the tail, lying nearly parallel to the equator, deviated a little from the op
position of the sun towards the north.
Nov. 23, O. S. at 5 1
. morning, at Nuremberg (that is, at 4^h
. at Lon
don), Mr. Zimmerman saw the comet in ^t 8 8 , with 2 31 south lat.
its place being collected by taking its distances from fixed stars.
Nov. 24, before sun-rising, the comet was seen by Montenari in TCI 1?
52 on the north side of the right line through Cor Leonis and Spica W,
and therefore its latitude was something less than 2 38 ; and since the
latitude, as we said, by the concurring observations of Montenari, A/io- ,
and Hook, was continually increasing, therefore, it was now, on the 24th,
something greater than 1 58" ; and, taking the mean quantity, may be
reckoned 2 18", without any considerable error. Ponthwns and Galletins
will have it that the latitude was now decreasing ; and Cellius, and the
observer in New England, that it continued the same, viz., of about 1,
or H. The observations of Ponthceus and Cellius are more rude, espe
cially those which were made by taking the azimuths and altitudes
; as
are also the observations of Galletins. Those are better which were
made by taking the position of the comet to the fixed stars by Montenari^
Hook, Ango, and the observer in New England, and sometimes by
BOOK III | O* NATURAL PHILOSOPHY. 4S3
Poii t/tfe and Cell lus. The same day, at 5h
. morning, at Ballasore, the
comet was observed in "I 11 45 ; and, therefore, at 5h
. morning at Lon
don, was in "I 13 nearly. And, by the theory, the comet was at that
time in n 13 22 42".
Nov. 25, before sunrise. Montenari observed the comet in 1Tl 17|
nearly ;
and Cellius observed at the same time that the comet was in a
right line between the bright star in the right thigh of Virgo and the
southern scale of Libra; and this right line cuts the comet s way in ^l
18 3(5 . And, by the theory, the comet was in ni 18-- nearly.
From all this it is plain that these observations agree with the theory,
so far as they agree with one another ; and by this agreement it is made
clear that it was one and the same comet that appeared all the time from
Nov. 4 to Mar. 9. The path of this comet did twice cut the plane of the
ecliptic, and therefore was not a right line. It did cut the ecliptic not in
opposite parts of the heavens, but in the end of Virgo and beginning of
Capricorn, including an arc of about 98 : and therefore the way of the
comet did very much deviate from the path of a great circle ;
for in the
month of Nov. it declined at least 3 from the ecliptic towards the south :
and in the month of Dec. following it declined 29 from the ecliptic to
wards the north ;
the two parts of the orbit in which the comet descended
towards the sun, and ascended again from the sun, declining one from the
other by an apparent angle of above 30, as observed by Montenari. This
comet travelled over 9 signs, to wit, from the last dcg. of 1 to the begin
ning of n, beside the sign of 1, through wrhich it passed before it began
to be seen ; and there is no other theory by which a comet can go over so
great a part of the heavens with a regular motion. The motion of this
comet was very unequable ;
for about the 20th of Nov. it described about
5 a day. Then its motion being retarded between Nov. 26 and Dec.
12, to wit, in the space of 15^ days, it described only 40 But the mo
tion thereof being afterwards accelerated, it described near 5 a day, till
its motion began to be again retarded. And the theory which justly cor
responds with a motion so unequable, and through so great a part of the
heavens, which observes the same laws with the theory of the planets, and
which accurately agrees with accurate astronomical observations, cannot
be otherwise than true.
And, thinking it would not be improper, 1 have given a true representa
tion of the orbit which this comet described, and of the tail which it
emitted in several places, in the annexed figure; protracted in the plane of
the trajectory. In this scheme ABC represents the trajectory of the comet,
D the sun DE the axis of the trajectory, DF the line of the nodes, GH
the intersection of the sphere of the orbis magnus with the plane of the
trajectory. I the place of the comet Nov. 4, Ann. 1680; K the place of the
same AT
/r. 11 ; L the place of the same Nov. 19; M its place Dec. 12; IS
484 THE MATHEMATICAL PRINCIPLES |BOOK 111.
its place Dec. 21 ; O its place Dec. 29 ; P its place Jan. 5 following ; Q,
its place Jan. 25 ; R its place Feb. 5 ; S its place Feb. 25 ; T its place
March 5 ; and V its place March 9. In determining the length of the
tail, I made the following observations.
