The discoveries which gained Sir Isaac Newton so universal a reputation,
relate to the system of the world, to light, to geometrical infinities;
and, lastly, to chronology, with which he used to amuse himself after the
fatigue of his severer studies.
I will now acquaint you (without prolixity if possible) with the few
things I have been able to comprehend of all these sublime ideas. With
regard to the system of our world, disputes were a long time maintained,
on the cause that turns the planets, and keeps them in their orbits: and
on those causes which make all bodies here below descend towards the
surface of the earth.
The system of Descartes, explained and improved since his time, seemed to
give a plausible reason for all those phenomena; and this reason seemed
more just, as it is simple and intelligible to all capacities. But in
philosophy, a student ought to doubt of the things he fancies he
understands too easily, as much as of those he does not understand.
Gravity, the falling of accelerated bodies on the earth, the revolution
of the planets in their orbits, their rotations round their axis, all
this is mere motion. Now motion cannot perhaps be conceived any
otherwise than by impulsion; therefore all those bodies must be impelled.
But by what are they impelled? All space is full, it therefore is filled
with a very subtile matter, since this is imperceptible to us; this
matter goes from west to east, since all the planets are carried from
west to east. Thus from hypothesis to hypothesis, from one appearance to
another, philosophers have imagined a vast whirlpool of subtile matter,
in which the planets are carried round the sun: they also have created
another particular vortex which floats in the great one, and which turns
daily round the planets. When all this is done, it is pretended that
gravity depends on this diurnal motion; for, say these, the velocity of
the subtile matter that turns round our little vortex, must be seventeen
times more rapid than that of the earth; or, in case its velocity is
seventeen times greater than that of the earth, its centrifugal force
must be vastly greater, and consequently impel all bodies towards the
earth. This is the cause of gravity, according to the Cartesian system.
But the theorist, before he calculated the centrifugal force and velocity
of the subtile matter, should first have been certain that it existed.
Sir Isaac Newton, seems to have destroyed all these great and little
vortices, both that which carries the planets round the sun, as well as
the other which supposes every planet to turn on its own axis.
First, with regard to the pretended little vortex of the earth, it is
demonstrated that it must lose its motion by insensible degrees; it is
demonstrated, that if the earth swims in a fluid, its density must be
equal to that of the earth; and in case its density be the same, all the
bodies we endeavour to move must meet with an insuperable resistance.
With regard to the great vortices, they are still more chimerical, and it
is impossible to make them agree with Kepler's law, the truth of which
has been demonstrated. Sir Isaac shows, that the revolution of the fluid
in which Jupiter is supposed to be carried, is not the same with regard
to the revolution of the fluid of the earth, as the revolution of Jupiter
with respect to that of the earth. He proves, that as the planets make
their revolutions in ellipses, and consequently being at a much greater
distance one from the other in their Aphelia, and a little nearer in
their Perihelia; the earth's velocity, for instance, ought to be greater
when it is nearer Venus and Mars, because the fluid that carries it
along, being then more pressed, ought to have a greater motion; and yet
it is even then that the earth's motion is slower.
He proves that there is no such thing as a celestial matter which goes
from west to east since the comets traverse those spaces, sometimes from
east to west, and at other times from north to south.
In fine, the better to resolve, if possible, every difficulty, he proves,
and even by experiments, that it is impossible there should be a plenum;
and brings back the vacuum, which Aristotle and Descartes had banished
from the world.
Having by these and several other arguments destroyed the Cartesian
vortices, he despaired of ever being able to discover whether there is a
secret principle in nature which, at the same time, is the cause of the
motion of all celestial bodies, and that of gravity on the earth. But
being retired in 1666, upon account of the Plague, to a solitude near
Cambridge; as he was walking one day in his garden, and saw some fruits
fall from a tree, he fell into a profound meditation on that gravity, the
cause of which had so long been sought, but in vain, by all the
philosophers, whilst the vulgar think there is nothing mysterious in it.
