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Letter XV
Letter XV of 24. Read it here for reference, or continue through the entire work without leaving the reader.
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histoire de l’attraction.
Je n’entrerai point ici dans une explication mathématique de ce qu’on appelle l’attraction, ou la gravitation: je me borne à l’histoire de cette nouvelle propriété de la matière, devinée longtemps avant Newton, et démontrée par lui; c’est donner en quelque sorte l’histoire d’une création nouvelle.
Copernic, ce Christophe Colomb de l’astronomie, avait à peine appris aux hommes le véritable ordre de l’univers, si longtemps défiguré; il avait à peine fait voir que la terre tourne, et sur elle-même et dans un espace immense, lorsque tous les docteurs firent à peu près les mêmes objections que leurs devanciers avaient faites contre les antipodes. Saint Augustin, en niant ces antipodes, avait dit: Eh quoi! ils auraient donc la tête en bas, et ils tomberaientdans le ciel. Les docteurs disaient à Copernic: Si la terre tournaitsur elle-même, toutes ses parties se détacheraient et tomberaient dans leciel. Il est certain que la terre tourne, répondit Copernic, et queses parties ne s’envolent pas; il faut donc qu’une puissance lesdirige toutes vers le centre de la terre; et probablement, dit-il,cette propriété existe dans tous les globes, dans le soleil, dans lalune, dans les étoiles; c’est un attribut donné à la matière par ladivine Providence. C’est ainsi qu’il s’explique dans son premierlivre Des Révolutions célestes, sans avoir osé ni peut-être pu allerplus loin.
Kepler, qui suivit Copernic et qui perfectionna l’admirabledécouverte du vrai système du monde, approcha un peu dusystème de la pesanteur universelle. On voit, dans son traité del’étoile de Mars, des veines encore mal formées de cette mine dontNewton a tiré son or. Kepler admet non-seulement une tendancede tous les corps terrestres au centre, mais aussi des astres lesuns vers les autres. Il ose entrevoir et dire que si la terre et la lunen’étaient pas retenues dans leurs orbites, elles s’approcheraientl’une de l’autre, elles s’uniraient. Cette vérité étonnante étaitobscurcie chez lui de tant de nuages et de tant d’erreurs qu’on adit qu’il l’avait devinée par instinct.
Cependant le grand Galilée, partant d’un principe plus mécanique,examinait quelle est la chute des corps sur la terre; commentet en quelle proportion cette chute s’accélère; et le chancelierBacon voulait qu’on expérimentât si ces chutes se faisaient égalementaux plus grandes profondeurs et aux plus grandes hauteursoù l’on pût atteindre.
Il est bien singulier que Descartes, le plus grand géomètre deson temps, ne se soit pas servi de ce fil dans le labyrinthe qu’ils’était bâti lui-même. On ne trouve nulle trace de ces vérités dansses ouvrages; aussi n’est-il pas surprenant qu’il se soit égaré. Ilvoulut créer un univers. Il fit une philosophie comme on fait unbon roman: tout parut vraisemblable, et rien ne fut vrai. Il imaginades éléments, des tourbillons, qui semblaient rendre uneraison plausible de tous les mystères de la nature; mais en philosophieil faut se défier de ce qu’on croit entendre trop aisémentaussi bien que des choses qu’on n’entend pas. Descartes était plusdangereux qu’Aristote parce qu’il avait l’air d’être plus raisonnable.M. Conduit, neveu du chevalier Newton, m’a assuré queson oncle avait lu Descartes à l’âge de vingt ans, qu’il crayonnales marges des premières pages, et qu’il n’y mit qu’une seule note, souvent répétée, consistant en ce mot: error; mais que, las d’écrireerror partout, il jeta le livre et ne le relut jamais.
