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Voltaire (1694-1778):
Letters on Newton
from the Letters on the English or Lettres Philosophiques, c. 1778


Letter XIV: On Descartes And Sir Isaac Newton

A Frenchman who arrives in London, will find philosophy, like everything else, very much changed there. He had left the world a plenum, and he now finds it a vacuum. At Paris the universe is seen composed of vortices of subtile matter; but nothing like it is seen in London. In France, it is the pressure of the moon that causes the tides; but in England it is the sea that gravitates towards the moon; so that when you think that the moon should make it flood with us, those gentlemen fancy it should be ebb, which very unluckily cannot be proved. For to be able to do this, it is necessary the moon and the tides should have been inquired into at the very instant of the creation.

You will observe farther, that the sun, which in France is said to have nothing to do in the affair, comes in here for very near a quarter of its assistance. According to your Cartesians, everything is performed by an impulsion, of which we have very little notion; and according to Sir Isaac Newton, it is by an attraction, the cause of which is as much unknown to us. At Paris you imagine that the earth is shaped like a melon, or of an oblique figure; at London it has an oblate one. A Cartesian declares that light exists in the air; but a Newtonian asserts that it comes from the sun in six minutes and a half. The several operations of your chemistry are performed by acids, alkalies and subtile matter; but attraction prevails even in chemistry among the English.

The very essence of things is totally changed. You neither are agreed upon the definition of the soul, nor on that of matter. Descartes, as I observed in my last, maintains that the soul is the same thing with thought, and Mr. Locke has given a pretty good proof of the contrary.

Descartes asserts farther, that extension alone constitutes matter, but Sir Isaac adds solidity to it.

How furiously contradictory are these opinions!

"Non nostrum inter vos tantas componere lites."

Virgil, Eclog. III.

"'Tis not for us to end such great disputes."

This famous Newton, this destroyer of the Cartesian system, died in March, anno 1727. His countrymen honoured him in his lifetime, and interred him as though he had been a king who had made his people happy.

The English read with the highest satisfaction, and translated into their tongue, the Elogium of Sir Isaac Newton, which M. de Fontenelle spoke in the Academy of Sciences. M. de Fontenelle presides as judge over philosophers; and the English expected his decision, as a solemn declaration of the superiority of the English philosophy over that of the French. But when it was found that this gentleman had compared Descartes to Sir Isaac, the whole Royal Society in London rose up in arms. So far from acquiescing with M. Fontenelle's judgment, they criticised his discourse. And even several (who, however, were not the ablest philosophers in that body) were offended at the comparison, and for no other reason but because Descartes was a Frenchman.

It must be confessed that these two great men differed very much in conduct, in fortune, and in philosophy.

Nature had indulged Descartes with a shining and strong imagination, whence he became a very singular person both in private life and in his manner of reasoning. This imagination could not conceal itself even in his philosophical works, which are everywhere adorned with very shining, ingenious metaphors and figures. Nature had almost made him a poet; and indeed he wrote a piece of poetry for the entertainment of Christina, Queen of Sweden, which however was suppressed in honour to his memory.

He embraced a military life for some time, and afterwards becoming a complete philosopher, he did not think the passion of love derogatory to his character. He had by his mistress a daughter called Froncine, who died young, and was very much regretted by him. Thus the experienced every passion incident to mankind.

He was a long time of opinion that it would be necessary for him to fly from the society of his fellow creatures, and especially from his native country, in order to enjoy the happiness of cultivating his philosophical studies in full liberty.

Descartes was very right, for his contemporaries were not knowing enough to improve had enlighten his understanding, and were capable of little else than of giving him uneasiness.

He left France purely to go in search of truth, which was then persecuted by the wretched philosophy of the schools. However, he found that reason was as much disguised and depraved in the universities of Holland, into which he withdrew, as in his own country. For at the time that the French condemned the only propositions of his philosophy which were true, he was persecuted by the pretended philosophers of Holland, who understood him no better; and who, having a nearer view of his glory, hated his person the more, so that he was obliged to leave Utrecht. Descartes was injuriously accused of being an atheist, the last refuge of religious scandal: and he who had employed all the sagacity and penetration of his genius, in searching for new proofs of the existence of a God, was suspected to believe there was no such Being.

Such a persecution from all sides, must necessarily suppose a most exalted merit as well as a very distinguished reputation, and indeed he possessed both. Reason at that time darted a ray upon the world through the gloom of the schools, and the prejudices of popular superstition. At last his name spread so universally, that the French were desirous of bringing him back into his native country by rewards, and accordingly offered him an annual pension of a thousand crowns. Upon these hopes Descartes returned to France; paid the fees of his patent, which was sold at that time, but no pension was settled upon him. Thus disappointed, he returned to his solitude in North Holland, where he again pursued the study of philosophy, whilst the great Galileo, fourscore years of age, was groaning in the prisons of the Inquisition, only for having demonstrated the earth's motion.

