to the computation of Mr. Bradley, Savilian Professor of Astronomy at
Oxford) was in T 14 16 . The inclination of the orbit to the plane of
the ecliptic 49 59 . Its perihelion was in 8 12 15 20". Its perihelion
distance from the sim 998651 parts, of which the radius of the orbis mag*
nits contains 1000000, and the equal time of its perihelion September 16 1
BOOK III.] OF NATURAL PHILOSOPHY. 50!
16h . 10 . The places of this comet computed in this orbit by Mr. Bradley,
and compared with the places observed by himself, his uncle Mr. Pound,
and Dr. Halley, may be seen in the following table.
From these examples it is abundantly evident that the motions of com
ets are no less accurately represented by our theory than the motions of the
planets commonly are by the theories of them ; and, therefore, by means of
this theory, we may enumerate the orbits of comets, and so discover the
periodic time of a comet s revolution in any orbit
; whence, at last, we
shall have the transverse diameters of their elliptic orbits and their aphe
lion distances.
That retrograde comet which appeared in the year 1607 described an
orbit whose ascending; node (according to Dr. Halley s computation) was in
b 20 2V ; arid the inclination of the plane of the orbit to the plane of
the ecliptic 17 2 ;, whose perihelion was in ox 2 16 ; and its perihelion
distance from the sun 58680 of such parts as the radius of the orbis mag--
nns contains 100000; and the comet was in its perihelion October 16(l
. 3".
50 : which orbit agrees very nearly with the orbit of the comet which WHS
seen in 1682. If these were not two cliiferent comets, but one and the
same, that comet will finish one revolution in the space of 75 years ; and
the greater axis of its orbit will be to the greater axis of the nrbis magims
as v/
3 75 X 75 to 1, or as 1778 to 100, nearly. And the aphelion dis
tance of this comet from the sun will be to the mean distance of the earth
from the sun as about 35 to 1
; from which data it will be no hard matter
to determine the elliptic orbit of this comet. But these things are to be
supposed on condition, that, after the space of 75 years, the same comet
shall return again in the same orbit. The other comets seem to ascend to
greater heights, and to require a longer time to perform their revolutions.
But. because of the great number of comets, of the great distance of their
502 THE MATHEMATICAL PRINCIPLES [BOOK IIL
aphelions from the sun, and of the slowness of their motions in the aphe
lions, they will, by their mutual gravitations, disturb each other ; so that
their eccentricities arid the times of their revolutions will be sometimes a
little increased, and sometimes diminished. Therefore we are not to ex
pect that the same comet will return exactly in the same orbit, and in the
same periodic times : it will be sufficient if we find the changes no greater
than may arise from the causes just spoken of.
And hense a reason may be assigned why comets are not comprehend-ed
within the limits of a zodiac, as the planets are; but, being confined to no
bounds, are with various motions dispersed all over the heavens; namely,
to this purpose, that in their aphelions, where their motions are exceedingly
slow, receding to greater distances one from another, they may suffer less
disturbance from their mutual gravitations: and hence it is that the comets
which descend the lowest, and therefore move the slowest in their aphelions,
ought also to ascend the highest.
The comet which appeared in the year 1GSO was in its perihelion less
distant from the sun than by a sixth part of the sun s diameter; and be
cause of its extreme velocity in that proximity to the sun, and some density
of the sun s atmosphere, it must have suffered some resistance and retarda
tion ; and therefore, being attracted something nearer to the sun in evry
revolution, will at last fall down upon the body of the sun. Nay. in its
aphelion, where it moves the slowest, it may sometimes happen to be yet
farther retarded by the attractions of other comets, and in consequence of
this retardation descend to the sun. So fixed stars, that have been gradu
ally wasted by the light and vapours emitted from them for a long time,
may be recruited by comets that fall upon them ; and from tlrs fresh sup
ply of new fuel those old stars, acquiring new splendor, may pass for new
stars. Of this kind are such fixed stars as appear on a sudden, and shine
with a wonderful brightness at first, and afterwards vanish by little and
little. Such was that star which appeared in Cassiopeia s chair ; which
Cornelius Gemma did not see upon the 8th of November, 1572, though
he was observing that part of the heavens upon that very night, and the
sky was perfectly serene; but the next night (November 9) he saw it
shining much brighter than any of the fixed stars, and scarcely inferior to
Venus in splendor. Tycho Brake saw it upon the llth of the same month,
when it shone with the greatest lustre; and from that time he observed it
to decay by little and little
; and in 16 months time it entirely disap
peared. In the month of November, when it first appeared, its light was
equal to that of Venus. In the month of December its light was a littie
diminished, and was now become equal to that of Jupiter. In January
1573 it was less than Jupiter, and greater than Siriits ; and about the
end of February and the beginning of March became equal to that star.