Nov. 4 and 6, the tail did not appear ; Nov. 1 1, the tail just begun to
shew itself, but did not appear above | deg. long through a 10 feet tele
scope ; Nov. 17, the tail was seen by Ponthc&us more than 15 long ; Nov.
18, in New-England, the tail appeared 30 long, and directly opposite to
the sun, expending itself to the planet Mars, which was then in njZ, 9 54 ;
Nov. 19. in Manjltnd, the tail was found 15 or 20 Ions:; Dec. 10 (by
BOOK III.] OF NATURAL PHILOSOPHY. 4S5
the observation of Mr. Flamsted), the tail passed through the middle of
the distance intercepted between the tail of the Serpent of Ophiuchus and
the star 6 in the south wing of Aquila, and did terminate near the stars
A, w, l>,
in Bayer s tables. Therefore the end of the tail was in Y? 19|
5
;
with latitude about 34^ north ; Dec 11, it ascended to the head of Sag-itta
(Bayer s a, 0), terminating in V? 26 43 , with latitude 38 34 north;
Dec. 12, it passed through the middle of Sa^itta, nor did it reach much
farther; terminating in ~ 4, with latitude 42^ north nearly. But these
things are to be understood of the length of the brighter part of the tail;
for with a more faint light, observed, too, perhaps, in a serener sky, at
Rome, Dec. 12, 5h
. 40 , by the observation of PcBu.Sj the tail arose to
10 above the rump of the Swan, and the side thereof towards the west
and towards the north was 45 distant from this star. But about that time
the tail was 3 broad towards the upper end ; and therefore the middle
thereof was 2 15 distant from that star towards the south, and the upper
end was X in 22, with latitude 61 north; and thence the tail was about
70 long; Dec. 21, it extended almost to Cassiopeia s chair, equally dis
tant from j3 and from Schedir, so as its distance from either of the two
was equal to the distance of the one from the other, and therefore did ter
minate in T 24, with latitude 47^ ; Dec. 29, it reached to a contact with
Scheal on its left, and exactly filled up the space between the two stars in
the northern foot of Andromeda, being 54 in length; and therefore ter
minated in & 19, with 35 of latitude; Jan 5, it touched the star -rr in
the breast of Andromeda on its right side, and the star \i of the girdle on
its left; and, according to our observations, was 40 long; but it was
curved, and the convex side thereof lay to the south ;
arid near the head of
the comet it made an angle of 4 with the circle which passed through the
sun and the comet s head ; but towards the other end it was inclined to
that circle in an angle of about 10 or 11
; and the chord of the tail con
tained with that circle an angle of 8. Jan. 13, the tail terminated be
tween Alamech and Algol, with a light that was sensible enough : but
with a faint light it ended over against the star K in Perseus s side. The
distance of the end of the tail from the circle passing through the sun and
the comet was 3 50 ; and the inclination of the chord of the tail to that
circle was S|. Jan. 25 and 26, it shone with a faint light to the length
of 6 or 7 ; and for a night or two after, when there was a very clear sky.
it extended to the length of 12. or something more, with a light that was
very faint and very hardly to be seen; but the axis thereof was exactly di
rected to the bright star in the eastern shoulder of Auriga, and therefore
deviated from the opposition of the sun towards the north by an angle of
10. Lastly, Feb. 10, with a telescope I observed the tail 2 long ;
for that
fainter light which I spoke of did not appear through the glasses. But
Ponthftiis writes, that, on Feb. 7, lie saw the tail 12 lone:. Feb. 25, the
fjrnet was without a tail, and so continued till it disappeared
THE MATHEMATICAL PRINCIPLES [BOOK III.
Now if one reflects upon the orbit described, and duly considers the other
appearances of this comet, he will be easily satisfied that the bodies of
comets are solid, compact, fixed, and durable, like the bodies of the planets ;
for if they were nothing else but the vapours or exhalations of the earth, of
the sun, and other planets, this comet, in its passage by the neighbourhood
of the sun, would have been immediately dissipated; for the heat of the
sun is as the density of its rays, that is, reciprocally as the square of the
distance of the places from the sun. Therefore, since on Dec. 8, when the
comet was in its perihelion, the distance thereof from the centre of the sun
was to the distance of the earth from the same as about 6 to 1000; the
sun s heat on the comet was at that time to the heat of the summer-sun
with us as 1000000 to 36, or as 28000 to 1. But the heat of boiling
water is about 3 times greater than the heat which dry earth acquires from
the summer-sun, as I have tried : and the heat of red-hot iron (if my con
jecture is right) is about three or four times greater than the heat of boil
ing water. And therefore the heat which dry earth on the comet, while in
its perihelion, might have conceived from the rays of the sun, was about
2000 times greater than the heat of red-hot iron. But by so fierce a heat,
vapours and exhalations, and every volatile matter, must have been imme
diately consumed and dissipated.
