The princess being assured of the usefulness of this operation, caused her own children to be inoculated. A great part of the kingdom followed her example, and since that time ten thousand children, at least, of persons of condition owe in this manner their lives to her Majesty and to the Lady Wortley Montague; and as many of the fair sex are obliged to them for their beauty.
Upon a general calculation, threescore persons in every hundred have the small-pox. Of these threescore, twenty die of it in the most favourable season of life, and as many more wear the disagreeable remains of it in their faces so long as they live. Thus, a fifth part of mankind either die or are disfigured by this distemper. But it does not prove fatal to so much as one among those who are inoculated in Turkey or in England, unless the patient be infirm, or would have died had not the experiment been made upon him. Besides, no one is disfigured, no one has the small-pox a second time, if the inoculation was perfect. It is therefore certain, that had the lady of some French ambassador brought this secret from Constantinople to Paris, the nation would have been for ever obliged to her. Then the Duke de Villequier, father to the Duke d’Aumont, who enjoys the most vigorous constitution, and is the healthiest man in France, would not have been cut off in the flower of his age.
The Prince of Soubise, happy in the finest flush of health, would not have been snatched away at five-and-twenty, nor the Dauphin, grandfather to Louis XV., have been laid in his grave in his fiftieth year. Twenty thousand persons whom the small-pox swept away at Paris in 1723 would have been alive at this time. But are not the French fond of life, and is beauty so inconsiderable an advantage as to be disregarded by the ladies? It must be confessed that we are an odd kind of people. Perhaps our nation will imitate ten years hence this practice of the English, if the clergy and the physicians will but give them leave to do it; or possibly our countrymen may introduce inoculation three months hence in France out of mere whim, in case the English should discontinue it through fickleness.
I am informed that the Chinese have practised inoculation these hundred years, a circumstance that argues very much in its favour, since they are thought to be the wisest and best governed people in the world. The Chinese, indeed, do not communicate this distemper by inoculation, but at the nose, in the same manner as we take snuff. This is a more agreeable way, but then it produces the like effects; and proves at the same time that had inoculation been practised in France it would have saved the lives of thousands.
Not long since the trite and frivolous question following was debated in a very polite and learned company, viz., Who was the greatest man, Cæsar, Alexander, Tamerlane, Cromwell, &c.?
Somebody answered that Sir Isaac Newton excelled them all. The gentleman’s assertion was very just; for if true greatness consists in having received from heaven a mighty genius, and in having employed it to enlighten our own mind and that of others, a man like Sir Isaac Newton, whose equal is hardly found in a thousand years, is the truly great man. And those politicians and conquerors (and all ages produce some) were generally so many illustrious wicked men. That man claims our respect who commands over the minds of the rest of the world by the force of truth, not those who enslave their fellow-creatures: he who is acquainted with the universe, not they who deface it.
Since, therefore, you desire me to give you an account of the famous personages whom England has given birth to, I shall begin with Lord Bacon, Mr. Locke, Sir Isaac Newton, &c. Afterwards the warriors and Ministers of State shall come in their order.
I must begin with the celebrated Viscount Verulam, known in Europe by the name of Bacon, which was that of his family. His father had been Lord Keeper, and himself was a great many years Lord Chancellor under King James I. Nevertheless, amidst the intrigues of a Court, and the affairs of his exalted employment, which alone were enough to engross his whole time, he yet found so much leisure for study as to make himself a great philosopher, a good historian, and an elegant writer; and a still more surprising circumstance is that he lived in an age in which the art of writing justly and elegantly was little known, much less true philosophy. Lord Bacon, as is the fate of man, was more esteemed after his death than in his lifetime. His enemies were in the British Court, and his admirers were foreigners.
When the Marquis d’Effiat attended in England upon the Princess Henrietta Maria, daughter to Henry IV., whom King Charles I. had married, that Minister went and visited the Lord Bacon, who, being at that time sick in his bed, received him with the curtains shut close. “You resemble the angels,” says the Marquis to him; “we hear those beings spoken of perpetually, and we believe them superior to men, but are never allowed the consolation to see them.”