He said to himself; that from what height soever in our hemisphere, those
bodies might descend, their fall would certainly be in the progression
discovered by Galileo; and the spaces they run through would be as the
square of the times. Why may not this power which causes heavy bodies to
descend, and is the same without any sensible diminution at the remotest
distance from the centre of the earth, or on the summits of the highest
mountains, why, said Sir Isaac, may not this power extend as high as the
moon? And in case its influence reaches so far, is it not very probable
that this power retains it in its orbit, and determines its motion? But
in case the moon obeys this principle (whatever it be) may we not
conclude very naturally that the rest of the planets are equally subject
to it? In case this power exists (which besides is proved) it must
increase in an inverse ratio of the squares of the distances. All,
therefore, that remains is, to examine how far a heavy body, which should
fall upon the earth from a moderate height, would go; and how far in the
same time, a body which should fall from the orbit of the moon, would
descend. To find this, nothing is wanted but the measure of the earth,
and the distance of the moon from it.
Thus Sir Isaac Newton reasoned. But at that time the English had but a
very imperfect measure of our globe, and depended on the uncertain
supposition of mariners, who computed a degree to contain but sixty
English miles, whereas it consists in 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 planet; and in this manner shows, from the simple laws of
mechanics, that every celestial globe ought necessarily to be where it is
placed.
His bare principle of the laws of gravitation accounts for all the
apparent inequalities in the course of the celestial globes. The
variations of the moon are a necessary consequence of those laws.
Moreover, the reason is evidently seen why the nodes of the moon perform
their revolutions in nineteen years, and those of the earth in about
twenty-six thousand. The several appearances observed in the tides are
also a very simple effect of this attraction. The proximity of the moon,
when at the full, and when it is new, and its distance in the quadratures
or quarters, combined with the action of the sun, exhibit a sensible
reason why the ocean swells and sinks.
After having shown by his sublime theory the course and inequalities of
the planets, he subjects comets to the same law. The orbit of these
fires (unknown for so great a series of years), which was the terror of
mankind and the rock against which philosophy split, placed by Aristotle
below the moon, and sent back by Descartes above the sphere of Saturn, is
at last placed in its proper seat by Sir Isaac Newton.
He proves that comets are solid bodies which move in the sphere of the
sun's activity, and that they describe an ellipsis so very eccentric, and
so near to parabolas, that certain comets must take up above five hundred
years in their revolution.
The learned Dr. Halley is of opinion that the comet seen in 1680 is the
same which appeared in Julius Caesar's time. This shows more than any
other that comets are hard, opaque bodies; for it descended so near to
the sun, as to come within a sixth part of the diameter of this planet
from it, and consequently might have contracted a degree of heat two
thousand times stronger than that of red-hot iron; and would have been
soon dispersed in vapour, had it not been a firm, dense body. The
guessing the course of comets began then to be very much in vogue. The
celebrated Bernoulli concluded by his system that the famous comet of
1680 would appear again the 17th of May, 1719. Not a single astronomer
in Europe went to bed that night. However, they needed not to have broke
their rest, for the famous comet never appeared. There is at least more
cunning, if not more certainty, in fixing its return to so remote a
distance as five hundred and seventy-five years. As to Mr. Whiston, he
affirmed very seriously that in the time of the Deluge a comet overflowed
the terrestrial globe. And he was so unreasonable as to wonder that
people laughed at him for making such an assertion. The ancients were
almost in the same way of thinking with Mr. Whiston, and fancied that
comets were always the forerunners of some great calamity which was to
befall mankind. Sir Isaac Newton, on the contrary, suspected that they
are very beneficent, and that vapours exhale from them merely to nourish
and vivify the planets, which imbibe in their course the several
particles the sun has detached from the comets, an opinion which, at
least, is more probable than the former. But this is not all. If this
power of gravitation or attraction acts on all the celestial globes, it
acts undoubtedly on the several parts of these globes. For in case
bodies attract one another in proportion to the quantity of matter
contained in them, it can only be in proportion to the quantity of their
parts; and if this power is found in the whole, it is undoubtedly in the
half; in the quarters in the eighth part, and so on in _infinitum_.
