gravity. 
portion of the quantity of such portions to 
the whole mass. Hence also the gravi- 
tating powers of bodies at the same dis- 
tance from the centre are proportional to 
the quantities of matter in the bodies. 
General or universal gravity, is that by 
which all the planets tend towards one ano- 
ther ; and indeed, by which all bodies or 
particles of matter in the universe tend to- 
wards one another. 
The existence of the same principles of 
gravitation in the superior regions of the 
heavens as on the earth, is one of the great 
discoveries of Newton, who made the proof 
of it as easy as that on the earth. This was 
at first only a conjecture in his mind : he 
observed, that all bodiesi near the earth, 
and in its atmosphere, had the. property of 
tending directly towards it ; he soon con- 
jectured, that it probably extended much 
higher than to any distance to which we 
could reach to make experiments ; and so 
on, from one distance to another, till he 
at length saw no reason why it might 
not extend to the moon, by means of 
which she might be retained in her orbit, 
as a stone in a sling is retained by the hand ; 
and if so, he next inferred, why might not 
a similar principle exist in the other great 
bodies in the universe, the sun, and all the 
other planets, both primary and secondary, 
which might all be retained in their orbits, 
and perform their revolutions by means of 
the same universal principle of gravitation. 
He soon realized and verified these by 
mathematical proofs. Kepler had found 
out, by contemplating the motions of the 
planets about the sun, that the area de- 
cribed by a line connecting the sun and pla- 
net, as this revolved in its orbit, was always 
proportional to the time of its description, 
or that it described equal areas in equal 
times in whatever part of its orbit the planet 
might be, moving always as much the quicker 
as its distance from the sun was less. And 
it is also found, that the satellites, or se- 
condary planets, respect the same law in 
revolving about their primaries. But it 
was soon proved, by Newton, that all bo- 
dies moving in any curve line described on 
a plane, and which, by radii drawn to any 
certain point, describes areas about the 
point proportional to the times, are im- 
pelled or acted on by some power tending 
towards that point. Consequently, 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 sa- 
tellites to their several primaries. 
Again, Newton demonstrates that if seve- 
ral bodies revolve with an equable motion 
in several circles about the same centre, 
and that if the squares of their periodical 
times be 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 dis- 
tances. But it had been agreed on by the 
astronomers, and particularly Kepler, that 
both these cases obtain in all the planets ; 
and therefore he inferred that the centri- 
petal forces of all the planets were recipro- 
cally proportional to squares of the dis- 
tances from the centres of their orbits. 
Upon the whole, it appears that the 
planets are retained in their orbits by some 
power which 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 towards the centre, and dimi- 
nishes on receding from the same, and that 
in the reciprocal duplicate ratio of the dis- 
tances ; and that by comparing this cen- 
tripetal force with the force of gravity on 
the earth, they are found to be perfectly 
alike, as may easily be shown in various 
instances. For example, in the case of the 
moon, the nearest of all the planets, the 
rectilinear spaces described in any given 
time, by a body urged by any power, 
reckoning from the beginning of its descent, 
are proportionate to those powers. Con- 
sequently the centripetal force of the moon, 
revolving in its orbit, will be to the force 
of gravity on the surface of the earth as the 
space which the moon would describe in 
falling, during any small time, by her cen- 
tripetal force towards the earth, if she had 
no motion at all, to the space a body near 
the earth would describe in falling by its 
gravity towards the same. 
Now by an easy calculation of these, 
two spaces, it appears that the former force 
is to the latter as the square of the semi- 
diameter of the earth is to the square of 
that of the moon’s orbit. The moon's 
centripetal force, therefore, is equal to the 
force of gravity; and consequently these 
forces are not different, but they are one 
and the same : for if they were different 
bodies acted on by the two powers con- 
jointly, would fall towards the earth with a 
velocity double to that arising from the 
sole power of gravity. 
It is evident, therefore, that the moon’s 
centripetal force, by which she is retained 
