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general, the later astronomers have agreed in ; but
have differed in explaining the particular manner in
v/hich the sun produces such an appearance. Some
have thought the tails of Comets to be nothing but
th.e rays of the sun transmitted through the body or
head of the Comet, which for this purpose they are
obliged to suppose transparent; and so yielding the
appearance of a sun-beam behind the Comet, that is, on
the side opposite to the sun. And others have added,
that the rays are refracted in passing through the
head, as through a glass lens. This they illustrate
by the example of the sun*s shining through a small



10 ON COMETS.

hole into a darkened room, in which case a stream of
light is seen extended from the hole. But this hy-
pothesis will by no means account for the phaenome-
non in question. It might be urged against it, that
the transparence of the Comet is an arbitrary suppo-
sition; and that for the most part, the figure does not
answer ; such a stream of light in a darkened room
being always perfectly straight, whereas the tails of
Comets are often curved : neither does the direction
answer; such a stream of light being always exactly
opposite to the sun, whereas the tails of Comets usu-
ally deflect a little from the precise point of opposition.
But not to insist upon these arguments, it should be
considered, that a sun-beam in a darkened room i&
perceived, only so far as the light is reflected from
the particles of dust and smoke, which are always
floating in the air. For the rays of light in the beam
are not discerned by an eye placed on the side of it,
any otherwise than by being reflected to the eye from
some substance in the place where the beam appears.
And hence it is, that when the air is full of thick
smoke and dust, such a sun-beam appears brighter ;
for there being then a greater number of reflecting
particles, a greater number of rays are reflected, and
strike the eye more strongly. When the air is more
clear and free from motes, the sun-beam appears
fainter, and is not so easily perceived; and if there
were no reflecting matter there at all, it could not at
all be perceived. Since therefore vision is caused
only by those rays which fall on the eye, it is neces-



ON COMfiTS. 11

sary to suppose some reflectiisg matter where the
tail appears ; and this matter must be grosser and
denser in that place than in the other aetherial regions ;
otherwise, the whole heaven, being equally illu-
minated by the sun, would shine as much as the
tail of the Comet, and appear throughout of an uni-
form brightness. The tail therefore does not pro-
ceed from the rays of the sun transmitted through
the head of the Comet.

A late author has attempted to mend this hypothe-
sis, by supposing that the rays of the sun are refract-
ed in passing through the atmosphere of the Comet,
and so made to converge on the part opposite to the
sun ; and the light being by this means condensed,
illuminates that part of the atmosphere, enough to
render it visible to us ; and that this illuminated part
is what is called the Comet's tail. But besides that
this opinion is liable to almost the same difficulties as
the foregoing, it supposes the atmosphere of a Co-
met to be extended all round the body, though invi-
sibly, to the same distance as the tail is, which in
some cases has been many millions of miles ; — a sup-
position, which, without some further proof, will not
easily gain belief.

Others, who saw the insufficiency of the forego-
ing hypothesis of the transmission of light, have ad-
vanced another, still more improbable, and endea-
voured to account for the tails of Comets by the re-
fraction of light in its passage from the head of the
Comet to the earth. They have supposed that as the



12 ON COMETS.

round image of the sun, by being refracted in pass-
ing through a glass prism, is thrown into an oblong
form ; so the light proceeding from the round head
of the Comet may, in passing through the aetheriai re-
gions, be refracted in such a manner as to appear long,
and produce this phsenomenon of the tail. To this opi-
nion it is an obvious objection, that the rays of the
fixed stars and planets, since they pass through the
same medium as those which come from Comets,
are liable to the same refraction, and ought therefore
to exhibit the same appearance ; and some of these
should have larger and brighter tails than most Co-
mets, since their light is much stronger. But even
those stars and planets, whose light is strongest and
most copious, have no tails ; nor can any be discovered
belonging to them by the best telescopes, which will
increase their lieht above an hundred times; while
some Comets, whose lightwas but weak and dull, have
had very large and bright tails. Besides, the tails of Co-
mets are never variegated with colours, as the oblong
image produced by the prism is ; which variety of co-
lours is a necessary result of that unequal refrangi-
bility of the rays, by which the prismatic image, in-
stead of being round, is made oblong. Farther: If
the tail arose from the refraction of light in its pas-
sage througli the heavens; whenever the light pusses
through the same part of the heavens ; it ought to be
refracted the same way. But this is contrary to obser-
vation. For two Comets have been seen in the same
place of the heavens, when t!ie earth was likewise