In the months of April and May it was equal to a star of the second mag
HI.] OF NATURAL PHILOSOPHY. 503
uitude; in June, July, and August, to a star of the third magnitude; in
September, October, and November, to those of the fourth magnitude; in
December and January 1574 to those of the fifth
;
in February to those
of the sixth magnitude; and in March it entirely vanished. Its colour at
the beginning was clear, bright, and inclining to white; afterwards il
turned a little yellow; and in March 1573 it became ruddy, like Mars or
Alclebaran : in May it turned to a kind of dusky whiteness, like that we
observe in Saturn ; and that colour it retained ever after, but growing al
ways more and more obscure. Such also was the star in the right foot oi
Serpentarius, which Kepler s scholars first observed September 30, O.S.
1604, with a light exceeding that of Jupiter, though the night before it
was not to be seen; and from that time it decreased by little and little,
and in 15 or 16 months entirely disappeared. Such a new star appearing
with an unusual splendor is said to have moved Hipparchus to observe,
and make a catalogue of, the fixed stars. As to those fixed stars that ap
pear and disappear by turns, and increase slowly and by degrees, and
scarcely ever exceed the stars of the third magnitude, they seem to be of
another kind, which revolve about their axes, and, having a light and a
dark side, shew those two different sides by turns. The vapours which
arise from the sun, the fixed stars, and the tails of the comets, may meet
at last with, and fall into, the atmospheres of the planets by their gravity,
and there be condensed and turned into water and humid spirits; and from
thence, by a slow heat, pass gradually into the form of salts, and sulphurs,
and tinctures, and mud, and clay, and sand, and stones, and coral, and other
terrestrial substances.
GENERAL SCHOLIUM.
The hypothesis of vortices is pressed with many difficulties. That every
planet by a radius drawn to the sun may describe areas proportional to the
times of description, the periodic times of the several parts of the vortices
should observe the duplicate proportion of their distances from the sun ;
but that the periodic times of the planets may obtain the sesquiplicate pro
portion of their distances from the sun; the periodic times of the parts of
the vortex ought to be in the sesquiplicate proportion of their distances.
That the smaller vortices may maintain their lesser revolutions about
Saturn, Jupiter, and other planets, and swim quietly and undisturbed in
the greater vortex of the sun, the periodic times of the parts of the sun s
vortex should be equal ; but the rotation of the sun and planets about their
axes, which ought to correspond with the motions of their vortices, recede
far from all these proportions. The motions of the comets are exceedingly
regular, are governed by the same laws with the motions of the planets,
and can by no means be accounted for by the hypothesis of vortices ; for
comets are carried with very eccentric motions through all parts of the
501 THE MATHEMATICAL PRINCIPLES [BOOK IIL
heavens indifferently, with a freedom that is incompatible with the notion
of a vortex.
Bodies projected in our air suffer no resistance but from the air. With
draw the air, as is done in Mr. Boyle s vacuum, and the resistance ceases ;
for in this void a bit of tine down and a piece of solid gold descend with
equal velocity. Ajid the parity of reason must take place in the celestial
spaces above the earth s atmosphere; in which spaces, where there is no
air to resist their motions, all bodies will move with the greatest freedom;
and the planets and comets will constantly pursue their revolutions in or
bits given in kind and position, according to the laws above explained ; but
though these bodies may, indeed, persevere in their orbits by the mere laws
of gravity, yet they could by no means have at first derived the regular
position of the orbits themselves from those laws.
The six primary planets are revolved about the sun in circles concentric
with the sun, and with motions directed towards the same parts, and al
most in the same plane. Ten moons are revolved about the earth, Jupiter
and Saturn, in circles concentric with them, wi h the same direction of
motion, and nearly in the planes of the orbits of those planets ; but it is
not to be conceived that mere mechanical causes could give birth to so
many regular motions, since the comets range over all parts of the heavens
in very eccentric orbits
; for by that kind of motion they pass easily through
the orbs of the planets, and with great rapidity ; and in their aphelions,
where they move the slowest, and are detained the longest, they recede to
the greatest distances from each other, and thence suffer the least disturb
ance from their mutual attractions. This most beautiful system of the sun,
planets, and comets, could only proceed from the counsel and dominion of an
intelligent and powerful Being. And if the fixed stars are the centres of oth
er like systems, these, being formed by the like wise counsel, must be all sub
ject to the dominion of One ; especially since the light of the fixed stars is
of the same nature with the light of the sun, and from every system light
passes into all the other systems : and lest the systems of the fixed stars
should, by their gravity, fall on each other mutually, he hath placed those
systems at immense distances one from another.