Newton, ayant quitté les abîmes de la théologie dans lesquelsil avait été élevé pour les vérités mathématiques, avait déjà trouvéà l’âge de vingt-trois ans son calcul infinitésimal dont son maîtreWallis lui avait ouvert la route. Il s’appliquait à chercher ceprincipe secret et universel de la nature, indiqué par Copernic,par Kepler, par Bacon, et déjà saisi par le célèbre Hooke: c’est-à-direcette cause de la pesanteur et du mouvement de toute lamatière. S’étant retiré en 1666, à cause de la peste, à la campagneprès de Cambridge, un jour qu’il se promenait dans son jardin,et qu’il voyait des fruits tomber d’un arbre, il se laissa aller à uneméditation profonde sur cette pesanteur dont tous les philosophesont cherché si longtemps la cause en vain, et dans laquelle levulgaire ne soupçonne pas même de mystère. Il se dit à lui-même:De quelque hauteur dans notre hémisphère que tombassentces corps, leur chute, serait certainement dans laprogression découverte par Galilée; et les espaces parcourus pareux seraient comme les carrés des temps. Ce pouvoir, qui faitdescendre les corps graves, est le même sans aucune diminutionsensible, à quelque profondeur qu’on soit dans la terre, et sur laplus haute montagne. Pourquoi ce pouvoir ne s’étendrait-il pasjusqu’à la lune? Et, s’il est vrai qu’il pénètre jusque-là, n’y a-t-ilpas grande apparence que ce pouvoir la retient dans son orbite etdétermine son mouvement? Mais si la lune obéit à ce principe,quel qu’il soit, n’est-il pas encore très-raisonnable de croire queles autres planètes y sont également soumises?
Si ce pouvoir existe, il doit (ce qui est prouvé d’ailleurs)augmenter en raison renversée des carrés des distances. Il n’ya donc plus qu’à examiner le chemin que ferait un corps graveen tombant sur la terre d’une hauteur médiocre, et le cheminque ferait dans le même temps un corps qui tomberait de l’orbitede la lune. Pour en être instruit, il ne s’agit plus que d’avoirla mesure de la terre, et la distance de la lune à la terre.
Voilà comment M. Newton raisonna. Mais on n’avait alors enAngleterre que de très-fausses mesures de notre globe; on s’enrapportait à l’estime incertaine des pilotes, qui comptaientsoixante milles d’Angleterre pour un degré, au lieu qu’il en fallaitcompter près de soixante et dix. Ce faux calcul ne s’accordantpas avec les conclusions que M. Newton voulait tirer, il lesabandonna. Un philosophe médiocre, et qui n’aurait eu que dela vanité, eût fait cadrer comme il eût pu la mesure de la terre avec son système. M. Newton aima mieux abandonner alors son projet. Mais depuis que M. Picart eut mesuré la terre exactement, en traçant cette méridienne qui fait tant d’honneur à la France, M. Newton reprit ses premières idées, et il trouva son compte avec le calcul de M. Picart. Les autres planètes doivent être soumises à cette loi générale;et si cette loi existe, ces planètes doivent suivre les règlestrouvées par Kepler. Toutes ces règles, tous ces rapports, sont eneffet gardés par les planètes. Son seul principe des lois de la gravitationrend raison de toutes les inégalités apparentes dans lecours des globes célestes. Les variations de la lune deviennentune suite nécessaire de ces lois. Le flux et le reflux de la mer estencore un effet très-simple de cette attraction. La proximité dela lune dans son plein et quand elle est nouvelle, et son éloignementdans ses quartiers, combinés avec l'action du soleil, rendentune raison sensible de l’élévation et de l'abaissement de l'Océan.
Après avoir rendu compte, par sa sublime théorie, du courset des inégalités des planètes, il assujettit les comètes au frein dela même loi.
Il prouve que ce sont des corps solides, qui se meuvent dansla sphère de l'action du soleil, et décrivent une ellipse si excentriqueet si approchante de la parabole, que certaines comètesdoivent mettre plus de cinq cents ans dans leur révolution.
