ed the sun s parallax at most 10".
Whence it follows that the distance of the moon from the earth bears
no greater proportion to the distance of the earth from the sun than 29 to
IOUOO : nor to the distance of Venus from the sun than 29 to 7233.
From which distances, together with the periodic times, by the method
above explained, it is easy to infer that the absolute circum-soiar force is
greater than the absolute circum-terrestrial force at least 229400 times.
And though we were only certain, from the observations of Ricciolus
and Vcitdelin, that the sun s parallax was less than half a minute, yet from
this it will follow that the absolute circum-solar force exceeds the absolute
circum-terrestrial force S500 times.
By the like computations I happened to discover an analogy, that is ob
served between the forces and the bodies of the planets ; but, before I ex
plain this analogy, the apparent diameters of the planets in their mean
distances from the earth must be first determined.
Mr. Flamsted (p. 387), by the micrometer, measured the diameter of
Jupiter 40" or 41"; the diameter of Saturn s ring 50"
; and the diameter
of the sun about 32 13" (p. 387).
But the diameter of Saturn is to the diameter of the ring, according to
Mr. Huygens and Dr. Halley, as 4 to 9; according to Gullet-ins, as 4 to
10; and according to Hooke (by a telescope of 60 feet), as 5 to 12. And
from the mean proportion, 5 to 12, the diameter of Saturn s body is in
ferred about 21".
Such as we have said are the apparent magnitudes; but. because of the
unequal refrano-ibility of light, all lucid points are dilated by the tele
scope, and in the focus of the object-glass possess a circular space whose
breadth is about the 50th part of the aperture of the glass.
It is true, that towards the circumference the light is Su rare as hardly
to move the sense
;
but towards the middle, where it is of greater density,
and is sensible enough, it makes a small lucid circle, whose breadth varies
according to the splendor of the lucid point, but is generally about the 3d,
or 4th, or 5th part of the breadth of the whole.
Let ABD represent the circle of the whole light; PQ the small circle
of the denser and clearer light; C the centre of both; CA, CB, semi-di
ameters of the greater circle containing a right angle at C ; ACBE the
square comprehended under these semi-diameters ; AB the diagonal of that
square; EGH an hyperbola with the centre C and asymptotes CA, CB
PG a perpendicular erected from any point P of the line BC, and meeting
the hyperbola in G, and the right lines AB, AE, in K and F : and th
THE SYSTEM OF THE WORLD. 523
density of the light in any place P, will, by my computation, be as the
line FG, and therefore at the centre infinite, but near the circumference
very small. And the whole light within the small circle PQ, is to the
without as the area of the quadrilateral figure CAKP to the triangle
PKB. And we are to understand the small circle PQ, to te there
terminated, where FG, the density of the light, begins to be less than what
is required to move the sense.
Hence it was, that, at the distance of 191 382 feet, a fire of 3 feet in di
ameter, through a telescope of 3 feet, appeared to Mr. Picart of S" in
breadth, when it should have appeared only of 3" 14 "
; and hence it is
that the brighter fixed stars appear through the telescope as of 5" or 6" in
diameter, and that with a good full light ; but with a fainter light they
appear to run out to a greater breadth. Hence, likewise, it was that Hevelius,
by diminishing the aperture of the telescope, did cut off a great part
of the light towards the circumference, and brought the disk of the star to
be more distinctly defined, which, though hereby diminished, did yet ap
pear as of 5" or 6" in diameter. But Mr. Hvygetis, only by clouding the
eye-glass with a little smoke, did so effectually extinguish this scattered
light, that the fixed stars appeared as mere points, void of all sensible
breadth. Hence also it was that Mr. Huygens, from the breadth of bodies
interposed to intercept the whole light of the planets, reckoned their diam
eters greater than others hav measured them by the micrometer : for the
524 THE SYSTEM OF THE WORLD.
scattered light, which could not be seen before for the stronger light of the
planet, when the planet is hid, appears every way farther spread. Lastly,
from hence it is that the planets appear so small in the disk of the sun,
being lessened by the dilated light. For to Hevelius, Galletius, and Dr.