You know that this great man was accused of a crime very unbecoming a philosopher: I mean bribery and extortion. You know that he was sentenced by the House of Lords to pay a fine of about four hundred thousand French livres, to lose his peerage and his dignity of Chancellor; but in the present age the English revere his memory to such a degree, that they will scarce allow him to have been guilty. In case you should ask what are my thoughts on this head, I shall answer you in the words which I heard the Lord Bolingbroke use on another occasion. Several gentlemen were speaking, in his company, of the avarice with which the late Duke of Marlborough had been charged, some examples whereof being given, the Lord Bolingbroke was appealed to (who, having been in the opposite party, might perhaps, without the imputation of indecency, have been allowed to clear up that matter): “He was so great a man,” replied his lordship, “that I have forgot his vices.”
I shall therefore confine myself to those things which so justly gained Lord Bacon the esteem of all Europe.
The most singular and the best of all his pieces is that which, at this time, is the most useless and the least read, I mean hisNovum Scientiarum Organum. This is the scaffold with which the new philosophy was raised; and when the edifice was built, part of it at least, the scaffold was no longer of service.
The Lord Bacon was not yet acquainted with Nature, but then he knew, and pointed out, the several paths that lead to it. He had despised in his younger years the thing called philosophy in the Universities, and did all that lay in his power to prevent those societies of men instituted to improve human reason from depraving it by their quiddities, their horrors of the vacuum, their substantial forms, and all those impertinent terms which not only ignorance had rendered venerable, but which had been made sacred by their being ridiculously blended with religion.
He is the father of experimental philosophy. It must, indeed, be confessed that very surprising secrets had been found out before his time—the sea-compass, printing, engraving on copper plates, oil-painting, looking-glasses; the art of restoring, in some measure, old men to their sight by spectacles; gunpowder, &c., had been discovered. A new world had been fought for, found, and conquered. Would not one suppose that these sublime discoveries had been made by the greatest philosophers, and in ages much more enlightened than the present? But it was far otherwise; all these great changes happened in the most stupid and barbarous times. Chance only gave birth to most of those inventions; and it is very probable that what is called chance contributed very much to the discovery of America; at least, it has been always thought that Christopher Columbus undertook his voyage merely on the relation of a captain of a ship which a storm had driven as far westward as the Caribbean Islands. Be this as it will, men had sailed round the world, and could destroy cities by an artificial thunder more dreadful than the real one; but, then, they were not acquainted with the circulation of the blood, the weight of the air, the laws of motion, light, the number of our planets, &c. And a man who maintained a thesis on Aristotle’s “Categories,” on the universalsa parte rei, or such-like nonsense, was looked upon as a prodigy.
The most astonishing, the most useful inventions, are not those which reflect the greatest honour on the human mind. It is to a mechanical instinct, which is found in many men, and not to true philosophy, that most arts owe their origin.
The discovery of fire, the art of making bread, of melting and preparing metals, of building houses, and the invention of the shuttle, are infinitely more beneficial to mankind than printing or the sea-compass: and yet these arts were invented by uncultivated, savage men.
What a prodigious use the Greeks and Romans made afterwards of mechanics! Nevertheless, they believed that there were crystal heavens, that the stars were small lamps which sometimes fell into the sea, and one of their greatest philosophers, after long researches, found that the stars were so many flints which had been detached from the earth.
In a word, no one before the Lord Bacon was acquainted with experimental philosophy, nor with the several physical experiments which have been made since his time. Scarce one of them but is hinted at in his work, and he himself had made several. He made a kind of pneumatic engine, by which he guessed the elasticity of the air. He approached, on all sides as it were, to the discovery of its weight, and had very near attained it, but some time after Torricelli seized upon this truth. In a little time experimental philosophy began to be cultivated on a sudden in most parts of Europe. It was a hidden treasure which the Lord Bacon had some notion of, and which all the philosophers, encouraged by his promises, endeavoured to dig up.
But that which surprised me most was to read in his work, in express terms, the new attraction, the invention of which is ascribed to Sir Isaac Newton.
We must search, says Lord Bacon, whether there may not be a kind of magnetic power which operates between the earth and heavy bodies, between the moon and the ocean, between the planets, &c. In another place he says either heavy bodies must be carried towards the centre of the earth, or must be reciprocally attracted by it; and in the latter case it is evident that the nearer bodies, in their falling, draw towards the earth, the stronger they will attract one another. We must, says he, make an experiment to see whether the same clock will go faster on the top of a mountain or at the bottom of a mine; whether the strength of the weights decreases on the mountain and increases in the mine. It is probable that the earth has a true attractive power.