ON COMETS. 13

in the same part of its orbit; yet their tails have not
been turned the same way, but have contained a large
angle between them.* This difference in their di-
rection could not be the effect of a refraction in the
heavens, which in such circumstances must have been
the same. These causes therefore being rejected,
the phenomena of the tails must be derived from
some matter in them, which reflects light.

The ascent of the tails towards the parts opposite to
the sun, some authors of note have ascribed to the
action of the sun's rays, driving the matter of the
tail before them. And considering the extreme ra-
rity of the vapour which composes the tail, and the
surprising velocity of the rays of light, perhaps it
may not be altogether impossible for the matter of
the tail to yield in some measure to the impulse of
the rays, and be driven before them that way towards
which their motion is directed; that is, to the parts
opposite to the sun. But if such a cause should be
allowed to have some small share in producing the
phasnomenon, yet this can hardly be deemed an ade-
quate solution ; nor should much stress be laid upon
it, as we know of no parallel instance in nature to
support it.

As to the line in which Comets move, some of the
most considerable astronomers of the last century
supposed it to be a strait line, or nearly so. Kepler,
from his own observations of two Comets, concluded

* A remarkable instance of this may be seen in Newtoni
Principia, p. 510, 511.



14 ON COMETS.

that they moved freely any way between the orbits of
the planets, with a motion not very different from a
rectilinear one. Hevelius, who carefully observed
several Comets, embraced the same hypothesis; but
was sensible that his calculations founded upon it did
not perfectly agree with the heavens, and perceived
that the path of a Comet was in a line incurvated to-
wards the sun. But what this curve is, these astro-
nomers, like all who went before them, were unable
to determine.

We have now set aside some of the false opinions
concerning Comets, which have been most regarded.
It has been shewed that they are neither below the
moon, nor among the fixed stars; that they consist
not of any kind of exhalations ; — that their tails are
not produced by the transmission of light through
their bodies ; nor by any refraction of light, caused
either by their atmospheres or by the celestial matter
through which it passes; — that the tails are not turn-
ed opposite to the sun by the impulse of his rays; and
lastly, that the motion of Comets is not in strait lines.
Some better account of these things is therefore to
be sought for.

Indeed, the opinions concerning Comets, which
formerly passed current with many, were suspected
by others. Thus Seneca the philosopher, dissatis-
fied with the doctrine of his time relating to them,
and unable to substitute a better, foretold, that " in
" future ages, some man would demonstrate in what
" parts of the heavens the Comets wander, why they



ON C0MET5. 15

" depart so far from the other wandering stars, and
" what sort of bodies they are."* The prediction
has been fulfilled in the present age ; and this man
was Sir Isaac Newton. After many centuries
elapsed, with little insight gained into the true con-
stitution of these bodies, and none at all into their
real motions, this great genius arose, and with a
strength of mind peculiar to himself (I had almost
said, more than human)

" Pursu'd the Comets where they farthest run,
** And brought them back obsequious, to the sun,"

as Pope has happily expressed it. Formed to pene-
trate into the most abstruse recesses of nature, he
traced these unknown travellers through every step
of their long journey, delineated the particular tour
they make, and shewed by what secret influence they
are determined to revisit our planetary regions, after
an absence of scores, or rather centuries of years.
The explication of these particulars you may expect
in the next discourse.

* Seneca Natural. Qiissst. Lib. vii. Cap. xsvi.
Read, 11th of April, 1759.



LECTURE II.



i-N the last discourse we examined such of those
false hypotheses concerning Comets, as had been
most regarded in the world. I then took no notice
of some others which have been advanced upon this
head, because, as they carried less shew of probabi-
lity, they have had fewer and less considerable advo-
cales,and in consequence have fallen into neglect. And
for the same reason, I shall not spend any of the time
allotted for the present exercise in the confutation of
such hypotheses, but enter immediately upon the
explanation of the true theory of Comets, for which
the world is indebted to the unparalleled invention of
Sir Isaac Newton. And here we shall begin with
shewing what their real course in the heavens is, as
that will throw light upon some other parts of their
theory.