This comet, therefore, must have conceived an immense heat from the
sun, and retained that heat for an exceeding long- time ;
for a globe of iron
of an inch in diameter, exposed red-hot to the open air, will scarcely lose
all its heat in an hour s time; but a greater globe would retain its heat
longer in the proportion of its diameter, because the surface (in proportion
to which it is cooled by the contact of the ambient air) is in that proportion
less in respect of the quantity of the included hot matter; and therefore a
globe of red hot iron equal to our earth, that is, about 40000000 feet in
diameter, would scarcely cool in an equal number of days, or in above
50000 years. But I suspect that the duration of heat may, on account of
some latent causes, increase in a yet less proportion than that of the
diameter ; and I should be glad that the true proportion was investigated
by experiments.
It is farther to be observed, that the comet in the month of December.
just after it had been heated by the sun, did emit a much longer tail, and
much more splendid, than in the month of November before, when it had
not yet arrived .it its perihelion; and, universally, the greatest and most
fulgent tails always arise from comets immediately , fter their passing by
the neighbourhood of the sun. Therefore the heat received by the comet
conduces to the greatness of the tail: from whence, I thiufc I may infer,
that the tail is nothing else but a very fine vapour, which the head or
nucleus of the comet emits by its heat.
Jbut we have had three several opinions about the tails of comets; for
BOOK III.] OF NATURAL PHILOSOPHY. 48?
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 refraction which light suf
fers in passing from the comet s head to the earth : and, lastly, others, thac
they are a sort of clouds or vapour constantly rising from the comets7 heads.
and tending towards the parts opposite to the sun. The first is the opin
ion of such as are yet unacquainted with optics : for the beams of the sun
are seen in a darkened room only in consequence of the light that is re
flected from them by the little particles of dust and smoke which are
always flying about in the air; and, for that reason, in air impregnated
with thick smoke, those beams appear with great brightness, and move the
sense vigorously ;
in a yet finer air they appear more faint, and are less
easily discerned ; but in the heavens, where there is no matter to reflect
the light they can never be seen at all. Light is not seen as it is in the
beam, but as it is thence reflected to our eyes ; for vision can be no other
wise produced than by rays falling upon the eyes ; and. therefore, there
must be some reflecting matter in those parts where the tails of the comets
are seen : for otherwise, since all the celestial spaces are equally illumin
ated 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 those colours which
commonly are inseparable from refraction
; and the distinct transmission
of the light of the fixed stars and planets to us is a demonstration that
the aether or celestial medium is not endowed with any refractive power :
for as to what is alleged, that the fixed stars have been sometimes seen by
the Egyptians environed with a Coma or Capit/itinm, because that has
but rarely happened, it is rather to be ascribed to a casual refraction of
clouds; and so the radiation and scintillation of the fixed stars to tin
refractions both of the eyes and air
; for upon laying a telescope to the
eye, those radiations and scintillations immediately disappear. By the trem
ulous 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 ob
ject-glass of a telescope ; and hence it is that a scintillation is occasioned ir,
the former case, wrhich ceases in the latter
; and this cessation in the latter
case is a demonstration of the regular transmission 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 af
fect the eyes, and for that 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 an hundred fold, and yet no tails
are seen ; that the light of the planets is yet more copious without any
488 THE MATHEMATICAL PRINCIPLES [BOOK 111.
tail
; but that comets are seen sometimes with huge tails, when the light
of their heads is but faint and dull. For so it happened in the comet of
the year 1680, when in the month of December it was scarcely equal in
light to the stars of the second magnitude, and yet emitted a notable tail,
extending to the length of 40, 50, 60, or 703
, and upwards ; and after
wards, on the 27th and 28th of January, when the head appeared but us
a star of the 7th magnitude, yet the tail (as we said above), with a light
that was sensible enough, though faint, was stretched out to 6 or 7 degrees
in length, and with a languishing light that was more difficultly seen, even
to .12, and upwards. But on the 9th and 10th of February, when to the
naked eye the head appeared no more, through a telescope I viewed the
tail of 2 in length. But farther; if the tail was owing to the refrac
tion of the celestial matter, and did deviate from the opposition of the
sun, according to the figure of the heavens, that deviation in the same
places of the heavens should be always directed towards the same parts.