This Being governs all things, not as the soul of the world, but as Lord
over all
; and on account of his dominion he is wont to be called Lord God
-rra TOKpaTup, or Universal Rider ; for God is a relative word, and has a
respect to servants ; and Deity is the dominion of God not over his own
body, as those imagine who fancy God to be the soul of the world, but over
servants. The Supreme God is a Being eternal, infinite, absolutely per
fect ; but a being, however perfect, without dominion, cannot be said to be
Lord God ; for we say, my God, your God, the God of Israel, the God of
Gods, and Lord of Lords ; but we do not say, my Eternal, your Eternal.
the Eternal of Israd} the Eternal of Gods; we do not say, my Infinite, o?
{JOCK III.J Of NATURAL PHILOSOPHY. 505
my Perfect : these are titles which have no respect to servants. The word
God* usually signifies Lord ; but every lord is not a God. It is the do
minion of a spiritual being which constitutes a God: a true, supreme, or
imaginary dominion makes a true, supreme, or imaginary God And from
his true dominion it follows that the true God is a living, intelligent, and
powerful Being ; and, from his other perfections, that he is supreme, or
most perfect. He is eternal and infinite, omnipotent and omniscient ; that
is, his duration reaches from eternity to eternity; his presence from infinity
to infinity; he governs all things, and knows all things that are or can be
done. He is not eternity or infinity, but eternal and infinite; he is not
duration or space, but he endures and is present. He endures for ever, and
is every where present ; and by existing always and every where, he consti
tutes duration and space. Since every particle of space is always, and
every indivisible moment of duration is every where, certainly the Maker
and Lord of all things cannot be never and no where. Every soul that
has perception is, though in different times and in different organs of sense
and motion, still the same indivisible person. There are given successive
parts in duration, co-existent parts in space, but neither the one nor the
other in the person of a man, or his thinking principle ; and much less
can they be found in the thinking substance of God. Every man, so far
as he is a thing that has perception, is one and the same man during his
whole life, in all and each of his organs of sense. God is the same God,
always and every where. He is omnipresent not virtually only, but also
substantially ; for virtue cannot subsist without substance. In himf are
all things contained and moved; yet neither affects the other: God suffers
nothing from the motion of bodies ; bodies find no resistance from the om
nipresence of God. It is allowed by all that the Supreme God exists
necessarily ; and by the same necessity he exists always and every where.
Whence also he is all similar, all eye, all ear, all brain, all arm, all power
to perceive, to understand, and to act
; but in a manner not at all human,
in a manner not at all corporeal, in a manner utterly unknown to us. As
a blind mail has no idea of colours, so have we no idea of the manner by
* Dr. Pocock derives the Latin word Deus from the Arabic du (in the oblique case tit).
which signifies Lord. And in this sense princes are called gods, Psal. Ixxxii. ver. 6; and
John x. ver. 35. And Moses is called a god to his brother Aaron, and a god to Pharaoh,
(Exod. iv. ver. 16 ; and vii. ver. 1). And in the same sense the souls of dead princes were
formerly, by the Heathens, culled gods, but falsely, because of their want of dominion.
t This was the opinion of the Ancients. So Pythagoras, in Cicer. de Nat. Deor. lib. i
Thafes, Anaxagoras, Virgil, Georg. lib. iv. ver. 220; and ^Eneid, lib. vi. ver. 721. Philo
Allegor, at the beginning of lib. i. Aratu$, in his Phaenom. at the beginning. So also the
sacred writers ; as St. Paul, Acts, xvii. ver 27, 28. St. John s Gosp. chap. xiv. ver. 2. Mo
tet, in Dent. iv. ver. 39; and x ver. 14. David, Psal. cxxxix. ver. 7, 8, 9. Solomon, 1
Kings, viii. ver. 27. Job, xxii. ver. 12, 13, 14. Jeremiah, xxiii. ver. 23, 24. The Idolaters
supposed the sun, moon, and stars, the souls of men, and other parts of the world, to be
parts of the Supreme God, and therefore to be worshipped ; but erroneously.