An essential part of Sir Isaac's doctrine is, that
ancient Pythagortan one already mentioned,* viz.
that Comets are a kind of wandering stars, which are
moved in peculiar orbits of their own. This doctrine
received hardly any improvement until his time, but
he alone carried it to an height, which might rather

* In p. 4.



ON COMETS, 17

have been wished for than expected ; and has left those
who come after him little to do, but to apply his the-
ory to the several Comets, as they shall appear. Ac-
cording to this excellent philosopher then, The Co-
mets are a kind of planets, that is, firm, compact,
durable bodies; revolving round the sun in conic sec-
tions, and, by right lines drawn to the sun, describ-
ing areas proportional to the times. That they are
not formed of exhalations or vapors, but are firm, du-
rable bodies, was shewed the last time ; as also, that
the astronomers before Newton, who supposed their
trajectories to be nearly rectilinear, perceived they
were not accuratelv so, but were rather bent in to-
wards the sun ; though what the particular line of this
motion was, they were not able to determine. But
Sir Isaac Newton has demonstrated from his prin-
ciple of gravity^ that it must be some one of the conic
sections. For, having discovered that all the globes
in our system mutually gravitate towards each other
with forces reciprocally proportional to the squares
of their distances ; and that by this gravitation of the
primary planets to the sun, I hey are restrained from
going on in right lines, and are compelled to move
in curvilinear orbits ; he next demonstrated,* that
whenever a body is niade to revolve round another,
by such a centripetal force as this, — by a force which
at all distances from the central body is reciprocally as
the squares of the distances, the revolving body must
necessarily describe some conic section, in one focus

* Princip. Lib. i. Prop. xvli.
*2



■is - ON COMETS*

of which the central body will be placed. And the
species of the orbit will depend on these two circum-
stances ; — on the proportion which the velocity or
projectile force of the revolving body bears to the
force of its gravitation towards the central one ; and
on the angle contained between the directions of these
two forces. The planets therefore, whose motions are
governed by such a gravitating force, will move
in some conic section. Accordingly, what Kepler
discovered is now established by the general consent
of astronomers, that the orbits of all the primary pla-
nets are one sort of conic sections, viz. ellipses, in
one focus of which the sun resides. The law is ge-
neral, and extends to the secondary planets also ; and
the moon moves in an elliptic orbit which has the
earth in one focus. And each of these planets, pri-
mary and secondary, by straight lines drawn to the
central body, describes areas proportional to the
times ; and so moves swifter, as it comes nearer the
centre : which law of their motion Sir Isaac New-
ton has demonstrated to take place in all bodies re-
volving by any kind of centripetal force whatsoever.
These points being settled, and Sir Isaac, finding,
as has been mentioned,* that the Comets come with-
in the planetary regions, and consequently within the
reach of gravitation to the sun, concludes, by force
of the forementioned demonstration, that they, as
well as the planets, must move in some conic section
about the sun. But there is no necessity that their

* See above p. 7.



ON COMETS. 19

orbits should be of the same species as those of the
planets. The elliptic orbits of the planets are all dif-
ferent, and the orbits of the Comets may be differ-
ent from any of them. The conic sections are three,
viz. the hyperbola, parabola, and ellipsis; to which
may be added, the circle. The two former of these
are extended infinitely ; the latter return into them-
selves. If the velocity of a Comet, at any distance
from the sun, were in the same proportion to the ve-
locity of a planet revolving in a circle at that dis-
tance, as the diagonal of a square is to its side, that
is, nearly as 7 to 5, the Comet would move in a pa-
rabola ;* and with a greater velocity, in an hyperbola :
and in both these cases, having once passed by the
sun, it would never return more ; the velocity ac-
quired in its descent being now great enough to
throw it off to the fixed stars, so that its gravitation
to the sun would never be able to bring it back.
With a less velocity than this, a Comet would move
in an ellipsis ; or, with a certain adjustment of the
circumstances, in a circle. If Comets be supposed
to move in a parabola or hyperbola, their number
must be vastly great, because the number of their
appearances hath been so ; and each appearance must
have been of a different Comet, since, on this suppo-
sition, no Comet could be seen twice. Besides: we
have no reason to think, that any of the bodies, which
belong to our system, can belong also to any system
among the fixed stars ; which seem to be placed at

* Newt. Princip. Lib. i. Prop. xvi. Corol. 7.