Le savant M. Halley croit que la comète de 1680 est la mêmequi parut du temps de Jules César: celle-là surtout sert plusqu'une autre à faire voir que les comètes sont des corps durs etopaques, car elle descendit si près du soleil qu'elle n'en étaitéloignée que d'une sixième partie de son disque; elle dut parconséquent acquérir un degré de chaleur deux mille fois plusviolent que celui du fer le plus enflammé. Elle aurait été dissouteet consommée en peu de temps si elle n'avait pas été uncorps opaque. La mode commençait alors de deviner le coursdes comètes. Le célèbre mathématicien Jacques Bernouilli conclut,par son système, que cette fameuse comète de 1680 reparaîtraitle 17 mai 1719. Aucun astronome de l'Europe ne se couchacette nuit du 17 mai, mais la fameuse comète ne parut point. Ily a au moins plus d'adresse, s'il n'y a pas plus de sûreté, àlui donner cinq cent soixante-quinze ans pour revenir. Pour M. Wilston, il a sérieusement affirmé que du temps du délugeil y avait eu une comète qui avait inondé notre globe, et il a eul’injustice de s’étonner qu’on se soit moqué de lui. L’antiquitépensait à peu près dans le goût de Wilston; elle croyait queles comètes étaient toujours les avant-courrières de quelquegrand malheur sur la terre. Newton au contraire soupçonnequ’elles sont très-bienfaisantes, et que les fumées qui en sortentne servent qu’à secourir et vivifier les planètes qui s’imbibentdans leur cours de toutes ces particules que le soleil a détachéesdes comètes. Ce sentiment est du moins plus probable quel’autre.
Ce n’est pas tout, si cette force de gravitation, d’attraction,agit dans tous les globes célestes, elle agit sans doute sur toutesles parties de ces globes: car, si les corps s’attirent en raison deleurs masses, ce ne peut être qu’en raison de la quantité deleurs parties; et si ce pouvoir est logé dans le tout, il l’est sansdoute dans la moitié, il l’est dans le quart, dans la huitièmepartie, ainsi jusqu’à l’infini. Voilà donc l’attraction qui est legrand ressort qui fait mouvoir toute la nature.
Newton avait bien prévu, après avoir démontré l’existence dece principe, qu’on se révolterait contre ce seul nom: dans plusd’un endroit de son livre il précautionne son lecteur contre l’attractionmême, il l’avertit de ne la pas confondre avec les qualitésoccultes des anciens, et de se contenter de connaître qu’il ya dans tous les corps une force centrale qui agit d’un bout del’univers à l’autre sur les corps les plus proches et sur les pluséloignés, suivant les lois immuables de la mécanique.
Il est étonnant qu’après les protestations solennelles de cegrand philosophe, M. Saurin et M. de Fontenelle, qui eux-mêmesméritent ce nom, lui aient reproché nettement les chimères dupéripatétisme: M. Saurin, dans les Mémoires de l’Académie, de1709; et M. de Fontenelle, dans l’éloge même de M. Newton.
Presque tous les Français, savants et autres, ont répété cereproche. On entend dire partout: Pourquoi Newton ne s’est-il pas servi du mot d’impulsion, que l’on comprend si bien, plutôtque du terme d’attraction, que l’on ne comprend pas?
Newton aurait pu répondre à ces critiques:
Premièrement, vous n’entendez pas plus le mot d’impulsionque celui d’attraction, et si vous ne concevez pas pourquoi uncorps tend vers le centre d’un autre corps, vous n’imaginez pasplus par quelle vertu un corps en peut pousser un autre.
Secondement, je n’ai pas pu admettre l’impulsion: car il faudraitpour cela que j’eusse connu qu’une matière céleste pousseen effet les planètes; or, non-seulement je ne connais point cettematière, mais j’ai prouvé qu’elle n’existe pas.
Troisièmement, je ne me sers du mot d’attraction que pourexprimer un effet que j’ai découvert dans la nature, effet certainet indisputable d’un principe inconnu, qualité inhérente dansla matière, dont de plus habiles que moi trouveront, s’ils peuvent,la cause.
Que nous avez-vous donc appris, insiste-t-on encore, et pourquoitant de calculs pour nous dire ce que vous-même ne comprenez pas?