506 THE MATHEMATICAL PRINCIPLES [BOOK I1J.
which the all-wise God perceives and understands all things. He is ut
terly void of all body and bodily figure, and can therefore neither l^e seen,
nor heard, nor touched ; nor ought he to be worshipped under the repre
sentation of any corporeal thing. We have ideas of his attributes, but
what the real substance of any thing is we know not. In bodies, we see
only their figures and colours, we hear only the sounds, we touch only their
outward surfaces, we smell only the smells, and taste the savours ; but their
inward substances are not to be known either by our senses, or by any
reflex act of our minds : much less, then, have we any idea of the sub
stance of God. We know him only by his most wise and excellent con
trivances of things, and final causes ; we admire him for his perfections ;
but we reverence and adore him on account of his dominion : for we adore
him as his servants ; and a god without dominion, providence, and final
causes, is nothing else but Fate and Nature. Blind metaphysical neces
sity, which is certainly the same always and every where, could produce
no variety of things. All that diversity of natural things which we find
suited to different times and places could arise from nothing but the ideas
and will of a Being necessarily existing. But, by way of allegory, God
is said to see, to speak, to laugh, to love, to hate, to desire, to give, to re
ceive, to rejoice, to be angry, to fight, to frame, to work, to build ; for all
our notions of God are taken from the ways of mankind by a certain
similitude, which, though not perfect, has some likeness, however. And
thus much concerning God ; to discourse of whom from the appearances
of things, does certainly belong to Natural Philosophy.
Hitherto we have explained the phenomena of the heavens and of our
sea by the power of gravity, but have not yet assigned the cause of this
power. This is certain, that it must proceed from a cause that penetrates
to the very centres of the sun and planets, without suffering the least
diminution of its force; that operates not according to the quantity of
the surfaces of the particles upon which it acts (as mechanical causes use
to do), but according to the quantity of the solid matter which they con
tain,, and propagates its virtue on all sides to immense distances, decreasing
always in the duplicate proportion of the distances. Gravitation towards
the sun is made up out of the gravitations towards the several particles
of which the body of the sun is composed ; and in receding from the sun
decreases accurately in the duplicate proportion of the distances MS far as
the orb of Saturn, as evidently appears from the quiescence of the aphe
lions of the planets ; nay, and even to the remotest aphelions of the comets,
if those aphelions are also quiescent. But hitherto I have not been able
to discover the cause of those properties of gravity from phenomena, and
I frame no hypotheses ; for whatever is not deduced from the phenomena
is to be called an hypothesis ; and hypotheses, whether metaphysical 01
physical, whether of occult qualities or mechanical, have no place in ex
BOOK III.] OF NATURAL PHILOSOPHY. 507
perimental philosophy. In this philosophy particular propositions are
inferred from the phenomena, and afterwards rendered general by induc
tion. Thus it was that the impenetrability, the mobility, and the impul
sive force of bodies, and the laws of motion and of gravitation, were
discovered. And to us it is enough that gravity does really exist, and act
according to the laws which we have explained, and abundantly serves to
account for all the motions of the celestial bodies, and of our sea.
And now we might add something concerning a certain most subtle
Spirit which pervades and lies hid in all gross bodies ; by the force and
action of which Spirit the particles of bodies mutually attract one another
at near distances, and cohere, if contiguous ; and electric bodies operate to
greater distances, as well repelling as attracting the neighbouring corpus
cles
; and light is emitted, reflected, refracted, inflected, and heats bodies ;
and all sensation is excited, and the members of animal bodies move at the
command of the will, namely, by the vibrations of this Spirit, mutually
propagated along the solid filaments of the nerves, from the outward or
gans of sense to the brain, and from the brain into the muscles. But these
are things that cannot be explained in few words, nor are we furnished
with that sufficiency of experiments which is required to an accurate deter
mination and demonstration of the laws by which this electric and elastic
Spirit operates.
END OP THE MATHEMATICAL P&LNCIPLE8.
THE SYSTEM OF THE WORLD,
THF
SYSTEM OF THE WORLD
It. was the ancient opinion of not a few, in the earliest ages of philoso
phy, that the fixed stars stood immoveable in the highest parts of the world ;
that, under the fixed stars the planets were carried about the sun ; that the
earth, us one of the planets, described an annual course about the sun, while
by a diurnal motion it was in the mean time revolved about its own axis;
and that the sun, as the common fire which served to warm the whole, was
fixed in the centre of the universe.
This was the philosophy taught of old by Philolans, Aristarchus of
Santos, Plato in his riper years, and the whole sect of the Pythagoreans ;
and this was the judgment of Anaximander, more ancient than any of
them ; and of that wise Iring of the Rovnans, Numa Pompilins, who, as
a symbol of the figure of the world with the sun in the centre, erected a
temple in honour of Vesta, of .% i^und form, and ordained perpetual fire to
be kept in the middle of it.