Halley, Mercury did not seem to exceed 12" or 15"
; and Venus appeared
to Mr. Crabtrie only 1 3 ;/
;
to Horrox but 1 12"
; though by the men
surations of Hevelius and Hu&enius without the sun s disk, it ought to
have been seen at least 1 24". Thus the apparent diameter of the moon,
which in 1 684, a few days both before and after the sun s eclipse, was
measured at the observatory of Paris 31 30", in the eclipse itself did not
seem to exceed 30 or 30 05"
; and therefore the diameters of the planets
are to be diminished when without the sun, and to be augmented when
within it, by some seconds. But the errors seem to be less than usual in
the mensurations that are made by the micrometer. So from the diameter
of the shadow, determined by the eclipses of the satellites, Mr. Flamsted
found that the semi- diameter of Jupiter was to the greatest elongation of
the outmost satellite as 1 to 24,903. Wherefore since that elongation is
8 13 , the diameter of Jupiter will be 39^-" ; and, rejecting the scattered
light, the diameter found by the micrometer 40" or 41" will be reduced to
39|-" 5 and the diameter of Saturn 21" is to be diminished by the like cor
rection, and to be reckoned 20", or something less. But (if I am not mis
taken) the diameter of the sun, because of its stronger light, is to be dimin
ished something more, and to be reckoned about 32 , or 32 6 1
.
That bodies so different in magnitude should come so near to an analogy
with their forces, is not without some mystery (p. 400).
It may be that the remoter planets, for want of heat, have not those me
tallic substances and ponderous minerals with which our earth abounds ;
and that the bodies of Venus and Mercury, as they are more exposed to the
sun s heat, are also harder baked, and more compact.
For, from the experiment of the burning-glass, we see that the heat in
creases with the density of light ; and this density increases in the recipro
cal duplicate proportion of the distance from the sun ; from whence the
san s heat in Mercury is proved to be sevenfold its heat in our summer
seasons. But with this heat our water boils ; and those heavy fluids, quick
silver and the spirit of vitriol, gently evaporate, as I have tried by the
thermometer ; and therefore there can be no fluids in Mercury but what
are heavy, and able to bear a great heat, and from which substances of great
density may be nourished.
And why not, if God has placed different bodies at different distances
from the sun, so as the denser bodies always possess the nearer places, and
each body enjoys a degree of heat suitable to its condition, and proper for
its nourishment? From this consideration it will best appear that the
weights of all the planets are one to another as their forces.
THE SYSTEM OF THE WORLD.
But I should be glad the diameters of the planets were more accurately
measured ; and that may be done, if a lamp, set at a great distance, is made
to shine through a circular hole, and both the hole and the light of the
lamp are so diminished that the spectrum may appear through the telescope
just like the planet, and may be defined by the same measure : then the
diameter of the hole will be to its distance from the objective glass as the
true diameter of the planet to its distance from us. The light of the lamp
may be diminished by the interposition either of pieces of cloth, or of
smoked glass.
Of kin to the analogy we have been describing, there is another observed
between the forces and the bodies attracted (p. 395, 396, 397). Since the
action of the centripetal force upon the planets decreases in the duplicate
proportion of the distance, and the periodic time increases in the sesquiplicate
thereof, it is evident that the actions of the centripetal force, and
therefore the periodic times, would be equal in equal planets at equal dis
tances from the sun ; and in equal distances of unequal planets the total
actions of the centripetal force would be as the bodies of the planets ; for
if the actions were not proportional to the bodies to be moved, they could
not equally retract these bodies from the tangents of their orbs in equal
times : nor could the motions of the satellites of Jupiter be so regular, if it
was not that the circum-solar force was equally exerted upon Jupiter and
all its satellites in proportion of their several weights. And the same thing
is to be said of Saturn in respect of its satellites, and of our earth in re
spect of the moon, as appears from Cor. II and III, Prop. LXV. Arid,
therefore, at equal distances, the actions of the centripetal force are equal
upon all the planets in proportion of their bodies, or of the quantities of
matter in their several bodies; and for the same reason must be the same
upon all the particles of the same size of which the planet is composed ; for
if the action was greater upon some sort of particles than upon others than
in proportion to their quantity of matter, it would be also greater or less
upon the whole planets not in proportion to the quantity only, but like
wise of the sort of the matter more copiously found in one and more
sparingly in another.
In such bodies as are found on our earth of very different sorts, I exam
ined this analogy with great accuracy (p. 343, 344).
If the action of the circum-terrestrial force is proportional to the bodies
to be moved, it will (by the Second Law of Motion) move them with equal
velocity in equal times, and will make all bodies let fall to descend through
equal spaces in equal times, and all bodies hung by equal threads to vibrate
in equal times. If the action of the force was greater, the times would be
less ; if that was less, these would be greater.
