an hundred fold and yet no tails are seen; that the light of the planets is
yet more copious without any 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 De
THE SYSTEM OF THE WORLD. 557
cember 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
70, and upwards ; and afterwards, on the 27th and 28th of January, the
head appeared but as a star of the seventh magnitude ; but the tail (as
was 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,
I saw through a telescope the tail of 2 in length. But farther : if the
tail was owing to the refraction of the celestial matter, and did deviate
from the opposition of the sun, according as the figure of the heavens re
quires, that deviation, in the same places of the heavens, should be always
directed towards the same parts : but the comet of the year 1680, Decem
ber 28 1
. SJ
1
. P. M. at London, was seen in Pisces, 8 41 , with latitude
north 28 6 , while the sun was in Capricorn 18 26 . And the comet of
the year 1577, December 29, was in Pisces 8 41 , with latitude north
2SD 40 ; and the sun, as before, in about Capricorn 18 26 . In both
cases the situation of the earth was the same, and the comet appeared 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| de
grees, whereas in the latter there was (according to the observation of
Tycht] a deviation of 21 degrees towards the south. The refraction,
therefore, of the heavens being thus disproved, it remains that the phaenomeria
of the tails of comets must be derived from some reflecting matter.
That vapours sufficient to fill such immense spaces may arise from the
comet s atmospheres, may be easily understood from what follows.
It is well known that the air near the surface of our earth possesses a
space about 1200 times greater than water of the same weight ; and there
fore a cylindric column of air 1200 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 reaching 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 1200 feet high is taken away, the
remaining upper part will be of equal weight with a cylinder of water 32
feet high. Wherefore at the height of 1200 feet, or two furlongs, the
weight of the incumbent air is less, and consequently the rarity of the
compressed air greater, than near the surface of the earth in the ratio of
33 to 32. And, having this ratio, we may compute the rarity of the air
in all places whatsoever (by the help of Cor. Prop. XXII, Book II), sup
posing the expansion thereof to be reciprocally proportional to its compres
sion ; and this proportion has been proved by the experiments of Hooke
and others. The result of the computation I have set down in the follow
558 THE SYSTEM CF THE WORLD.
ing table, in the first column of which you have the height o the air in
miles, whereof 4000 m:ike a semi-diameter of the earth; in the second the
compression of the air, or the incumbent weight ; in the third its rarity or
expansion, supposing gravity to decrease in the duplicate ratio of the
distances from the earth s centre. And the Latin numeral characters
are here used for certain numbers of ciphers, as 0,xvii 1224 for
IMJ00000000000000001224, and 26950 xv for 26956000000000000000,
AlR s
But from this table it appears that the air, in proceeding upwards, is
rarefied in such manner, that a sphere of that air which is nearest to the
earth, of but one inch in diameter, if dilated with that rarefaction which
it would have at the height of one semi-diameter of the earth, would fill all
the planetary regions as far as the sphere of Saturn, and a great way be
yond ; and at the height of ten semi-diameters of the earth would fill up
more space than is contained in the whole heavens on this side the fixed
stars, according to the preceding computation of their distance. And
though, by reason of the far greater thickness of the atmospheres of comets,
and the great quantity of the circum-solar centripetal force, 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 ^s plain that a very small
quantity of air and vapour is abundantly sufficient to produce all the ap
pearances 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 atmos
phere of the earth, illuminated by the sun s light, though but of a few miles
in thickness, obscures arid 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.
Kepler ascribes the ascent of the tails of comets to the atmospheres of
their heads, and their direction towards the parts opposite to the sun to the
action of the rays of light carrying along with them the matter of the
comets tails
; and without any great incongruity we may suppose that, in
so free spaces, so fine a matter as that of the aether may yield to the action
THE SYSTEM OF THE WORLD. 559
of the rays of the sun s light, though those rays are not able sensibly to move
the gross substances in our parts, which are clogged with so palpable a re
sistance. Another author thinks that there may be a sort of particles of
matter endowed with a principle of levity as well as others are with a
power of gravity ; that the matter of the tails of comets may be of the
former sort, and that its ascent from the sun may be owing to its levity ;
but, considering the gravity of terrestrial bodies is as the matter of the
bodies, and therefore can be neither more nor less in the same quantity of
matter, I am inclined to believe that this ascent may rather proceed from
the rarefaction of the matter of the comets tails. The ascent of smoke in
a chimney is owing to the impulse of the air with which it is entangled.
The air rarefied by heat ascends, because its specific gravity is diminished,
and in its ascent carries along with it the smoke with which it is engaged.