At last Descartes was snatched from the world in the flower of his age at Stockholm. His death was owing to a bad regimen, and he expired in the midst of some literati who were his enemies, and under the hands of a physician to whom he was odious.

The progress of Sir Isaac Newton's life was quite different. He lived happy, and very much honoured in his native country, to the age of fourscore and five years.

It was his peculiar felicity, not only to be born in a country of liberty, but in an age when all scholastic impertinences were banished from the world. Reason alone was cultivated, and mankind could only be his pupil, not his enemy.

One very singular difference in the lives of these two great men is, that Sir Isaac, during the long course of years he enjoyed, was never sensible to any passion, was not subject to the common frailties of mankind, nor ever had any commerce with women-a circumstance which was assured me by the physician and surgeon who attended him in his last moments.

We may admire Sir Isaac Newton on this occasion, but then we must not censure Descartes.

The opinion that generally prevails in England with regard to these new philosophers is, that the latter was a dreamer, and the former a sage.

Very few people in England read Descartes, whose works indeed are now useless. On the other side, but a small number peruse those of Sir Isaac, because to do this the student must be deeply skilled in the mathematics, otherwise those works will be unintelligible to him. But notwithstanding this, these great men are the subject of everyone's discourse. Sir Isaac Newton is allowed every advantage, whilst Descartes is not indulged a single one. According to some, it is to the former that we owe the discovery of a vacuum, that the air is a heavy body, and the invention of telescopes. In a word, Sir Isaac Newton is here as the Hercules of fabulous story, to whom the ignorant ascribed all the feats of ancient heroes.

In a critique that was made in London on M. de Fontenelle's discourse, the writer presumed to assert that Descartes was not a great geometrician. Those who make such a declaration may justly be reproached with flying in their master's face. Descartes extended the limits of geometry as far beyond the place where he found them, as Sir Isaac did after him. The former first taught the method of expressing curves by equations. This geometry which, thanks to him for it, is now grown common, was so abstruse in his time, that not so much as one professor would undertake to explain it; and Schotten in Holland, and Format in France, were the only men who understood it.

He applied this geometrical and inventive genius to dioptrics, which, when treated of by him, became a new art. And if he was mistaken in some things, the reason of that is, a man who discovers a new tract of land cannot at once know all the properties of the soil. Those who come after him, and make these lands fruitful, are at least obliged to him for the discovery. I will not deny but that there are innumerable errors in the rest of Descartes' works.

Geometry was a guide he himself had in some measure fashioned, which would have conducted him safely through the several paths of natural philosophy. Nevertheless, he at last abandoned this guide, and gave entirely into the humour of forming hypotheses; and then philosophy was no more than an ingenious romance, fit only to amuse the ignorant. He was mistaken in the nature of the soul, in the proofs of the existence of a God, in matter, in the laws of motion, and in the nature of light. He admitted innate ideas, he invented new elements, he created a world; he made man according to his own fancy; and it is justly said, that the man of Descartes is, in fact, that of Descartes only, very different from the real one.

He pushed his metaphysical errors so far, as to declare that two and two make four for no other reason by because God would have it so. However, it will not be making him too great a compliment if we affirm that he was valuable even in his mistakes. He deceived himself, but then it was at least in a methodical way. He destroyed all the absurd chimeras with which youth had been infatuated for two thousand years. He taught his contemporaries how to reason, and enabled them to employ his own weapons against himself. If Descartes did not pay in good money, he however did great service in crying down that of a base alloy.

I indeed believe that very few will presume to compare his philosophy in any respect with that of Sir Isaac Newton. The former is an essay, the latter a masterpiece. But then the man who first brought us to the path of truth, was perhaps as great a genius as he who afterwards conducted us through it.

Descartes gave sight to the blind. These saw the errors of antiquity and of the sciences. The path he struck out is since become boundless. Robault's little work was, during some years, a complete system of physics; but now all the Transactions of the several academies in Europe put together do not form so much as the beginning of a system. In fathoming this abyss no bottom has been found. We are now to examine what discoveries Sir Isaac Newton has made in it.

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 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 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.

Letter XVII: On Infinites In Geometry, And Sir Isaac Newton's Chronology

The labyrinth and abyss of infinity is also a new course Sir Isaac Newton has gone through, and we are obliged to him for the clue, by whose assistance we are enabled to trace its various windings.

Descartes got the start of him also in this astonishing invention. He advanced with mighty steps in his geometry, and was arrived at the very borders of infinity, but went not farther. Dr. Wallis, about the middle of the last century, was the first who reduced a fraction by a perpetual division to an infinite series.