20 ©N COMETS.

such immense distances from us, with design to cut
off all intercourse between them and us. Farther :
it is certain that Comets do not revolve in circles, or
in ellipses of a small eccentricity, as the planets do ;
for if they did, they would be seen constantly, a.s the
planets are. But it is well known, that Comets are
visible but a little while,* and continue invisible tor
a long time. It remains thei etore, that they move in
elliptic orbits of very great eccentricity ; that is,
whose length is very great in proportion to their
breadth. But that small part of such an orbit, near
the perihelion, which is all that can come under our
observation, will almost coincide with a parabola ; and
may therefore, without any sensible error, be taken
for one.

Here our author had occasion to exert his great
abilities in solving a problem, the extreme difficulty
of which rendered it worthy of his genius, and indeed
insuperable by any other. From three select obser-
vations of the place of a Comet, supposed to move in
a parabola, he has taught a method of delineating its
trajectory geometrically ;t and has given an example
of this solution in determining the trajectory of that
famous Comet which he himself observed in the year
1680. He made it certain that the Comet really
moved in the trajectory he had delineated, by com-
puting its places therein for the times of several ob-

* p. 3. t Newt. Princip. Lib. iii. Prop. xli.



ON COMETS. 21

servations ; which agreed with its places as they were
actually observed at those times.*

This excellent discovery has since been abundantly
confirmed by the labours of the learned Dr. Halley,
who, following the steps of Sir Isaac Newton, has
performed the same thing arithmetically, which that
great man had done geometrically, and has expressed
the orbits and motions of Comets by numbers. And
having in this manner settled the orbits of all which
had been well observed before the present century, to
the number of 25, he found that their places comput-
ed in these orbits agreed as well with their observed
places, as the computed places of the planets usually
agree with their observed places. The like compu-
tations having been since made by other astronomers
for the Comets which have been seen in this century,
the theory is constantly found to answer the observa-
tions. In this manner have the orbits of about 40
Comets been settled.

All these calculations have been made on the sup-
position, that the visible part of a Comet's trajectory
is so nearly parabolic, that it may safely be taken for
such; though the whole orbit be really an ellipsis of
very great eccentricity. Now the true species of an
ellipsis so eccentric as the orbit of a Comet must be,
cannot be determined with any exactness from such a
small part of it as a Comet describes, while it conti-

* Jam patet horrificis qujs sit via flexa cometls ;
Jam non miramur barbati phscnomena astri. As Dr. Mai-
ley sings on this occasion*



22 ON COMETS.

nues visible : it can be determined no other way than
from the periodical time of the Comet ; and the peri-
odical time will be known, by remarking the times
when two Comets have describe dth e same orbit. The
only method, therefore, to perfect the astronomy of
Comets is, to determine the trajectory of every one
that appears, on the supposition of its being a para-
bola ; for such a trajectory will always agree with the
observations very nearly, as is evident from the
great number of Comets whose trajectories have
been thus settled. Then, when a Comet appears, if
it be found to describe the same trajectory as some
Comet has formerly done, that is, one whose nodes
are in the same place ; whose plane has the same in-
clination to the ecliptic; and which has its perihelion
in the same place and at the same distance from the
sun ; — it may be concluded, that these are two ap-
pearances of one and the same Comet. And the
conclusion will be the stronger, if it be found that
several Comets, after equal intervals of timcj have
described the same trajectory; for then there will be
no reason to doubt, that all these were one Comet,
revolving in the same orbit. The intervals between
these appearances will be the periodic time of the
Comet ; from whence its return may be predicted ;
and from whence also the longer axis of its elliptic
orbit may be found, by the help of that ft\mous rule
which Kepler first discovered to obtain in fact, and
which Sir Isaac Newton afterwards demonstrated
must necessarily obtain in the revolutions of the pla-