But it has been long ago observed by others, that (allowance being made
for the small resistance of the air) all bodies descend through equal spaces
526 THE SYSTEM OF THE WORLD.
in equal times ; and, by the help of pendulums, that equality of tim-es may
be distinguished to great exactness.
1 tried the thing in gold, silver, lead, glass, sand, common salt wood,
water, and wheat. I provided two equal wooden boxes. I filled the one
with wood, and suspended an equal weight of gold (as exactly as I could)
in the centre of oscillation of the other. The boxes, hung by equal threads
of 11 feet, made a couple of pendulums perfectly equal in weight and fig
ure, and equally exposed to the resistance of the air : and, placing the one
by the other, I observed them to play together forwards and backwards for
a long while, with equal vibrations. And therefore (by Cor. 1 and VI,
Prop. XXIV. Book II) the quantity of matter in the gold was to the quan
tity of matter in the wood as the action of the motive force upon all the
gold to the action of the same upon all the wood ; that is, as the weight of
the one to the weight of the other.
And by these experiments, in bodies of the same weight, could have dis
covered a difference of matter less than the thousandth part of the whole.
Since the action of the centripetal force upon the bodies attracted is, at
equal distances, proportional to the quantities of matter in those bodies,
reason requires that it should be also proportional to the quantity of mat
ter in the body attracting.
For all action is mutual, and (p. 83, 93. by the Third Law of Motion)
makes the bodies mutually to approach one to the other, and therefore must
be the same in both bodies. It is true that we may consider one body as
attracting, another as attracted; but this distinction is more mathematical
than natural. The attraction is really common of either to other, and
therefore of the same kind in both.
And hence it is that the attractive force is found in both. The sun at
tracts Jupiter and the other planets ; Jupiter attracts its satellites ; and,
for the same reason, the satellites act as well one upon another as upon Ju
piter, and all the planets mutually one upon another.
And though the mutual actions of two planets may be distinguished
and considered as two, by which each attracts the other, yet, as those ac
tions are intermediate, they do not make two but one operation between
two terms. Two bodies may be mutually attracted each to the other by
the contraction of a cord interposed. There is a double cause of action,
to wit, the disposition of both bodies, as well as a double action in so far
as the action is considered as upon two bodies ; but as betwixt two bodies
it is but one single one. It is not one action by which the sun attracts
Jupiter, and another by which Jupiter attracts the sun ; but it is one ac
tion by which the sun and Jupiter mutually endeavour to approach each
the other. By the action with which the sun attracts Jupiter, Jupiter and
the sun endeavours to come nearer together (by the Third Law of Mo
tion) ; and by the action with which Jupiter attracts the sun, likewise Ju
THE SYSTEM OF THE WORLD. 527
pitcr and the sun endeavor to come nearer together. But the sun is not
attracted towards Jupiter by a twofold action, nor Jupiter by a twofold
action towards the sun ; but it is one single intermediate action, by which
both approach nearer together.
Thus iron draws the load-stone (p. 93), as well as the load-stone
draws the iron : for all iron in the neighbourhood of the load-stone draws
other iron. But the action betwixt the load-stone and iron is single, and
is considered as single by the philosophers. The action of iron upon the
load-stone, is, indeed, the action of the load-stone betwixt itself and the
iron, by which both endeavour to come nearer together : and so it mani
festly appears ; for if you remove the load-stone, the whole force of the
iron almost ceases.
Tn this sense it is that we are to conceive one single action to be ex
erted betwixt two planets, arising from the conspiring natures of both :
and this action standing in the same relation to both, if it is proportional
to the quantity of matter in the one, it will be also proportional to the
quantity of matter in the other.
Perhaps it may be objected, that, according to this philosophy (p. 39S),
all bodies should mutually attract one another, contrary to the evidence
of experiments in terrestrial bodies ; but I answer, that the experiments in
terrestrial bodies come to no account ; for the attraction of homogeneous
spheres near their surfaces are (by Prop. LXXII) as their diameters.
Whence a sphere of one foot in diameter, and of a like nature to the
earth, would attract a small body placed near its surface with a force
20UOOOOO times less than the earth would do if placed near its surface;
but so small a force could produce no sensible effect. If two such spheres
were distant but by 1 of an inch, they would not, even in spaces void of
528 THE SYSTEM OF THE WORLD.
resistance, come together by the force of their mutual attraction in less
than a month s time j and less spheres will come together at a rate yet
slower, viz.. in the proportion of their diameters. Nay, whole mountains
will not be sufficient to produce any sensible effect. A mountain of an
hemispherical figure, three miles high, and six broad, will not, by its at
traction, draw the pendulum two minutes out of the true perpendicular :
and it is only in the great bodies of the planets that these forces are to be
perceived, unless we may reason about smaller bodies in manner following.
