Letters on England [31]
reality of near
seventy. As this false computation did not agree with the
conclusions which Sir Isaac intended to draw from them, he laid
aside this pursuit. A half-learned philosopher, remarkable only for
his vanity, would have made the measure of the earth agree, anyhow,
with his system. Sir Isaac, however, chose rather to quit the
researches he was then engaged in. But after Mr. Picard had
measured the earth exactly, by tracing that meridian which redounds
so much to the honour of the French, Sir Isaac Newton resumed his
former reflections, and found his account in Mr. Picard's
calculation.
A circumstance which has always appeared wonderful to me, is that
such sublime discoveries should have been made by the sole
assistance of a quadrant and a little arithmetic.
The circumference of the earth is 123,249,600 feet. This, among
other things, is necessary to prove the system of attraction.
The instant we know the earth's circumference, and the distance of
the moon, we know that of the moon's orbit, and the diameter of this
orbit. The moon performs its revolution in that orbit in twenty-
seven days, seven hours, forty-three minutes. It is demonstrated,
that the moon in its mean motion makes an hundred and fourscore and
seven thousand nine hundred and sixty feet (of Paris) in a minute.
It is likewise demonstrated, by a known theorem, that the central
force which should make a body fall from the height of the moon,
would make its velocity no more than fifteen Paris feet in a minute
of time. Now, if the law by which bodies gravitate and attract one
another in an inverse ratio to the squares of the distances be true,
if the same power acts according to that law throughout all nature,
it is evident that as the earth is sixty semi-diameters distant from
the moon, a heavy body must necessarily fall (on the earth) fifteen
feet in the first second, and fifty-four thousand feet in the first
minute.
Now a heavy body falls, in reality, fifteen feet in the first
second, and goes in the first minute fifty-four thousand feet, which
number is the square of sixty multiplied by fifteen. Bodies,
therefore, gravitate in an inverse ratio of the squares of the
distances; consequently, what causes gravity on earth, and keeps the
moon in its orbit, is one and the same power; it being demonstrated
that the moon gravitates on the earth, which is the centre of its
particular motion, it is demonstrated that the earth and the moon
gravitate on the sun which is the centre of their annual motion.
The rest of the planets must be subject to this general law; and if
this law exists, these planets must follow the laws which Kepler
discovered. All these laws, all these relations are indeed observed
by the planets with the utmost exactness; therefore, the power of
attraction causes all the planets to gravitate towards the sun, in
like manner as the moon gravitates towards our globe.
Finally, as in all bodies re-action is equal to action, it is
certain that the earth gravitates also towards the moon; and that
the sun gravitates towards both. That every one of the satellites
of Saturn gravitates towards the other four, and the other four
towards it; all five towards Saturn, and Saturn towards all. That
it is the same with regard to Jupiter; and that all these globes are
attracted by the sun, which is reciprocally attracted by them.
This power of gravitation acts proportionably to the quantity of
matter in bodies, a truth which Sir Isaac has demonstrated by
experiments. This new discovery has been of use to show that the
sun (the centre of the planetary system) attracts them all in a
direct ratio of their quantity of matter combined with their
nearness. From hence Sir Isaac, rising by degrees to discoveries
which seemed not to be formed for the human mind, is bold enough to
compute the quantity of matter contained in the sun and in every
seventy. As this false computation did not agree with the
conclusions which Sir Isaac intended to draw from them, he laid
aside this pursuit. A half-learned philosopher, remarkable only for
his vanity, would have made the measure of the earth agree, anyhow,
with his system. Sir Isaac, however, chose rather to quit the
researches he was then engaged in. But after Mr. Picard had
measured the earth exactly, by tracing that meridian which redounds
so much to the honour of the French, Sir Isaac Newton resumed his
former reflections, and found his account in Mr. Picard's
calculation.
A circumstance which has always appeared wonderful to me, is that
such sublime discoveries should have been made by the sole
assistance of a quadrant and a little arithmetic.
The circumference of the earth is 123,249,600 feet. This, among
other things, is necessary to prove the system of attraction.
The instant we know the earth's circumference, and the distance of
the moon, we know that of the moon's orbit, and the diameter of this
orbit. The moon performs its revolution in that orbit in twenty-
seven days, seven hours, forty-three minutes. It is demonstrated,
that the moon in its mean motion makes an hundred and fourscore and
seven thousand nine hundred and sixty feet (of Paris) in a minute.
It is likewise demonstrated, by a known theorem, that the central
force which should make a body fall from the height of the moon,
would make its velocity no more than fifteen Paris feet in a minute
of time. Now, if the law by which bodies gravitate and attract one
another in an inverse ratio to the squares of the distances be true,
if the same power acts according to that law throughout all nature,
it is evident that as the earth is sixty semi-diameters distant from
the moon, a heavy body must necessarily fall (on the earth) fifteen
feet in the first second, and fifty-four thousand feet in the first
minute.
Now a heavy body falls, in reality, fifteen feet in the first
second, and goes in the first minute fifty-four thousand feet, which
number is the square of sixty multiplied by fifteen. Bodies,
therefore, gravitate in an inverse ratio of the squares of the
distances; consequently, what causes gravity on earth, and keeps the
moon in its orbit, is one and the same power; it being demonstrated
that the moon gravitates on the earth, which is the centre of its
particular motion, it is demonstrated that the earth and the moon
gravitate on the sun which is the centre of their annual motion.
The rest of the planets must be subject to this general law; and if
this law exists, these planets must follow the laws which Kepler
discovered. All these laws, all these relations are indeed observed
by the planets with the utmost exactness; therefore, the power of
attraction causes all the planets to gravitate towards the sun, in
like manner as the moon gravitates towards our globe.
Finally, as in all bodies re-action is equal to action, it is
certain that the earth gravitates also towards the moon; and that
the sun gravitates towards both. That every one of the satellites
of Saturn gravitates towards the other four, and the other four
towards it; all five towards Saturn, and Saturn towards all. That
it is the same with regard to Jupiter; and that all these globes are
attracted by the sun, which is reciprocally attracted by them.
This power of gravitation acts proportionably to the quantity of
matter in bodies, a truth which Sir Isaac has demonstrated by
experiments. This new discovery has been of use to show that the
sun (the centre of the planetary system) attracts them all in a
direct ratio of their quantity of matter combined with their
nearness. From hence Sir Isaac, rising by degrees to discoveries
which seemed not to be formed for the human mind, is bold enough to
compute the quantity of matter contained in the sun and in every