871 
•ways proportional to the time of its descrip- 
tion : or that it described equal areas in equal 
times, in whatever part of its orbit the planet 
might be, moving always so much the quicker 
as its distance from the sun was less. And it 
is also found that the satellites, or secondary 
planets, respect the same law in revolving 
about their primaries. But it was soon prov- 
ed by Newton, that all bodies moving in any 
curve line described on a plane, and which, 
by radii drawn to any certain point, describe 
areas about the point proportional to the 
times, are impelled or acted on by some 
power tending towards that point. Conse- 
quently the power by which all these planets 
revolve, and are retained in their orbits, is 
directed to the centre about which they 
move, viz. the primary planets to the sun, 
and the satellites to their several primaries. 
Again, Newton demonstrated, that if se- 
veral bodies revolve with an equable motion 
in several circles about the same centre, and 
that if the squares of their periodical times 
are in the same proportion as- the cubes of 
their distances from the common centre, then 
the centripetal forces of the revolving bodies, 
by which they tend to their central body, will 
be in the reciprocal or inverse ratio of the 
squares of the distances. Or if bodies re- 
volve in orbits approaching to circles, and 
the apses of those orbits are at rest, then a'so 
the centripetal forces of the revolving bodies 
will be reciprocally proportional to the 
squares of the distances. But it had been 
agreed on by the astronomers, and particu- 
larly Kepler, that both these cases obtain in 
all the planets. And therefore he inferred, 
that the centripetal forces of all the planets 
are reciprocally proportional to the squares 
of the distances from the centres of their or- 
bits. 
Upon the whole it appears, that the planets 
are retained in their orbits by some power 
w hich is continually acting upon them : that 
this power is directed towards the centre of 
their orbits : that the intensity or efficacy of 
this power increases upon an approach to- 
wards the centre, and diminishes on receding 
from the same, and that in the reciprocal du- 
plicate ratio of the distances : and that, by 
comparing this centripetal force of the planets 
with the force of gravity on the earth, they 
are found to be perfectly alike, as may easily 
be shewn in various instances. For example, 
in the case of the moon, the nearest of al! 
the planets. The rectilinear spaces describ- 
ed in any given time by a falling body, urged 
by any powers, reckoning from the beginning 
of its descent, are proportional to those pow- 
ers. Consequently the centripetal force of 
the moon revolving in her orbit, will be to 
the force of gravitv on the surface of the 
earth, as the space which the moon would de- 
scribe in falling during any small time, by her 
centripetal force towards the earth, if she. had 
no circular motion at all, to the space of a 
body near the earth would describe in falling 
by its gravity towards the same. 
Now by an easy calculation of those two 
spaces, it appears tiiat the former force is to 
the latter, as the square of the semidiameter 
of the earth is t ; the square of that of the 
moon’s orbit. The moon’s centripetal force 
therefore is equal to the force of gravitv ; 
and consequently these forces are not dif- I 
ferent, but they are one and the same : for if j 
they were different, bodies acted on by the [ 
GRAVITY. 
two powers conjointly would fail towards the 
earth with a velocity double to that arising 
from the sole power of gravity. 
It is evident therefore tiiat the moon’s cen- 
tripetal force, by which she is retained in her 
orbit, and prevented from running oh in 
tangents, is the very power of gravity ot the 
earth extended thither. See Newton’s Prin- 
cip. lib. 1, prop. 45, and lib. 3, prop, j; 
where the numeral calculation may be seen at 
full length. 
The moon therefore gravitates towards the 
earth, and reciprocally the earth towards the j 
moon. And this is also farther confirmed by 
the phenomena of the tides. 
The like reasoning may also be applied to 
the other planets. For as the revolutions of 
the primary planets round the sun, and those 
of the satellites of Jupiter and Saturn round 
their primaries, are phenomena of the same 
kind with the revolution of the moon about 
the earth ; and as the centripetal powers of 
the primary are directed towards the centre 
of the sun, and those of the satellites towards 
the centres of their primaries; and, lastly, as 
all these powers are reciprocally as the squares 
of the distances from the centres, it may safe- 
ly be concluded that the power and cause are 
the same in all. 
As the moon, therefore, gravitates towards 
the earth, and the earth towards the moon ; 
so do all the secondaries to tiieir primaries, 
and these to their secondaries ; and so also do 
the primaries to the sun, and the sun to the 
primaries. Newton’s Prineip. lib. 3, prop. 
4, 5, 6; Greg. Astron. lib. 1, sect. 7, prop. 
46 and 47. 
The laws of universal gravity are the same 
as those of bodies gravitating towards the 
earth, before laid down. 
