, because nearer to the sun, it appeared far
more lucid than towards the end, as the same Hevelius declares. Where
fore in all this interval of time, on account of its recess from the sun,
it decreased in splendor, notwithstanding its access towards the earth. The
comet of the year 1618, about the middle of December, and that of the
year 1680, about the end of the same month, did both move with their
greatest velocity, and were therefore then in their perigees : but the greatest
splendor of their heads was seen two weeks before, when they had just got
clear of the sun s rays : and the greatest splendor of their tuild a little
more early, when yet nearer to the sun. The head of the former comet,
according to the observations of Cysattis, Dec. 1, appeared greater than
the stars of the first magnitude: and, Dec. 16 (being then in its perigee),
)i a small magnitude, and the splendor or clearness was much diminished.
Jan. 7, Kepler, being uncertain about the head ? left off observing. Dec.
12, the head of the last comet was seen and observed by Flamxted at the
distance of 9 degrees from the sun, which a star of the third magnitude
could hardly have been. December 15 and 17, the same appeared like a
star of the third magnitude, its splendor being diminished by the bright
clouds near the setting sun. Dec. 26, when it moved with the greatest
swiftness, and was almost in its perigee, it was inferior to Os Pegasi, a
star of the third magnitude. Jait. 3, it appeared like a star of the fourth :
fan. 9, like a star of the fifth. Jan. 13. it disappeared, by reason of tb<~
THE SYSTEM OF THE WORLD. 555
brightness of the moon, which was then in its increase. Jan. 25, it was
scarcely equal to the stars of the seventh magnitude. If we take equal
times on each hand of the perigee, the heads placed at remote distances
would have shined equally before and after, because of their equal distances
frjin the earth. That in one case they shined very bright, and in the
other vanished, is to be ascribed to the nearness cf the sun in the first case,
and his distance in the other; and from the great difference of the light
in these two cases we infer its great nearness in the first of them : for
the light of the comets uses to be regular, and to appear greatest when
their heads move the swiftest, and are therefore in their perigees ; except
ing in so fur as it is increased by their nearness to the sun.
From thee things I at last discovered why the comets frequent so much
the region of the sun. If they were to be seen in the regions a great way
beyond Saturn, they must appear oftener in these parts of the heavens
that are opposite to the sun ; for those which are in that situation would
be nearer to the earth, and the interposition of the sun would obscure the
others: but, looking over the history of comets, I find that four or five
times more have been seen in the hemisphere towards the sun than in th-3
opposite hemisphere ; besides, without doubt, not a few which have been
hid by the light of the sun ; fur comets descending into our parts neither
emit tails, nor are so well illuminated by the sun, as to discover them
selves to our naked eyes, till they are come nearer to us than Jupiter. But
the far greater part of that spherical space, which is described about the
sun with so small an interval, lies en that side of the earth which regards
the sun, and the comets in that greater part are more strongly illuminated,
as being for the most part nearer to the sun : besides, from the remarka
ble eccentricity of their orbits, it comes to pass that their lower apsides
are much nearer to the sun than if their revolutions were performed in
circles concentric to the sun.
Hence also we understand why the tails of the comets, while their heads
are descending towards the sun, always appear short and rare, and are sel
dom said to have exceeded 15 or 20 deg. in length ;
but in the recess of
the heads from the sun often shine like fiery beams, and soon after reach
to 40, 50, 60, 70 deg. in length, or more. This great splendor and length
of the tails arises from the heat which the sun communicates to the comet
as it passes near it. And thence, I think, it may be concluded, that all the
comets that have had such tails have passed very near the sun.
Hence also we may collect that the tails arise from the atmospheres of
the heads (p. 487 to 488) : but we have had three several opinions about
the tails of comets ; for some will have it that they are nothing else but
the beams of the sun s light transmitted through the comets heads, which
they suppose to be transparent ; others, that they proceed from the refrac
tion which light suffers in passing from the comet s head to the earth ;
55fi THE SYSTEM OF THE WORLD.
and, lastly, others, that they are a sort of clouds or vapour constantly
rising from the cornets heads, and tending towards the parts opposite to
the sun. The first is the opinion of such as are yet unacquainted with
optics ; for the beams of the sun are not seen in a darkened room, but in
consequence of the light that is reflected from them by the little particles
of dust and smoke which are always flying about in the air
; and hence it
is that in air impregnated with thick smoke they appear with greater
brightness, and are more faintly and more difficultly seen in a finer air;
but in the heavens, where there is no matter to reflect the light, they are
not to be seen at all. Light is not seen as it is in the beams, but as it is
thence reflected to our eyes ;
for vision is not made but by rays falling
upon the eyes, and therefore there must be some reflecting matter in those
parts where the tails of comets are seen
; and so the argument turns upon
the third opinion ;
for that reflecting matter can be no where found but in
the place of the tail, because otherwise, since all the celestial spaces are
equally illuminated by the sun s light, no part of the heavens could appear
with more splendor than another. The second opinion is liable to many
difficulties. The tails of comets are never seen variegated with thos-e
colours which ever use to be inseparable from refraction ; and the distinct
transmission of the light of the fixed stars and planets to us is a demon
stration that the aether or celestial medium is not endowed with any re
fractive power. For as to what is alledged that the fixed stars have been
sometimes seen by the Egyptians environed with a coma or capillitium
because that has but rarely happened, it is rather to be ascribed to a casual
refraction of clouds, as well as the radiation and scintillation of the fixed
stars to the refractions both of the eyes and air
; for upon applying a tele
scope to the eye, those radiations and scintillations immediately disappear.
By the tremulous agitation of the air and ascending vapours, it happens
that the rays of light are alternately turned aside from the narrow space
of the pupil of the eye ; but no such thing can have place in the much
wider aperture of the object-glass of a telescope ; and hence it is that a
scintillation is occasioned in the former case which ceases in the latter
;
and this cessation in the latter case is a demonstration of the regular trans
mission of light through the heavens without any sensible refraction.
But, to obviate an objection that may be made from the appearing of no
tail in such comets as shine but with a faint light, as if the secondary
rays were then too weak to affect the eyes, and for this reason it is that
the tails of the fixed stars do not appear, we are to consider that by the
means of telescopes the light of the fixed stars may be augmented above