/Vnd why may not the tail of a comet rise from the sun after the same
manner? for the sun s rays do not act any way upon the mediums which
they pervade but by reflection and refraction ; and those reflecting parti
cles heated by this action, heat the matter of the aether which is involved
with them. That matter is rarefied by the heat which it acquires, and
because by this rarefaction the specific gravity, with which it tended
towards the sun before, is diminished, it will ascend therefrom like a stream,
and carry along with it the reflecting particles of which the tail of the
comet is composed ; the impulse of the sun s light, as we have said, pro
moting the ascent.
But that the tails of comets do arise from their heads (p. 488), and tend
towards the parts opposite to the sun, is farther confirmed from the laws
which the tails observe ; for, lying in the planes of the comets orbits which
pass through the sun, they constantly deviate from the opposition of the
sun towards the parts which the comets heads in their progress along those
orbits have left
; and to a spectator placed in those planes they appear in
the parts directly opposite to the sun ;
but as the spectator recedes from
those planes, their deviation begins to appear, and daily becomes greater.
And the deviation, c&teris paribits, appears less when the tail is more ob
lique to the orbit of the comet, as well as when the head of the comet ap
proaches nearer to the sun .; especially if the angle of deviation is estimated
near the head of the comet. Farther; the tails which have no deviation
appear straight, but the tails which deviate are likewise bended into a cer
tain curvature ; and this curvature is greater when the deviation is greater,
and is more sensible when the tail, cccteris paribus, is longer; for in the
shorter tails the curvature is hardly to be perceived. And the angle of
deviation is less near the comet s head, but greater towards the other end
of the tail, and that because the lower 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 the tails that are
560 THE SYSTEM OF THE WORLD.
longer and broader; 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 comet? de
pend 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 tailg of
the 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 the bodies gravitate towards the sun, smoke and vapour
must (as we have already said) ascend from the sun, and either rise perpen
dicularly, if the smoking body is at rest, or obliquely, if the body, in the
progress of its motion, is always leaving those places from which the upper
or higher parts of the vapours had risen before. And that obliquity will
be less where the vapour ascends with more velocity, to wit, near the
smoking body, when that is near the sun ;
for there the force of the sun by
which the vapour ascends is stronger. But because the obliquity is varied,
the column of vapour will be incurvated ; and because the vapour in the
preceding side is something more recent, that is, has ascended something
more lately 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 ;
the vapour on the other side languishing by degrees, and vanish
ing out of sight.
But it is none of our present business to explain the causes of the ap
pearances of nature. Let those things which we have last said be true or
false, we have at least made out, in the preceding discourse, that the rays
of light are directly propagated from the tails of comets in right lines
through the heavens, in which those tails appear to the spectators wherever
placed ; and consequently the tails must ascend from the heads of the comets
towards the parts opposite to the sun. And from this principle we may
determine anew the limits of their dis-
<~ tances in manner following. Let S represent
the sun, T the earth, STA the
elongation of a comet from the sun, and
ATB the apparent length of its tail;
and because the light is propagated from
the extremity of the tail in the direction
of the right, line TB, that extremity
must lie somewhere in the line TB.
Suppose it in D, and join DS cutting
TA in C. Then, because the tail is al -
ways stretched out towards the parts
nearly opposite to the sun, and there! ore
THE SYSTEM OF THE WORLD. 561
the sun, the head of the comet, and the extremity of the tail, lie in a right
line, the comet s head will be found in C. Parallel to TB draw SA, meet
ing the line TA in A, arid the comet s head C must necessarily be found
between T and A, because the extremity of the tail lies somewhere in the
infinite line TB ; and all the lines SI) which can possibly be drawn from
the point S to the line TB must cut the line TA somewhere between T
and A. Wherefore the distance of the comet from the earth cannot exceed
the interval TA. nor its distance from the sun the interval SA beyond, or
ST on this side the sun. For instance : the elongation of the comet of
16SO from the sun, Dec. 12, was 9, and the length of its tail 35 at least.
If, therefore, a triangle TSA is made, whose angle T is equal to the elon
gation 9, and angle A equal to ATB, or to the length of the tail, viz., 35,
then SA will be to ST, that is, the limit of the greatest possible distance
of the comet from the sun to the semi -diameter of the oj-bis magnus, as
the sine of the angle T to the sine of the angle A, that is, as about 3 to
11. And therefore the comet at that time was less distant from the sun
than by T
3
T of the earth s distance from the sun, and consequently either
was within the orb of Mercury, or between that orb and the earth. Again,
Dec. 21, the elongation of the comet from the sun was 32f , and the length
of its tail 70. Wherefore as the sine of 3^| to the sine of 70, that is,
as 4 to 7, so was the limit of the comet s distance from the sun to the dis
tance of the earth from the sun, and consequently the comet had not then
got without the orb of Venus. Dec. 28, the elongation of the comet from
the sun was 55, and the length of its tail 56 ; and therefore the limit of
the comet s distance from the sun was not yet equal to the distance of the
earth from the same, and consequently the comet had not then got without
the earth s orbit. But from its parallax we find that its egress from the
orbit happened about Jan. 5, as well as that it had descended far within
the orbit of Mercury. Let us suppose it to have been in its perihelion
Dec. the 8th, when it was in conjunction with the sun ; and it will follow
that in the journey from its perihelion to its exit out of the earth s orbit
it had spent 28 days ; and consequently that in the 26 or 27 days fol
lowing, in which it ceased to be farther seen by the naked eye, it had
scarcely doubled its distance from the sun ; and by limiting the distances
of other comets by the like arguments, we come at last to this conclu
sion, that all comets, during the time in which they are visible by us,
are within the compass of a spherical space described about the sun as a
centre, with a radius double, or at most triple, of the distance of the earth
from the sun.