Je vous ai appris (pourrait continuer Newton) que la mécaniquedes forces centrales fait seule mouvoir les planètes et lescomètes dans des proportions marquées. Je suis, continuerait-il,dans un cas bien différent des anciens: ils voyaient par exemplel’eau monter dans les pompes, et ils disaient: L’eau monte parcequ’elle a horreur du vide; mais moi, je suis dans le cas de celuiqui aurait remarqué le premier que l’eau monte dans les pompes,et qui laisserait à d’autres le soin d’expliquer la cause de cet effet.L’anatomiste qui a dit le premier que le bras se remue parce queles muscles se contractent enseigna aux hommes une véritéincontestable: lui en aura-t-on moins d’obligation parce qu’il n’apas su pourquoi les muscles se contractent? La cause du ressort de l’air est inconnue, mais celui qui a découvert ce ressort a rendu un grand service à la physique. Le ressort que j’ai découvert était plus caché, plus universel; ainsi, on doit m’en savoir plus de gré. J’ai découvert une propriété de la matière, un des secrets du Créateur; j’en ai calculé, j’en ai démontré les effets; peut-on me chicaner sur le nom que je lui donne?
Ce sont les tourbillons qu’on peut appeler une qualité occulte, puisqu’on n’a jamais prouvé leur existence. L’attraction au contraire est une chose réelle, puisqu’on en démontre les effets et qu’on en calcule les proportions. La cause de cette cause est dans le sein de Dieu. Procedes huc, et non ibis amplius.
Musean translation
Mouseia’s complete machine-assisted Musean translation, made directly from the French text of all twenty-four letters (Garnier edition, 1879, French Wikisource) for fidelity, the author’s force and cadence, and modern clarity.
History of Attraction
I shall not enter here into a mathematical explanation of what is called attraction, or gravitation. I confine myself to the history of this new property of matter, divined long before Newton and demonstrated by him; in a sense, it is the history of a new creation.
Copernicus, that Christopher Columbus of astronomy, had scarcely taught mankind the true order of the universe, so long disfigured; he had scarcely shown that the earth turns both on its axis and through an immense expanse, when all the learned doctors raised much the same objections their predecessors had raised against the antipodes. Saint Augustine, denying the antipodes, had said: “What! They would have their heads downward and would fall into the sky.” The doctors said to Copernicus: “If the earth turned on its axis, all its parts would break away and fall into the sky.” “It is certain that the earth turns,” Copernicus replied, “and that its parts do not fly away; there must therefore be a power directing them all toward the center of the earth. And probably,” he said, “this property exists in all heavenly bodies, in the sun, the moon, and the stars; it is an attribute bestowed on matter by divine Providence.” So he explains himself in the first book of On the Revolutions of the Heavenly Spheres, without daring, or perhaps being able, to go further.
Kepler, who followed Copernicus and perfected the marvelous discovery of the true system of the world, came somewhat closer to the system of universal gravity. In his treatise on the star Mars one can see the still unformed veins of the mine from which Newton drew his gold. Kepler admits not only a tendency of all terrestrial bodies toward the center, but also a tendency of the heavenly bodies toward one another. He dares to glimpse and say that if the earth and moon were not held in their orbits, they would approach each other and unite. This astonishing truth was obscured in his work by so many clouds and so many errors that it has been said he divined it by instinct.
Meanwhile the great Galileo, starting from a more mechanical principle, examined how bodies fall on earth, and how and in what proportion their fall accelerates; and Chancellor Bacon wished experiments to determine whether these falls occurred in the same way at the greatest depths and heights one could reach.
It is very strange that Descartes, the greatest geometer of his time, did not use this thread to guide him through the labyrinth he had built for himself. No trace of these truths is found in his works; it is no wonder, then, that he lost his way. He wanted to create a universe. He made a philosophy as one makes a good novel: everything seemed plausible, and nothing was true. He imagined elements and vortices that seemed to give a plausible account of all the mysteries of nature; but in philosophy one must distrust what one thinks one understands too easily no less than what one does not understand. Descartes was more dangerous than Aristotle because he appeared more reasonable. Mr. Conduit, nephew of Sir Isaac Newton, assured me that his uncle had read Descartes at the age of twenty, had marked the margins of the first pages, and had written only one note, often repeated: error. But, weary of writing error everywhere, he threw the book aside and never read it again.