Bu n e comet of the year 1680, December 28d
. S^
h
. P. M. at London, was
seen in X 8 41 , with la itude north 28 6 ; while the sun was in V? 18
26 . And the cornet of the year 1577, December 29d
. was in X 8 41 ,
with latitude north 28 40 , and the sin, as before, in about V^ 18 26 .
In both cases the situation of the earth was the same, and the comet ap
peared in the same place of the heavens ; yet in the former case the tail
of the comet (as well by my observations as by the observations of others)
deviated from the opposition of the sun towards the north by an angle of
4|- degrees ; whereas in the latter there was (according to the observations
of Tychfi) a deviation of 21 degrees towards the south. The refraction,
therefore, of the heavens being thus disproved, it remains that the phatiomena
of the tails of comets must be derived from some reflecting matter.
And that the tails of comets do arise from their heads, and tend towards
the parts opposite to the sun, is. farther confirmed from the laws which
the tails observe. As that, lying in the planes of the comets orbits
which pass tl trough the sun, they constantly deviate from the opposition
of the sun towards the parts which the comets heads in their progress
along these orbits have left. That to a spectator, placed in those planes,
they appear in the parts directly opposite to the sun ; but, as the spectator
recedes from th >se planes, their deviation begins to appear, and daily be
comes greater. That the deviation, cceteris paribus, appears less when
the tail is more oblique to the orbit of the comet, as well as when the
head of the comet approaches nearer to the sun, especially if the angle of
deviation is estimated near the head of the comet. That the tails which
have no deviation appear straight, but the tails which deviate are like
wise bended into a certain curvature. That this curvature is greater when
the deviation is greater ; and is more sensible when the tail, cceteris paribus
is longer ;
for in the shorter tails the curvature is hardly to be p-jr
HOOK HI.] or NATURAL PHILOSOPHY. 489
ccived. That the angle of deviation is less near the comet s head, but
greater towards the other end of the tail
; and that because the convex
side of the tail regards the parts from which the deviation is made, and
which lie in a right line drawn out infinitely from the sun through the
comet s head. And that the tails that are long and broad, and shine with
a stronger light, appear more resplendent and more exactly defined on the
convex than on the concave side. Upon which accounts it is plain that
the phenomena of the tails of comets depend upon the motions of their
heads, and by no means upon the places of the heavens in which their
heads are seen ; and that, therefore, the tails of comets do not proceed from
the refraction of the heavens, but from their own heads, which furnish the
matter that forms the tail. For, as in our air, the smoke of a heated body
ascends either perpendicularly if the body is at rest, or obliquely if the
body is moved obliquely, so in the heavens, where all bodies gravitate to
wards the sun, smoke and vapour must (as we have already said) ascend
from the sun, and either rise perpendicularly if the smoking body is at
rest, or obliquely if the body, in all the progress of its motion, is always
leaving those places from which the upper or higher parts of the vapour
had risen before ; and that obliquity will be least where the vapour ascends
with most velocity, to wit, near the smoking body, when that is near the
sun. But, because the obliquity varies, the column of vapour will be incurvated
; and because the vapour in the preceding sides is something more
recent, that is, has ascended something more late from the body, it will
therefore be something more dense on that side, and must on that account
reflect more light, as well as be better defined. I add nothing concerning
the sudden uncertain agitation of the tails of comets, and their irregular
figures, which authors sometimes describe, because they may arise from the
mutations of our air, and the motions of our clouds, in part obscuring
those tails ; or, perhaps, from parts of the Via Laclea, which might have
been confounded with and mistaken for parts of the tails of the comets JIB
they passed by.
