Apples, Feathers, and Coals
March 20, 2020Isaac Newton |
François Marie Arouet
de Voltaire (1694–1778). Letters on the English.
Vol. 34, pp. 113-124 of
The Harvard Classics
Sir Isaac Newton was
aided in his momentous discoveries by the most insignificant objects
- even apples, feathers, and coal. Voltaire discusses the wondrous
discoveries of Newton.
(Sir Isaac Newton
died March 20, 1727.)
Letter
XV—On Attraction
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 is 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
Cæsar’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 than 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
quarter, 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
M. 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 M. 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 that 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.
“Procedes huc, et
non amplius.”
(Thus far shalt
thou go, and no farther.)
Letter
XVI—On Sir Isaac Newton’s Optics
THE PHILOSOPHERS of the
last age found out a new universe; and a circumstance which made its
discovery more difficult was that no one had so much as suspected its
existence. The most sage and judicious were of opinion that it was a
frantic rashness to dare so much as to imagine that it was possible
to guess the laws by which the celestial bodies move and the manner
how light acts. Galileo, by his astronomical discoveries, Kepler, by
his calculation, Descartes (at least, in his dioptrics), and Sir
Isaac Newton, in all his works, severally saw the mechanism of the
springs of the world. The geometricians have subjected infinity to
the laws of calculation. The circulation of the blood in animals, and
of the sap in vegetables, have changed the face of Nature with regard
to us. A new kind of existence has been given to bodies in the
air-pump. By the assistance of telescopes bodies have been brought
nearer to one another. Finally, the several discoveries which Sir
Isaac Newton has made on light are equal to the boldest things which
the curiosity of man could expect after so many philosophical
novelties.
Till Antonio de Dominis the rainbow
was considered as an inexplicable miracle. This philosopher guessed
that it was a necessary effect of the sun and rain. Descartes gained
immortal fame by his mathematical explication of this so natural a
phenomenon. He calculated the reflections and refractions of light in
drops of rain. And his sagacity on this occasion was at that time
looked upon as next to divine.
But what would he have said had it
been proved to him that he was mistaken in the nature of light; that
he had not the least reason to maintain that it is a globular body?
That it is false to assert that this matter, spreading itself through
the whole, waits only to be projected forward by the sun, in order to
be put in action, in like manner as a long staff acts at one end when
pushed forward by the other. That light is certainly darted by the
sun; in fine, that light is transmitted from the sun to the earth in
about seven minutes through a cannon-ball, which were not to lose any
of its velocity, could not go that distance in less than twenty-five
years. How great would have been his astonishment had he been told
that light does not reflect directly by impinging against the solid
parts of bodies, that bodies are not transparent when they have large
pores, and that a man should arise who would demonstrate all these
paradoxes, and anatomise a single ray of light with more dexterity
than the ablest artist dissects a human body. This man is come. Sir
Isaac Newton has demonstrated to the eye, by the bare assistance of
the prism, that light is a composition of coloured rays, which, being
united, form white colour. A single ray is by him divided into seven,
which all fall upon a piece of linen, or a sheet of white paper, in
their order, one above the other, and at unequal distances. The first
is red, the second orange, the third yellow, the fourth green, the
fifth blue, the sixth indigo, the seventh a violet-purple. Each of
these rays, transmitted afterwards by a hundred other prisms, will
never change the colour it bears; in like manner, as gold, when
completely purged from its dross, will never change afterwards in the
crucible. As a superabundant proof that each of these elementary rays
has inherently in itself that which forms its colour to the eye, take
a small piece of yellow wood, for instance, and set it in the ray of
a red colour; this wood will instantly be tinged red. But set it in
the ray of a green colour, it assumes a green colour, and so of all
the rest.
From what cause, therefore, do colours
arise in Nature? It is nothing but the disposition of bodies to
reflect the rays of a certain order and to absorb all the rest.
What, then, is this secret
disposition? Sir Isaac Newton demonstrates that it is nothing more
than the density of the small constituent particles of which a body
is composed. And how is this reflection performed? It was supposed to
arise from the rebounding of the rays, in the same manner as a ball
on the surface of a solid body. But this is a mistake, for Sir Isaac
taught the astonished philosophers that bodies are opaque for no
other reason but because their pores are large, that light reflects
on our eyes from the very bosom of those pores, that the smaller the
pores of a body are the more such a body is transparent. Thus paper,
which reflects the light when dry, transmits it when oiled, because
the oil, by filling its pores, makes them much smaller.
It is there that examining the vast
porosity of bodies, every particle having its pores, and every
particle of those particles having its own, he shows we are not
certain that there is a cubic inch of solid matter in the universe,
so far are we from conceiving what matter is. Having thus divided, as
it were, light into its elements, and carried the sagacity of his
discoveries so far as to prove the method of distinguishing compound
colours from such as are primitive, he shows that these elementary
rays, separated by the prism, are ranged in their order for no other
reason but because they are refracted in that very order; and it is
this property (unknown till he discovered it) of breaking or
splitting in this proportion; it is this unequal refraction of rays,
this power of refracting the red less than the orange colour, &c.,
which he calls the different refrangibility. The most reflexible rays
are the most refrangible, and from hence he evinces that the same
power is the cause both of the reflection and refraction of light.
But all these wonders are merely but
the opening of his discoveries. He found out the secret to see the
vibrations or fits of light which come and go incessantly, and which
either transmit light or reflect it, according to the density of the
parts they meet with. He has presumed to calculate the density of the
particles of air necessary between two glasses, the one flat, the
other convex on one side, set one upon the other, in order to operate
such a transmission or reflection, or to form such and such a colour.
From all these combinations he
discovers the proportion in which light acts on bodies and bodies act
on light.
He saw light so perfectly, that he has
determined to what degree of perfection the art of increasing it, and
of assisting our eyes by telescopes, can be carried.
Descartes, from a noble confidence
that was very excusable, considering how strongly he was fired at the
first discoveries he made in an art which he almost first found out;
Descartes, I say, hoped to discover in the stars, by the assistance
of telescopes, objects as small as those we discern upon the earth.
But Sir Isaac has shown that dioptric
telescopes cannot be brought to a greater perfection, because of that
refraction, and of that very refrangibility, which at the same time
that they bring objects nearer to us, scatter too much the elementary
rays. He has calculated in these glasses the proportion of the
scattering of the red and of the blue rays; and proceeding so far as
to demonstrate things which were not supposed even to exist, he
examines the inequalities which arise from the shape or figure of the
glass, and that which arises from the refrangibility. He finds that
the object glass of the telescope being convex on one side and flat
on the other, in case the flat side be turned towards the object, the
error which arises from the construction and position of the glass is
above five thousand times less than the error which arises from the
refrangibility; and, therefore, that the shape or figure of the
glasses is not the cause why telescopes cannot be carried to a
greater perfection, but arises wholly from the nature of light.
For this reason he invented a
telescope, which discovers objects by reflection, and not by
refraction. Telescopes of this new kind are very hard to make, and
their use is not easy; but, according to the English, a reflective
telescope of but five feet has the same effect as another of a
hundred feet in length.
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