The Lord Brouncker employed this series to square the hyperbola. Mercator published a demonstration of this quadrature; much about which time Sir Isaac Newton, being then twenty-three years of age, had invented a general method, to perform on all geometrical curves what had just before been tried on the hyperbola.

It is to this method of subjecting everywhere infinity to algebraical calculations, that the name is given of differential calculations or of fluxions and integral calculation. It is the art of numbering and measuring exactly a thing whose existence cannot be conceived.

And, indeed, would you not imagine that a man laughed at you who should declare that there are lines infinitely great which form an angle infinitely little?

That a right line, which is a right line so long as it is finite, by changing infinitely little its direction, becomes an infinite curve; and that a curve may become infinitely less than another curve?

That there are infinite squares, infinite cubes, and infinites of infinites, all greater than one another, and the last but one of which is nothing in comparison of the last?

All these things, which at first appear to be the utmost excess of frenzy, are in reality an effort of the sublety and extent of the human mind, and the art of finding truths which till then had been unknown.

This so bold edifice is even founded on simple ideas. The business is to measure the diagonal of a square, to give the area of a curve, to find the square root of a number, which has none in common arithmetic. After all, the imagination ought not to be startled any more at so many orders of infinites than at the so well-known proposition, viz., that curve lines may always be made to pass between a circle and a tangent, or at that other, namely, that matter is divisible in infinitum. These two truths have been demonstrated many years, and are no less incomprehensible than the things we have been speaking of.

For many years the invention of this famous calculation was denied to Sir Isaac Newton. In Germany Mr. Leibnitz was considered as the inventor of the differences or moments, called fluxions, and Mr. Bernoulli claimed the integral calculus. However, Sir Isaac is now thought to have first made the discovery, and the other two have the glory of having once made the world doubt whether it was to be ascribed to him or them. Thus some contested with Dr. Harvey the invention of the circulation of the blood, as others disputed with Mr. Perrault that of the circulation of the sap.

Hartsocher and Leuwenhoek disputed with each other the honour of having first seen the vermiculi of which mankind are formed. This Hartsocher also contested with Huygens the invention of a new method of calculating the distance of a fixed star. It is not yet known to what philosopher we owe the invention of the cycloid.

Be this as it will, it is by the help of this geometry of infinites that Sir Isaac Newton attained to the most sublime discoveries. I am now to speak of another work, which, though more adapted to the capacity of the human mind, does nevertheless display some marks of that creative genius with which Sir Isaac Newton was informed in all his researches. The work I mean is a chronology of a new kind, for what province soever he undertook he was sure to change the ideas and opinions received by the rest of men.

Accustomed to unravel and disentangle chaos, he was resolved to convey at least some light into that of the fables of antiquity which are blended and confounded with history, and fix an uncertain chronology. It is true that there is no family, city, or nation, but endeavours to remove its original as far backward as possible. Besides, the first historians were the most negligent in setting down the eras: books were infinitely less common than they are at this time, and, consequently, authors being not so obnoxious to censure, they therefore imposed upon the world with greater impunity; and, as it is evident that these have related a great number of fictitious particulars, it is probable enough that they also gave us several false eras.

It appeared in general to Sir Isaac that the world was five hundred years younger than chronologers declare it to be. He grounds his opinion on the ordinary course of Nature, and on the observations which astronomers have made.

By the course of Nature we here understand the time that every generation of men lives upon the earth. The Egyptians first employed this vague and uncertain method of calculating when they began to write the beginning of their history. These computed three hundred and forty-one generations from Menes to Sethon; and, having no fixed era, they supposed three generations to consist of a hundred years. In this manner they computed eleven thousand three hundred and forty years from Menes' reign to that of Sethon.

The Greeks before they counted by Olympiads followed the method of the Egyptians, and even gave a little more extent to generations, making each to consist of forty years.

Now, here, both the Egyptians and the Greeks made an errenous computation. It is true, indeed, that, according to the usual course of Nature, three generations last about a hundred and twenty years; but three reigns are far from taking up so many. It is very evident that mankind in general live longer than kings are found to reign, so that an author who should write a history in which there were no dates fixed, and should know that nine kings had reigned over a nation; such a historian would commit a great error should he allow three hundred years to these nine monarchs. Every generation takes about thirty-six years; every reign is, one with the other, about twenty. Thirty kings of England have swayed the sceptre from William the Conqueror to George I., the years of whose reigns added together amount to six hundred and forty-eight years; which, being divided equally among the thirty kings, give to every one a reign of twenty-one years and a half very near. Sixty-three kings of France have sat upon the throne; these have, one with another, reigned about twenty years each. This is the usual course of Nature. The ancients, therefore, were mistaken when they supposed the durations in general of reigns to equal that of generations. They, therefore, allowed too great a number of years, and consequently some years must be subtracted from their computation.