Newton, having left the depths of theology in which he had been brought up for mathematical truths, had already discovered, at the age of twenty-three, his infinitesimal calculus, toward which his teacher Wallis had shown him the way. He devoted himself to seeking that secret and universal principle of nature indicated by Copernicus, Kepler, and Bacon, and already grasped by the celebrated Hooke: that is, the cause of gravity and of the movement of all matter. Having withdrawn to the countryside near Cambridge in 1666 because of the plague, one day as he walked in his garden and saw fruit falling from a tree, he sank into deep reflection on this gravity whose cause all philosophers have so long sought in vain, and in which ordinary people do not even suspect a mystery. He said to himself: “From whatever height in our hemisphere these bodies might fall, their fall would certainly follow the progression discovered by Galileo; and the distances they traveled would be as the squares of the times. This power that brings heavy bodies down is the same, without any perceptible diminution, at whatever depth one may be within the earth, and on the highest mountain. Why should this power not extend as far as the moon? And if it truly reaches that far, is it not highly likely that this power holds the moon in its orbit and determines its motion? But if the moon obeys this principle, whatever it may be, is it not also most reasonable to believe that the other planets are subject to it as well?”
“If this power exists, it must (as is proved on other grounds) increase in inverse proportion to the squares of the distances. All that remains, therefore, is to compare the distance a heavy body would travel in falling to earth from a moderate height with the distance a body falling from the moon's orbit would travel in the same time. To learn this, we need only the size of the earth and the moon's distance from the earth.”
This was how Mr. Newton reasoned. But at that time England had only very inaccurate measurements of our globe; people relied on the uncertain estimates of pilots, who reckoned sixty English miles to a degree when they should have reckoned nearly seventy. As this erroneous calculation did not agree with the conclusions Mr. Newton wished to draw, he abandoned them. A lesser philosopher, with nothing but vanity, would have made the earth's measurement fit his system as best he could. Mr. Newton preferred to abandon his project for the time being. But after Mr. Picart had measured the earth accurately by tracing that meridian which does France so much honor, Mr. Newton returned to his first ideas and found that Mr. Picart's calculation suited them. The other planets must be subject to this general law; and if this law exists, these planets must follow the rules discovered by Kepler. All these rules, all these relations, are in fact observed by the planets. His single principle of the laws of gravitation accounts for all the apparent irregularities in the courses of the heavenly bodies. The moon's variations become a necessary consequence of these laws. The ebb and flow of the sea is another very simple effect of this attraction. The moon's proximity when full and when new, and its remoteness at its quarters, combined with the action of the sun, furnish a clear explanation of the ocean's rise and fall.
Having accounted, through his sublime theory, for the courses and irregularities of the planets, he brought the comets under the rule of the same law.
He proves that they are solid bodies moving within the sphere of the sun's action, describing an ellipse so eccentric and so close to a parabola that certain comets must take more than five hundred years to complete a revolution.
The learned Mr. Halley believes that the comet of 1680 is the same one that appeared in the time of Julius Caesar. This comet above all helps to show that comets are hard and opaque bodies, for it came so near the sun that it was only a sixth of the sun's disk away from it; consequently it must have acquired a degree of heat two thousand times more intense than that of the most incandescent iron. It would have dissolved and been consumed in a short time if it had not been an opaque body. It was then becoming fashionable to predict the courses of comets. The celebrated mathematician Jacques Bernouilli concluded from his system that this famous comet of 1680 would reappear on 17 May 1719. Not an astronomer in Europe went to bed that night of 17 May, but the famous comet did not appear. There is at least more ingenuity, if not more certainty, in allotting it five hundred and seventy-five years before its return. As for Mr. Wilston, he seriously asserted that in the time of the Flood there had been a comet that inundated our globe, and he was unfair enough to be surprised that people laughed at him. Antiquity thought much as Wilston did; it believed that comets were always the heralds of some great calamity on earth. Newton, on the contrary, suspects that they are very beneficial, and that the vapors issuing from them serve only to replenish and invigorate the planets, which in their courses absorb all the particles the sun has detached from the comets. This view is at least more probable than the other.