But that the atmospheres of comets may furnish a supply of vapour
great enough to fill so immense spaces, we may easily understand from the
rari ty of our own air
; for the air near the surface of our earth possesses
a space 850 times greater than water of the same weight ; arid therefore
a cylinder of air 850 feet high is of equal weight with a cylinder of water
of the same breadth, and but one foot high. But a cylinder of air reach
ing to the top of the atmosphere is of equal weight with a cylinder of
water about 33 feet high : and, therefore, if from the whole cylinder of
air the lower part of 850 feet high is taken away, the remaining upper
part will be of equal weight with a cylinder of water 32 feet high : and
from thence (and by the hypothesis, confirmed by many experiments, that
the compression of air is as the weight of the incumbent atmosphere, and
400 THE MATHEMATICAL PRINCIPLES [BOOK III
that the force of gravity is reciprocally as the square of the distance from
the centre of the earth) raising a calculus, by Cor. Prop. XXII, Book II,
I found, that, at the height of one semi-diameter of the earth, reckoned
from the earth s surface, the air is more rare than with us in u far greater
proportion than of the whole space within the orb of Saturn to a spherical
space of one inch in diameter ; and therefore if a sphere of our air of but
one inch in thickness was equally rarefied with the air at the height of
one semi-diameter of the earth from the earth s surface, it would rill all
the regions of the planets to the orb of Saturn, and far beyond it. Where
fore since the air at greater distances is immensely rarefied, and the coma
or atmosphere of comets is ordinarily about ten times higher, reckoning
from their centres, than the surface of the nucleus, and the tails rise yet
higher, they must therefore be exceedingly rare ; and though, on account
of the much thicker atmospheres of comets, and the great gravitation of
their bodies towards the sun, as well as of the particles of their air and
vapours mutually one towards another, it may happen that the air in the
celestial spaces and in the tails of comets is not so vastly rarefied, yet
from this computation it is plain that a very small quantity of air and
vapour is abundantly sufficient to produce all the appearances of the tails
of comets : for that they are, indeed, of a very notable rarity appears from
the shining of the stars through them. The atmosphere of the earth,
illuminated by the sun s light, though but of a few miles in thickness,
quite obscures and extinguishes the light not only of all the stars, but
even of the moon itself; whereas the smallest stars are seen to shine
through the immense thickness of the tails of comets, likewise illuminated
by the sun, without the least diminution of their splendor. Nor is the
brightness of the tails of most comets ordinarily greater than that of our
air, an inch or two in thickness, reflecting in a darkened room the light of
the sun-beams let in by a hole of the window-shutter.
And we may pretty nearly determine the time spent during the ascent
of the vapour from the comet s head to the extremity of the tail, by draw
ing a right line from the extremity of the tail to the sun, and marking
the place where that right line intersects the comet s orbit : for the vapour
that is now in the extremity of the tail, if it has ascended in a right line
from the sun, must have begun to rise from the head at the time when the
head was in the point of intersection. It is true, the vapour does not rise
in a right line from the sun, but, retaining the motion Avhich it had from
the comet before its ascent, and compounding that motion witli its motion
of ascent, arises obliquely ; and, therefore, the solution of the Problem will
be more exact, if we draw the line which intersects the orbit parallel to
the length of the tail
; or rather (because of the curvilinear motion of the
comet) diverging a little from the line or length of the tail. And by
means of this principle I found that the vapour which, Ja/iutiry 25, was
BOOK III.] OF NATURAL PHILOSOPHY. 491
in the extremity of the tail, had begun to rise from the head before De
cember 11, and therefore had spent in its whole ascent 45 days ; but that
the whole tail which appeared on December 10 had finished its ascent in
the space of the two days then elapsed from the time of the comet s being
in its perihelion. The vapour, therefore, about the beginning and in the
neighbourhood of the sun rose with the greatest velocity, and afterwards
continued to ascend with a motion constantly retarded by its own gravity ;
and the higher it ascended, the more it added to the length of the tail
;
and while the tail continued to be seen, it was made up of almost all that
vapour which had risen since the time of the comet s being in its perihe
lion
; nor did that part of the vapour which had risen first, and which
funned the extremity of the tail, cease to appear, till its too great dis
tance, as well from the sun, from which it received its li^it, as from our
eyes, rendered it invisible. Whence also it is that the tails of other comets
which are short do riot rise from their heads with a swift and continued
motion, and soon after disappear, but are permanent and lasting columns
of vapours and exhalations, which, ascending from the heads with a slowmotion