Cause of gravity. Various theories have 
been advanced by the philosophers of dif- 
ferent ages to account for this grand principle 
of gravitation. The antients, who were 
only Acquainted with particular gravity, or 
the* tendency of sublunar bodies towards the 
earth, aimed no farther than to establish a 
system that might answer the more obvious 
phenomena of it. Some hints, however, are 
found concerning the gravitation of celestial 
bodies in the account given of the doctrine 
of Thales and his successors; and it would 
seem that Pythagoras was still better acquaint- 
ed with it, and which it is supposed he had in 
view in what he taught concerning the har- 
mony of the spheres. 
Aristotle and the Peripatetics content 
themselves with referring gravity or weight 
to a native inclination in heavy bodies to be 
in tiieir proper place or sphere, the centre of 
the earth. And Copernicus ascribes it to an 
innate principle in all parts of matter, by 
which, when separated from tiieir wholes, 
they endeavour to return to them again the 
nearest way. 
Kepler, in his preface to the Commentaries 
concerning the planet Mars, speaks of gra- 
vity as of a power that was mutual between 
bodies ; and says that the earth and moon 
tend towards each other, and would meet in 
a point so many times nearer to the earth 
than to the moon, as the earth is greater than 
the moon, if the motions did not hinder it 
He adds, tiiat the tides arise from the gra- 
vity of the waters towards the moon. To 
him we also owe the important discovery of 
the analogy between the distances of the se 
verul planets troin the sun, and the periods 
in which they complete their revolutions, 
viz. that the squares of their periodic times 
are always in the same pro; ortion as the 
cubes of their mean distances from the sun. 
However, Kepler, Gassendi, Gilbert, and 
others, ascribe gravity to a certain magnetic 
attraction of the earth ; conceiving the ea th 
to be one great magnet continually emitting 
effluvia, which take hold of ail bodies, and 
draw them o wards the earth. But this is in- 
consistent with the sevei al phenomena. 
Dcs Cartes and his followers, Rohault, &c. 
attribute gravity to an external impulse or 
trusion of some subtle matter. By the rota- 
tion of the earth, say they, ail the parts and 
appendages of it necessarily endeavour to re- 
cede from the centre of rotation ; but whence 
they cannot all actually recede, as there is 
no vacuum or space to receive them. But 
this hypothesis, founded on the supposition 
of a plenum, is overthrown by what has been 
since proved of die existence of a vacuum. 
Dr. Halley, despairing of any satisfactory 
theory, chooses to have immediate recourse 
to the agency of the Deity. So Dr. Clarke, 
from a view of several properties of gra- 
vity, concludes that it is no adventitious ef- 
fect of any motion, or subtle matter, but an 
original and general law impressed by God 
on all matter, and preserved in it by some 
efficient power penetrating the very solid and 
intimate substance of it ; being found always 
proportional, not to the surfaces of bodies or 
corpuscles, but to their solid quantity and 
contents. It should therefore be no more 
enquired why bodies gravitate, than how 
they came to be first put in motion. 
Gravesande, in his Introduct. ad Philos. 
Newton, contends, that the cause of gravity 
is utterly unknown ; and that we are to con- 
sider it no otherwise than as a law of nature 
originally and immediately impressed by the 
Creator, without any dependance on any se- 
cond law or cause at all. Of this he thinks 
the three following considerations sufficient 
proof. 1 . That gravity requires the presence 
of the gravitating or attracting body : so that 
the satellites of Jupiter, for example gravitate 
towards Jupiter, wherever he may be. 2. 
That the distance being supposed the same,, 
the velocity with which bodies are moved by 
the force of gravity, depends on the quantity 
of matter in the attracting body ; and the 
velocity is not changed, whatever die mass 
of the gravitating body may be. 3. That it 
gravity depends on any known law ot mo- 
tion, it must be some impulse from an extra- 
neous body ; so that as gravity is continual, a 
continual stroke must also be required. Now 
if there is any such matter continually strik- 
ing on bodies, it must be fluid, and subtle 
enough to penetrate the substance of all bo- 
dies: but how shall a body subtle enough to 
penetrate the substance of the- hardest bo- 
dies, and so rare as not sensibly tO' hinder 
the motion of bodies, be able to impel va-t 
masses towards each other with such force ? 
How does this force increase the ratio of the 
mass of the body, towards which the other 
body is moved? Whence is it that all bodies 
move with the same velocity, the distance 
and body gravitated to being the same ? Can 
a fluid which only acts on the surface either 
of the bodies themselves, or their internal 
particles, communicate such a quantity o£ 