That is not all. If this force of gravitation, of attraction, acts in all heavenly bodies, it doubtless acts upon every part of those bodies: for if bodies attract one another in proportion to their masses, that can only be in proportion to the quantity of their parts; and if this power resides in the whole, it doubtless resides in the half, in the quarter, in the eighth part, and so on without end. Attraction, then, is the great spring that sets all nature in motion.
Newton had clearly foreseen, after demonstrating the existence of this principle, that people would rebel against the very name. In more than one passage of his book he cautions his reader against attraction itself, warning him not to confuse it with the occult qualities of the ancients, and to be content with knowing that there is in all bodies a central force that acts from one end of the universe to the other upon the nearest and the most distant bodies, according to the immutable laws of mechanics.
It is astonishing that after this great philosopher's solemn protestations, Mr. Saurin and Mr. de Fontenelle, themselves worthy of that title, should have expressly charged him with the fantasies of Peripatetic philosophy: Mr. Saurin in the Memoirs of the Academy of 1709, and Mr. de Fontenelle in his very eulogy of Mr. Newton.
Almost all the French, learned and otherwise, have repeated this charge. Everywhere one hears: “Why did Newton not use the word impulse, which we understand so well, instead of the term attraction, which we do not understand?”
Newton could have replied to these critics:
“First, you understand the word impulse no better than attraction; and if you cannot conceive why one body tends toward the center of another, you can no more imagine by what power one body can push another.
“Second, I could not admit impulse: for that I would have had to know that a celestial matter actually pushes the planets; yet not only do I know nothing of such matter, I have proved that it does not exist.
“Third, I use the word attraction only to express an effect I have discovered in nature, a certain and indisputable effect of an unknown principle, a quality inherent in matter, whose cause those more skillful than I may find, if they can.”
“What, then, have you taught us,” people insist, “and why so many calculations to tell us something you yourself do not understand?”
“I have taught you,” Newton might continue, “that the mechanics of central forces alone moves the planets and comets in definite proportions. My case,” he would continue, “is quite different from that of the ancients: they saw, for example, water rising in pumps and said: ‘Water rises because it abhors a vacuum.’ But I am in the position of the first person to notice that water rises in pumps, leaving to others the task of explaining the cause of this effect. The anatomist who first said that the arm moves because the muscles contract taught mankind an incontestable truth: do we owe him less because he did not know why muscles contract? The cause of the elasticity of air is unknown, but whoever discovered that elasticity rendered physics a great service. The spring I have discovered was more hidden, more universal; I deserve still greater thanks. I have discovered a property of matter, one of the Creator's secrets; I have calculated and demonstrated its effects. Can anyone quibble with me over the name I give it?”
It is the vortices that may be called an occult quality, since their existence has never been proved. Attraction, on the contrary, is a real thing, since its effects can be demonstrated and its proportions calculated. The cause of this cause lies in the bosom of God. Procedes huc, et non ibis amplius.
Plain English translation
Mouseia’s complete Plain English edition, made independently and directly from the French text of all twenty-four letters (Garnier edition, 1879, French Wikisource).
History of Attraction
I will not give a mathematical explanation here of what is called attraction or gravitation. I will stick to the history of this new property of matter, which people guessed at long before Newton and which he demonstrated. In a way, that is the history of a new creation.
Copernicus, the Christopher Columbus of astronomy, had barely taught people the true arrangement of the universe, which had been misrepresented for so long. He had barely shown that the earth turns both on its own axis and through an immense space when all the scholars raised much the same objections that their predecessors had raised against the antipodes. Saint Augustine, denying that the antipodes existed, had said: “What? Would their heads be pointing down? Would they fall into the sky?” The scholars said to Copernicus: “If the earth turned on its axis, all its parts would break away and fall into the sky.” “The earth certainly turns,” Copernicus replied, “and its parts do not fly off. Some force must therefore direct them all toward the center of the earth. And this property probably exists in all heavenly bodies: in the sun, the moon, and the stars. Divine Providence gave it to matter.” That is how he puts it in his first book, On the Revolutions of the Heavenly Spheres, without daring, or perhaps being able, to go any further.