ON COMETS. 23

nets ; viz. that the squares of their periodic times are
proportional to the cubes of their mean distances
from the sun, or to the cubes of the longer axes of
their orbits, which are double of those mean distances.
In this manner Dr. Halley first shewed, that the
same Comet had, in all probability, made two or
three appearances. For a Comet, which he himself
observed in the year 1682, described an orbit that
agreed very well with the orbit of the Comet observ-
ed by Kepler in 1607. If these were one and the
same, it revolves in the space of about 75 years ; and
the longer axis of its orbit will be founds by Kepler's
rule, to be about 17|- times greater than that of the
earth's orbit ; and its distance from the sun in its
aphelion about 35 times greater than the earth's
mean distance from the sun. And that they were the
same, is confirmed from hence, that in the year
1531 a Comet described an orbit, whose elements
agree well with those of the other two ; there being
no considerable difference, excepting only in the pe-
riodical time ; one interval being 75 years ; the other,
76. But the inequality of the periods is not greater
than what may be attributed to physical causes. For
as the comet moved slowly in its aphelion, at which
distance the sun's regulating power is but weak, its
motion was liable to be much disturbed by the attrac-
tion of other Comets ; by which means its periodic
time might be considerably altered. The astronomers
have found the motion of Saturn so much disturbed by
Jupiter \\hen near him, that some of his periods, ob-



24 ON COMETS.

served accurately within a century past have been
above 1 3 days longer than others. And by a calcu-
lation from the theory of gravity, some of Saturn's
periods may be a month longer than others.* How
much greater irregularities of this sort must our Co-
met be exposed to, v^^hich in its aphelion runs off
from the sun almost four times as far as Saturn ;
where its gravitation to the sun is 16 times weaker;
and whose velocity in its aphelion is not the tenth
part of Saturn's velocity? It is not therefore to be
wondered at, if its periodic time, and its orbit too,
were somewhat changed. v ' .; •*. .

Upon the supposition that it was the same Comet
which appeared these three several times, the sega-
cious Doctor predicted,* that " it would appear
" again about the end of the year 1758, or the begin-
" ning of the following year.'* This prediction we
have now the satisfaction to see verified ; the present
Comet agreeing hitherto so well with the former, as
to leave little room for doubt that they are the same.
We may therefore, upon sure grounds, expect that
the rest of the Comets will return too ; though we
are not able as yet to prefix the years of their re-
turns. f As it is not certain, that any other Comet
has appeared twice, since Comets have been duly ob-
served, we may conclude that all the other Cornets
have longer periods than this; and consequently run
off to greater distances from the sun. From the cur-
vature of the path of that which appeared in 1 680,

* Halleii Tub. Astron. f See the Appendix.



ON COMETS. 25

Sir Isaac Newton collected that its period must be
above 500 years ; which wiil make its greatest dis-
tance from the sun to be above 126 times greater
than the earth's. And this, by the way, shews the
vast extent of the power of gravity ; for it must ex-
tend to the utmost distance to which any Comets rise
from the sun; — in order to turn them round their
Ophelia, and bring them back in their orbits, as it
does the planets. To close the present article : a
theory, which so accurately answers to the motions
of all the Comets which have been accurately ob-
served, even to some which have been very extraor-
dinary,* and which accounts for them by the same
laws as the motions of the planets are accounted for,
cannot but be true.

Since Comets move in the planetary regions, we
may argue that they shine i)y reflecting the sun's light ;
another circumstance, in which they resemble the
planets. Accordingly, the brightness of their heads
has been observed to increase as they have approach-
ed to the sun, and to decrease as they have depai'ted
from him ; although they have been going farther
from the earth in the former case, and in the latter,
coming towards it. Which shews that their bright-
ness depends, not on their nearness to the earth, as
their apparent magnitude does; but on their near-
ness to the sun. And that Comets shine only by the
light of the sun, is manifest from an observation of

* See (be instances of the Comets in 1664 and 1680, in
Newt. Princip. p. 505 and 522.


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Online LibraryJohn WinthropTwo lectures on comets → online text (page 3 of 14)