This forerunner in philosophy was also an elegant writer, an historian, and a wit.
His moral essays are greatly esteemed, but they were drawn up in the view of instructing rather than of pleasing; and, as they are not a satire upon mankind, like Rochefoucauld’s “Maxims,” nor written upon a sceptical plan, like Montaigne’s “Essays,” they are not so much read as those two ingenious authors.
His History of Henry VII. was looked upon as a masterpiece, but how is it possible that some persons can presume to compare so little a work with the history of our illustrious Thuanus?
Speaking about the famous impostor Perkin, son to a converted Jew, who assumed boldly the name and title of Richard IV., King of England, at the instigation of the Duchess of Burgundy, and who disputed the crown with Henry VII., the Lord Bacon writes as follows:—
“At this time the King began again to be haunted with sprites, by the magic and curious arts of the Lady Margaret, who raised up the ghost of Richard, Duke of York, second son to King Edward IV., to walk and vex the King.
“After such time as she (Margaret of Burgundy) thought he (Perkin Warbeck) was perfect in his lesson, she began to cast with herself from what coast this blazing star should first appear, and at what time it must be upon the horizon of Ireland; for there had the like meteor strong influence before.”
Methinks our sagacious Thuanus does not give in to such fustian, which formerly was looked upon as sublime, but in this age is justly called nonsense.
Perhaps no man ever had a more judicious or more methodical genius, or was a more acute logician than Mr. Locke, and yet he was not deeply skilled in the mathematics. This great man could never subject himself to the tedious fatigue of calculations, nor to the dry pursuit of mathematical truths, which do not at first present any sensible objects to the mind; and no one has given better proofs than he, that it is possible for a man to have a geometrical head without the assistance of geometry. Before his time, several great philosophers had declared, in the most positive terms, what the soul of man is; but as these absolutely knew nothing about it, they might very well be allowed to differ entirely in opinion from one another.
In Greece, the infant seat of arts and of errors, and where the grandeur as well as folly of the human mind went such prodigious lengths, the people used to reason about the soul in the very same manner as we do.
The divine Anaxagoras, in whose honour an altar was erected for his having taught mankind that the sun was greater than Peloponnesus, that snow was black, and that the heavens were of stone, affirmed that the soul was an aërial spirit, but at the same time immortal. Diogenes (not he who was a cynical philosopher after having coined base money) declared that the soul was a portion of the substance of God: an idea which we must confess was very sublime. Epicurus maintained that it was composed of parts in the same manner as the body.
Aristotle, who has been explained a thousand ways, because he is unintelligible, was of opinion, according to some of his disciples, that the understanding in all men is one and the same substance.
The divine Plato, master of the divine Aristotle,—and the divine Socrates, master of the divine Plato—used to say that the soul was corporeal and eternal. No doubt but the demon of Socrates had instructed him in the nature of it. Some people, indeed, pretend that a man who boasted his being attended by a familiar genius must infallibly be either a knave or a madman, but this kind of people are seldom satisfied with anything but reason.
With regard to the Fathers of the Church, several in the primitive ages believed that the soul was human, and the angels and God corporeal. Men naturally improve upon every system. St. Bernard, as Father Mabillon confesses, taught that the soul after death does not see God in the celestial regions, but converses with Christ’s human nature only. However, he was not believed this time on his bare word; the adventure of the crusade having a little sunk the credit of his oracles. Afterwards a thousand schoolmen arose, such as the Irrefragable Doctor, the Subtile Doctor, the Angelic Doctor, the Seraphic Doctor, and the Cherubic Doctor, who were all sure that they had a very clear and distinct idea of the soul, and yet wrote in such a manner, that one would conclude they were resolved no one should understand a word in their writings. Our Descartes, born to discover the errors of antiquity, and at the same time to substitute his own, and hurried away by that systematic spirit which throws a cloud over the minds of the greatest men, thought he had demonstrated that the soul is the same thing as thought, in the same manner as matter, in his opinion, is the same as extension. He asserted, that man thinks eternally, and that the soul, at its coming into the body, is informed with the whole series of metaphysical notions: knowing God, infinite space, possessing all abstract ideas—in a word, completely endued with the most sublime lights, which it unhappily forgets at its issuing from the womb.