And hence it follows that the comets, during the whole time of their
appearance unto us, being within the sphere of activity of the circum
solar force, and therefore agitated by the impulse of that force, will (by
Cor. 1, Prop. XII, Book I, for the same reason as the planets) be made tc
36
562 THE SYSTEM OF THE WORLD.
move in conic sections that have one focus in the centre of the sun, and
by radii drawn to the sun, to describe areas proportional to the times ;
for
that force is propagated to an immense distance, and will govern the
motions of bodies far beyond the orbit of Saturn.
There are three hypotheses about comets (p. 466) ; for some will have it
that they are generated and perish as often as they appear and vanish ;
others, that they come from the regions of the rixed stars, and are seen by
us in their passage through the system of our planets ; and, lastly, others,
that they are bodies perpetually revolving about the sun in very eccentric
orbits. In the first case, the comets, according to their different vel cities,
will move in conic sections of all sorts; in the second, they will describe
hyperbolas, and in either of the two will frequent indifferently all quar
ters of the heavens, as well those about the poles as those towards the
ecliptic ;
in the third, their motions will be performed in ellipses very ec
centric, and very nearly approaching to parabolas. But (if the law of the
planets is observed) their orbits will not much decline from the plane of
the ecliptic; and, so far as I could hitherto observe, the third case obtains;
for the comets do, indeed, chiefly frequent the zodiac, and scarcely ever
attain to a heliocentric latitude of 40. And that they move in orbits
very nearly parabolical, I infer from their velocity ;
for the velocity with
which a parabola is described is every where to the velocity with which a
comet or planet may be revolved about the sun in a circle at the same dis
tance in the subduplicate ratio of 2 to 1 (by Gor. VII, Prop. XVI) ; and,
by my computation, the velocity of comets is found to be much about
the same. I examined the thing by inferring nearly the velocities from
the distances, and the distances both from the parallaxes and the phaenornena
of the tails, and never found the errors of excess or defect in the ve
locities greater than what might have arose from the errors in the dis
tances collected after that manner. But I likewise made use of the reason
ing that follows.
Supposing the radius of the nrbis magiius to be divided into 1000
parts: let the numbers in the first column of the following table represent
the distance of the vertex of the parabola from the sun s centre, expressed
by those parts : and a comet in the times expressed in col. 2, will pass
from its perihelion to the surface of the spheie which is described about
the sun as a centre with the radius of the orbis magnus ; and in the
times expressed in col. 3, 4, and 5, it will double, triple, and quadruple,
that its distance from f.l:o sun.
THE SYSTEM 0* THE WORLD. 563
TABLE L
[This table, here corrected, is made on the supposition that the earth s
diurnal motion is just 59 , and the measure of one minute loosely 0,2909,
in respect of the radius 1000. If those measures are taken true, the
true numbers of the table will all come out less. But the difference,
even when greatest, and to the quadruple of the earth s distance from
the sun, amounts only to 16h
. 55 .]
The time of a comet s ingress into the sphere of the orbis magnus, or
of its egress from the same, may be inferred nearly from its parallax, bn1
with more expedition by the following
TABLE II.
564 THE SYSTEM OF THE WORLD.
The ingress 01 a comet into the sphere of the orbis magnus, or its
egress from the same, happens at the time of its elongation from the sun,
expressed in col. 1, against its diurnal motion. So in the comet of 1681.
Jan. 4, O.S. the apparent diurnal motion in its orbit was about 3 5 , and
the corresponding elongation 71 J ; and the comet had acquired this elon
gation from the sun Jan. 4, about six in Ae evening. Again, in the year
1680, Nov. 11, the diurnal motion of the comet that then appeared was
about 4| ; and the corresponding elongation 79f happened Now. 10, a
little before midnight. Now at the times named these comets had arrived
at an equal distance from the sun with the earth, and the earth was then
almost in its perihelion. But the first table is fitted to the earth s mean
distance from the sun assumed of 1000 parts ; and this distance is greater
by such an excess of space as the earth might describe by its annual motion
in one day s time, or the comet by its motion in 16 hours. To reduce the
comet to this mean distance of 1000 parts, we add those 16 hours to the
former time, and subduct them from the latter
; and thus the former be
comes Jan. 4d
. 10 1
. afternoon ;
the latter Nov. 10, about six in the morn
ing. But from the tenor and progress of the diurnal motions it appears
that both comets were in conjunction with the sun between Dec. 7 and Dec.