Kepler followed Copernicus and improved on his remarkable discovery of the true system of the world. He came a little closer to the theory of universal gravity. In his treatise on the planet Mars, you can see early, still poorly formed traces of the vein from which Newton extracted his gold. Kepler accepts not only that all earthly bodies tend toward the center, but also that the heavenly bodies tend toward one another. He even dares to suggest, and to say, that if the earth and the moon were not kept in their orbits, they would move toward one another and come together. So many obscurities and mistakes clouded this astonishing truth in his work that people have said he guessed it by instinct.
Meanwhile, the great Galileo began with a more mechanical principle. He examined how bodies fall to the earth and how, and by what proportion, their fall speeds up. Chancellor Bacon wanted experiments to test whether bodies fell in the same way at the greatest depths and the greatest heights that people could reach.
It is very strange that Descartes, the greatest geometer of his time, did not use this thread to find his way through the labyrinth he had built for himself. There is no trace of these truths in his work, so it is no surprise that he lost his way. He wanted to create a universe. He built a philosophy the way one writes a good novel: everything seemed plausible, and nothing was true. He imagined elements and vortices that seemed to offer a plausible explanation for every mystery of nature. But in philosophy we should distrust things we think we understand too easily as much as things we do not understand at all. Descartes was more dangerous than Aristotle because he appeared more reasonable. Mr. Conduit, Sir Newton's nephew, assured me that his uncle had read Descartes at the age of twenty. He marked the margins of the first pages, writing just one note over and over: “error.” But he grew tired of writing “error” everywhere, threw the book aside, and never read it again.
Newton had left behind the depths of theology in which he had been raised and turned to mathematical truths. By the age of twenty-three, he had already found his infinitesimal calculus, after his teacher Wallis had shown him the way. He was trying to find the secret, universal principle of nature that Copernicus, Kepler, and Bacon had pointed to and the famous Hooke had already grasped: the cause of gravity and of the motion of all matter. In 1666 he went to the countryside near Cambridge because of the plague. One day, as he walked in his garden and watched fruit falling from a tree, he fell into deep thought about gravity. Philosophers had searched in vain for its cause for so long, while ordinary people do not even suspect that there is a mystery in it. He said to himself: “No matter how high these bodies might fall from in our hemisphere, their fall would surely follow the progression Galileo discovered. The distances they covered would be proportional to the squares of the times. The force that makes heavy bodies descend shows no noticeable decrease, however deep we go into the earth or even on the highest mountain. Why should this force not reach as far as the moon? And if it really reaches that far, is it not very likely that it keeps the moon in its orbit and governs its motion? But if the moon obeys this principle, whatever it is, is it not also very reasonable to think that the other planets obey it too?”
“If this force exists, it must increase as the inverse square of the distance, as is proved on other grounds. So all that remains is to examine how far a heavy body falls toward the earth from a moderate height, and how far, in the same amount of time, a body would fall from the moon's orbit. To find out, we only need the size of the earth and the distance from the moon to the earth.”
That is how Mr. Newton reasoned. But at the time England had very inaccurate measurements of our planet. People relied on sailors' uncertain estimates: they allowed sixty English miles to a degree, when they should have allowed nearly seventy. Because this wrong figure did not agree with the conclusions Mr. Newton hoped to draw, he abandoned them. A lesser philosopher concerned only with his own vanity would somehow have made the earth's measurements fit his theory. Mr. Newton preferred to set his project aside. Later, Mr. Picart measured the earth accurately by plotting the meridian line that does France so much credit. Mr. Newton returned to his first ideas and found that Mr. Picart's figures worked. The other planets must obey this general law. And if the law exists, the planets must follow the rules Kepler discovered. The planets do indeed follow all these rules and relationships. His single principle of the laws of gravitation explains all the apparent irregularities in the movements of heavenly bodies. The variations in the moon's movement follow necessarily from these laws. The rise and fall of the sea are another very simple effect of this attraction. The moon's closeness when it is full or new, and its greater distance in its quarters, combined with the action of the sun, provide a clear explanation of the ocean's rise and fall.
After his remarkable theory had explained the movements and irregularities of the planets, he brought comets under the control of the same law.
He proves that comets are solid bodies moving within the range of the sun's action. They trace an ellipse so elongated and so close to a parabola that some comets must take more than five hundred years to complete an orbit.