Astronomical observations seem to have lent a still greater assistance to our philosopher. He appears to us stronger when he fights upon his own ground.

You know that the earth, besides its annual motion which carries it round the sun from west to east in the space of a year, has also a singular revolution which was quite unknown till within these late years. Its poles have a very slow retrograde motion from east to west, whence it happens that their position every day does not correspond exactly with the same point of the heavens. This difference which is so insensible in a year, becomes pretty considerable in time; and in threescore and twelve years the difference is found to be of one degree, that is to say, the three hundred and sixtieth part of the circumference of the whole heaven. Thus after seventy-two years the colure of the vernal equinox which passed through a fixed star, corresponds with another fixed star. Hence it is that the sun, instead of being in that part of the heavens in which the Ram was situated in the time of Hipparchus, is found to correspond with that part of the heavens in which the Bull was situated; and the Twins are placed where the Bull then stood. All the signs have changed their situation, and yet we still retain the same manner of speaking as the ancients did. In this age we say that the sun is in the Ram in the spring, from the principle of condescension that we say that the sun turns round.

Hipparchus was the first among the Greeks who observed some change in the constellations with regard to the equinoxes, or rather who learnt it from the Egyptians. Philosophers ascribed this motion to the stars; for in those ages people were far from imagining such a revolution in the earth, which was supposed to be immovable in every respect. They therefore created a heaven in which they fixed the several stars, and gave this heaven a particular motion by which it was carried towards the east, whilst that all the stars seemed to perform their diurnal revolution from east to west. To this error they added a second of much greater consequence, by imagining that the pretended heaven of the fixed stars advanced one degree eastward every hundred years. In this manner they were no less mistaken in their astronomical calculation than in their system of natural philosophy. As for instance, an astronomer in that age would have said that the vernal equinox was in the time of such and such an observation, in such a sign, and in such a star. It has advanced two degrees of each since the time that observation was made to the present. Now two degrees are equivalent to two hundred years; consequently the astronomer who made that observation lived just so many years before me. It is certain that an astronomer who had argued in this manner would have mistook just fifty-four years; hence it is that the ancients, who were doubly deceived, made their great year of the world, that is, the revolution of the whole heavens, to consist of thirty-six thousand years. But the moderns are sensible that this imaginary revolution of the heaven of the stars is nothing else than the revolution of the poles of the earth, which is performed in twenty-five thousand nine hundred years. It may be proper to observe transiently in this place, that Sir Isaac, by determining the figure of the earth, has very happily explained the cause of this revolution.

All this being laid down, the only thing remaining to settle chronology is to see through what star the colure of the equinoxes passes, and where it intersects at this time the ecliptic in the spring; and to discover whether some ancient writer does not tell us in what point the ecliptic was intersected in his time, by the same colure of the equinoxes.

Clemens Alexandrinus informs us, that Chiron, who went with the Argonauts, observed the constellations at the time of that famous expedition, and fixed the vernal equinox to the middle of the Ram; the autumnal equinox to the middle of Libra; our summer solstice to the middle of Cancer, and our winter solstice to the middle of Capricorn.

A long time after the expedition of the Argonauts, and a year before the Peloponnesian war, Methon observed that the point of the summer solstice passed through the eighth degree of Cancer.

Now every sign of the zodiac contains thirty degrees. In Chiron's time, the solstice was arrived at the middle of the sign, that is to say to the fifteenth degree. A year before the Peloponnesian war it was at the eighth, and therefore it had retarded seven degrees. A degree is equivalent to seventy-two years; consequently, from the beginning of the Peloponnesian war to the expedition of the Argonauts, there is no more than an interval of seven times seventy-two years, which make five hundred and four years, and not seven hundred years, as the Greeks computed. Thus in comparing the position of the heavens at this time with their position in that age, we find that the expedition of the Argonauts ought to be placed about nine hundred years before Christ, and not about fourteen hundred; and consequently that the world is not so old by five hundred years as it was generally supposed to be. By this calculation all the eras are drawn nearer, and the several events are found to have happened later than is computed. I don't know whether this ingenious system will be favourably received; and whether these notions will prevail so far with the learned, as to prompt them to reform the chronology of the world. Perhaps these gentlemen would think it too great a condescension to allow one and the same man the glory of having improved natural philosophy, geometry, and history. This would be a kind of universal monarchy, with which the principle of self-love that is in man will scarce suffer him to indulge his fellow-creature; and, indeed, at the same time that some very great philosophers attacked Sir Isaac Newton's attractive principle, others fell upon his chronological system. Time, that should discover to which of these the victory is due, may perhaps only leave the dispute still more undetermined.


French and English philosophers : Descartes, Rousseau, Voltaire, Hobbes : with introductions and notes. New York : P.F. Collier, c1910. Series: The Harvard classics v. 34.

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