8 ; and from thence to Jan. 4d
. 10h
. afternoon on one side, and to Nov.
10 . 6h
. of the morning on the other, there are about 28 days. And so
many days (by Table 1) the motions in parabolic trajectories do require.
But though we have hitherto considered those comets as two, yet, from
the coincidence of their perihelions and agreement of their velocities, it is
probable that in effect they were but one and the same ; and if so, the
orbit of this comet must have either been a parabola, or at least a conic
section very little differing from a parabola, and at its vertex almost in
contact with the surface of the sun. For (by Tab. 2) the distance of the
comet from the earth, Nov. 10, was about 360 parts, and Jan. 4, about
630. From which distances, together with its longitudes and latitudes,
we infer the distance of the places in which the comet was at those times
to have been about 280 : the half of which, viz., 140, is an ordinate to the
comet s orbit, cutting off a portion of its axis nearly equal to the radius
of the orbis magnus, that is, to 1000 parts. And, therefore, dividing the
square of the ordinate 140 by 1000, the segment of the axis, we find the
latu$ rectum 19, 16, or in a round number 20 ; the fourth part whereof,
5, is the distance of the vertex of the orbit from the sun s centre. But the
time corresponding to the distance of 5 parts in Tab. 1 is 27d
. 16h
. 7 . Ir.
which time, if the comet moved in a parabolic orbit, it would have been
carried from its perihelion to the surface of the sphere of the orbis mag*
nus described with the radius 1000, and would have spent the double of
that time, viz., 55d
. 8|
h
. in the whole course of its motion within that
sphere : and so in fact it did ; for from Nov. 10d
. 6h
. of the morning, thf
THE SYSTEM OF THE WORLD. OOC
time of the comet s ingress into the sphere of the orbis magnns, to Jan..
4 1
. 10h
. afternoon, the time of its egress from the same, there are 55(1
. 16h
.
The small difference of 7 u
. in this rude way of computing is to be neg
lected, and perhaps may arise from the comet s motion being some small
matter slower, as it must have been if the true orbit in which it was car
ried was an ellipsis. The middle time between its ingress and egress was
December Sd
. 21
. of the morning ; and therefore at this time the comet
ought to have been in its perihelion. And accordingly that very day, just
before sunrising, Dr. Halley (as we said) saw the tail short and broad, butvery
bright, rising perpendicularly from the horizon. From the position
of the tail it is certain that the comet had then crossed over the ecliptic,
and got into north latitude, and therefore had passed by its perihelion,
which lay on the other side of the ecliptic, though it had not yet come into
conjunction with the sun ; and the comet [see more of this famous comet,
p. 475 to 486] being at this time between its perihelion and its conjunc
tion with the sun, must have been in its perihelion a few hours before;
for in so near a distance from the sun it must have been carried with great
velocity, and have apparently described almost half a degree every hour.
By like computations I find that the comet of 1618 entered the sphere
of the orbis maxims December 7, towards sun-setting ; but its conjunc
tion with the sun was Nov. 9, or 10, about 28 days intervening, as in the
preceding comet ;
for from the size of the tail of this, in wtrch it was
equal to the preceding, it is probable that this comet likewise did come
almost into a contact with the sun. Four comets were seen that year of
which this was the last. The second, which made its first appearance
October 31, in the neighbourhood of the rising sun, and was soon after hid
under the sun s rays, 1 suspect to have been the same with the fourth,
which emerged out of the sun s rays about Nov. 9. To these we may add
the comet of 1607, which entered the sphere of the orbis mi^-tnis Sept.
14, O.S. and arrived at its perihelion distance from the sun about October
19, 35 days intervening. Its perihelion distance subtended an apparent
angle at the earth of about 23 degrees, and was therefore of 390 parts.
And to this number of parts about 34 days correspond in Tab. 1 . Far
ther ; the comet of 1665 entered the sphere of the orbis nta^tnts about
March 17, and came to its perihelion about April 16, 30 days intervening.
Its perihelion distance subtended an angle at the earth of about seven
degrees, and therefore was of 122 parts : and corresponding to this number
of parts, in Tab. 1, we find 30 days. Again ; the comet of 1 682 entered
the sphere of the orbis magnus about Aug. 11, and arrived at its perihe
lion about Sep. 16, being then distant from the sun by about 350 parts, to
