_That all bodies gravitate towards every planet; and that the weights
of bodies towards any the same planet, at equal distances from the
centre of the planet, are proportional to the quantities of matter
which they severally contain._
It has been, now of a long time, observed by others, that all sorts of
heavy bodies (allowance being made for the inequality of retardation
which they suffer from a small power of resistance in the air) descend
to the earth _from equal heights_ in equal times; and that
equality of times we may distinguish to a great accuracy, by the help
of pendulums. I tried the things in gold, silver, lead, glass, sand,
common salt, wood, water, and wheat. I provided two wooden boxes,
round and equal; 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 hanging by equal threads of 11 feet made a
couple of pendulums perfectly equal in weight and figure, and equally
receiving the resistance of the air. And, placing the one by the
other, I observed them to play together forwards and backwards, for
a long time, with equal vibrations ... and the like happened in the
other bodies. By these experiments, in bodies of the same weight, I
could manifestly have discovered a difference of matter less than
the thousandth part of the whole, had any such been. But, without
all doubt, the nature of gravity towards the planets is the same
as towards the earth.... Moreover, since the satellites of Jupiter
perform their revolutions in times which observe the sesquiplicate
proportion of their distances from Jupiter’s centre--that is, equal
at equal distances. And, therefore, these satellites, if supposed
to fall _towards Jupiter_ from equal heights, would describe
equal spaces in equal times, in like manner as heavy bodies do on
our earth.... If, at equal distances from the sun, any satellite, in
proportion to the quantity of its matter, did gravitate towards the
sun with a force greater than Jupiter in proportion to his, according
to any given proportion, suppose of _d_ to _e_; then the
distance between the centres of the sun and of the satellite’s orbit
would be always greater than the distance between the centres of the
sun and of Jupiter nearly in the sub-duplicate of that proportion; as
by some computations I have found. And if the satellite did gravitate
towards the sun with a force, lesser in the proportion of _e_ to
_d_, the distance of the centre of the satellite’s orbit from
the sun would be less than the distance of the centre of Jupiter from
the sun in the sub-duplicate of the same proportion. Therefore if, at
equal distances from the sun, the accelerative gravity of any satellite
towards the sun were greater or less than the accelerative gravity of
Jupiter towards the sun but one 1-1000 part of the whole gravity, the
distance of the centre of the satellite’s orbit from the sun would be
greater or less than the distance of Jupiter from the sun by one 1-2000
part of the whole distance--that is, by a fifth part of the distance
of the utmost satellite from the centre of Jupiter; an eccentricity of
the orbit which would be very sensible. But the orbits of the satellite
are concentric to Jupiter, and therefore the accelerative gravities of
Jupiter, and of all its satellites towards the sun, are equal among
themselves....
But further; the weights of all the parts of every planet towards
any other planet are one to another as the matter in the several
parts; for if some parts did gravitate more, others less, than for
the quantity of their matter, then the whole planet, according to the
sort of parts with which it most abounds, would gravitate more or less
than in proportion to the quantity of matter in the whole. Nor is it
of any moment whether these parts are external or internal; for if,
for example, we should imagine the terrestrial bodies with us to be
raised up to the orb of the moon, to be there compared with its body;
if the weights of such bodies were to the weights of the external parts
of the moon as the quantities of matter in the one and in the other
respectively; but to the weights of the internal parts in a greater or
less proportion, then likewise the weights of those bodies would be to
the weight of the whole moon in a greater or less proportion; against
what we have showed above.
Cor. 1. Hence the weights of bodies do not depend upon their forms and
textures; for if the weights could be altered with the forms, they
would be greater or less, according to the variety of forms in equal
matter; altogether against experience.
Cor. 2. Universally, all bodies about the earth gravitate towards the
earth; and the weights of all, at equal distances from the earth’s
centre, are as the quantities of matter which they severally contain.
This is the quality of all bodies within the reach of our experiments;
and therefore (by rule 3) to be affirmed of all bodies whatsoever....
Cor. 5. The power of gravity is of a different nature from the power of
magnetism; for the magnetic attraction is not as the matter attracted.
Some bodies are attracted more by the magnet; others less; most bodies
not at all. The power of magnetism in one and the same body may be
increased and diminished; and is sometimes far stronger, for the
quantity of matter, than the power of gravity; and in receding from
the magnet decreases not in the duplicate but almost in the triplicate
proportion of the distance, as nearly as I could judge from some rude
observations.