Father Malebranche, in his sublime illusions, not only admitted innate ideas, but did not doubt of our living wholly in God, and that God is, as it were, our soul.
Such a multitude of reasoners having written the romance of the soul, a sage at last arose, who gave, with an air of the greatest modesty, the history of it. Mr. Locke has displayed the human soul in the same manner as an excellent anatomist explains the springs of the human body. He everywhere takes the light of physics for his guide. He sometimes presumes to speak affirmatively, but then he presumes also to doubt. Instead of concluding at once what we know not, he examines gradually what we would know. He takes an infant at the instant of his birth; he traces, step by step, the progress of his understanding; examines what things he has in common with beasts, and what he possesses above them. Above all, he consults himself: the being conscious that he himself thinks.
“I shall leave,” says he, “to those who know more of this matter than myself, the examining whether the soul exists before or after the organisation of our bodies. But I confess that it is my lot to be animated with one of those heavy souls which do not think always; and I am even so unhappy as not to conceive that it is more necessary the soul should think perpetually than that bodies should be for ever in motion.”
With regard to myself, I shall boast that I have the honour to be as stupid in this particular as Mr. Locke. No one shall ever make me believe that I think always: and I am as little inclined as he could be to fancy that some weeks after I was conceived I was a very learned soul; knowing at that time a thousand things which I forgot at my birth; and possessing when in the womb (though to no manner of purpose) knowledge which I lost the instant I had occasion for it; and which I have never since been able to recover perfectly.
Mr. Locke, after having destroyed innate ideas; after having fully renounced the vanity of believing that we think always; after having laid down, from the most solid principles, that ideas enter the mind through the senses; having examined our simple and complex ideas; having traced the human mind through its several operations; having shown that all the languages in the world are imperfect, and the great abuse that is made of words every moment, he at last comes to consider the extent or rather the narrow limits of human knowledge. It was in this chapter he presumed to advance, but very modestly, the following words: “We shall, perhaps, never be capable of knowing whether a being, purely material, thinks or not.” This sage assertion was, by more divines than one, looked upon as a scandalous declaration that the soul is material and mortal. Some Englishmen, devout after their way, sounded an alarm. The superstitious are the same in society as cowards in an army; they themselves are seized with a panic fear, and communicate it to others. It was loudly exclaimed that Mr. Locke intended to destroy religion; nevertheless, religion had nothing to do in the affair, it being a question purely philosophical, altogether independent of faith and revelation. Mr. Locke’s opponents needed but to examine, calmly and impartially, whether the declaring that matter can think, implies a contradiction; and whether God is able to communicate thought to matter. But divines are too apt to begin their declarations with saying that God is offended when people differ from them in opinion; in which they too much resemble the bad poets, who used to declare publicly that Boileau spake irreverently of Louis XIV., because he ridiculed their stupid productions. Bishop Stillingfleet got the reputation of a calm and unprejudiced divine because he did not expressly make use of injurious terms in his dispute with Mr. Locke. That divine entered the lists against him, but was defeated; for he argued as a schoolman, and Locke as a philosopher, who was perfectly acquainted with the strong as well as the weak side of the human mind, and who fought with weapons whose temper he knew. If I might presume to give my opinion on so delicate a subject after Mr. Locke, I would say, that men have long disputed on the nature and the immortality of the soul. With regard to its immortality, it is impossible to give a demonstration of it, since its nature is still the subject of controversy; which, however, must be thoroughly understood before a person can be able to determine whether it be immortal or not. Human reason is so little able, merely by its own strength, to demonstrate the immortality of the soul, that it was absolutely necessary religion should reveal it to us. It is of advantage to society in general, that mankind should believe the soul to be immortal; faith commands us to do this; nothing more is required, and the matter is cleared up at once. But it is otherwise with respect to its nature; it is of little importance to religion, which only requires the soul to be virtuous, whatever substance it may be made of. It is a clock which is given us to regulate, but the artist has not told us of what materials the spring of this chock is composed.
