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_ 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.) _
Read next: LETTER XVI - ON SIR ISAAC NEWTON'S OPTICS
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