Let ABCD (p. 93) represent the globe of the earth cut by any plane
AC into two parts ACB, and A CD. The part ACB bearing upon the
part ACD presses it with its whole weight; nor can the part ACD sustain
this pressure and continue unmoved, if it is not opposed by an equal con
trary pressure. And therefore the parts equally press each other by their
weights, that is, equally attract each other, according to the third Law of
Motion ; and, if separated and let go, would fall towards each other with
velocities reciprocally as the bodies. All which we may try and see in the
load-stone, whose attracted part does not propel the part attracting, but is
only stopped and sustained thereby.
Suppose now that ACB represents some small body on the earth s sur
face : then, because the mutual attractions of this particle, and of the re
maining part ACD of the earth towards each other, are equal, but the
attraction of the particle towards the earth (or its weight) is as the matter
of the particle (as we have proved by the experiment of the pendulums),
the attraction of the earth towards the particle will likewise be as the
matter of the particle ; and therefore the attractive forces of all terres
trial bodies will be as their several quantities of matter.
The forces (p. 396), which are as the matter in terrestrial bodies of all
forms, and therefore are not mutable with the forms, must be found in all
sorts of bodies whatsoever, celestial as well as terrestrial, and be in all
proportional to their quantities of matter, because among all there is no
difference of substance, but of modes and forms only. But in the celes
tial bodies the same thing is likewise proved thus. We have shewn that
the action of the circum-solar force upon all the planets (reduced to equal
distances) is as the matter of the planets ; that the action of the circumjovial
force upon the satellites of Jupiter observes the same law ; and the
same thing is to be said of the attraction of all the planets towards every
planet : but thence it follows (by Prop. LXIX) that their attractive forces
are as their several quantities of matter.
As the parts of the earth mutually attract one another, so do those of
all the planets. If Jupiter and its satellites were brought together, and
formed into one globe, without doubt they would continue mutually to
attract one another as before. And, on the other hand, if the body of
Jupiter was broke into more globes, to be sure, these would no less attract.
THE SYSTEM OF THE WORLD. 529
3ne another than they do the satellites now. From these attractions it is
that the bodies of the earth and all the planets effect a spherical figure, and
their parts cohere, and are not dispersed through the aether. But we have
before proved that these forces arise from the universal nature of matter
(p. 398), and that, therefore, the force of any whole globe is made up of
the several forces of all its parts. And from thence it follows (by Cor.
III, Prop. LXXIV) that the force of every particle decreases in the dupli
cate proportion of the distance from that particle ; and (by Prop. LXXIII
and LXXV) that the force of an entire globe, reckoning from the surface
outwards, decreases in the duplicate, but, reckoning inwards, in the sim
ple proportion of the distances from the centres, if the matter of the globe
be uniform. And though the matter of the globe, reckoning from the
centre towards the surface, is not uniform (p. 398, 399), yet the decrease in
the duplicate proportion of the distance outwards would (by Prop. LXXVI)
take place, provided that difformity is similar in places round about at
equal distances from the centre. And two sucli globes will (by the same
Proposition) attract one the other with a force decreasing in the duplicate
proportion of the distance between, their centres.
Wherefore the absolute force of every globe is as the quantity of matter
which the globe contains ; but the motive force by which every globe is
attracted towards another, and which, in terrestrial bodies, we commonly
call their weight, is as the content under the quantities of matter in both
globes applied to the square of the distance between their centres (by Cor.
IV, Prop. LXXVI), to which force the quantity of motion, by which each
globe in a given time will be carried towards the other, is proportional.
And the accelerative force, by which every globe according to its quantity
of matter is attracted towards another, is as the quantity of matter in that
other globe applied to the square of the distance between the centres of
the two (by Cor. II, Prop. LXXVI): to which force, the velocity by which
the attracted globe will, in a given time, be carried towards the other is
proportional. And from these principles well understood, it will be now
easy to determine the motions of the celestial bodies among themselves.