This is attraction, the great spring by which all Nature is moved. Sir
Isaac Newton, after having demonstrated the existence of this principle,
plainly foresaw that its very name would offend; and, therefore, this
philosopher, in more places than one of his books, gives the reader some
caution about it. He bids him beware of confounding this name with what
the ancients called occult qualities, but to be satisfied with knowing
that there is in all bodies a central force, which acts to the utmost
limits of the universe, according to the invariable laws of mechanics.
It is surprising, after the solemn protestations Sir Isaac made, that
such eminent men as Mr. Sorin and Mr. de Fontenelle should have imputed
to this great philosopher the verbal and chimerical way of reasoning of
the Aristotelians; Mr. Sorin in the Memoirs of the Academy of 1709, and
Mr. de Fontenelle in the very eulogium of Sir Isaac Newton.
Most of the French (the learned and others) have repeated this reproach.
These are for ever crying out, "Why did he not employ the word
_impulsion_, which is so well understood, rather than that of
_attraction_, which is unintelligible?"
Sir Isaac might have answered these critics thus:--"First, you have as
imperfect an idea of the word impulsion as of that of attraction; and in
case you cannot conceive how one body tends towards the centre of another
body, neither can you conceive by what power one body can impel another.
"Secondly, I could not admit of impulsion; for to do this I must have
known that a celestial matter was the agent. But so far from knowing
that there is any such matter, I have proved it to be merely imaginary.
"Thirdly, I use the word attraction for no other reason but to express an
effect which I discovered in Nature--a certain and indisputable effect of
an unknown principle--a quality inherent in matter, the cause of which
persons of greater abilities than I can pretend to may, if they can, find
out."
"What have you, then, taught us?" will these people say further; "and to
what purpose are so many calculations to tell us what you yourself do not
comprehend?"
"I have taught you," may Sir Isaac rejoin, "that all bodies gravitate
towards one another in proportion to their quantity of matter; that these
central forces alone keep the planets and comets in their orbits, and
cause them to move in the proportion before set down. I demonstrate to
you that it is impossible there should be any other cause which keeps the
planets in their orbits than that general phenomenon of gravity. For
heavy bodies fall on the earth according to the proportion demonstrated
of central forces; and the planets finishing their course according to
these same proportions, in case there were another power that acted upon
all those bodies, it would either increase their velocity or change their
direction. Now, not one of those bodies ever has a single degree of
motion or velocity, or has any direction but what is demonstrated to be
the effect of the central forces. Consequently it is impossible there
should be any other principle."
Give me leave once more to introduce Sir Isaac speaking. Shall he not be
allowed to say? "My case and that of the ancients is very different.
These saw, for instance, water ascend in pumps, and said, 'The water
rises because it abhors a vacuum.' But with regard to myself; I am in
the case of a man who should have first observed that water ascends in
pumps, but should leave others to explain the cause of this effect. The
anatomist, who first declared that the motion of the arm is owing to the
contraction of the muscles, taught mankind an indisputable truth. But
are they less obliged to him because he did not know the reason why the
muscles contract? The cause of the elasticity of the air is unknown, but
he who first discovered this spring performed a very signal service to
natural philosophy. The spring that I discovered was more hidden and
more universal, and for that very reason mankind ought to thank me the
more. I have discovered a new property of matter--one of the secrets of
the Creator--and have calculated and discovered the effects of it. After
this, shall people quarrel with me about the name I give it?"
Vortices may be called an occult quality, because their existence was
never proved. Attraction, on the contrary, is a real thing, because its
effects are demonstrated, and the proportions of it are calculated. The
cause of this cause is among the _Arcana_ of the Almighty.
"Precedes huc, et non amplius."
(Thus far shalt thou go, and no farther.)