I am a body, and, I think, that’s all I know of the matter. Shall I ascribe to an unknown cause, what I can so easily impute to the only second cause I am acquainted with? Here all the school philosophers interrupt me with their arguments, and declare that there is only extension and solidity in bodies, and that there they can have nothing but motion and figure. Now motion, figure, extension and solidity cannot form a thought, and consequently the soul cannot be matter. All this so often repeated mighty series of reasoning, amounts to no more than this: I am absolutely ignorant what matter is; I guess, but imperfectly, some properties of it; now I absolutely cannot tell whether these properties may be joined to thought. As I therefore know nothing, I maintain positively that matter cannot think. In this manner do the schools reason.
Mr. Locke addressed these gentlemen in the candid, sincere manner following: At least confess yourselves to be as ignorant as I. Neither your imaginations nor mine are able to comprehend in what manner a body is susceptible of ideas; and do you conceive better in what manner a substance, of what kind soever, is susceptible of them? As you cannot comprehend either matter or spirit, why will you presume to assert anything?
The superstitious man comes afterwards and declares, that all those must be burnt for the good of their souls, who so much as suspect that it is possible for the body to think without any foreign assistance. But what would these people say should they themselves be proved irreligious? And indeed, what man can presume to assert, without being guilty at the same time of the greatest impiety, that it is impossible for the Creator to form matter with thought and sensation? Consider only, I beg you, what a dilemma you bring yourselves into, you who confine in this manner the power of the Creator. Beasts have the same organs, the same sensations, the same perceptions as we; they have memory, and combine certain ideas. In case it was not in the power of God to animate matter, and inform it with sensation, the consequence would be, either that beasts are mere machines, or that they have a spiritual soul.
Methinks it is clearly evident that beasts cannot be mere machines, which I prove thus. God has given to them the very same organs of sensation as to us: if therefore they have no sensation, God has created a useless thing; now according to your own confession God does nothing in vain; He therefore did not create so many organs of sensation, merely for them to be uninformed with this faculty; consequently beasts are not mere machines. Beasts, according to your assertion, cannot be animated with a spiritual soul; you will, therefore, in spite of yourself, be reduced to this only assertion, viz., that God has endued the organs of beasts, who are mere matter, with the faculties of sensation and perception, which you call instinct in them. But why may not God, if He pleases, communicate to our more delicate organs, that faculty of feeling, perceiving, and thinking, which we call human reason? To whatever side you turn, you are forced to acknowledge your own ignorance, and the boundless power of the Creator. Exclaim therefore no more against the sage, the modest philosophy of Mr. Locke, which so far from interfering with religion, would be of use to demonstrate the truth of it, in case religion wanted any such support. For what philosophy can be of a more religious nature than that, which affirming nothing but what it conceives clearly, and conscious of its own weakness, declares that we must always have recourse to God in our examining of the first principles?
Besides, we must not be apprehensive that any philosophical opinion will ever prejudice the religion of a country. Though our demonstrations clash directly with our mysteries, that is nothing to the purpose, for the latter are not less revered upon that account by our Christian philosophers, who know very well that the objects of reason and those of faith are of a very different nature. Philosophers will never form a religious sect, the reason of which is, their writings are not calculated for the vulgar, and they themselves are free from enthusiasm. If we divide mankind into twenty parts, it will be found that nineteen of these consist of persons employed in manual labour, who will never know that such a man as Mr. Locke existed. In the remaining twentieth part how few are readers? And among such as are so, twenty amuse themselves with romances to one who studies philosophy. The thinking part of mankind is confined to a very small number, and these will never disturb the peace and tranquillity of the world.
Neither Montaigne, Locke, Bayle, Spinoza, Hobbes, the Lord Shaftesbury, Collins, nor Toland lighted up the firebrand of discord in their countries; this has generally been the work of divines, who being at first puffed up with the ambition of becoming chiefs of a sect, soon grew very desirous of being at the head of a party. But what do I say? All the works of the modern philosophers put together will never make so much noise as even the dispute which arose among the Franciscans, merely about the fashion of their sleeves and of their cowls.
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.”
“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 he 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 and 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, at 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 Mr. 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 but 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. Rohault’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.
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 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 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 ininfinitum.
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 wordimpulsion, which is so well understood, rather than that ofattraction, 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 theArcanaof the Almighty.
“Precedes huc, et non amplius.”
“Precedes huc, et non amplius.”
(Thus far shalt thou go, and no farther.)
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, though a cannonball, 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.
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 no 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 subtlety 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 ininfinitum. 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. Bernouilli 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 thevermiculiof 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’s 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 erroneous 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 an 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 same 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.