From comparing the forces of the planets one with another, we have
above seen that the circum-solar does more than a thousand times exceed
all the rest ; but by the action of a force so greab it is unavoidable but that
all bodies within, nay, and far beyond, the bounds of the planetary system
must descend directly to the sun, unless by other motions they are impelled
towards other parts : nor is our earth to be excluded from the number of
such bodies : for certainly the moon is a body of the same nature with the
planets, and subject to the same attractions with the other planets, seeing
it is by the circum-terrestrial force that it is retained in its orbit. But
that the earth and moon are equally attracted towards the sun, we have
above proved ; we have likewise before proved that all bodies are subject to
530 THE SYSTEM OF THE WORLD.
the said common laws of attraction. Nay, supposing any of those bodies
to be deprived of its circular motion about the sun, by having its distance
from the sun, we may find (by Prop. XXXVI) in what space of time it
would in its descent arrive at the sun ;
to wit, in half that periodic time in
.vhich the body might be revolved at one half of its former distance; or in
a space of time that is to the periodic time of the planet as 1 to
4</2; as
that Venus in its descent would arrive at the sun in the space of 40 days,
Jupiter in the space of two years and one month, and the earth and moon
together in the space of 66 days and 19 hours. But, since no such thing
happens, it must needs be, that those bodies are moved towards other parts
(p. 75), nor is every motion sufficient for this purpose. To hinder such a
descent, a due proportion of velocity is required. And hence depends the
force of the argument drawn from the retardation of the motions of the
planets. Unless the circum-solar force decreased in the duplicate ratio of
their increasing slowness, the excess thereof would force those bodies to de
scend to the sun ; for instance, if the motion (c&teris paribns) was retarded
by one half, the planet would be retained in its orb by one fourth of the
former circum-solar force, and by the excess of the other three fourths
would descend to the sun. And therefore the planets (Saturn, Jupiter,
Mars, Venus, and Mercury) are not really retarded in their perigees, nor
become really stationary, or regressive with slow motions. All these are
but apparent, and the absolute motions, by which the planets continue to
revolve in their orbits, are always direct, and nearly equable. But that
such motions are performed about the sun, we have already proved ; and
therefore the sun, as the centre of the absolute motions, is quiescent. For
we can by no means allow quiescence to the earth, lest the planets in their
perigees should indeed be truly retarded, and become truly stationary and
regressive, and so for want of motion should descend to the sun. But
farther ; since the planets (Venus, Mars, Jupiter, and the rest) by radi:
drawn to the sun describe regular orbits, and areas (as WTC have shewn)
nearly and to sense proportional to the times, it follows (by Prop. III. and
Cor. Ill, Prop. LXV) that the sun is moved with no notable force, unless
perhaps wT ith such as all the planets are equally moved with, according to
their several quantities of matter, in parallel lines, and so the whole sys
tem is transferred in right lines. Reject that translation of the whole
system, and the sun will be almost quiescent in the centre thereof. If the
gun was revolved about the earth, and carried the other planets round about
itself, the earth ought to attract the sun with a great force, but the cir
cum-solar planets with no force producing any sensible effect, which is
contrary to Cor. Ill, Prop. LXV. Add to this, that if hitherto the earth,
because of the gravitation of its parts, has been placed by most authors in
the lowermost region of the universe ; now, for better reason, the sun pos
sessed of a centripetal force exceeding our terrestrial gravitation a thousand
THE SYSTEM OF THE WJP.I.D. 53L
times and more, ought to be depressed into the lowermost place, and to be
held for the centre of the system. And thus the true disposition of the
whole system will be more fully and more exactly understood.
Because the fixed stars are quiescent one in respect of another (p. 401,
4U2), we may consider the sun, earth, and planets, as one system of bodies
carried hither and thither by various motions among themselves; and the
common centre of gravity of all (by Cor. IT of the Laws of Motion) will
either be quiescent, or move uniformly forward in a right line : in which
case the whole system will likewise move uniformly forward in right lines.
But this is an hypothesis hardly to be admitted ; and, therefore, setting it
arfide, that common centre will be quiescent: and from it the sun is never
far removed. The common centre of gravity of the sun and Jupiter falls
on the surface of the sun ;
and though all the planets were placed towards
the same parts from the sun with Jupiter the common centre of the sun
and all of them would scarcely recede twice as far from the sun s centre ;
and, therefore, though the sun, according to the various situation of the
planets, is variously agitated, and always wandering to and fro with a slow
motion of libration, yet it never recedes one entire diameter of its own body
from the quiescent centre of the whole system. But from the weights of
the sun and planets above determined, and the situation of all among them
selves, their common centre of gravity may be found ; and, this being given,
the sun s place to any supposed time may be obtained.
About the sun thus librated the other planets are revolved in elliptic