The Egyptians were early observers of the heavens ; and from them.,
probably, this philosophy was spread abroad among other nations ; for from
them it was, and the nations about them, that the Greeks, a people of
themselves more addicted to the study of philology than of nature, derived
their first, as well as soundest, notions of philosophy ; and in the vestal
ceremonies we may yet trace the ancient spirit of the Egyptians ; for it
was their way to deliver their mysteries, that is, their philosophy of things
above the vulgar way of thinking, under the veil of religious rites and
hieroglyphic symbols.
It is not to be denied but that Anaxa&oras, Democritus, and others,
did now and then start up, who would have it that the earth possessed the
centre of the world, and that the stars of all sorts were revolved towards
the west about the earth quiescent in tk^ centre, some at a swifter, others
at a slower rate.
However, it was agreed on both sides that the motions of the celestial
bodies were performed in spaces altogether free and void of resistance. The
whim of solid orbs was of a later date, introduced by Eudoxus, Calippus,
and Aristotle; when the ancient philosophy began to decline, and to give
nlace to the new prevailing fictions of the Greeks.
But. above all things, the phenomena of comets can by no means consist
612 THE SYSTEM OF THE WORLD.
with the notion of solid orbs. The Chaldeans, the most learned astrono
mers of their time, looked upon the comets (which of ancient times before
had been numbered among the celestial bodies) as a particular sort of plan
ets, which, describing very eccentric orbits, presented themselves to our view
only by turns, viz., once in a revolution, when they descended into the
lower parts of their orbits.
And as it was the unavoidable consequence of the hypothesis of solid
orbs, while it prevailed, that the comets should be thrust down below the
moon, so no sooner had the late observations of astronomers restored the
comets to their ancient places in the higher heavens, but these celestial spaces
were at once cleared of the incurnbrance of solid orbs, which by these ob
servations were broke into pieces, and discarded for ever.
Whence it was that the planets came to be retained within any certain
bounds in these free spaces, and to be drawn off from the rectilinear courses,
which, left to themselves, they should have pursued, into regular revolu
tions in curvilinear orbits, are questions which we do not know how the
ancients explained ; and probably it was to give some sort of satisfaction
to this difficulty that solid orbs were introduced.
The later philosophers pretend to account for it either by the action of
certain vortices, as Kepler and Des Cartes ; or by some other principle of
impulse or attraction, as Borelli, Honke, and others of our nation ; for,
from the laws of motion, it is most certain that these effects must proceed
from the action of some force or other.
But our purpose is only to trace out the quantity and properties of this
force from the phenomena (p. 218), and to apply what we discover in some
simple cases as principles, by which, in a mathematical way, we may esti
mate the effects thereof in more involved cases : for it would be endless and
impossible to bring every particular to direct and immediate observation.
We said, in a mathematical way, to avoid all questions about the na
ture or quality of this force, which we would not be understood to deter
mine by any hypothesis; and therefore call it by the general name of a
centripetal force, as it is a force which is directed towards some centre ;
and as it regards more particularly a body in that centre, we call it circum
solar, circum-terrestrial, circum-jovial ; and in like manner in respect of
other central bodies.
That by means of centripetal forces the planets may be retained in cer
tain orbits, we may easily understand, if we consider the motions of pro
jectiles (p. 75, 76, 77) ; for a stone projected is by the pressure of its own
weight forced out of the rectilinear path, which by the projection alone it
should have pursued, and made to describe a curve line in the air
; and
through that crooked way is at last brought down to the ground ; and the
greater the velocity is with which it is projected, the farther it goes before
it falls to the earth. We may therefore suppose the velocity to be so in
THE SYSTEM OF THE WORLD. 513
creased, that it would describe an arc of 1, 2, 5, 10, 100. 1000 miles before
it arrived at the earth, till at last, exceeding the limits of the earth, it
should pass quite by without touching it.
Let AFB represent the surface of the earth, C its centre, VD, VE, VF,
the curve lines which a body would describe, if projected in an horizontal
direction from the top of an high mountain successively "with more and
more velocity (p. 400) ; and, because the celestial motions are scarcely re
tarded by the little or no resistance of the spaces in which they are per
formed, to keep up the parity of cases, let us suppose either that there is
no air about the earth, or at least that it is endowed with little or no power
of resisting ; and for the same reason tl a*: the body projected with a less
velocity describes the lesser arc VD, and with a greater velocity the greater
arc VE. and, augmenting the velocity, it goes farther and farther to F and
G, if the velocity was still more and more augmented, it would reach at
last quite beyond the circumference of the earth, and return to the moun
tain from which it was projected.
And since the areas which by this motion it describes by a radius drawn