The learned Mr. Halley believes that the comet of 1680 is the same one that appeared in the time of Julius Caesar. That comet, more than any other, helps show that comets are hard, opaque bodies. It came so close to the sun that it was only a sixth of the sun's diameter away. As a result, it must have reached a level of heat two thousand times more intense than that of the hottest glowing iron. It would have melted and been consumed in a short time if it had not been an opaque body. At the time, predicting the paths of comets was becoming fashionable. The famous mathematician Jacques Bernoulli concluded from his system that this famous comet of 1680 would return on May 17, 1719. No astronomer in Europe went to bed that night of May 17, but the famous comet did not appear. It takes at least more cleverness, if not more certainty, to give it five hundred and seventy-five years before its return. As for Mr. Wilston, he has seriously claimed that there was a comet at the time of the Flood that inundated our planet. He was unfair enough to be surprised when people made fun of him. The ancients thought much as Wilston does. They believed comets always came ahead of some great disaster on earth. Newton, on the contrary, suspects that comets are very beneficial. He thinks the vapors coming from them serve to replenish and revive the planets, which soak up along their paths all the particles the sun has drawn from the comets. His view is at least more likely than the other one.
There is more. If this force of gravitation or attraction acts on all heavenly bodies, it surely acts on every part of them. If bodies attract one another in proportion to their masses, that can only be because of the number of their parts. If this power resides in the whole, it must reside in half of it, in a quarter, in an eighth, and so on without end. Attraction, then, is the great driving force that sets all nature in motion.
After proving that this principle exists, Newton expected people to object to the name alone. In several places in his book he warns readers against misunderstanding attraction itself. He tells them not to confuse it with the hidden qualities invoked by the ancients. They should be satisfied to know that all bodies have a force directed toward a center. It acts across the universe on both the nearest and the farthest bodies, according to the unchanging laws of mechanics.
It is surprising that, despite this great philosopher's solemn statements, Mr. Saurin and Mr. de Fontenelle, who themselves deserve to be called philosophers, plainly accused him of the fantasies of Aristotelian philosophy. Mr. Saurin did so in the Academy's Memoirs of 1709, and Mr. de Fontenelle in his very tribute to Mr. Newton.
Almost everyone in France, scholars and others alike, has repeated the accusation. Everywhere one hears: “Why did Newton not use the word ‘impulsion,’ which we understand so well, instead of the word ‘attraction,’ which we do not understand?”
Newton could have answered these critics:
“First, you understand the word ‘impulsion’ no better than ‘attraction.’ If you cannot understand why a body moves toward the center of another body, you cannot imagine what power allows one body to push another either.
“Second, I could not accept impulsion. For that, I would have had to know that some heavenly matter really does push the planets. But not only do I know of no such matter; I have proved it does not exist.
“Third, I use the word ‘attraction’ only to describe an effect I have discovered in nature. It is a certain, undeniable effect of an unknown principle, a property inherent in matter. People more capable than I am may find its cause, if they can.”
“What have you taught us, then?” people keep asking. “Why make so many calculations to tell us something you yourself do not understand?”
“I have taught you,” Newton might continue, “that only the mechanics of forces directed toward centers make the planets and comets move in definite proportions. My case,” he would go on, “is quite different from that of the ancients. They saw, for example, that water rises in pumps, and they said: ‘Water rises because it hates a vacuum.’ But my position is like that of a person who first noticed that water rises in pumps and left it to others to explain why. The anatomist who first said that an arm moves because its muscles contract taught people an undeniable truth. Should we be any less grateful to him because he did not know why muscles contract? We do not know the cause of the springiness of air, but the person who discovered that springiness did physics a great service. The force I have discovered was more hidden and more universal, so I deserve still more thanks. I have discovered a property of matter, one of the Creator's secrets. I have calculated and proved its effects. Can you really quibble over the name I give it?”
Vortices are what one can call a hidden quality, since no one has ever proved they exist. Attraction, by contrast, is real: its effects can be demonstrated and their proportions calculated. The cause behind this cause lies with God. Come this far, and you will go no further.